In vitro and in vivo measures of evoked excitatory and inhibitory conductance dynamics in sensory cortices

Journal of Neuroscience Methods 169 (2008) 323–365

In vitro and in vivo measures of evoked excitatory and inhibitory conductance dynamics in sensory cortices C. Monier ∗ , J. Fournier, Y. Fr´egnac Unit´e de Neurosciences Int´egratives et Computationnelles (UNIC), UPR CNRS 2191, 91198 Gif-sur-Yvette Cedex, France Received 13 September 2007; received in revised form 2 November 2007; accepted 10 November 2007

Abstract In order to better understand the synaptic nature of the integration process operated by cortical neurons during sensory processing, it is necessary to devise quantitative methods which allow one to infer the level of conductance change evoked by the sensory stimulation and, consequently, the dynamics of the balance between excitation and inhibition. Such detailed measurements are required to characterize the static versus dynamic nature of the non-linear interactions triggered at the single cell level by sensory stimulus. This paper primarily reviews experimental data from our laboratory based on direct conductance measurements during whole-cell patch clamp recordings in two experimental preparations: (1) in vitro, during electrical stimulation in the visual cortex of the rat and (2) in vivo, during visual stimulation, in the primary visual cortex of the anaesthetized cat. Both studies demonstrate that shunting inhibition is expressed as well in vivo as in vitro. Our in vivo data reveals that a high level of diversity is observed in the degree of interaction (from linear to non-linear) and in the temporal interplay (from push–pull to synchronous) between stimulus-driven excitation (E) and inhibition (I). A detailed analysis of the E/I balance during evoked spike activity further shows that the firing strength results from a simultaneous decrease of evoked inhibition and increase of excitation. Secondary, the paper overviews the various computational methods used in the literature to assess conductance dynamics, measured in current clamp as well as in voltage clamp in different neocortical areas and species, and discuss the consistency of their estimations. © 2007 Elsevier B.V. All rights reserved. Keywords: Excitation; Inhibition; Conductance measurement; Cat visual cortex; Voltage-clamp; In vivo patch clamp

1. Introduction A basic feature in the connectivity of neocortical networks is the profusion of synaptic contacts, established both locally within a given cortical area and across distinct cortical areas (White, 1989). Each pyramidal neuron (the major type of excitatory cell in cortex) receives approximately 104 synaptic inputs, of which about 75% are excitatory and 25% inhibitory. Recurrent connectivity between pyramidal cells is expressed, within a given cortical lamina as well as across laminae, as a dense plexus of local horizontal and vertical interconnections. GABAergic inhibitory interneurons, although far less numerous, but having multiple subtypes, seem to control the dynamics of this unstable recurrent excitatory assembly at various target locations (review in Markram et al., 2004; Monyer and Markram,

∗

Corresponding author. E-mail address: [email protected] (C. Monier).

0165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2007.11.008

2004; Silberberg and Markram, 2007). In addition to this dominant interlaced pattern of excitation and inhibition originating from the cortex itself, subsets of both types of cells are directly innervated by excitatory thalamic relay neurons, which are the main source of extrinsic input to the neocortex (Binzegger et al., 2004). Axons from the thalamus make stronger and more frequent excitatory connections onto inhibitory interneurons than onto excitatory cells, and their activation produces robust disynaptic feedforward inhibition of cells that receive concomitant direct thalamocortical excitation (Agmon and Connors, 1992; Cruikshank et al., 2007; Gil and Amitai, 1996). One might therefore expect that the selective firing of any single neuron is the concerted result at any point in time of the dynamic balance between a large numbers of co-active synaptic afferents, mostly intrinsic to cortex. Indeed, intracellular recordings in vivo have revealed consistently that cortical neurons are subjected to an intense ongoing synaptic bombardment (Azouz and Gray, 1999; Bringuier et al., 1997; Par´e et al., 1998). Although differences were observed

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depending on the type of anaesthetic used, the resting conductance is generally higher in the intact brain than in partially deafferented networks in vitro (review in Destexhe et al., 2003). Thus, neocortical networks most likely operate in a ‘highconductance’ state, i.e. with a leak conductance three to five times larger than the resting synaptic conductance (Par´e et al., 1998 but see Waters and Helmchen, 2006). This, in turn, is expected to change the integrative properties of the neurons (Bernander et al., 1991; Destexhe and Par´e, 1999; Rudolph and Destexhe, 2003), by reducing the apparent membrane time constant and allowing faster transients in membrane potential dynamics. An important issue in the mammalian sensory neocortex is to determine the functional impact of this high conductance resting state on the processing of sensory information itself. Since the first intracellular recordings in visual cortex (Creutzfeldt and Ito, 1968; Innocenti and Fiore, 1974), many electrophysiological studies have shown that the membrane potential strongly fluctuates in response to visual stimuli. However, no definite canonical generative mechanism has been yet identified since these fluctuations could potentially result from the interplay of a diversity of conductances. For instance, the push–pull arrangement hypothesized in Simple receptive fields supposes that an increase in excitation will correspond to an in-phase decrease in inhibition, and vice versa (Ferster, 1988; Heggelund, 1986). In contrast, the dominance of recurrent circuit architecture predicts that most of the time excitation and inhibition should occur conjointly (Ben-Yishai et al., 1995; Douglas et al., 1995; Somers et al., 1995; Suarez et al., 1995). In addition, these models of visual cortex suggest that response selectivity can arise from recurrent networks operating at high gain. However, such networks operate close to instability and respond slowly to rapidly changing stimuli. Theoretical studies show that divisive inhibition, acting through interneurons that are themselves divisively inhibited, can stabilize network activity for any arbitrarily large excitatory coupling (Chance and Abbott, 2000). From a theoretical computational perspective, two alternative regimes may be envisioned: (1) the total input conductance of the cell does not change significantly during sensory stimulation. In this case, the ratio between the evoked synaptic conductance and the resting conductance is low or negligible, the excitatory and inhibitory currents add algebraically and the input integration process may be considered as linear; (2) the evoked synaptic conductance increase is in the same range or larger than the resting conductance, leading to a regime where excitatory and inhibitory synaptic inputs interact non-linearly. In other words, if the evoked synaptic input fluctuations are small when compared to the resting conductance, the inputs can be modeled as currents; in the opposite case, the conductance increases must be taken into account. The amplitude of depolarization and/or hyperpolarization in the evoked voltage response, when recorded in current clamp mode, results from the combined integration of both excitatory and inhibitory inputs and depends on multiple parameters: the voltage at rest, the time constant of the membrane, the leak conductance, the amplitude of excitatory and inhibitory conduc-

tances, their kinetics and the degree of temporal overlap between their respective recruitment, as well as their reversal potentials. In order to understand the nature of the full integration process, it is thus necessary to devise methods that allow one to infer, from the current or voltage recordings: (1) the dynamics of the balance between excitation and inhibition (E/I), (2) the level of conductance increase evoked by the sensory stimulation, and (3) if possible, to characterize the static versus dynamic nature of the non-linear interaction process. Consensus on these points has been hindered up to now by the fact that different methods have been used in vitro and in vivo to estimate the E/I balance, and seldom compared together. A classical method, mostly applicable in vitro, consists of dissecting out pharmacologically the excitation from the inhibition and thereafter comparing the relative amplitudes of the remaining components (for example Varela et al., 1999). The disadvantage of this method is that the diffuse blockade of a class of receptors by antagonist bath application disrupts the integrity of the network under study and ignores the impact of all types (pre–pre, pre–post) of interactions between excitation and inhibition. In vivo studies rarely rely on iontophoretic approaches (but see Nelson et al., 1994; Sillito, 1975) but usually infer the dominant presence of inhibition and excitation from the peak amplitudes of evoked hyperpolarization and/or depolarisation, respectively (Berman et al., 1991; Ferster, 1986; Pei et al., 1994; Volgushev et al., 1993). Such approaches have been unable to detect the presence of inhibition when concurrent with excitation (see, for a systematic comparative survey, Monier et al., 2003). Thus, although the membrane potential change may reflect in a qualitative way the ratio between excitation and inhibition, it remains impossible from knowledge solely of the mean membrane potential dynamics to deduce the amplitude of the global input conductance change, this measure being crucial to understand the dynamic regime under which the neuronal network operates. A quantification step, reflecting more directly the functional impact of synaptic input on the spike trigger mechanism, is to measure conductance changes seen at the soma. Detailed simulations have shown that the increase in conductance due to the activity of inhibitory basket cells should be visible from the cell body of pyramidal cells (Koch et al., 1990). These authors estimated that the shunting inhibitory effect would significantly reduce the amplitude of the excitatory postsynaptic potential for somatic input conductance increases larger than 30%. Experimentally, evidence for or against shunting inhibition is still a matter of debate. As early as 40 years ago, large increases in input conductance (up to 300%) were demonstrated in cortical neurons (Dreifuss et al., 1969), both after electrical stimulation of the cortical surface and during exogenous iontophoretic application of GABA. Nevertheless, the first measurements of input conductance performed in vivo, using current pulse injection or electrical stimulation of thalamic afferents, revealed only limited relative changes in input conductance (5–20%) during visual stimulation (Berman et al., 1991; Carandini and Ferster, 1997; Douglas et al., 1988; Ferster and Jagadeesh, 1992; Pei et al., 1991). These negative reports were not in agreement with findings in vitro where Berman et al. (1989, 1991), using the

C. Monier et al. / Journal of Neuroscience Methods 169 (2008) 323–365

same technique (current pulse injection), found large conductance increases during electrically evoked hyperpolarization in slices of rat and cat visual cortex. Similarly, Connors et al. (1988) reported 200% changes in input conductance during electrically evoked inhibition in cortical pyramidal cells in neocortical slices. These different findings long supported the view that inhibition and excitation would interact in different ways in the in vitro slice and the intact in vivo network. We have, during the past 10 years, re-examined the issue of conductance dynamics during sensory processing by applying, both in vitro and in vivo, a conductance measurement method based on somatic current clamp and voltage-clamp recordings. This method allows, for any delay relative to the stimulus onset, the continuous monitoring of changes in visually evoked conductance. Its application in area 17 of the anaesthetized cat revealed, in some cells, large conductance increases and a high diversity in the observed temporal phase patterns between evoked excitatory and inhibitory conductance changes (BorgGraham et al., 1998; Monier et al., 2003). This original method, first engineered in voltage-clamp mode (Borg-Graham et al., 1996), has since then been reproduced by many independent research teams in in vivo studies, mostly in current clamp but also in voltage clamp. These findings have been confirmed in the visual cortex of the cat in current-clamp (Anderson et al., 2000, 2001; Hirsch et al., 1998; Marino et al., 2005; Priebe and Ferster, 2005, 2006), in the rat auditory cortex in voltageclamp (Tan et al., 2004; Wehr and Zador, 2003, 2005; Zhang et al., 2003), in the rat barrel cortex in current clamp (Higley and Contreras, 2006; Wilent and Contreras, 2004, 2005) and in the ferret prefrontal cortex in current and voltage clamp (Haider et al., 2006). This conductance measurement method has been also applied in vitro in the ferret prefrontal cortex (Shu et al., 2003), in the rat visual cortex (Le Roux et al., 2006) and in the mouse somatosensory thalamocortical slice (Cruikshank et al., 2007). This paper primarily reviews experimental data from our laboratory based on direct conductance measurements during whole-cell patch clamp recordings in two experimental preparations: (1) in vivo, during visual stimulation, in the primary visual cortex of the anaesthetized cat (Borg-Graham et al., 1998; Monier et al., 2003), and (2) in vitro, during electrical stimulation in the visual cortex of the rat. Both studies demonstrate that shunting inhibition is expressed as well in vivo as in vitro. Our in vivo data reveals that a high level of diversity is observed in the degree of interaction (from linear to non-linear) and in the temporal interplay (from push–pull to synchronous) between stimulus-driven excitation (E) and inhibition (I). A detailed analysis of the E/I balance during the evoked spike activity further shows that the firing strength results from a simultaneous decrease of evoked inhibition and increase of excitation. Secondary, the paper overviews the various computational methods used in the literature to assess conductance dynamics and compare the various assumptions associated with each method. It also underlines possible methodological reasons that may explain why the functional role of shunting inhibition has been contradicted to such an extent in the past.

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2. Materials and methods 2.1. In vitro preparation Parasagittal slices containing primary visual cortex were obtained from 20- to 25-day-old Wistar rats as described by Edwards et al. (1989). Briefly, rats were decapitated and brains were quickly removed and placed in cold (5 ◦ C) artificial extracellular solution, in accordance with guidelines of the American Neuroscience Association. Slices of 350 ␮m thickness were cut on a vibratome and then incubated for at least 1 h at 36 ◦ C in extracellular solution containing (in mM): 126 NaCl, 26 NaHCO3 , 10 glucose, 2 CaCl2 , 1.5 KCl, 1.5 MgSO4 and 1.25 KH2 PO4 , which was bubbled with a mixture of 95% O2 –5% CO2 (pH 7.5, osmolarity 310/330 mOsm). All extracellular drug applications were delivered through perfusion and were added to the bathing solution for at least 15 min before recording. 2-amino-5-phosphonovalerianic acid (APV), bicuculline, 6-cyano-7-nitroquino-xaline-2,3-dione (CNQX) and picrotoxin were obtained from Sigma (St Louis, MO). Slices were perfused continuously and viewed with standard optics using a 40× long-working-distance water immersion lens of a Zeiss microscope on an X–Y translation stage with a videoenhanced differential interference contrast system. Pyramidal neurons, identified on the basis of the shape of their soma and the proximal part of the apical dendrite, were recorded in layer 5 using the whole-cell configuration of patch-clamp techniques. Somatic whole-cell recordings were performed at room temperature using borosilicate glass pipettes (3–5 M in the bath) filled with an internal solution (in mM): 140 K-gluconate, 10 Hepes, 4 ATP, 2 MgCl2 , 0.4 GTP, 0.5 EGTA, pH adjusted to 7.3 with KOH and the osmolarity adjusted to 285 mOsm. For some experiments, the quaternary lidocaine derivative QX-314 (Tocris, Bristol, UK) was added (3 mM) in the internal patch electrode solution to block sodium conductance, hence spike initiation, and GABAb receptor activation. The internal pipette solution was also supplemented with 1% Neurobiotin (Vector) to label some of the pyramidal neurons and reconstruct their morphology. After giga-seal attachment, whole cell configuration was achieved with low access resistance. All membrane potential values obtained with this filling solution were corrected offline by −10 mV in order to subtract the junction potential (Neher, 1992). After capacitance neutralization, bridge balancing was done on-line under current clamp to make initial estimates of the access resistance (Rs ). These values were checked and revised as necessary off-line by fitting subthreshold hyperpolarizing current clamp responses to the sum of two exponentials (Rs = 13.1 ± 5 M (4–25 M), n = 177). The access resistance was not compensated in voltage-clamp mode. Electrical stimulations (10–100 ␮A, 0.2 ms duration) were delivered using 1 M impedance bipolar tungsten electrodes (TST33A10KT, WPI) with a tip separation of 125 ␮m. Tungsten bipolar electrodes were positioned in (i) white matter (WM), at around 500 ␮m from the recording site and along the same radial columnar axis, (ii) layer 4, near the recording site, (iii) in the top of layer 2/3, at a lateral distance of around 800 ␮m from the recording site. The frequency of input stimulation was set at

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0.05 Hz and five to eight trials were repeated for a given holding current or potential. Current clamp and voltage-clamp modes were carried out using an Axopatch 1D (Axon Instrument, USA). Recordings were filtered at 2 kHz, stored and analyzed with specialized in-house dedicated software (Acquis1TM : G´erard Sadoc-UNIC-CNRS). 2.2. In vivo preparation Most of the data presented here are new off-line measurements made on sets of previous recordings realized in collaboration with Lyle Graham and published elsewhere (BorgGraham et al., 1998; Monier et al., 2003). Cells in the primary visual cortex of anaesthetized (Althesin) and paralyzed cats (for details on the surgical preparation, see Bringuier et al., 1997) were recorded intracellularly using an Axoclamp 2A amplifier. Blind whole-cell patch recordings were made in vivo with 3–5 M glass patch electrodes filled with the same solution as that used in vitro. The seal resistance in attached mode was between 1 and 8 G. Only recordings with an access resistance lower than 40 M were selected for further voltage-clamp analysis (average value of Rs = 21.8 ± 13 M, n = 217 cells). The estimate of access resistance was revised as often as necessary over the course of the experiment and off-line, by fitting the response to subthreshold hyperpolarizing current steps to the sum of two exponentials. Three-millimeter artificial pupils were used and appropriate corrective optical lenses were added. The receptive field of each cell was quantitatively characterized using sparse noise mapping. Receptive fields were classified as simple or complex using classical criteria based on the space–time separation between On and Off responses. Orientation and direction tuning curves were measured with moving bars (direction of motion perpendicular to orientation) swept across the full extent of the subthreshold receptive field, and using random sequences of 8 or 12 directions (angular step: 45◦ and 30◦ , respectively) repeated 10 times. In one case, orientation and direction tuning curve were equally measured with drifting gratings (with optimal spatial and temporal frequencies and optimal size) in 12 different directions. In addition, 1D-profile mapping across the receptive field width with optimally oriented bars (1 s) flashed in different positions was carried out. For data analysis, we quantified the following response components: spiking activity and spike suppression, membrane potential depolarization and hyperpolarization. For subthreshold activity, spike events were removed from the raw record and replaced by the low-pass filtered membrane potential. The depolarizing and hyperpolarizing evoked components were defined on the basis of a quantitative amplitude selection criterion as the integral of voltage, respectively, above and below the mean depolarizing and hyperpolarizing fluctuations in the resting potential measured during spontaneous activity. To determine the statistical significance of responses calculated over the whole period of visual stimulation, the mean of each component, defined by its integral normalized by the effective time during which its presence was detected (see above amplitude selection criterion), was compared with the normalized mean of

this component during spontaneous activity prior to the stimulus, using a paired Student’s t-test. All data processing and visual stimulation protocols were carried out using specialized in-house dedicated software (Acquis1TM : G´erard Sadoc-UNICCNRS). 2.3. Continuous estimation of the synaptic conductance in voltage-clamp Data were analyzed using a method based on the continuous measurement of conductance dynamics during stimulus-evoked synaptic response, whose principle has been described previously (Borg-Graham et al., 1998; Monier et al., 2003). To estimate conductances, the neuron is considered as the pointconductance model of a single-compartment cell, described by the following general membrane equation: Cm

dVm (t) = −Gleak (Vm (t) − Eleak ) − Gexc (t)(Vm (t) − Eexc ) dt − Ginh (t)(Vm (t) − Einh ) + Iinj

where Cm denotes the membrane capacitance, Iinj the injected current, Gleak the leak conductance and Eleak is the leak reversal potential. Gexc (t) and Ginh (t) are the excitatory and inhibitory conductances, with respective reversal potentials Eexc and Einh . I–V plots are commonly used to characterize input conductance and cellular excitability in a static way and can be characterized in voltage clamp or current clamp mode. The present study is mainly performed in voltage-clamp mode, which minimizes distortion of synaptic events by transient voltagedependent channels and capacitance near to the recording site (the derivative of the voltage is consider to be zero). Our method aims at a dynamic measure of input conductance, phase-locked to the time of the electrical stimulation, and relies on raw stimulus-locked I/V measurements made at each point in time: the current value includes both evoked and resting components, and the holding potential is corrected for the ohmic drop through the access resistance (Vhc (t) = Vh (t) − I(t) × Rs ). In this situation, the slope of the best linear I/V fit gives the total input conductance of the cell Gin (t) at time t. In order to compare different approaches that have been previously used in vitro (Haider et al., 2006; Shu et al., 2003), we have also computed the best third order polynomial fit. In this latter case the total input conductance is estimated as the tangent at the membrane potential value where the current is found to be null. The synaptically evoked component (Gsyn (t)) is then measured by subtracting the resting conductance observed in the absence of stimulation (i.e. at a negative delay) from the total conductance: Gsyn (t) = Gin (t) − Grest (t)

or

Gsyn (t) = Gin (t) − (Gleak + Gsynrest (t)) The synaptic reversal potential of the synaptic conductance increase (Esyn ) is taken as the voltage of the intersection between the IV-curve during the synaptic response and the IV-curve during the resting condition. Gsyn (t) can be expressed directly in

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absolute measurement units (nS) or in relative units (%) when compared to the conductance at rest (named Gsyn (t)(%)). As a first qualitative step, and in order to determine from Esyn (t) the type of synaptic input underlying the conductance changes, we computed dynamic phase plots of Gsyn (t) against Esyn (t) over time. In order to compare synaptic activation profiles across cells, we extracted the peak value of the evoked synaptic conductance (Gpeak ) in absolute or relative units and the apparent synaptic reversal potential at this peak (Esyn Gpeak ). The mean value of the evoked synaptic response was averaged over a 200 ms window for the in vitro experiments. For in vivo experiments, each response was integrated during the whole stimulation duration (1–3 s) for the moving bar tuning protocols and for a period of 500 ms following the onset and the offset for the flashed bar protocols. In order to address the problem of the correction of access resistance for the voltage-clamp recordings (VC), a bootstrap method was used. This method theoretically makes it possible to estimate the mean and standard deviation of the slope of the regression without any assumptions about the actual statistics of the studied population. In the present case, the bootstrap method consists of repeating a calculation of linear (or polynomial) regression on subsets of values that are derived from the original set of data points, at any given time T. Each set is obtained by a random sampling of the actual data set, with substitution and thus possible repetition, with the constraint that there must be at least one data point for each holding potential, and that the total number of sampled points equals the total number of actual data points, that is the actual number of trials over the different holding potentials. The mean and standard deviation of the distribution of the slopes calculated over all the regressions are then estimated on the basis of at least 200 regressions. This computation is realized on both visual activity segments where each trace is temporally synchronized with the appearance of the visual stimulation, and spontaneous activity periods (recorded without visual stimulation and with shuffling across trials). 2.4. Estimation of the leak conductance The temporal profile of the conductance observed at rest is decomposed arbitrarily into two components, one constant or static (Gleak ) and the other strictly positive or null, reflecting the dynamic changes above baseline (Gsynrest (t)). The global variance of Grest (t) is approximated by 2 2 2 σG = σG + σG , rest rest  rest 2 2  is the variance of the mean of Grest (t) and σG where σG rest  rest is the mean of the variances of Grest (t) at each point in time (calculated with a bootstrap method). Assuming a Gaussian distribution, one can thus derive an estimator of Gleak , defined here as the lower boundary of the Grest value distribution: 

