Diffusion of Finite-Size Particles in Confined Geometries

Bruna, María; Chapman, S. Jonathan

doi:10.1007/s11538-013-9847-0

Cited by 33 publications

(42 citation statements)

References 31 publications

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“…Taking the occupied volume fraction as a small parameter , they used matched asymptotic expansions in to derive a nonlinear diffusion equation, and found that the diffusion coefficient for collective movement of the population was an increasing function of . Bruna and Chapman (2012a) extended the model to deal with multiple species, each with its own diffusivity, and Bruna and Chapman (2014) considered the case where the particles are moving in a severely confined domain (e.g. a narrow channel whose width is comparable to the diameter of the particles).…”

Section: Discussionmentioning

confidence: 99%

“…By working in continuous space, we avoid the need to specify an artificial lattice for the agent locations. The use of lattice-based models is usually for technical convenience rather than biological realism (Bruna and Chapman 2014), and the choice of lattice can influence model behaviour (Fernando et al 2010;Plank and Simpson 2012). The idea behind spatial-moment dynamics is to capture spatial correlations between pairs of agents in the dynamics, moving on from mean-field approaches that ignore spatial correlations altogether.…”

Section: Introductionmentioning

confidence: 99%

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Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions

Plank

Law

2014

Bull Math Biol

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Mathematical models of dynamical systems in the life sciences typi-6 cally assume that biological systems are spatially well mixed (the mean-field as-7 sumption). Even spatially explicit differential equation models typically make 8 a local mean-field assumption. In effect, the assumption is that diffusive move-9 ment is strong enough to destroy spatial structure, or that interactions between 10 individuals are sufficiently long-ranged that the effects of spatial structure are of agents in space, in which no information about spatial structure is retained. 21By including the dynamics of at least the second moment, the method re- 22tains some information about spatial structure. Whereas mean-field models 23 effectively use a closure assumption for the second moment, spatial-moment 24 models use a closure assumption for the third (or a higher-order) moment. 25The aim of the paper is to provide a parsimonious and intuitive derivation 26 of spatial-moment dynamic equations that is accessible to non-specialists. The

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions

Plank

Law

2014

Bull Math Biol

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“…More recent biologically inspired lattice-free models have incorporated crowding effects by ensuring that individual agents in the model cannot occupy the same location, and cannot step across other agents in the system. These previous studies have investigated collective motion in one-and two-dimensional geometries [22][23][24], combined motility and proliferation mechanisms [19], as well as considering the collective motion of different subpopulations of agents within a multispecies framework [25]. We note that none of these previous lattice-free models of collective cell motion have incorporated any kind of adhesion mechanism.…”

Section: Introductionmentioning

confidence: 99%

Lattice-free descriptions of collective motion with crowding and adhesion

2013

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Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

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“…We look for a solution of (20), (21), and (22) in the left (x < −1) and right (x > 1) subdomains in powers of ǫ,P ∼P 0 + ǫP 1 + · · · . The leading-order problem is, in both subdomains,…”

Section: Matched Asymptotic Expansionsmentioning

confidence: 99%

One-dimensional model for chemotaxis with hard-core interactions

2020

Self Cite

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In this paper we consider a velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where the size of each particle affects the motion. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach, based on matched asymptotic expansions, is systematic and hence does not rely on a closure assumption. It is valid in the limit of small but finite particle occupied fraction and in the presence of external signals. The second method, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding non-interacting linear model as well as stochastic simulations of the underlying particle system.

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Diffusion of Finite-Size Particles in Confined Geometries

Cited by 33 publications

References 31 publications

Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions

Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions

Lattice-free descriptions of collective motion with crowding and adhesion

One-dimensional model for chemotaxis with hard-core interactions

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