The Architecture of Functional Interaction Networks in the Retina

Sensory information is represented in the brain by the joint activity of large groups of neurons. Recent studies have shown that, although the number of possible activity patterns and underlying interactions is exponentially large, pairwise-based models give a surprisingly accurate description of neural population activity patterns. We explored the architecture of maximum entropy models of the functional interaction networks underlying the response of large populations of retinal ganglion cells, in adult tiger salamander retina, responding to natural and artificial stimuli. We found that we can further simplify these pairwise models by neglecting weak interaction terms or by relying on a small set of interaction strengths. Comparing network interactions under different visual stimuli, we show the existence of local network motifs in the interaction map of the retina. Our results demonstrate that the underlying interaction map of the retina is sparse and dominated by local overlapping interaction modules.

[1]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[2]  H. Barlow,et al.  Changes in the maintained discharge with adaptation level in the cat retina , 1969, The Journal of physiology.

[3]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[4]  I. Csiszár $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[5]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[6]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[7]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

[8]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[9]  Jianhua Lin,et al.  Divergence measures based on the Shannon entropy , 1991, IEEE Trans. Inf. Theory.

[10]  TJ Gawne,et al.  How independent are the messages carried by adjacent inferior temporal cortical neurons? , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[11]  Gerasimos Potamianos,et al.  Partition function estimation of Gibbs random field images using Monte Carlo simulations , 1993, IEEE Trans. Inf. Theory.

[12]  Markus Meister,et al.  Multi-neuronal signals from the retina: acquisition and analysis , 1994, Journal of Neuroscience Methods.

[13]  D. Baylor,et al.  Concerted Signaling by Retinal Ganglion Cells , 1995, Science.

[14]  Gerasimos Potamianos,et al.  Stochastic approximation algorithms for partition function estimation of Gibbs random fields , 1997, IEEE Trans. Inf. Theory.

[15]  Y. Dan,et al.  Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus , 1998, Nature Neuroscience.

[16]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[17]  Naftali Tishby,et al.  Synergy and Redundancy among Brain Cells of Behaving Monkeys , 1998, NIPS.

[18]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[19]  Kathryn B. Laskey,et al.  Neural Coding: Higher-Order Temporal Patterns in the Neurostatistics of Cell Assemblies , 2000, Neural Computation.

[20]  Pieter R. Roelfsema,et al.  The Effects of Pair-wise and Higher-order Correlations on the Firing Rate of a Postsynaptic Neuron , 1998, Neural Computation.

[21]  H Barlow,et al.  Redundancy reduction revisited , 2001, Network.

[22]  Partha P. Mitra,et al.  Scalable architecture in mammalian brains , 2001, Nature.

[23]  M. Diamond,et al.  Population Coding of Stimulus Location in Rat Somatosensory Cortex , 2001, Neuron.

[24]  Stan Z. Li,et al.  Markov Random Field Modeling in Image Analysis , 2001, Computer Science Workbench.

[25]  W. Bair,et al.  Correlated Firing in Macaque Visual Area MT: Time Scales and Relationship to Behavior , 2001, The Journal of Neuroscience.

[26]  Shun-ichi Amari,et al.  Information geometry on hierarchy of probability distributions , 2001, IEEE Trans. Inf. Theory.

[27]  S. Shen-Orr,et al.  Networks Network Motifs : Simple Building Blocks of Complex , 2002 .

[28]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[29]  Martin Suter,et al.  Small World , 2002 .

[30]  Dmitri B. Chklovskii,et al.  Wiring Optimization in Cortical Circuits , 2002, Neuron.

[31]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[32]  M. Newman,et al.  On the uniform generation of random graphs with prescribed degree sequences , 2003, cond-mat/0312028.

[33]  M. Schnitzer,et al.  Multineuronal Firing Patterns in the Signal from Eye to Brain , 2003, Neuron.

[34]  Michael J. Berry,et al.  Network information and connected correlations. , 2003, Physical review letters.

[35]  J. H. van Hateren,et al.  A theory of maximizing sensory information , 2004, Biological Cybernetics.

[36]  Michael J. Berry,et al.  Recording spikes from a large fraction of the ganglion cells in a retinal patch , 2004, Nature Neuroscience.

[37]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[38]  Sen Song,et al.  Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS biology.

[39]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[40]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[41]  Michael J. Berry,et al.  Redundancy in the Population Code of the Retina , 2005, Neuron.

[42]  Marla B. Feller,et al.  Spontaneous patterned retinal activity and the refinement of retinal projections , 2005, Progress in Neurobiology.

[43]  K. Kaski,et al.  Intensity and coherence of motifs in weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  G. Shepherd,et al.  Geometric and functional organization of cortical circuits , 2005, Nature Neuroscience.

[45]  Michael J. Berry,et al.  Ising models for networks of real neurons , 2006, q-bio/0611072.

[46]  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.

[47]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[48]  Jonathon Shlens,et al.  The Structure of Multi-Neuron Firing Patterns in Primate Retina , 2006, The Journal of Neuroscience.

[49]  D. Chklovskii,et al.  Wiring optimization can relate neuronal structure and function. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[50]  Pieter Abbeel,et al.  Learning Factor Graphs in Polynomial Time and Sample Complexity , 2006, J. Mach. Learn. Res..

[51]  R. W. Draft,et al.  Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system , 2007, Nature.

[52]  U. Alon Network motifs: theory and experimental approaches , 2007, Nature Reviews Genetics.

[53]  Michael I. Ham,et al.  Functional structure of cortical neuronal networks grown in vitro. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  C. Stam,et al.  Small-world networks and functional connectivity in Alzheimer's disease. , 2006, Cerebral cortex.

[55]  Charles F Stevens,et al.  General design principle for scalable neural circuits in a vertebrate retina , 2007, Proceedings of the National Academy of Sciences.

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

[57]  Robert E. Schapire,et al.  Faster solutions of the inverse pairwise Ising problem , 2008 .

[58]  John M. Beggs,et al.  A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks In Vitro , 2008, The Journal of Neuroscience.

[59]  R. Segev,et al.  How fast can we learn maximum entropy models of neural populations? , 2009 .

[60]  Michel A. Picardo,et al.  GABAergic Hub Neurons Orchestrate Synchrony in Developing Hippocampal Networks , 2009, Science.

[61]  Jonathon Shlens,et al.  The Structure of Large-Scale Synchronized Firing in Primate Retina , 2009, The Journal of Neuroscience.

[62]  Stefano Panzeri,et al.  The impact of high-order interactions on the rate of synchronous discharge and information transmission in somatosensory cortex , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[63]  Sami El Boustani,et al.  Prediction of spatiotemporal patterns of neural activity from pairwise correlations. , 2009, Physical review letters.

[64]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[65]  S. Leibler,et al.  Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods , 2009, Proceedings of the National Academy of Sciences.

[66]  Dietmar Plenz,et al.  Hierarchical Interaction Structure of Neural Activities in Cortical Slice Cultures , 2010, The Journal of Neuroscience.

[67]  Radford M. Neal Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .