Feedback Models in Biological Physics

Abstract

Feedback models play a crucial role in biological physics. They underlie many of the phenomena that are essential for life, from regularity and homeostasis to growth and rhythms. Using these models to analyze biological systems is more involved than simply solving the equations. In order for the models to be valuable tools for a research community it is necessary to connect these formal models to experimental observations, and to use experimental observations to distinguish between different types of model. How the details of the structure of a model relate to the experimental observables it predicts for the biophysical system can sometimes be obscure, especially for numerical models. This thesis presents two studies in which the feedback structures of models for biological systems are analyzed. In each case, differences in the feedback structure are shown to predict experimentally observable consequences. In a simple post-translational protein oscillator it is possible to determine the sign of the feedback present in the biophysical system by comparing model oscillators with opposing signs for the dominant feedback. When the feedback strength is modulated, the positive and negative feedback models predict that the period of the oscillation changes in opposing directions. We show that this is a generic property of the distinct families of oscillator models by considering extensions that have been proposed for each and demonstrating that the results hold. We then compare different models of tissue growth in the Drosophila wing disk epithelium based on experimental observables such as precision of the final size, the uniformity of growth, and the presence of spatiotemporal patterns of apoptosis. Using an analytic framework we connect these observables to the feedback structures of different model families, defined by characteristics such as which quantities participate in the feedback and whether or not growth is allowed at all points in the tissue. We show that mechanical feedback models that disallow growth over macroscopic sections of the tissue cannot predict a unique final size.