Asymmetry Factors Shaping Regular and Irregular Bursting Rhythms in Central Pattern Generators

Central Pattern Generator (CPG) circuits are neural networks that generate rhythmic motor patterns. These circuits are typically built of half-center oscillator subcircuits with reciprocally inhibitory connections. Another common property in many CPGs is the remarkable rich spiking-bursting dynamics of their constituent cells, which balance robustness and flexibility to generate their joint coordinated rhythms. In this paper, we use conductance-based models and realistic connection topologies inspired by the crustacean pyloric CPG to address the study of asymmetry factors shaping CPG bursting rhythms. In particular, we assess the role of asymmetric maximal synaptic conductances, time constants and gap-junction connectivity to establish the regularity of half-center oscillator based CPGs. We map and characterize the synaptic parameter space that lead to regular and irregular bursting activity in these networks. The analysis indicates that asymmetric configurations display robust regular rhythms and that large regions of both regular and irregular but coordinated rhythms exist as a function of the asymmetry in the circuit. Our results show that asymmetry both in the maximal conductances and in the temporal dynamics of mutually inhibitory neurons can synergistically contribute to shape wide regimes of regular spiking-bursting activity in CPGs. Finally, we discuss how a closed-loop protocol driven by a regularity goal can be used to find and characterize regular regimes when there is not time to perform an exhaustive search, as in most experimental studies.