An essential property of life is that cells and organisms have the ability to protect themselves against external disturbances/attacks by using homeostatic mechanisms. These defending mechanisms are based on negative feedback regulation and often contain additional features, such as integral control, where the integrated error between a controlled variable and its set-point is used to achieve homeostasis. Although the concept of integral control has its origin in industrial processes, recent findings suggest that biological systems are also capable of showing integral control. We recently described a basic set of negative feedback structures (controller motifs) where robust homeostasis is achieved against different but constant perturbations. As many perturbations in biology, such as infections, increase rapidly over time, we investigated how the different controller motifs equipped with different implementations of integral control perform in relation to rapidly changing perturbations, including exponential and hyperbolic changes. The findings show that the construction of an optimum biochemical controller design for time-dependent perturbations requires a certain match between the structure of the negative feedback loop, its signaling kinetics, and the kinetics of how integral control is implemented within the negative feedback loop.

Most cancer cells rely on aerobic glycolysis and increased glucose uptake for the production of biosynthetic precursors needed to support rapid proliferation. Increased glucose uptake and glycolytic activity may result in intracellular acidosis and increase of osmotically active substances, leading to cell swelling. This causes dilution of cellular constituents, which can markedly influence cellular reactions and the function of proteins, and hence, control mechanisms used by cancer cells to maintain a highly glycolytic phenotype must be robust to dilution. In this paper, we review the literature on cancer cell metabolism and glucose uptake, and employ mathematical modeling to examine control mechanisms in cancer cell metabolism that show robust homeostatic control in the presence of dilution. Using differential gene expression data from the Expression Atlas database, we identify the key components of glucose uptake in cancer, in order to guide the construction of a mathematical model. By simulations of this model we show that while negative feedback from downstream glycolytic metabolites to glucose transporters is sufficient for homeostatic control of glycolysis in a constant cellular volume, it is necessary to control intermediate glycolytic enzymes in order to achieve homeostatic control during growth. With a focus on glucose uptake in cancer, we demonstrate a systems biology approach to the identification, reduction, and analysis of complex regulatory systems. SIGNIFICANCE Rapid proliferation and increased glycolytic activity in cancer cells lead to dilution of cellular constituents, which can markedly influence cellular reactions and the function of proteins. Therefore, control mechanisms used by cancer cells to maintain a highly glycolytic phenotype must be robust to dilution. We construct a mathematical model of glucose uptake in cancer, and using a systems biology approach to the analysis of regulatory networks, identify the presence of integral control motifs as a means for achieving dilution resistance. Furthermore, we show that while negative feedback from downstream glycolytic metabolites to glucose transporters is sufficient for homeostatic control of glycolysis in a constant cellular volume, it is necessary to control intermediate glycolytic enzymes to achieve homeostatic control during growth.

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