CAREER: How Diffusion, Dimension, Geometry, and Redundancy Affect Cellular Dynamics

该项目旨在使用数学建模来揭示潜在的原理(I)身体如何防御细菌和病毒等外来入侵者，(Ii)细胞如何应对压力环境，以及(Iii)细胞过程如何使用随机搜索以惊人的速度找到隐藏的目标。这些不同的问题是统一的，因为它们都需要扩展我们对随机性的数学理解，以应对现代细胞生物学中数据的复杂性。事实上，这个项目的一个广泛目标是了解细胞如何可靠和有效地运作，尽管细胞水平上的随机性无处不在。此外，该项目将增加STEM的参与，并培训下一代科学家，以继续这项研究的跨学科方法。特别是，研究生将密切参与工作的方方面面，目前无法进入研究型数学系的本科生将在参加暑期课程时预览研究和研究生课程。细胞生物学要求数学迅速进步，因为数据引发的问题远远超出了现有随机过程理论的限制。在T细胞与抗原相互作用的情况下，PI将开发并应用随机模型来从原始的二进制数据推断动力学。在蛋白质-蛋白质相互作用的情况下，PI将制定和分析一类新的随机偏微分方程式，旨在揭示与二维和三维结合有关的特征。这些模型有望解决某些体内和体外测量之间的差异，并展示细胞如何利用依赖于维度的相互作用来调节功能。此外，PI将回答极端第一通过理论这一新兴领域的基础性问题。首次通过理论被广泛用于研究生物学中的时间尺度，但绝大多数工作都集中在给定的单个搜索者找到目标所需的时间上。然而，更相关的时间尺度往往是大量搜索者中最快的搜索者的第一次通过时间，因为细胞生物学中的许多事件都是由许多分子中的第一个分子到达引发的。极端第一通道理论的发展试图发现冗余性(蛋白质、分子等的许多副本)影响细胞激活率，并允许对传统首次传代理论的广泛应用进行修订。该项目由分子和细胞生物科学部的细胞动力学和功能计划共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project aims to use mathematical modeling to reveal principles underlying (i) how the body defends against foreign invaders such as bacteria and viruses, (ii) how cells cope with stressful environments, and (iii) how cellular processes use random search to find hidden targets with remarkable speed. These diverse problems are united as they all require extending our mathematical understanding of randomness to cope with the complexity of data in modern cell biology. Indeed, a broad goal of this project is to understand how cells function reliably and efficiently despite the ubiquity of randomness at the cellular level. In addition, this project will increase STEM participation and train the next generation of scientists to continue the interdisciplinary approach of this research. In particular, graduate students will be closely involved in all aspects of the work and undergraduates who currently lack access to a research mathematics department will be given a preview of research and graduate school as they participate in summer programs.Cell biology is requiring rapid advances in mathematics, as the data is prompting questions far beyond the limits of existing stochastic processes theory. In the case of T cells interacting with antigens, the PI will develop and apply stochastic models to infer kinetics from raw binary data. In the case of protein-protein interactions, the PI will formulate and analyze a new class of stochastic partial differential equations aimed at uncovering features relating two-dimensional and three-dimensional binding. These models are expected to resolve discrepancies between certain in vivo and in vitro measurements and to show how cells can exploit dimensional-dependent interactions to regulate function. Further, the PI will answer foundational questions in the emerging field of extreme first passage theory. First passage theory has been used extensively to study timescales in biology, but the vast majority of works have focused on the time it takes a given single searcher to find a target. However, the more relevant timescale is often the first passage time of the fastest searcher from a large collection of searchers, as many events in cell biology are initiated by the arrival of the first molecule out of many. The development of extreme first passage theory seeks to discover how redundancy (many copies of proteins, molecules, etc.) affects cellular activation rates and allow a wide range of previous applications of traditional first passage theory to be revised. This project is co-funded by the Cellular Dynamics and Function program in the Division of Molecular and Cellular Biosciences.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.