Mathematically Modeling Chemokine Ligand-Receptor Kinetics in the Context of Pancreatic Cancer

Pancreatic cancer is an aggressive form of cancer that has poor prognosis and survival rate. Although this cancer is difficult to detect and treat, experimentation has illustrated that chemokines largely impact the tumor microenvironment as they have specific roles in developing and restricting the immune interactions of the tumor. Chemokines include ligands that bind to specific receptors and give signals for their cell development and movement. In a complex biological environment, there can likely be many competitors to ligand binding to the receptor, affecting the movement and development of a particular cell. To model chemokine ligand and receptor interactions, we developed an ordinary differential equations (ODEs) model to quantify the ligand-receptor binding kinetics for a radioligand competing with either an agonist or antagonist to bind with a heterodimeric receptor, described using uncompetitive inhibition. To test our model, we chose published data that reported binding dynamics of two ligands CXCL10 and CXCL12 to the heterodimeric receptor CXCR3-CXCR4, competing with a series of agonists and antagonists to either the singular receptor or the heterodimer receptor. We estimated the kinetic parameters in the ODEs using the reported PIC50 values in the article. Our model showed similar dynamics of the ligand and receptor competition model compared to the experimental data. The model is compared to data from three published experimental cases. The first case involves binding of the radioligand CXCL10 or CXCL12 with increasing concentrations of an unlabeled CXC10, unlabeled CXCL12, and VUF10661 as agonists to the receptors. The second case details the competition of the radioligand CXCL10 and CXCL12 with increasing concentrations of VUF10085, TAK-779, and AMD3100 as antagonists to the receptors. The third case details the full system dynamics with the radioligand CXCL12 competing with an unlabeled CXC10, unlabeled CXCL12, and VUF10661 as agonists, binding to the CXCR4 singular receptor and the CXCR3-CXCR4 heterodimeric receptor, and considers ligand-receptor dissociation half-lives. By creating an in-depth mathematical model of this complex system, the time and resources of wet-lab researchers can be saved during their experimentations and a greater understanding can be gained about the physical nature of their experiments. We aim to apply this model to pancreatic cancer for designing ligands to enhance immune infiltration into these immunologically cold tumors.