title: Edge effects in game-theoretic dynamics of spatially structured tumours.
abstract: Cancer dynamics are an evolutionary game between cellular phenotypes. A typical assumption in this modelling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard for local neighbourhood structure. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go versus grow game. We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary--such as a blood vessel, organ capsule or basement membrane--we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (epithelial-mesenchymal transition-positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Our results caution that pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. Although we concentrate on applications in mathematical oncology, we expect our approach to extend to other evolutionary game models where interaction neighbourhoods change at fixed system boundaries.
authors.affiliation: School of Computer Science and Department of Psychology, McGill University, Montreal, Quebec, Canada Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA artem.kaznatcheev@mail.mcgill.ca.
authors.forename: Artem
authors.initials: A
authors.lastname: Kaznatcheev
authors.affiliation: Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK.
authors.forename: Jacob G
authors.initials: JG
authors.lastname: Scott
authors.affiliation: Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.
authors.forename: David
authors.initials: D
authors.lastname: Basanta
mesh_terms: D000818:Animals; D005716:Game Theory; D006801:Humans; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D009369:Neoplasms / Q000098:blood supply / Q000378:metabolism* / Q000473:pathology
keywords: edge effect; evolutionary game theory; go-versus-grow game; heterogeneity; spatial structure