Emergent Properties of Biological Interaction Systems

生物学家已经成功地揭示了细胞生物学中涉及的许多分子成分。现在的注意力从识别组件转移到理解连接组件的突发或系统行为。人们一直希望通过研究特定系统的数学模型来揭示一般原理，但到目前为止，这种研究形式在发现生物学的隐藏原理方面还没有得到普遍证明。在生物系统中发现的复杂网络是如何产生突现特性和行为的仍然是一个谜。理论数学提供了一条可能的前进之路，它迟早会对生物学产生深远的影响。该研究项目旨在突破生物模型的复杂性，阐明细胞生物学的一般原理。此外，该项目旨在开发新的计算方法，以解决目前无法解决的问题。对训练有素的数学科学家有很高的需求，他们必须有兴趣和专业知识，为解决生物学中出现的问题做出贡献；这个项目将为研究生提供肥沃的训练土壤。离散空间、连续时间马尔可夫链模型通常用于模拟生物相互作用网络，包括基因调控网络、病毒感染、信号系统、神经网络等。这些模型可以通过反应图来描述，反应图是模型组成分子之间相互作用的图形表示。交互网络可能非常复杂；例如，人类基因组中有超过20,000个基因，它们编码的蛋白质可以通过无数种方式进行修饰。此外，细胞系统通常有不同的子系统，这些子系统在多个不同的尺度上运行（时间上和拷贝数上），在一个尺度上运行的物种极大地影响了在不同尺度上运行的物种。目前文献中研究的反应网络通常非常复杂，以至于通常认为数值模拟是分析它们的唯一方法。然而，隐藏在复杂性之中的往往是一些潜在的结构，如果适当地量化，就可以深入了解系统的动态或静态行为。该项目旨在发展数学理论，将这些系统的紧急性质与相关反应图的易于检查的性质联系起来。该项目的第二个方面是开发和分析生化相互作用网络随机模型的计算方法。使用的主要工具和方法将来自概率论、随机分析、动力系统理论、化学反应网络理论和计算数学。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Biologists have been successful in revealing many of the molecular components involved in cell biology. Attention is now moving from identification of components to understanding the emergent, or system, behavior of the connected components. It has been hoped that general principles would emerge via the study of mathematical models of specific systems, but to date this form of study has not generally proven effective at discovering the hidden principles of biology. How the complex networks found in biological systems produce their emergent properties and behaviors remains elusive. Theoretical mathematics offers a possible route forward, and one which could, in time, have a profound influence on biology. This research project aims to cut through the complexity of biological models to elucidate the general principles of cell biology. Additionally, the project aims to develop new computational methods that can address currently infeasible problems. There is high demand for well-trained mathematical scientists with the interest and expertise necessary to contribute to the solution of questions arising in biology; this project will provide fertile training ground for graduate students.Discrete-space, continuous-time Markov chain models are commonly used to model biological interaction networks, including gene regulatory networks, viral infections, signaling systems, neuronal networks, etc. These models can be depicted via a reaction graph, which is a graphical representation of the interactions between the constituent molecules of the model. Interaction networks can be extraordinarily complex; for example, there are over 20,000 genes in the human genome and the proteins they encode may be modified in myriad ways. Further, cellular systems often have different sub-systems that operate on multiple different scales (both temporally and in terms of copy numbers), with the species operating at one scale greatly influencing those at a different scale. The reaction networks currently studied in the literature are typically so complex that numerical simulation is often considered the only way to analyze them. However, hidden within the complexity there are often underlying structures that, if properly quantified, give great insight into the dynamical or stationary behavior of the system. This project aims to develop mathematical theory that relates the emergent properties of these systems to easily-checked properties of the associated reaction graphs. A second aspect of the project is development and analysis of computational methods for stochastic models of biochemical interaction networks. The primary tools and methods utilized will be from probability theory, stochastic analysis, dynamical systems theory, chemical reaction network theory, and computational mathematics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.