Neural networks of different species, brain areas and states can be characterized by the probability polling state

Cortical networks are complex systems of a great many interconnected neurons that operate from collective dynamical states. To understand how cortical neural networks function, it is important to identify their common dynamical operating states from the probabilistic viewpoint. Probabilistic characteristics of these operating states often underlie network functions. Here, using multi‐electrode data from three separate experiments, we identify and characterize a cortical operating state (the “probability polling” or “p‐polling” state), common across mouse and monkey with different behaviors. If the interaction among neurons is weak, the p‐polling state provides a quantitative understanding of how the high dimensional probability distribution of firing patterns can be obtained by the low‐order maximum entropy formulation, effectively utilizing a low dimensional stimulus‐coding structure. These results show evidence for generality of the p‐polling state and in certain situations its advantage of providing a mathematical validation for the low‐order maximum entropy principle as a coding strategy.

[1]  R. Segev,et al.  Sparse low-order interaction network underlies a highly correlated and learnable neural population code , 2011, Proceedings of the National Academy of Sciences.

[2]  D. McCormick,et al.  Neocortical Network Activity In Vivo Is Generated through a Dynamic Balance of Excitation and Inhibition , 2006, The Journal of Neuroscience.

[3]  Pak-Ming Lau,et al.  Synaptic mechanisms of persistent reverberatory activity in neuronal networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Wenjun Yan,et al.  Medial prefrontal activity during delay period contributes to learning of a working memory task , 2014, Science.

[5]  William Bialek,et al.  Collective Behavior of Place and Non-place Neurons in the Hippocampal Network , 2016, Neuron.

[6]  Gregory C. DeAngelis,et al.  The Effects of Population Tuning and Trial-by-Trial Variability on Information Encoding and Behavior , 2019, The Journal of Neuroscience.

[7]  P. Dayan,et al.  Supporting Online Material Materials and Methods Som Text Figs. S1 to S9 References the Asynchronous State in Cortical Circuits , 2022 .

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

[9]  Christian K. Machens,et al.  Predictive Coding of Dynamical Variables in Balanced Spiking Networks , 2013, PLoS Comput. Biol..

[10]  Christian K. Machens,et al.  Efficient codes and balanced networks , 2016, Nature Neuroscience.

[11]  A. Pouget,et al.  Neural correlations, population coding and computation , 2006, Nature Reviews Neuroscience.

[12]  Peter Dayan,et al.  The Effect of Correlated Variability on the Accuracy of a Population Code , 1999, Neural Computation.

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

[14]  Zhi-Qin John Xu,et al.  Maximum Entropy Principle Analysis in Network Systems with Short-time Recordings , 2018, Physical review. E.

[15]  R. Traub,et al.  Cellular mechanism of neuronal synchronization in epilepsy. , 1982, Science.

[16]  R. Quiroga,et al.  Extracting information from neuronal populations : information theory and decoding approaches , 2022 .

[17]  Zhi-Qin John Xu,et al.  Dynamical and Coupling Structure of Pulse-Coupled Networks in Maximum Entropy Analysis , 2018, Entropy.

[18]  Alexandre Pouget,et al.  Origin of information-limiting noise correlations , 2015, Proceedings of the National Academy of Sciences.

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

[20]  Zhi-Qin John Xu,et al.  A dynamical state underlying the second order maximum entropy principle in neuronal networks , 2017 .

[21]  B. Hyman,et al.  Synchronous Hyperactivity and Intercellular Calcium Waves in Astrocytes in Alzheimer Mice , 2009, Science.

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

[23]  O. Schwartz,et al.  Flexible Gating of Contextual Influences in Natural Vision , 2015, Nature Neuroscience.

[24]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[25]  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.

[26]  Michael N. Shadlen,et al.  Noise, neural codes and cortical organization , 1994, Current Opinion in Neurobiology.

[27]  Rubén Moreno-Bote,et al.  Poisson-Like Spiking in Circuits with Probabilistic Synapses , 2014, PLoS Comput. Biol..

[28]  D. Knill,et al.  The Bayesian brain: the role of uncertainty in neural coding and computation , 2004, Trends in Neurosciences.

[29]  Mattias P. Karlsson,et al.  Awake replay of remote experiences in the hippocampus , 2009, Nature Neuroscience.

[30]  A. Pouget,et al.  Information-limiting correlations , 2014, Nature Neuroscience.

[31]  Joshua W Shaevitz,et al.  Whole-brain calcium imaging with cellular resolution in freely behaving Caenorhabditis elegans , 2015, Proceedings of the National Academy of Sciences.

[32]  M. Cohen,et al.  Measuring and interpreting neuronal correlations , 2011, Nature Neuroscience.

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

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