The next meeting of the seminar of the Department of

Mathematical Modeling and Numerical Analysis

will be held on October 5, 2026, Monday, at 2:00 pm, in Room 503 of the Institute of Mathematics and Informatics.

A talk on:

An ODE model for non-monotone dose response to the PD-L1 blockade in vitro

will be delivered by Assoc. Prof. Peter Rashkov (IMI – BAS).

Abstract: PD-1 is a cell surface receptor on T cells and B cells that has a role in regulating the body’s immune response by promoting self-tolerance. The PD-L1 protein on human cells acts as an immune checkpoint, or a „brake“ that prevents T cells from attacking normal cells by binding to PD-1. Cancer cells, however, express high amounts of PD-L1 in order to evade the body’s immune response by binding to the PD1 receptor. Development of immune checkpoint inhibitors is an important field in drug design because these molecules can serve as blockers to PD-L1, restoring the ability of T cells to attack cancer cells. We present a model for T cell re-activation in vitro under the action of therapeutic compounds targeting the PD-1/PD-L1 interaction. The effector T cells in the assay express firefly luciferase upon TCR-mediated activation, which is diminished by the presence of PD-1/PD-L1 interaction provided by co-cultured artificial antigen-presenting cells. Upon PD-L1 blockade with tested compounds at different dose concentrations, the activation of effector T cells is restored, reflected by increased luminescence signals. The resulting dose-response curve is non-monotone due to the existence of two separate and antagonizing effects (specific activation of T cells and unspecific toxicity). A linear ODE system helps estimate two quantities of interest: the compound concentration achieving maximum T cell activation and the EC50 concentration. The model presents a mechanism for the temporal change in the luciferase activity over the course of the experiment. Parameters of the model are estimated from experimental in vitro data for different tested compounds and the quantities are computed by a Monte Carlo method. This is joint work with Dr. Łukasz Skalniak (Faculty of Chemistry, Uniwersytet Jagielloński w Krakowie).