Modelling Population-Level Hes1 Dynamics: Insights from a Multi-framework Approach

by Gesina Menz and Stefan Engblom

We investigate the behaviour of the Hes1-Delta-Notch signalling pathway governing cell differentiation during neuronal development using both an ordinary differential equation (ODE) model and a related reaction-diffusion master equation (RDME) framework. The ODE model captures transient oscillatory behaviour followed by stable patterning reflecting cell differentiation into neurons and glial cells and is reduced for analytical tractability. The RDME approach, however, allows us to assess the impact of intrinsic noise on pattern formation. Together, the models show that the characteristic dynamics are robust under stochastic fluctuations and that the deterministic stability analysis reflects behaviour in the stochastic setting.

Modelling the Hes1-Notch GRN using both ODE and RDME models allows us to capture behaviour in the deterministic and stochastic settings.