Quantitative prediction of intracellular dynamics and synaptic currents in a small neural circuit

Fitting models to experimental intracellular data is challenging. While detailed conductance-based models are difficult to train, phenomenological statistical models often fail to capture the rich intrinsic dynamics of circuits such as central pattern generators (CPGs). A recent trend has been to employ tools from deep learning to obtain data-driven models that can quantitatively learn intracellular dynamics from experimental data. This paper addresses the general questions of modeling, training, and interpreting a large class of such models in the context of estimating the dynamics of a neural circuit. In particular, we use recently introduced Recurrent Mechanistic Models to predict the dynamics of a Half-Center Oscillator (HCO), a type of CPG. We construct the HCO by interconnecting two neurons in the Stomatogastric Ganglion using the dynamic clamp experimental protocol. This allows us to gather ground truth synaptic currents, which the model is able to predict-even though these currents are not used during training. We empirically assess the speed and performance of the training methods of teacher forcing, multiple shooting, and generalized teacher forcing, which we present in a unified fashion tailored to data-driven models with explicit membrane voltage variables. From a theoretical perspective, we show that a key contraction condition in data-driven dynamics guarantees the applicability of these training methods. We also show that this condition enables the derivation of data-driven frequency-dependent conductances, making it possible to infer the excitability profile of a real neuronal circuit using a trained model.