Survival Probability Approaches and Scalable Algorithms to Elucidate Molecular-Tether Reactions in Immunoreception and Cell Mechanics

许多生物学研究都集中在具有稳定刚性形状的蛋白质的化学活性部分。然而，超过30%的蛋白质的区域不是刚性的，而是连接化学活性区域的软系绳。拴链的两个例子是：免疫受体，参与免疫细胞如何接收其他细胞信号的蛋白质；形成蛋白是一种维持细胞结构骨架的蛋白质，会被包括霍乱在内的入侵细菌劫持。缆绳很容易被忽视。在某种程度上，这是因为用于理解刚性蛋白质的数学描述不适用于系绳。因此，数学表征系链可能会导致生物学和医学研究的新途径，而这些研究只关注蛋白质的刚性区域。这个项目将开发一种绳索的数学描述。首先，数学将用于开发一种快速计算算法来模拟免疫细胞如何对外部信号作出反应的最初几个步骤，包括它们如何通过蛋白质PD-1对关闭信号作出反应，这些信号被癌症利用来逃避免疫检测。其次，数学将被用来研究在形式的系绳。由此产生的数学将在两个独立的数学领域之间建立新的联系：随机过程理论和聚合物物理学。该项目还将培养具有免疫学、细胞生物学、应用数学、计算科学和生物物理学技能的研究生。还将开发供计算科学研究人员使用的开放获取资源。这些课程将特别侧重于为远程时代的研究创造工具，包括为高中生和本科生提供教程。许多蛋白质（在人类中约占30%）的区域缺乏明确的结构，而是在一系列具有高度内在无序性的结构中波动。其中许多起着连接化学反应位点的纽带作用。例子包括免疫受体，如T细胞受体、PD1和CD28，以及调节细胞骨架组装的形成蛋白。栓系反应无处不在；它们具有与标准溶液反应截然不同的性质，需要新颖的数学表征；它们被生物学利用；在某些情况下，它们为治疗提供了新的途径。该项目利用并扩展了随机过程理论和聚合物物理之间长期已知的数学对应关系，以研究系缚反应。数学理论旨在解决生物学之谜，首先，关于双胍系链和它们组装细胞骨架的能力，即使在两端结合时，以力响应的方式。其次，该项目涉及免疫受体拴系信号的实验数据，这些数据无法通过忽略体积排斥（拥挤）的模型来解释。该项目还将开发3种在线资源，包括面向高中生和本科生的教程，这些资源将帮助数学生物学社区在未来以在线互动为主的时代蓬勃发展。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。

Much of biological inquiry has focused on the chemically-active parts of proteins that have a stable, rigid shape. However, over 30% of our proteins have regions that are not rigid, but rather are floppy tethers that connect the chemically-active regions. Two examples of tethers are: immunoreceptors, the proteins involved in how immune cells receive signals from other cells; and formins, proteins that maintain the cell's architectural skeleton and are hijacked by invading bacteria including cholera. Tethers are easy to overlook. In part, this is because the mathematical descriptions that allow understanding of rigid proteins do not work for tethers. Therefore, mathematically characterizing tethers may lead to novel avenues of research in biology and medicine that were missed by focusing only of the rigid regions of proteins. This project will develop a mathematical description of tethers. The mathematics will be used to, first, develop a rapid computational algorithm to simulate the first few steps of how immune cells respond to external signals, including how they respond to off-switch signals through the protein PD-1, signals that is exploited by cancers to evade immune detection. Second, the mathematics will be used to study the tethers in formins. The resulting mathematics will create new connections between two separate fields of mathematics: stochastic process theory, and polymer physics. The project will also result in the training of graduate students with skills in immunology, cell biology, applied mathematics, computational science, and biophysics. Open-access resources for enabling computational science researchers will also be developed. These will have a special focus on creating tools for research in the remote era, including tutorials for high school and undergraduate students. Many proteins (around 30% in humans) have regions that lack well-defined structure, but rather fluctuate through an ensemble of configurations characterized by high intrinsic disorder. Many of these act as tethers that connect chemical reaction sites. Examples include immunoreceptors like the T Cell Receptor, PD1 and CD28, and formins, which regulate cytoskeleton assembly. Tethered reactions are ubiquitous; they have properties that are fundamentally distinct from standard solution reactions, requiring novel mathematical characterization; they are exploited by biology; and, in some cases, they provide novel avenues for therapeutics. This project exploits and extends a long-known mathematical correspondence between stochastic process theory and polymer physics to study tethered reactions. The mathematical theory aims to resolve biological mysteries, first, concerning the formin tethers and their ability to assemble the cytoskeleton even when bound at both termini, in a force-responsive manner. Second, the project addresses experimental data on immunoreceptor tethered signaling that cannot be explained by models that omit volume exclusion (crowding). The project will also develop 3 online resources that will help the Mathematical Biology community thrive in a future dominated by online interaction, including tutorials for high school and undergraduate students.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.