Bayesian inference and information criteria for selection of reaction-diffusion models of collective cell behaviour

Spatial models of collective cell behaviour are often based on reaction-diffusion models that describe a population of motile cells that proliferate and die. Various flux and source terms within the reaction-diffusion framework can be used to model different mechanisms. For example, motility may involve random motion (diffusion), adhesion, haptotaxis, chemokinesis and chemotaxis. In many applications, such as wound healing, it is not always clear which motility mechanisms are most important. As a result, heuristic choices are often made without quantitative validation against real data. Those studies that do perform model validation and model comparison typically base decisions on the minimisation of residual errors. Unfortunately, this approach is known to favour over-parameterised models. We demonstrate the utility of Bayesian methods and information criteria for robust model selection that accounts for model complexity, model consistency and residual error. Our approach also provides insights into the current limitations with in vitro cell culture experimental protocols to inform model selection in practice