2 Gleak = Grest (t) − σG × 2.96. Since, in vitro, the global rest spontaneous activity was very low with our extracellular solution, Gsynrest (t) was set to 0, and Gleak and Eleak were assumed, respectively, equal to Grest and Erest . In vivo, the reversal poten-

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tial Eleak was fixed at −80 mV (Par´e et al., 1998). Note that this value is more negative than the resting potentials found in vivo. 2.5. Decomposition of the global synaptic conductance Assuming that the evoked conductance change measured at the soma reflects the composite synaptic input effective in driving the cell (since visible at the soma and presumably at the axon hillock), Esyn (t) characterizes the effective balance between excitation and inhibition over time. The global synaptic conductance (Gsyn (t) = Gin (t) − Gleak ) was further decomposed into three conductance components corresponding to the activation of one type of excitatory synapse and two types of inhibitory synapses, each associated with known and fixed reversal potentials. The reversal potentials were set at 0 mV for excitatory (Eexc ), −80 mV for chloride conductance (Einha ) and −95 mV for potassium conductances (Einhb ). In order to make the equation system solvable, Gsyn (t) was expressed, at any point in time, as the sum of two at most of these three components. The choice was dictated by the value of the synaptic reversal potential (Esyn (t)): if Esyn (t) > Eexc

then

Gsyn (t) = Gexc (t)

if Einha < Esyn (t) < Eexc + Gexc (t)

then

Gsyn (t) = Ginha (t)

if Einhb < Esyn (t) < Einha + Ginha (t)

then

Gsyn (t) = Ginhb (t)

if Esyn (t) < Einhb

then

Gsyn (t) = Ginhb (t)

The evoked excitatory and inhibitory conductance components (Gexc (t), Ginha (t), Ginhb (t)) were obtained by subtracting the mean resting conductance levels (Gexcrest , Ginharest , Ginhbrest ) from the corresponding global synaptic conductance component (for example: Gexc (t) = Gexc (t) − Gexcrest ). Note here that the net evoked conductance change (excitatory or inhibitory) can become negative. Significance criteria were reached when the measured change was 2.96 times larger than the standard deviation of the resting conductance component value. Onset latencies were determined from stimulus onset to the time at which the conductance waveform began to deviate significantly from the average baseline value. 2.6. Direct extraction of excitatory and inhibitory conductance based on solving the conductance model equation The method for extracting conductances from voltage-clamp recordings can also be applied to current-clamp data. However, since, in this case, the derivative of the voltage can no longer be considered as null, conductances must be estimated by taking into account the capacitive current passing through the membrane. At each time point, a linear system composed of as many equations as these are applied current levels with two variables, is be solved by doing a bidimensional regression over Gexc (t)

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and Ginh (t): Ginh (t)(Vm1 (t) − Einh ) + Gexc (t)(Vm1 (t) − Eexc ) dVm1 (t) − Gleak (Vm1 (t) − Eleak ) dt Ginh (t)(Vm2 (t) − Einh ) + Gexc (t)(Vm2 (t) − Eexc ) 1 −C = Iinj m

= ...

2 Iinj

dV 2 (t) − Cm m − Gleak (Vm2 (t) − Eleak ) dt

Ginh (t)(Vmk (t) − Einh ) + Gexc (t)(Vmk (t) − Eexc ) k −C = Iinj m

dVmk (t) − Gleak (Vmk (t) − Eleak ) dt

The capacitance Cm is obtained from the time constant of the exponential fit of the membrane voltage in response to a test hyperpolarizing pulse applied at rest and the leak conductance is estimated as described above. The use of the derivative terms has already been introduced in several studies (Priebe and Ferster, 2005; Wilent and Contreras, 2005) but this explicit description of the conductance measurement method has the advantage of clarifying the effects produced by different assumptions. For instance, assuming that the membrane time constant is very fast (i.e. Cm is very small) is equivalent to solving the same system without the derivative terms. Moreover, instead of extracting directly two types of conductances, one can also rewrite the equations (by linear combinations) to estimate the global conductance and synaptic reversal potential, which allows decomposition of the global conductance in more than two terms according to the values taken by Esyn (t). When applied to voltage-clamp measurements, the derivative terms are set to zero, giving: 1 − E ) + G (t)(V 1 − E ) Ginh (t)(Vhc exc exc inh hc 1 (t) − G 1 = Iin leak (Vhc − Eleak ) 2 − E ) + G (t)(V 2 − E ) Ginh (t)(Vhc exc exc inh hc 2 (t) − G 2 = Iin leak (Vhc − Eleak )

...

Gsyn (t) = Gexc (t) + Ginh (t)

or

Gsyn (t)

= Gexcrest (t) + Gexc (t) + Ginhrest (t) + Ginh (t) We also computed the membrane potential trajectories that would have been produced if the stimulus evoked exclusively inhibition (Vinh (t)) or excitation (Vexc (t)). For Vinh when Gexc (t) is significant: Gsyn (t) = Ginh (t) + Gexcrest (t) else Gsyn (t) = Ginh (t) + Gexc (t). For Vexc when Ginh (t) is significant: Gsyn (t) = Gexc (t) + Ginhrest (t) else Gsyn (t) = Ginh (t) + Gexc (t). From these three membrane potential values (integrated over 200 ms following the stimulus onset for in vitro and integrated over 50 ms in vivo), the M factor was extracted (Koch et al., 1990): M=

Vrec  − Vinh  Vexc  − Vrest

This calculation was performed only when the evoked Gexc (t) and Ginh (t) were both significant. The M ratio quantifies the degree of non-linear interaction between excitation and inhibition: if one assumes that the effects of excitation and inhibition add linearly, M is equal to 1 since Vrec  = Vinh  + Vexc  − Vrest. If excitation and inhibition interact non-linearly, M drops towards zero. In order to check the coherence between the different estimates, we calculated the root mean square error (“RMS error”) between the actual mean voltage measured in current clamp (V¯ m (t)) and that predicted (Vrec (t)) from the excitatory and inhibitory conductances estimated in voltage clamp or current clamp (Wehr and Zador, 2003):   T 1 2 (V¯ m (t) − Vrec (t)) RMS error =  T 0

k − E ) + G (t)(V k − E ) Ginh (t)(Vhc exc exc inh hc k (t) − G k = Iin leak (Vhc − Eleak )

where Vhc is the holding voltage (corrected for the ohmic drop) and Iin is the measured current. 2.7. Reconstruction of the membrane potential trajectory The computation of the excitatory and inhibitory conductances on the basis of the voltage-clamp measurements allows to predict the membrane potential trajectory (Vrec (t)) that would have been observed in current clamp. This is done by solving numerically the following differential equation: Cm

Cm is estimated from τ m (the membrane time constant, Cm = Gleak τ m ) of the cell measured at rest with a small step of hyperpolarizing current. Gsyn (t) takes in account inhibitory and excitatory components (for simplicity the GABAb component is not considered here):

dVrec (t) = −Gleak (Vrec (t) − Eleak ) − Gsyn (t)(Vrec (t) dt −Esyn (t)) + Iinj

In addition we computed the synaptic currents underlying the fluctuations of the voltage record in order to directly visualize the strength and the temporal impact of each type of synaptic input: Iinh (t) = Ginh (Vrec (t) − Einh ) Iexc (t) = Gexc (Vrec (t) − Eexc ) 3. Results 3.1. Intrinsic excitability properties of cortical neurons 3.1.1. In vitro recordings Patch-clamp recordings were obtained from pyramidal neurons (n = 177), the somata of which were exclusively located in layer 5 of rat visual cortex (P20–P25). Excitability properties of cortical neurons were characterized by the pattern of discharge in

For the in vivo population, cells were classified into the following excitability subcategories by taking into account the shape of the action potential and the temporal profile of their spiking patterns to current pulses: RS, regular spiking; IB, bursting with inactivation; NIB, non-inactivating bursting; FSA, fast spiking adapting; FS, fast spiking.

80 96 110 179 246 ± ± ± ± ±

151 ± 141

110 145 177 190 383 0.9 0.8 0.2 0.7 0.5 ± ± ± ± ±

−2.8 ± 1.0

−3.0 −3.2 −1.4 −2.0 −1.2 13 15 13 12 13 ± ± ± ± ±

57 ± 15

60 59 45 55 55 0.2 0.2 0.2 0.2 0.03 ± ± ± ± ±

0.82 ± 0.3

0.88 0.91 0.39 0.57 0.36 5 4 7 7 3 ± ± ± ± ± −49.2 −50.4 −54.5 −51.0 −59.5

−50.2 ± 6

5 5 4 10 28 ± ± ± ± ±

13.0 ± 7

13.3 12.1 6.7 14.3 20.0 5 5 7 4 4 ± ± ± ± ± −72.8 −71.4 −71.1 −73.8 −74.0

−72.3 ± 5

30 31 26 41 45 ± ± ± ± ± 119 63 7 25 4 RS IB NIB FSA FS

63.4 ± 36 217 In vivo

62.2 64.1 37.2 73.2 74.6

70 ± 41 −2.4 ± 0.6 84 ± 10 1.7 ± 0.4 −50.3 ± 5 31.8 ± 11 −70.0 ± 5 177 In vitro

208.3 ± 89

Spike threshold (mV) Time constant (ms) Resting potential (mV) Input resistance (M) Nb of cells Cell types

Table 1 General descriptive parameters at rest: global conductance measurements and intrinsic excitability patterns, in vitro and in vivo

Spike width (ms)

Spike amplitude (mV)

Spike dVratio

F/I ((Pa s−1 )/pA)

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response to test depolarizing current pulses using a current clamp mode protocol. They were correlated when possible with the morphological description obtained by intracellular filling with neurobiotin. The dominant discharge pattern of pyramidal neurons was found to be of the regular type with adaptation (RS), as defined by (McCormick et al., 1985). Among the recorded neurons successfully labelled with neurobiotin (n = 31), all exhibited the typical morphology of pyramidal cells (Larkman and Mason, 1990). The voltage waveform, obtained in response to the intracellular injection of a negative pulse of current of small amplitude and small duration (see Fig. 1B), was fitted with a double exponential, giving a mean input membrane resistance estimate around 200 M (Rin = 208.3 ± 89 M, n = 177) and a membrane time constant around 30 ms (␶m = 31.8 ± 11 ms, n = 177). The mean resting potential was −70.0 mV (± 5 mV) and the fluctuations of the voltage stayed very small during the resting condition (σ v = 0.36 ± 0.2 mV, n = 177). Some additional neurons (n = 60) were recorded with QX314 in the intracellular solution. Their input resistances were significantly larger than with the control filling solution (Rin = 254.3 ± 132 M vs. 208.1 ± 89, p < 0.01). A similar observation was made for the membrane time constant (τ m = 42.6 ± 20 ms vs. 31.8 ± 12 ms, p < 0.001). The resting membrane potential was slightly, but significantly, more hyperpolarized (Erest = −71.9 ± 5 mV vs. −70.0 ± 5, p < 0.01). Long pulses of positive currents were also injected to reveal the excitability pattern (see example on Fig. 1). For cells recorded with the control solution, specific shape parameters were measured on the first spike triggered by the intracellular current pulse. The absolute spike threshold, the width at half height and the spike amplitude were, respectively, −50.3 ± 5 mV, 1.7 ± 0.4 ms and 84 ± 10 mV. The asymmetry dVratio of the spikes was 2.4 ± 0.6 (rising slope, 99.6 ± 20 mV ms−1 , fall-off slope −45.8 ± 13 mV ms−1 ). The F/I curves were fitted with a linear function with a mean slope estimate of 70 ± 41 a.p. s−1 nA−1 (Table 1). 3.1.2. In vivo recordings The present study is based on the quantitative analysis of 217 cells, recorded using patch electrodes, for which the intrinsic properties of cells were characterized in current clamp mode by injecting a short duration hyperpolarizing current pulse, as done in vitro. In contrast with the in vitro situation, these cells were spontaneously active (mean rate: 0.45 ± 0.6 a.p. s−1 ; n = 211) and the level of spontaneous activity varied greatly between cells. The fluctuation of the membrane potential measured in the resting condition was around 4 mV (σVm = 3.9 ± 2.3 mV; range: 1.0–10.1 mV, n = 211). 55% of these cells (n = 119) were found to be of the regular spiking type (RS) with a clear adaptation of successive spike intervals; 29% of cells (n = 63) were intrinsic bursting cells (IB) with a progressive inactivation of action potential generation within the burst; 3% of cells (n = 7) were bursting cells without spike inactivation (NIB or chattering), but with a large amplitude AHP (we follow the classification of Baranyi et al., 1993). The rest of the cells qualified as fast spiking cells (FS), since they

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Fig. 1. In vitro and in vivo measurements of intrinsic properties of V1 neurons. Measures of input resistance (Rin ) and I/V curves are illustrated in pyramidal regular spiking cells (RS), recorded in current clamp mode in vitro and in vivo, with patch electrodes filled with gluconate (with or without QX314). (A) Intracellular membrane potential (Vm ) responses of three cortical RS neurons to negative and positive current pulse injections in three different conditions: (left) control internal pipette gluconate solution in vitro; (center) control gluconate solution + QX314 in vitro; (right) control gluconate solution in vivo. Each 1 s current pulse used for the I/V measurement was preceded by a short (200 ms in vitro, 100 ms in vivo) negative pulse at the end of which the input resistance (Rin ) was estimated. (B) Zoom on the membrane response to the short negative current pulse (black) fitted by a sum of two exponentials (red): the fast decaying exponential was used to fit the electrode response (access resistance Rs and electrode time constant τ electrode ) and the slower one to extract the membrane response (input resistance Rin and time constant τ m ). (C) I/V characteristics obtained in the same (see (A)) three recording conditions, showing a significant inflexion of the slope around −50 mV. The slopes of the regression lines fitting each linearity domain below (R1) or above (R2) the rectification point, correspond to the R1 and R2 input resistance values. (D) Mean input resistances (Rin , R1 and R2) obtained across the three experimental conditions (see (A)). Right panels, mean membrane time constant (τ m ) and resting potential (Erest ).

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showed thin spikes (< 0.4 ms duration), among which the majority showed spike frequency adaptation (12% of the total sample: n = 25, FSA) and the rest none (2%, n = 4, FS) (see Table 1). 3.1.3. In vitro versus in vivo comparison Since we recorded only pyramidal cells in the in vitro preparation, the comparison was limited to the equivalent type of cell in the in vivo preparation, the class of RS pyramidal cells (n = 119). Neurons recorded in vivo had a resting potential more hyperpolarized than in vitro (−72.8 ± 5 mV vs. −70.0 ± 5) and showed a lower input membrane resistance (Rin = 63.4 ± 30 M in vivo vs. 208 M in vitro) and a shorter membrane time constant (τ = 13.5 ± 5 ms in vivo vs. 31.8 ms in vitro) with a scaling factor in both cases around three. As expected due to the difference of temperature between the in vivo and in vitro preparations, the width of the spike was larger in vitro (1.7 ± 0.4 ms in vitro vs. 0.88 ± 0.2 ms in vivo) but the spiking threshold values were undistinguishable (−50.3 ± 5 mV in vitro vs. −49.2 ± 5 mV in vivo). For further details, see Table 1. 3.2. Linearity domain of I/V curves 3.2.1. In vitro recordings I/V curves were measured in current clamp using long pulse current injection (Fig. 1A) whose intensity was increased in 50 pA steps (starting from −200 pA, 15 steps on average, range: 10–40, see Fig. 1A). I/V curves were best fitted by two linear segments whose intersection point was chosen to optimize the explained variance and whose abscissa (−53.7 ± 7 mV) was usually close to the spike initiation threshold (−50.3 ± 5 mV). The input resistance of the cell (with the control solution) for the higher range of voltage values was on average four times smaller than that measured for voltage values below the rectification point (174.3 ± 76 M, Rin (Vm < threshold) vs. 45.2 ± 23 M, Rin (Vm > threshold), ratio: 4.0 ± 3, n = 177, see Fig. 1C and D). For cells recorded with QX314 in the intracellular solution, a rectification in the I/V-curves was observed as well, (Rin : 226.9 ± 109 M (Vm < threshold) vs. 77.3 ± 34 M (Vm > threshold)), ratio: 3.2 ± 1, rectification point abscissa: −54.7 ± 11 mV, n = 60) but the change in slope was of slightly lesser amplitude (ratio: 3.2 instead of 4.0 for the control solution). These rectifications observed for membrane potential values above the spike threshold seem to be due to the recruitment of voltage dependent potassium conductances, which are not fully blocked by QX314. In a subpopulation of cells (n = 50), we checked the steadystate linearity of the I/V curves in voltage-clamp mode for holding potentials ranging from −100 to 0 mV in steps of 10 mV, during both the resting condition and the synaptic response. In almost all cells, the I/V curves showed a slight rectification for membrane potentials more hyperpolarized than −90 mV or more depolarized than −40 mV, although the precise range over which this non-linear behavior was expressed varied greatly across cells. The average value of the Pearson correlation coefficients calculated from the linear regressions in the resting condition over the full range of holding potentials was 0.94 ± 0.05. If the regression was limited to holding potentials ranging only

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between −90 mV and −40 mV, the averaged correlation coefficient value became significantly higher (0.97 ± 0.02, paired t-test, p < 0.001). A similar analysis, when applied to the first 200 ms of the synaptically evoked response for the full range of holding potentials, gave significantly higher correlation coefficients when compared to the resting condition (0.98 ± 0.02 vs. 0.94 ± 0.05, paired t-test, p < 0.001). This suggests that the recruitment of additional synaptic responses by the sensory stimulation tends to linearize the I/V relationship. One should note that (i) the rectification observed in the resting condition had only a negligible effect on the total I/V-curve during synaptic response, due to the fact that the synaptically evoked conductance increase was large compared to the resting conductance (see below), and (ii) that the putative NMDA involvement during synaptic activation does not seem to contribute significantly to a noticeable non-linear behavior at more positive holding potentials. In summary, our linear conductance estimation method was considered valid for cells whose I/V linear correlation coefficient was larger than 0.95 for holding potentials between −90 and −40 mV. Nevertheless, the linearity of the reconstructed I/V curves is increased when measurements are made in voltage clamp with steady holding voltage steps. These observations justify the method we have used for conductance extrapolation, which takes into consideration only the initial linear segment of the I/V curve (thus restricting the analysis to membrane potential values below spike threshold). 3.2.2. In vivo recordings As previously observed in vitro, I/V curves obtained in current clamp (see Fig. 1) were best fitted by two linear segments whose intersection point abscissa was found close to the spike threshold (for RS cells: −50.1 ± 3 mV). The input resistance of the cell above this threshold was on average 2.6 times smaller than that measured below spike threshold (35.0 ± 23 M vs. 62.7 ± 29 M, ratio 2.6 ± 3, n = 119, see Table 2). This ratio was smaller than that observed in vitro (4.0 ± 3, t-test, p < 0.001), reflecting most likely a linearization of the behavior of cortical cells by the synaptic bombardment observed in the intact organism preparation. However, in contrast with RS and IB cells, NIB, FSA and FS cells tended to behave more non-linearly, due to a strong potassium conductance mediated rectification characterized by a fast and large AHP (see Table 2). 3.3. Measurements of the evoked global synaptic conductance change and the apparent composite reversal potential 3.3.1. In vitro recordings We recorded synaptic responses in identified pyramidal neurons of layer 5 in current clamp and voltage-clamp modes. Tungsten bipolar electrodes were positioned at different distances from the recording site to focally stimulate different cortical layers and afferent circuits: (a) in white matter (WM), in order to directly stimulate thalamo-cortical fibers, (b) in layer 4, in order to stimulate local recurrent circuits and optimize the recruitment of monosynaptic short-range inhibition and (c) in the

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Table 2 Summary of in vivo and in vitro measurements of input resistance, made in the linear (below spike threshold) and rectifying (above spike threshold) segments of the I/V curve and their relative ratio Cell types

Nb of cells

R1 (Vm < threshold) (M)

R2 (Vm > threshold) (M)

R1 /R2 ratio

In vitro control In vitro QX3214

177 60

174.3 ± 76 226.9 ± 109

45.2 ± 23 77.3 ± 34

4.0 ± 3 3.2 ± 1

In vivo RS In vivo IB In vivo NIB In vivo FSA In vivo FS

119 63 7 24 4

62.7 62.8 36.0 71.9 76.3

± ± ± ± ±

29 32 26 49 42

top part of layer 2/3, in order to stimulate more distal inputs. The intensity of the stimulation was adjusted in current clamp mode to induce a subthreshold postsynaptic response and set at half the threshold intensity required to obtain reliable suprathreshold activation. This amplitude of stimulation was around two to three times the amplitude of stimulation necessary to induce a minimal response. Stimulation strength was thus strong enough to activate excitatory and inhibitory circuits, but weak enough to avoid recruiting dominant non-linear processes, linked for instance to NMDA receptor activation or action potential initiation. In current clamp, whatever the stimulation location, and taking into account the intensity of the test stimulation (see above), the evoked synaptic responses mainly exhibited two temporal phases: an early and fast depolarization followed by a hyperpolarization. The full decomposition into simultaneously recruited conductance activation components is required since knowledge solely of the composite potential response does not allow the relative strength and timing of evoked excitation and inhibition to be dissected. The first step of the analysis (see Section 2) is to measure synaptic conductance profiles and the composite (or apparent) reversal potential. Fig. 2 illustrates the membrane current (Im ) measurements, performed in voltage-clamp and whole cell modes, for 5 different holding potentials (between −80 and −40 mV) and averaged over 10 interleaved trials. The voltage abscissa of the intersection point between the I/V curve at a time delay t after the electrical stimulation (i.e. during the synaptic evoked response) and the I/V curve at rest (i.e. before stimulation) gives a continuous estimation of the stimulus-locked dynamics of the composite apparent reversal potential (Esyn (t)), monitored from the soma (see Section 2 for more details). In all recordings, the phase plots of the relative change in synaptic drive, Gsyn (t), versus the apparent reversal potential, Esyn (t), presented typically three phases (Fig. 2): (1) in the first phase (1–2 ms), the initial conductance increase was weak but the reversal potential shifted in a few milliseconds to more positive potential values close to 0 mV, indicative of a significant recruitment of AMPAmediated excitation; (2) in a second phase, the conductance increased strongly, while concomitantly the synaptic reversal potential became more negative and converged typically in the neighborhood of −60 to −70 mV; this value is suggestive of dominant GABAa receptor activation; (3) in the last phase, the conductance decreased again and the synaptic reversal potential became slightly more hyperpolarized (around −80 mV).

