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Abstract

Cultured networks of neurons are one of the basic neural systems that exhibit population dynamics. A collective phenomenon that robustly emerges in cultured neural networks is called network bursting. This type of activity consists of bursts that rapidly propagate through the network and long, irregular periods of quiescence. The temporal footprint of network bursting is highly variable across different culture preparations [1]. Despite a long history of modeling different aspects of population activity in cultures, a unified picture of how to map the variability of culture dynamics is currently missing.

To portray the variability observed across different preparations experimentally we focused on a simplified population model fitted to the experimental data by the Bayesian parameter inference. The simplified model was composed of a leak term with sigmoid non-linearity and activity-dependent adaptation term. Driven by white noise, the model is capable of reproducing the main aspects of the average temporal population bursting [3].

The model can exhibit both noise-driven limit cycle and noise-driven bistable regimes, which closely resemble experimentally recorded temporal dynamics. We analytically study the distribution of inter-burst intervals (IBI) in the reduced model. We apply mean escape time calculations and survival analysis [2]. Assuming the separation of timescales, we estimated the distributions of transitions between bursting and non-bursting states and approximated the distribution of IBI.

As a next step, we study the dependencies between model parameters and features of the collective dynamics. We estimated the posterior distribution of parameters using simulation-based inference. In particular, we fit a conditional density estimator to predict the distribution of excitability and adaptation strength given a set of summary statistics [4]. The surrogate model allows us to estimate an amortized posterior and study it for different summary statistics. We find that the activity regime with low irregularity is close to the saddle-node bifurcation, whereas the irregular patterns are closer to the Hopf-bifurcation.

Overall, our results show that the variability of temporal dynamics can be matched with a simplified 2D model of population activity. We find that the system close to either Hopf or saddle-node bifurcations in presence of additive noise exhibit behavior that is consistent with experimental data.