Collaborative Research: Spatial Stochastic Rare Events by Asymptotics and Weighted Ensemble Sampling to Understand how Cells Make Space

细胞的表面挤满了许多不同的生物分子。这些包括受体和其他大的蛋白质分子，使细胞能够感知其环境。例如，作为免疫系统一部分的细胞可以感知感染的细胞外分子信号。细胞表面也是一个高度动态的环境，表面分子的运动和相互作用在细胞外信号的响应中起着至关重要的作用。数学建模使研究人员能够比目前的实验更详细地研究这些复杂的，动态的分子过程。研究人员将开发新的数学方法和计算机模拟方法，以研究拥挤细胞表面的分子运动如何影响细胞过程。开发的工具将使研究人员能够预测启动细胞-细胞界面形成和信号传导过程的分子事件序列。通过对生物分子/细胞工程的新策略进行计算测试，这些工具将在免疫治疗等领域开辟新的发现手段。研究人员将通过培训数学生物学和科学计算方面的本科研究人员来扩大科学参与，并将与科学代表性不足的中学生开展教学活动。这项研究的具体重点将是对分子扩散中的随机罕见事件进行建模。在发生分子拥挤的许多情况下，解拥挤也可能是关键的。例如，在T细胞中，许多大的表面分子必须从细胞表面的局部区域撤离，以允许T细胞与其靶相互作用。相对于单个分子扩散的时间尺度，这种集体疏散是罕见的事件。该项目的目标是开发一个框架来研究随机疏散，包括在罕见事件的限制，并将此框架应用于T细胞表面。本计画的具体目标是：（1）发展一个结合渐近与计算的稀有事件架构，以解决简单情形下的扩散疏散问题。(2)开发能够模拟复杂情景的增强型空间分布罕见事件方法。(3)使用开发的工具来了解T细胞表面分子如何克服或利用罕见的疏散。该项目的数学新奇在于：将渐近方法有效地扩展到高维问题;扩展计算罕见事件采样方法，不仅处理空间，而且利用空间;以及在一个新的组合框架中创建渐近方法和计算方法之间的协同作用。

The surface of a cell is crowded with many different biomolecules. These include receptors and other large protein molecules that enable the cell to sense its environment. For example, cells that function as part of the immune system can sense extra-cellular molecular signals of infection. The cell surface is also a highly dynamic environment, and the movement and interactions of surface molecules play a crucial role in the response to extra-cellular signals. Mathematical modeling enables researchers to study these complex, dynamic, molecular processes in more detail than is currently afforded by experiments. The investigators will develop new mathematical approaches and computer simulation methods tailored to the study of how molecular motion on crowded cell surfaces influences cellular processes. The developed tools will enable researchers to predict the sequence of molecular events that initiate cell-cell interface formation and signaling processes. By enabling computational testing of novel strategies for biomolecular/cellular engineering, these tools will open up new means of discovery in areas such as immunotherapeutics. The investigators will contribute to broadening science participation by training undergraduate researchers in mathematical biology and scientific computing, and will carry out pedagogical activities with middle school students from groups underrepresented in science. The specific focus of this research will be on modeling stochastic rare events in molecular diffusion. In many circumstances where molecular crowding occurs, un-crowding may also be critical. For example, in T cells, many large surface molecules must evacuate from a local region of the cell surface to allow for the T cell to interact with its target. This collective evacuation is a rare event relative to the timescale of individual molecular diffusion. The goal of this project is to develop a framework to study stochastic evacuation, including in rare event limits, and apply this framework to the T cell surface. Specific aims of this project are to: (1) Develop a combined asymptotic and computational rare event framework to solve diffusional evacuation in simple scenarios. (2) Develop enhanced spatially-distributed rare event methods capable of simulating complex scenarios. (3) Use the developed tools to understand how T cell surface molecules overcome or exploit rare evacuation. The mathematical novelty of this project is: the extension of asymptotic methods to effectively high-dimensional problems; the extension of computational rare event sampling methods, not only handling space but harnessing it; and the creation of synergies between asymptotic and computational approaches in a novel combined framework.