Menz Gesina, Engblom Stefan
Division of Scientific Computing, Department of Information Technology, Uppsala University, 751 05, Uppsala, Sweden.
Science for Life Laboratory, Department of Information Technology, Uppsala University, Uppsala, Sweden.
Bull Math Biol. 2025 May 16;87(6):74. doi: 10.1007/s11538-025-01447-9.
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.
随着实验技术的进步，活细胞的数学模型也在不断完善。一个主要问题是在建模能力和相关数学分析的易处理性之间取得平衡。在这项工作中，我们对转录因子Hairy和分裂增强子1（Hes1）的动力学进行建模，其表达在神经发育过程中振荡，并且在胚胎大脑中对于稳定的命运决定至关重要。我们使用常微分方程（ODEs）在一个网格上设计、参数化并分析了一个详细的空间模型，该模型捕捉了群体水平上的瞬态振荡行为和命运决定。我们还研究了这个ODE模型与一个更现实的基于网格的包含内在噪声的模型之间的关系，该模型大多使用直接基于生物学的参数。虽然我们特别关注神经发育中的Hes1，但将确定性和基于网格的随机模型联系起来的方法在对细胞群体中发生的各种生物过程进行建模方面显示出了前景。在这种情况下，我们的工作强调了将复杂计算模型解释到一个适合数学分析的框架中的重要性。
