How cellular movement determines the collective force generated by the Dictyostelium discoideum slug.

How the collective motion of cells in a biological tissue originates in the behavior of a collection of individuals, each of which responds to the chemical and mechanical signals it receives from neighbors, is still poorly understood. Here we study this question for a particular system, the slug stage of the cellular slime mold Dictyostelium discoideum (Dd). We investigate how cells in the interior of a migrating slug can effectively transmit stress to the substrate and thereby contribute to the overall motive force. Theoretical analysis suggests necessary conditions on the behavior of individual cells, and computational results shed light on experimental results concerning the total force exerted by a migrating slug. The model predicts that only cells in contact with the substrate contribute to the translational motion of the slug. Since the model is not based specifically on the mechanical properties of Dd cells, the results suggest that this behavior will be found in many developing systems.

[1]  L. Davidson,et al.  Neural tube closure in Xenopus laevis involves medial migration, directed protrusive activity, cell intercalation and convergent extension. , 1999, Development.

[2]  D R Soll,et al.  Behavior of Dictyostelium amoebae is regulated primarily by the temporal dynamic of the natural cAMP wave. , 1992, Cell motility and the cytoskeleton.

[3]  V. Katanaev Signal Transduction in Neutrophil Chemotaxis , 2001, Biochemistry (Moscow).

[4]  A. Harris,et al.  Silicone rubber substrata: a new wrinkle in the study of cell locomotion. , 1980, Science.

[5]  E. Hill Journal of Theoretical Biology , 1961, Nature.

[6]  Lewis Wolpert,et al.  Principles of Development , 1997 .

[7]  A. Mogilner,et al.  A Simple 1-D Physical Model for the Crawling Nematode Sperm Cell , 2003, Journal of statistical physics.

[8]  Bretschneider,et al.  A model for dictyostelium slug movement , 1999, Journal of theoretical biology.

[9]  M. Sheetz,et al.  Cell migration as a five-step cycle. , 1999, Biochemical Society symposium.

[10]  F. MacKintosh Theoretical models of viscoelasticity of actin solutions and the actin cortex. , 1998, The Biological bulletin.

[11]  Erich Sackmann,et al.  Dictyostelium cells' cytoplasm as an active viscoplastic body , 2001, European Biophysics Journal.

[12]  R. Futrelle,et al.  Cell behavior in Dictyostelium discoideum: preaggregation response to localized cyclic AMP pulses , 1982, The Journal of cell biology.

[13]  S Chien,et al.  Leukocyte relaxation properties. , 1988, Biophysical journal.

[14]  H G Othmer,et al.  Differentiation, cell sorting and proportion regulation in the slug stage of Dictyostelium discoideum. , 1986, Journal of theoretical biology.

[15]  Hans G. Othmer,et al.  A continuum model of motility in ameboid cells , 2004, Bulletin of mathematical biology.

[16]  G. Gerisch Chemotaxis in Dictyostelium. , 1982, Annual review of physiology.

[17]  E. Evans,et al.  Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets. , 1989, Biophysical journal.

[18]  K. Inouye Measurement of the motive force of the migrating slug ofDictyostelium discoideum by a centrifuge method , 1984, Protoplasma.

[19]  P. Fey,et al.  SadA, a novel adhesion receptor in Dictyostelium , 2002, The Journal of cell biology.

[20]  J Hardin,et al.  Cell Behaviour During Active Cell Rearrangement: Evidence and Speculations , 1987, Journal of Cell Science.

[21]  J. Small,et al.  Microfilament-based motility in non-muscle cells. , 1989, Current opinion in cell biology.

[22]  H. Othmer,et al.  A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum. , 1997, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[23]  H G Othmer,et al.  Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum. , 1995, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[24]  A. Bresnick,et al.  Mechanisms of amoeboid chemotaxis: an evaluation of the cortical expansion model. , 1990, Developmental genetics.

[25]  H. Othmer,et al.  A G protein-based model of adaptation in Dictyostelium discoideum. , 1994, Mathematical biosciences.

[26]  R. Firtel,et al.  Signaling pathways controlling cell polarity and chemotaxis. , 2001, Trends in biochemical sciences.

[27]  Alex Mogilner,et al.  A Minimal Model of Locomotion Applied to the Steady Gliding Movement of Fish Keratocyte Cells , 2001 .

[28]  I. Takeuchi,et al.  Motive force of the migrating pseudoplasmodium of the cellular slime mould Dictyostelium discoideum. , 1980, Journal of cell science.

[29]  M. Titus,et al.  A Dictyostelium myosin I plays a crucial role in regulating the frequency of pseudopods formed on the substratum. , 1996, Cell motility and the cytoskeleton.

[30]  N. Caille,et al.  Contribution of the nucleus to the mechanical properties of endothelial cells. , 2002, Journal of biomechanics.

