The Analysis of Neural Heterogeneity Through Mathematical and Statistical Methods

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach. Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network (different effects from presynaptic inputs). From a phase-reduced model, I derive asymptotic approximations of the firing rate statistics assuming weak noise and coupling. I then qualitatively validate them with high-dimensional network simulations. My analytic calculations reveal how the interaction between intrinsic and network heterogeneity results in different firing rate distributions. Turning to the statistical approach, I examine the data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli. Using a generalized linear model (GLM) to encode stimuli into firing rate intensity, I then assess the accuracy of the Bayesian decoding of the stimulus from spike trains of various networks. For a variety of fixed network sizes and various metrics, I generally find that the optimal levels of heterogeneity are at intermediate values. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R2 values. Taken together, intermediate levels of neural heterogeneity is indeed a prominent attribute for efficient coding, but the performance is highly variable