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A model of visual cortical temporal frequency tuning
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A model of visual cortical temporal frequency tuning夽 A.E. Krukowski*, T.W. Troyer, K.D. Miller Graduate Group in Biophysics, Department of Physiology, Sloan Center for Theoretical Neurobiology, W.M. Keck Center for Integrative Neuroscience, University of California, San Francisco, CA 94143-0444, USA
Abstract There are several response properties that distinguish cortical simple cells of cat V1 layer 4 from the geniculate cells that provide their input. We have recently demonstrated that a developmentally motivated pattern of intracortical inhibition, in conjunction with the observed pattern of geniculocortical connections, can robustly account for the contrastinvariance of simple cell orientation tuning. We now show that this same model circuit unexpectedly accounts for the low-pass shift in the temporal frequency tuning curves of cortical cells relative to geniculate cells. This arises when NMDA-mediated excitatory conductances are included in the thalamocortical synapses, at levels observed experimentally. 2001 Published by Elsevier Science B.V. Keywords: NMDA; LGN; Striate cortex; Inhibition; Cat
1. Introduction Cells in the primary visual cortex (V1) fail to respond to fast-moving stimuli that evoke strong responses in the lateral geniculate nucleus (LGN), the source of visual inputs to V1. This is exempli"ed by the temporal frequency tuning of V1 neurons, de"ned by studying neuronal response to a drifting sinusoidal luminance grating, of the neuron's preferred spatial frequency and orientation, as a function of the grating's temporal frequency. Cortical cells cease responding, with increasing temporal frequency, at frequencies to which LGN cells respond vigorously, e.g. [9,10,14}16]. Similar temporally low pass behavior is seen in other cortical areas, e.g. primary 夽 Supported by a HHMI predoctoral fellowship (AEK) and RO1-EY11001 from the NEI (KDM). * Corresponding author. Present address: NASA Ames Research Center, Mail Stop 262-2, Mo!ett Field, CA 94035-1000, USA. E-mail address: [email protected] (A.E. Krukowski).
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auditory cortex [4]. The origin of this temporal behavior remains an outstanding puzzle for the understanding of cerebral cortical circuitry. We recently introduced a model of the circuitry of layer 4, the input-recipient layer, of cat V1. This model addressed the orientation tuning of cortical neurons, including its invariance with changes in stimulus contrast and its variation with other stimulus parameters such as spatial frequency, while satisfying constraints from intracellular studies [18]. Here, we report that this same circuit model provides a natural and unexpected explanation of cortical temporal frequency tuning. In the proposed circuit, feedforward inhibition dominates over feedforward excitation, ensuring that simultaneous activation of both the excitation and the inhibition received by a cell will fail to activate a cell. Cortical cells will only respond when there is su$cient modulation of excitation and/or inhibition to avoid simultaneous activation. For example, a drifting sinusoidal grating of the preferred orientation and spatial frequency alternately evokes excitation and inhibition, i.e. as light bands of the grating alternately drift over on- and then o!-subregions of the RF. However, cortical cells will cease to respond with increasing temporal frequency, when the alternating activations of excitation and inhibition become su$ciently close together in time as to be e!ectively simultaneous. Our modeling task thus becomes to determine, in terms of the biophysics of the cells and synapses, at what temporal frequency excitation and inhibition become e!ectively simultaneous, and under what conditions this can account for the observed temporal frequency tuning of cortical cells. If signi"cant portions of the thalamocortical synaptic currents are carried by slow synaptic conductances, for example NMDA-mediated conductances, feedforward excitation onto cortical cells will be demodulated at higher temporal frequencies, as will the feedforward inhibition carried through cortical inhibitory cells. The presence of an NMDA-mediated component of thalamocortical EPSPs has been demonstrated in the thalamocortical slice preparation [3,8]. Futhermore, pharmacological studies have demonstrated that blockade of normal NMDA mediated excitatory transmition can completely block [13] or interfere [6] with the response of cortical cells to visual stimuli in vivo. In this study, we use the model of [18] to demonstrate that NMDA conductances in the thalamocortical connections can robustly account for the cortical low-pass behavior.
