Quantifying Nonlinearity in C. elegans Neural Dynamics via Perturbations and Free Behavior

Abstract

In the pursuit to understand the physical mechanisms governing the brain, it is crucial that we develop rigorous, quantitative methods for studying the dynamics of neural activity. A powerful model organism upon which to build these analytical tools is the nematode Caenorhabditis elegans. Not only is C. elegans accompanied by a wealth of knowledge accumulated over decades of research, including a complete mapping of its neural connections, but it is also an organism that is anatomically and behaviorally positioned at a generative point in the spectrum of simplicity to complexity. Furthermore, it is one of only a few organisms in which whole-brain neural activity can be measured at cellular resolution. Numerous models have been used to fit and interpret these wholebrain recordings, with an important question in the construction of these models being the degree to which C. elegans neural dynamics are nonlinear. Both globally linear and piecewise-linear (nonlinear) models have been used to fit neural activity in immobilized C. elegans, yet these approaches yield disparate predictions about the effective linearity of the C. elegans brain. Here, we explore two parallel tracks with the shared aim of elucidating the necessity of nonlinear modeling for the neural dynamics of C. elegans. First, we compare two methods of modeling spontaneous neural activity in immobilized worms—a switching linear model and a controlled linear model—to assess which description more accurately reflects the true, biological framework of synaptic connections. We perform in silico single neuron perturbations to illustrate how the networks respond differently in each model when the stimulus is applied at different points in time. We then use Green’s functions to model these responses in a manner that is accessible more directly in experiments. We conclude by using the switching linear dynamical systems to analyze neural activity in freely moving worms and study the increased nonlinear characteristics of these richer, more complex neural dynamics as compared to those exhibited in immobilized worms.