Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focused on parameter inference of stochastic and ordinary differential equation models using Approximate Bayesian Computation (ABC). While there is some recent work on inference in spatial models, this remains an open problem. Simultaneously, advances in topological data analysis (TDA), a field of computational mathematics, have enabled spatial patterns in data to be characterised. Here we focus on recent work using topological data analysis to study different regimes of parameter space for a well-studied model of angiogenesis. We propose a method for combining TDA with ABC to infer parameters in the Anderson-Chaplain model of angiogenesis. We demonstrate that this topological approach outperforms ABC approaches that use simpler statistics based on spatial features of the data. This is a first step towards a general framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorisations, and summary statistics to be considered. All code used to produce our results is available as a Snakemake workflow.
翻译:对描述生物系统的模型参数进行推论是这些系统机制的反向工程中的一个重要问题。许多工作的重点是使用Apbear Bayesian Computation(ABC)对随机和普通等式模型参数进行参数推论。虽然最近对空间模型的推论进行了一些工作,但这仍然是一个尚未解决的问题。与此同时,地形数据分析的进展(TDA)是计算数学的一个领域,使数据的空间模式得以定性。这里我们侧重于最近的工作,利用地形数据分析来研究参数空间的不同系统,以形成一个研究周密的血管生成模型。我们提出了一种将TDA与ABC结合的方法,以推断安德森-查普兰血管起源模型中的参数。我们证明,这种表理学方法优于ABC方法,而后者使用基于数据空间特征的简单统计数据。这是向生物系统空间参数推论总框架迈出的第一步,其中可能存在各种过滤、矢量和摘要统计,供考虑。我们用于产生结果的所有代码都用作蛇体的工作流程。