2. Results We model a network of conductance based integrate and "re cells, representing a sheet of cat V1 layer 4 cells, and their thalamic inputs, as described in detail previously [18]. Thalamocortical NMDA conductances were modeled according to experimental constraints on timing [2] and overall strength [3]. The e!ect of NMDA in the thalamocortical connections can be seen from looking at traces of a single cell in the model, chosen at random from the bin of cells that are tuned to the orientation of the grating presented (Fig. 1). Without NMDA (Fig. 1, left) the excitation and inhibition are su$ciently well separated at all frequencies, that the cell is able to respond whenever the excitation is high and the inhibition is low. The long decay time
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Fig. 1. An example of excitatory and inhibitory input to a single cell at three di!erent temporal frequencies. Lower plots: excitatory current traces (AMPA plus NMDA) are shown in gray, inhibitory current traces (GabaA) are shown in black. Upper plots: Voltage responses are in black. Left: No NMDA. Right: With NMDA. Thalamocortical NMDA onto excitatory and inhibitory cells is included; the relative amplitudes of NMDA to AMPA conductances are matched to those found in thalamocortical synapses at the oldest ages studied in [3].
Fig. 2. Temporal frequency tuning of the population of cells found at the preferred orientation with and without (dotted line) thalamocortical NMDA, as compared to the tuning of LGN input (thick solid line), taken from [16]. We show three cases that include NMDA, as shown in the key: NMDA in all thalamocortical synapses, as in Fig. 1, thalamocortical NMDA only onto excitatory cells, and thalamocortical NMDA only onto inhibitory cells.
constant of NMDA demodulates the input at higher temporal frequencies (Fig. 1, right). At 16 Hz the modulations of both excitation and inhibition are greatly reduced, and the dominance of the mean inhibition over the mean excitation prevents the cell from "ring.
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This demodulation at higher frequencies, therefore, induces low pass shifts in the cortical temporal frequency tuning relative to the tuning of the LGN inputs (Fig. 2). The strongest shifts are observed with NMDA included in thalamocortical connections onto both excitatory and inhibitory cells, whereas without any NMDA the tuning is similar to the LGN input. Signi"cent shifts are still observed in the model by including NMDA only onto excitatory or inhibitory cells. While NMDA is more e!ective when it is acting on inhibitory cells, of particular interest is the case of NMDA only onto excitatory cells, because there is some experimental evidence that inhibitory cortical cells receive less NMDA input than excitatory cells [1,11]. 3. Discussion We have demonstrated that in a simple model of cortical circuitry that has previously accounted for the contrast invariance of orientation tuning of layer 4 simple cells, the presence of NMDA-mediated conductances in the thalamocortical synapses onto these cells, in proportions that have been measured experimentally, is su$cient to robustly account for the low-pass shift in temporal frequency tuning from the LGN to the cortex. A previous model has argued that slow conductances in the intracortical excitatory connections can account for the low-pass shift in temporal frequency tuning [12]. We "nd that NMDA on the thalamocortical synapses robustly mimics cortical behavior (Fig. 2), while NMDA in intracortical synapses can amplify low-frequency responses but does not su$ciently suppress high-frequency responses to achieve low-pass tuning. A prediction of the model is that animals that have NMDA receptors that open for longer durations should show temporal frequency tuning shifts toward lower frequencies. This potential link between the timing of NMDA conductances and the temporal frequency tuning of visual cortical cells is supported by the results of developmental studies. The temporal frequency tuning of visual cortical cells is more low-pass shifted in kittens than in adult cats [5], and the decay time constant of NMDA conductances is reduced over the course of development [2,3]. Furthermore, cortical cells of kittens that have been deprived of visual experience are tuned to even lower temporal frequencies than those of normally reared kittens of the same age [7], consistent with the observation that the presence of the slow component of the NMDA conductance is prolonged in dark reared animals [2]. A strong test of the model is given by the prediction that animals genetically engineered to overexpress the slow NR2B subunit of the NMDA receptor at maturity [17] should show lower temporal frequency tuning than normal animals. References [1] M.C. Angulo, J. Rossier, E. Audinat, Postsynaptic glutamate receptors and integrative properties of fast-spiking interneurons in the rat neocortex, J. Neurophysiol. 82 (1999) 1295}1302. [2] G. Carmignoto, S. Vicini, Activity-dependent decrease in NMDA receptor responses during development of the visual cortex, Science 258 (1992) 1007}1011. [3] M.C. Crair, R.C. Malenka, A critical period for long-term potentiation at thalamocortical synapses, Nature 375 (1995) 325}328.
