Integrin transmembrane proteins conduct mechanotransduction at the cell–extracellular matrix (ECM) interface. This process is central to cellular homeostasis and therefore is particularly important when designing instructive biomaterials and organoid culture systems. Previous studies suggest that fine-tuning the ECM composition and mechanical properties can improve organoid development. Toward the bigger goal of fully functional organoid development, we hypothesize that resolving the dynamics of ECM–integrin interactions will be highly instructive. To this end, we developed a mathematical model that enabled us to simulate three main interactions, namely integrin activation, ligand binding, and integrin clustering. Different from previously published computational models, we account for the binding of more than one type of ligand to the integrin. This competition between ligands defines the fate of the system. We have demonstrated that an increase in the initial concentration of ligands does not ensure an increase in the steady state concentration of ligand-bound integrins. The ligand with higher binding rate occupies more integrins at the steady state than does the competing ligand. With cell type specific, quantitative input on integrin-ligand binding rates, this model can be used to develop instructive cell culture systems.