Thomas Thorne1, Paul D W Kirk2,3,4, Heather A Harrington5,6. 1. Department of Computer Science, University of Surrey, Guildford, GU2 7XH, United Kingdom. 2. MRC Biostatistics Unit, University of Cambridge, Cambridge, CB2 0SR, United Kingdom. 3. Cambridge Institute of Therapeutic Immunology & Infectious Disease (CITIID), University of Cambridge, Cambridge, CB2 0AW, United Kingdom. 4. Cancer Research UK Cambridge Centre, Ovarian Cancer Programme, Cambridge, CB2 0RE, United Kingdom. 5. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, United Kingdom. 6. Wellcome Centre for Human Genetics, University of Oxford, Oxford, OX3 7BN, United Kingdom.
Abstract
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 characterised. RESULTS: 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. AVAILABILITY AND IMPLEMENTATION: All code used to produce our results is available as a Snakemake workflow from github.com/tt104/tabc_angio.
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 characterised. RESULTS: 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. AVAILABILITY AND IMPLEMENTATION: All code used to produce our results is available as a Snakemake workflow from github.com/tt104/tabc_angio.
Authors: Juliane Liepe; Paul Kirk; Sarah Filippi; Tina Toni; Chris P Barnes; Michael P H Stumpf Journal: Nat Protoc Date: 2014-01-23 Impact factor: 13.491
Authors: Oliver Vipond; Joshua A Bull; Philip S Macklin; Ulrike Tillmann; Christopher W Pugh; Helen M Byrne; Heather A Harrington Journal: Proc Natl Acad Sci U S A Date: 2021-10-12 Impact factor: 11.205
Authors: John T Nardini; Bernadette J Stolz; Kevin B Flores; Heather A Harrington; Helen M Byrne Journal: PLoS Comput Biol Date: 2021-06-28 Impact factor: 4.475