How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations

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

doi:10.1103/physreve.94.012408

Cited by 15 publications

(15 citation statements)

References 44 publications

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“…Yates et al (2012) extended these studies and demonstrated that different ways to split the lattice sites ensures that individual-based stochastic simulations provide equivalent results to PDE models on any non-uniformly growing domain. Ross et al (2016Ross et al ( , 2017 investigated different ways to implement domain growth in lattice-based models. They simulated a one-dimensional random walk with volume exclusion, cell proliferation and death.…”

Section: Domain Growthmentioning

confidence: 99%

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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Section: Domain Growthmentioning

confidence: 99%

Modelling collective cell migration: neural crest as a model paradigm

et al. 2019

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“…From Eq. (19) and the relation σ 2 y (t) = a 2 (t)σ 2 x (t), one can also easily calculate an exact expression for the semi-variance of the physical propagator. One obtains…”

Section: A Power-law Growthmentioning

confidence: 99%

“…For instance, embryonic tissue growth via cellular division takes place during the spreading process leading to the formation of a morphogen gradient [8,9], whereby the local concentration of morphogens may influence the growth process itself [9]. Diffusion of substances throughout growing organs [5,[10][11][12][13][14][15][16][17][18][19] has also been invoked to explain phenomena such as the formation of pigmentation patterns [5], teeth primordia in animals [10], or the growth of microorganisms into colonies [20]. Finally, stochastic transport in growing domains is also a topic of great interest in finance, where random walk models have played a major role since the seminal work of Bachelier [21].…”

Section: Introductionmentioning

confidence: 99%

Standard and fractional Ornstein-Uhlenbeck process on a growing domain

2019

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We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing/contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive Continuous-Time Random Walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the ageing of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing/contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.

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“…The most usual approach for studying diffusion processes on growing media is the macroscopic, continuum description based on the use of partial differential equations for modeling the space-time evolution of the density of diffusing agents [16,22]. A more recent alternative approach is based on microscopic/mesoscopic descriptions in which the starting point is the stochastic movement of the individual agents, often modeled as random walkers [20,23,[37][38][39]. In particular, the Continuous-Time Random-Walk (CTRW) model has been used in Ref.…”

Section: Introductionmentioning

confidence: 99%

Continuous-time random walks and Fokker-Planck equation in expanding media

Vot

Yuste

2018

Phys. Rev. E

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We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation that relates the probability distribution function (pdf) of finding a particle at a given position and time to the single-step jump length and waiting time pdfs is provided. The equation takes the form of a generalized Fokker-Planck equation when the jump length pdf of the particle has a finite variance. This generalized equation becomes a fractional Fokker-Planck equation in the case of a heavy-tailed waiting time pdf. These equations allow us to study the relationship between expansion, diffusion and external force. We establish the conditions under which the dominant contribution to transport stems from the diffusive transport rather than from the drift due to the medium expansion. We find that anomalous diffusion processes under a constant external force in an expanding medium described by means of our continuous random walk model are not Galilei invariant, violate the generalized Einstein relation, and lead to propagators that are qualitatively different from the ones found in a static medium. Our results are supported by numerical simulations.

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How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations

Cited by 15 publications

References 44 publications

Modelling collective cell migration: neural crest as a model paradigm

Modelling collective cell migration: neural crest as a model paradigm

Standard and fractional Ornstein-Uhlenbeck process on a growing domain

Continuous-time random walks and Fokker-Planck equation in expanding media

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