Model for self-polarization and motility of keratocyte fragments

Computational modelling of cell motility on substrates is a formidable challenge; regulatory pathways are intertwined and forces that influence cell motion are not fully quantified. Additional challenges arise from the need to describe a moving deformable cell boundary. Here, we present a simple mathematical model coupling cell shape dynamics, treated by the phase-field approach, to a vector field describing the mean orientation (polarization) of the actin filament network. The model successfully reproduces the primary phenomenology of cell motility: discontinuous onset of motion, diversity of cell shapes and shape oscillations. The results are in qualitative agreement with recent experiments on motility of keratocyte cells and cell fragments. The asymmetry of the shapes is captured to a large extent in this simple model, which may prove useful for the interpretation of experiments.

[1]  Wouter-Jan Rappel,et al.  Computational model for cell morphodynamics. , 2010, Physical review letters.

[2]  Steven P. Levitan,et al.  Designing communicating colonies of biomimetic microcapsules , 2010, Proceedings of the National Academy of Sciences.

[3]  Thomas Duke,et al.  Simulation of cell motility that reproduces the force–velocity relationship , 2010, Proceedings of the National Academy of Sciences.

[4]  Jean-Jacques Meister,et al.  Force transmission in migrating cells , 2010, The Journal of cell biology.

[5]  Hans G Othmer,et al.  Multi-scale models of cell and tissue dynamics , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  David J Odde,et al.  Traction Dynamics of Filopodia on Compliant Substrates , 2008, Science.

[7]  S. Whitelam,et al.  Transformation from spots to waves in a model of actin pattern formation. , 2008, Physical review letters.

[8]  Julie A. Theriot,et al.  Mechanism of shape determination in motile cells , 2008, Nature.

[9]  K. Kruse,et al.  Self-organization of treadmilling filaments. , 2007, Physical review letters.

[10]  M. Carlier,et al.  Control of Actin Assembly Dynamics in Cell Motility* , 2007, Journal of Biological Chemistry.

[11]  J. Lewis,et al.  Self-healing materials with microvascular networks. , 2007, Nature materials.

[12]  K. Kassner,et al.  Nonlinear study of symmetry breaking in actin gels: implications for cellular motility. , 2007, Physical review letters.

[13]  F. Ziebert,et al.  Macroscopic dynamics of polar nematic liquid crystals. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  J. Joanny,et al.  Contractility and retrograde flow in lamellipodium motion , 2006, Physical biology.

[15]  J. M. Oliver,et al.  Thin-film modelling of poroviscous free surface flows , 2005, European Journal of Applied Mathematics.

[16]  Gaudenz Danuser,et al.  Tracking retrograde flow in keratocytes: news from the front. , 2005, Molecular biology of the cell.

[17]  J. M. Oliver,et al.  Thin-film theories for two-phase reactive flow models of active cell motion. , 2005, Mathematical medicine and biology : a journal of the IMA.

[18]  L. Addadi,et al.  Hierarchical assembly of cell-matrix adhesion complexes. , 2004, Biochemical Society transactions.

[19]  J. Joanny,et al.  Asters, vortices, and rotating spirals in active gels of polar filaments. , 2004, Physical review letters.

[20]  M. Sheetz,et al.  Periodic Lamellipodial Contractions Correlate with Rearward Actin Waves , 2004, Cell.

[21]  T. Biben,et al.  Tumbling of vesicles under shear flow within an advected-field approach. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  I. Aranson,et al.  Phase separation and coarsening in electrostatically driven granular media. , 2001, Physical review letters.

[23]  L. Tsimring,et al.  Continuum description of avalanches in granular media. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  I. Aranson,et al.  Continuum field description of crack propagation , 2000, Physical review letters.

[25]  Gary G. Borisy,et al.  Self-polarization and directional motility of cytoplasm , 1999, Current Biology.

[26]  K. Sekimoto,et al.  Polarity Sorting in a Bundle of Actin Filaments by Two-Headed Myosins , 1996 .

[27]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[28]  O. Parodi,et al.  ÉMULSIONS NÉMATIQUES. EFFETS DE CHAMP MAGNÉTIQUES ET EFFETS PIÉZOÉLECTRIQUES , 1969 .

[29]  Alex Mogilner,et al.  Mathematics of Cell Motility: Have We Got Its Number? , 2022 .

[30]  T. Pollard,et al.  Cellular Motility Driven by Assembly and Disassembly of Actin Filaments , 2003, Cell.

[31]  T D Pollard,et al.  Molecular mechanisms controlling actin filament dynamics in nonmuscle cells. , 2000, Annual review of biophysics and biomolecular structure.