Power-Law Input-Output Transfer Functions Explain the Contrast-Response and Tuning Properties of Neurons in Visual Cortex

We develop a unified model accounting simultaneously for the contrast invariance of the width of the orientation tuning curves (OT) and for the sigmoidal shape of the contrast response function (CRF) of neurons in the primary visual cortex (V1). We determine analytically the conditions for the structure of the afferent LGN and recurrent V1 inputs that lead to these properties for a hypercolumn composed of rate based neurons with a power-law transfer function. We investigate what are the relative contributions of single neuron and network properties in shaping the OT and the CRF. We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model. The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs. Last, we show that it is possible to account for the diversity in the measured CRFs by introducing heterogeneities either in single neuron properties or in the input to the neurons. We show how correlations among the parameters that characterize the CRF depend on these sources of heterogeneities. Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

[1]  R. Shapley,et al.  New perspectives on the mechanisms for orientation selectivity , 1997, Current Opinion in Neurobiology.

[2]  O. Creutzfeldt,et al.  The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat , 1984, Pflügers Archiv.

[3]  P. Lennie,et al.  Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque. , 1984, The Journal of physiology.

[4]  Robert A. Frazor,et al.  Visual cortex neurons of monkeys and cats: temporal dynamics of the contrast response function. , 2002, Journal of neurophysiology.

[5]  U. Eysel,et al.  Orientation-specific relationship between populations of excitatory and inhibitory lateral connections in the visual cortex of the cat. , 1997, Cerebral cortex.

[6]  E. Callaway.  Local circuits in primary visual cortex of the macaque monkey. , 1998, Annual review of neuroscience.

[7]  Dario L Ringach,et al.  Untuned Suppression Makes a Major Contribution to the Enhancement of Orientation Selectivity in Macaque V1 , 2011, The Journal of Neuroscience.

[8]  Maria V. Sanchez-Vives,et al.  Lack of orientation and direction selectivity in a subgroup of fast-spiking inhibitory interneurons: cellular and synaptic mechanisms and comparison with other electrophysiological cell types. , 2008, Cerebral cortex.

[9]  J. Kremers,et al.  Influence of contrast on the responses of marmoset lateral geniculate cells to drifting gratings. , 2001, Journal of neurophysiology.

[10]  Henry J. Alitto,et al.  Influence of contrast on orientation and temporal frequency tuning in ferret primary visual cortex. , 2004, Journal of neurophysiology.

[11]  K. Miller,et al.  Neural noise can explain expansive, power-law nonlinearities in neural response functions. , 2002, Journal of neurophysiology.

[12]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[13]  D. McCormick,et al.  Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. , 1985, Journal of neurophysiology.

[14]  A. B. Bonds,et al.  Classifying simple and complex cells on the basis of response modulation , 1991, Vision Research.

[15]  J. Kremers,et al.  Interaction between rod and cone signals in responses of lateral geniculate neurons in dichromatic marmosets (Callithrix jacchus) , 1998, Visual Neuroscience.

[16]  John H. R. Maunsell,et al.  Coding of image contrast in central visual pathways of the macaque monkey , 1990, Vision Research.

[17]  A. L. Humphrey,et al.  Spatial and temporal response properties of lagged and nonlagged cells in cat lateral geniculate nucleus. , 1990, Journal of neurophysiology.

[18]  M. Carandini,et al.  Predictions of a recurrent model of orientation selectivity , 1997, Vision Research.

[19]  D. Ferster,et al.  Dynamics of the orientation-tuned membrane potential response in cat primary visual cortex , 2001, Nature Neuroscience.

[20]  Matteo Carandini,et al.  Contrast invariance of functional maps in cat primary visual cortex. , 2004, Journal of vision.

[21]  D. G. Albrecht,et al.  Motion selectivity and the contrast-response function of simple cells in the visual cortex , 1991, Visual Neuroscience.

[22]  R. Freeman,et al.  Orientation selectivity in the cat's striate cortex is invariant with stimulus contrast , 2004, Experimental Brain Research.

[23]  T. Harkany,et al.  Pyramidal cell communication within local networks in layer 2/3 of rat neocortex , 2003, The Journal of physiology.

[24]  R. Freeman,et al.  Origins of cross-orientation suppression in the visual cortex. , 2006, Journal of neurophysiology.

[25]  R. Miles,et al.  Cell‐attached measurements of the firing threshold of rat hippocampal neurones , 1999, The Journal of physiology.

[26]  R. Shapley,et al.  The primate retina contains two types of ganglion cells, with high and low contrast sensitivity. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Alex M Thomson,et al.  Excitatory and inhibitory connections show selectivity in the neocortex , 2005, The Journal of physiology.

