Regulation of information passing by synaptic transmission: A short review

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a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m

w w w. e l s e v i e r. c o m / l o c a t e / b r a i n r e s

Review

Regulation of information passing by synaptic transmission: A short review Vito Di Maio⁎ Istituto di Cibernetica “E. Caianiello” del CNR, c/o Comprensorio “Olivetti”, Building 70, Via Campi Flegrei, 34, 80078, Pozzuoli (NA), Italy

A R T I C LE I N FO

AB S T R A C T

Article history:

The largest part of information passed among neurons in the brain occurs by the means of

Accepted 6 June 2008

chemical synapses connecting the axons of presynaptic neurons to the dendritic tree of the

Available online 14 June 2008

postsynaptic ones. In the present paper, the most relevant open problems related to the mechanisms of control of the information passing among neurons by synaptic transmission

Keywords:

will be shortly reviewed. The “cross talking” between synapses, their mutual interactions

Synaptic interaction

and the control of the information flow between different areas of the dendritic tree will be

Synaptic integration

also considered. The threshold mechanism based on the “reversal potential” will be

Neural coding

considered for its role in the control of information transfer among neurons and also for its

Neuronal modelling

contribution to the information flow among different areas of the dendritic tree and to the

Neural information processing

computational ability of the single neuron. The concept of “competition for plasticity” will

Synaptic competition

be proposed as a mechanism of competition based on the synaptic activation time. © 2008 Elsevier B.V. All rights reserved.

Contents 1. 2. 3. 4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General schema of synaptic transmission . . . . . . . . . . . . . . . . . . . . . . . . . . Presynaptic regulation of information passing . . . . . . . . . . . . . . . . . . . . . . . Postsynaptic regulation of information passing . . . . . . . . . . . . . . . . . . . . . . . 4.1. Psd, neurotransmitter diffusion and synaptic variability . . . . . . . . . . . . . . 4.2. Interaction between synaptic transmission and the passive dendritic properties 4.3. Inter-synaptic interaction on the dendritic tree . . . . . . . . . . . . . . . . . . . 4.4. The influence of active dendritic mechanisms in information passing . . . . . . 4.5. Interaction among dendritic branches . . . . . . . . . . . . . . . . . . . . . . . . 5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

⁎ Fax: +39 081 8675143. E-mail address: [email protected]. URL: http://www-biocib.cib.na.cnr.it/DiMaio/dimaio.html. 0006-8993/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.brainres.2008.06.016

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1.

Introduction

The basic activities of the brain are devoted to relate the individuals with the physical world and for this task it collects environmental information (stimuli) by the means of specialized neurons (sensory receptors). The input information, collected outside the brain by the sensory receptors, is transferred into the brain and compared with memory traces to correctly elaborate the appropriate outputs (behaviour) and to create new memory traces (update of the system). Activities much more complex than the collection of stimuli can occur internally to the brain (for example cognitive processes) the results of which can be either output directed to the external world (behaviour) and/or to other systems of the brain. In general, all these operations can be defined as “Information Processing” that, probably, is the most important activity of the brain since all the others belong to it. To perform information processing, a relevant computational ability is needed and it is still a matter of debate if this ability is proper of neural networks, as proposed earlier by McCulloch and Pitts (1943), or if a key contribution can be already given at the level of the single neuron. To understand both the role in information processing and the computational ability of the single neuron, it is important to analyze the way it receives and manages information. In the single neuron, information seems to be coded in sequences of spikes, which can be considered the basic elements of the neuronal language, and is transferred to the other neurons by the means of synaptic contacts. Concerning the input of external stimuli, the first step of their elaboration is the conversion of their properties (amplitude, duration, etc.) in the appropriate sequence of spikes. Sensory pathways usually are made of a sequence of three neurons, located outside the brain, the first of which is modified to receive the appropriate stimulus (sensory receptor) and the last has the role to carry the information into the brain. Although the coded stimulus is passed along the chain from one neuron to the other, the information is not represented in all the neurons as a copy of the same sequence of spikes. Usually, each neuron receives inputs from several different neurons and its outputs are the results of complex processes of integration (but also of compression and/or re-coding). In the retinal system of light (image) perception, for example, in some cases, a single ganglion cell (the last cells of this sensory pathway the axons of which form the optical nerve) on the average receives inputs from about 10 bipolar cells (the second neuron of the chain) each of which receives inputs from about 10 photoreceptors (cones and/or rods). The information collected by 100 photoreceptors is integrated (compressed) onto a single ganglion cell with a ratio of 100:1 before entering the brain. In addition, the process of integration of the visual information is further “contaminated” by the activity of both the amacrine and horizontal cells that contribute to modify the signals generated by the photoreceptors into the retina. Similar integration and compression systems are common to all the types of sensory transduction. The most common point of view in this respect is that the sensory systems remove (filtering) the part of information that is irrelevant to the identification and to the elaboration of the stimuli by the brain

