REU Advisor: Dr. Julia Arciero, Mathematical Sciences

Solid organ transplantation is a life-saving procedure that requires lifelong immunosuppression to prevent transplant rejection. Students working on this project will adapt an existing ODE model of murine heart transplant rejection that includes immunosuppression and adoptive transfer treatment strategies to predict how the immune response will respond when a bacterial infection is introduced into the system. The presence of immunosuppression causes a higher risk of susceptibility to opportunistic infections, and the students will explore the impact of bacterial infection on a heart transplant patient undergoing a typical immunosuppression treatment regimen. Students will gain experience coding in MATLAB and building and analyzing mathematical models of the immune response.

REU Advisor: Dr. Jared Barber, Mathematical Sciences

Cell migration plays a major role in both healthy (e.g. vessel creation and embryo development) and pathogenic (e.g. cancer and wound healing) scenarios. By combining our mathematical/computational model of cell migration with a collaborator’s experimental force measurements, we hope to better understand the role forces play during cell migration. Students will work with the model which is a set of interconnected damped springs that represent the cell and are governed by a system of ODEs. They will enhance it by adding cellular components such as the cell’s nucleus and/or use data assimilation techniques (e.g. deep learning) to help usefully compare simulation results with experiments. In addition to the research experience, students will also learn about fluid and solid mechanics, computer programming/model actualization, and some level of cellular biology.

REU Advisor: Dr. Horia Petrache, Physics

In order to survive and grow, biological cells need nutrients such as glucose. We will use the CompuCell3D platform to analyze the diffusion of glucose in cellular aggregates with the goal of finding optimum geometries and cell growth rates. Since uptake of glucose is through cellular membranes, we will also analyze membrane transport using Molecular Dynamics simulations of lipid bilayers.

REU Advisor: Dr. Sebastian Sensale, Physics

Students working on this project will develop mathematical models to understand how biological populations survive or go extinct when particles must cross spatial barriers to reach activation sites. This phenomenon occurs in systems like calcium wave propagation in neural tissue and viral spread dynamics. Using differential equations and computer simulations, students will determine the critical conditions that predict whether a population persists or dies out, focusing on how barrier strength, activation timing, and local recruitment interact to control survival. Students will calibrate models using experimental data from the literature and will learn to compute a basic reproduction number R₀ that predicts extinction versus persistence. This project requires only undergraduate-level differential equations and will provide hands-on experience with mathematical modeling, MATLAB/Python coding, and analysis of stochastic biological systems.