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

TL;DR

This paper develops and analyzes a multi-framework model of Hes1 dynamics during neural development, combining deterministic and stochastic approaches to better understand population-level oscillations and fate decisions.

Contribution

It introduces a detailed spatial ODE model for Hes1 oscillations and links it with a stochastic grid-based model, enhancing interpretability and biological relevance.

Findings

The ODE model captures transient oscillatory behavior.

The stochastic model incorporates intrinsic noise effects.

Linking models improves understanding of cell population dynamics.

Abstract

Mathematical models of living cells have been successively refined with advancements in experimental techniques. A main concern is striking a balance between modelling power and the tractability of the associated mathematical analysis. In this work we model the dynamics for the transcription factor Hairy and enhancer of split-1 (Hes1), whose expression oscillates during neural development, and which critically enables stable fate decision in the embryonic brain. We design, parametrise, and analyse a detailed spatial model using ordinary differential equations (ODEs) over a grid capturing both transient oscillatory behaviour and fate decision on a population-level. We also investigate the relationship between this ODE model and a more realistic grid-based model involving intrinsic noise using mostly directly biologically motivated parameters. While we focus specifically on Hes1 in neural development, the approach of linking deterministic and stochastic grid-based models shows promise in modelling various biological processes taking place in a cell population. In this context, our work stresses the importance of the interpretability of complex computational models into a framework which is amenable to mathematical analysis.