Balancing Stability and Flexibility: Dynamical Signatures of Learning in In-Vitro Neuronal Networks
Forough Habibollahi*1, Brett J. Kagan1
1Cortical Labs, Melbourne, Australia
*Email: forough@corticallabs.com
Introduction
CL1 is a novel system which bridges biological intelligence and adaptive neuronal traits by integrating in-vitro neuronal networks with in-silico computational elements using micro-electrode arrays (MEAs) [1]. These cultivated neuronal ensembles demonstrate self-organized, biological adaptive intelligence in dynamic gaming environments via closed-loop stimulation and concurrent recordings. While in-vitro neuronal networks are shown to achieve real-time adaptive learning, the underlying network dynamics enabling this learning remain under explored.
Methods We investigated pairwise causal relationships between recorded channels using Granger causality analysis [2], reconstructing a connectivity network from statistically significant causal interactions. The most influential/influenced nodes were identified as those with highest outgoing/incoming connections. To explore dynamic properties, we reconstructed the phase space of the spiking time series from all recorded channels using state-space reconstruction [3]. Optimal embedding dimensions were determined by minimizing false nearest neighbors, while time delays were selected by detecting the first local minimum of mutual information across different delays. Recurrence plots were generated from the reconstructed phase spaces to analyze temporal patterns. Results We analyzed 45-minute spiking recordings at 25 kHz from 23 neuronal cultures, comprising 111 rest sessions and 133 gameplay sessions. Across both rest and gameplay conditions, we observed distinct dynamic patterns between “influential” and “influenced” nodes. Overall, the gameplay sessions exhibited higher recurrence (RR) and determinism (DET) compared to rest (Fig. 1.a). However, in both conditions, the “influenced” nodes displayed lower RR and more negative Lyapunov exponents—indicative of more ordered behavior that lies farther from the edge of chaos. In contrast, the most influential nodes showed higher RR, reflecting recurrent and cyclic dynamics, and had small negative Lyapunov exponents, consistent with behavior near the edge of chaos (Fig 1.b.). Discussion Our findings reveal a functional dichotomy in in-vitro neuronal networks. Influential channels exhibit cyclic behavior near the edge of chaos, marked by high RR and near-zero negative Lyapunov exponents, balancing order and chaos. These “near-chaotic” nodes drive network dynamics, enabling rapid influence and adaptability.
In contrast, influenced channels remain more ordered, with lower recurrence and more negative Lyapunov exponents, suggesting stable responsiveness. This interplay between near-chaotic drivers and stable receivers enables neuronal cultures to balance robustness with adaptability. By defining how distinct dynamical states interact, our results shed light on coordinated neuronal activity and the role of near-chaotic dynamics in flexible behavior.
Figure 1. a) Comparison of dynamic metrics between rest and gameplay sessions. Bar plots show mean values (±SEM) for recurrence rate (RR), determinism (DET), laminarity (LAM), and Lyapunov exponent across all recorded electrodes. b) Dynamic properties of influential vs. influenced nodes across rest and gameplay conditions. Acknowledgements F.H. and B.J.K. are employees of Cortical Labs. B.J.K. is a shareholder of Cortical Labs. B.J.K. holds an interest in patents related to this publication. References [1]https://doi.org/10.1016/j.neuron.2022.09.001 [2]https://doi.org/10.2307/1912791 [3]https://doi.org/10.1007/BFb0091924