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although, probably, these processes produce a relocation of the information in a compressed code more than a simple filtering. The successive integrations and re-codifications along the sensory pathways modify the structure of the original code so dramatically that, once passed the receptor level (sensory perception), the identification of particular information by the spike sequence of a single neuron (decoding) becomes very hard, if not impossible and, very likely, this is one of the most important reasons why the structure of the neural code still remains a mystery. At the brain level the situation is even more dramatic because a classical pyramidal neuron, in the hippocampus or in the cortex, receives tens of thousands of synaptic contacts and some of them can be active simultaneously. In these neurons, the largest part of the synaptic contacts is located on the dendritic tree and only a minority rests on the soma and on the axon. The location of the synaptic inputs plays an important role because the weight they can have on the spiking activity of the neuron is a function of their distance from the hillock (but see section 4.4). The complex structures and dynamics of pyramidal neurons rarely permit that the spiking activity of one of them is determined by the stimulation of another single neuron connected on the far dendritic districts. Usually a pyramidal neuron requires the simultaneous activation of several dendritic synaptic contacts (but see section 4.4) to reach the threshold level for the spike generation. This evidence suggests that normally the information carried by the single neuron to the dendritic tree is irrelevant to the activity of the postsynaptic neuron if not transferred “in coincidence” with the information carried by other neurons (coincidence detection). When the “coincidence” of several inputs occurs and the threshold level is reached, the resulting sequence of spikes represents, in the coded form, the integration of the information carried by all the stimulating neurons. The identification of the information carried by the single neuron becomes almost an impossible task since it is mixed into the information carried by all the other simultaneously active neurons. The information expressed alone by a neuron (not in coincidence) is apparently lost because it does not contribute to the output of the postsynaptic neuron. However, these “isolated activities” (subthreshold stimulations) produce postsynaptic responses able to modify the synaptic properties with long lasting effects (see later). Several parameters of the synaptic transmission, involved in the regulation of the synaptic efficacy, in fact, change as a function of the synaptic activity (see later) and this can be independent from the output of the postsynaptic neuron. An immediate consideration in this respect is that the passage of information from the pre- to the postsynaptic neuron is more complex than a simple mechanism attempting to induce the postsynaptic neuron to produce spikes. The large number of synaptic contacts, their intrinsic variability, their position relative to the hillock, the complex geometry and the variability of the dendritic properties, make difficult the definition of a simple general model of the relationships between the synaptic inputs, the spiking activity and the information processing tasks performed by the single neuron. Presently, the clear identification of how and what

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information is passed among neurons is still not clear but, if we assume that the single presynaptic spike represents a sort of “elementary quantum of information” and that the Post Synaptic Potential (PSP) represents the same information transferred to the postsynaptic side, then, irrespectively of the real meaning of the single spike (and of the single PSP) in terms of “information”, we can try some speculations in the attempt to clarify some aspects of the information passing among neurons by synaptic transmission. In the present paper, the main aspects of synaptic transmission will be reviewed to show the relationship between synaptic transmission and the passage of information among neurons. The role of the single neuron in the information processing will be focused by considering the great complexity and the interdependence of the mechanisms involved in the control of the synaptic transmission both at the pre- and postsynaptic side. Attention will be paid to the mechanisms of interaction and integration of the synaptic activity on the dendritic tree. The inter-synaptic “talk”, its dependence on the synaptic activation time, on the reciprocal synaptic distance and on the hierarchy of the dendritic properties will be outlined to stress the importance of the information flowing between the different districts of the same neuron. The analysis of the synaptic interaction, combined with the analysis of the influence of the dendritic properties on the synaptic dynamics, suggests also the existence of mechanisms of “Synaptic Competition For Plasticity” that could be the base for important phenomena both related to Long Term Potentiation (LTP) and to the dominance of some inputs, with respect to others, in the neuronal responses. The main goal of the present review is far from presenting an exhaustive discussion of the problems related to the information processing in the brain or in the single neuron. The underlying idea is just to show some of the open problems

of synaptic transmission that can be connected to the role of the single neuron in the information processing in the brain. From the exposition of the above problems, some considerations on the computational ability of the single neuron will emerge, too.

2.

General schema of synaptic transmission

Synaptic transmission can be thought as a mechanism of conversion of the presynaptic spike, or a sequence of spikes, into a graded variation of the postsynaptic membrane potential (PSP) that is another form of codification of the same information (synaptic coding of the information). A schematic representation of the structure of a synapse is given in Fig. 1. From the geometrical point of view, a synapse can be approximated to a flat cylinder (Ventriglia and Di Maio, 2000a, among many others) delimited on one side by the presynaptic terminal button and on the other side, at a distance of about 20 nm, by the Post Synaptic Density (PSD). The PSD is composed of the synaptic receptors that are arranged as a disk (radius 200– 400 nm) and can be located alternatively on the dendritic spines (excitatory synapses), on the dendritic shaft (mainly inhibitory synapses), on the soma and on the axon (Ishizuka et al., 1995; Megias et al., 2001). In a typical pyramidal neuron, excitatory synapses are the majority ranging 80–90% of the total (Ishizuka et al., 1995; Megias et al., 2001). On the presynaptic side, the terminal button is crowded with vesicles, filled with neurotransmitter molecules, some of which docked to the presynaptic membrane and ready to release their content. Other vesicles are located behind the docked vesicles and constitute a repository from where they move in the docking position when necessary to replace the vesicles that have released their content.

Fig. 1 – Schematic representation of a synaptic structure.

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The most common excitatory and inhibitory synapses are, respectively, those connecting pyramidal neurons, which have vesicles loaded with glutamate (glutamatergic synapses), and those connecting the inter-neurons with the pyramidal neurons, the vesicle of which are loaded with γ-aminobutyric-acid (gabaergic synapses). In this paper, the generic definition of “excitatory” and “inhibitory” synapses refers to these two types of synapses, respectively. When a synaptic vesicle opens, the molecules of neurotransmitter diffuse by Brownian motion into the synaptic space and can bind to the appropriate binding sites of postsynaptic receptors (Ventriglia and Di Maio, 2000a,b, 2002, 2003, among many others). Postsynaptic receptors are complex proteins composed of different chains organized to form ionic channels in the bi-layer structure of the postsynaptic membrane. The ionic channels of these receptors at the resting conditions are in the “close” configuration and go transiently in the “open” configuration if bound by the neurotransmitter molecules (at least two molecules for the glutamate receptors). The EPSC (Excitatory Post Synaptic Current) generated by the opening of the glutamate receptors, is a flux of positive ions inside the cell that produces a depolarizing wave named EPSP (Excitatory Post Synaptic Potential). The IPSC (Inhibitory Post Synaptic Current) is the repolarizing (or hyperpolarizing) current generated by inhibitory synapses that produces the IPSP (Inhibitory Post Synaptic Potential). Both the EPSP and the IPSP are transient, localized, variations of the postsynaptic membrane potential the amplitude of which decreases with the distance from the synaptic location according to the cable properties of the dendrites (Rall, 1959, 1964; Rall and Rinzel 1973; Rinzel and Rall, 1974). The reduction of the amplitude of the EPSP with the distance is the reason why the weight of the synapses in influencing the spiking activity of the neuron depends on their distance from the hillock (see above). An example of (simulated) EPSP, as could be registered at the synaptic location, is shown in Fig. 2. Glutamatergic synapses have two types of co-localized receptors: the α-amino-3hydroxy-5-metil-4-isoxazole-propionic-activated (AMPA) and the N-methyl-D-aspartate (NMDA) sensible receptors. Gabaergic synapses have γ-amino-butyricacid (GABA) binding receptors.

