Analysis of Mechanisms of Biochemical Homeostasis

细胞代谢产生于一个巨大的、高度互连的、层次化的遗传和生化相互作用网络，其行为依赖于大量随时间变化的输入。 这些输入中的一些在网络的局部区域引起大的响应，并且这些局部网络中的许多已经成为生物学和数学研究的主题。 这些局部网络不是孤立存在的，而是与小区中的许多其他这样的局部网络互连的，这一事实没有得到足够的注意。 由于全球基因-生化网络是高度相互关联的，人们可以预期，一个局部网络中的巨大变化会传播并可能破坏其他局部网络的正常功能。 这提出了具有挑战性的数学问题，因为网络具有复杂的拓扑结构和反应动力学往往是非线性的。 研究人员将分析随机波动如何在具有均匀局部反应动力学的大型复杂网络（随机和确定性）中衰减。 他们还将研究小的非均匀网络中特定生化机制的调节特性，这些网络稳定特定的浓度和通量以对抗外部扰动。这项研究建立在研究人员以前的工作基础上，他们发现了一系列在一碳代谢中产生稳态的新的调节机制。细胞的特性取决于一个巨大的、高度互联的、层次化的遗传和生化相互作用网络。 这些网络不是孤立存在的，而是与细胞中的许多其他网络相互连接。 由于全球基因-生化网络是高度相互关联的，人们可以预期，一个位置的巨大变化会传播并破坏其他位置的正常功能。 我们将发展一个数学理论，解释扰动如何通过大型生物化学网络传播。 我们将应用该理论来增加我们对叶酸和蛋氨酸循环的结构和功能的理解，这是细胞代谢的重要组成部分。 叶酸和甲硫氨酸循环的缺陷与癌症和许多发育异常有关。 我们期望数学理论将广泛适用于其他生物化学和基因网络以及许多其他复杂的生物系统，如神经生物学和生态学。 本科生，研究生和博士后研究员的跨学科培训是研究项目的核心部分。

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.