Application of symbolic dynamics to characterize coordinated activity in the context of biological neural networks

The generation of coordinated patterns of activity in the nervous system is essential to drive complex behavior in animals, both vertebrates and invertebrates. In many cases rhythmic patterns of activity are the result of the cooperation between groups of small number of neurons bearing overall network dynamics. These patterns encode information in different spatio-temporal scales based on the history-dependent capabilities of neuronal dynamics. In this work we analyze a simple neural network, a Central Pattern Generator, by identifying and characterizing the dynamical patterns sustaining the coordination among the constituent neurons. The description of the corresponding coordination states is performed with the guidance of the theory of applied symbolic dynamics. We show that symbolic dynamics enables the automatic detection of meaningful events with low computational cost, endorsing the analysis of both individual and global neuronal dynamics. Furthermore, symbolic dynamics can be used to compute entropy and distinguish between networks with the same topology but different dynamics for the underlying nodes. The results obtained along the paper are not restricted to simple systems, and the proposed methodology can be applied to the generalization of closed-loop observation and control of complex biological systems.