Analysis of Mechanisms of Biochemical Homeostasis

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Cell metabolism emerges from a large, highly interconnected, hierarchical network of genetic and biochemical interactions whose behaviors depend on a great many time varying inputs. Some of these inputs induce large responses in local areas of the network and many of these local networks have been the subject of biological and mathematical investigations. Insufficient attention has been paid to fact that these local networks do not exist in isolation but are interconnected with many other such local networks in the cell. Because the global gene-biochemical network is so highly interconnected, one would expect that large changes in one local network would propagate and potentially disrupt the normal functions of other local networks. This raises challenging mathematical issues since the networks have complicated topology and the reaction dynamics are often nonlinear. The investigators will analyze how random fluctuations are attenuated in large complex networks (both random and deterministic) with homogeneous local reaction dynamics. They will also investigate the regulatory properties of specific biochemical mechanisms in small inhomogeneous networks that stabilize particular concentrations and fluxes against outside perturbations. The research builds on previous work of the investigators who discovered a range of novel regulatory mechanisms that produce homeostasis in one-carbon metabolism. The properties of cells depend on a large, highly interconnected, hierarchical network of genetic and biochemical interactions. These networks do not exist in isolation but are interconnected with many other such networks in the cell. Because the global gene-biochemical network is so highly interconnected, one would expect that large changes in one location would propagate and disrupt the normal functions at other locations. We will develop a mathematical theory of how disturbances propagate through large biochemical networks. We will apply the theory to increase our understanding of the structure and function of the folate and methionine cycles, which are important parts of cell metabolism. Defects in the folate and methionine cycles are associated with cancer and many developmental abnormalities. We expect that the mathematical theory will be broadly applicable to other biochemical and gene networks and to many other complex biological systems, such as neurobiology and ecology. Interdisciplinary training of undergraduate students, graduate students, and a postdoctoral fellow is a central part of the research project.