Fig. 2 – Example of a simulated Excitatory Post Synaptic Potential produced by the opening of AMPA receptors.

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AMPA and NMDA receptors produce two different types of EPSP. AMPA receptors (AMPARs) have a lower affinity for glutamate than NMDA receptors (NMDARs) and mediate a fast rising (0.2 ms for the peak) with a fast decay (return to the resting in less than 10 ms) EPSC (Ventriglia and Di Maio, 2000a,b; among others). The EPSC generated by NMDARs has both a slow rising and slow decaying phase (up to 500 ms and more of total duration, Clements, 1996). In addition NMDARs channels at the resting potential are blocked by Mg 2+ that normally is removed by a consistent depolarization (or experimentally by reducing the Mg 2+ concentration in the medium). Despite this apparently simple schematic representation, the information passed by a synapse in the dendritic tree is regulated by very complex mechanisms active both at the preand postsynaptic side.

3. Presynaptic regulation of information passing On the presynaptic side, several factors can influence the information passing by synaptic transmission and some of them are related to the probability that a vesicle releases its content following the arrival of a spike. Although for any spike a single vesicle can open, this is not a deterministic event (see, for example, Jonas et al., 1993) and the probability of release following a spike changes among the different neurons and as a function of the synaptic activity and can be modulated by influencing the releasing mechanisms. For example, the release of neurotransmitter from a vesicle depends on the presynaptic influx of Ca2+ that is consequent to the arrival of a spike. The Ca2+ influx triggers the formation of a fusion pore that, connecting the internal of the vesicle with the open synaptic space, starts the Brownian diffusion of the neurotransmitter. Modulation of free Ca2+ in the proximity of the presynaptic button can influence the probability of release and consequently the passage of information between the pre- and the postsynaptic neuron. The formation of the fusion pore between a docked vesicle and the presynaptic membrane is produced by complex reactions involving the assembly of different proteins into a complex system called the SNARE (Soluble NSF Attachment Receptor) complex. The formation and the dynamics of this complex is not yet completely clear (Fasshauer et al., 1997; Hanson et al., 1997; Coorssen et al., 1998; Weber et al 1998; Bock and Shiller 1999; Fasshauer et al., 1999; Mayer, 1999), however, anything influencing the formation or the functionality of the SNARE complex, acting on the dynamics of the pore formation, can either modify the probability of release or modulate the information transmitted by contributing to the shape of the postsynaptic response. Other presynaptic mechanisms of regulation of the information passing by synaptic transmission can be found in the properties of the vesicles. Important parameters, for example, are the number of molecules packed in each vesicle and the vesicle position. Although it is still in use the concept of “quantum” release referred to synaptic transmission, its meaning is no longer referred to a fixed number of molecules of neurotransmitter packed in all the vesicles to form the elementary “quantum” of information. This number is

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variable also among the vesicles of the same synapse and, actually, the concept of “quantum release” refers more correctly to a variable number of molecules packed into a vesicle (Ventriglia and Di Maio 2000a,b; among many others). The “quantum” content of a given vesicle is a very important factor determining the amplitude of the postsynaptic response and, consequently, the type and quality of the information transferred to the postsynaptic neuron. Position of the vesicle with respect to the central axis of the PSD (eccentricity) is another important factor in shaping the PSP (Kruk et al., 1997; Ventriglia and Di Maio, 2000b). Although in the presynaptic button there are several vesicles docked to the cell membrane, usually only a single one starts the pore formation and its eccentricity influences the rate of neurotransmitter molecules that bind the postsynaptic receptors (Ventriglia and Di Maio, 2000b), the rate of molecules that “spillover” the synaptic space and, consequently, the amplitude and time course of the PSP. It is intuitive, but also shown by diffusion modelling (Ventriglia and Di Maio, 2000b), that molecules of neurotransmitter released from a vesicle located on the border of the synaptic space can easily spillover loosing the chance to bind the postsynaptic receptors while those released close to the centre of the PSD have a higher probability to bind the receptors. A clear consequence of this is that, for the same amount of neurotransmitter molecules, several different possible postsynaptic responses can be produced dependent on the eccentricity of the releasing vesicle (Kruk et al., 1997; Ventriglia and Di Maio, 2000b). Combining the eccentricity and the number of molecules packed into the vesicles, a large number of possible combinations can be obtained and the appropriate modulation of these two factors could be a great system of regulation of the information transfer. However, if the opening of a given vesicle with a given position is a random event or a deterministic one related to the information carried by the presynaptic spike sequence is a matter of pure theoretical speculation that needs the support of experimental evidences. An interesting question in this context is “if many vesicles are docked and ready to release their quantum, why only one opens the pore?” The answer to this question could be found in the mechanisms of regulation of the pore formation and in the possible relationship between these mechanisms and the activity of some presynaptic metabotropic receptors. The molecules of neurotransmitter released by the first vesicle opened could bind the presynaptic metabotropic receptors starting a series of reactions that block the pore formation of the other vesicles. The same feedback system could be involved also in a type of release called “kiss-and-run” that consists in a quick closing of the fusion pore after the opening (Fesce et al., 2001; Schneider, 2001; Valtorta et al., 2001). The evidence of the kiss-and-run mechanism of release introduces another possible mechanism of regulation of the information passing by synaptic transmission that is the time (duration) of the opening of the pore. The process of inhibition of the fusion pore, however, seems to be involved also in other presynaptic mechanisms of regulation of the synaptic transmission (Cochilla and Alford, 1998; Miller, 1998; Duguid and Sjöström, 2006; Langer, 2008; among others) and it has to be kept in the correct consideration. In short, any modification of the structure of the fusion pore, which has been imagined with

