C. elegans locomotion : an integrated approach

he popular model organism Caenorhabditis elegans is a tiny nematode worm with a largely invariant nervous system, consisting of exactly 302 neurons with known connectivity. Moreover, the behavioural roles of many of these neurons have been uncovered using experimental techniques including targeted cell killing and genetic mutations. The result is an organism in which the locomotion subsystem is mapped at cellular resolution. Despite its small size and the apparent simplicity of the underlying nervous system, the worm is capable of a surprisingly rich repertoire of behaviours including navigation and foraging, mating, learning, and even rudimentary social behaviour. Indeed, this humble worm provides us with the first tangible possibility of understanding the complex behaviours of an organism from the genetic level, right up to the system level. The focus of this thesis on the locomotion system is motivated at least in part by the fact that most, if not all, of the worm’s behaviours are mediated by some form of locomotion. The main objective of this thesis is to help elucidate the mechanisms underlying C. elegans forward locomotion. In pursuit of this goal I apply an integrated methodology that emphasises collaboration between modellers like myself and experimentalists, ensuring that models are grounded in the biological reality and experiments are well designed and poignant. In contrast to previous models of C. elegans forward locomotion, the starting point of this investigation is the realization that the ability of the worm to locomote through a variety of different physical environments can shed light on the mechanism of neural and neuromuscular control of this behaviour. This work therefore begins with the presentation of several stand-alone studies, both theoretical and experimental, aimed at answering a number of preliminary questions. These include the development of a suitable model of the worm’s low Reynolds number physical environments; a preliminary study of the importance of body physics on the kinematics of locomotion; an electrophysiological modelling study of the worm’s body wall muscles; and an experimental investigation of the worm’s locomotion in different environments, ranging from liquid to dense gels. These results lead to a new perspective on the worm’s locomotion. Indeed, the conventional wisdom is that two kinematically distinct C. elegans locomotion behaviours – swimming in liquids and crawling on dense gel-like media – correspond to distinct locomotory gaits. By analysing the worm’s motion through these different media, we reveal a smooth modulation of the undulations from swimming to crawling, marked by a linear relationship between key locomotion metrics. These results point to a single locomotory gait, governed by the same underlying control mechanism. The core of this thesis is an integrated neuromechancial model of C. elegans forward locomotion. This model incorporates the results of the preliminary investigation of muscle, body and locomotion properties. The neural circuitry is grounded in the literature but simplified to a set of repeating units. Neuronal properties are modelled at different levels of abstraction, with a proof-of-concept continuous model that is used to ground assumptions in physiological data, and a simplified binary model that is then used to study the locomotion control in detail. A key property of the motor neurons in both these models is their bistable response, inspired by a recent publication demonstrating such properties in other motor neurons. Interestingly, the model is quite different to any that have come before, both in terms of its underlying neural dynamics and the behaviours that it addresses. The key achievement of this model is its ability to qualitatively and quantitatively account for locomotion across a range of media from water to agar, as well as in more complex (heterogeneous) environments. One particularly interesting result is the demonstration that a proprioceptive oscillatory mechanisms can account not only for the generation of the body undulation, but also the observed modulation in response to the changing physical environments. Indeed, this model lacks any form of centrally generated nervous system control. Finally, the model makes a number of important predictions about neuronal functions, synaptic functions and the proprioceptive response to different physical environments. A number of experiments and experimental designs are suggested to test these predictions. Preliminary experimental results are then presented to address each of these predictions. To date, these results all appear to validate the model and uncover new information about the locomotion system, hence demonstrating the power of the holistic, integrated methodology of this work. Specifically I address the role of the inhibitory D-class neurons and find evidence suggesting that they are part of the core circuit for forward locomotion, but that the phenotype associated with their removal only manifests strongly in less resistive (more fluid) media. Furthermore, I shed light on the relative roles of neural and muscle inhibition and suggest that it may be an absence of neural inhibition that underlies the forward locomotion defect of GABA defective worms.