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[4] O. Creutzfeldt, F. C. Hellweg, C. Schreiner, Thalamocortical transformation of responses to complex auditory stimuli, Exp. Brain Res. 39 (1980) 87}104. [5] G.C. DeAngelis, I. Ohzawa, R.D. Freeman, Spatiotemporal organization of simple-cell receptive "elds in the cat's striate cortex, I. General characteristics and postnatal development, J. Neurophysiol. 69 (1993) 1091}1117. [6] K. Fox, H. Sato, N. Daw, The location and function of NMDA receptors in cat and kitten visual cortex, J. Neurosci. 9 (1989) 2443}2454. [7] E. Gary-Bobo, J. Przybyslawski, P. Saillour, Experience-dependent maturation of the spatial and temporal characteristics of the cell receptive "elds in the kitten visual cortex, Neurosci. Lett. 189 (1995) 147}150. [8] Z. Gil, Y. Amitai, Adult thalamocortical transmission involves both NMDA and non-NMDA receptors, J. Neurophysiol. 76 (1996) 2547}2554. [9] M.J. Hawken, R.M. Shapley, D.H. Grosof, Temporal-frequency selectivity in monkey visual cortex, Vis. Neurosci. 13 (1996) 477}492. [10] R.A. Holub, M. Morton-Gibson, Response of visual cortical neurons of the cat to moving sinusoidal gratings: response-contrast functions and spatiotemporal interactions, J. Neurophysiol. 46 (1981) 1244}1259. [11] D.S.F. Ling, L.S. Benardo, Recruitment of GABA inhibition in rat neocortex is limited and not NMDA dependent, J. Neurophysiol. 74 (1995) 2329}2335. [12] R. Maex, G.A. Orban, A model circuit for cortical temporal low-pass "ltering, Neural Comput. 4 (1992) 932}945. [13] K.D. Miller, B. Chapman, M.P. Stryker, Responses of cells in cat visual cortex depend on NMDA receptors, Proc. Natl. Acad. Sci. USA 86 (1989) 5183}5187. [14] A.B. Saul, A.L. Humphrey, Spatial and temporal response properties of lagged and nonlagged cells in cat lateral geniculate nucleus, J. Neurophysiol. 64 (1990) 206}224. [15] A.B. Saul, A.L. Humphrey, Evidence of input from lagged cells in the lateral geniculate nucleus to simple cells in cortical area 17 of the cat, J. Neurophysiol. 68 (1992) 1190}1208. [16] G. Sclar, Expression of `retinala contrast gain control by neurons of the cat's lateral geniculate nucleus, Exp. Brain Res. 66 (1987) 589}596. [17] Y.-P. Tang, E. Shimizu, G.R. Dube, C. Rampon, G.A. Kerchner, M. Zhuo, G. Liu, J.Z. Tsien, Genetic enhancement of learning and memory in mice, Nature 401 (1999) 63}69. [18] T.W. Troyer, A. Krukowski, N.J. Priebe, K.D. Miller, Contrast-invariant orientation tuning in cat visual cortex: Feedforward tuning and correlation-based intracortical connectivity, J. Neurosci. 18 (1998) 5908}5927.
Anton Krukowski received his B.S. degree in mathematics and physics from Yale University in 1991, and his Ph.D. in biophysics from the University of California, San Francisco in 2000. He is currently a post doctoral fellow at NASA Ames Research Center. Todd Troyer received his B.A. degree in mathematics and physics from Washington University, St. Louis, Mo. in 1985, and his Ph.D. in mathematics from the University of California, Berkeley in 1993. He is currently Assistant Professor in the Department of Psychology at the University of Maryland in College Park. Ken Miller received his B.S. degree in biology in 1980 from Reed College, his M.S. in physics in 1981 and his Ph.D. in Neuroscience in 1989 from Stanford University. He is currently Associate Professor in the Departments of Physiology & Otolaryngology at the University of California at San Francisco.
