Statistical complexity and connectivity relationship in cultured neural networks

Abstract We explore the interplay between the topological relevance of a neuron and its dynamical traces in experimental cultured neuronal networks. We monitor the growth and development of these networks to characterise the evolution of their connectivity. Then, we explore the structure-dynamics relationship by simulating a biophysically plausible dynamical model on top of each networks’ nodes. In the weakly coupling regime, the statistical complexity of each single node dynamics is found to be anti-correlated with their degree centrality, with nodes of higher degree displaying lower complexity levels. Our results imply that it is possible to infer the degree distribution of the network connectivity only from individual dynamical measurements.

[1]  C. Letellier.  Symbolic sequence analysis using approximated partition , 2008 .

[2]  E. Hulata,et al.  Coemergence of regularity and complexity during neural network development , 2007, Developmental neurobiology.

[3]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[4]  Dane Taylor,et al.  Optimal synchronization of complex networks. , 2014, Physical review letters.

[5]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

[6]  J. M. Sancho,et al.  Emergent bimodal firing patterns implement different encoding strategies during gamma-band oscillations , 2012, Front. Comput. Neurosci..

[7]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[8]  Alex Arenas,et al.  Paths to synchronization on complex networks. , 2006, Physical review letters.

[9]  Olaf Sporns,et al.  Network attributes for segregation and integration in the human brain , 2013, Current Opinion in Neurobiology.

[10]  Morten L. Kringelbach,et al.  The most relevant human brain regions for functional connectivity: Evidence for a dynamical workspace of binding nodes from whole-brain computational modelling , 2017, NeuroImage.

[11]  Amir Ayali,et al.  Emergence of Small-World Anatomical Networks in Self-Organizing Clustered Neuronal Cultures , 2013, PloS one.

[12]  G. Edelman,et al.  A measure for brain complexity: relating functional segregation and integration in the nervous system. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[13]  M. Corner,et al.  Dynamics and plasticity in developing neuronal networks in vitro. , 2005, Progress in brain research.

[14]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[15]  I Leyva,et al.  Effective centrality and explosive synchronization in complex networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  M. Burrows.  The Neurobiology of an Insect Brain , 1996 .

[17]  O Sporns,et al.  Predicting human resting-state functional connectivity from structural connectivity , 2009, Proceedings of the National Academy of Sciences.

[18]  J M Buldú,et al.  Synchronization interfaces and overlapping communities in complex networks. , 2008, Physical review letters.

[19]  Amir Ayali,et al.  Graph‐based unsupervised segmentation algorithm for cultured neuronal networks' structure characterization and modeling , 2015, Cytometry. Part A : the journal of the International Society for Analytical Cytology.

[20]  Amir Ayali,et al.  The locust frontal ganglion: a central pattern generator network controlling foregut rhythmic motor patterns. , 2002, The Journal of experimental biology.

[21]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[22]  F del Pozo,et al.  Topological measure locating the effective crossover between segregation and integration in a modular network. , 2012, Physical review letters.

[23]  Alex Arenas,et al.  Synchronization reveals topological scales in complex networks. , 2006, Physical review letters.

[24]  Morten L. Kringelbach,et al.  Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs , 2016, Scientific Reports.

[25]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[26]  A. Ayali,et al.  The role of gap junction proteins in the development of neural network functional topology , 2013, Insect molecular biology.

[27]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[28]  O. Sporns,et al.  Network hubs in the human brain , 2013, Trends in Cognitive Sciences.

[29]  Osvaldo A. Rosso,et al.  Statistical complexity and disequilibrium , 2003 .

[30]  Jean-Pierre Eckmann,et al.  The physics of living neural networks , 2007, 1007.5465.

[31]  A. Pluchino,et al.  CHANGING OPINIONS IN A CHANGING WORLD: A NEW PERSPECTIVE IN SOCIOPHYSICS , 2004 .

[32]  Javier M. Buldú,et al.  Functional brain networks: great expectations, hard times and the big leap forward , 2014, Philosophical Transactions of the Royal Society B: Biological Sciences.

[33]  J. Kurths,et al.  Synchronization in networks of mobile oscillators. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Francesco Sorrentino,et al.  Cluster synchronization and isolated desynchronization in complex networks with symmetries , 2013, Nature Communications.

[35]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[36]  F. Varela,et al.  Perception's shadow: long-distance synchronization of human brain activity , 1999, Nature.

[37]  T. Pereira.  Hub synchronization in scale-free networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  J. Kurths,et al.  Hierarchical synchronization in complex networks with heterogeneous degrees. , 2006, Chaos.

[39]  Marc Timme,et al.  Self-organized synchronization in decentralized power grids. , 2012, Physical review letters.

[40]  J M Buldú,et al.  Synchronization waves in geometric networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  L. Pecora.  Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems , 1998 .