35.0 46.3 14.4 37.2 14.5

± ± ± ± ±

23 27 14 48 20

2.6 1.5 4.7 3.9 8.9

± ± ± ± ±

3 1 6 5 5

The correlation between the peak conductance value (Gpeak ) and its corresponding apparent synaptic reversal, established on the basis of cell-by-cell paired measurements, is illustrated in Fig. 2. The global shape of the correlation between Gsyn (t) and Esyn (t) for the whole population is roughly similar to the phase plots observed on a cell-by-cell basis for a single stimulation. The peak conductance values were observed for reversal potentials ranging between −60 and −70 mV. The increase in peak conductance varied from 100% to up to 1500%. Independent of the stimulation site, the conductance increase reached on average 460 ± 326% (n = 152, 88 cells with control solution and 64 cells with QX314). When the analysis is further constrained as a function of site location, the smallest conductance increases were observed for white matter stimulation (340 ± 265%, 20.7 ± 13 nS, n = 56), while a slightly higher value was observed for stimulation of the layer 2/3 top (483 ± 296%, 26.9 ± 24 nS, n = 65) and the strongest changes were obtained for direct stimulation of the layer 4 neighborhood of the recorded cell (637 ± 392%, 32.0 ± 27 nS, n = 31). However, when taking into account the high variability of the peak of the conductance in any subpopulation, these differences did not reach a statistically significant level. The presence of QX314 in the intracellular solution in order to block fast sodium and GABAb conductances did not affect the absolute increase of the global synaptic conductance (24.7 ± 16 nS with control recording solution (n = 88) vs. 26.5 ± 27 nS with QX314 (n = 64)). However, since the leak conductance was significantly smaller in the presence of QX314 (5.5 ± 3.8 nS vs. 6.9 ± 3.6 nS with the control solution), the relative conductance increase was higher in this former condition (543 ± 404% with QX314 vs. 395 ± 233% with the control solution). The apparent synaptic reversal potential corresponding to the peak conductance value was −62.6 ± 9 mV for all cells (n = 188) and no significant differences were found across stimulation sites (WM: −63.6 ± 10 mV; layer 2/3 top: −62.4 ± 8 mV; layer 4: −62.3 ± 10 mV). The presence of QX314 in the pipette did not produce any significant change in the apparent synaptic reversal potential at the conductance peak (−61.8 ± 10 mV with QX314 vs. −63.7 ± 8 mV without QX314). 3.3.2. In vivo recordings The data analyzed here are taken from a variety of visual protocols. The spatio-temporal structure of the spiking and voltage

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Fig. 2. Continuous measures of input conductance changes, evoked in vitro and in vivo. (A) In vitro response of a layer 5 pyramidal RS cell to electrical stimulation from white matter (WM). (B) In vivo example of a subthreshold response in a complex cell (sensory responses detailed in Fig. 6, cell 8). (a) VC current waveforms (Im ) measured at four (in vivo) and five (in vitro) levels of potential (between −90 and −40 mV). All responses are averages of 10 trials. (b) Time courses of relative change in input conductance Gsyn (%) and (c) its apparent reversal potential Esyn (t), evoked by the stimulation (arrow). (d) I/V characteristics are derived from linear regressions corresponding to the resting state (black circles), the slope of which gives Grest , and during visual activation (red circles), the slope of which gives Gin (T). The measure is done at time T marked by a red dotted line in the voltage-clamp Im records. The voltage abscissa axis, Vhc , corresponds to the command holding potential corrected for the Rs ohmic drop. (e) Phase plot of relative Gsyn (%) vs. Esyn (t) illustrates the time-course of the trajectory of the E/I balance following the stimulation onset. (f) Population analysis ((A) in vitro, cells with and without QX314, each dot representing a given response for a given cell, n = 188; (B) in vivo, n = 300), distributions and correlation between the peak value in the relative conductance increase (Gpeak (%)) evoked by the stimulation and the apparent composite reversal potential at which it occurred (Esyn Gpeak ).

receptive fields (RF) was mapped using 2D sparse noise (157 cells) or 1D-randomized exploration with an optimally oriented flashed bar across the RF width (46 cells). Orientation selectivity tuning curves of spiking and voltage responses were also determined in response to light bars moving at an optimal speed (49 cells). A diversity of sensory responses was observed in current clamp recording mode, with in general a strong net Vm depolarization and spikes for the preferred stimulus, occasionally sharp hyperpolarizing potentials for non-optimal stimuli, but most often a composite sequence of subthreshold depolarizations and hyperpolarizations (see examples in Fig. 4 for moving bars and Fig. 6 for flashed static bars). When the stability of

recordings and the value of the access resistance in voltage clamp allowed it, inward/outward current responses were also recorded for the same stimulus sequences under voltage-clamp (VC) conditions imposed at two to four holding potentials or under current clamp (CC) condition with different levels of negative current injection. Quantitative conductance measurements were carried out during directional tuning protocols with moving bars (19 cells, 11 cells in VC only, 4 cells in both VC and CC and 4 cells in CC only) and spatial sensitivity profile protocols with static flashed bars of optimal orientation randomly positioned across the RF width (7 cells, 5 cells in VC only and 2 cells in both

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Fig. 3. Decomposition of the conductance change into excitatory and inhibitory components. Same conventions as in Fig. 2. (A) Decomposition method. Responses to WM electrical stimulation, recorded in a layer 5 pyramidal cell. From top to bottom: current recordings (Im ) in voltage clamp (VC), global synaptic conductance waveform Gsyn (t) and its apparent reversal potential Esyn (t), the three underlying conductance component waveforms (Gexc in red, Ginha in blue and Ginhb in green), reconstituted Vm changes (Vrec in black), and reconstituted profiles due to excitation only (Vexc in red) and inhibition only (Vinh in blue). (B) Blocking excitation. Measure of the relative synaptic conductance increase Gsyn (%) and the synaptic reversal potential of the inhibitory conductances evoked by stimulating layer 4. (a) Recordings are made with QX314 in the intracellular pipette solution in order to block GABAb conductance (b). The additional application of CNQX and APV completely suppresses the excitatory conductance and reduces the inhibitory conductance (demonstrating a polysynaptic origin of inhibition). (c) Superimposed phase plots Gsyn (%) vs. Esyn (t) in the absence (black) and presence (red) of CNQX + APV, recorded in the same cell. (d) Distribution of the synaptic reversal potential

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VC and CC). In one cell, additional conductance measurements in VC in response to drifting gratings in different directions were carried out (illustrated in Fig. 5) but not pooled with other data. For the global cell population (n = 26), the mean resting conductance was 14.6 ± 9.2 nS and the mean input resistance 97.0 ± 60.6 M. The access resistance was estimated off-line for the VC recordings (mean Rin : 27 ± 13 M; n = 22). In addition, we extracted several measures from the CC Vm records: mean and variance of evoked spiking activity and evoked membrane potential depolarization and hyperpolarization. If at least one of these components changed significantly during sensory activation in comparison to the resting case, the response was used in further analyses even if it was not accompanied by a significant global conductance change. With this criterion, three hundred responses from a total of four hundred recorded responses were used (200/200 for moving bars, 100/200 for flashing bars, extending across the discharge field and the surrounding “silent” receptive field). The mean peak conductance increase (relative to the resting conductance) across cells (one peak value for each cell) was 95.3 ± 61.2% (n = 26). The mean absolute value of the global synaptic conductance peak was 16.1 ± 13.8 nS and the mean reversal potential at which the conductance peak was observed was −62.5 ± 8.4 mV. If we consider now all the significant responses (n = 300, see Fig. 3) the mean conductance change observed at the peak corresponded to a mean increase of 57.5 ± 43.7% (range 5–270%) and absolute conductance values of 10.2 ± 9.7 nS (range 0.7–53 nS). The mean composite reversal potential for the peak response remained around −60 mV (−63.1 ± 8.6 mV) although its value could vary, across stimulations and cells, between −80 and −30 mV. In spite of the variability across cells (Gpeak : range: 5–270%, 0.7–53 nS), we did not observe a significant dependency of the relative or absolute conductance peak on the stimulus condition, i.e. static versus moving bars. However, whereas flashed stimuli evoked only transient changes in input conductance (lasting for a few tens of ms), longer conductance increases were evoked by moving bars and could last for several hundreds of milliseconds (see examples in Figs. 4 and 5). Although the ohmic drop was systematically compensated offline in our calculations, we checked if the diversity in conductance measures could be explained in part by the differences in access resistance across the different recordings. The weak negative correlation between the peak conductance increase and the access resistance in our experiment (r2 = 0.21) indicated the tendency that the higher the access resistance was, the weaker the conductance increase. This suggests that our calculation probably underestimated conductance increase for relatively high access resistance conditions. A simple and likely explanation is

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that the access resistance and the capacitance of the electrode act as a low-pass filter on the conductance estimate. 3.4. Conductance decomposition into excitatory and inhibitory components 3.4.1. Methodological issues In order to quantify the balance between excitation and inhibition during afferent stimulation (electrical or visual), the synaptic conductance change was decomposed into components specific to the activation of different types of receptors. The simplest method, used previously in the literature (see for example Anderson et al., 2000), is to linearly decompose the global conductance into two components associated with two distinct reversal potentials, one for the excitation and one for the inhibition. With this simple dual decomposition method, if the apparent synaptic reversal potential is below the assumed inhibitory reversal potential, the excitatory conductance change will be negative and the inhibitory conductance change larger than the global conductance increase. The determination of realistic values for Einh thus becomes crucial in the interpretation of the conductance changes. For instance, in their study of cortical conductance increases produced by thalamic electrical stimulation (see Fig. 14 in Anderson et al., 2000), Anderson et al. concluded these was a suppression of excitation. However, a different interpretation may be given if the synaptic reversal potential (during the period when their measure gives a negative excitatory conductance) reaches values below the preset value of the inhibitory reversal potential used in their decomposition. The inhibitory component is in fact reflecting the composite effect of at least two distinct GABAa and GABAb-mediated inhibitory processes, with two distinct reversal potentials. Considering only the major component (GABAa) or choosing an intermediate value between GABAa and GABAb reversal potentials (as done in Anderson et al., 2000) introduces consequently errors in the estimation of the relative contribution of inhibition and excitation. In the present study, the global synaptic conductance is decomposed into three components Gexc (t), Ginha (t) and Ginhb (t) corresponding, respectively, to the activation of one type of excitatory synapse and two types of inhibitory synapses, each associated with fixed reversal potentials (Eexc for the excitation, Einha for the GABAa inhibition and Einhb for the GABAb inhibition). We chose the simplifying assumption that, depending on the actual value of the apparent composite synaptic reversal potential, only two out of the three possible types of synaptic inputs contribute in a dominant manner to synaptic activation (see Section 2). When applying this three-component decomposition method to activation cases similar to those reported by Anderson et al. (2000) (see above), no withdrawal of excita-

(Esynpeak ) at which the peak conductance increase is observed, for the population of cells recorded in the presence of CNQX + APV (n = 19), with a mode centered around −80 mV. (C) Paired pulse stimulation. (a and b) Examples of conductance change measurements (Gsyn (%), Gexc and Ginh ) and inhibitory conductance reduction evoked by paired pulse stimulation (ISI = 200 ms), from WM (a) and layer 4 (b): (a) control solution; (b) recordings with QX314 in the intracellular pipette solution without (left) or in the presence (right) of CNQX/APV in the bath. (c and d) Population analysis (n = 81) pooling both stimulation sites (WM and layer 4): distribution of the response change ratios for the first vs. the second stimulation pulse (arrows), averaged over the full time course (c) or based on the peak conductance values (d) (global synaptic (black), inhibitory (blue) and excitatory (red)).

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Fig. 4. Voltage-clamp measurement of conductance dynamics evoked by moving stimuli. For each cell: light drifting bars were presented 10 times at the preferred (P) and non-preferred (NP) orientations/directions (cross-oriented for cells 2–6 and null-direction for cell 1). Grey inset waveforms, from top to bottom: (1) single trial current clamp (CC) Vm responses (black, with truncated spikes) superimposed with the mean (V¯ m , orange), (2) evoked changes in synaptic conductance (Gsyn (%)) measured from VC recordings), (3) inhibitory (Ginh in blue) and excitatory (Gexc in red) conductance components relative to their respective resting values (thin horizontal line), (4) reconstituted inhibitory and excitatory currents, derived from the evoked conductance changes, (5) reconstituted membrane potential responses, considering solely significant increases in the mean excitatory (Vexc ) or inhibitory (Vinh ) conductance contributions, and (6) observed average CC measures (V¯ m in black) superimposed with the reconstructed Vm trajectory (Vrec , orange), derived from the conductance measurements. In the inset boxes, cross-correlation functions between excitatory and inhibitory conductance waveforms. For cells 1–3 only: spatio-temporal maps of subthreshold visual responses (XT-RT). The color code is, respectively, warm/red for depolarisation and cold/blue for hyperpolarization. All cells shown here have Simple receptive fields with inseparable (cell 1) or separable (cells 2 and 3) XT-RFs. The stimulus (moving light bar in the preferred orientation and direction) is presented in the space–time domain in three different positions reached at different times (labelled 1–3 in each RF map).

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Fig. 5. Voltage-clamp measurement of conductance dynamics evoked by a drifting grating in a simple RF (cell 2, illustrated also in Fig. 4). Drifting gratings (contrast: 0.7, spatial frequency: 0.5 cycle/◦ , temporal frequency: 1.32 cycle s−1 and size: 6◦ radius) were presented for five cycles in the preferred orientation and direction (left column, P), non-preferred orientation (centre, NPO) or non-preferred direction (right, NPD). The conventions and traces are the same as in Fig. 4. The black indented line below each stimulus delineates the time window during which the stimulus is visible (up = ON; shaded inset) or not (down = OFF). The two bottom panels give an expanded view of the onset responses (*). They show a transient Vm depolarization (black), a transient increase in excitatory conductance (red), accompanied by a fast and large increase in inhibitory conductance followed by a tonic component of weaker amplitude (see Section 4).

tion is found and the conductance change is instead explained by the recruitment of an inhibitory potassium (GABAb) conductance (see Fig. 3A). Of course, this decomposition scheme cannot account for a temporal overlap between the potassium inhibitory conductance and the excitatory conductance changes. An unavoidable limitation of the voltage-clamp method is that the spatial clamp of the cell is inevitably incomplete (Spruston et al., 1993), which affects the reversal values seen from the soma. Consequently, the apparent composite synaptic

reversal potential can become more negative than the reversal potential of the inhibition or more positive than the reversal potential of the excitation if the synapses are away from the soma. In the case where the conductance is decomposed linearly with a synaptic reversal potential more negative than the reversal potential of GABAb, the excitatory conductance would be negative and the extrapolated inhibitory conductance would become larger than the global synaptic conductance. In order to overcome this problem, the synaptic conductance was equated

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to the excitatory or to the GABAb component (see Section 2), in cases where the reversal potential was found to be, respectively, either above Eexc or below Einhb . This ensures that all the global synaptic conductance terms in the decomposition are positive or null. A theoretical possibility (the linear case) is that the excitation and inhibition operate in a push–pull arrangement with a similar visibility from the soma. In such situation, a weak or null change in global conductance might be expected during visual stimulation whereas large changes in the apparent reversal potential might be observed and indicate rapid successive reversals in the E/I balance. Since the global conductance change is null, it is also no longer possible to calculate the reversal potential of the composite drive. In the framework of our decomposition method, the only way to overcome this problem is to estimate the leak conductance and subtract it from the global conductance to obtain the global synaptic conductance (which is the sum of the resting synaptic conductance and evoked synaptic conductance). The assumption we made (see Section 2) was to consider that Gleak is the constant baseline component and Gsynrest represents an additive stochastic component, positive in sign since it corresponds to the ongoing bombardment by excitatory and inhibitory conductance events in the absence of any sensory drive. The computational advantage is that the decomposition is made on conductance components which are always positive and thus does not require during sensory or electrical activation a net conductance increase from the resting level to be tractable. 3.4.2. In vitro measurements of inhibitory synaptic reversal potentials In order to solve the equations detailed in Section 2, the first required step is to estimate Einha, the reversal potential of the GABAa inhibition, mainly mediated by a chloride conductance. A partial “clamping” of the intracellular chloride concentration is likely to occur in whole cell mode patch recordings. It has been previously reported that complex regulatory mechanisms of the intracellular chloride tend to stabilize the internal concentration between 4 and 10 mM depending on the chloride concentration of the pipette (DeFazio et al., 2000). The estimated GABAa reversal potential depends in vitro on the various extracellular ionic concentrations chosen for the ACSF solution, and in particular that of extracellular potassium and chloride (respectively, 1.5 and 131.5 mM in the present study). The estimated intracellular chloride concentration under our experimental conditions was 5 mM and the chloride concentration in the external solution was fixed at 131.5 mM. These values yield a theoretical ECl− value around −80 mV. In order to precisely determine the GABAa reversal potential under our experimental conditions, we pharmacologically blocked the GABAb and excitatory components. The GABAb component (and sodium conductance) was blocked intracellularly by adding (to the filling solution) 3 mM QX314, a quaternary lidocaine derivative, which does not affect GABAa receptor activation (Nathan et al., 1990). AMPA/Kainate and NMDA receptors were blocked by adding to the ACSF bath solution CNQX (25 ␮M) and APV (20 ␮M), respectively. Electrical

stimulation was applied to layer 4, with the aim of activating maximally monosynaptic inhibitory inputs (see Fig. 4). After application of CNQX/APV, the synaptic conductance was reduced and the apparent synaptic reversal potential of the peak conductance shifted from −62.1 ± 12 mV to −80.1 ± 3 mV (n = 19, see Fig. 3). The remaining component of synaptic conductance was further abolished by bath application of 10 ␮M bicuculline (n = 6) or 50 ␮M picrotoxin (n = 2), selective antagonists of the GABAa receptors. Following stimulation of layer 2/3 top, the apparent reversal potential of synaptic responses after application of CNQX/APV was −80.9 ± 1.3 mV (n = 25), a value which is slightly more negative than that found for the layer 4 stimulation. In summary, the reversal potential of GABAa-mediated currents observed in the different stimulation conditions is compatible with the reversal potential of the chloride conductance predicted by the Nernst equation. A possible explanation for the more negative values found when stimulating the top part of layer 2/3 could be that such responses are mediated by a distal inhibitory input, whose spatial location partially escapes the voltage-clamp imposed at the soma (Spruston et al., 1993). Accordingly, we have set Einha to −80 mV for all decomposition of conductances measurements in vitro and in vivo. The other inhibitory reversal potential, corresponding to the activation of a potassium conductance, Einhb , was fixed at −95 mV, in agreement with the standard estimate from the literature. 3.4.3. In vitro measurements of excitatory reversal potentials Assuming that the global conductance change is solely due to excitatory and inhibitory conductance changes and taking into account the fact that the global I–V curves observed during synaptic stimulation and/or blockade of the excitation (CNQX, APV, QX314) were non-rectifying, we extrapolated the view that the IV curve of the excitatory AMPA conductance is also linear. This conclusion could not be tested within our experimental paradigms because the pharmacological blockade of inhibition gives rise to uncontrolled bursts in the spontaneous activity. Using the same preparation, recording set-up and analysis tools as ours, (Le Roux et al., 2006) performed a related control (see Figure D in their supplementary data) where voltage-clamped ramps were applied between −80 and +30 mV in the absence of exogenous application of glutamate. The crossover point between the two linear I–V relationships (control vs. glutamate) established that the reversal potential for the excitatory equals 0 mV for our experimental conditions. In the same run of pharmacological experiments, we checked the possible involvement of NMDA conductances in our experimental conditions. We compared synaptic response with QX314 in the intracellular electrode, evoked before and during application of APV (20 ␮M) in the ACSF bath solution (n = 20). The global conductance was not significantly modified during application of APV. Although it cannot be excluded that in some conditions (in particular strong stimulation) in vitro, and supposedly in vivo, an NMDA contribution is expressed, we conclude that in our experimental conditions in vitro no strong NMDA activation was discernable. In addition, the literature reports that

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the voltage sensitivity of NMDA receptors is such that more than one-half of them can be opened only at membrane potentials more positive than −30 mV (Hestrin et al., 1990; Jahr and Stevens, 1990). In order to suppress the NMDA current, we clamped neurons only at membrane potentials more hyperpolarized than −40 mV, and reduced the possibility of recruiting excitatory current non-linearities. Accordingly, the excitatory reversal potential used in our decompositions was fixed at 0 mV. 3.5. In vitro measurements of excitatory and inhibitory conductances 3.5.1. Balance between excitation and inhibition For cells recorded with the control solution (n = 88) and stimulated either from WM (n = 34) or layer 2/3 (n = 54), the conductance peak value was 6.0 ± 4.0 nS for the excitatory AMPA conductance, 20.0 ± 13.1 nS for the chloride conductance (GABAa) and 0.5 ± 0.4 nS for the potassium conductance (GABAb). Thus, when normalizing each component by the global conductance change, GABAa inhibition was found to be dominant (82.9 ± 5%), relative to excitation (15.3 ± 5%) and GABAb mediated inhibition (2.2 ± 2%). No significant dependency on the electrical stimulation site was found. For recordings done with QX314 in the intracellular recording solution, we checked that our method could appropriately detect the blockade of potassium conductance. Effectively, the percentage of the conductance component mediated with a reversion potential of −95 mV was five times smaller for cells with QX314 than for cells with the control solution (0.4 ± 1% vs. 2.2 ± 2%, p < 0.001). In cells with QX314, the balance between excitation and inhibition was 17.3 ± 7% (excitation) and 82.7 ± 7% (inhibition). Similar findings with QX314 have been previously reported in auditory cortex by Wehr and Zador (2005). They recorded, in the rat A1 cortex in vivo, responses to isolated tones at the optimal frequency, either with or without QX-314 in a potassium-based internal solution. Cells recorded without QX-314 showed a small, slow inhibitory conductance change, whereas cells recorded with QX-314 showed no such slow inhibitory conductance change in response to the same stimuli. 3.5.2. Kinetics of excitatory and inhibitory conductance changes The onset latency of the evoked synaptic conductance varied as a function of the site of stimulation. The shortest onset latencies were observed for proximal stimulation sites (3.1 ± 0.8 ms), the longest for layer 2/3 stimulation (6.5 ± 1.5 ms) while intermediate values were found for WM stimulation (4.5 ± 1.5 ms). The onset latencies were shorter for excitation than for inhibition (paired statistics) with temporal delay of 0.2 ± 1 ms for proximal, 0.7 ± 1 ms for WM and 1.2 ± 1 ms for layer 2/3 stimulation. The peak latencies were also shorter for Gexc than for Ginha (layer 4, 6.7 ms vs. 9.8 ± 3 ms; WM: 8.4 ± 2 ms vs. 11.5 ± 3 ms, layer 2/3, 12.1 ± 3 ms vs. 16.2 ± 4 ms, paired t-test, p < 0.001). The temporal shift between excitatory and inhibitory conductance peaks was, on average, 3.5 ± 3 ms.

