Fluctuation Theories for Complex Biological Systems

智力价值：这个项目解决了随机波动在生物学中的作用，它们是如何产生和传播的，以及它们如何被控制和利用。在所有复杂程度的生活中，都是在随机化和纠正统计趋势之间的斗争。单个细胞或生物体的出生和死亡造成了种群大小的自发波动，这种波动可以通过相互作用网络传播，并可能使系统的其他部分随机化。该项目将专注于推导适用于大家族过程的定理，以严格理解生物系统的更广泛的设计原则，而不是为特定系统构建详细的模型。例如，该理论将被应用于分子系统，以阐明基因如何可靠地表达以产生蛋白质和RNA分子，以及如何在细胞和有机体种群中解释种群大小的自然波动。该项目在技术和实验上都是创新的，因为来自传统上分离的应用数学领域的结果将被综合起来，以提供一个框架来隔离和测试关于实验系统行为的个人假设。预计该项目的结果将广泛适用于任意复杂的生物系统的定量分析。更广泛的影响：对波动复杂系统的基本理论的拟议扩展将提供更好的理解，从单个细胞中的分子网络到生物体种群，大小不等的生物系统如何通过种群大小的波动而导致灭绝。为了确保成果和方法对更广泛的科学界产生最大影响，将为高级本科生和研究生开发适当的课程，这些课程旨在向自然科学所有领域的学生开放。此外，还将组织会议，让来自不同学科的科学家聚集在一起，主要是来自分子生物学和生态学的科学家。最后，PI将为哈佛自然历史博物馆的家庭项目提供非专业层面的讲座，向公众展示同样的动态原理如何出现在从分子到病毒、细胞甚至大型生物体的所有生物复杂性水平上。

Intellectual Merit: This project addresses the roles of random fluctuations in biology, how they arise and spread, and how they can be controlled and exploited. Life at all levels of complexity is a battle between randomizing and correcting statistical tendencies. Births and deaths of individual cells or organisms create spontaneous fluctuations in population sizes that can spread through interaction networks and potentially randomize other parts of the system. The project will focus on the derivation of theorems that hold for large families of processes, to rigorously understand the broader design principles of biological systems, rather than constructing detailed models for specific systems. The theory will be applied to molecular systems to elucidate, for example, how genes are reliably expressed to produce protein and RNA molecules, as well as to populations of cells and organisms to account for the natural fluctuations in population sizes. The project is technically and experimentally innovative in that results from traditionally separate areas of applied mathematics will be synthesized to provide a framework for isolating and testing individual assumptions regarding the behavior of experimental systems. It is anticipated that the results of the project will be broadly applicable to quantitative analysis of arbitrarily complex biological systems. Broader Impacts: The proposed extensions of fundamental theory for fluctuating complex systems will provide a better understanding for how biological systems ranging in size from molecular networks in individual cells to populations of organisms can be driven to extinction through fluctuations in population sizes. To ensure that the results and methods have maximal impact on the broader scientific community, appropriate courses will be developed for advanced undergraduate and graduate levels, that are designed to be accessible to students from all areas of natural science. In addition, conferences will be organized to bring together scientists from very different disciplines, primarily from molecular biology and ecology. Finally, the PI will provide lectures at a lay level for the family program of the Harvard Museum of Natural History, demonstrating to the general public how the same dynamic principles appear at all levels of biological complexity from molecules to viruses, cells or even large organisms.