several possible configurations, and/or of its opening velocity (Ventriglia and Di Maio, 2003) and/or of the opening duration, can affect the shape of the postsynaptic response and consequently the quantity and quality of information passed by each single spike. Another mechanism of presynaptic modulation of the information passing can be dependent on the processes of glutamate reuptake and vesicle re-filling. These processes follow important metabolic pathways involving the reuptake of neurotransmitter by the glial cells (see for example Grewer and Rauen, 2005), the passage of this to the presynaptic neuron, the filling of the new vesicles and, finally, their docking in the releasing position. These mechanisms have been considered as responsible for the regulation of the excitability of the presynaptic neurons by several authors (see Campbell and Hablitz, 2004, for example) and this is essentially a way to regulate information passing at the presynaptic level. In summary, the different factors influencing the probability of release of a vesicle following a presynaptic spike, the amount of molecules stored in the released vesicle (Ventriglia and Di Maio, 2000a), its eccentricity with respect to the centre of the PSD (Ventriglia and Di Maio, 2000b, 2002), the structure of the fusion pore (Ventriglia and Di Maio, 2003), the Ca2+ dynamics, the number and availability of vesicles properly docked to the presynaptic membrane and the recycling mechanisms of glutamate (Campbell and Hablitz, 2004), are variables that can contribute, on the presynaptic side, to the regulation of information passing by synaptic transmission.

4. Postsynaptic regulation of information passing 4.1. Psd, neurotransmitter diffusion and synaptic variability The PSD composition is one of the most important factors of regulation of the information passing by synaptic transmission. The AMPARs present in the PSD of excitatory synapses are complex proteins composed of four chains arranged by any combination of four subunits (GluR1, GluR2, GluR3 and GluR4). Only two types of subunits (NMDAR1 and NMDAR2) participate to the composition of the NMDARs. The subunit composition of the receptors in a given synapse is not a constant but depends on the level of “maturation” of the synapse and it changes during the development and as a function of the synaptic activity (see for example, Jensen et al., 1996; Park et al., 1999). Receptors with different subunit composition give different responses to glutamate application and this is a very fine postsynaptic mechanism of regulation of the information passing. Even more important than the receptor subunit composition is the variability of the absolute and relative number of AMPARs and NMDARs on the PSD that determines the larger part of the variability of the postsynaptic response. Some (immature) glutamatergic synapses can be AMPARs silent (no AMPARs on the PSD) and the number of AMPARs in these synapses increases with the synaptic activity produced by the activation of the NMDARs (Isaac, 2003; Itami et al., 2000;

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Montgomery et al., 2001; Renger et al., 2001; among others). The number of the NMDARs also can be modulated by the migration of these receptors from (or to) the extrasynaptic space as a function of the synaptic activity (Tovar and Westbrook, 2002). Phenomena like Long Term Potentiation (LTP) and Long Term Depression (LTD), which are the base of memory formation, also depend on the variability of the absolute and the relative number of AMPARs (Malenka and Nicoll, 1999; Lu et al., 2001) and on the insertion (or deletion) of NMDARs onto the PSD (Tovar and Westbrook, 2002). In excitatory synapses, a sort of “noise” in the transmission of information can be generated by the spillover of glutamate outside the synaptic space. As mentioned in the section 3, the probability that this occurs depends on the eccentricity of the vesicle but can be also due to a transient high-frequency spiking of the presynaptic neuron that can open, in a short time, a relatively large number of vesicles. If the spillover is quantitatively significant, then, with some probability, molecules of neurotransmitter can activate neighbouring synapses (Kullmann and Asztely, 1998). The resulting EPSP, not corresponding to the proper presynaptic activity, will furnish spurious information to the postsynaptic neuron. A common interpretation of the spillover is that the activation of neighbouring synapses reinforces the signal arriving in a given dendritic region. However, if the spillover can really play a role in the modulation of synaptic transmission it is still a controversial problem. Glial cells, located very close to the synaptic space, efficiently remove the free glutamate and this process of reuptake should prevent the diffusion to the neighbouring synapses. The reuptake process of glutamate by the glial cells is followed by the transfer of the glutamate to the presynaptic neuron and this is the basic mechanism for the presynaptic vesicle filling. In summary, the postsynaptic regulation of the information passing by synaptic transmission is governed by several different mechanisms involving: the diffusion of the neurotransmitter in the synaptic space (Ventriglia and Di Maio, 2000a,b); the absolute and relative number of receptors on the PSD (Malenka and Nicoll, 1999; Ventriglia and Di Maio, 2000b; Lu et al., 2001; Tovar and Westbrook, 2002; Ventriglia and Di Maio, 2002;2003); and their dynamics and/or their composition (Jensen et al., 1996; Park et al., 1999; Itami et al., 2000; Montgomery et al., 2001; Renger et al., 2001; Isaac, 2003).

4.2. Interaction between synaptic transmission and the passive dendritic properties The postsynaptic response following the vesicle release can be consistently dependent on the dendritic properties such that the same synaptic input, producing the activation of the same number and types of receptors, can produce different postsynaptic responses dependent on the location of the synapse in the dendritic tree. Some dendritic properties, varying among different districts of the same neurons as a function of the dendritic geometry, produce a different passage of information for the same presynaptic event. To explain the concept in a simplified way, let us consider only the EPSC produced by the activation of the AMPARs following a presynaptic spike. The amplitude of the resulting peak has been found highly variable ranging between 5 and 67 × 10− 12

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Amperes (pA) with a coefficient of variation (CV) of 0.51 even in the same synapse (Liu et al., 1999, but see also Jonas et al., 1993; Forti et al., 1997; Ventriglia and Di Maio, 2000a, 2000b, 2002). A large fraction of this variability can be explained by the synergic effects of all the factors mentioned above (Ventriglia and Di Maio, 2002). However, if we consider the large variability between different synapses a significant role can be played by the cable properties of the dendrites where the synapses are located. This assumption becomes clear if we look to the mechanisms involved in the EPSP formation following the localized variation of the membrane conductance (gm = 1/Rm) due to the AMPARs activation. The variation of the conductance (ge(t)), can be expressed by the difference of two exponentials (Di Maio, 2007, 2008)
t   t ge ðtÞ ¼ k e s2  e s1 ; ð1Þ where, τ1 and τ2 represent the rising and decay time constants, respectively determined by the opening and the closing the AMPARs, and k is related to the peak value of the conductance (which depends on the maximal number of simultaneously opened channels). Alternatively, the classical notation of an alpha-function can be used t

gsyn ðtÞ ¼ kte

t peak

;

ð2Þ

egpeak tpeak

with k ¼ (Bernander et al., 1991). The EPSC (Im(t)) can be computed, once the variation of conductance is known, by   dVm ðtÞ Vm ðtÞ  Vr ð3Þ þ ge ðtÞðVm ðtÞ  Eions Þ  Im ðtÞ ¼ Cm Rm dt where Vm(t) is the membrane potential at time t, Eions is the equilibrium potential (also called “reversal potential”) as computed by the Nernst equation for the ions involved in the synaptic current, Cm, Rm and Vm(t) are the membrane capacitance, resistance and voltage, respectively, and Vr is the dVm ðtÞ membrane resting potential. The term Cm represents a dt   Vm ðtÞ  Vr is a leaky capacitative component while the term Rm current that is generated when the membrane potential departs from the resting level. The term (Vm(t) − Eions) of Eq. 3 is the driving force that induces the ions to flow through the channels producing the EPSC. The value of Eions, the time evolution of g(t) and the types of ions involved are characteristics of each type of synapses and make the difference in the amplitude, the time course and the direction (excitatory or inhibitory) of the synaptic currents. Usually, the value of Eions for excitatory synapses is more positive (about 0 mV) than the membrane potential at the resting level (Vr ∼ −70 mV) and this produces a current flow inside the cell (depolarizing current). On the contrary, the Eions for the inhibitory current is more negative (close to the resting potential if not more negative) and the IPSC is a repolarizing (or hyperpolarizing) current (Koch et al., 1983, 1989, 2000; Quian and Sejnowsky, 1990; Ling and Benardo, 1995). By considering the Eq. 3 for the excitatory synapses, the depolarization (increase of Vm(t)) decreases the driving force that produces the EPSC and, consequently, the EPSC is controlled by a self-limiting process governed by a threshold (Eions). Considering the amplitude of the EPSC (on the average ~25 pA, see for example, Forti et al., 1997) one would expect a

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Fig. 3 – Variability of the peak of a simulated AMPA-EPSP as a function of the membrane input resistance Ri. negligible EPSP with a non-significant variation of the driving force that produces the EPSC. The EPSP amplitude, however, depends on the relationship between the current applied and the input resistance of the membrane Ri at the synaptic location. The input resistance of the far dendritic regions is expected to be in the gigaohms (GΩ) order (Rall, 1959, 1964; Rall and Rinzel, 1973; Rinzel and Rall, 1974; Segev et al., 1995; Segev and London, 2000). With a current of few pAs in amplitude and a resistance of some GΩ, the difference of potential will be in the order of 10− 3 V (mV) that is in the normal range of all the membrane potential variations in the neurons. If we simplify the problem applying the Ohm's law and neglecting the capacitative component and the leaky current we have the variation of membrane potential (EPSP) by Vm ðtÞ ¼ Vr  Ri IðtÞ

ð4Þ

By this equation we can have an idea of the real variations of potential induced by an EPSC of a few pAs in amplitude. The peak values of the EPSP computed by Eq. 4 for the same value of the synaptic conductance are shown in Fig. 3 as a function of the input resistance of the dendrites. The diversity of input resistance between the far dendritic regions and the large dendrites connected to the soma suggests the existence of a gradient of the input resistances

from the periphery to the soma. A similar gradient already exists for the axial resistance that, being inversely proportional to the dendritic diameter, decreases from the periphery (the far dendritic regions) to the centre (the soma). These gradients, probably, follow a dendritic hierarchy that is the base of the information flow from the periphery to the centre (and vice versa) in the single neuron (Di Maio, 2007, 2008). Very likely, the development and the branching of the dendritic tree are organized to create the proper hierarchy of the dendritic properties to obtain the maximal efficacy in the correct flow of information both from the periphery to the centre and between different areas of the dendritic tree to permit the “cross talking” among the synapses. Another important consideration emerging from Eq. 3 is that the value of Eions (the reversal potential value) acts as a threshold against which the membrane potential is continuously compared and the current flow (EPSC) is regulated. This threshold mechanism, as the threshold mechanism for the spike generation, is an important point of nonlinearity that can influence the computational ability of the single neuron.

4.3.

Inter-synaptic interaction on the dendritic tree

The electrical activity of each synapse can influence the activity of the others. To explain this concept let us consider the simplified situation of a terminal dendritic branch with few synapses, as shown in Fig. 4. Although in a simplified way, the following equation can describe the total synaptic current produced on the dendrite schematized in Fig. 4. " # n X dVmðtÞ þ ðVm ðtÞ  Ee Þ gei ðtÞ IðtÞ ¼ Cm dt 2 3 i¼1   m X Vm ðtÞ  Vr gij ðtÞ5  þ 4ðVm ðtÞ  Ei Þ Rm j¼1

ð5Þ

with I(t) being the dendritic current, ge(t) and gi(t) are the variation of conductance of the n excitatory and the m inhibitory synapses, respectively, and Ee and Ei are the excitatory and inhibitory reversal potentials. This equation is clearly an extension of Eq. 3 because it sums up the activities of all the synapses located on the dendritic branch. The equation sums the contribution of all the synapses of the

Fig. 4 – Schematic representation of a terminal dendritic branch with excitatory and inhibitory synapses.