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In order to quantify the global shape and kinetics of synaptic conductances, we used three different types of templates (simple alpha function, attenuated alpha function and double alpha function (sum of two alpha functions)). The double alpha function, with 4 fitting parameters, was found to be the best fit for all experimental traces. The mean value and the peak (and latency), derived from the double alpha fit function, were strongly correlated with the direct measures made on the conductance waveforms (r2 = 0.98 ± 0.05 on average). The first part of the conductance was captured by a “fast” and large amplitude alpha function, whereas the second part of the curve was fitted by a “slow” and lower amplitude alpha function. For excitatory and inhibitory conductances (pooling WM and layer 4), the time constant of the fast alpha function was found to be on average almost 5 times faster than that of the slow alpha function, with a peak amplitude 15–20 times larger. Nevertheless, in 45% of these cells, the excitatory conductance was adequately fitted with a single alpha function. In terms of conductance profiles, the inhibitory evoked change globally had slower kinetics than the excitatory one (5.5 ± 5 ms vs. 3.1 ± 1 ms for the fast alpha function and 30.2 ± 15 ms vs. 16.8 ± 15 ms for the slow alpha function). Similar differences were observed when stimulating layer 2/3: the time constant of Ginha was slower than Gexc (8.6 ± 3.0 ms vs. 4.9 ± 2.0 ms for the fast alpha function and 47.2 ± 21.0 vs. 32.2 ± 27.0 ms for the slow alpha function). However, on average, the synaptic conductance profiles evoked by stimulation in layer 2/3 had slower kinetics compared with these produced by stimulation in layer 4 or WM. 3.5.3. Separability between monosynaptic and disynaptic inhibition An important feature reflected in the time-course of the observed conductance changes is that the synaptic response results from the composite activation of monosynaptic and at least disynaptic pathways. The proportion of monosynaptic inhibition can be estimated with a blockade of excitatory transmission with CNQX/APV bath application. As seen in Fig. 3B, for layer 4 stimulation, the inhibitory conductance change was reduced by the blockade of excitatory transmission. On average, about 45 ± 20% (n = 19) of the inhibitory conductance remained during CNQX/APV application, and this inhibition component can be considered to be of monosynaptic origin. For stimulation at the top of layer 2/3, synaptic responses disappeared in around 20% of cells after blockade of excitation, suggesting that, for this contingent of cells, no monosynaptic inhibitory fibers were activated from this layer. For the remaining 80% of cells, the part of monosynaptic inhibition was small (14.0 ± 7.0%, n = 29). For WM electrical stimulations, the application of CNQX/APV suppressed completely all evoked synaptic conductances (n = 3). 3.5.4. Modulation of the E/I balance during paired pulse stimulation In order to check the sensitivity of our method, we applied a paired pulse stimulation protocol with a delay of three hundred milliseconds between each successive afferent volley, which is known to produce a sizeable depression of the inhibitory synaptic response in pyramidal cells (Thomson, 2000). When

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stimulating WM (n = 50), the conductance increase evoked by the second stimulation was reduced by 35% (32% ± 20% for the peak conductance and 35 ± 19% for the mean of the conductance, see Fig. 3C). The composite apparent reversal potential of the peak shifted towards a more depolarized potential by 5.9 ± 11 mV (Esyn : −64.3 ± 9 mV for the first stimulation, −58.4 ± 11 mV for the second). All these difference were statistically significant (paired t-test: p < 0.01). When stimulating layer 4 (n = 31), the observed modulations were of the same magnitude (reduction of 26 ± 23% for the peak conductance, 28 ± 25% for the conductance mean and a shift of +4.3 mV for the composite reversal potential). The decrease in the evoked conductance change and the shift in the apparent reversal potential of the peak of the conductance increase towards more depolarized values, both suggest that the relative contribution of inhibition is decreased during paired-pulse stimulation. The decomposition method permits this differential modulation to be quantified. In the histograms of the Fig. 3C, in order to simplify the presentation, we pooled GABAa and GABAb inhibitory changes into a single component and combined the effects of paired stimulation in layer 4 and WM that were not significantly different. On average, and in spite of variability across cells, the peak of the excitatory conductance was slightly but significantly depressed (88 ± 26%, paired t-test, p < 0.01). In contrast, the mean value of the excitatory conductance did not change significantly (98 ± 30%, p = 0.27). The depression seen after the second stimulation pulse in the global conductance increase was mainly expressed in the inhibitory conductance component (WM stimulation: 64 ± 22% and 61 ± 20%, layer 4 stimulation: 70 ± 23% and 68 ± 25% for peak and mean values, respectively, see Fig. 3C). Because of the mixed recruitment of monosynaptic and polysynaptic inhibition, the depression of the inhibitory conductance component could have been produced by a reduction of the excitatory drive of the inhibitory interneuron or by a depression of inhibitory synapses directly targeting the recorded pyramidal neuron. In order to distinguish between the monosynaptic and polysynaptic nature of the paired-pulse change in inhibition, we blocked excitation and polysynaptic inhibition (mediated by an excitatory drive) with CNQX/APV (n = 21) and observed a similar level of depression of the inhibitory conductance component (69 ± 17% for the peak and 68 ± 25% for the mean). We conclude that most of the regulatory effect concerns monosynaptically evoked inhibition. In summary, during paired-pulse stimulation of intracortical or WM afferents in vitro, the balance between the excitatory and inhibitory drive (Gexc /Ginha ) increases from 20.3% ± 18.9% in response to the first shock to 30.8% ± 26.3% in response to the second shock. This effect results mostly from a down-regulation of monosynaptic inhibitory activation. 3.6. In vivo measurements of excitatory and inhibitory conductances 3.6.1. Estimation of the leak conductance and the E/I balance at rest The assumption we made in the methods section was to consider that Gleak is the lower boundary, constant component of

Grest and Gsynrest represents an additive positive or null stochastic component. The intrinsic standard deviation of the resting conductance derived from our VC recordings (n = 22) ranged from 0.5 to 8.0 nS (mean: 2.6 ± 2.0 nS). The mean resting conductance was 14.6 ± 9.2 nS (Rrest : 97.0 ± 60.6 M) and could be decomposed for each cell into the sum of a Gleak term (mean: 8.6 ± 4.2 nS, Rleak : 245.5 ± 162.1 M) and a synaptic resting conductance component Gsynrest (mean: 6.0 ± 4.3 nS). Thus, according to our conventions, the synaptic conductance resulting from ongoing bombardment corresponded to roughly half of the global input conductance at rest (45.1 ± 22.1%). Taking into account the value of the mean resting potential (−73.5 ± 5.8 mV) and assuming a leak reversal potential around −80 mV (Par´e et al., 1998), we can further estimate the apparent synaptic reversal potential of the global synaptic conductance and decompose it during spontaneous activity (in the absence of any visual stimulation) into three receptor activation specific components (AMPA: Gexcrest = 1.0 ± 0.9 nS; GABAa: Giarest = 4.9 ± 3.6 nS; GABAb: Gibrest = 0.7 ± 0.21 nS). Since the global inhibitory conductance amounts to 4.93 ± 3.6 nS, Gexcrest and Ginhrest represent, respectively, 21.3 ± 17% and 79.4 ± 16% of the resting synaptic conductance (E/I ratio of 1/4). 3.6.2. Decomposition of evoked excitatory and inhibitory components During visual stimulation, the global synaptic conductance can be decomposed again into three components, Gex , Ginha , and Ginhb . The evoked synaptic conductance is calculated for each component by subtracting the mean value at rest (Gex (t) = Gex (t) − Gexrest and Ginh (t) = Ginh (t) − Ginhrest ). This convention implies that both net terms, Gex (t) and Ginh (t), can become negative when the level of activation during visual stimulation is lower than that already present during spontaneous activity. The sum of the positive component of the evoked synaptic conductances (Gex + Ginha + Ginhb ) was found to be larger than the global synaptic conductance increase Gsyn derived previously from the global I/V method (113%). This indicates that the different evoked conductance components have to be integrated over the whole time-course of the sensory activation since direct estimates from average conductance changes would lead to an underestimation of the different synaptic components. The diversity in the levels of changes observed in excitatory and inhibitory conductances is illustrated in Fig. 4 for moving bars with optimal and non-optimal orientations in 6 cells and in Fig. 6 for static light bars flashed in the center of the discharge field in 4 other cells. In Fig. 4, three cells (cell 1, 5 and 6) present large increases in conductance whereas the three other (cells 2, 3 and 4) exhibit changes of a lesser amplitude. In spite of this diversity in the global conductance change strength, the increase of excitation is generally much lower that of inhibition. Large fluctuations in the temporal profile of the inhibitory conductance were commonly observed, while the excitatory conductance waveforms presented fluctuations of only limited amplitude. A second form of diversity is seen in the sign and degree of temporal co-variation between excitatory and inhibitory conductances, evolving sometimes in synchrony (non-preferred stimuli (NP) in

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Fig. 6. Voltage-clamp measurement of conductance dynamics evoked by static stimuli four different cells is illustrated (cells 7–10). Light bars were flashed ten times in the same RF position, with the same (optimal) orientation, for 1 s duration. The black indented line below each stimulus delineates the time window during which the stimulus is visible (up = ON; grey inset) or not (down = OFF). The conventions and traces are the same as in Fig. 4.

cells 1, 3, 5 and 6 in Fig. 4; but also preferred stimulus (P) in cells 5 and 6), sometimes in phase opposition (preferred stimulus (P) in cells 1, 2, 3 and 4 in Fig. 4). For static stimuli, the evoked changes were qualitatively similar to those produced by white matter stimulation in the in vitro

preparation, sometimes with an early excitatory drive followed by a large inhibitory conductance increase (see Off response in cell 9 in Fig. 6). However a high diversity of interaction patterns between excitation and inhibition was observed across cells, as shown in Fig. 6: the response (Off, here) in cell 10 is mainly dom-

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inated by excitation, resulting in a strong evoked spike discharge in current clamp (CC) mode; cells 7 and 8 present large and symmetric conductance increases for On and Off stimulation, associated sometimes with a spike discharge in CC mode. Before studying in greater detail the temporal interplay between excitation and inhibition and its role in the control of the evoked discharge, we first focus our analysis on the global E/I balance averaged over the whole duration of the visual response. More specifically, the calculation applied here was to integrate the conductance increases (positive components only) produced during the first 500 ms following the On and Off transitions of the flashed stimulus (On duration = 1 s) for static protocols, and during the 1–2 s sweep across the RF for moving bar protocols. When averaged across all studied responses (n = 300), the mean peak amplitudes of the excitatory AMPA and inhibitory GABAa and GABAb conductance increases were, respectively, 2.27 ± 2.1 nS (range 0.2–8), 8.64 ± 8.2 nS (range 0.2–45) and 0.28 ± 1.8 nS (range −0.4 to 4). Thus, the average distribution of the various synaptic conductance components was 30% ± 15% for excitation, 68% ± 14% for GABAa inhibition and 2% ± 4% for GABAb inhibition. To determine if the modulation of E/I balance was involved in the spiking selectivity of the response, the sensory responses were classified into two categories, optimal (evoked by preferred stimuli (P)) and non-optimal (evoked by non-preferred stimuli (NP)). The optimal responses were defined on the basis of the maximal suprathreshold integral spiking response, i.e. optimal direction (or optimal orientations for a non-directional cell) in response to moving bars and optimal position and contrast in response to light and dark bars of optimal orientation, flashed across the receptive field width. The comparison of optimal responses (n = 51) with non-optimal ones (n = 249) shows, as expected, that the “preferred” stimulus elicited more spikes (20.5 ± 16.9 a.p. s−1 vs. 5.4 ± 6.8 a.p. s−1 ; t-test, p < 0.005) associated with an evoked depolarisation of larger amplitude (8.0 ± 4.8 mV vs. 4.9 ± 3.9 mV; t-test, p < 0.005). More counter-intuitively, the peak of the global conductance increase was not significantly different between the two classes of stimuli (60.4 ± 40.1% (optimal) vs. 56.9 ± 39.1% (nonoptimal), t-test, p > 0.29). However, the corresponding reversal potentials of the responses were more depolarized for optimal stimuli than for non-optimal ones, supportive of the interpretation that there is a differential change in the mean E/I balance (−58.7 ± 10.1 mV (optimal) vs. −64.1 ± 8.3 mV (nonoptimal), t-test, p < 0.005). The conductance decomposition further demonstrates that the excitatory conductance component was significantly stronger (35.5 ± 16.4% vs. 28.9 ± 16.4%, ttest, p < 0.01) and the inhibition globally weaker (62.4 ± 16.2% vs. 69.1 ± 16.1%, t-test, p < 0.005), for the optimal stimuli when compared to the non-optimal stimuli. Thus, on average, the E/I balance, integrated over the full time-course of the response, indicates more recruitment of excitation by optimal than by non-optimal stimuli, but this measure of the global increase of excitation and inhibition ignores possible dynamic changes in the temporal interplay between the two antagonist synaptic components, which may be a key point in the emergence of response selectivity.

In order to visualize the dynamics of evoked E/I balance with a better temporal resolution (i.e. a shorter time of integration), we correlated the instantaneous evoked excitatory and inhibitory synaptic conductance components (Gexc (t) and Ginh (t)) with the instantaneous increase of global conductance (Gsyn (t)(%)) at all points in time during the response. Each dot in Fig. 7 represents measurements of synaptic conductances averaged over a 50 ms temporal window. In the present analysis, note that the mean change of excitation and inhibition can be positive or negative (negative meaning a reduction of the evoked conductance component relative to the mean synaptic conductance at rest). Although the two x–y variables are linked, the correlation plots are fitted with a linear regression in order to best visualize the ratio of excitation to inhibition in the global conductance increase. Our data show that the global conductance increase is mainly due to the inhibitory conductance component but that the ratio between the relative contributions of excitation and inhibition varies between cells. In some cells, significant withdrawals of inhibition are seen, which result in a reduction of the global synaptic conductance (examples in cells 2, 3, 4, 7 in Fig. 6). In contrast, the net excitatory conductance component becomes negative in only rare instances. In general, the scaling between both synaptic components remains constant across the stimulus time course, although a few cases of non-uniform scaling were found when excitation predominates (left part of the cell 3 plot). 3.6.3. Excitatory and inhibitory synaptic currents In both Figs. 4 and 5, the excitatory and inhibitory currents (see Section 2) have been calculated during the response timecourse in order to illustrate that when the excitatory conductance change is low, the excitatory current remains strong relative to the inhibitory current. The main reason for this normalization effect is of course that the driving force of the excitation is two to three times larger than that of the inhibition. The synaptic current records also illustrate the fact that excitation and inhibition act in opposition, an increase of inhibition increasing the driving force of excitation and, conversely, increase of excitation increasing the driving force of the inhibition. These balancing effects result in more symmetrical records in current compared to conductance waveforms. Thus, the dynamic regime in which cortical neurons operate during sensory integration appears to be balanced in term of currents (in the sense that the ratio between excitatory and inhibitory currents is close to one) but not balanced in term of conductances. 3.6.4. Reconstruction of voltage dynamics from VC-based conductance measurements The continuous decomposition at any point in time of the total conductance into excitatory and inhibitory components allows us to recalculate the dynamics of the membrane potential trajectory during sensory activation on the basis of the measurements of the membrane time constant (τ m ). This reconstituted potential response is the prediction based on voltage-clamp recordings of the behavior that normally should be observed during current clamp measurements.

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Fig. 7. Correlation between Gex , Ginh vs. Gsyn (%). Same cell numbering, as illustrated before, in Figs. 4 and 6. Evoked excitatory (Gexc , red dots) and inhibitory (Ginh , blue dots) conductance changes were binned every 50 ms along the response course and plotted against the relative increase in the global synaptic conductance (Gsyn (%)) measured at the same time abscissae. Linear regressions (in black), corresponding to the conductance dynamics measured over the full response duration, are shown separately for excitation and inhibition.

The direct comparison between the reconstructed and CCrecorded voltages is illustrated for different cells in Figs. 4 and 5. We see clearly that both traces fit relatively well together. The difference observed between the two traces gives some indication of the existence of non-linear conductance activation processes during current-clamp recordings (for more details, see spike triggered average (STA) analysis in Fig. 7). One should note that both Vm trace estimates are totally independent and based on different recording modes used at different times (VC and CC). In order to quantify the difference between VC-reconstructed voltages and raw CC-records, we calculated the root mean square error (RMS error) for each response (2.26 ± 1.24 mV, n = 252 responses from 22 cells in VC). The same method was also used for conductances estimated in current-clamp but in this case, since the two traces were based on the same CC recordings, the RMS error was, as expected, much lower than in the VC case (RMS error = 0.60 ± 0.28 mV, n = 60 responses from five cells). We also applied the same comparison between CC measurements and VC reconstructions in the in vitro preparation, and observed good agreement between the two data sets (RMS error = 0.96 ± 0.3 mV (n = 50)). The fact that the RMS error is low supports the view that the inputs measured in voltage-clamp are the same as the inputs

producing voltage fluctuations in current clamp. However, it does not constitute a proof that the conductance measurements are valid, since multiple combinations between excitatory and inhibitory input conductances can produce the same voltage output. 3.7. Temporal interplay between evoked excitation and inhibition The precise timing of spike emission is often considered as critical in encoding information. The generation of action potentials at the initial segment of the axon hillock depends on the temporal interplay of excitatory and inhibitory synaptic inputs distributed onto the dendritic tree and soma. One strategic issue, at the functional level, is to assess the role of synaptic inhibition in the control of the timing of the neuronal discharge: is it merely permissive, for instance down-regulating cortical excitability in a non-specific way, or does inhibition act selectively by barrages of large and transient conductance bursts vetoing the depolarizing impact of synchronous excitatory input? Does it also contribute to the timing precision of spike emission by an optimal interplay of its phase with that of the excitatory drive?

