A small-world-based population encoding model of the primary visual cortex

A wide range of evidence has shown that information encoding performed by the visual cortex involves complex activities of neuronal populations. However, the effects of the neuronal connectivity structure on the population’s encoding performance remain poorly understood. In this paper, a small-world-based population encoding model of the primary visual cortex (V1) is established on the basis of the generalized linear model (GLM) to describe the computation of the neuronal population. The model mainly consists of three sets of filters, including a spatiotemporal stimulus filter, a post-spike history filter, and a set of coupled filters with the coupling neurons organizing as a small-world network. The parameters of the model were fitted with neuronal data of the rat V1 recorded with a micro-electrode array. Compared to the traditional GLM, without considering the small-world structure of the neuronal population, the proposed model was proved to produce more accurate spiking response to grating stimuli and enhance the capability of the neuronal population to carry information. The comparison results proved the validity of the proposed model and further suggest the role of small-world structure in the encoding performance of local populations in V1, which provides new insights for understanding encoding mechanisms of a small scale population in visual system.

[1]  René Schüffny,et al.  Developing structural constraints on connectivity for biologically embedded neural networks , 2012, Biological Cybernetics.

[2]  Eero P. Simoncelli,et al.  Spatio-temporal correlations and visual signalling in a complete neuronal population , 2008, Nature.

[3]  Olaf Sporns,et al.  Mapping the Connectome: Multi-Level Analysis of Brain Connectivity , 2012, Front. Neuroinform..

[4]  Stefan Rotter,et al.  How Structure Determines Correlations in Neuronal Networks , 2011, PLoS Comput. Biol..

[5]  Rong Jin,et al.  Identifying Functional Connectivity in Large-Scale Neural Ensemble Recordings: A Multiscale Data Mining Approach , 2009, Neural Computation.

[6]  Stefan Rotter,et al.  The relevance of network micro-structure for neural dynamics , 2013, Front. Comput. Neurosci..

[7]  A. P. Georgopoulos,et al.  Movement parameters and neural activity in motor cortex and area 5. , 1994, Cerebral cortex.

[8]  Ashish Kumar,et al.  L1 Regularized Logistic Regression , 2005 .

[9]  Roman Filipovych,et al.  Identifying Sparse Connectivity Patterns in the brain using resting-state fMRI , 2015, NeuroImage.

[10]  Artur Luczak,et al.  Multivariate receptive field mapping in marmoset auditory cortex , 2004, Journal of Neuroscience Methods.

[11]  J. P. Jones,et al.  The two-dimensional spatial structure of simple receptive fields in cat striate cortex. , 1987, Journal of neurophysiology.

[12]  D. Brillinger Maximum likelihood analysis of spike trains of interacting nerve cells , 2004, Biological Cybernetics.

[13]  Liam Paninski,et al.  Population decoding of motor cortical activity using a generalized linear model with hidden states , 2010, Journal of Neuroscience Methods.

[14]  E J Chichilnisky,et al.  Prediction and Decoding of Retinal Ganglion Cell Responses with a Probabilistic Spiking Model , 2005, The Journal of Neuroscience.

[15]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[16]  J. P. Jones,et al.  The two-dimensional spectral structure of simple receptive fields in cat striate cortex. , 1987, Journal of neurophysiology.

[17]  J. Donoghue,et al.  Collective dynamics in human and monkey sensorimotor cortex: predicting single neuron spikes , 2009, Nature Neuroscience.

[18]  L. Paninski Maximum likelihood estimation of cascade point-process neural encoding models , 2004, Network.

[19]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[20]  Alexander S. Ecker,et al.  Reassessing optimal neural population codes with neurometric functions , 2011, Proceedings of the National Academy of Sciences.

[21]  E. The Cognitive Neurosciences , 1995, Journal of Cognitive Neuroscience.

[22]  Wulfram Gerstner,et al.  Extraction of Network Topology From Multi-Electrode Recordings: Is there a Small-World Effect? , 2011, Front. Comput. Neurosci..

[23]  M. Wilson,et al.  Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity , 2005, Neural Computation.

[24]  Danielle Smith Bassett,et al.  Small-World Brain Networks , 2006, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[25]  Stefan Rotter,et al.  Correlations and Population Dynamics in Cortical Networks , 2008, Neural Computation.

[26]  Moritz Helias,et al.  Correlations in spiking neuronal networks with distance dependent connections , 2009, Journal of Computational Neuroscience.

[27]  T. Prescott,et al.  The brainstem reticular formation is a small-world, not scale-free, network , 2006, Proceedings of the Royal Society B: Biological Sciences.

[28]  E. S. Chornoboy,et al.  Maximum likelihood identification of neural point process systems , 1988, Biological Cybernetics.

[29]  J. Csicsvari,et al.  Organization of cell assemblies in the hippocampus , 2003, Nature.

[30]  Alan C. Evans,et al.  Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. , 2007, Cerebral cortex.

[31]  Shan Yu,et al.  A Small World of Neuronal Synchrony , 2008, Cerebral cortex.

[32]  Emery N. Brown,et al.  Encoding Through Patterns: Regression Tree–Based Neuronal Population Models , 2013, Neural Computation.

[33]  Haishan Yao,et al.  Contrast‐dependent OFF‐dominance in cat primary visual cortex facilitates discrimination of stimuli with natural contrast statistics , 2014, The European journal of neuroscience.

[34]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

[35]  Uri T Eden,et al.  A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. , 2005, Journal of neurophysiology.

[36]  Marius-F. Danca,et al.  Noise induced complexity: patterns and collective phenomena in a small-world neuronal network , 2013, Cognitive Neurodynamics.

[37]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[38]  T. Ebner,et al.  Temporal encoding of movement kinematics in the discharge of primate primary motor and premotor neurons. , 1995, Journal of neurophysiology.

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

[40]  Y. Dan,et al.  Layer-specific network oscillation and spatiotemporal receptive field in the visual cortex , 2009, Proceedings of the National Academy of Sciences.

[41]  Eric Shea-Brown,et al.  Impact of Network Structure and Cellular Response on Spike Time Correlations , 2011, PLoS Comput. Biol..

[42]  Marcus Kaiser Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks , 2008, 0802.2512.

[43]  Edward T. Bullmore,et al.  Efficiency and Cost of Economical Brain Functional Networks , 2007, PLoS Comput. Biol..

[44]  Li Shi,et al.  An information integration model of the primary visual cortex under grating stimulations. , 2011, Biochemical and biophysical research communications.

[45]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[46]  Yunqing Wen,et al.  Ensemble cortical responses to rival visual stimuli: effect of monocular transient. , 2009, Biochemical and biophysical research communications.

[47]  Eric Shea-Brown,et al.  A generative spike train model with time-structured higher order correlations , 2013, Front. Comput. Neurosci..

[48]  Radford M. Neal Pattern Recognition and Machine Learning , 2007, Technometrics.