A mathematical modeling technique to understand the role of decoy receptors in ligand-receptor interaction

The ligand-receptor interaction is fundamental to many cellular processes in eukaryotic cells such as cell migration, proliferation, adhesion, signaling and so on. Cell migration is a central process in the development of organisms. Receptor induced chemo-tactic sensitivity plays an important role in cell migration. However, recently some receptors identified as decoy receptors, obstruct some mechanisms of certain regular receptors. DcR3 is one such important decoy receptor, generally found in glioma cell, RCC cell and many various malignant cells which obstruct some mechanism including apoptosis cell-signaling, cell inflammation, cell migration. The goal of our work is to mathematically formulate ligand-receptor interaction induced cell migration in the presence of decoy receptors. We develop here a novel mathematical model, consisting of four coupled partial differential equations which predict the movement of glioma cells due to the reaction-kinetic mechanism between regular receptors CD95, its ligand CD95L and decoy receptors DcR3 as obtained in experimental results. The aim is to measure the number of cells in the chamber's filter for different concentrations of ligand in presence of decoy receptors and compute the distance travelled by the cells inside filter due to cell migration. Using experimental results, we validate our model which suggests that the concentration of ligands plays an important role in cell migration.