Inferring the collective dynamics of neuronal populations from single-trial spike trains using mechanistic models

Multi-neuronal spike-train data recorded in vivo often exhibit rich dynamics as well as considerable variability across cells and repetitions of identical experimental conditions (trials). Efforts to characterize and predict the population dynamics and the contributions of individual neurons require model-based tools. Abstract statistical models allow for principled parameter estimation and model selection, but possess only limited interpretive power because they typically do not incorporate prior biophysical constraints. Here we present a statistically principled approach based on a population of doubly-stochastic integrate-and-fire neurons, taking into account basic biophysics. This model class comprises an idealized description for the dynamics of the neuronal membrane voltage in response to fast independent and slower shared input fluctuations. To efficiently estimate the model parameters and compare different model variants we compute the likelihood of observed single-trail spike trains by leveraging analytical methods for spiking neuron models combined with inference techniques for hidden Markov models. This allows us to reconstruct the shared input variations, classify their dynamics, obtain precise spike rate estimates, and quantify how individual neurons couple to the low-dimensional overall population dynamics, all from a single trial. Extensive evaluations based on simulated data show that our method correctly identifies the dynamics of the shared input process and accurately estimates the model parameters. Validations on ground truth recordings of neurons in vitro demonstrate that our approach successfully reconstructs the dynamics of hidden inputs and yields improved fits compared to a typical phenomenological model. Finally, we apply the method to a neuronal population recorded in vivo, for which we assess the contributions of individual neurons to the overall spiking dynamics. Altogether, our work provides statistical inference tools for a class of reasonably constrained, mechanistic models and demonstrates the benefits of this approach to analyze measured spike train data.