self regulated learning (SRL)

Self-regulated homoclinic chaos in neural
networks activity

Vladislav Volman, Itay Baruchi and Eshel Ben-Jacob
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy,
Tel-Aviv University, Tel-Aviv 69978, Israel
Abstract. 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 construction, the spontaneous activity of these networks exhibits rich dynamical behav-
ior, 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 dynam-
ical 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 uti-
lizing 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 prin-
cipal 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.