Mean-field descriptions of collective migration with strong adhesion.

Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean-field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

[1]  Kerry A Landman,et al.  Building macroscale models from microscale probabilistic models: a general probabilistic approach for nonlinear diffusion and multispecies phenomena. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  A theoretical stochastic model for the A+1/2B2→0 reaction , 1993 .

[3]  Matthew J Simpson,et al.  Nonlinear diffusion and exclusion processes with contact interactions. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  T. Prabhakar Clement,et al.  Assessment of a non-traditional operator split algorithm for simulation of reactive transport , 2005, Math. Comput. Simul..

[5]  Matthew J Simpson,et al.  Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  M. Keeling,et al.  Integrating stochasticity and network structure into an epidemic model , 2008, Journal of The Royal Society Interface.

[7]  Matthew J Simpson,et al.  Correcting mean-field approximations for birth-death-movement processes. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Matthew J Simpson,et al.  Migration of breast cancer cells: understanding the roles of volume exclusion and cell-to-cell adhesion. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Michael Chopp,et al.  Collective behavior of brain tumor cells: the role of hypoxia. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  K. Seki,et al.  Reaction under vacancy-assisted diffusion at high quencher concentration. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Matthew J Simpson,et al.  Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Vito Quaranta,et al.  A novel circular invasion assay mimics in vivo invasive behavior of cancer cell lines and distinguishes single-cell motility in vitro , 2008, BMC Cancer.

[13]  Ruben Juanes,et al.  Nonmonotonic traveling wave solutions of infiltration into porous media , 2008 .

[14]  A. Singer,et al.  Maximum entropy formulation of the Kirkwood superposition approximation. , 2004, The Journal of chemical physics.

[15]  C. Schmeiser,et al.  A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion , 2009, Journal of mathematical biology.

[16]  Christophe Deroulers,et al.  Modeling tumor cell migration: From microscopic to macroscopic models. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  W. von Niessen,et al.  A general stochastic model for the description of surface reaction systems , 1994 .

[18]  Leonard M. Sander,et al.  The Role of Cell-Cell Adhesion in Wound Healing , 2006, q-bio/0610015.

[19]  H. Weinberger,et al.  Maximum principles in differential equations , 1967 .

[20]  Edward A. Codling,et al.  Random walk models in biology , 2008, Journal of The Royal Society Interface.

[21]  Matthew J. Simpson,et al.  A model for mesoscale patterns in motile populations , 2010 .

[22]  Andrew G. Glen,et al.  APPL , 2001 .

[23]  U. Dieckmann,et al.  POPULATION GROWTH IN SPACE AND TIME: SPATIAL LOGISTIC EQUATIONS , 2003 .

[24]  Ulf Dieckmann,et al.  On moment closures for population dynamics in continuous space. , 2004, Journal of theoretical biology.

[25]  Thomas P. Witelski.  Shocks in nonlinear diffusion , 1995 .

[26]  Katsuhiro Nishinari,et al.  Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms , 2005 .

[27]  Ulf Dieckmann,et al.  A multiscale maximum entropy moment closure for locally regulated space–time point process models of population dynamics , 2011, Journal of mathematical biology.

[28]  B. M. Fulk.  MATH , 1992 .

[29]  K. Sharkey.  Deterministic epidemiological models at the individual level , 2008, Journal of mathematical biology.

[30]  Kerry A. Landman,et al.  Myopic random walkers and exclusion processes: Single and multispecies , 2011 .

[31]  John Comyn.  Molecular adhesion and its applications: the sticky universe: Kevin Kendall; Kluwer Academic/Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2001, 429pp.+xix, ISBN 0-306-46520-5. £59.50, €97.75. , 2002 .

[32]  Matthew J Simpson,et al.  Modeling proliferative tissue growth: a general approach and an avian case study. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.