[28]  Oren Shriki,et al.  Rate Models for Conductance-Based Cortical Neuronal Networks , 2003, Neural Computation.

[29]  Pascal Barone,et al.  Contrast Adaptation Contributes to Contrast-Invariance of Orientation Tuning of Primate V1 Cells , 2009, PloS one.

[30]  Jessica A. Cardin,et al.  Stimulus Feature Selectivity in Excitatory and Inhibitory Neurons in Primary Visual Cortex , 2007, The Journal of Neuroscience.

[31]  Haim Sompolinsky,et al.  Course 9 - Irregular Activity in Large Networks of Neurons , 2005 .

[32]  D. Ferster,et al.  Strength and Orientation Tuning of the Thalamic Input to Simple Cells Revealed by Electrically Evoked Cortical Suppression , 1998, Neuron.

[33]  Nicholas J. Priebe,et al.  The Emergence of Contrast-Invariant Orientation Tuning in Simple Cells of Cat Visual Cortex , 2007, Neuron.

[34]  B. Connors,et al.  Two dynamically distinct inhibitory networks in layer 4 of the neocortex. , 2003, Journal of neurophysiology.

[35]  R. Shapley,et al.  A neuronal network model of macaque primary visual cortex (V1): orientation selectivity and dynamics in the input layer 4Calpha. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[36]  K. Miller,et al.  Different Roles for Simple-Cell and Complex-Cell Inhibition in V1 , 2003, The Journal of Neuroscience.

[37]  Paul R. Martin,et al.  Extraclassical Receptive Field Properties of Parvocellular, Magnocellular, and Koniocellular Cells in the Primate Lateral Geniculate Nucleus , 2002, The Journal of Neuroscience.

[38]  J. Peirce.  The potential importance of saturating and supersaturating contrast response functions in visual cortex. , 2007, Journal of vision.

[39]  R. Shapley,et al.  Orientation Selectivity in Macaque V1: Diversity and Laminar Dependence , 2002, The Journal of Neuroscience.

[40]  Nicholas J. Priebe,et al.  Short-Term Depression in Thalamocortical Synapses of Cat Primary Visual Cortex , 2005, The Journal of Neuroscience.

[41]  J. Cowan,et al.  A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn. , 2003, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[42]  M. Carandini,et al.  A Synaptic Explanation of Suppression in Visual Cortex , 2002, The Journal of Neuroscience.

[43]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[44]  D. Heeger.  Normalization of cell responses in cat striate cortex , 1992, Visual Neuroscience.

[45]  S. Nelson,et al.  An emergent model of orientation selectivity in cat visual cortical simple cells , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[46]  D. Ferster,et al.  The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. , 2000, Science.

[47]  R. Reid,et al.  Rules of Connectivity between Geniculate Cells and Simple Cells in Cat Primary Visual Cortex , 2001, The Journal of Neuroscience.

[48]  Bb Lee,et al.  Visual responses in the lateral geniculate nucleus of dichromatic and trichromatic marmosets (Callithrix jacchus) , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[49]  Klaus Obermayer,et al.  A mean-field model for orientation tuning, contrast saturation, and contextual effects in the primary visual cortex , 2000, Biological Cybernetics.

[50]  Idan Segev,et al.  A Biologically Realistic Model of Contrast Invariant Orientation Tuning by Thalamocortical Synaptic Depression , 2007, The Journal of Neuroscience.

[51]  A. B. Bonds,et al.  Differential contributions of magnocellular and parvocellular pathways to the contrast response of neurons in bush baby primary visual cortex (V1) , 2000, Visual Neuroscience.

[52]  L. Maffei,et al.  The visual cortex as a spatial frequency analyser. , 1973, Vision research.

[53]  E. Callaway,et al.  Excitatory cortical neurons form fine-scale functional networks , 2005, Nature.

[54]  D. G. Albrecht,et al.  Striate cortex of monkey and cat: contrast response function. , 1982, Journal of neurophysiology.

[55]  D. Hubel,et al.  Receptive fields and functional architecture of monkey striate cortex , 1968, The Journal of physiology.

[56]  Jose-Manuel Alonso,et al.  Functionally distinct inhibitory neurons at the first stage of visual cortical processing , 2003, Nature Neuroscience.

[57]  C D Woody,et al.  Electrophysiological characterization of different types of neurons recorded in vivo in the motor cortex of the cat. II. Membrane parameters, action potentials, current-induced voltage responses and electrotonic structures. , 1993, Journal of neurophysiology.

[58]  D. Ferster,et al.  Neural mechanisms of orientation selectivity in the visual cortex. , 2000, Annual review of neuroscience.

