CNS*2026 Halifax

Introduction
Bursting neural activity is widely expressed in many neural systems and has been proposed to underlie reliable information multiplexing, propagation, and execution. This type of neural activity typically involves interactions at slow and fast timescales. In the context of central pattern generators (CPGs), bursting is part of the sequential motor control mechanisms responsible for respiration, locomotion, chewing, and other key motor tasks. In various CPGs, sequential dynamical invariants in the form of cycle-by-cycle relationships between specific intervals have been identified. These invariants are thought to balance sequence robustness with flexibility by creating timing constraints to the events that compose the sequence [1,2,3].

Methods
We combined models and experiments to examine how modulations introducing trends in the CPG rhythm shape the cycle-by-cycle and cross-cycle structure of these invariants. We quantified the variability of the intervals forming the sequence between the LP and PD neurons, as well as their pairwise invariant relationships in the pyloric CPG and also in a conductance-based model [4]. Relationships between intervals belonging to the same and to different cycles were assessed in experiments and in the model where ionic and synaptic currents were linked to interval durations. Invariants were identified with pairplots and quantified using the coefficient of determination R².

Results
We show that, both in computational models and electrophysiological experiments, sequential dynamical invariants are generally present only between intervals that compose the sequence within the same cycle. Only when a slow external modulation introduces a trend can intervals from different cycles become related. This is observed when modulation arises naturally or is experimentally induced in the pyloric CPG, and when a slow modulating current is injected into the model CPG. Model ionic and synaptic currents reset in every cycle and do not influence intervals in the next one, but modulating the CPG causes intervals to be related across cycles.

Discussion
Assessing sequential dynamical invariants is key to understanding the autonomous coordination of rhythmic motor sequences produced by CPGs. Not all intervals in the sequence are related, which contributes to the timing flexibility within the constraints of the invariants. The persistence of relationships between intervals across cycles can serve as a means to characterize CPG modulation. Combining models and electrophysiological experiments, we established the conditions under which sequential intervals can be related both cycle-by-cycle and across cycles when perturbations introduce trends in the CPG rhythm. These results are also relevant for bio-inspired robotics, where such principles could support autonomous motor control.

References
[1] Elices et al (2019). doi:https://doi.org/10.1038/s41598-019-44953-2.
[2] Berbel et al (2025). doi:https://doi.org/10.1016/j.neucom.2025.130218.
[3] Garrido-Peña et al (2021). doi:https://doi.org/10.1016/j.neucom.2020.08.093.
[4] Deistler et al (2022). doi:https://doi.org/10.1073/pnas.2207632119.

Acknowledgement
Research funded by grants PID2024-155923NB-I00, PID2023-149669NB-I00, CPP2023-010818 (MCIN/AEI and ERDF- "A way of making Europe").