Theoretical bases for the relation between excitability, variability and synchronization in sequential neural dynamics

Functional neural rhythms arise from the excitability of individual neurons and the collective dynamics of the circuits in which they are embedded. The self-organization of neural networks can be best investigated in circuits where these two aspects can be elucidated. In this context, Central Pattern Generators (CPGs) are an ideal model system where the interplay between synaptic and ionic currents shapes robust yet flexible rhythmic sequences underlying a wide range of motor functions. CPGs often integrate both chemical and electrical synapses, forming closed-loop network topologies that autonomously generate and coordinate functional rhythms. Recent findings in CPGs show the existence of sequential dynamical invariants, which are robust relationships between specific time intervals that build the rhythmic sequence constraining their cycle-by-cycle variability. However, the precise mechanisms by which electrical and chemical synapses interact to modulate sequential neural dynamics remain largely unknown. This modeling study examines the role of electrical currents in rhythm modulation within CPGs, with a particular focus on how these currents influence neural excitability and, in turn, modulate the variability of the rhythmic pattern on a cycle-by-cycle basis. We show that changes in neuronal excitability induced by electrical currents can modulate dynamical invariants, leading to the emergence of distinct sequence interval relationships that facilitate the rhythm adaptability. Synchronization between electrically coupled neurons is thus a key factor in regulating these effects. Finally, our results show that sequential dynamical invariants sustain the balance between excitability, variability, and synchronization, underscoring their essential role in the adaptive coordination of functional neural rhythmic patterns. • Electrical coupling modulates excitability in sequential neural dynamics. • Both electrical and chemical synapses shape cycle-by-cycle time interval variability. • Neuronal synchronization affects sequential intervals and individual firing patterns. • Flexible rhythms emerge from dynamical invariants constraining sequential intervals. • Changes in neuronal excitability lead to new sequential dynamical invariants.