Dynamics of a Hes1-Dll1 regulatory network in coupled muscle stem cells: stability, bifurcations, and coexistence of oscillatory states

Muscle regeneration relies on the coordinated activation of muscle stem cells, whose fate decisions are regulated by intracellular gene expression dynamics and intercellular coupling via the Notch-Dll1 signaling pathway. Central components of this regulatory network include the transcriptional repressor Hes1, its target gene Dll1, and the myogenic regulator MyoD. Experimental and theoretical studies have shown that proliferating muscle stem cells exhibit oscillatory dynamics of these molecules, whereas sustained expression is associated with differentiation. Here, we investigate the dynamics of a previously established delay differential equation model of two coupled muscle stem cells. Using linear stability analysis, we systematically characterize how model parameters affect the transition between stable and unstable steady states. In addition, numerical bifurcation analysis is employed to study the influence of intercellular coupling strength and delay on the system dynamics. Our analysis shows that continuous variation of the coupling delay induces repetitive changes in the stability of the steady state. However, this sensitivity towards the coupling delay is confined to a narrow region of parameter space and therefore requires a fine tuning of all other parameters. Beside the identification of parameter sets for in-phase and out-of-phase oscillations, we demonstrate the possibility of coexisting stable in-phase and out-of-phase oscillations, a dynamical feature that has not been reported previously. While oscillation periods are largely determined by intracellular regulatory mechanisms, oscillation amplitudes can be strongly modulated by intercellular coupling. These results provide new insight into how the intracellular network and intercellular communication interact to generate different collective dynamics.