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3.7.1. Cross-correlation between evoked excitation and inhibition In order to dissect the role of the temporal relation between the excitatory and inhibitory conductance components on the genesis of direction and orientation selectivity, we first calculated the normalized cross-correlation between Ginh (t) and Gexc (t) (Monier et al., 2003) and measured the level of correlation for a null time shift between the two waveforms (Cτ(0)). This calculation was done only for the 15 cells for which conductance measurement was achieved in VC mode. In 60% of these cells (9 out of 15), the temporal relationship between excitation and inhibition (see cross-correlation graph insets in Fig. 4, for cells 1, 2, 3 and 4) was highly dependent on the optimality of the stimulation: for the preferred (P) stimuli, both conductances were in anti-phase (negative correlation peak for a null shift value, Cτ(0) = −0.29 ± 0.19, n = 15 responses), whereas for the nonpreferred stimuli (NP) they were in-phase (positive correlation peak for a null shift value, Cτ(0) = 0.26 ± 0.19, n = 95). This stimulus-dependent differential behavior was statistically significant at the population level (paired t-test, p < 0.01). In these cells we observe different degrees of orientation/direction selectivity of the mean excitatory conductance increase: some cells were poorly selective and others were very narrowly tuned, reflecting a diversity in the balance level between thalamocortical input and recurrent cortical amplification (see Monier et al. (2003) for complete tuning curve measures). Thus, for Simple cells dominated by thalamo-cortical inputs (low tuning selectivity of mean conductances, Fig. 4, cell 2), the mode of synaptic integration was linear and the main factor for generating selective spiking responses appeared to be the change of phase between excitation and inhibition as a function of the orientation/direction of the stimulus. For the simple cell 2 (shown in Fig. 5), drifting gratings were also used to estimate the orientation selectivity of the excitation and the inhibition. Conclusions are similar as those reached with a moving bar, the excitatory and inhibitory conductance increases being found in anti-phase for the optimal direction and in phase for the non-preferred directions/orientations. In addition, the differential interplay between excitation and inhibition can be roughly predicted on the basis of the subthreshold spatio-temporal activation profile of the receptive field (XT-RF, Fig. 4 cells 1, 2 and 3). Cell 1 in Fig. 4 illustrates, however, the case of more complex and diverse modes of interaction where, in addition, the inhibitory and excitatory conductances increases were both found to be the largest for the null (NP) direction. In this cell, both the push–pull behavior of the excitatory and inhibitory inputs for the preferred stimulus (P) and the shunting effect of inhibition in the null direction (NP) generate the functional selectivity of the cell output (which, in this case, is opposite to the directional preference or bias expressed by the excitatory input alone). The inseparability of the subthreshold spatio-temporal map (XT-RF in Fig. 4) predicts accordingly the direction preference of this cell. In the remaining 40% of cells (6 out of 15, illustrated by cells 5 and 6 in Fig. 4), excitatory and inhibitory conductances were either synchronous or largely overlapped temporally, independent of the optimality of the stimulus (Cτ 0 = 0.71 ± 0.17

for the preferred stimuli (P: n = 7); Cτ 0 = 0.73 ± 0.17, for the non-preferred stimuli (NP: n = 45). In these cells, the inhibitory conductance was often of large amplitude and selective to nonoptimal stimuli (see example in cell 6). For this contingent of cells, the selectivity of spiking activity resulted mainly from the broader tuning of excitation and the competitive imbalance produced by the difference in tuning width and asymmetry between excitation and inhibition. Thus, we concluded that there is a diversity of ways through which orientation and direction selectivity emerge (Monier et al., 2003). 3.7.2. Control of the evoked spiking response by the E/I balance In order to determine the level of balance that controls the triggering of spike activity, we correlated together the instantaneous evoked excitatory and inhibitory synaptic conductance components (Gexc (t) and Ginh (t)) during the response course. Each dot in Fig. 8 represents measurements of evoked excitatory (ordinates) and inhibitory (abscissa) synaptic conductances averaged over a 50 ms temporal window. Two populations of points are represented in Fig. 8, for eight representative cells, according to whether (orange dots) or not (empty dots) these conductance changes were associated with significant spike emission. In addition, for each cell, we calculated the spike triggered average (STA) of excitatory (red curve) and inhibitory (blue curve) conductance waveforms as well the membrane voltage trajectory measured in current clamp (black curve) and reconstructed from voltage-clamp recordings (orange curve). It is important to note that, in both calculations, the respective timing of spike occurrences were measured in current clamp whereas the conductance waveforms, although synchronized by the exact same stimuli, were extracted from an independent series of voltage-clamp recordings. As exemplified in cells 1–4, the relation between evoked excitation and inhibition by moving stimuli changes drastically when the conductance increases cause significant spike activity (compare the regression lines for orange dots and empty dots in Fig. 8). Spikes are mainly elicited when simultaneously inhibition decreases (negative change in inhibitory synaptic conductance) and excitation increases. For these cells, the STA analysis shows clearly that inhibitory and excitatory waveforms are in anti-phase at the time the spike is emitted, confirming the conclusion of the previous cross-correlation analysis. In cells 5 and 6, the behavior of the two populations of dots associated or not with spikes is relatively similar but the excitation is globally higher during the spike activity. This effect is less prominent in the STA analysis, and the integration window may be of too short duration to reveal a systematic behavior. For flashed stimuli, a larger variety of conductance dynamics is found. Cell 10 (Fig. 6) illustrates the case of strong discharges where the amplitude of firing is directly proportional to the increase of excitatory conductance. In cell 9, early and fast excitatory input was rapidly quenched by inhibition, truncating the spiking response within a few milliseconds (On response) or suppressing the spike activity (Off response). Fig. 8 illustrates the case (cells 7 and 8) of high conductance levels preceding the spike discharge, where the sudden drop in

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Fig. 8. Spike triggered average conductances. The top inset (methods) shows successive measurements of mean conductance changes (Gexc and Ginh ) in successive 50 ms time bins. The orange colored rectangles correspond the bins for which a significant larger number of spikes were found compared to the resting condition. For each of the eight illustrated cells, the correlation between Gexc and Ginh is shown in the left plot and linear regressions are calculated separately for periods corresponding to a significant (orange dots) or no (empty dots) change in firing. Right top inset boxes, spike trigger averaging (STA) of mean membrane potential (V¯ m in black) and of reconstituted voltage from conductances estimates (Vrec in orange). The differences between the two membrane voltage trajectories, detected just after the spike, are due to intrinsic conductance activation by the spike itself. Left bottom boxes, STA of the relative excitatory (Gexc in red) and inhibitory (Ginh in blue) conductance increases. In most cases, the excitatory conductance increased and the inhibitory conductance decreased, in anti-phase, just before spike generation.

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inhibition, faster than in excitation, seems to control the spike emission. 3.7.3. Evidence for shunting inhibition In the case where the reversal potential of the synaptic conductance is above the resting voltage of the cell, the synaptic conductance produces a depolarization; if it is below, the synaptic conductance produces a hyperpolarization. It is only in the case where the resting and the synaptic reversal potentials have the same value that no voltage change is observed despite the increase in synaptic conductance. Such a configuration is referred to as “silent” inhibition (Koch et al., 1990) or “shunting” inhibition (Torre and Poggio, 1978). However, it is probably more correct to refer to a “shunting” effect only in the context of a large conductance increase suppressing the depolarization produced by a concomitant excitatory current, rather than to focus on whether the synaptic battery reverses at rest or below the resting potential. The functional view is that inhibition with a reversal potential close to the resting voltage can only be efficient if the increase of inhibitory conductance is large enough. If we consider the membrane equation, it is clear that the inhibition can reduce the impact of excitation in two complementary ways, by producing a current of opposite sign to the excitatory current (“subtractive” effect) or by increasing the global conductance strongly in such a way as to divide all the currents (“shunting” effect). The GABAa inhibition acts in both ways, the inhibitory current reconstituted in the examples of visual responses in Figs. 4–6 is never zero and, in many cases, large increases of conductance are observed in temporal overlap with excitation, in particular during non-preferred stimulation (for instance, moving bars in the “null” direction or orthogonal orientation). In order to quantify the effectiveness of the inhibition in reducing excitation when both these conductances are in temporal overlap, we reconstituted the voltage change that would have been evoked if the same excitation was applied alone (in the absence of significant evoked inhibition). From our calculations, we extracted a shunting factor (M) proportional to the degree of linearity in the interaction between the excitation and the inhibition for the considered voltage value. The detailed calculation is the following: on the basis of our estimations of conductances, we computed the voltage profile when excitation was acting (Vexc ) in the absence of evoked inhibition but still in the presence of ongoing resting inhibition. A converse calculation was made for inhibition (Vinh ). In addition, we also reconstructed the voltage trajectory (Vrec ) predicted from the VC-measurements of all (rest and evoked) excitatory and inhibitory components combined together. Note that in the in vitro preparation, the resting synaptic conductances are zero. In addition, when the evoked increases in excitation and inhibition were found to be significant, we calculate the correlation of mean voltage based on both synaptic components with the mean voltage based on excitation only (see central column of correlation plots in Fig. 9). The M factor, defined by Koch et al. (1990), quantifies the prevalence of the “shunting” effect versus the “subtractive” effect produced by the inhibitory input. A low M factor implies

that the interaction between the inhibition and excitation is nonlinear, whereas an M value of 1 implies linearity. Koch et al. (1990), on the basis of simulations of different cell types (pyramidal layer 5 or 2/3 cells) with different scenarios (only GABAa inhibition or mixed between GABAa and GABAb inhibition), reported that the M factor decreased with increasing inhibitory conductance. Roughly speaking, for weak increases of conductance (10%) M is close to 1, whereas for large increases (1000–1500%) M is close to 0.1. In order to compare with our data, we plot the values of the simulations of Koch et al. (1990) as red dots in Fig. 9A(c). The correlation between Vrec and Vexc , established across cells and stimulations, shows in vitro that inhibition largely reduces the amplitude of the depolarization evoked by excitation (by as much as 30 mV for some cells, see Fig. 9A). The shunting factor M values are equal, respectively, to 0.57 ± 0.03 for layer 2/3 stimulation, 0.48 ± 0.06 for layer 4 stimulation and 0.58 ± 0.03 for WM stimulation. The correlation of the M index with the conductance increase (Gsyn (t)(%)) shows, as expected, that the shunting effect is more pronounced for large relative conductance increases (reaching an asymptotic value of 0.2 when the conductance increase goes beyond 1000%). In the in vivo situation, the analysis has been limited to cells with large conductance increases and temporal overlap between excitation and inhibition (cells 1, 6 and 8), for which a shunting interaction can be expected (Fig. 9B). The reduction of the evoked depolarization is as pronounced as 20 mV in these cells, and M tends towards an asymptotic value of 0.5. Since it is based on somatic impedance measurements, our experimental method does not compensate for the loss of visibility of dendritic inputs due to on-path synaptic interactions or cable attenuation. Thus, the nonlinear processes that are potentially localized in the dendritic tree but are filtered out by space clamping are not taken into account, and the remaining sources of non-linear interaction necessarily lie at the somatic level. In this regard, our shunt factor measure is not strictly equivalent to the M factor of Koch et al. (1990) since, in their simulations, these authors totally removed both somatic and dendritic inhibition. In conclusion, the asymptotic M factor estimates that we have obtained (close to 0.2 for the in vitro situation and 0.5 for in vivo) demonstrate that shunting inhibition might be strong enough to play a functionally significant role, at least in certain cells and for certain stimulus configurations. 3.8. Impact of methodological considerations 3.8.1. Comparison of between voltage-clamp (VC) and current clamp (CC) measurements The advantage of using voltage-clamp mode is that distortion of synaptic events by transient voltage-dependent channels and capacitance local to the recording site is minimized. In order to estimate the impact of the membrane capacitance on the measure of conductance, we compared current-clamp and voltage-clamp measurements for a subpopulation of cells in the in vitro (n = 54) and in vivo preparations (n = 6). The CC measures are based on the same principle as the VC method, and

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Fig. 9. Evidence for shunting inhibition in vitro (A) and in vivo (B). All the examples shown here correspond to stimuli which evoked increases in excitatory and inhibitory conductances in almost complete temporal overlap. The three in vivo examples (B) correspond to responses to non-preferred stimuli in cells 1, 6 and 8 (see Fig. 4). (a) Reconstituted membrane potential response based on excitatory and inhibitory conductances estimates (Vrec in black) and predicted Vm trajectories, considering either excitation only (Vexc ) or inhibition only (Vinh ). For these calculations, only significant conductance increases have been considered. The amplitude of the evoked depolarization Vrec is smaller that predicted by excitation only (Vexc ), illustrating the impact of the interaction between excitation and inhibition at the voltage level. This suppressive effect is quantified in (b) where predictions of Vexc , calculated on consecutive 50 ms bins (see methods in Fig. 8) are plotted vs. Vrec . Only the bins where both the excitatory and inhibitory conductances were found to be simultaneously increased, have been used for this calculation. (c) Shunting factor (M, see Section 3) plotted against the global synaptic conductance increase (Gsyn (%)). The larger the conductance increase, the lower the shunting factor was. In the plot shown in (a), the red dots represent the values taken from simulations of Koch et al. (1990).

required to record evoked PSPs at different holding hyperpolarizing currents (to avoid spike activity contamination and the recruitment of voltage-dependent non-linearities). The population analysis summarized in Fig. 10 illustrates, in the in vitro case, the general observation of a lower conductance peak (247 ± 193% vs. 471 ± 318%, p < 0.01) and slower kinetics (peak latency: 21.1 ± 6.0 ms vs. 12.0 ± 4.0 ms, p < 0.01) than

voltage-clamp. However, the mean conductance increase integrated over 300 ms (following the electrical stimulation) was the same, whether measured in current-clamp or voltage-clamp. Note that this result would be expected in the case where the downscaling of the detected conductance increase in current clamp results mostly from capacitive integration by the neuronal membrane.

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Fig. 10. Comparison of conductance estimates in voltage-clamp and current clamp modes. Current clamp (CC) and voltage-clamp (VC) recordings were performed consecutively in the same cells either in vitro (A) or in vivo (B). Left: relative synaptic conductance increase (Gsyn (%)), excitatory (Gexc , red) and inhibitory (Ginh , blue) conductance changes, deduced from membrane potential responses (Vm ) recorded at different current levels (CC) or from current input responses (Im ) recorded at different holding potentials (VC). Right: comparison of mean and peaks of conductance (Gsyn , Gexc and Ginh ) between CC and VC modes. (B) Left, in vivo example of a response evoked by a non-preferred stimulus in cell 6 (see Fig. 4).

The same analysis in VC and CC modes was carried out in six cells recorded in vivo (four cells stimulated with moving bars and two cells with light bars flashed across the RF). In contrast to the in vitro case, the extracted global conductance waveforms extracted (as well as their peak and mean values) are indistinguishable when comparing CC and VC measurements, whether one considers the global input conductance or its excitatory and inhibitory components. We conclude that the effect of the membrane capacitance has mainly a large impact on the estimation of peak conductance in the in vitro situation. 3.8.2. Comparison between different conductance extraction methods In previously published studies (including ours), and depending on the research teams, different methods have been used in vivo and in vitro to estimate excitatory and inhibitory conductances on the sole basis of I–V curves. For sake of comparison

and methodological clarification, we have illustrated these various methods in Fig. 11, for a representative cell recorded in vitro, in voltage-clamp mode at ten different holding potentials (panels A–D, G and H) and in current clamp mode at four different levels of injected current (panels E and F). Since the only distinction between methods is the handling or not of the nonlinearities in the I–V profile, we chose the illustrative case of a cell presenting strong non-linearity in the IV curve established at rest (rectification above −50 mV and below −90 mV), as well as in the evoked states. The Pearson correlation coefficient (0.80), calculated on ten values in voltage clamp at rest, is lower in that specific cell than in most cells that we have recorded in the same condition (0.94 ± 0.05; n = 50). Note that, in the case of cells with perfectly linear I–V curves, all the represented methods would give identical results in the VC recording mode. Fig. 11 illustrates the various conductance measurements, given by the slopes of regression lines or local tangents mea-

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Fig. 11. Comparison of different methods of conductance estimation. This figure summarizes the evoked conductance waveform (Gex in red, Ginh in blue) estimates, obtained by different methods (A–H), on the basis of VC and CC in vitro recordings in a pyramidal layer 5 cell. Current and voltage responses, evoked by WM stimulation, were recorded, respectively, at 10 levels of holding potential (between −90 and −30 mV, 10 trials) in VC (voltage clamp) and four levels of current in CC mode (current clamp), and illustrated in two specific insets. For each method, the relative excitatory and inhibitory contributions are expressed, respectively, in red and blue, in % of the total synaptic conductance waveform (integrated over 200 ms). The part of explained variance in the I/V relationship (r2 ) is plotted as a function of the post-stimulation delay (t) over the full duration of the response. Voltage-clamp measurements-(A) direct decomposition of excitatory (Gexc ) and inhibitory (Ginh ) conductances by the linear system resolution (for holding Vhc values below −50 mV, detailed in (B)). (B) Linear part of the I/V curve obtained from voltage-clamp currents. Linear regressions are shown for measurements made in the resting state (black, at the black dotted line delay preceding stimulation) and at the peak of activation (red, red dotted line delay following stimulation). (C) Same method as in (B), but the linear regression is extended for the full range of holding potentials (10 levels, up to −30 mV). (D) Polynomial regression on the full I/V curve. Gsyn is given by the slope of the tangent to the fitted curve at Im = 0 (black and red line). (G) I/V synaptic curve. Extraction of Isyn from Im recordings in VC mode after subtraction of passive membrane current deduced from measures at rest. Gexc and Ginh are deduced from linear regressions made over the 10 potential levels. (H) Same method as in (G), but with a polynomial fit. Current clamp measurements—(E and F) same as in (A) and (B) but in current clamp mode. The lower panel (conductance increase (%)) represent, in superposition, the conductance increase estimates (Gsyn (%)) obtained by each method. Right, the conductance waveforms are expanded and their peak values normalized, in order to compare their respective kinetics.

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sured before the stimulus onset (black, resting state) or at the peak of the global conductance activation (red). In addition, we compare the excitatory (red) and inhibitory (blue) conductances, obtained by decomposition of the global synaptic conductance and the reversal potential, or calculated directly by solving the detailed conductance model equation membrane. For each method, we represent the conductance profile of each synaptic component and the fraction of explained variance (calculated for each post-stimulus delay) below the corresponding I–V plot. In the panels B and C, the regression model between the membrane currents Im and the voltages Vhc (corrected for the ohmic drop through the access resistance) is assumed to be linear. It is established either on the basis of the linear part of the I–V curve (for hyperpolarized Vh values below the rectification threshold, ranging here between −80 and −50 mV; panel B in Fig. 11) or of the full I–V curve (including the rectification, for Vh values ranging between −90 and −30 mV; panel C in Fig. 11). A similar rationale is applied when the conductance measures are done in current clamp (Fig. 11, panel F). Method F is thus the analog, in CC recording mode, of the linear regression method B applied in VC mode. The other VC methods (panels D, G and H in Fig. 11) no longer assume linearity in membrane behavior. In panel D, a third-order polynomial regression is applied to the full I–V curve, which significantly reduces the residual error due to the rectification; hence, the correlation coefficient values are close to 1.0 at all delays. In this latter case, since conductances are now dependent on voltage values, the resting conductance is estimated as the tangent to the I–V curve measured at the resting potential and the global conductance is measured for the voltage value corresponding to a zero current value. The synaptic conductance is then taken as the difference between the global input conductance and the resting conductance. Another variant in method consists of subtracting the resting current Irest , which allows extraction of the evoked synaptic current (Isyn (t)). Thus, once the contribution of the resting conductance has been removed, the evoked change in the synaptic current amplitude Isyn (and no longer Im ) is plotted against the corrected holding potential Vhc (panels G and H, middle row in Fig. 10). The evoked synaptic conductance Gsyn (t) is then given by the slope of the best linear fit of the experimental IV curves (Wehr and Zador, 2003; Wehr and Zador, 2005). It is however necessary to add a corrective term in the synaptic current (Isyn (t) = (Iin (t) − Irest )(Rrest + Rs )/Rrest , Rrest and Rs being, respectively, the resistance at rest and the access resistance). In its implementation, method G differs slightly from that initially introduced by (Wehr and Zador, 2003, 2005), who measured Rrest by using additional test current pulse injection: since the linear fit to the global I–V curve strongly underestimates the resting conductance, Rrest (given by the tangent at Vrest ) and Irest are extracted here directly from the polynomial fit. The synaptic conductances were extracted by linear regression on the Isyn –Vhc curves (plot G). We have also applied a polynomial regression to fit the Isyn –Vhc curve in order to obtain a better estimation of the synaptic reversal potential Esyn (plot H). The synaptic conductance increase was then derived from calculation of the tangent

to the polynomial curve at the membrane voltage at which the current is zero. In order to compare these different methods, we have extracted, for each of them, the excitatory and inhibitory conductance components and quantified the E/I balance on the basis of the mean values of the evoked conductance waveforms. In all cases, as expected, the evoked inhibition was found to be systematically larger than the excitation, with slight quantitative differences: the excitatory contribution ranges, according to the chosen method, between 11 and 16% of the global conductance change. The minimal value for excitation was obtained with the methods using polynomial fits (methods D and H). These methods were indeed developed to account specifically for the observed non-linearity in the I–V profile (both at rest and during the synaptic response). In particular, the synaptic reversal potential estimates, given by the abscissa of the crossing point between both polynomial curves (corresponding to the resting and evoked states) in D and by the intersection with the abscissa axis (null synaptically evoked current value) in H, are in agreement. Linear regression models performed for all holding potential values (methods C or G), which include the non-linear domain, tend to produce a shift of the reversal potential Esyn estimate towards more depolarized values and attribute a slightly larger impact to excitation. The restriction of the linear fit to the domain of the IV curve closest to the resting state and below the rectification threshold reduces this problem (methods A and B) and gives, as expected, the same estimate (here 12% for excitation). The choice of the fit function has also an impact on the estimate of the global conductance increase. In the bottom panel in Fig. 11, we have superimposed the different waveform estimates obtained using the different methods. When measured in VC, the global conductance kinetics appears highly similar, whichever method is used, and the variations across methods affect mostly the peak amplitude estimate. This is mainly is due to differences in the estimates of the resting conductance, which, for instance, vary by a factor 2 between the linear method (C) and the polynomial fit (D) methods. When measured in CC, and as already shown in Fig. 10, the conductance estimate is affected by the filtering of the membrane capacitance (see method F). Consequently, the amplitude of the peak is reduced and the decay times of the excitatory and inhibitory are clearly slower compared to the VC measurements (as shown by the superposition of global conductance waveforms in the lower right panel of Fig. 11). If we take into account the membrane capacitance in the computation of the conductance components (method E, as introduced by Priebe and Ferster, 2005; Wehr and Zador, 2003) and measure the time constant of the cell with current pulse injection (τ = 29 ms for this cell), we see that the amplitude and the temporal kinetics become comparable to those observed in voltage clamp. We conclude from this example, where a rather large nonlinearity was apparent in the resting and synaptic I–V curves, that differences between methods have a moderate impact. The linear method that we have used in this article both in vitro and in vivo (method B in Fig. 11) is the simplest and, because of the limited number of unknown variables to identify, it reduces the number of recordings required at different holding potentials. Its applicability is of particular interest in the in vivo situation

