The correlation structure of local cortical networks intrinsically results from recurrent dynamics

The co-occurrence of action potentials of pairs of neurons within short time intervals is known since long. Such synchronous events can appear time-locked to the behavior of an animal and also theoretical considerations argue for a functional role of synchrony. Early theoretical work tried to explain correlated activity by neurons transmitting common fluctuations due to shared inputs. This, however, overestimates correlations. Recently the recurrent connectivity of cortical networks was shown responsible for the observed low baseline correlations. Two different explanations were given: One argues that excitatory and inhibitory population activities closely follow the external inputs to the network, so that their effects on a pair of cells mutually cancel. Another explanation relies on negative recurrent feedback to suppress fluctuations in the population activity, equivalent to small correlations. In a biological neuronal network one expects both, external inputs and recurrence, to affect correlated activity. The present work extends the theoretical framework of correlations to include both contributions and explains their qualitative differences. Moreover the study shows that the arguments of fast tracking and recurrent feedback are not equivalent, only the latter correctly predicts the cell-type specific correlations.

[1]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[2]  Chris Eliasmith,et al.  Neural populations can induce reliable postsynaptic currents without observable spike rate changes or precise spike timing. , 2007, Cerebral cortex.

[3]  Stefan Rotter,et al.  Recurrent interactions in spiking networks with arbitrary topology. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Wulfram Gerstner,et al.  Phenomenological models of synaptic plasticity based on spike timing , 2008, Biological Cybernetics.

[5]  Eugene M. Izhikevich,et al.  Polychronization: Computation with Spikes , 2006, Neural Computation.

[6]  Xiao-Jing Wang,et al.  Decorrelation by Recurrent Inhibition in Heterogeneous Neural Circuits , 2011, Neural Computation.

[7]  C. Petersen,et al.  Membrane Potential Dynamics of GABAergic Neurons in the Barrel Cortex of Behaving Mice , 2010, Neuron.

[8]  Sompolinsky,et al.  Theory of correlations in stochastic neural networks. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  W Singer,et al.  Visual feature integration and the temporal correlation hypothesis. , 1995, Annual review of neuroscience.

[10]  Ad Aertsen,et al.  A modeler's view on the spatial structure of intrinsic horizontal connectivity in the neocortex , 2010, Progress in Neurobiology.

[11]  G. Buzsáki,et al.  Mechanisms of gamma oscillations. , 2012, Annual review of neuroscience.

[12]  Nicolas Brunel,et al.  How Connectivity, Background Activity, and Synaptic Properties Shape the Cross-Correlation between Spike Trains , 2009, The Journal of Neuroscience.

[13]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Moritz Helias,et al.  Invariance of covariances arises out of noise , 2013 .

[15]  Moritz Helias,et al.  Echoes in correlated neural systems , 2012, 1207.0298.

[16]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[17]  E. Bienenstock A model of neocortex , 1995 .

[18]  Robert Rosenbaum,et al.  Mechanisms That Modulate the Transfer of Spiking Correlations , 2011, Neural Computation.

[19]  W. Singer,et al.  Synchronization of neuronal responses in primary visual cortex of monkeys viewing natural images. , 2008, Journal of neurophysiology.

[20]  Sonja Grün,et al.  Saccade-Related Modulations of Neuronal Excitability Support Synchrony of Visually Elicited Spikes , 2011, Cerebral cortex.

[21]  T. Sejnowski,et al.  Correlated neuronal activity and the flow of neural information , 2001, Nature Reviews Neuroscience.

[22]  B. Doiron,et al.  Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations. , 2013, Journal of neurophysiology.

[23]  Moritz Helias,et al.  Decorrelation of Neural-Network Activity by Inhibitory Feedback , 2012, PLoS Comput. Biol..

[24]  Carl van Vreeswijk,et al.  Temporal Correlations in Stochastic Networks of Spiking Neurons , 2002, Neural Computation.

[25]  Brent Doiron,et al.  The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity , 2012, PLoS Comput. Biol..

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

[27]  Moritz Helias,et al.  A General and Efficient Method for Incorporating Precise Spike Times in Globally Time-Driven Simulations , 2010, Front. Neuroinform..

[28]  Brent Doiron,et al.  Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Marc-Oliver Gewaltig,et al.  NEST (NEural Simulation Tool) , 2007, Scholarpedia.

[30]  Ehud Zohary,et al.  Correlated neuronal discharge rate and its implications for psychophysical performance , 1994, Nature.

[31]  Matthieu Gilson,et al.  Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways , 2009, Biological Cybernetics.

[32]  Klas H. Pettersen,et al.  Modeling the Spatial Reach of the LFP , 2011, Neuron.

[33]  Ad Aertsen,et al.  Stable propagation of synchronous spiking in cortical neural networks , 1999, Nature.

[34]  Philip Sterne,et al.  Information Recall Using Relative Spike Timing in a Spiking Neural Network , 2012, Neural Computation.

[35]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[36]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[37]  J. Poulet,et al.  Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice , 2008, Nature.

[38]  R. Douglas,et al.  A Quantitative Map of the Circuit of Cat Primary Visual Cortex , 2004, The Journal of Neuroscience.

[39]  Stefan Rotter,et al.  Dependence of Neuronal Correlations on Filter Characteristics and Marginal Spike Train Statistics , 2008, Neural Computation.

[40]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[41]  D. Amit,et al.  Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. , 1997, Cerebral cortex.

[42]  J. Poulet,et al.  Synaptic Mechanisms Underlying Sparse Coding of Active Touch , 2011, Neuron.

[43]  Michael A. Buice,et al.  Systematic Fluctuation Expansion for Neural Network Activity Equations , 2009, Neural Computation.

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

[45]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[46]  F. Attneave,et al.  The Organization of Behavior: A Neuropsychological Theory , 1949 .

[47]  Néstor Parga,et al.  ournal of Statistical Mechanics : J Theory and Experiment Towards a self-consistent description of irregular and asynchronous cortical activity , 2013 .

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

[49]  John Hertz,et al.  Cross-Correlations in High-Conductance States of a Model Cortical Network , 2010, Neural Computation.