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dendrite irrespectively of their status (active or silent) because if silent their current is automatically null being null the conductance (g(t) = 0) and of the synaptic type (excitatory or inhibitory). A simplification introduced in Eq. 4 is that the distance between synapses is neglected assuming that each of them is so close to the others that all of them can experience simultaneously the same events and then can be considered as located on the same point. In addition, the current flowing away from the dendrites due to the difference of potential generated by the local synaptic activity is omitted. With these simplifications we can neglect the capacitative current and consider the resistance of the membrane as an input resistance (Ri) so that the variation of potential can be simply computed by the Ohm's law Vm ðtÞ ¼ Vr  Ri IðtÞ:

ð6Þ

A first consideration, emerging by looking Eq. 3 and 5, is that Eq. 3 can be applied only for the study of a single synapse and assuming that all the others are silent. Each active synapse, in fact, gives a contribution to the local depolarization that is also a contribution to the reduction of the driving force that produces the EPSC of the other synapses. This effect of mutual interaction becomes negligible or null if the distance between the synapses increases so much that the variation of potential induced by one is not experienced by the others. In short, although the production of a single EPSP can be considered an independent event produced by the combination of different presynaptic and postsynaptic parameters (see above), its shape and amplitude not only depend on the mechanisms of regulation intrinsic to the single synapse (see sections 4.1 and 4.2) but also on the coincidence of activity of other synapses located in its proximity. To have an idea of the degree of interaction between synapses depending on their mutual distance, the decrease of the EPSP with distance from the origin should be computed according to the cable equation that, in the classical form as proposed by Rall (1959; 1964), can be expressed as k2

A2 V AV ¼Vþs ; AX2 dt

ð7Þ

where X is
the q distance ffiffiffiffiffiffiffi  from the active synapse, λ is the space constant k ¼ R4Rmad depending on the membrane resistance (Rm), on the axial resistance (Ra) and on the diameter (d) of the dendrite; τ is the time constant (τ = RmCm), which depends on the membrane resistance and capacitance expressed in Farads (Rall 1959, 1964). The variation of potential induced by the active synapses, combined with the hierarchy of the dendritic properties, is the basic mechanism for the synaptic interaction on the dendritic tree and the flow of information among different dendritic districts. The contribution given by each active synapse to the membrane depolarization is a contribution to the reduction of the driving force for the EPSC production and consequently is an “inhibitory” action on the activity of the other excitatory synapses. A result of this inhibition is the nonlinear summation of the excitatory synaptic activities on the dendritic tree (Di Maio, 2007, 2008, among others). An immediate visible effect of this nonlinearity is that two perfectly synchronous and equal EPSPs do not produce a composite (c) EPSC with a

33

peak amplitude twice the single EPSP peak but a smaller one (Di Maio 2007, 2008; among others). A second important effect is that, if several synapses, located close to each other become active simultaneously, the amplitude of the resulting cEPSP can be so high as to drive the membrane potential close to the value of the reversal potential (Ee). If Vm(t) ∼ Ee, the difference (Vm(t) − Ee) ~ 0, and consequently the synaptic current (EPSC), becomes null. Even worse, if Vm(t) > Ee (i.e. if the membrane potential crosses the value of the reversal potential), the direction of current is inverted becoming a repolarizing current like the one produced by the inhibitory synapses. An important point to stress in this context is that, if a presynaptic activity starts in a given dendritic district when the membrane potential has locally reached the reversal potential value, then the increase of the conductance produced by the receptor activation will not produce an EPSC and this corresponds to the inhibition of the passage of the information. A direct consequence of this is that the activation time of the synapses is an important factor in the transmission of the information. Synapses activated sooner, while transmit their information, can modify the membrane conditions nullifying (or reducing) the possibility to pass information to the synapses activated later. This can be not only a mechanism of synaptic regulation of information passing but also a mechanism of competition among synapses located in the same dendritic region for the passage of information. If the plasticity of a synapse depends on the generation of the EPSC, then the competition based on the synaptic activation time results also in a “Competition for Plasticity" among synapses located in the same dendritic district. A consideration in this respect is that the reversal potential is the basic mechanism not only to prevent the excess of local excitation (London and Häusser, 2005) but also for the regulation of the passage of information among neurons and in different districts of the same neuron. In addition, it can be a determinant point of nonlinearity necessary to improve the computational ability of the single neuron. A further important point to stress is that the thresholds represented by the reversal potentials of excitatory and inhibitory synapses produce paradox effects. The excitatory synapses “inhibit” the activity of other excitatory synapses by reducing the driving force that produces the EPSC and can reduce or nullify the transmission of their information. Alternatively, the inhibitory synapses “excite” the excitatory synapses restoring this force and favoring the passage of their information. A conclusion suggested by the paradox effect is that, although the strategic position of the inhibitory synapses on the dendritic tree permits them to regulate, and also “veto”, the excitatory activity (Liu, 2004), the real interaction between excitatory and inhibitory synapses is much more complicated and is based on delicate equilibriums and precise mechanisms that regulate the information flow in the dendritic tree. Local depolarization produced by the excitatory synaptic activity driven by AMPARs can produce a further effect by removing the Mg2+ and starting the EPSC produced by NMDARs. Unblocked NMDARs furnish an additional depolarizing current (Schiller et al., 2000) with a different dynamic with respect to the EPSC AMPARs-driven (see section 2). The EPSCs produced by NMDARs can have long lasting effects (up

34

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to 500 ms) sustaining the membrane depolarization for a “long” time and this could be one of the reasons why NMDA are involved in LTP phenomena. However, once again the EPSC produced by the NMDARs, sustaining the depolarization, reduces the driving force “inhibiting” the activity of the excitatory synapses but, at the same time, gives also a sustained long lasting contribution the spiking activity of the neuron.

