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

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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.