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where the recording time is limited. However, in vitro, the polynomial fit to the synaptic IV curve (method H in Fig. 11) because it takes into account the nonlinearities recruited in the more depolarized states, will potentially give the most refined quantifications. Note however that a linear regression on the synaptic I–V curve between −80 and −50 mV (without inclusion of the depolarized states) seems on equally a good compromise (as carried out for instance by Cruikshank et al., 2007). 4. Discussion When overviewing the existing literature on neocortical conductance dynamics, one faces many issues which are still a matter of debate: how much does the resting conductance differ from the leak conductance? What is the E/I balance in the resting condition, in terms of average and fluctuations? Are the synaptically evoked conductances weak or strong, or in other terms, does the synaptically driven input regime operate, respectively, in the linear or nonlinear mode? What is the E/I balance in terms of evoked synaptic conductances, and does it differ from the spontaneous ongoing case? Finally, what is the temporal relationship between excitatory and inhibitory conductance waveforms during sensory stimulation? The following discussion will address in depth two particular aspects: how does the E/I balance control the spike output and how does inhibition regulate excitation during optimal and non-optimal stimulation? For this purpose, we have compared results taken from the main experimental studies conducted so far, which gave quantified estimates of the conductance (or input resistance) waveforms in sensory cortex. These studies relied on measurements of I–V curves in response to sensory or electrical stimulations or synchronous with spontaneous or evoked up/down state transitions in neocortical cells. In vitro or in vivo recordings were performed in the primary sensory (visual, auditory, barrel), associative or prefrontal cortices, in different species (mice, rat, ferret, cat, tree shrew), with different bath solutions (in vitro) or types of anesthesia (in vivo). They were done using either sharp or patch electrodes (filled with QX314, Cs2+ or not), in voltage-clamp or current-clamp mode and the analysis relied on a variety of tools that we have presented at length in Section 2 and the last section of the Results (Fig. 11). We will review data taken from the following studies measuring evoked conductance dynamics: (1) in vitro, in rat visual cortex (Le Roux et al., 2006) and in the mouse somatosensory thalamocortical slice (Cruikshank et al., 2007); (2) in vivo, CC studies in cat visual cortex of the cat (Anderson et al., 2000, 2001; Hirsch et al., 1998; Marino et al., 2005; Priebe and Ferster, 2005, 2006); (3) in vivo, CC studies in rat barrel cortex (Higley and Contreras, 2006; Wilent and Contreras, 2004, 2005); (4) in vivo VC studies in rat auditory cortex (Tan et al., 2004; Wehr and Zador, 2003, 2005; Zhang et al., 2003). 4.1. Estimation of the leak conductance and the resting synaptic conductances In this study, we proposed to decompose the resting conductance into three components: a non-synaptically mediated basal

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leak component and two (excitatory and inhibitory) components corresponding to the ongoing synaptic bombardment at rest. The assumption made here is that the variability of the resting conductance is purely of synaptic origin, and that each component found in the decomposition is positive or null. In most in vitro preparations, the cortical network is considered as ‘silent’ and the synaptic resting conductance is set to zero. In the in vivo preparation, in the absence of sensory drive, cortical neurons are still submitted to an intense synaptic bombardment, producing fluctuations in the membrane voltage. However, the irregular or periodic dynamics of these fluctuations depend on the global activation state of the network (wake/sleep) or on the type of anaesthetics used. 4.1.1. Dynamics of the brain During wakefulness, cortical neurons have a tonically depolarized resting membrane potential which fluctuates around −60 mV (Steriade et al., 2001; Timofeev et al., 2001) and irregular spiking activity, giving rise at the ensemble population level to a desynchronized electroencephalogram (EEG) characterized by low-voltage, fast-activity patterns. During slow-wave sleep (SWS), the EEG shows slow oscillations reflecting large synchronizations of neuronal assemblies. This oscillatory behaviour is also found at the single cell level, where Vm alternates between a hyperpolarized silent phase or down-state and a depolarized active phase or up-state (Steriade and Timofeev, 2003) during which neurons fire at rates that are even higher than in quiet wakefulness. These two Vm states are correlated, respectively, with negative and positive fluctuations in the EEG, of large amplitude. The transition from the waking mode to the sleep mode is controlled by the brainstem activating system, regulating the release of various neuromodulators, which in turn modulate intrinsic as well as synaptic currents. For instance, an important correlate of the induction of slow Vm oscillations seems to be the increase in the potassium leak conductance, corresponding to the unblocking of background potassium leak channels, which arise from the reduced actions of neuromodulators during sleep, such as acetylcholine (Benardo and Prince, 1982; Krnjevic, 1993; Krnjevic et al., 1971; McCormick, 1992; McCormick and Prince, 1986, see Hill and Tononi, 2005 for a detailed model of transition between SWS and awake states). In spite of the fact that consciousness is associated with the wakefulness state, but is not reported during slow oscillations, some electrophysiological reports and computational models from the cortex and thalamus conclude that the up-states observed during SWS and the ‘activated’ state of wakefulness are “remarkably similar dynamical entities” (Destexhe et al., 2007). By generalization, some authors also consider that the up-state in the anaesthetized brain is a valid model to understand the wakefulness state in the intact unanaesthetized brain (review in Destexhe and Contreras, 2006). However, a similarity in dynamical signature would not necessarily imply an identity in the elementary underlying mechanisms. In particular, we noted that the SWS and wakefulness states differ in their neuromodulation context, the repertoire and strength of expressed intrinsic and synaptic conductances corresponding in

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each case to a different level of global network synchronization. In addition, the alternation of silent and active synaptic phases during SWS produces a particular activity-dependent context for fast depression and facilitation of excitatory and inhibitory synapses. Interestingly, several anaesthetics regimens, including urethane and Ketamine–Xylazine (which blocks N-methyl-daspartate (NMDA) receptors (Anis et al., 1983) and activates ␣2 -noradrenergic receptors (Nicoll et al., 1990) can also lead to a slow oscillation in the EEG correlated with up- and down-states in individual cortical neurons, similarly to those observed during natural sleep. During this anaesthetics treatment, brain activation can be mimicked by stimulation of the ascending arousal system (Steriade, 1996; Steriade et al., 1991). For example, under Ketamine–Xylazine anaesthesia, a brief electrical stimulation of the pedonculopontine tegmentum (PPT) typically induces a prolonged period (∼20 s) of desynchronized EEG activity that is paralleled by a continuous depolarized state of the membrane potential, similar to that observed during natural waking (Rudolph et al., 2005; Steriade et al., 1991). In our in vivo preparation, we used althesin, a synthetic steroid, for general anaesthesia induction and maintenance and observed a diversity of membrane potential dynamics. In some neurons, the membrane potential was strongly correlated with the EEG and presented a bimodal distribution (with slow upand down-state transitions), in others, the membrane potential was desynchronized from the EEG and presented a unimodal distribution with a more or less important level of fluctuation (Bringuier et al., 1997, 1999; Monier et al., 2003). The same diversity of individual cell dynamics has been reported with pentobarbital (Anderson et al., 2000). This variability in cortical dynamics, often found during the course of a 3-day long experiment, may be explained by small fluctuations in the level of effective anesthesia, changes in the basal level neuromodulation or/and by the local “awakening” of the thalamocortical pathway produced by various regimes of sensory stimulation. In our study, in vivo conductance measurements have been reported from cells exhibiting a unimodal resting membrane potential distribution, some neurons showing weak spontaneous fluctuations (cell 10 in Fig. 6), other neurons larger fluctuations (others examples in Figs. 4–6). The consequences of this background activity are obviously important for the integrative properties of cortical neurons (Bernander et al., 1991; Destexhe et al., 2003) and crucial for the measure of the relative change in evoked conductance during sensory stimulation relative to the resting state. Consequently, it is important to determine with accuracy each of the different components of the resting conductance, i.e. the leak conductance, the mean ongoing excitatory and inhibitory synaptic conductance components and their intrinsic levels of fluctuation. The leak conductance is mainly a potassium conductance with a reversal potential in vivo on the order of −80 mV (Par´e et al., 1998). The resting inhibitory synaptic conductance has a reversal potential close to −80/−70 mV (depending on chloride concentration and the type of recording (patch or sharp)) whereas that of the excitatory conductance is close to zero. In principle,

multiple combinations of the resting conductance components may account for a similar resting potential between −60 and −70 mV, and at least two balance terms have to be identified: the ratio between the leak conductance and the resting synaptic conductance and the ratio between the inhibitory and the excitatory resting conductances. If the ratio between the leak and the synaptic conductances is highly imbalanced (in a proportion of 1–5) the mean inhibitory conductance component should be much larger than the excitatory one at rest. If the same ratio is close to 1, the mean resting synaptic excitatory and inhibitory components should be equal. We discuss, in the following sections, different approaches to estimate the ratio between the leak conductance and the resting conductance as well as the operating point of the E/I balance at rest. One also has to keep in mind that there may be no such thing as a fixed operating point and that the same network can exhibit a variety of states characterized by a diversity of E/I balance levels fluctuating over time. 4.1.2. In vitro versus in vivo comparison Since the resting synaptic conductance is zero in the in vitro situation, the global resting conductance in vitro can be viewed as a rough estimation of the leak conductance in the in vivo situation (for the same type of recordings). In addition, we restricted our comparison to RS type cells. We found that the resting conductance of V1 neurons in vivo is on average three times larger, and the membrane time constant three times faster than in vitro. The leak conductance thus would constitute one third of the resting conductance in vivo. Other factors could also play a role, such as the regulation of the leak conductance by neuromodulators (acetylcholine or noradrenaline), whose basal concentrations are higher in vivo than in vitro. The preservation in vivo of the morphological integrity of the cell and the unavoidable artifact produces by slicing process in vitro may also play a part in the observed differences. 4.1.3. Estimation of leak conductance and E/I balance The estimation of the leak conductance in this study is motivated mainly by the necessity of decomposing not only the increase of the global evoked synaptic conductance but also the modulation of the balance between excitation and inhibition during visual stimulation. We have shown that this balance could be strongly modulated without any change in the global synaptic conductance. However, note that similar results can be obtained with direct estimation of the excitatory and inhibitory conductances (method H, Fig. 11). In our population of cells, the mean resting conductance was 14.6 nS and could be decomposed for each cell into the sum of a Gleak term (8.6 nS on average) and a synaptic resting conductance component (around 6 nS on average). Thus, with this method, the synaptic conductance resulting from ongoing bombardment corresponded to roughly half of the global input conductance at rest (45%). Taking into account the measurement of the mean resting potential for this population of cells (−73.5 mV), and assuming a leak potential value around −80 mV (Par´e et al., 1998), we obtain an E/I balance at rest on the order of 20%/80%, the standard deviation of the inhibitory conductance being 4 times larger than for excitation.

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4.1.4. Effect of cesium Another source of information relevant for the estimation of the leak conductance is the impact of cesium in the intracellular solution, which blocks all potassium conductances and thus may change the membrane potential. Priebe and Ferster (2005, 2006) reported indeed with cesium (and QX314) filled patch electrodes a progressive depolarization until reaching a membrane potential near −20 mV and a large increase of input resistance (two times). Consequently, they applied throughout the recording a continuous hyperpolarizing current to hold the Cs-recorded neurons at more negative potentials. The fact that the input conductance was increased by a factor two argues in favor of equality between the real leak conductance (without cesium) and the synaptic resting conductance values in patch clamp recordings of neurons of cat visual cortex (anaesthetized with pentobarbital). It may be expected that this ratio does not vary much across cells, since, although the leak will increase with the cell size, the synaptic input might also increase proportionally (assuming a constant synaptic density). A similar effect of cesium was also observed (but more indirectly) with sharp electrodes. The resting conductance level reported by (Tucker and Fitzpatrick, 2006) appears very low for sharp recordings in vivo (on the order of 7–8 nS, 140–125 M). For comparison, Higley and Contreras (2006) reported without cesium a resting conductance on the order of 40 nS, which is in agreement with a 30 nS estimate in our lab. 4.1.5. Sharp versus patch recording comparison An additional leak component with low ionic selectivity may be taken into consideration with sharp electrode recordings. However, this additional leak depends on the quality of the recordings and it is sometimes necessary to apply, at least initially before the stabilization of the recording, a retention current in order to re-equilibrate the electrode leak conductance which otherwise would tend to depolarize the recorded cell. This suggests that the electrode leak component has a more depolarized reversal potential than that of the basal cell leak conductance and leads to underestimation of the increase of evoked conductances relative to the true resting value. In our lab, we practice both sharp and patch recordings in the same preparation (with the same anesthesia), which allows to directly compare both types of recordings. In our population of cells recorded in whole cell patch clamp (n = 217), the average input resistance was 63.4 ± 36 M and the resting conductance 20.2 ± 10 nS. In the population of cells recorded with sharp electrodes in the course of the same experiments (n = 81, Monier et al., 2003), the average input resistance was 40.0 ± 14 M and the resting conductance 28.0 ± 10 nS. In all cases, the estimation of the input resistance was done using the same method (negative pulse current injection). Similar differences have also been observed in the level of spontaneous activity: we reported in Monier et al. (2003) that the spontaneous spiking activity recorded with sharp electrodes was significantly higher than for patch recordings (spontaneous activity: 3.8 ± 5 a.p. s−1 (n = 39) vs. 0.3 ± 0.5 a.p. s−1 (n = 49), p < 0.01). At the subthreshold level, the average resting membrane potential was also more depolarized in sharp recordings

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than in whole cell patch clamp (−67.5 mV vs. −72.3 mV) and the spontaneous membrane potential fluctuations higher (4.2 mV vs. 1.8 mV). Two possible reasons may be considered: on the one hand, the membrane penetration produced by sharp electrodes may induce a non-selective “electrode” leak conductance, possibly contributing to the depolarization of the resting membrane potential. Thus, if this leak were the only causal factor, the upper estimate of this leak, inferred from the respective sharp and patch Rin values (8 nS), would represent around 30% of the resting conductance. On the other hand, the dialysis of the intracellular solution during patch recording with the pipette solution (which imposes a low level of chloride) may modify the driving force of the GABAa conductance. In vitro, with low (4 mM) intracellular chloride concentration, we found a reversal potential of −80 mV, a value which is more hyperpolarized than that obtained with sharp electrodes (ranging between −65 and −75 mV, Bringuier et al., 1997; Connors et al., 1988; Kaila et al., 1993; Luhmann and Prince, 1991). If the resting GABAa conductance contribution is relatively significant, we expect, in such recording conditions, a further hyperpolarization in the resting membrane potential. If we compare now the resting conductance estimates for pyramidal neurons recorded with sharp (Par´e et al., 1998) or patch electrodes (our data) in brain slice preparations, the difference is, as expected, much higher in term of input resistance (208 M vs. 70 M). Thus, the in vitro difference computed in terms of absolute levels of conductance (9 nS = 14 nS (sharp) −5 nS (patch)) is roughly the same as the one found in previously in vivo (8 nS = 28 nS (sharp) −20 nS (patch)). We conclude that the difference in leak conductances between sharp and patch are the same in vivo as in vitro, but its relative impact will be more important in vitro. These values are similar to the supplementary leak of 10 nS representing the leak in the soma due to electrode impalement, used by Destexhe and Par´e (1999) in their simulations. 4.1.6. Direct estimation of synaptic resting and leak conductances with TTX application Par´e and colleagues (Par´e et al., 1998; Destexhe and Par´e, 1999) devised elegant and difficult experiments to compare the resting properties of intracellularly recorded pyramidal neurons in vivo (in cat parietal cortex, with Xylazine–Ketamine (KX) or pentobarbital) before and after blocking synaptic transmission with tetrodotoxin (TTX). As previously described, the membrane potential presented up- and down-state transitions with KX, whereas a more bursty profile was observed in the presence of pentobarbital. In Par´e et al. (1998), the “control” situation was the period of disfacilitation (down-state) where the membrane potential was hyperpolarized. The transition to the up-state produced a drop in the input resistance of around 70% for KX and 60% for pentobarbital, corresponding, respectively, to an increase of the resting conductances of around 250 and 150% (ratio of 1/3 and 2/5, respectively). Conversely, the external application of TTX suppressed activity and produced an increase of the input resistance of around 70% for the KX and 30% for the pentobarbital preparations, corresponding to a reduction in the resting conductance of around 40 and 25%, respectively (Rin values under TTX = 46 ± 8 M; n = 9). Thus,

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the down-state is not a fully quiescent state, a significant part of the resting conductance is blocked during the application of TTX and the residual component may be considered as a valid estimate of the leak conductance. Accordingly, the leak conductance represents around 20 and 30% of the global conductance during active states under KX and pentobarbital anaesthesia, respectively (ratios leak/resting conductance, respectively, equal to 1/5 and 1/3) (Destexhe and Par´e, 1999). 4.1.7. Estimation of the resting E/I balance with the membrane potential distribution method To investigate the fluctuating activity present in neocortical neurons in vivo, Destexhe et al. (2001) have proposed a simplified ‘point-conductance’ model representing the “massaction” of the combined stochastic release by thousands of simultaneously active synapses. Synaptic activity was thus simulated by two independent excitatory and inhibitory conductances each described by a single-variable stochastic Ornstein–Uhlenbeck process (Uhlenbeck and Ornstein, 1930). This point-conductance model captures both the amplitude and spectral characteristics of the synaptic conductances during background activity. The main variables defining this model are the leak conductance, the mean excitatory and inhibitory conductance values at rest, their variances and their time constant, related, respectively, to the level of correlation of the input, and to the decay time of synaptic conductance. Based on this fluctuating conductance model and the invertibility of the analytical expression of the steady-sate distribution of the voltage fluctuations (Rudolph and Destexhe, 2003, 2005; Rudolph et al., 2004) formalized a mathematical approximation allowing them to estimate the mean and variance of excitatory and inhibitory conductances from CC Vm recordings realized at two or more different current levels in different conditions. This analytical method is based on several hypotheses: (1) preset values are assumed for the ratio between the global synaptic conductance and the leak conductance and for the reversal potential of the leak conductance; (2) the excitatory and inhibitory conductances are assumed to be (temporally) uncorrelated stochastic processes; (3) the dynamics of each conductance component is dominated by only one time constant estimated from its power spectrum. The first hypothesis may have a profound potential impact on the predicted results since the mean resting E/I balance is directly affected by the ratio between the synaptic conductance and the leak conductance. The second hypothesis may lack biological relevance, since the global organization of neocortical microcircuit can induce temporal correlation between the excitatory and inhibitory conductances (for example, feed-forward excitation and inhibition or recurrent excitation and inhibition). This method has been applied to various preparations (see the paper of Piwkowska et al., this volume) and, in agreement with Destexhe and Par´e (1999), the ratio between resting synaptic conductance and the leak conductance was estimated to be 5 and the reversal potential of the leak −80 mV. In areas 5–7 of cats anesthetized with ketamine xylazine, electrical stimulation of the pedonculopontine tegmental (PPT) nucleus produced long-lasting periods of desynchronized EEG

activity similar to the EEG of awake animals (Rudolph et al., 2005; Steriade et al., 1991). In initially bistable cortical neurons recorded intracellularly, PPT stimulation locked the membrane into a depolarized state. On the basis of current clamp recordings at different levels, Rudolph et al. (2005) estimated the relative contribution of inhibitory and excitatory synaptic conductances during these different states. As described before, the input resistance was always significantly lower during up-states than in down-states, although one may note that the reported ratio was two times lower than the initial estimate of Par´e et al. (1998) (1.5 vs. 3.0). After PPT stimulation, the input resistance increased significantly compared to both up- and down-states, yielding a ratio of 2 between the resistance during the up-states and the post-PPT states. If one assumes that the leak conductance is constant across conditions and that the ratio between the leak conductance and the up-state conductance is 1/5 (Destexhe and Par´e, 1999), the ratio between the leak conductance and the conductance during EEG-activated state is around 1/2.5. Under these assumptions, the Vm distribution method leads to the following estimates: the ratio between the mean inhibitory and excitatory conductances is larger during up-states than during the post-PTT-stimulation state (14 vs. 10); moreover, inhibitory conductances display the largest variance, and the standard deviation of the inhibitory synaptic conductance is 4.5 times larger than that of the excitatory conductance for up-states and 3.2 larger times for post-PPT-stimulation induced states. Since the ratio between the resting synaptic conductance and the leak conductance is assumed to be high, the resting synaptic conductance is largely dominated by the inhibition. A more recent analysis (Rudolph et al., 2007), relying on the same working assumptions, was realized on the basis of intracellular recordings performed by the group of Timofeev in the association cortex of awake and naturally sleeping cats (area 5, 7 and 21 of the parietal cortex). Inhibition was found to be more pronounced in up-states during SWS than during wakefulness (ratio of the means (Ginh /Gexc ) equal to 2.7 and 1.8, respectively), the ratio of the level of fluctuations being in the same range. However, a large diversity at the single cell level in the balance between excitatory and inhibitory synaptic conductances was apparent in the different states (up- and awake state), with dominant inhibition in more than half of the cells and excitation and inhibition of equal magnitude in the remaining cells (and even dominant excitation in two cells during the wake state). In addition, these authors showed that half of the excitatory neurons ceased all firing during wakefulness (“wake-silent”) while the majority of inhibitory FS cells increased their firing, suggesting that there could be less excitation and more inhibition during wakefulness than during SWS. These observations are somehow contradictory to the predictions derived from the Vm distribution-model (see above). In order to explain this discrepancy, one may be forced to consider that the leak conductance is in fact state-dependent and could be strongly reduced during the wake state (and, in a similar way, during PTT stimulation). This reduction could be produced by release of acetylcholine (and noradrenaline, serotonine), resulting in the blockade of various potassium conductances, mainly IA , IM , IAHP , and the

