The impact of phenotypic heterogeneity on chemotactic self-organisation

F.R.M. gratefully acknowledges support from the RSE Saltire Early Career Fellowship ‘Multiscale mathematical modelling of spatial eco-evolutionary cancer dynamics’ (Fellowship No. 1879). T.L. gratefully acknowledges support from the Italian Ministry of University and Research (MUR) through the grant “Dipartimenti di Eccellenza 2018–2022” (Project no. E11G18000350001) and the PRIN 2020 project (No. 2020JLWP23) “Integrated Mathematical Approaches to Socio-Epidemiological Dynamics” (CUP: E15F21005420006). K.J.P. acknowledges “MIUR-Dipartimento di Eccellenza” funding to the Dipartimento Interateneo di Scienze, Progetto e Politiche del Territorio (DIST).The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phenotypically homogeneous population that secretes its own attractant, with the well known system introduced more than five decades ago by Keller and Segel proving resolutely popular in modelling studies. The typical assumption of population phenotypic homogeneity, however, often lies at odds with the heterogeneity of natural systems, where populations may comprise distinct phenotypes that vary according to their chemotactic ability, attractant secretion, etc. To initiate an understanding into how this diversity can impact on autoaggregation, we propose a simple extension to the classical Keller and Segel model, in which the population is divided into two distinct phenotypes: those performing chemotaxis and those producing attractant. Using a combination of linear stability analysis and numerical simulations, we demonstrate that switching between these phenotypic states alters the capacity of a population to self-aggregate. Further, we show that switching based on the local environment (population density or chemoattractant level) leads to diverse patterning and provides a route through which a population can effectively curb the size and density of an aggregate. We discuss the results in the context of real world examples of chemotactic aggregation, as well as theoretical aspects of the model such as global existence and blow-up of solutions.Publisher PDFPeer reviewe