Neurocomputing 38}40 (2001) 1379}1383
A model of visual cortical temporal frequency tuning夽 A.E. Krukowski*, T.W. Troyer, K.D. Miller Graduate Group in Biophysics, Department of Physiology, Sloan Center for Theoretical Neurobiology, W.M. Keck Center for Integrative Neuroscience, University of California, San Francisco, CA 94143-0444, USA
Abstract There are several response properties that distinguish cortical simple cells of cat V1 layer 4 from the geniculate cells that provide their input. We have recently demonstrated that a developmentally motivated pattern of intracortical inhibition, in conjunction with the observed pattern of geniculocortical connections, can robustly account for the contrastinvariance of simple cell orientation tuning. We now show that this same model circuit unexpectedly accounts for the low-pass shift in the temporal frequency tuning curves of cortical cells relative to geniculate cells. This arises when NMDA-mediated excitatory conductances are included in the thalamocortical synapses, at levels observed experimentally. 2001 Published by Elsevier Science B.V. Keywords: NMDA; LGN; Striate cortex; Inhibition; Cat
1. Introduction Cells in the primary visual cortex (V1) fail to respond to fast-moving stimuli that evoke strong responses in the lateral geniculate nucleus (LGN), the source of visual inputs to V1. This is exempli"ed by the temporal frequency tuning of V1 neurons, de"ned by studying neuronal response to a drifting sinusoidal luminance grating, of the neuron's preferred spatial frequency and orientation, as a function of the grating's temporal frequency. Cortical cells cease responding, with increasing temporal frequency, at frequencies to which LGN cells respond vigorously, e.g. [9,10,14}16]. Similar temporally low pass behavior is seen in other cortical areas, e.g. primary 夽 Supported by a HHMI predoctoral fellowship (AEK) and RO1-EY11001 from the NEI (KDM). * Corresponding author. Present address: NASA Ames Research Center, Mail Stop 262-2, Mo!ett Field, CA 94035-1000, USA. E-mail address: [email protected] (A.E. Krukowski).
0925-2312/01/$ - see front matter 2001 Published by Elsevier Science B.V. PII: S 0 9 2 5 - 2 3 1 2 ( 0 1 ) 0 0 4 9 9 - 4
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auditory cortex [4]. The origin of this temporal behavior remains an outstanding puzzle for the understanding of cerebral cortical circuitry. We recently introduced a model of the circuitry of layer 4, the input-recipient layer, of cat V1. This model addressed the orientation tuning of cortical neurons, including its invariance with changes in stimulus contrast and its variation with other stimulus parameters such as spatial frequency, while satisfying constraints from intracellular studies [18]. Here, we report that this same circuit model provides a natural and unexpected explanation of cortical temporal frequency tuning. In the proposed circuit, feedforward inhibition dominates over feedforward excitation, ensuring that simultaneous activation of both the excitation and the inhibition received by a cell will fail to activate a cell. Cortical cells will only respond when there is su$cient modulation of excitation and/or inhibition to avoid simultaneous activation. For example, a drifting sinusoidal grating of the preferred orientation and spatial frequency alternately evokes excitation and inhibition, i.e. as light bands of the grating alternately drift over on- and then o!-subregions of the RF. However, cortical cells will cease to respond with increasing temporal frequency, when the alternating activations of excitation and inhibition become su$ciently close together in time as to be e!ectively simultaneous. Our modeling task thus becomes to determine, in terms of the biophysics of the cells and synapses, at what temporal frequency excitation and inhibition become e!ectively simultaneous, and under what conditions this can account for the observed temporal frequency tuning of cortical cells. If signi"cant portions of the thalamocortical synaptic currents are carried by slow synaptic conductances, for example NMDA-mediated conductances, feedforward excitation onto cortical cells will be demodulated at higher temporal frequencies, as will the feedforward inhibition carried through cortical inhibitory cells. The presence of an NMDA-mediated component of thalamocortical EPSPs has been demonstrated in the thalamocortical slice preparation [3,8]. Futhermore, pharmacological studies have demonstrated that blockade of normal NMDA mediated excitatory transmition can completely block [13] or interfere [6] with the response of cortical cells to visual stimuli in vivo. In this study, we use the model of [18] to demonstrate that NMDA conductances in the thalamocortical connections can robustly account for the cortical low-pass behavior.
