The effect of domain growth on spatial correlations

Ross, Robert; Yates, Christian A.; Baker, Ruth E.

doi:10.1016/j.physa.2016.09.002

Cited by 8 publications

(15 citation statements)

References 40 publications

(140 reference statements)

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“…This approximation has been previously published [26], and reasonably implies that domain growth 'dilutes' the agent density [16] (we present analysis of the accuracy of this approximation in Section S2 of the supplementary information). Finally, we simplify Eq.…”

mentioning

confidence: 61%

“…The approximation we employ in Eq. (6) in the main text has been previously published [16,17,26], and in Ross et al [16] its accuracy for a one-dimensional lattice-based model has been demonstrated. In terms of one-point density functions this approximation…”

Section: S2: Analysis Of Closure Approximationmentioning

confidence: 83%

“…(2) 2 As ρ Nx×Ny A (m; t) denotes a probability its domain of definition is [0, 1]. 3 A simpler (one-dimensional) version of this derivation can be found in Ross et al [16].…”

Section: Individual Density Functionsmentioning

confidence: 99%

“…It can be seen that the average relative error associated with the closure decreases as the domain grows larger, meaning the approximation improves as the domain grows. Other plots examining the error associated with the moment closures presented in this manuscript can be found in Ross et al [16]. 7 To compute the average relative error we proceed as follows: we initialise a domain of length Nx = 100, Ny = 100, with Pg x = 0.1 and Pg y = 0 (i.e.…”

Section: S2: Analysis Of Closure Approximationmentioning

confidence: 99%

“…To do so we employ an agent-based, discrete random-walk model on a two-dimensional square lattice with volume-exclusion. We have previously shown that the way in which domain growth is implemented in an IBM can alter the behaviour of a population of identical agents [16,17]. Therefore, we hypothesised that the way in which domain growth is implemented in a simulation with multiple agent species could change the dominant agent species.…”

Section: Introductionmentioning

confidence: 99%

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Variable species densities are induced by volume exclusion interactions upon domain growth

Ross

Yates

Baker

2016

Preprint

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In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long term behaviour of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behaviour, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long term behaviour of multispecies populations, and in certain circumstances, establish spatially varying species densities.

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mentioning

confidence: 61%

Section: S2: Analysis Of Closure Approximationmentioning

confidence: 83%

“…(2) 2 As ρ Nx×Ny A (m; t) denotes a probability its domain of definition is [0, 1]. 3 A simpler (one-dimensional) version of this derivation can be found in Ross et al [16].…”

Section: Individual Density Functionsmentioning

confidence: 99%

Section: S2: Analysis Of Closure Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Variable species densities are induced by volume exclusion interactions upon domain growth

Ross

Yates

Baker

2016

Preprint

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Modelling collective cell migration: neural crest as a model paradigm

et al. 2019

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A huge variety of mathematical models have been used to investigate collective cell migration. The aim of this brief review is twofold: to present a number of modelling approaches that incorporate the key factors affecting cell migration, including cell-cell and cell-tissue interactions, as well as domain growth, and to showcase their application to model the migration of neural crest cells. We discuss the complementary strengths of microscale and macroscale models, and identify why it can be important to understand how these modelling approaches are related. We consider neural crest cell migration as a model paradigm to illustrate how the application of different mathematical modelling techniques, combined with experimental results, can provide new biological insights. We conclude by highlighting a number of future challenges for the mathematical modelling of neural crest cell migration.

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Stochastic models of cell invasion with fluorescent cell cycle indicators

Simpson

Wang

Vittadello

et al. 2018

Physica A: Statistical Mechanics and its Applications

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Fluorescent cell cycle labelling in cell biology experiments provides real time information about the location of individual cells, as well as the phase of the cell cycle of individual cells. We develop a stochastic, lattice-based random walk model of a two-dimensional scratch assay where the total population is composed of three distinct subpopulations which we visualise as red, yellow and green subpopulations. Our model mimics FUCCI technology in which cells in the G1 phase of the cell cycle fluoresce red, cells in the early S phase fluoresce yellow, and cells in the S/G2/M phase fluoresce green. The model is an exclusion process so that any potential motility or proliferation event that would place an agent on an occupied lattice site is aborted. Using experimental images and previous experimental measurements we explain how to apply the stochastic model to simulate a scratch assay initialised with a low to moderate density monolayer of human melanoma cell line. We obtain additional mathematical insight by deriving an approximate partial differential equation (PDE) description of the stochastic model, leading to a novel system of three coupled nonlinear reaction diffusion equations. Comparing averaged simulation data with the solution of the continuum limit model confirms that the PDE description is accurate for biologically-relevant parameter combinations.

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The effect of domain growth on spatial correlations

Cited by 8 publications

References 40 publications

Variable species densities are induced by volume exclusion interactions upon domain growth

Variable species densities are induced by volume exclusion interactions upon domain growth

Modelling collective cell migration: neural crest as a model paradigm

Stochastic models of cell invasion with fluorescent cell cycle indicators

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