Analytical Investigations of the Mechanotransduction of Mesenchymal Stem Cell for Regulating Cell Fate Decisions

Abstract

Background: The evolution of new biomaterials in tissue engineering is under constant investigation. These biomaterials undergo mechanical stimuli induced cell-differentiation of the mesenchymal stem cell in their transition stage, and the developed dynamic model for this mechanotransduction (mechanical stimuli) process for regulating the fate of the mesenchymal stem cell is a set of coupled nonlinear differential equations whose exact solutions cannot be easily obtained with the common analytical methods. Objective: The analytical investigation of the dynamical model for the mechanotransduction of mesenchymal stem cell for regulating cell fate decisions is presented. Methods: A special analytic technique known as Differential transform method (DTM) was applied to obtain the solutions for the developed dynamic model and was validated with the fourth order Runge-Kutta numerical method (RK4). Results: The obtained analytical solutions have good agreement with the RK4 numerical solutions and past simulated studies. The effects of systems’ large (30k–300k) and low (0k–1.0k) stiffness levels, k 1 and degradation rate of the corresponding gene factor d1 on effective stiffness adhesion area were investigated. At low values of the system’s high stiffness (30k–300k), the effective stiffness adhesion area reduces, and at large stiffness level, the curve becomes asymptotic, but when it is further increased, it has a negligible impact on the effective stiffness adhesion area. It is also observed that at low values of the system’s low stiffness (0k–1.0k), the low stiffness k 1 and degradation rate of the corresponding gene factor d1 shows a negligible impact on the effective stiffness adhesion area at the initial state of response, while an increase in the low stiffness k 1 causes a corresponding increase in effective stiffness adhesion area, but an increase in degradation rate factor d1 causes a decrease in effective stiffness adhesion area. Conclusion: The obtained results from the dynamical analysis can be applied in developing new techniques in controlling the fate of mesenchymal stem cell’s transplantation and designs of new biomaterials.