2. Results We model a network of conductance based integrate and "re cells, representing a sheet of cat V1 layer 4 cells, and their thalamic inputs, as described in detail previously [18]. Thalamocortical NMDA conductances were modeled according to experimental constraints on timing [2] and overall strength [3]. The e!ect of NMDA in the thalamocortical connections can be seen from looking at traces of a single cell in the model, chosen at random from the bin of cells that are tuned to the orientation of the grating presented (Fig. 1). Without NMDA (Fig. 1, left) the excitation and inhibition are su$ciently well separated at all frequencies, that the cell is able to respond whenever the excitation is high and the inhibition is low. The long decay time
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Fig. 1. An example of excitatory and inhibitory input to a single cell at three di!erent temporal frequencies. Lower plots: excitatory current traces (AMPA plus NMDA) are shown in gray, inhibitory current traces (GabaA) are shown in black. Upper plots: Voltage responses are in black. Left: No NMDA. Right: With NMDA. Thalamocortical NMDA onto excitatory and inhibitory cells is included; the relative amplitudes of NMDA to AMPA conductances are matched to those found in thalamocortical synapses at the oldest ages studied in [3].
Fig. 2. Temporal frequency tuning of the population of cells found at the preferred orientation with and without (dotted line) thalamocortical NMDA, as compared to the tuning of LGN input (thick solid line), taken from [16]. We show three cases that include NMDA, as shown in the key: NMDA in all thalamocortical synapses, as in Fig. 1, thalamocortical NMDA only onto excitatory cells, and thalamocortical NMDA only onto inhibitory cells.
constant of NMDA demodulates the input at higher temporal frequencies (Fig. 1, right). At 16 Hz the modulations of both excitation and inhibition are greatly reduced, and the dominance of the mean inhibition over the mean excitation prevents the cell from "ring.
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A.E. Krukowski et al. / Neurocomputing 38}40 (2001) 1379}1383
This demodulation at higher frequencies, therefore, induces low pass shifts in the cortical temporal frequency tuning relative to the tuning of the LGN inputs (Fig. 2). The strongest shifts are observed with NMDA included in thalamocortical connections onto both excitatory and inhibitory cells, whereas without any NMDA the tuning is similar to the LGN input. Signi"cent shifts are still observed in the model by including NMDA only onto excitatory or inhibitory cells. While NMDA is more e!ective when it is acting on inhibitory cells, of particular interest is the case of NMDA only onto excitatory cells, because there is some experimental evidence that inhibitory cortical cells receive less NMDA input than excitatory cells [1,11]. 3. Discussion We have demonstrated that in a simple model of cortical circuitry that has previously accounted for the contrast invariance of orientation tuning of layer 4 simple cells, the presence of NMDA-mediated conductances in the thalamocortical synapses onto these cells, in proportions that have been measured experimentally, is su$cient to robustly account for the low-pass shift in temporal frequency tuning from the LGN to the cortex. A previous model has argued that slow conductances in the intracortical excitatory connections can account for the low-pass shift in temporal frequency tuning [12]. We "nd that NMDA on the thalamocortical synapses robustly mimics cortical behavior (Fig. 2), while NMDA in intracortical synapses can amplify low-frequency responses but does not su$ciently suppress high-frequency responses to achieve low-pass tuning. A prediction of the model is that animals that have NMDA receptors that open for longer durations should show temporal frequency tuning shifts toward lower frequencies. This potential link between the timing of NMDA conductances and the temporal frequency tuning of visual cortical cells is supported by the results of developmental studies. The temporal frequency tuning of visual cortical cells is more low-pass shifted in kittens than in adult cats [5], and the decay time constant of NMDA conductances is reduced over the course of development [2,3]. Furthermore, cortical cells of kittens that have been deprived of visual experience are tuned to even lower temporal frequencies than those of normally reared kittens of the same age [7], consistent with the observation that the presence of the slow component of the NMDA conductance is prolonged in dark reared animals [2]. A strong test of the model is given by the prediction that animals genetically engineered to overexpress the slow NR2B subunit of the NMDA receptor at maturity [17] should show lower temporal frequency tuning than normal animals. References [1] M.C. Angulo, J. Rossier, E. Audinat, Postsynaptic glutamate receptors and integrative properties of fast-spiking interneurons in the rat neocortex, J. Neurophysiol. 82 (1999) 1295}1302. [2] G. Carmignoto, S. Vicini, Activity-dependent decrease in NMDA receptor responses during development of the visual cortex, Science 258 (1992) 1007}1011. [3] M.C. Crair, R.C. Malenka, A critical period for long-term potentiation at thalamocortical synapses, Nature 375 (1995) 325}328.
