Topological approximate Bayesian computation for parameter inference of an angiogenesis model

Motivation 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 characterized. Results Here, we focus on recent work using TDA 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 toward a general framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorizations and summary statistics to be considered. Availability and implementation All code used to produce our results is available as a Snakemake workflow from github.com/tt104/tabc_angio.

Automated summary

This article discusses the importance of inferring the parameters of models describing biological systems in reverse engineering and proposes a method combining topological data analysis with Approximate Bayesian Computation (ABC) to infer parameters in angiogenesis. The results demonstrate that this topological approach outperforms ABC methods using simpler spatial statistics. This is a first step towards a general framework for spatial parameter inference in biological systems.