CNS*2026 Halifax

Pablo Sanchez-Martin^*1, Alicia Garrido-Peña¹, Irene Elices¹, Carlos Garcia-Saura¹, Rafael Levi¹, Francisco B. Rodriguez¹, Pablo Varona<sup>1 

1</sup>Grupo de Neurocomputación Biológica (GNB), Department of Computer Engineering, Universidad Autónoma de Madrid, Madrid, Spain

^*Email: [email protected]

Introduction
Rhythmic sequential activity is present in many nervous systems. Neural circuits that generate this activity usually involve intrinsic neuronal variability and different synapse types [1]. Sequential rhythms often require coordination at different time scales to adapt to specific conditions, or to adjust speed and timing to meet functional needs. Previous studies in computational models have assessed how synchronization and excitability can modulate cycle-by-cycle sequential dynamical invariants [2,3]. In this study, we analyzed the interplay among neural synchronization, excitability, and variability to understand how they are related to the sequentiality timing in CPG rhythms.

Methods
We acquired long recordings of pyloric CPG neurons of  Carcinus maenas  and extracted the spike timings from intracellular and extracellular time series followed by calculation of all sequence intervals between the PD neurons and the LP. We used metrics of synchronization between the electrically coupled PDs (Victor-Purpura distance, Euclidean distance), excitability for all three neurons (Spike Density Function -SDF-, average ISIs), and interval variability. We identified dynamical invariants in the form of relationships between specific intervals and the instantaneous period. To find relationships between these metrics, we performed analysis at three time scales: whole experiment, segments inside experiments, and cycle-by-cycle analysis.

Results
We observed a high level of variability for synchronization, excitability, and the intervals in this system. Ranking each experiment for all metrics revealed a relationship between the variability in the period, the neurons’ SDF, and the strength of the dynamical invariant relationship. Segmenting the data, we found that, in addition to these relationships, synchronization in the PD neurons is related to their excitability. We found non-linear relationships between the excitability of all neurons and their period variability and dynamical invariants. Excitability changes in any neuron were related to the other neurons' excitability at each cycle, although other relationships present at larger time scales were not preserved cycle-by-cycle.

Discussion
It is still unclear how robustness and flexibility can be autonomously balanced in neural sequences. Previous works have found evidence that suggests that connectivity asymmetry, i.e., the presence of both slow and fast synapses, could be responsible for the emergence of coordination rules such as sequential dynamical invariants [2, 3]. The LPPDdelay interval and instantaneous period are related cycle-by-cycle, as well as the excitability of all neurons among them. In an intermediate scale, the excitability is non-linearly related to synchronization, variability and strength of the dynamical invariants. In a larger time scale, excitability, variability, and the strength of dynamical invariants are all related, but not synchronization.

References
[1] Selverston, A. I., Rabinovich, M. I., Abarbanel, H. D., Elson, R., Szücs, A., Pinto, R. D., ... & Varona, P. (2000). Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. Journal of Physiology-Paris, 94(5-6), 357-374. 
[2] Berbel, B., Latorre, R., & Varona, P. (2025). Theoretical bases for the relation between excitability, variability and synchronization in sequential neural dynamics. Neurocomputing, 645, 130218. 
[3] Elices, I., Levi, R., Arroyo, D., Rodriguez, F. B., & Varona, P. (2019). Robust dynamical invariants in sequential neural activity. Scientific Reports, 9(1), 9048. 

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