title: From invasion to latency: intracellular noise and cell motility as key controls of the competition between resource-limited cellular populations.
abstract: In this paper we analyse stochastic models of the competition between two resource-limited cell populations which differ in their response to nutrient availability: the resident population exhibits a switch-like response behaviour while the invading population exhibits a bistable response. We investigate how noise in the intracellular regulatory pathways and cell motility influence the fate of the incumbent and invading populations. We focus initially on a spatially homogeneous system and study in detail the role of intracellular noise. We show that in such well-mixed systems, two distinct regimes exist: In the low (intracellular) noise limit, the invader has the ability to invade the resident population, whereas in the high noise regime competition between the two populations is found to be neutral and, in accordance with neutral evolution theory, invasion is a random event. Careful examination of the system dynamics leads us to conclude that (i) even if the invader is unable to invade, the distribution of survival times, PS(t), has a fat-tail behaviour (PS(t) ∼ t(-1)) which implies that small colonies of mutants can coexist with the resident population for arbitrarily long times, and (ii) the bistable structure of the invading population increases the stability of the latent population, thus increasing their long-term likelihood of survival, by decreasing the intensity of the noise at the population level. We also examine the effects of spatial inhomogeneity. In the low noise limit we find that cell motility is positively correlated with the aggressiveness of the invader as defined by the time the invader takes to invade the resident population: the faster the invasion, the more aggressive the invader.
authors.affiliation: Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK. pguerrero@ucl.ac.uk.
authors.forename: Pilar
authors.initials: P
authors.lastname: Guerrero
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK. byrne@maths.ox.ac.uk.|Department of Computer Science, Computational Biology Group, University of Oxford, Oxford, OX1 3QD, UK. byrne@maths.ox.ac.uk.
authors.forename: Helen M
authors.initials: HM
authors.lastname: Byrne
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK. maini@maths.ox.ac.uk.
authors.forename: Philip K
authors.initials: PK
authors.lastname: Maini
authors.affiliation: Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193, Bellaterra, Barcelona, Spain. tomasalarc@gmail.com.|Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193, Bellaterra, Barcelona, Spain. tomasalarc@gmail.com.
authors.forename: Tomás
authors.initials: T
authors.lastname: Alarcón
mesh_terms: D000465:Algorithms; D002465:Cell Movement; D002468:Cell Physiological Phenomena; D049109:Cell Proliferation; D055641:Mathematical Concepts; D008954:Models, Biological; D015398:Signal Transduction; D013269:Stochastic Processes; D049490:Systems Biology
keywords: Invasion; Latency; Motility; Noise
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