4.4. The influence of active dendritic mechanisms in information passing Local depolarization induced by excitatory synapses or by the back propagation of the spikes into the dendrites, can activate voltage dependent channels located in some dendritic areas (Golding and Sprustonm 1998; Marsálek and Santamarίa 1998; Isomura et al., 1999; Häusser and Mel 2003; Isomura and Kato, 2000; Schiller et al., 2000; Golding et al., 2002; Lazarewicz et al., 2002; among others). These channels can be either Ca2+ (Isomura et al., 1999; Isomura and Kato, 2000; Häusser and Mel 2003) or Na+ channels (Golding and Sprustonm 1998; Marsálek and Santamarίa 1998; Golding et al., 2002; Lazarewicz et al., 2002; Häusser and Mel 2003) and their role strongly depends on the dendritic distribution. The activation of these channels can produce local depolarization contributing to an amplification system which extends spatially the influence of some excitatory synapses favoring the “talk” with synapses located not so close. Another proposed role is that, by selective mechanisms of amplification, they equalize the power of synapses located on the far dendritic areas to that of synapses located closer to the hillock nullifying the effect of the distance on the neuronal spiking activity and favoring a sort of “dendritic synaptic democracy” (Häusser, 2001; Starrett and van Ooyen, 2004). In some cases, the activation of the voltage dependent dendritic channels can produce real “dendritic spikes” that can be so strong to diffuse up to the hillock and trigger directly the neuronal spiking activity (Lazarewicz et al., 2002; Marsálek and Santamarίa 1998).

Another possible role of these channels is a contribution to the spreading of the neuronal spike into the dendritic tree (see for example, Marsálek and Santamarίa, 1998). The resulting strong depolarization of the dendritic area can produce a sort of “system resetting” because the amplitude of the dendritic spikes generated in this way could abolish momentarily the driving force that produces the EPSCs resetting all the information passing. In general, the activity of these channels can be interpreted as finalized to “a cross talk” between the periphery and the centre and between different areas of the dendritic tree and, absolving these roles, they contribute to the regulatory mechanisms of the information trafficking.

4.5.

Interaction among dendritic branches

Different levels of synaptic activity on different dendritic branches produce differences of potential among them with a consequent flow of current (information). These difference of potential combined with the hierarchy of the dendritic properties (mainly with the input and the axial resistances) constitute a functional architecture optimized for the trafficking of information in the dendritic tree. The difference of potential between the branches at the two sides of the grafting points is the key factor for the flow of information among different branches of the dendritic tree. Schematically, if we indicate with n the largest level of branching of the dendrites, we can name the dendrites of the farther branching level (with respect to the soma) as An. Dendrites of the level An are grafted onto “mother branches” that are at the level An-1 that, in turn, are grafted to their mother branches at the level An-2 and so on up to the main dendrite (A0) emerging directly from the soma. A difference of potential due to the synaptic activity on a dendrite positioned at a given level can produce a depolarizing effect on the connected branches. As the synapses are the points of passage of the information among the neurons, the grafting points can be considered the points of passage of information among the dendritic branches. A good approximation to this situation could be a model where each

Fig. 5 – Schematic representation of dendritic branches with synapses and daughter branches.

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daughter branch is considered a sort of a bidirectional “electrical synapse” of the mother branch (Di Maio, 2007, 2008). As for all the other synapses, the activity of each branch can influence the activity of synapses located in the proximity of the grafting point of the other branch. This becomes clear by looking Fig. 5 where a schematic representation of some synapses on the dendritic tree is presented. It is clear from this figure that the activity of each branch of the level An can influence the activity of the branch of the level An-1 and vice versa (bi-directionality). A simplified description of the passage of information between daughter and mother branches in the form of current flow can be proposed as follows IðtÞ ¼

VAn  VAn1 Rg

ð8Þ

where I(t) is the current flowing between the branches of the level An and An-1, Rg is the resistance at the grafting point and VAn and VAn-1 are the potential levels at the two sides of the grafting point. The direction of the current depends on the values of VAn and VAn-1, respectively, being in the direction of the mother for VAn N VAn-1. and in the direction of the daughter in the opposite case. In summary, the excitatory activity on a dendritic branch can influence and also regulates the activity on the other connected branches because of the transfer of the depolarization wave due to differences of potential between the branches. The activity of these “electrical synapses” has the maximal influence on the synapses located close to the grafting point. As for normal synapses, their influence decreases with the distance from the grafting point. This mechanism, based on the difference of potential between mother and daughter branches, promotes on one side the trafficking of information in the direction of the soma and on the other side the inter-synaptic “talk” between synapses located on different branches. The grafting points represent “nodes” for the information flowing in the dendritic tree but also important points of information regulation since the direction of the current flow (which depends on the difference of potential) and the amount of depolarization (which depends on the resistance of the nodes) can greatly influence the activity of synapse located in their proximity.

5.

Discussion

Although information processing is probably the most important activity of the brain, its basic mechanisms remain to be clarified. A first important problem to solve is the definition of the neuronal representation of the information. Although it is generally accepted that the spike sequence is the way the information is coded by the single neuron, the structure and the mechanisms of formation of the code are still mysteries. Two main ideas, not excluding each other, face on this issue and both of them are supported by some evidences (Konig et at., 1996). The first is one of the theories based on the idea of “temporal code” and is called “coincidence detection” theory (Abeles, 1982; 1991; Agmon-Snir et al., 1998; Duguid and Siöström, 2006; among others). This theory assumes that the neuron detects the “temporal” coincidence of synaptic inputs

