Numerical analysis of mesenchymal stem cell mechanotransduction dynamics reveals homoclinic bifurcations

Abstract

We perform one and two-parameter numerical bifurcation analysis of a mechanotransduction model approximating the dynamics of mesenchymal stem cell differentiation into neurons, adipocytes, myocytes and osteoblasts. For our analysis, we use as bifurcation parameters the stiffness of the extracellular matrix and parameters linked with the positive feedback mechanisms that up-regulate the production of the YAP/TAZ transcriptional regulators (TRs) and the cell-substrate adhesion area. Our analysis reveals regimes of hysteresis and multistability, stable oscillations of the effective adhesion area, the YAP/TAZ TRs and the PPARγ receptors associated with the adipogenic fate, as well as homoclinic bifurcations that interrupt high-amplitude oscillations abruptly. The two-parameter bifurcation analysis of the Andronov–Hopf points that give birth to the oscillating patterns predicts their existence for soft extracellular substrates (<1kPa), a regime that favours the neurogenic and the adipogenic cell fate. Furthermore, in these regimes, the analysis reveals the presence of homoclinic bifurcations that result in the sudden loss of stable oscillations of the cell-substrate adhesion towards weaker adhesions and high expression levels of the gene encoding Tubulin beta-3 chain, thus favouring the phase transition from the adipogenic to the neurogenic fate.