Effective excitability captures network dynamics across development and phenotypes

Neuronal cultures in vitro are a versatile system for studying the fundamental properties of individual neurons and neuronal networks. Recently, this approach has gained attention as a precision medicine tool. Mature neuronal cultures in vitro exhibit synchronized collective dynamics called network bursting. If analyzed appropriately, this activity could offer insights into the network's properties, such as its composition, topology, and developmental and pathological processes. A promising method for investigating the collective dynamics of neuronal networks is to map them onto simplified dynamical systems. This approach allows the study of dynamical regimes and the characteristics of the parameters that lead to data-consistent activity. We designed a simple biophysically inspired dynamical system and used Bayesian inference to fit it to a large number of recordings of in vitro population activity. Even with a small number of parameters, the model showed strong inter-parameter dependencies leading to invariant bursting dynamics for many parameter combinations. We further validated this observation in our analytical solution. We found that in vitro bursting can be well characterized by each of three dynamical regimes: oscillatory, bistable, and excitable. The probability of finding a data-consistent match in a particular regime changes with network composition and development. The more informative way to describe the in vitro network bursting is the effective excitability, which we analytically show to be related to the parameter-invariance of the model's dynamics. We establish that the effective excitability can be estimated directly from the experimentally recorded data. Finally, we demonstrate that effective excitability reliably detects the differences between cultures of cortical, hippocampal, and human pluripotent stem cell-derived neurons, allowing us to map their developmental trajectories. Our results open a new avenue for the model-based description of in vitro network phenotypes emerging across different experimental conditions.