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voltage independent leak conductance GK (Benardo and Prince, 1982; Krnjevic, 1993; Krnjevic et al., 1971; McCormick, 1992; McCormick and Prince, 1986). This interpretation raises the possibility that the expression of intrinsic conductances might be dependent on the global network state of the preparation (reflected by the EEG) and that their modulation would account for effects otherwise attributed to putative changes in the E/I balance during up-states. However, neuromodulation can also change the synaptic strength of excitatory and inhibitory cortical inputs, making predictions difficult in this context. 4.1.8. Conductance measurement in voltage-clamp with sharp electrode, in vitro and in vivo Discontinuous voltage-clamp (SEVC) mode presents the advantage that the access resistance no longer interferes with current measurements. An inconvenience is the difficulty of application of this technique in vivo and its limitation in temporal switching frequency when achieved through 70–100 M sharp electrodes (Bringuier et al., 1997). This recording mode has been used recently to estimate conductance increase during up-states in vitro (Shu et al., 2003) and in vivo (Haider et al., 2006). In slices of ferret prefrontal and occipital cortex, the use of a modified ACSF allowed in vitro the observation of the spontaneous and periodic generation of barrages of synaptic and action potential activity, self-sustained for periods of 1–3 s, similar to the slow up- and down- oscillations observed during KX anesthesia (Shu et al., 2003; Haider et al., 2006). Both studies estimated the I–V curve using voltage-clamp recordings with the addition of both QX314 and Cs2+ in the intracellular pipette solution. Their common result is that local cortical circuits, responsible for the genesis of up-states, do indeed operate through a proportional balance of excitation and inhibition generated through local recurrent connections. However, the ratio between the excitation and the inhibition, fixed for one cell, varied from cell to cell, showing dominance of either inhibition or excitation. These observations do not support the estimations made by analytical Vm D methods asserting that inhibitory conductances should dominate largely excitatory ones during up-states (Rudolph and Destexhe, 2005). However, the conductance estimates in the two studies are not directly comparable and differ in several aspects. First, Haider et al. (2006) used the I–V curve during the down-state as a reference to estimate the synaptic conductance change and its reversal potential during the up-state. Although this was not explicitly quantified, one can extrapolate from Haider et al. data that the conductance strength seems to double between up- and down-states. In contrast, Rudolph and Destexhe (2005) used as a reference an estimate of the leak conductance. Second, as reported by Shu and colleagues, extrapolating the reversal potential from limited portions of the I–V curve (between rest and action potential initiation threshold) gives an estimate which may be significantly different from that given by a polynomial fit applied to the entire voltage range (with holding potentials between −80 to +30 mV (Haider et al., 2006; Shu et al., 2003)). This difference, due to non-linearities in the IV curve, could be explained by the presence of an NMDA-mediated component during in the up-state (in vitro, bath application of an

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NMDA receptor antagonist completely blocked the generation of recurrent activity in the circuit (Shu et al., 2003). This additional NMDA component could displace the composite reversal potential towards more depolarized values, modifying the E/I balance estimate. Third, the presence of intrinsic voltage-dependent conductances (such as persistent sodium or potassium) can also modify the estimation of the reversal potential. Fourth, voltage-clamp measurements were performed in the presence of sodium and potassium channel blockers and these drugs are known to affect somatodendritic attenuation by reducing the resting conductance. This effect can modify the visibility of excitation and inhibition at the soma (Rudolph and Destexhe, 2005). A last possibility is a difference in the E/I balance operating in various species (here ferret vs. cat). A large discrepancy has been already reported between cat and rat SI cortex: no change in input conductance is observed between the down- and up-states in the rat barrel cortex in vivo (Zou et al., 2005; Waters and Helmchen, 2006). 4.2. Evoked conductance measurements 4.2.1. Current pulse injection and temporally discretized conductance measurements The most classical approach to measure the input resistance or its inverse, conductance, is to measure in current clamp the amplitude of the voltage deflection in response to a negative step of current. The visually evoked kinetics can be reconstructed by applying current pulses at various delays following flashed stimulus onset or offset (Berman et al., 1991; Douglas et al., 1988; Pei et al., 1991). This method was used to estimate the modulation of the input resistance during static visual stimulation with sharp electrode (Berman et al., 1991; Douglas et al., 1988; Douglas and Martin, 1991) and patch electrode (Pei et al., 1991) recordings and revealed either no or only limited changes in input conductance during optimal and non-optimal visual stimulation (5–20% conductance increase). The main limitation of this method is its discretization, hence its low temporal resolution: the sampling frequency is limited by the pulse duration, which has to be long enough to overcome the capacitive effect of the membrane. Taking into account the later demonstration that stimulations with flashing bars indeed produces large but highly phasic (100–200 ms duration) increases of conductance (Borg-Graham et al., 1998), it remains likely that a method with low temporal resolution is prone to miss transient increases. This reservation does not apply to the case of moving stimulus protocols, where the evoked conductance activation can last for a few seconds (Monier et al., 2003). Rather surprisingly, Berman et al. (1989) were able to measure large conductance increases during electrically evoked hyperpolarization in in vitro slices of rat and cat visual cortex, but not in vivo in the intact animal for both static and moving stimuli. A possible technical explanation is that these authors probably under-estimated the access resistance during their recordings, as suggested by the particularly high input resistance values (around 100 M) reported during these sharp electrode recording. An overestimation of the input resistance at rest (through

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an imperfect adjustment of the bridge balance) would possibly lead to an underestimation of the relative conductance increase during visual stimulation. With sharp electrodes, the input resistance being relatively low and the electrode resistance being relatively high, a small error in the bridge balance may have indeed a strong impact on the estimate of the evoked synaptic conductance. A similar situation is met during whole cell patch recordings, and the correct estimation of the electrode access resistance is equally a critical step in measuring the input conductance. In the in vitro preparation, the electrode and cell time constants are so different that the capacitive effects due to the electrode or linked to the cell membrane impedance are easily distinguishable. This situation no longer holds during in vivo patch recordings, where the time constant of the electrode approaches that of the cell, making it difficult to distinguish the electrode and cell capacitive components of the response to a current pulse. Therefore, more quantitative off-line methods are needed for careful estimates of the access resistance. Some of the first conductance estimations published with in vivo patch recordings (Carandini and Ferster, 1997; Pei et al., 1991) used only on-line bridge-balance technique for compensating the electrode access resistance, which may explain why these authors, at that time, concluded that visual stimulation had little or no effect on the input conductance of neocortical neurons. In later studies (Anderson et al., 2000), the same group used two off-line methods to estimate the access resistance in current clamp. The first method was based on off-line fitting of the responses to current pulses with a double exponential and the second method was based on the assumption that the threshold for action potential generation should be invariant for different levels of constant current injection. With these corrections, the same authors (Anderson et al., 2000, 2001) finally confirmed our initial report of high conductance increases during visual stimulation (Borg-Graham et al., 1996). One should note that the access resistances in their studies were particularly high for patch recordings (100–200 M, on the order of a sharp electrode resistance) whereas we selected only recordings with low access resistance (<40 M) in order to minimize its impact on the conductance increase estimation. Many authors have studied the voltage dependence of synaptic input with different levels of current injection, but estimated the input resistance drop or the conductance increase only at ad hoc times during the current injection, and not in a continuous way. For example, Contreras et al. (1997), recording with sharp electrodes in the suprasylvian (association) cortex of adult cats (anaesthetized with pentobarbital sodium), measured the input resistance of cortical neurons at the peak of hyperpolarization after cortical or thalamic electrical stimulation. Neurons responded with a combination of excitatory and inhibitory postsynaptic potentials to both stimulations. The input resistance dropped by 80% (mean 400% increase of input conductance) during cortical stimulation and 60% (mean 150% increase of conductance) during thalamic stimulation, when measured at the peak of hyperpolarization, with an apparent composite reversal potential close to −65 mV. Similar estimates were obtained with the same preparation by Fuentealba et al. (2004).

4.2.2. In vitro continuous conductance measurement in voltage-clamp The optimal way to measure conductance dynamics is to characterize the IV curve in continuous voltage-clamp mode using patch electrodes with low access resistance. As shown in Fig. 9, the advantage of using the voltage-clamp method is that the filtering of synaptic events by the membrane capacitance near to the recording site, observed in current clamp, is suppressed. In addition, voltage-clamping minimizes the activation of intrinsic voltage-sensitive conductances and ensures that the recorded current is of synaptic origin. Our in vitro study shows that the peak of the relative increase of conductance evoked by afferent electrical stimulation, and compared to the resting condition, was on average 400% (varying between 100 and 1500%), which corresponds in absolute conductance values to an average increase of 25 nS, the mean resting conductance being 7 nS. When decomposing the conductance change into three synaptic components, the excitatory conductance was found to represent only 15% of the total conductance increase, the GABAa inhibition 83% and the GABAb inhibition only 2%. In general, and more prominently when stimulating from WM, the excitatory conductance component had an onset latency earlier than that of the inhibitory one (difference 0.7 ms), and faster kinetics resulting, on average, in a 3.2 ms difference in latency between the peak activations of the excitatory and inhibitory components. Furthermore, paired pulse stimulation protocols demonstrated a down-regulation of the effective connectivity mainly due to a direct and fast depression of inhibitory synapses targeting mono-synaptically the recorded cell without affecting the excitatory drive. Our in vitro study was independently reproduced by Le Roux et al. (2006), using the same analysis method (and same set-up), and extending our primary observations to a larger population of cells in rat visual cortex. They reported a similar level of E/I balance, corresponding to 20% of excitation for 80% of inhibition, independent of the electrical stimulated layers (layers 2/3, 4 or 6). Using LTP/LTD plasticity protocols, they further showed that this balance was unchanged even when the conditioning high frequency or low frequency stimulation train of afferent fibers resulted, respectively, in a global conductance increase or decrease. In a recent study in the somatosensory thalamocortical slice of young mice (Cruikshank et al., 2007) estimated the excitatory and inhibitory conductance increases in response to electrical stimulation in thalamus in whole cell patch voltage-clamp mode, for identified inhibitory (FS) and excitatory (RS) neurons. The conductance was estimated by linear regression between the evoked synaptic current Isyn and the corrected holding potential Vhc (same method as Wehr and Zador, 2003; method G in Fig. 11). In spite of the fact that the GABAb and NMDA components were already blocked with Cesium and APV, the authors restricted the analysis to the linear part of the I–V curves. As shown in the previous studies, the excitatory conductance rise preceded that of inhibitory conductances by 1–2 ms, which is consistent with the monosynaptic nature of the thalamocortical projection versus the disynaptic nature of feedforward inhibition. The waveforms and the kinetics of excitatory and inhibitory

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conductances components were also very similar to those we observed in the rat visual cortex after stimulation of the white matter, with a slightly faster kinetics of excitatory conductance change compared to inhibitory. By comparing the precise strength and kinetics of conductance changes in FS and RS cells, additional findings emerge from the Cruikshank et al. (2007) study, namely a differential recruitment in time by excitation and a differential E/I balance in excitatory cells versus interneurons: on the one hand, thalamocortical excitatory conductance rose more quickly in interneurons, allowing them to fire action potentials before the bulk of the inhibitory conductance activation suppressed their membrane depolarization; on the other hand, thalamocortical excitatory conductances were activated later in excitatory cells than inhibitory ones. These findings suggest that the resulting temporal overlap between the monosynaptic excitatory drive and the inhibitory action of faster interneurons allows an efficient control of firing in pyramidal cells by feedforward inhibition. In addition, the evoked excitatory and inhibitory conductance increases were, respectively, almost eight and three times larger in inhibitory cells (FS) than in excitatory cells (RS) (excitation: 22 nS vs. 3 ns; inhibition: 45 ns vs. 15 ns) but this difference was in part attenuated by the fact that the leak conductance was found to be five times larger in FS cells than in RS cells. Thus the E/I balance differed between the two classes of cells: the excitatory component represented around 30% of the total conductance increase for FS cells, but only 15% for RS cells. In summary, a high level of consistency in the in vitro preparation is found across studies: white matter or thalamic electrical stimulation produce first an early and fast increase in excitatory conductance followed by a stronger delayed increase in inhibitory conductance. The excitation contributes only 15–30% of the total conductance increase. However, this balance can be modulated during paired pulse stimulation and is highly specific to the excitatory/inhibitory nature of the postsynaptic cell type (RS vs. FS). Despite larger increases in the inhibitory conductance than in the excitatory one, the temporal relation between both conductance components (excitation being first) and the difference in their respective kinetics (excitation rising faster) both account for the general observation that the stimulation of thalamic afferent evoked a significant depolarization in RS cells and a significant discharge in FS cells, followed in both cases by hyperpolarization. In this context, a moderate modulation of evoked inhibition will bear only a small impact on the voltage trajectory of the cell if it is not accompanied by a change of its temporal phase with evoked excitation. 4.2.3. In vitro and in vivo comparison of conductance measurement in voltage clamp The only difference between the methods applied in vitro and in vivo is in the estimate of the leak conductance. In vitro, the leak conductance and the resting conductance are assumed to be the same. In vivo, the resting conductance is the sum of the leak and resting synaptic conductances. All studies have chosen the resting conductance as the reference value for estimating the relative evoked conductance increases.

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Our VC in vivo experiments showed that evoked responses, for static and to even a larger extent for moving stimuli, exhibit a much stronger diversity than the stereotyped profile of conductance dynamics evoked by electrical stimulation of afferent fibers in vitro (Borg-Graham et al., 1998; Monier et al., 2003). The mean relative conductance increase appeared to be five times lower in vivo than in vitro (95% vs. 460%). This quantitative difference can be explained mainly by the fact that the resting conductance is more than two times higher in vivo than in vitro (14.6 nS vs. 6.3 nS). Note that the absolute augmentation of conductance is only 1.5 times larger (25.4 nS vs. 16.1 nS), which reflects probably the fact that the access resistance Rs is larger in vivo than in vitro, and that the synchronization produced by specific sensory stimuli in vivo is presumably weaker than that produced in vitro by a massive unselective stimulation. The global evoked E/I balance was around 30% for the excitation and 70% for inhibition, close to the E/I balance evoked in vitro. In addition to a global modulation of the relative strength between the two antagonist synaptic components, a major factor that explains the stimulus feature selectivity of the response and the production of spikes appears to be the temporal relationship between the changes in the excitatory and inhibitory drives. In a large proportion of simple cells excitation and inhibition were found to be in anti-phase for the optimal stimulus and in-phase for non-optimal ones. 4.2.4. Continuous conductance measurement in current clamp and the issue of spike contamination When recordings are done using sharp or patch electrodes with high access resistance (in particular in vivo), continuous measurements in voltage-clamp mode are no longer possible and most experimenters rely on current clamp estimates of conductances achieved by comparing Vm response profiles at different levels of current injection. Numerous current clamp studies have addressed conductance dynamics evoked by visual stimulation in the mammalian primary visual cortex. Different teams, using patch electrodes, estimated the conductance increase in area 17 neurons recorded in anaesthetized (thiopental or isoflurane) and paralysed adult cats. More recently, similar experiments have been conducted with sharp electrodes in V1 cortex of the anaesthetized (halothane) ferret. Stimulus dependency has been searched for, using a variety of visual features ranging from full-field luminance transients (Tucker and Fitzpatrick, 2006), static light bars or squares (Hirsch et al., 1998), moving light bars (Monier et al., 2003) or sinusoidal luminance gratings moving in different orientations/directions (Anderson et al., 2000; Marino et al., 2005; Priebe and Ferster, 2005, 2006) or flashed with different axial lengths (Anderson et al., 2001). In most of these studies (apart from Monier et al., 2003), the access resistance was higher than in the previously reported VC studies (above 80 M in Hirsch et al., 1998); 137.5 ± 39.7 M in (Anderson et al., 2000) and 70.5 ± 39.7 M in Marino et al., 2005) and in all studies measurements were corrected off-line. Before centering the discussion on the comparison of functional findings, it is necessary to point out technical and methodological issues that are specific to current clamp stud-

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ies and that one has to keep in mind before confronting the different experimental conclusions. A problem common to all current clamp studies is the possible bias in estimates introduced by intrinsic conductance transients associated with neuronal spiking (sodium and potassium as well as the AHP currents). Simulations by Guillamon et al. (2006) showed that conductance estimations obtained during spiking periods are strongly overestimated, both for excitation and inhibition. These errors are still present after filtering the spikes, and are due to the saturation of the voltage due to the spike threshold. Although the synaptic conductances were overestimated, the reconstructed voltage trace (equivalent to Vrec (t) in our study) trace and the real membrane potential value were strongly correlated (Guillamon et al., 2006). Thus, it may be concluded that a high correlation between the estimated and the real membrane potential values in current clamp is not per se a valid argument for the accuracy of the estimation of excitatory and inhibitory conductances (see for instance Anderson et al., 2000, 2001; Boudreau and Ferster, 2005). Since, by definition, spikes are more likely to occur for the preferred stimulus, this effect can bias estimates for excitatory and inhibitory synaptic tuning towards the preferred stimulus (see, for instance Anderson et al., 2001; Marino et al., 2005). Nevertheless, this artifact does not occur during conductance changes measured during Vm evoked hyperpolarisation or weak depolarization. To avoid the problem of the contamination of spike activity in current clamp studies, the simplest approach is to use only hyperpolarizing currents in order to suppress when possible suprathreshold activity (Boudreau and Ferster, 2005; Monier et al., 2003). Another pharmacological technique is to block spike generation with QX314 in the intracellular pipette solution (Higley and Contreras, 2006; Wilent and Contreras, 2005). However, since voltage dependant potassium conductances are not fully blocked by QX314 and produce a rectification in current clamp for membrane potential values above the spike threshold, some authors have also added cesium to the QX314 in the internal solution with either patch (Priebe and Ferster, 2005, 2006) or sharp electrodes (Tucker and Fitzpatrick, 2006). 4.2.5. Visually evoked dynamics of excitatory and inhibitory conductances In identified and reconstructed layer four cells, Hirsch et al. (1998) studied conductance activation processes responsible for the generation and integration of excitation (push) and suppression (pull) in first-order Simple receptive fields. These authors reported large increases of conductance (from 100 to 150%) during the presentation of antagonist stimuli (dark or light squares, flashed, respectively, in an On or Off subfield), producing a suppression of spikes and/or a hyperpolarization at the voltage level. In accordance with our VC results (Borg-Graham et al., 1998), these authors concluded that intracortical inhibition plays a dominant role in generating suppressive responses, and confirmed that this suppression was accompanied by a substantial change in the membrane conductance. If static stimuli are best suited to chart the on–off organization of the RF without involving spatial summation, moving gratings extending over the full discharge field can also be used

to extract the linear core of the receptive field. However in this latter case, the reconstructed RF is the expression of the combination of the simultaneous stimulation of subzones of the RF and its apparent functional linearity may stem from the spatiotemporal summation of multiple local non-linear interactions. In response to drifting gratings under various current clamp conditions in thiopenthal aneasthetized cat, Anderson et al. (2000) reported relative change in peak conductance ranging from 20 to 300% depending on the stimulus contrast (128% in average). They also observed that the maximal conductance increase was quite variable from cell to cell. Inhibitory conductances were on average two to five times higher than the excitatory conductance, this ratio varying across cells. The conductance increase showed a substantial temporal modulation during the responses to optimal drifting gratings in Simple cells and a lack of temporal modulation in Complex cells. As already observed by us in VC with oriented bars (Borg-Graham et al., 1998), the peak conductance increases were higher in simple than in Complex cells (167% vs. 66%). Their results indicate a clear push–pull organization in excitation and inhibition in simple cells, best revealed when the direction of the stimuli was close to the preferred one: the excitatory and inhibitory components in the optimal direction were out of phase by an average of 150◦ (Anderson et al., 2000). In contrast, during non-optimal stimulation, the excitatory and inhibitory conductances were found to be in temporal overlap and did not modulate with the phase of the stimuli. However this anti-phase relationship between excitation and inhibition in the optimal direction is less apparent in a recent study by Marino et al. (2005). Also using drifting gratings, these author reported large conductance increases (100–150% for the peak, see Figs. 1 and 2 in Marino et al., 2005), but found that the mean absolute change and the level of fluctuation in the inhibitory conductance were always larger than for the excitatory conductance and that in most cells, Simple or not, both excitatory and inhibitory conductance changes occurred in temporal overlap during the optimal orientation/direction presentation. In later experiments, Priebe and Ferster (2005) estimated conductance changes evoked by 1D dense noise stimulation. This study (see also Boudreau and Ferster, 2005; Priebe and Ferster, 2006) used a refined method to estimate excitatory and inhibitory conductances based on a direct solution of the conductance model equation (Fig. 11, method E) where the effect of the voltage derivative is taken into account. During drifting grating stimulation at a low temporal frequency, the modulation of the membrane potential is slow, and the derivative and the capacitive terms from the membrane equation can be considered in this case as negligible (Anderson et al., 2000). With 1D dense noise stimulation or electrical thalamic stimulation, inclusion of the derivative and capacitive terms may be required. During the time-course of the 1D ternary dense noise stimulation (bars at the preferred orientation, randomly and independently switched between dark, light and mean luminance levels, every 10 ms), the basal activation level of excitatory and inhibitory conductances increases significantly producing an elevated level of background synaptic bombardment and setting the target neurons in a higher conductance state than at rest (without stimu-

