LEAPS-MPS: Stochastic Frameworks for Control of a Class of Aberrant Signaling Pathways in Esophageal Cancer

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。食管癌是美国癌症死亡率的主要原因之一，生存率很低。晚期诊断是主要原因，因为食管癌不存在早期症状。因此，迫切需要开发快速有效的食管癌靶向治疗方法，提高耐药性和临床疗效。来自有限临床研究的证据表明，细胞信号传导途径在食管癌细胞中呈现显著改变的基因表达，并且已发现与不良预后和疾病进展相关。此外，与其他恶性实体瘤相比，食管癌具有更多的随机异质性和多样的起源，这已被发现是耐药的主要因素。因此，由于临床试验的成本和时间限制，开发能够准确表示信号通路的随机行为并提供快速且具有成本效益的联合治疗评估以控制食管癌的计算框架至关重要。本研究旨在通过对食管癌中一类信号通路的动力学行为和相关治疗策略进行新的数学建模来阐明上述问题。该框架也可以适用于其他癌症类型和慢性疾病治疗的快速评估。该项目将在德克萨斯大学阿灵顿分校进行，这是一个为西班牙裔服务的机构。该项目将支持来自研究人数不足群体的学生，并通过基于项目的学习模块和新的计算数学生物学研究生课程提供培训机会。最后，该项目将为研究者的长期目标奠定基础，即建立一个综合数学-生物和实验研究中心（CIMBEX）。该中心将促进综合数学生物学和实验研究环境的学生从代表性不足的群体，并加强学生保留在干。该项目旨在定义和验证一种新的随机数学框架，用于分析和控制食管癌中关键随机信号通路（称为表皮生长因子受体）的动力学行为，以便更好地了解相关的监测和治疗策略。具体的研究目标是（1）开发和分析一个受控的混合开关扩散过程，在福克-普朗克设置，占异质性诱导的随机性在表皮生长因子受体信号传导途径的动力学，和（2）建立一个新的无梯度的最优控制算法，基于庞特里亚金的最大值原理，它提供了使用组合疗法的治疗结果的定性准确和计算高效的数值模拟，并通过实验室实验的食管癌信号数据进行了验证。该项目的成果将是开发新的动态过程建模和控制框架，促进与生物学家的跨学科研究，以及为来自代表性不足群体的本科生和研究生提供研究和培训机会。虽然重点是癌症的机制，该项目旨在定义一个数学框架，同样适用于其他慢性疾病，其中随机性发挥了重要作用。该奖项反映了NSF的法定使命，并已被认为是值得支持的评估使用基金会的智力价值和更广泛的影响审查标准。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Esophageal cancer is one of the leading causes of cancer mortality in the USA, with a poor survival rate. Late diagnosis is a primary reason for this since esophageal cancer does not present early symptoms. Thus, there is an urgent need to develop fast and effective targeted therapies for esophageal cancer, improving drug tolerance and clinical outcomes. Evidence from limited clinical studies has shown that cell signaling pathways present significantly altered genetic expressions in esophageal cancer cells and have been found to correlate with poor prognosis and disease progression. Moreover, compared with other solid tumor malignancies, esophageal cancer presents many more stochastic heterogeneities and diverse origins, which have been found to be major factors of drug resistance. Thus, due to the cost and time limitations of clinical trials, it is of paramount importance to develop computational frameworks that can accurately represent the stochastic behavior of signaling pathways and provide a rapid and cost-effective evaluation of combination therapies to control esophageal cancer. This project aims to elucidate the aforementioned questions by new mathematical modeling of the dynamical behavior of a class of signaling pathways in esophageal cancer and associated treatment strategies. The framework can also be adapted for the rapid evaluation of treatments in other cancer types and chronic diseases. The project will be conducted at the University of Texas at Arlington, a Hispanic-Serving institution. The project will bolster students from underrepresented groups in research and provide training opportunities through project-based learning modules and a new graduate course in computational mathematical biology. Finally, this project will lay the foundation for the investigator's long-term goal to develop a Center for Integrative Math-Bio and Experimental Research (CIMBEX). The center will promote integrative mathematical biology and experimental research environment for students from underrepresented groups and bolster student retention in STEM. This project aims to define and validate a novel stochastic mathematical framework for analyzing and controlling the dynamical behavior of a key stochastic signaling pathway in esophageal cancer, known as epidermal growth factor receptor, for a better understanding of associated monitoring and treatment strategies. The specific research objectives are to (1) develop and analyze a controlled hybrid switching diffusion process, in a Fokker-Planck setting, that accounts for heterogeneity-induced stochasticity in the epidermal growth factor receptor signaling pathway dynamics, and (2) build a new gradient-free optimal control algorithm, based on Pontryagin's maximum principle, that provides qualitatively accurate and computationally efficient numerical simulations of treatment outcomes using combination therapies, validated by esophageal cancer signaling data from laboratory experiments. The outcomes of this project will be the development of a new modeling and control framework for dynamical processes, the promotion of interdisciplinary research with biologists, and research and training opportunities for undergraduate and graduate students from underrepresented groups. While the focus is on cancer mechanisms, the project aims to define a mathematical framework that applies equally well to other chronic diseases, where stochasticity plays an important role.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.