Journal of Mathematical Biology

, Volume 72, Issue 1–2, pp 123–156 | Cite as

From invasion to latency: intracellular noise and cell motility as key controls of the competition between resource-limited cellular populations

  • Pilar Guerrero
  • Helen M. Byrne
  • Philip K. Maini
  • Tomás Alarcón


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, \(P_S(t)\), has a fat-tail behaviour (\(P_S(t)\sim t^{-1}\)) 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.


Invasion Latency Noise Motility 

Mathematics Subject Classification

92D25 97M60 60J80 



PG and TA gratefully acknowledge the Spanish Ministry for Science and Innovation (MICINN) for funding under grants MTM2008-05271, MTM2010-18318-E, MTM2011-29342 and Generalitat de Catalunya for funding under grant 2009SGR345. PG thanks the Wellcome Trust for support under grant 098325. This publication was based on work supported in part by Award No. KUK-013-04, made the King Abdullah University of Science and Technology (KAUST).

Supplementary material

285_2015_883_MOESM1_ESM.pdf (616 kb)
Supplementary material 1 (pdf 616 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Pilar Guerrero
    • 1
  • Helen M. Byrne
    • 2
    • 3
  • Philip K. Maini
    • 2
  • Tomás Alarcón
    • 4
    • 5
  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.Wolfson Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK
  3. 3.Department of Computer Science, Computational Biology GroupUniversity of OxfordOxfordUK
  4. 4.Centre de Recerca MatemàticaBellaterraSpain
  5. 5.Departament de MatemàtiquesUniversitat Atonòma de BarcelonaBellaterraSpain

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