Locally embedded presages of global network bursts

Significance This paper reports an approach to detecting the “early warnings” of upcoming global state transitions in a network based on its local dynamics, demonstrating that seemingly stochastic global events can be predicted by local deterministic dynamics. Based on the method using a nonlinear state-space reconstruction, we show that, surprisingly, dynamics of individual neurons can robustly predict the upcoming synchronous burst in the neural population at high signal-to-noise ratios, which even outperform the predictions based on population activity. We explain this apparently counterintuitive property by the network structures realizing in the nonbursting period, which is supported by a manipulative experiment and analyses. These results reveal basic properties of the bursting network dynamics. Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially nonbursting network state is not fully understood. In this study, we develop a state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in “local” dynamics of individual neurons during nonbursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean-field activity for predicting future global bursts. Moreover, the intercell variability in the burst predictability is found to reflect the network structure realized in the nonbursting periods. These findings suggest that deterministic local dynamics can predict seemingly stochastic global events in self-organized networks, implying the potential applications of the present methodology to detecting locally concentrated early warnings of spontaneous seizure occurrence in the brain.

[1]  T. H. Brown,et al.  Giant synaptic potential hypothesis for epileptiform activity. , 1981, Science.

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

[3]  Woodrow L. Shew,et al.  Maximal Variability of Phase Synchrony in Cortical Networks with Neuronal Avalanches , 2012, The Journal of Neuroscience.

[4]  T.B. DeMarse,et al.  MeaBench: A toolset for multi-electrode data acquisition and on-line analysis , 2005, Conference Proceedings. 2nd International IEEE EMBS Conference on Neural Engineering, 2005..

[5]  G Sugihara,et al.  Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Hisashi Arakaki,et al.  The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process , 2012 .

[7]  Andreas Hierlemann,et al.  Switch-Matrix-Based High-Density Microelectrode Array in CMOS Technology , 2010, IEEE Journal of Solid-State Circuits.

[8]  D. Plenz,et al.  Spontaneous cortical activity in awake monkeys composed of neuronal avalanches , 2009, Proceedings of the National Academy of Sciences.

[9]  Andreas Hierlemann,et al.  Compact Voltage and Current Stimulation Buffer for High-Density Microelectrode Arrays , 2010, IEEE Transactions on Biomedical Circuits and Systems.

[10]  D. Chialvo.  Emergent complex neural dynamics , 2010, 1010.2530.

[11]  Henry D I Abarbanel,et al.  False neighbors and false strands: a reliable minimum embedding dimension algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[13]  C. Elger,et al.  Seizure prediction by non‐linear time series analysis of brain electrical activity , 1998, The European journal of neuroscience.

[14]  C. Elger,et al.  Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. , 1995, Electroencephalography and clinical neurophysiology.

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

[16]  John M. Beggs,et al.  Behavioral / Systems / Cognitive Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures , 2004 .

[17]  George Sugihara,et al.  Detecting Causality in Complex Ecosystems , 2012, Science.

[18]  John Rinzel,et al.  Intrinsic and network rhythmogenesis in a reduced traub model for CA3 neurons , 2004, Journal of Computational Neuroscience.

[19]  J. Lisman.  Bursts as a unit of neural information: making unreliable synapses reliable , 1997, Trends in Neurosciences.

[20]  G. Sugihara,et al.  Generalized Theorems for Nonlinear State Space Reconstruction , 2011, PloS one.

[21]  George Sugihara,et al.  Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling , 2015, Proceedings of the National Academy of Sciences.

[22]  F. Dudek,et al.  Interictal Spikes and Epileptogenesis , 2006, Epilepsy currents.

[23]  J. Elsner,et al.  Nonlinear prediction as a way of distinguishing chaos from random fractal sequences , 1992, Nature.

[24]  N. Crone,et al.  Network dynamics of the brain and influence of the epileptic seizure onset zone , 2014, Proceedings of the National Academy of Sciences.

[25]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[26]  Mu-ming Poo,et al.  Self-Control in Decision-Making Involves Modulation of the vmPFC Valuation System , 2012 .

[27]  Rodney J. Douglas,et al.  Synchronization of Bursting Action Potential Discharge in a Model Network of Neocortical Neurons , 1991, Neural Computation.

[28]  Jaume Casademunt,et al.  Noise focusing and the emergence of coherent activity in neuronal cultures , 2013, Nature Physics.

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

[30]  Thomas Nowotny,et al.  Dynamical origin of independent spiking and bursting activity in neural microcircuits. , 2007, Physical review letters.

[31]  George Sugihara,et al.  Distinguishing time-delayed causal interactions using convergent cross mapping , 2015, Scientific Reports.

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

[33]  Danah Boyd,et al.  Tweet, Tweet, Retweet: Conversational Aspects of Retweeting on Twitter , 2010, 2010 43rd Hawaii International Conference on System Sciences.

[34]  Jie Zhou,et al.  Influence of network structure on rumor propagation , 2007 .

[35]  John Rinzel,et al.  Intrinsic and network rhythmogenesis in a reduced traub model for CA3 neurons , 1995, Journal of Computational Neuroscience.

[36]  Ofer Feinerman,et al.  Identification and dynamics of spontaneous burst initiation zones in unidimensional neuronal cultures. , 2007, Journal of neurophysiology.

[37]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.

[38]  K. Harris,et al.  Spontaneous Events Outline the Realm of Possible Sensory Responses in Neocortical Populations , 2009, Neuron.

[39]  Hirokazu Takahashi,et al.  Parameters for burst detection , 2014, Front. Comput. Neurosci..

[40]  C. Stam,et al.  Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field , 2005, Clinical Neurophysiology.

[41]  Toru Yanagawa,et al.  Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding , 2015, PLoS Comput. Biol..

[42]  R. Miles,et al.  Single neurones can initiate synchronized population discharge in the hippocampus , 1983, Nature.

[43]  B. Connors,et al.  Initiation, Propagation, and Termination of Epileptiform Activity in Rodent Neocortex In Vitro Involve Distinct Mechanisms , 2005, The Journal of Neuroscience.

[44]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[45]  Ryohei Kanzaki,et al.  Light-addressed single-neuron stimulation in dissociated neuronal cultures with sparse expression of ChR2 , 2012, Biosyst..

[46]  U. Frey,et al.  Tracking axonal action potential propagation on a high-density microelectrode array across hundreds of sites , 2013, Nature Communications.

[47]  Jean-Pierre Eckmann,et al.  Leader neurons in population bursts of 2D living neural networks , 2008 .

[48]  P. Taylor,et al.  Phase space approach for modeling of epileptic dynamics. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  G Sugihara,et al.  Distinguishing error from chaos in ecological time series. , 1990, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[50]  D. McCormick,et al.  On the cellular and network bases of epileptic seizures. , 2001, Annual review of physiology.

[51]  J. D. Farmer,et al.  State space reconstruction in the presence of noise" Physica D , 1991 .

[52]  E. Lorenz.  Atmospheric Predictability as Revealed by Naturally Occurring Analogues , 1969 .

[53]  H. Ye,et al.  Information leverage in interconnected ecosystems: Overcoming the curse of dimensionality , 2016, Science.

[54]  Yuji Ikegaya,et al.  Synfire Chains and Cortical Songs: Temporal Modules of Cortical Activity , 2004, Science.

[55]  Danny Eytan,et al.  Dynamics and Effective Topology Underlying Synchronization in Networks of Cortical Neurons , 2006, The Journal of Neuroscience.

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

[57]  Frank C. Hoppensteadt,et al.  Bursts as a unit of neural information: selective communication via resonance , 2003, Trends in Neurosciences.