Improved dimensionally-reduced visual cortical network using stochastic noise modeling

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.

[1]  RussLL L. Ds Vnlos,et al.  SPATIAL FREQUENCY SELECTIVITY OF CELLS IN MACAQUE VISUAL CORTEX , 2022 .

[2]  Ganesh Srinivasamoorthy,et al.  Estimating weak ratiometric signals in imaging data. I. Dual-channel data. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  T. Sejnowski,et al.  Impact of Correlated Synaptic Input on Output Firing Rate and Variability in Simple Neuronal Models , 2000, The Journal of Neuroscience.

[4]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[5]  Andrew T. Sornborger,et al.  Dimensionally-reduced visual cortical network model predicts network response and connects system- and cellular-level descriptions , 2010, Journal of Computational Neuroscience.

[6]  T. Sejnowski,et al.  Human Brain Mapping 6:368–372(1998) � Independent Component Analysis of fMRI Data: Examining the Assumptions , 2022 .

[7]  Louis Tao,et al.  Orientation selectivity in visual cortex by fluctuation-controlled criticality , 2006, Proceedings of the National Academy of Sciences.

[8]  Michael Shelley,et al.  How Simple Cells Are Made in a Nonlinear Network Model of the Visual Cortex , 2001, The Journal of Neuroscience.

[9]  V. A. Krasil’nikov,et al.  Atmospheric turbulence and radio-wave propagation , 1962 .

[10]  Wulfram Gerstner,et al.  Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. , 2004, Journal of neurophysiology.

[11]  L. Sirovich,et al.  Coherent structures and chaos: A model problem , 1987 .

[12]  David McLaughlin,et al.  States of High Conductance in a Large-Scale Model of the Visual Cortex , 2002, Journal of Computational Neuroscience.

[13]  W. Gerstner,et al.  Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. , 2008, Journal of neurophysiology.

[14]  L. Sirovich,et al.  Extraction of the average and differential dynamical response in stimulus-locked experimental data , 2005, Journal of Neuroscience Methods.

[15]  G. Buzsáki,et al.  Gamma Oscillation by Synaptic Inhibition in a Hippocampal Interneuronal Network Model , 1996, The Journal of Neuroscience.

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

[17]  L. Sirovich.  Turbulence and the dynamics of coherent structures. III. Dynamics and scaling , 1987 .

[18]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[19]  Andrew T Sornborger,et al.  Drosophila TRPA channel modulates sugar-stimulated neural excitation, avoidance and social response , 2008, Nature Neuroscience.

[20]  Tzyy-Ping Jung,et al.  Independent Component Analysis of Electroencephalographic Data , 1995, NIPS.

[21]  Aaditya V. Rangan,et al.  Architectural and synaptic mechanisms underlying coherent spontaneous activity in V1. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Shiro Ikeda,et al.  Independent component analysis for noisy data -- MEG data analysis , 2000, Neural Networks.

[23]  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.

[24]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control) , 2005 .

[25]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[26]  B W Knight,et al.  Representation of spatial frequency and orientation in the visual cortex. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

[28]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[29]  Wulfram Gerstner,et al.  Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves , 2008, Biological Cybernetics.

[30]  Michael Rudolph,et al.  Inferring network activity from synaptic noise , 2004, Journal of Physiology-Paris.

[31]  Liam Paninski,et al.  Smoothing of, and Parameter Estimation from, Noisy Biophysical Recordings , 2009, PLoS Comput. Biol..

[32]  P. Mitra,et al.  Analysis of dynamic brain imaging data. , 1998, Biophysical journal.

[33]  Lawrence Sirovich,et al.  The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result , 2000, Neural Computation.

[34]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[35]  R. Shapley,et al.  An egalitarian network model for the emergence of simple and complex cells in visual cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Lawrence Sirovich,et al.  Extraction of periodic multivariate signals: mapping of voltage-dependent dye fluorescence in the mouse heart , 2003, IEEE Transactions on Medical Imaging.

[37]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[38]  Wulfram Gerstner,et al.  Reduction of the Hodgkin-Huxley Equations to a Single-Variable Threshold Model , 1997, Neural Computation.

[39]  Michael Rudolph,et al.  Note on “ Characterization of subthreshold voltage fluctuations in neuronal membranes ” , 2008 .

[40]  Aaditya V. Rangan,et al.  Modeling the spatiotemporal cortical activity associated with the line-motion illusion in primary visual cortex. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Liam Paninski,et al.  Efficient estimation of detailed single-neuron models. , 2006, Journal of neurophysiology.

[42]  H. Spitzer,et al.  Simple- and complex-cell response dependences on stimulation parameters. , 1985, Journal of neurophysiology.

[43]  David McLaughlin,et al.  Coarse-Grained Reduction and Analysis of a Network Model of Cortical Response: I. Drifting Grating Stimuli , 2002, Journal of Computational Neuroscience.

[44]  Donald B. Percival,et al.  Spectral Analysis for Physical Applications , 1993 .