Self-regulated homoclinic chaos in neural networks activity

Vladislav Volman
2004 AIP Conference Proceedings  
We compare the recorded activity of cultured neuronal networks with hybridized model simulations, in which the model neurons are driven by the recorded activity of special neurons. The latter, named 'spiker' neurons, that exhibit fast firing with homoclinic chaos like characteristics, are expected to play an important role in the networks' self regulation. The cultured networks are grown from dissociated mixtures of cortical neurons and glia cells. Despite the artificial manner of their
more » ... er of their construction, the spontaneous activity of these networks exhibits rich dynamical behavior, marked by the formation of temporal sequences of synchronized bursting events (SBEs), and additional features which seemingly reflect the action of underlying regulating mechanism, rather than arbitrary causes and effects. Our model neurons are composed of soma described by the two Morris-Lecar dynamical variables (voltage and fraction of open potassium channels), with dynamical synapses described by the Tsodyks-Markram three variables dynamics. To study the recorded and simulated activities we evaluated the inter-neuron correlation matrices, and analyzed them utilizing the functional holography approach: the correlations are re-normalized by the correlation distances -Euclidean distances between the matrix columns. Then, we project the N-dimensional (for N channels) space spanned by the matrix of re-normalized correlations, or correlation affinities, onto a corresponding 3-D causal manifold (3-D Cartesian space constructed by the 3 leading principal vectors of the N-dimensional space. The neurons are located by their principal eigenvalues and linked by their original (not-normalized) correlations. This reveals hidden causal motifs: the neuron locations and their links form simple structures. Similar causal motifs are exhibited by the model simulations when feeded by the recorded activity of the spiker neurons. We illustrate that the homoclinic chaotic behavior of the spiker neurons can be generated by glia-regulated self-synapses. Since in real networks the glia are regulated back by the networks' neuronal activity, our findings hint that the structure of the causal manifolds in the affinity space is self-regulated via collective regulation of the homoclinic behavior of the spiker neurons. We further propose that the existence of such simple causal motifs in the complex activity of stand-alone cultured networks calls for a new view of the neuro-glia interactions, where linked neurons and glia cells function as a hybridized fabric by which information is co-processed.
doi:10.1063/1.1846477 fatcat:mr6enpi2prhtpfmw5ya3f7yreu