Dynamics and synchronization of biochemical oscillators

该项目涉及生化振荡的数学模型的发展和理解其潜在行为所需的分析。 虽然表现出振荡的分子系统的列表正在增长，但对共同原理的把握受到各种潜在网络结构的挑战。负反馈的存在是所有振荡网络的唯一共同特征;除此之外，每个系统似乎都是独一无二的。 我们的目标是制定一个共同的原则，是共享的所有振荡网络。 它是以动态的广泛趋势而不是支持网络的详细结构来表达的。 细胞不断地与周围环境和邻居交流。 这种相互交流往往导致他们的行为同步。 一个理论将被开发来解释在细胞群落中的周期性信号的同步。 生物化学振荡器的同步将通过最近邻耦合和与共同产生和感知的分子的耦合来研究。最近，我们对基因调控网络的结构和功能的认识出现了前所未有的爆炸，这预示着人类疾病的看法和治疗将发生革命性的变化。 从细胞周期到人类24小时昼夜节律的许多生物过程在时间上都是周期性的。这种周期性是由单个细胞中化学物质浓度的振荡驱动的。 在许多情况下，这些信号在种群之间同步，并且可以在宏观水平上检测到周期性信号。 负责产生和维持这些节奏的调节网络每天都在被发现。 虽然这些网络的结构各不相同，但它们通常会产生类似的周期性信号。 该项目将研究振荡背后的基本广泛动力学原理，强调网络在其实现过程中的功能。 此外，还将研究细胞群体中周期性节律的同步化。 群体中缺乏同步性会导致发育和功能缺陷。 该项目将开发一种能够预测集体动力学的理论，并在失败的情况下提出修复机制。

This project concerns the development of mathematical models of biochemical oscillations and the analysis required to understand their underlying behavior. While the list of molecular systems that exhibit oscillations is growing, the grasp of the common principles is challenged by the variety of underlying network structures. The presence of negative feedback is the only feature shared by all oscillatory networks; beyond this each system seems to be unique. The goal is to formulate a common principle that is shared by all oscillatory networks. It is expressed in terms of broad tendencies of the dynamics, rather then the detailed structure of the supporting networks. Cells constantly communicate with their environment and their neighbors. This mutual communication often results in synchronization of their behavior. A theory will be developed to explain synchronization of periodic signals in cell communities. The synchronization of biochemical oscillators will be studied via the nearest neighbor coupling, and the coupling with a communally produced and sensed molecule.A recent unprecedented explosion in our knowledge of structure and function of genetic regulatory networks promises revolutionary changes in how human disease is viewed and treated. Many biological processes ranging from the cell cycle to the human 24 hour circadian rhythm are periodic in time. This periodicity is driven by oscillations in the concentration of chemicals in individual cells. In many cases these signals synchronize across populations and the periodic signal can be detected on a macroscopic level. The regulatory networks that are responsible for production and maintenance of these rhythms are being discovered every day. While the structures of these networks vary, they often produce similar periodic signals. This project will study the underlying broad dynamics principles behind the oscillations, emphasizing the function of the network over its implementation. Further, it will study synchronization of the periodic rhythms in population of cells. The lack of synchronization in the population can result in developmental and functional defects. This project will develop a theory that will be able to predict collective dynamics, as well as suggest repair mechanisms in the case of failure.