Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population

Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it is challenging to infer the interaction rules directly from data. In the field of equation discovery, the weak-form sparse identification of nonlinear dynamics (WSINDy) methodology has been shown to be computationally efficient for identifying the governing equations of complex systems from noisy data. Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for the second-order IPS to learn equations for communities of cells. Our approach learns the directional interaction rules for each individual cell that in aggregate govern the dynamics of a heterogeneous population of migrating cells. To sort a cell according to the active classes present in its model, we also develop a novel ad hoc classification scheme (which accounts for the fact that some cells do not have enough evidence to accurately infer a model). Aggregated models are then constructed hierarchically to simultaneously identify different species of cells present in the population and determine best-fit models for each species. We demonstrate the efficiency and proficiency of the method on several test scenarios, motivated by common cell migration experiments.

相互作用粒子系统（IPS）模型已被证明在描述生物体的空间运动方面非常成功。然而，直接从数据推断相互作用规则具有挑战性。在方程发现领域，非线性动力学的弱形式稀疏识别（WSINDy）方法已被证明在从含噪数据中识别复杂系统的控制方程方面具有计算效率。受IPS模型在描述生物体空间运动方面取得成功的启发，我们针对二阶IPS开发了WSINDy，用于学习细胞群落的方程。我们的方法学习每个单个细胞的定向相互作用规则，这些规则总体上控制着迁移细胞异质群体的动态。为了根据细胞模型中存在的活跃类别对细胞进行分类，我们还开发了一种新的特定分类方案（考虑到一些细胞没有足够证据来准确推断模型这一事实）。然后分层构建聚合模型，以同时识别群体中存在的不同细胞种类，并为每个种类确定最佳拟合模型。我们在一些受常见细胞迁移实验启发的测试场景中展示了该方法的效率和熟练度。