Mathematical modelling of signal sensing and transduction: revisiting classical mechanisms

Abstract

The ability of cells to react to changes in their environment is critical to their survival. Effective decision making strategies leading to the activation of specific intracellular pathways hinge on cells sensing and processing extracellular variation. We will only be able to understand and manipulate how cells make decisions if we understand the “design” of the mechanisms that enable them to make such decisions, in terms of how they function, and in terms of their limitations and architecture. In this thesis, using mathematical modelling, I revisited classical signal sensing and transduction mechanisms in light of recent developments in methodological approaches and data collection. I studied the sensing characteristics of one of the simplest of sensors, the allosteric sensor, to understand the limits and effectiveness of its “design”. Using the classical Monod-Wyman-Changeux model of allostery, I defined and evaluated six engineering-inspired characteristics as a function of the parameters and number of sensors. I found that specifying one characteristic strongly constrains others and I determined the trade-offs that follow from these constraints. I also calculated the probability distribution of the number of input molecules that maximizes information transfer and, as a consequence, the number of environmental states a given population of sensors can discriminate between. Next, I proposed a new general model of phosphorylation cycles that can account for experimental reports of ultrasensitivity occurring in regimes that are far away from Goldbeter and Koshland’s zero-order saturation, the classical ultrasensitivity-generating mechanism. The new model exhibits robust ultrasensitivity in “anti-zero-order” regimes. The degree of ultrasensitivity, its limits, and its dependence on the parameters of the system are analytically tractable. The model can, additionally, explain in an intuitive way some puzzling experimental observations. Finally, I addressed the problem of integrating different types of signals from multiple sources, and performed some preliminary exploration of how cells can “learn” to associate and dissociate correlated signals in non-evolutionary time-scales. This work provides insights into the function and robustness of signal sensing and transduction mechanisms and as such is applicable to both the study of endogenous systems and the design of synthetic ones.