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A sophisticated computational model is developed to consider different interactive parts between cells and its components and their local microenvironment. The present work is mainly focused on the modeling of the coupling of the stress and concentration of the signaling proteins within the cell domain. In this research; the fundamental aspects and details of a coupled Reaction-Diffusion-Contraction (RDC), is presented. The model accounts for diffusion of the proteins and equilibrium of the cells simultaneously while considering different subunits which are affecting the cell migration. For instance, cell-cell interaction, nucleus effects, focal adhesion distribution, anisotropic stress fiber formation, membrane tension, microtubule structure and growth and retraction of the cells are considered. Collectively, because of the interaction of these different subunits, the cell works as a single migratory machine. The model fills the gap in biomechanical models for the biological cells and predicts both the instantaneous and the long-term dynamic behavior of the cells. In order to evaluate the proposed computational cell model, biological experiments such as cell migration, durotaxis, and collective cell migration has been simulated using the proposed computational model. We believe that the proposed model presents a simple mechanistic understanding of mechanosensing of substrate stiffness gradient at the cellular scale, which can be incorporated in more sophisticated mechanobiochemical models to address complex problems in mechanobiology and bioengineering. The proposed model and computer program is able to simulate long-term interaction of hundreds of cells with each other (e.g. cell-cell contact) and with the elastic substrate. The simulations can be performed on a desktop workstation efficiently.