Structural Properties of Biological Integral Feedback Motifs

Cells are exposed to a range of external and internal disturbances that may influence the function of cellular processes. The ability of cells to self-regulate and adapt to disturbances enable them to maintain essential variables within narrow limits for proper biological function. This phenomenon is known as homeostasis, and is achieved through certain structural properties of cellular control processes. In particular, negative feedback and integral action play crucial roles in the regulation within cells. Many cellular processes are tightly regulated, and display so-called perfect adaptation to stepwise perturbations. It has been shown that integral feedback control achieves perfect adaptation in a variety biological systems. These observations have motivated researches to investigate cellular control processes from the perspective of robust control in recent years. It is clear that concepts from control theory, more commonly applied to the automation of engineered systems, are applicable to the analysis and construction of biological control networks. Whereas cellular control processes have been extensively studied with regards to stepwise perturbations in a regulated variable, less attention has been given to disturbances that affect cellular constituents globally, such as growth-induced dilution, and time-varying perturbations. In this thesis, we aim to take a bottom-up approach to investigate cellular control processes and characterize structural properties that give rise to homeostatic behaviors. In particular, we investigate a class of eight two-component control motifs, described by nonlinear saturation kinetics, to show asymptotic stability and robustness. We go on to show how parameters related to molecular and kinetic mechanisms influence set-point tracking and disturbance rejection properties of the two-component control motifs, and investigate how nonlinearities affect these properties. We also characterize certain constraints and trade-offs associated with the control motifs, and study their performance for time-varying perturbations. In the last part of the thesis, we investigate disturbances in the form of growth-induced dilution of cellular constituents and stochastic fluctuations. Especially for cancer cells is it expected that dilution poses a significant challenge for the effective regulation of metabolism, due to increased glycolytic and proliferative activity leading to cell swelling and growth-induced dilution. Based on the reported rewiring of glycolysis in cancer, and differential gene expression data from the Expression Atlas database, we construct a simplified mathematical model of glucose uptake. We show how cancer cells can regulate and maintain an increased uptake and metabolism of glucose during growth. In particular, a nested feedback architecture of the two-component control motifs is crucial to this end. To incorporate the effects of uncertainty and noise, we also present a stochastic version of the glucose uptake model, and show stochastic simulations relate to simulations of the deterministic version