Effective Stochastic Models of Neuroscientific Data with Application to Weakly Electric Fish

Abstract

Neural systems are often stochastic, non-linear, and non-autonomous. The complex manifestation of these aspects hinders the interpretation of neuroscientific data. Neuroscience thus benefits from the inclusion of theoretical models in its methodology. Detailed biophysical models of neural systems, however, are often plagued by high-dimensional and poorly constrained parameter spaces. As an alternative, data-driven effective models can often explain the core dynamical features of a dataset with few underlying assumptions. By lumping high-dimensional fluctuations into low-dimensional stochastic terms, observed time-series can be well-represented by stochastic dynamical systems. Here, I apply this approach to two datasets from weakly electric fish. The rate of electrosensory sampling of freely behaving fish displays spontaneous transitions between two preferred values: an active exploratory state and a resting state. I show that, over a long timescale, this rate can be modelled with a stochastic double-well system where a slow external agent modulates the relative depth of the wells. On a shorter timescale, however, fish exhibit abrupt and transient increases in sampling rate not consistent with a diffusion process. I develop and apply a novel inference method to construct a jump-diffusion process that fits the observed fluctuations. This same technique is successfully applied to intrinsic membrane voltage noise in pyramidal neurons of the primary electrosensory processing area, which display abrupt depolarization events along with diffusive fluctuations. I then characterize a novel sensory acquisition strategy whereby fish adopt a rhythmic movement pattern coupled with stochastic oscillations of their sampling rate. Lastly, in the context of differentiating between self-generated and external electrosensory signals, I model the sensory signature of communication signals between fish. This analysis provides supporting evidence for the presence of a sensory ambiguity associated with these signals.