Modeling and Stochastic Simulation of Close-Contact Dynamics in Immune Recognition

该奖项支持的项目将使用数学来理解免疫系统如何能够定位和抵御威胁。被称为T细胞的白血球是免疫系统的关键组成部分。他们的职责是寻找相对罕见的病原体分子特征。自身免疫、免疫缺陷疾病和癌症都是由于这一机制的失败而产生的。T细胞如何有效地区分稀有的外来细胞和丰富的宿主细胞的基本原理尚不完全清楚。该项目将开发新一代理论和计算工具，以大幅加快T细胞激活时间的随机抽样。与实验合作者合作，该项目将探索(通过数学建模、随机分析和大规模计算模拟)细胞对细胞接触拓扑学在免疫识别中所起的作用。该奖项将支持本科生和研究生研究人员在这个项目上工作。这个项目将通过在即将举行的会议和由美国数学学会主办的主题研讨会上的小型研讨会接触到更广泛的数学界。当T细胞遇到感兴趣的细胞时，它们会扫描其表面，寻找罕见的扩散信号分子。这种搜索是在繁忙和嘈杂的环境中进行的，因此T细胞激活是一个随机过程，在数学上被描述为首次通过问题。以前的这个过程的数学模型假设细胞之间的界面是大的和连续的。最近的实验工作表明，T细胞延伸出许多被称为微绒毛的指状突起，以塑造一个高度瞬时和分布的界面。这个项目将建立T细胞激活的新模型，该模型结合了最近发现的微绒毛采样产生的随机地形的作用。许多现有的首次通过理论都集中在确定分布的平均值上。由于T细胞激活的敏感性，该项目将需要开发新的概率工具来获得各种狭义逃逸问题中通过时间的完全分布。为了补充这些理论结果，该提案将开发一套新的计算(确定性和蒙特卡罗)工具，用于研究动态和异质环境中的随机过程。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。

The project supported under this award will use mathematics to understand how the immune system is able to locate and fend off threats. White blood cells known as T cells are a key component of the immune system. Their responsibility is to search for relatively rare molecular signatures of pathogens. Autoimmune, immunodeficient diseases and cancer arise from a failure of this mechanism. The basic principles of how T cells efficiently discriminate between rare foreign cells and abundant host cells is not completely understood. This project will develop a new generation of theoretical and computational tools to massively accelerate the random sampling of T cell activation times. Working with experimental collaborators, the project will explore (through mathematical modeling, stochastic analysis and large scale computational simulations) the role that the cell-to-cell contact topography plays in immune recognition. This award will support undergraduate and graduate student researchers to work on this project. This project will reach the broader mathematical community through mini-symposia at upcoming conferences and thematic workshops hosted by the American Mathematical Society.When T cells encounter a cell of interest, they scan its surface for rare diffusing signaling molecules. This search is conducted in a bustling and noisy environment and so T cell activation is a stochastic process described mathematically as a first passage problem. Previous mathematical models of this process assumed the interface between the cells was large and contiguous. Recent experimental work has revealed that T cells extend numerous finger-like projections called microvilli to sculpt a highly transient and distributed interface. This project will build new models of T cell activation that incorporate the recently discovered role of stochastic topography arising from microvilli sampling. Much existing first passage theory has focused on determination of the mean of the distribution. Owing to the sensitivity of T cell activation, this project will require the development of new probabilistic tools to obtain the full distribution of passage times in a variety of narrow escape problems. To complement these theoretical results, the proposal will develop a new suite of computational (deterministic and Monte-Carlo) tools for studying stochastic processes in dynamic and heterogeneous environments.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.