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lation). Illustration of a tonic effect of the stimulus context can be found in two neurons (recorded without cesium and QX314), in Fig. 6 of Priebe and Ferster (2005): the tonic rises in the levels of excitation and inhibition are, respectively, 2 and 3.5 nS on average, corresponding to a global conductance increase of 5.5 nS. In superimposition with this global conductance increase, the dense noise stimulation produces weak (0.5 nS amplitude, on average) and anti-correlated stimulus-locked fluctuations in the evoked excitation and inhibitory conductances. Thus, cortical dynamics evoked by dense noise seem to promote a linear integration mode, characterized by a large tonic conductance increase and low-amplitude anti-phase excitatory/inhibitory fluctuations (push–pull organization). This phenomenon could be particularly visible in first-order simple cells receiving strong feedforward excitation and inhibition (Priebe and Ferster, 2005), the thalamocortical synapse being less sensitive to depression during high-frequency stimulation (Boudreau and Ferster, 2005). In second-order cells, both the stronger depression of the active synaptic inputs (Boudreau and Ferster, 2005) and the possible lack of recruitment of excitatory interneurons (which also receive strong feedforward inhibition) lead to produce only limited conductance increases during dense noise stimulation. One should note that the ternary noise stimulation regime seems optimal for producing a “quasi-linearization” of the receptive field, as described by us recently in complex cells (Fournier et al., 2006). Tucker and Fitzpatrick (2006), using sharp electrodes filled with cesium and QX314 in the primary visual cortex of the tree shrew, explored the impact of full-field luminance transients on the responses of orientation-selective neurons in layer 2/3 and showed also clear examples where the balance between excitation and inhibition changes radically as a function of the stimulus. On the other hand, full field luminance transitions caused an increase in conductance entirely attributable to inhibition (33 ± 10%, n = 11), the excitatory conductance being either unchanged or slightly diminished throughout the response time-course (−5 ± 4% increase). On the other hand, high contrast equiluminant transitions revealed rapid and synchronous increases in both inhibitory and excitatory conductances (37% ± 4 for inhibition, 34 ± 10% for excitation, n = 10). In summary, static stimuli evoke transient increases of conductance, mostly inhibitory, whose amplitude and E/I balance depend both on the local contrast (in relation with the intrinsic organization of the RF) and mean full-field luminance changes. 4.2.6. Orientation selectivity of excitatory and inhibitory conductances A dominant view in the field comes from a long series of pioneering studies by Ferster’s group, and the most quantified findings were reported by Anderson et al. (2000). Measuring tuning curves of V1 cells in response to drifting gratings under various current clamp conditions, these authors concluded on the basis of the F1 component (modulated at the temporal frequency of the stimulus) that the global conductance increase was invariably maximal for the spike-based preferred orientation. They also claimed that orientation preference and tuning

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width were similar for both excitatory and inhibitory input conductances. This view has been since disputed by other independent VC and CC studies revealing a much greater diversity of input combinations (Monier et al., 2003; Marino et al., 2005). Apart from variability in sampling, several factors may help to account for such a discrepancy, which concern more the interpretative methods than the factual observations. One is linked to the fitting analysis of the orientation tuning curves carried out by Ferster’s group: in order to minimize the number of parameters, the mean and F1 modulation of the input conductance were fitted together, forcing them to peak at the same orientation with the same tuning width. In many of their examples, it is apparent that this double constraint can lead to poor fits and, in the instances where the respective tunings of the modulation and of the mean are uncorrelated, to erroneous conclusions. For instance, in Fig. 11 of their study (Anderson et al., 2000), cells 2 and 7 illustrate the case where only the mean response shows some form of orientation tuning, whereas cells 1 and 6 illustrate the case of a 90◦ shift between peaks of the mean and modulation tuning curves. For these last two cells, although the orientation tuning curve of the mean conductance was clearly cross-oriented with that of the spike preference, fitting curves were flat leading the authors to conclude there was an absence of orientation selectivity although the mean conductance increases were twice as large for the non-optimal as for the optimal orientation, in agreement with some examples that we present here in our own study (Fig. 4, cells 3 and 6). Thus, in spite of an apparent opposition in the conclusions, diversity in inhibitory tuning width and preference is present in both studies. The main conclusion of our VC orientation selectivity study with moving bars (Monier et al., 2003) was that, depending on the recorded cell, orientation and direction selectivities stemmed from a variety of combinations of excitatory and inhibitory synaptic tuning. We proposed that the main source of the diversity could be the heterogeneity of neighborhood interactions across the laminar plane of orientation/direction maps. This view is supported by the fact that cortical maps of orientation preference present a high level of spatial heterogeneity across the laminar plane with pinwheel singularity loci exhibiting high spatial gradients in orientation preference, and iso-orientation domains with low orientation gradients (Bonhoeffer et al., 1995). Accordingly, cells located at pinwheel centers should receive a much broader range of orientation tuned inputs than cells in the middle of iso-orientation domains, creating a source of structural diversity. This hypothesis was explored in a parallel fashion, and independently, by the group of Sur (Marino et al., 2005; Schummers et al., 2002) who estimated (with drifting gratings) the orientation tuning of excitatory and inhibitory synaptic conductances in neurons, and at the same time co-registered each individual recording position in the cortical orientation preference map (relative to pinwheels and iso-orientation domains) reconstructed by optical imaging methods. They showed that the conductance change was more selective in cells localized in iso-preference domains than in cells in pinwheels regions.

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4.2.7. Temporal relation of excitatory and inhibitory conductances in visual cortex Priebe and Ferster (2006) carried out a dual-stimulation protocol by varying the relative contrasts of a masking grating, drifting in the cross-oriented direction and a simultaneously presented (in superimposition) reference grating, moving in the optimal direction. When the reference grating contrast was set to a high value compared to that of the mask grating, the excitatory and inhibitory conductances remained in counterphase and the spiking response level was high. When the mask/reference contrasts were interchanged, the inhibitory and excitatory waveforms became temporal overlapped, producing a global suppression of the voltage response. The mean synaptic conductances increases during the plaid and during the test stimuli were very similar, but the modulation of synaptic conductance was higher during the test stimuli than during the plaid presentation. This “cross-orientation suppression” effect is thus not explained by global changes in conductance levels but simply by alterations of the temporal relationships between the excitatory and inhibitory conductance waveforms (see also Lauritzen et al., 2001). This mechanism is probably present only in a subpopulation of Simple cells, first order Simple cells in layer 4, receiving direct thalamocortical feedforward excitation and strong feedforward inhibition. Note that other mechanisms have been also proposed by Priebe and Ferster (2006), based mainly on the behaviour of the afferent geniculate cells in terms of contrast saturation and rectification. The temporal interplay between excitation and inhibition was further shown to participate to in the mergence of direction selectivity in linear Simple cells with inseparable spatio-temporal receptive fields: in such cells, the mean conductance increase was found generally to be of the same order for preferred and null directions; only the modulation of the conductance and the temporal overlap between excitation and inhibition were selective to direction (Priebe and Ferster, 2005). In order to explore more quantitatively the relationship between the spatio-temporal activation map of the receptive field (XT-RF) and the direction selectivity, these authors have estimated the conductance fluctuations during 1D ternary dense noise. They confirmed that, in linear simple cells with inseparable XT-RF, the tilt in space–time (in Fourier space) allows, to a certain extent, to predict the index of direction selectivity of the subthreshold Vm responses. In addition, the XT-RF permits prediction of the directional dependence of the temporal relation between excitatory and inhibitory conductances, in anti-phase in the preferred direction and in-phase in the opposite direction. This linear prediction does not exclude the possibility that non-linear mechanisms can participate in direction selectivity. Evidence from our laboratory showed in addition the recruitment for certain cells of a non-linear shunting inhibitory process in the null direction. Fig. 4 illustrates the case of a simple cell with an inseparable receptive field, where shunting inhibition is strong enough to reverse, at the spike level, the directional preference or bias expressed at the input conductance level. Furthermore, for simple cells with separable spatio-temporal subfields and Complex cells selective to the direction, second-order non-linear mechanisms predominate

in the emergence of direction selectivity (Emerson et al., 1987; Baker, 2001). 4.2.8. Steady-state versus transient visual stimuli An important factor in the visibility of conductance changes concerns the temporal nature of the various stimuli used in the literature: on the one hand, drifting gratings or plaids are steadystate stimuli; on the other hand, moving or flashing light bars and flashed full-field luminance stimuli evoke only a transient wave of activation. Sinusoidal luminance gratings, drifting at the optimal temporal frequency in the preferred orientation/direction and optimized in spatial frequency, are considered as the most effective stimuli for V1 cells (Albrecht et al., 1980). These stimuli have low complexity since fully described by four parameters (contrast, direction, spatial and temporal frequencies). Optimal drifting gratings produce strong spiking discharges, with a large trial-to-trial variability in the spike timing and in the membrane voltage (Carandini, 2004) and can be considered “peculiar” in the sense that the cell produces strong hyperpolarizing currents during long presentation of high contrast drifting gratings, leading to a progressive decrease (adaptation) in the evoked firing cycle after cycle (Sanchez-Vives et al., 2000). In contrast, reductions in trial-to-trial variability are found when applying transient changes in local contrast (moving bars) concurrent with large conductance increases (Monier et al., 2003). Such effects are apparent in Figs. 4 and 5 of the present paper. Furthermore, the reduction of trial-to-trial variability during the response is detectable in the stimulus-locked membrane potential trajectories in current clamp as well in the input current waveform in voltage-clamp recording (data not shown). A similar dichotomy between transient and steady-state stimulations is apparent when one compares the conductance dynamics observed at the onset of the presentation of a drifting grating and during the later steady-state period of the same stimulation (see bottom of Fig. 5). The onset (and the offset) of the grating presentation produces a transient and highly reproducible response in the membrane potential corresponding to a large transient increase in both excitatory and inhibitory conductances in temporal overlap. In contrast, during the steady-state response, the excitatory and inhibitory conductance increases are of relatively low amplitude and in phase opposition for the optimal direction. In addition, the trial-to-trial variability of the voltage responses measured during steady state is high. Note that both conductance change components (the transient and the steady state) are orientation selective, whether one considers excitation or inhibition only. These observations suggest a differential recruitment over time of inhibitory mechanisms of different nature, and are supported by pharmacological iontophoresis of various GABA receptors antagonists (Allison et al., 1996; Pfleger and Bonds, 1995). These studies showed that the blockade of GABAa inhibition by bicuculline suppresses the orientation selectivity of the early part of the drifting grating response but not the steady-state response, whereas baclofen, an antagonist of GABAb inhibition, has the converse effect. Thus, it is likely that GABAa inhibition is recruited preferentially by transient stimuli or by the onset of grating presentations, whereas GABAb inhibition dominates during steady-state stimulation.

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Consequently, this also suggests that the addition of QX314 and cesium in the intracellular solution can generate an underestimation of the role of the inhibition for studies using long duration presentation of gratings and plaids. In summary, transient stimuli with large synchronisation of inputs are likely to produce large transient conductance increases. The absolute level of evoked conductance increase varies according to the laminar localisation of the recorded cell and the relative percentage of direct thalamic input it receives. Depending on the precise stimulus features, the resulting nonlinear interaction between concurrent excitation and inhibition allows a potentially precise control of the timing in the spike output. In contrast, steady-state stimuli, such as drifting gratings, by recruiting preferentially hyperpolarizing GABAb mediated inhibition, would generate a smaller conductance increase, hence forcing the cortical network to operate in a linear mode of integration without imposing precise timing in the spike output. Interestingly, this distinction between two operative modes in cortical dynamics and inhibitory subtype conductance activation supports the hypothesis of two modes of coding introduced by Mechler et al. (1998). On the basis of extracellular recordings, these authors proposed the presence of robust temporal coding for contrast with transient stimuli (moving bar) but not with steady-state stimuli (drifting grating). 4.2.9. Continuous conductance measurement in auditory cortex, in voltage clamp A second locus of VC studies of cortical conductance dynamics has been the rat auditory cortex, where series of whole cell voltage-clamp measurements of synaptic conductance changes, evoked by tones in rat auditory primary cortex (AI) neurons, were realized in vivo by two independent teams: Zhang et al. (2003), Tan et al. (2004) and Wehr and Zador (2003, 2005). Both groups reported that, after a tone, inhibition and excitation occurred in a precise and stereotyped temporal sequence: an initial barrage of excitatory input was rapidly quenched by inhibition, truncating the spiking response within a few 1–4 ms. In agreement with what has been found in visual cortex (Monier et al., 2003), Wehr and Zador (2003, 2005) reported a large diversity of conductance increases across cells and confirmed that the temporal relationship between the excitation and the inhibition seems to be the key process responsible for the emergence of functional selectivity. However, the studies from the two groups gave different estimates of the conductance changes and duration, and of the E/I balance in A1 neurons. These discrepancies, discussed below, may be due to methodological factors. Zhang and colleagues, working under pentobarbital-anesthesia in the adult rat, used only two levels of voltage (−80 and −40 mV) and added QX314 and cesium in the intracellular solution. Wehr and Zador, working under Xylazine–Ketamine in younger rats, used a linear regression method similar to ours, and the minimization of nonlinearity contamination was improved by computing directly the synaptic current Isyn (t) as a function of the corrected holding potential Vhc (method G in Fig. 11). An almost threefold difference was found in the resting conductance, estimated at around 6 nS (range 2–11 nS; n = 5) by

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Zhang and colleagues and 16 nS by Wehr and Zador, with a somewhat larger sample (n = 31). In consequence, although a similar peak value of the global conductance was found in both studies (around 8 nS), the estimates of the relative increase from rest differed (100% in the study of Tan et al., 2004 vs. 50% in Wehr and Zador, 2003, 2005). The major difference between the two studies concerned the kinetics of excitatory and inhibitory conductances and consequently, the global E/I balance. Wehr and Zador reported that the tone-evoked inhibitory conductances had mean durations of 50–100 ms, similar to that of excitatory conductances, at odds with the earlier measures of Tan and colleagues who found inhibitory conductances extending over several hundred milliseconds. Thus, the E/I balance, which was estimated at around 20% for excitation versus 80% for inhibition in Tan et al. (2004), was found to be 50%/50% in most cells in Wehr and Zador (2003, 2005). Wehr and Zador (2005) explained this discrepancy by showing that the prolonged inhibitory conductances reported by Tan et al. (2004) were the result of pentobarbital anesthesia. The mechanism of action of pentobarbital is indeed to increase the duration of open-states of GABA-activated chloride channels (MacDonald et al., 1989; Nicoll et al., 1975) and may result in a sevenfold increase of the decay time constant of the inhibitory conductance. Records from Wehr and Zador (2005) show that, not only the decay time constant of the inhibition, but also the global waveforms of excitatory and inhibitory conductances are modified during pentobarbital perfusion (see examples in their Fig. 3, Wehr and Zador, 2005). The amplitude of the synaptic waveforms is also higher and the decay time constant of the excitation is faster with the pentobarbital. Thus, pentobarbital seems to reduce the reverberation in the neuronal circuit, the inhibition quickly cutting the excitation in all neurons. Interestingly, the conductance profiles reported with pentobarbital are more similar to what we observed with the in vitro preparation, in particular for the kinetic of the inhibition, than what is reported under Xylazine–Ketamine anaesthesia. 4.2.10. Continuous conductance measurement in the somatosensory cortex, in current clamp A series of studies realized by the Contreras team, with sharp intracellular recordings in current clamp in barrel cortex neurons of anesthetized (barbiturate or isoflurane) rats, differentiated conductance dynamics observed in cells recorded in various cortical layers (Higley and Contreras, 2006; Wilent and Contreras, 2004, 2005). In the first study (Wilent and Contreras, 2004), the excitatory and inhibitory conductance profiles evoked with strong stimulus intensities were reconstituted in identified granular (Gr), supragranular (SGr) and infragranular (IGr) cells. Current-clamp responses were recorded at three different voltages, leading to the estimation of apparent synaptic reversal potential and input resistance. In granular cells, during the synaptic responses, Rin dropped sharply by 50% (Gsyn (t)(%) = 100%) at the peak latency of 20.7 ms and the composite synaptic reversal potential peaked early at 0 mV followed by a fast drop to −60 mV and a later hyperpolarization phase, ending at around −84 mV. In contrast, the synaptic responses of the SGr and the IGr cells were associated with

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peak drops of Rin , limited, respectively, to 26 and 30% (at 32 and 22 ms), and the most depolarized apparent synaptic reversal potential reached during the evoked state remained in all cases below −20 mV. In conclusion the time separation between excitatory and inhibitory conductance waveforms seems to be highest in granular cells, whereas excitatory and inhibitory conductances overlap in most cells recorded in infra- and supragranular layers. In order to further understand the role of the timing between excitatory and inhibitory conductances in the genesis of whisker direction selectivity in the barrel cortex, Wilent and Contreras (2005) measured the evoked conductance after whisker deflection stimulation in different directions (for five different levels of current injection and with QX314 in the pipette). They applied the same method of extraction of conductance components as used by Priebe and Ferster (2005, 2006) in visual cortex (method H in Fig. 10). As described in the previous study, whisker stimulation in the preferred direction evoked a stereotypical synaptic conductance and reversal potential waveform: the composite synaptic reversal potential Esyn reached a peak Vm value of −5 mV, while the conductance increase remained of limited strength, followed by a fast drop to −60 mV, corresponding to the peak conductance increase (35 nS, 200%), and then by a slow decay towards −80 mV. Thus, as expected from VC visual cortex studies, the decomposition method concludes also in CC clamp that sensory stimulation produces an increase of excitatory synaptic conductance, followed by a large increase of inhibitory synaptic conductance, corresponding, in the evoked state, to a mean global E/I balance of 20% for excitation and 80% for inhibition. The functional selectivity emerges, not from changes in absolute strength, but from the relative timing of the two antagonist synaptic components. Whereas only a weak selectivity was observed in the whisker direction tuning of excitatory and inhibitory conductances, the temporal shift of excitation relative to inhibition was clearly direction selective. For whisker deflections in the preferred direction, excitation preceded inhibition, but for movements opposite to the preferred direction, the degree of temporal overlap between the two synaptic waveforms increased. Thus, as seen in visual and auditory cortex with VC studies, the relative timing between excitation and inhibition is the key point in the emergence of functional selectivity in somatosensory cortex. Another important observation by the team of Contreras was that the duration of the whisker-evoked subthreshold excitation was much longer than that of the spiking responses, confirming that local feedforward inhibition is critical in limiting the temporal window during which spike generation is authorized in layer 4. A correlated issue, partly addressed by paired-pulse protocols in the in vitro situation, is to determine if the E/I balance changes during the time course of the prolonged discharges. In spite of the fact that most in vitro experiments suggest a stronger adaptation for inhibition than for excitation during repetitive afferent stimulation, and thus a progressive differential change in the E/I balance in favor of excitation, Higley and Contreras (2006) found, in contrast, that the E/I balance remained unchanged in vivo throughout the burst. During 10 Hz whisker deflection, the peaks of both the excitatory and inhibitory conductances

decreased in layer 4 neurons to around 50% of their respective first-deflection-evoked magnitudes, and the effectiveness of this control of discharge by inhibition was modulated by the frequency of whisker stimulation. The interplay of these two processes, the down-regulation of the conductance peaks and the timing separability of the excitatory and inhibitory synaptic conductances explain why, during frequency adaptation, the synaptic potential response evoked by a single whisker deflection becomes smaller and slower and, consequently, the spike generation process weakened and delayed. Thus, the balanced adaptation of excitation and inhibition mediates in layer 4 a reduction in spike frequency output while preserving the narrow time window of spike generation. Another limitation in the comparison between studies, which may be of major consequence in vivo, is the dependence of the observed kinetics on the global network state imposed by the anaesthesia. The conductance dynamics observed by (Wilent and Contreras, 2005) in somatosensory cortex under barbiturate are very similar to that reported by Zhang et al. (2003), Tan et al. (2004) and Wehr and Zador (2005) in auditory cortex with pentobarbital anaesthetic. In a later study, Higley and Contreras (2006) used isoflurane and observed the same profile of evoked conductance in layer 4 neurons, suggesting a similar effect of isoflurane on GABAa receptor activation as pentobarbital. These observations are in contrast with response dynamics seen with Xylazine–Ketamine (Wehr and Zador, 2005) and, if one takes into account the possible impact of the fine timing between excitation and inhibition (in the millisecond range) proposed by Contreras and colleagues, the specific impact of anaesthetic should be readdressed quantitatively in a the near future. Acknowledgements Some of the new analysis presented here has been done off-line using an experimental database acquired in vivo in collaboration with Lyle Graham and published elsewhere (BorgGraham et al., 1998; Monier et al., 2003). We thank Estelle Lucas-Meunier for her participation in some of the in vitro experiments and G´erard Baux for his support. We acknowledge the invaluable technical assistance of G´erard Sadoc (IR CNRS, UNIC) for the development of specialized software and analysis libraries. This work was supported by the CNRS, the ANR (Natstats) and EC-funded grants (Bio-I3: Facets FP6-2004-ISTFETPI 15879) to Y.F. We also thank Drs. Andrew Davison and Alain Destexhe for helpful discussions and comments on earlier versions of the Ms. References Agmon A, Connors BW. Correlation between intrinsic firing patterns and thalamocortical synaptic responses of neurons in mouse barrel cortex. J Neurosci 1992;12:319–29. Albrecht DG, De Valois RL, Thorell LG. Visual cortical neurons: are bars or gratings the optimal stimuli. Science 1980;207:88–90. Allison JD, Kabara JF, Snider RK, Casagrande VA, Bonds AB. GABA B-receptor-mediated inhibition reduces the orientation selectivity of the sustained response of striate cortical neurons in cats. Vis Neurosci 1996;13:559–66.

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