Population rate codes carried by mean, fluctuation and synchrony of neuronal firings

A population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three kinds of inputs: mean-, fluctuation- and synchrony-driven inputs. The generalized rate-code model including additive and multiplicative noise [H. Hasegawa, Phys. Rev. E 75 (2007) 051904] has been studied by direct simulations (DSs) and the augmented moment method (AMM) in which equations of motion for mean firing rate, fluctuation and synchrony are derived. Results calculated by the AMM are in good agreement with those by DSs. The independent component analysis (ICA) of our results has shown that mean firing rate, fluctuation (or variability) and synchrony may carry independent information in the population rate-code model. The input–output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise, as recently observed in prefrontal cortex. A comparison is made between results obtained by the integrate-and-fire (IF) model and our rate-code model.

[1]  Xiao-Jing Wang,et al.  Mean-Driven and Fluctuation-Driven Persistent Activity in Recurrent Networks , 2007, Neural Computation.

[2]  Hideo Hasegawa,et al.  Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[4]  W. Rüemelin.  Numerical Treatment of Stochastic Differential Equations , 1982 .

[5]  A. Zador,et al.  Neural representation and the cortical code. , 2000, Annual review of neuroscience.

[6]  M. J. Richardson,et al.  Effects of synaptic conductance on the voltage distribution and firing rate of spiking neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  T. Sejnowski,et al.  Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  H. Hasegawa,et al.  Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[10]  Feng Liu,et al.  Propagation of firing rate in a feed-forward neuronal network. , 2006, Physical review letters.

[11]  E. Oja,et al.  Independent Component Analysis , 2013 .

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

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

[14]  L Schimansky-Geier,et al.  Transmission of noise coded versus additive signals through a neuronal ensemble. , 2001, Physical review letters.

[15]  Hideo Hasegawa.  Generalized rate-code model for neuron ensembles with finite populations. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[17]  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.

[18]  Roy,et al.  Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise. , 1988, Physical review. A, General physics.

[19]  R. Reid,et al.  Synchronous activity in the visual system. , 1999, Annual review of physiology.

[20]  J. Eggert,et al.  Unifying framework for neuronal assembly dynamics. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  R. Andersen,et al.  Selecting the signals for a brain–machine interface , 2004, Current Opinion in Neurobiology.

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

[23]  Hideo Hasegawa.  Dynamical mean-field theory of noisy spiking neuron ensembles: application to the Hodgkin-Huxley model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  D. Tranchina,et al.  Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size. , 2001, Network.

[25]  A. Reyes.  Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro , 2003, Nature Neuroscience.

[26]  D. Wilkin,et al.  Neuron , 2001, Brain Research.

[27]  H Markram,et al.  Dynamics of population rate codes in ensembles of neocortical neurons. , 2004, Journal of neurophysiology.

[28]  Hideo Hasegawa,et al.  Dynamical mean-field approximation to small-world networks of spiking neurons: from local to global and/or from regular to random couplings. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  David B. Grayden,et al.  Study of neuronal gain in a conductance-based leaky integrate-and-fire neuron model with balanced excitatory and inhibitory synaptic input , 2003, Biological Cybernetics.

[30]  Brent Doiron,et al.  Noise-induced divisive gain control in neuron models. , 2002, Bio Systems.

[31]  Wulfram Gerstner,et al.  From spiking neurons to rate models: a cascade model as an approximation to spiking neuron models with refractoriness. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[33]  Anthony N. Burkitt,et al.  A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input , 2006, Biological Cybernetics.

[34]  Anthony N. Burkitt,et al.  Synchronization of the Neural Response to Noisy Periodic Synaptic Input , 2001, Neural Computation.

[35]  Masato Okada,et al.  Higher order effects on rate reduction for networks of hodgkin-huxley neurons , 2007 .

[36]  André Longtin,et al.  Comment on Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes, by M. Rudolph and A. Destexhe , 2005, Neural Computation.

[37]  J García-Ojalvo,et al.  Noise-induced phase separation: mean-field results. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  Naoki Masuda,et al.  Simultaneous Rate-Synchrony Codes in Populations of Spiking Neurons , 2006, Neural Computation.

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

[40]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[41]  Paul H. E. Tiesinga,et al.  Rapid Temporal Modulation of Synchrony by Competition in Cortical Interneuron Networks , 2004, Neural Computation.

[42]  Peter Hänggi,et al.  Firing time statistics for driven neuron models: analytic expressions versus numerics. , 2004, Physical review letters.

[43]  Michele Giugliano,et al.  The Impact of Input Fluctuations on the Frequency–Current Relationships of Layer 5 Pyramidal Neurons in the Rat Medial Prefrontal Cortex , 2007, The Journal of Neuroscience.

[44]  Bruce W. Knight,et al.  Dynamics of Encoding in Neuron Populations: Some General Mathematical Features , 2000, Neural Computation.

[45]  K. Hoffmann,et al.  Synchronization of Neuronal Activity during Stimulus Expectation in a Direction Discrimination Task , 1997, The Journal of Neuroscience.

[46]  A. Aertsen,et al.  Neuronal Integration of Synaptic Input in the Fluctuation-Driven Regime , 2004, The Journal of Neuroscience.

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

[48]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[49]  Adi R. Bulsara,et al.  Analytic Expressions for Rate and CV of a Type I Neuron Driven by White Gaussian Noise , 2003, Neural Computation.

[50]  Lawrence Sirovich,et al.  On the Simulation of Large Populations of Neurons , 2004, Journal of Computational Neuroscience.

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

[52]  H. Tuckwell,et al.  Statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[53]  Brent Doiron,et al.  Stochastic synchronization in finite size spiking networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Bard Ermentrout,et al.  Reduction of Conductance-Based Models with Slow Synapses to Neural Nets , 1994, Neural Computation.

[55]  N. Parga,et al.  Response of spiking neurons to correlated inputs. , 2002, Physical review letters.

[56]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[57]  Miguel A. L. Nicolelis,et al.  Real-time control of a robot arm using simultaneously recorded neurons in the motor cortex , 1999, Nature Neuroscience.

[58]  Frances S. Chance,et al.  Gain Modulation from Background Synaptic Input , 2002, Neuron.

[59]  H. Hasegawa.  Effects of correlated variability on information entropies in nonextensive systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Alexa Riehle,et al.  Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time , 2003, Biological Cybernetics.

[61]  Jakob Heinzle,et al.  Modulation of synchrony without changes in firing rates , 2007, Cognitive Neurodynamics.

[62]  Hideo Hasegawa,et al.  Stationary and dynamical properties of information entropies in nonextensive systems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.