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

该奖项的全部或部分资金根据《2021 年美国救援计划法案》（公法 117-2）提供。食管癌是美国癌症死亡的主要原因之一，存活率很低。晚期诊断是造成这种情况的主要原因，因为食管癌不出现早期症状。因此，迫切需要开发快速有效的食管癌靶向治疗方法，改善耐药性和临床结果。来自有限临床研究的证据表明，细胞信号传导通路在食管癌细胞中呈现显着改变的基因表达，并被发现与不良预后和疾病进展相关。此外，与其他实体瘤恶性肿瘤相比，食管癌呈现出更多的随机异质性和多样化的起源，这已被发现是耐药性的主要因素。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控制食管癌联合疗法的快速且经济有效的评估的计算框架至关重要。该项目旨在通过对食管癌中一类信号通路的动态行为和相关治疗策略的新数学模型来阐明上述问题。该框架还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，这是一所为西班牙裔服务的机构。该项目将支持弱势群体的学生进行研究，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，该项目将为研究者建立数学生物综合与实验研究中心（CIMBEX）的长期目标奠定基础。该中心将为弱势群体的学生提供综合数学生物学和实验研究环境，并提高学生在 STEM 中的保留率。该项目旨在定义和验证一种新颖的随机数学框架，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）的动态行为，以便更好地理解相关的监测和治疗策略。具体研究目标是（1）在福克-普朗克环境中开发和分析受控混合切换扩散过程，该过程解释了表皮生长因子受体信号通路动力学中异质性引起的随机性，以及（2）基于庞特里亚金极大值原理构建了一种新的无梯度最优控制算法，该算法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一个新的动力学过程建模和控制框架，促进生物学家的跨学科研究，并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。虽然重点是癌症机制，但该项目旨在定义一个同样适用于随机性发挥重要作用的其他慢性疾病的数学框架。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.