[59]  P. Schiller,et al.  Response properties of single cells in monkey striate cortex during reversible inactivation of individual lateral geniculate laminae. , 1981, Journal of neurophysiology.

[60]  Maxim Volgushev,et al.  γ‐Frequency fluctuations of the membrane potential and response selectivity in visual cortical neurons , 2003, The European journal of neuroscience.

[61]  J. C. Anderson,et al.  Estimates of the net excitatory currents evoked by visual stimulation of identified neurons in cat visual cortex. , 1998, Cerebral cortex.

[62]  J. Lund,et al.  Specificity and non-specificity of synaptic connections within mammalian visual cortex , 2002, Journal of neurocytology.

[63]  Stephen D. Van Hooser,et al.  Orientation Selectivity without Orientation Maps in Visual Cortex of a Highly Visual Mammal , 2005, The Journal of Neuroscience.

[64]  M. Carandini,et al.  Summation and division by neurons in primate visual cortex. , 1994, Science.

[65]  Lyle J. Graham,et al.  Orientation and Direction Selectivity of Synaptic Inputs in Visual Cortical Neurons A Diversity of Combinations Produces Spike Tuning , 2003, Neuron.

[66]  Ning Qian,et al.  Comparison among some models of orientation selectivity. , 2006, Journal of neurophysiology.

[67]  Nicholas J. Priebe,et al.  The contribution of spike threshold to the dichotomy of cortical simple and complex cells , 2004, Nature Neuroscience.

[68]  D. Hansel,et al.  How Noise Contributes to Contrast Invariance of Orientation Tuning in Cat Visual Cortex , 2002, The Journal of Neuroscience.

[69]  Nicholas J. Priebe,et al.  Contrast-Invariant Orientation Tuning in Cat Visual Cortex: Thalamocortical Input Tuning and Correlation-Based Intracortical Connectivity , 1998, The Journal of Neuroscience.

[70]  E. Callaway,et al.  Fine-scale specificity of cortical networks depends on inhibitory cell type and connectivity , 2005, Nature Neuroscience.

[71]  P Heggelund,et al.  The effect of contrast on the visual response of lagged and nonlagged cells in the cat lateral geniculate nucleus. , 1992, Visual neuroscience.

[72]  D. Ferster,et al.  Orientation selectivity of thalamic input to simple cells of cat visual cortex , 1996, Nature.

[73]  Klaus Obermayer,et al.  Modelling Contrast Adaptation and Contextual Effects in Primary Visual Cortex , 1998, ICONIP.

[74]  Maria V. Sanchez-Vives,et al.  Electrophysiological classes of cat primary visual cortical neurons in vivo as revealed by quantitative analyses. , 2003, Journal of neurophysiology.

[75]  L. Palmer,et al.  Response to Contrast of Electrophysiologically Defined Cell Classes in Primary Visual Cortex , 2003, The Journal of Neuroscience.

[76]  J. Movshon,et al.  Linearity and Normalization in Simple Cells of the Macaque Primary Visual Cortex , 1997, The Journal of Neuroscience.

[77]  Mauro Ursino,et al.  Comparison of different models of orientation selectivity based on distinct intracortical inhibition rules , 2004, Vision Research.

[78]  M. Volgushev,et al.  Comparison of the selectivity of postsynaptic potentials and spike responses in cat visual cortex , 2000, The European journal of neuroscience.

[79]  R. Shapley,et al.  The Orientation Selectivity of Color-Responsive Neurons in Macaque V1 , 2008, The Journal of Neuroscience.

[80]  J. B. Levitt,et al.  Visual response properties of neurons in the LGN of normally reared and visually deprived macaque monkeys. , 2001, Journal of neurophysiology.

[81]  C. Gray,et al.  Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[82]  David C. Somers,et al.  An Emergent Model of Visual Cortical Orientation Selectivity , 1995 .

[83]  A. Delorme,et al.  Early Cortical Orientation Selectivity: How Fast Inhibition Decodes the Order of Spike Latencies , 2003, Journal of Computational Neuroscience.

[84]  Nicholas J. Priebe,et al.  Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning. , 2001, Journal of neurophysiology.

[85]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[86]  Bard Ermentrout,et al.  Linearization of F-I Curves by Adaptation , 1998, Neural Computation.

[87]  M. Carandini,et al.  Membrane Potential and Firing Rate in Cat Primary Visual Cortex , 2000, The Journal of Neuroscience.

[88]  Maria V. Sanchez-Vives,et al.  Impact of cortical network activity on short-term synaptic depression. , 2006, Cerebral cortex.

[89]  I. Ohzawa,et al.  The effects of contrast on visual orientation and spatial frequency discrimination: a comparison of single cells and behavior. , 1987, Journal of neurophysiology.