Functionality, Robustness and Control of Nonlinear Network Dynamics: Modeling and Understanding the C. elegans Connectome

Abstract

Networks of many nonlinearly-coupled dynamical components are ubiquitous in the physical sciences, but often difficult to characterize. However, their dynamics are often low-dimensional, being dominated by a few functional, coherent patterns. We wish to understand: (1) How do nonlinear networks generate functional responses? (2) What role does the network's structure play in generating such responses? (3) To what extent are the network dynamics robust to network damage? Towards these ends we model the C. elegans neuronal network, the connectivity of which is known. Chapter 2 constructs a full-Connectome dynamical model which can generate proxies for known behaviors (specifically demonstrating a proxy for forward motion). Chapter 3 explores the input space via interpretable bifurcation diagrams. The highly multistable dynamics give rise to long transient timescales (orders of magnitude longer than intrinsic nodal timescales). Chapter 4 models network injuries, which significantly distort dynamics. We develop a metric to quantify the injury level and help predict an injury's functional outcome. Chapter 5 uses Dynamic Mode Decomposition to relate connectivity to low-dimensional dynamical structure. In the process, we demonstrate consistency with proprioception-driven locomotion which is facilitated by network structure.