Abubaker-Sharif Bedri, Banerjee Tatsat, Devreotes Peter N, Iglesias Pablo A
Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, 21205, USA.
Department of Cell Biology and Center for Cell Dynamics, Johns Hopkins University, Baltimore, MD, 21205, USA.
bioRxiv. 2025 Mar 28:2024.10.02.616367. doi: 10.1101/2024.10.02.616367.
Pattern-forming stochastic systems arise throughout biology, with dynamic molecular waves observed in biochemical networks regulating critical cellular processes. Modeling these reaction-diffusion systems using handcrafted stochastic partial differential equations (PDEs) requires extensive trial-and-error tuning. Data-driven approaches for improved modeling are needed but have been hindered by data scarcity and noise. Here, we present a solution to the inverse problem of learning stochastic reaction-diffusion models from limited data by optimizing two spatiotemporal features: (1) stochastic dynamics and (2) spatiotemporal patterns. Combined with sparsity enforcement, this method identifies novel activator-inhibitor models with interpretable structure. We demonstrate robust learning from simulations of excitable systems with varying data scarcity, as well as noisy live-cell imaging data with low temporal resolution and a single observed biomolecule. This generalizable approach to learning governing stochastic PDEs enhances our ability to model and understand complex spatiotemporal systems from limited, real-world data.
模式形成随机系统在整个生物学中都有出现，在调节关键细胞过程的生化网络中观察到动态分子波。使用手工制作的随机偏微分方程（PDE）对这些反应扩散系统进行建模需要大量反复试验的调整。需要改进建模的数据驱动方法，但一直受到数据稀缺和噪声的阻碍。在这里，我们提出了一种解决方案，通过优化两个时空特征，从有限的数据中学习随机反应扩散模型的反问题：（1）随机动力学和（2）时空模式。结合稀疏性约束，该方法识别出具有可解释结构的新型激活剂-抑制剂模型。我们展示了从具有不同数据稀缺性的可激发系统模拟中进行稳健学习的能力，以及从具有低时间分辨率和单个观察到的生物分子的噪声活细胞成像数据中进行学习的能力。这种学习控制随机偏微分方程的通用方法增强了我们从有限的真实世界数据中对复杂时空系统进行建模和理解的能力。
