Criticality predicts maximum irregularity in recurrent networks of excitatory nodes

A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of cerebral cortex operate at a critical regime, which is defined as a transition point between two phases of short lasting and chaotic activity. However, despite the fact that criticality brings about certain functional advantages for information processing, its supporting evidence is still far from conclusive, as it has been mostly based on power law scaling of size and durations of cascades of activity. Moreover, to what degree such hypothesis could explain some fundamental features of neural activity is still largely unknown. One of the most prevalent features of cortical activity in vivo is known to be spike irregularity of spike trains, which is measured in terms of the coefficient of variation (CV) larger than one. Here, using a minimal computational model of excitatory nodes, we show that irregular spiking (CV > 1) naturally emerges in a recurrent network operating at criticality. More importantly, we show that even at the presence of other sources of spike irregularity, being at criticality maximizes the mean coefficient of variation of neurons, thereby maximizing their spike irregularity. Furthermore, we also show that such a maximized irregularity results in maximum correlation between neuronal firing rates and their corresponding spike irregularity (measured in terms of CV). On the one hand, using a model in the universality class of directed percolation, we propose new hallmarks of criticality at single-unit level, which could be applicable to any network of excitable nodes. On the other hand, given the controversy of the neural criticality hypothesis, we discuss the limitation of this approach to neural systems and to what degree they support the criticality hypothesis in real neural networks. Finally, we discuss the limitations of applying our results to real networks and to what degree they support the criticality hypothesis.

[1]  W. Bialek,et al.  Are Biological Systems Poised at Criticality? , 2010, 1012.2242.

[2]  C. Stevens,et al.  Input synchrony and the irregular firing of cortical neurons , 1998, Nature Neuroscience.

[3]  Woodrow L. Shew,et al.  Predicting criticality and dynamic range in complex networks: effects of topology. , 2010, Physical review letters.

[4]  Woodrow L. Shew,et al.  Neuronal Avalanches Imply Maximum Dynamic Range in Cortical Networks at Criticality , 2009, The Journal of Neuroscience.

[5]  D. Plenz,et al.  Criticality in neural systems , 2014 .

[6]  Woodrow L. Shew,et al.  Voltage Imaging of Waking Mouse Cortex Reveals Emergence of Critical Neuronal Dynamics , 2014, The Journal of Neuroscience.

[7]  Dan-Mei Chen,et al.  Self-organized criticality in a cellular automaton model of pulse-coupled integrate-and-fire neurons , 1995 .

[8]  J. Cowan,et al.  Statistical mechanics of the neocortex. , 2009, Progress in biophysics and molecular biology.

[9]  D. Plenz,et al.  Neuronal Avalanches in the Resting MEG of the Human Brain , 2012, The Journal of Neuroscience.

[10]  Srdjan Ostojic,et al.  Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons , 2014, Nature Neuroscience.

[11]  Woodrow L. Shew,et al.  Adaptation to sensory input tunes visual cortex to criticality , 2015, Nature Physics.

[12]  Wulfram Gerstner,et al.  Neuronal Dynamics: From Single Neurons To Networks And Models Of Cognition , 2014 .

[13]  William R. Softky,et al.  The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[14]  J. M. Herrmann,et al.  Finite-size effects of avalanche dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Marc Benayoun,et al.  Avalanches in a Stochastic Model of Spiking Neurons , 2010, PLoS Comput. Biol..

[16]  Andreas Klaus,et al.  Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches , 2011, PloS one.

[17]  E. Ott,et al.  Statistical properties of avalanches in networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Oren Shriki,et al.  Near-Critical Dynamics in Stimulus-Evoked Activity of the Human Brain and Its Relation to Spontaneous Resting-State Activity , 2015, The Journal of Neuroscience.

[19]  L. Hood,et al.  Gene expression dynamics in the macrophage exhibit criticality , 2008, Proceedings of the National Academy of Sciences.

[20]  Nicholas A. Steinmetz,et al.  Diverse coupling of neurons to populations in sensory cortex , 2015, Nature.

[21]  Thilo Gross,et al.  Self-organized criticality as a fundamental property of neural systems , 2014, Front. Syst. Neurosci..

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

[23]  D. Chialvo,et al.  Ising-like dynamics in large-scale functional brain networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  Narayan Srinivasa,et al.  Synaptic Plasticity Enables Adaptive Self-Tuning Critical Networks , 2015, PLoS Comput. Biol..

[26]  L. F. Abbott,et al.  Generating Coherent Patterns of Activity from Chaotic Neural Networks , 2009, Neuron.

[27]  O. Kinouchi,et al.  Optimal dynamical range of excitable networks at criticality , 2006, q-bio/0601037.

[28]  Woodrow L. Shew,et al.  Information Capacity and Transmission Are Maximized in Balanced Cortical Networks with Neuronal Avalanches , 2010, The Journal of Neuroscience.

[29]  W. Singer,et al.  Neuronal avalanches in spontaneous activity in vivo. , 2010, Journal of neurophysiology.

[30]  Pablo Balenzuela,et al.  Criticality in Large-Scale Brain fMRI Dynamics Unveiled by a Novel Point Process Analysis , 2012, Front. Physio..

[31]  M. A. Muñoz,et al.  Simple unified view of branching process statistics: Random walks in balanced logarithmic potentials. , 2016, Physical review. E.

[32]  John M. Beggs,et al.  Universal critical dynamics in high resolution neuronal avalanche data. , 2012, Physical review letters.

[33]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[34]  Benton,et al.  Criticality and scaling in evolutionary ecology. , 1997, Trends in ecology & evolution.

[35]  Robert A. Legenstein,et al.  2007 Special Issue: Edge of chaos and prediction of computational performance for neural circuit models , 2007 .

[36]  John M. Beggs,et al.  Being Critical of Criticality in the Brain , 2012, Front. Physio..

[37]  Michael J. Berry,et al.  Thermodynamics and signatures of criticality in a network of neurons , 2015, Proceedings of the National Academy of Sciences.

[38]  M. Magnasco,et al.  A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding , 2012, Proceedings of the National Academy of Sciences.

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

[40]  Tatyana O Sharpee,et al.  Critical and maximally informative encoding between neural populations in the retina , 2014, Proceedings of the National Academy of Sciences.

[41]  W. Bialek,et al.  Social interactions dominate speed control in poising natural flocks near criticality , 2013, Proceedings of the National Academy of Sciences.

[42]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[43]  Andreas Klaus,et al.  Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state , 2015, eLife.

[44]  H. Sompolinsky,et al.  Transition to chaos in random neuronal networks , 2015, 1508.06486.

[45]  R. Yuste,et al.  Neocortical activity is stimulus- and scale-invariant , 2017, PLoS ONE.