Robust dynamical invariants in sequential neural activity

By studying different sources of temporal variability in central pattern generator circuits, in this paper we unveil distinct aspects of the instantaneous balance between flexibility and robustness in sequential dynamics –a property that characterizes many systems that display neural rhythms. The level of irregularity and coordination was characterized using intrinsic time references and intervals in long recordings of the pyloric central pattern generator. The analysis demonstrated strong robustness of transient dynamics in keeping not only the activation sequences but also specific cycle-by-cycle temporal relationships in the form of dynamical invariants. The rich dynamics of neurons and connections balance flexibility and coordination to readily negotiate the interactions between neurons and produce the resultant rhythm. In particular, two dynamical invariants were identified between time intervals that build the sequence, existing even outside steady states. We suggest that invariant temporal sequence relationships could be present in other networks, including those related to brain rhythms, and underlie rhythm programming and functionality.