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[4] O. Creutzfeldt, F. C. Hellweg, C. Schreiner, Thalamocortical transformation of responses to complex auditory stimuli, Exp. Brain Res. 39 (1980) 87}104. [5] G.C. DeAngelis, I. Ohzawa, R.D. Freeman, Spatiotemporal organization of simple-cell receptive "elds in the cat's striate cortex, I. General characteristics and postnatal development, J. Neurophysiol. 69 (1993) 1091}1117. [6] K. Fox, H. Sato, N. Daw, The location and function of NMDA receptors in cat and kitten visual cortex, J. Neurosci. 9 (1989) 2443}2454. [7] E. Gary-Bobo, J. Przybyslawski, P. Saillour, Experience-dependent maturation of the spatial and temporal characteristics of the cell receptive "elds in the kitten visual cortex, Neurosci. Lett. 189 (1995) 147}150. [8] Z. Gil, Y. Amitai, Adult thalamocortical transmission involves both NMDA and non-NMDA receptors, J. Neurophysiol. 76 (1996) 2547}2554. [9] M.J. Hawken, R.M. Shapley, D.H. Grosof, Temporal-frequency selectivity in monkey visual cortex, Vis. Neurosci. 13 (1996) 477}492. [10] R.A. Holub, M. Morton-Gibson, Response of visual cortical neurons of the cat to moving sinusoidal gratings: response-contrast functions and spatiotemporal interactions, J. Neurophysiol. 46 (1981) 1244}1259. [11] D.S.F. Ling, L.S. Benardo, Recruitment of GABA inhibition in rat neocortex is limited and not NMDA dependent, J. Neurophysiol. 74 (1995) 2329}2335. [12] R. Maex, G.A. Orban, A model circuit for cortical temporal low-pass "ltering, Neural Comput. 4 (1992) 932}945. [13] K.D. Miller, B. Chapman, M.P. Stryker, Responses of cells in cat visual cortex depend on NMDA receptors, Proc. Natl. Acad. Sci. USA 86 (1989) 5183}5187. [14] A.B. Saul, A.L. Humphrey, Spatial and temporal response properties of lagged and nonlagged cells in cat lateral geniculate nucleus, J. Neurophysiol. 64 (1990) 206}224. [15] A.B. Saul, A.L. Humphrey, Evidence of input from lagged cells in the lateral geniculate nucleus to simple cells in cortical area 17 of the cat, J. Neurophysiol. 68 (1992) 1190}1208. [16] G. Sclar, Expression of `retinala contrast gain control by neurons of the cat's lateral geniculate nucleus, Exp. Brain Res. 66 (1987) 589}596. [17] Y.-P. Tang, E. Shimizu, G.R. Dube, C. Rampon, G.A. Kerchner, M. Zhuo, G. Liu, J.Z. Tsien, Genetic enhancement of learning and memory in mice, Nature 401 (1999) 63}69. [18] T.W. Troyer, A. Krukowski, N.J. Priebe, K.D. Miller, Contrast-invariant orientation tuning in cat visual cortex: Feedforward tuning and correlation-based intracortical connectivity, J. Neurosci. 18 (1998) 5908}5927.
Anton Krukowski received his B.S. degree in mathematics and physics from Yale University in 1991, and his Ph.D. in biophysics from the University of California, San Francisco in 2000. He is currently a post doctoral fellow at NASA Ames Research Center. Todd Troyer received his B.A. degree in mathematics and physics from Washington University, St. Louis, Mo. in 1985, and his Ph.D. in mathematics from the University of California, Berkeley in 1993. He is currently Assistant Professor in the Department of Psychology at the University of Maryland in College Park. Ken Miller received his B.S. degree in biology in 1980 from Reed College, his M.S. in physics in 1981 and his Ph.D. in Neuroscience in 1989 from Stanford University. He is currently Associate Professor in the Departments of Physiology & Otolaryngology at the University of California at San Francisco.