Cell migration is a fundamental process that is crucial to a variety of physiological events. While traditional approaches have focused on two-dimensional (2D) systems, recent efforts have shifted to studying migration in three-dimensional (3D) matrices. A major distinction that has emerged is the increased importance of cell-matrix interactions in 3D environments. In particular, cell motility in 3D matrices is more dependent on matrix metalloproteinases (MMPs) to degrade steric obstacles than in 2D systems. In this study, we implement the effects of MMP-mediated proteolysis in a force-based computational model of 3D migration, testing two matrix ligand-MMP relationships that have been observed experimentally: linear and log-linear. The model for both scenarios predicts maximal motility at intermediate matrix ligand and MMP levels, with the linear case providing more physiologically compelling results. Recent experimental results suggesting MMP influence on integrin expression are also integrated into the model. While the biphasic behavior is retained, with MMP-integrin feedback peak cell speed is observed in a low ligand, high MMP regime instead of at intermediate ligand and MMP levels for both ligand-MMP relationships. The simulation provides insight into the expanding role of cell-matrix interactions in cell migration in 3D environments and has implications for cancer research.