Models of spatio-temporal reaction systems with applications to systems and synthetic biology

申请人计划将联合收割机数学工具与多分辨率数据相结合，在考虑空间和时间的框架内开发模型和方法。由于现实世界的非线性性质，理解物理，生物和社会领域的行为需要通用和广泛适用的数学框架。为了做到这一点，申请人将专注于广泛关注的特定生物学问题：蛋白质相互作用及其调节细胞决策的能力。这是至关重要的;例如，在癌症中，细胞无法通过蛋白质相互作用传递死亡信号，导致细胞在应该停止时继续增殖。这些信号传递过程通常涉及许多代理人，所有代理人都以非平凡的方式在不同的位置和不同的组织级别上进行交互。描述蛋白质相互作用的数学模型的开发和分析将使我们能够理解它们的动力学，预测分子机制，揭示它们的功能，并指导细胞决策。这是一个正在进行的生物学和医学相关的问题，具有根本的重要性和数学/统计方法可以提供洞察细胞中的空间组织的作用和动态，但更一般地说，其他系统。动力学方法将用于模型开发，因为这些方法考虑了系统的时间确定性演变，并可能提供有关系统的机械信息。在整个奖学金，分析和方法将与蛋白质相互作用系统的化学解决数据开发。这些蛋白质相互作用的多分辨率数据将从Weizmann研究所，普林斯顿大学和东京大学的支持合作伙伴那里收集，以测试我们的预测和方法。一系列数学/统计方法将用于分析和方法开发。我们将关注的一个特殊问题是如何确定哪个模型可以描述从系统生成的数据。模型选择或模型辨别的这个问题已经导致申请人致力于研究并开发一系列方法来区分模型。在时空框架中理解蛋白质信号传导行为的机制将推动数学和生物学领域的发展。支持伙伴和申请人已经为研究复杂系统的这一竞技场做出了贡献;此外，他们有共同的兴趣，通过构建蛋白质相互作用的时空模型来推进该领域，并开发可能适用于其他固有空间系统的新数学技术。这项研究具有直接的生物学意义-这项工作可能为蛋白质信号传导功能障碍导致癌症等疾病提供见解，我们可以扩展我们的框架来分析生物体内的其他生物过程。这些类型的调查将受益于在这个项目中开发的数学，统计和计算协议。此外，为不同类型的空间模型开发的非参数和统计方法可以应用于其他环境。

The applicant plans to combine mathematical tools with multi-resolution data to develop models and methods in a framework that considers both space and time. Due to the nonlinear nature of the real-world, understanding behaviors of the physical, biological and social fields require general and widely applicable mathematical frameworks. To do this, the applicant will focus on a particular biological problem of widespread interest: protein interactions and their ability to regulate cellular decision making. This is of paramount importance; for example, in cancer, a cell is unable to transmit a death signal through protein interactions, causing the cell to continue to proliferate when it should arrest. Often these signaling processes involve many agents, all interacting in nontrivial ways, in different locations and at different levels of organization. The development and analysis of mathematical models describing protein interactions will, crucially, allow us to understand their dynamics, predict molecular mechanisms, reveal their function, and guide cell decisions. This is an ongoing biologically and medically relevant problem of fundamental importance and mathematical/statistical approaches may provide insights into the role and dynamics in spatial organization in cells, but more generally, to other systems. Dynamical approaches will be used for model development since these consider the temporal deterministic evolution of the system and may provide mechanistic information about the system. Throughout the fellowship, analysis and methods will be developed with chemically resolved data of the protein interaction system. Multi-resolution data of these protein interactions will be collected from Supporting Partners at the Weizmann Institute, Princeton University and University of Tokyo to test our predictions and methods. A range of mathematical/statistical approaches will be used for analysis and method development. One particular problem we will focus on is how to determine which model could describe data generated from a system. This question of model selection, or model discrmination, has led the applicant to work and develop a range of methods to distinguish between models. Understanding the mechanisms responsible for the behavior of protein signaling in a spatio-temporal framework would advance the fields of mathematics and biology. The Supporting Partners and applicant have already contributed to this arena of studying complex systems; moreover, they share a mutual interest to advance the field through the construction of spatio-temporal models of protein interactions and develop novel mathematical techniques that may be applicable to other inherently spatial systems.More generally, the research has direct biological implications-the work may provide insights for dysfunction of protein signaling resulting in diseases such as cancer, and we can extend our framework to analyze other biological processes inside living organism. These types of investigations will benefit from the mathematical, statistical and computational protocols that are developed in this project. Furthermore, the nonparametric and statistical methods developed for different types of spatial models can be applied to other contexts.