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Bull. Math. Biol. 87 (6) 74 [2025-05-16; online 2025-05-16]
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.
PubMed 40379916
DOI 10.1007/s11538-025-01447-9
Crossref 10.1007/s11538-025-01447-9
pmc: PMC12084287
pii: 10.1007/s11538-025-01447-9