35

producing a given sequence of spikes. The precise time occurrence of the spikes into the sequence should, in some way, represent the neuronal code expressing the information that the neuron can transmit to other neurons. The other, the “rate code” theory, assumes that the neural code is embedded in the spike frequency, defined as the number of spikes (N) emitted in the time unit in seconds (e.g., N/s), or as the reverse of the mean Inter Spike Interval (ISI) computed in an appropriate time window (Stein, 1965; Ricciardi and Sacerdote, 1979; Tuckwell, 1986; Lansky and Rospars, 1995; Lansky and Sacerdote, 2001; Di Maio et al., 2004; Ventriglia and Di Maio, 2005; among many others). New ideas are emerging, however, which extend the two theories above, or mix them in some way (see for example, Grande et al., 2004). The above theories give an idea of what neural code could be but none of them furnishes a precise indication of the meaning of the single spike or of the spike sequences or of the spike occurrence, in terms of “information” in the symbolic language of the neurons. Nevertheless, if we assume that a spike sequence encode for a given information, irrespectively of the structure and of the nature of the code, we can fix some basic points that could help in building up an idea or a preliminary model of the information transfer by synaptic transmission. The basic points that, probably, can be accepted by a wide community of neuroscientists are: i) a sequence of spikes emitted in a given time window by a single neuron encodes in some (unknown) way for a certain type of information; ii) each spike in the sequence represents an elementary quantum of information expressed by the presynaptic cell; iii) each single PSP, generated in the postsynaptic cell consequently to a presynaptic spike, is the synaptic representation of the quantum of information transported by the presynaptic spike; iv) a composite (c)PSP or a simple sequence of separated PSPs generated by a presynaptic spike sequence, is the representation of the information passed by the presynaptic cell to the postsynaptic one; and v) the cPSP produced by the simultaneous activity of more synapses represents, at the dendritic level, the integration of the information passed by more neurons to the postsynaptic one. Accepting the above points implicitly we admit that neuron does not use a single neural code but at least two. If the spikes emitted in a given time window represent the codification of the information in the neuronal language (neuronal code) the corresponding cPSP represents the codification of the same information in the synaptic language (“Synaptic Code”). Very likely, neuronal code will not be completely unveiled and its nature will remain obscure if not correctly related to the Synaptic Code or, at least, if not constantly compared with it. In this context, the study of the interrelations between the spike sequences and the shape of the postsynaptic responses and the study of the mechanisms that regulates synaptic transmission are of fundamental importance. As shown in the present review, many parameters regulate the passage of information among neurons and some of them simultaneously regulate also the flow of information between different dendritic regions. In addition, the time window of the spike sequence and the time sequence of synaptic activation are important factors to determine both the shape of the cEPSP and its influence on the output of the postsynaptic neuron. A clear example in this respect is given by some neurons of the

36

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Fig. 6 – Two examples of simulated cEPSP produced by the non linear summation of two EPSPs. The two cEPSP are respectively obtained by summing two identical EPSPs one of which started with a delay with respect to the other (1 ms and 3 ms, respectively).

auditory system in the brainstem of the birds. These neurons receive an input from both ears on the same dendritic district but they fire a spike sequence only if the input received by one ear arrives with a delay of 10–100 μs with respect to the input arriving from the other ear (Agmon-Snir et al., 1998). It has been shown that the two synaptic outputs sum up, that their integration triggers the spike generation in the postsynaptic cell and that the arrival of the input from only one ear or outside the proper time window does not produce the postsynaptic spike sequence (Agmon-Snir et al., 1998). The influence of the ISIs on the shape of the cEPSPs, either resulting by the spike sequence of a single presynaptic neuron or by the spike sequences of many presynaptic neurons simultaneously active is a very important factor. Fig. 6 shows the results of two simple examples of integration of two (simulated) EPSPs producing a cEPSP. In one case, one of the two EPSPs is delayed 1 ms with respect to the other and in the other case the delay is of 3 ms. The different shape is evident and it can be easily deduced that for two single spikes the shape of the resulting cEPSP can range from a single enlarged EPSP (if the two spikes are perfectly synchronous) to the shape of two independent single EPSPs if the ISI exceeds the duration time of the single EPSP. The shape of the cEPSP produced by the activity of many neurons can become very complicated and this makes very difficult the identification of the spike sequence (neuronal code) that produces a given cEPSP (the synaptic code). The paradox effect that excitatory synapses inhibits each other by the reduction of the driving force that produces the EPSC, seems to assert the principle that when a single neuron is transmitting its own information it tries to reduce the information transmitted by other neurons and mainly by the neurons that make synapses close to it. There is a sort of equilibrium between the cooperative effect due to the summation of the synaptic activities of excitatory neurons and the inhibitory effect due to the reduction of the driving force that produces the information transmission. This equilibrium

reflects probably also a sort of “Competition for Plasticity” (Di Maio, 2007, 2008). However, the activity and the strategic position of the inhibitory synapses contribute to this “equilibrium” and it is important to stress that phenomena like LTP, LTD and the dominance of some neuronal responses with respect to others can be determined by the shifting of this “equilibrium” in one or another direction. An important role in the synaptic trafficking is played by the reversal potential (Eions) that behaves like a threshold that apparently is even more powerful than the threshold mechanism for the spike generation. This threshold should be considered with great attention both for its role in the regulation of the information passing among neurons, for its role in the information flow among different dendritic areas and because it introduces an important factor of nonlinearity in the synaptic– dendritic dynamics that is the necessary requisite to have a neuronal computational system (Zador, 2000). Although how the single neuron performs computation and information processing still remain open problems, the fine regulation of the synaptic transmission of the information, the flow and regulation of information trafficking in the dendritic areas, the complex machinery that integrate such a complex input system to ultimately produce the spiking (code) activity, all suggest that the single neuron has to be considered a very complex computational device resembling more a processor of a modern computer than a simple device devoted to sum up analogical synaptic inputs (EPSPs) to convert them into a digital signal (the spike sequence). The present review is not exhaustive of all the problems related to the information passing by synaptic transmission. The main idea has been to outline some of the most relevant problems relating to the issue and to contribute to their identification in a general framework.

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