Multiscale Modelling of Biological Rhythms and Systems

Abstract

Living organisms possess the remarkable ability to both respond to rhythms and generate them. In some instances, unintended rhythms arise, leading to undesirable or even hazardous consequences, such as synchronized neuronal firing during epilepsy. However, in other cases, such biological rhythms are beneficial in regulating essential processes across all life forms. From bacteria to humans, rhythms permeate various aspects of life, influencing everything from biochemical reactions to lifestyle habits. Here, our focus is on understanding systems that actively generate rhythms, known as clocks. Clocks, in particular, are systems that not only generate rhythms but also respond to environmental signals. Examining rhythms in isolation, without considering their generation, alteration, or regulation, would provide limited insights into the complexities of biological systems. We study the interaction between biological clocks and physiological processes: sleep, the immune system, metabolism, and environmental perturbations such as fluctuations in photoperiods. We develop mathematical and computational frameworks to investigate rhythms and their influence on biological processes at tissue and system levels. We specifically study cell-cell interactions at the level of the suprachiasmatic neuleus (SCN) in the hypothalamus of the brain, also called the master circadian clock. We investigate how noise at the level of the individual cells affect properties of the ensemble: period, oscillation amplitude, and bifurcation boundaries. Starting from individual dynamics, we derive macroscopic descriptions called mean field limits for interacting cells. Going up in scale, we also study the interactions between the peripheral circadian clock in the lung and the innate immune system during inflammation. At this organ scale, we investigate protein-protein interactions between clock proteins and immune agents, called cytokines. We are interested in the reciprocal modulation between these two systems, especially when the circadian rhythm is disrupted. Finally, we move from organ-level to the whole-body level. We develop multi-organ models of metabolism. These whole-body models integrate exercise and diet. Given the ubiquity of circadian rhythms at all levels of our physiology, these models are intended for the study of the role of external signals, beside neural signals emanating from the SCN, on (re-)synchronizing rhythms in the periphery. The interplay between such signals and metabolic processes plays a role in maintaining homeostasis, while also organizing and timing physiological processes in a proactive rather than reactive manner. This thesis contributes to the development of novel frameworks aimed at understanding multiscale systems, analyzing the relationships between network structure and dynamics, and ultimately deriving candidate mechanisms that can be experimentally verified.