Numerical analysis of a mechanotransduction dynamical model reveals
homoclinic bifurcations of extracellular matrix mediated oscillations of the
mesenchymal stem cell fate
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 adhesion area. Our analysis reveals a rich nonlinear behaviour of the
cell differentiation including 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 relatively 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 the
stable oscillations of the cell-substrate adhesion towards weaker adhesion and
high expression levels of the gene encoding Tubulin beta-3 chain, thus
favouring the phase transition from the adipogenic to the neurogenic fate