[31]  S Chien,et al.  Locomotion forces generated by a polymorphonuclear leukocyte. , 1992, Biophysical journal.

[32]  R. Skalak,et al.  Leukocyte deformability: finite element modeling of large viscoelastic deformation. , 1992, Journal of theoretical biology.

[33]  M. Dembo,et al.  Cell movement is guided by the rigidity of the substrate. , 2000, Biophysical journal.

[34]  P. Maini,et al.  Mathematical Models for Biological Pattern Formation , 2001 .

[35]  T. Umeda,et al.  Possible role of contact following in the generation of coherent motion of Dictyostelium cells. , 2002, Journal of theoretical biology.

[36]  International review of cytology. Vol. IV. , 1954 .

[37]  Paulien Hogeweg,et al.  Modelling Dictyostelium discoideum morphogenesis: The culmination , 2002, Bulletin of mathematical biology.

[38]  A. Ravandi,et al.  Assembly of glycoprotein-80 adhesion complexes in Dictyostelium. Receptor compartmentalization and oligomerization in membrane rafts. , 2001, The Journal of biological chemistry.

[39]  Florian Siegert,et al.  A Hydrodynamic model forDictyostelium discoideumMound Formation , 1997 .

[40]  R. Skalak,et al.  Passive mechanical properties of human leukocytes. , 1981, Biophysical journal.

[41]  H. Othmer,et al.  A model for individual and collective cell movement in Dictyostelium discoideum. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[42]  J. T. Bonner,et al.  How the Dictyostelium Discoideum Grex Crawls , 1986 .

[43]  A Hydrodynamic model for Dictyostelium discoideum Mound Formation , 1997 .

[44]  T. Umeda,et al.  Theoretical model for morphogenesis and cell sorting in Dictyostelium discoideum , 1999 .

[45]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[46]  Yousef Saad,et al.  Hybrid Krylov Methods for Nonlinear Systems of Equations , 1990, SIAM J. Sci. Comput..

[47]  D. Taylor,et al.  Local and spatially coordinated movements in Dictyostelium discoideum amoebae during chemotaxis , 1982, Cell.

[48]  B. Shaffer The Acrasina: (continued from vol. 2, pp. 109-182) , 1964 .

[49]  T. Umeda A thermodynamical model of cell distributions in the slug of cellular slime mold , 1993 .

[50]  Bakhtier Vasiev,et al.  Modelling of Dictyostelium discoideum slug migration. , 2003, Journal of theoretical biology.

[51]  C. Parent,et al.  Localization of the G Protein βγ Complex in Living Cells During Chemotaxis , 2000 .

[52]  J. Bonner,et al.  A way of following individual cells in the migrating slugs of Dictyostelium discoideum. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[53]  D. Soll The use of computers in understanding how animal cells crawl. , 1995, International review of cytology.

[54]  S Chien,et al.  Membrane model of endothelial cells and leukocytes. A proposal for the origin of a cortical stress. , 1995, Journal of biomechanical engineering.

[55]  M. Titus,et al.  Myosin I Phosphorylation Is Increased by Chemotactic Stimulation* , 2001, The Journal of Biological Chemistry.

[56]  A. Noegel,et al.  The actin cytoskeleton of Dictyostelium: a story told by mutants. , 2000, Journal of cell science.

[57]  I. Takeuchi,et al.  Analytical studies on migrating movement of the pseudo-plasmodium ofDictyostelium discoideum , 1979, Protoplasma.

[58]  D A Lauffenburger,et al.  Mathematical model for the effects of adhesion and mechanics on cell migration speed. , 1991, Biophysical journal.

[59]  C. Weijer,et al.  Modelling Dictyostelium discoideum Morphogenesis , 2001 .

[60]  P. Skoglund,et al.  Mechanisms of convergence and extension by cell intercalation. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[61]  N. Blackstone,et al.  Molecular Biology of the Cell.Fourth Edition.ByBruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and, Peter Walter.New York: Garland Science.$102.00. xxxiv + 1463 p; ill.; glossary (G:1–G:36); index (I:1–I:49); tables (T:1). ISBN: 0–8153–3218–1. [CD‐ROM included.] 2002. , 2003 .

[62]  Peter Friedl,et al.  Compensation mechanism in tumor cell migration , 2003, The Journal of cell biology.

[63]  H G Othmer,et al.  A continuum analysis of the chemotactic signal seen by Dictyostelium discoideum. , 1998, Journal of theoretical biology.

[64]  M. Loeffler,et al.  Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. , 2005, Biophysical journal.

[65]  D. Wirtz,et al.  Strain Hardening of Actin Filament Networks , 2000, The Journal of Biological Chemistry.

[66]  J. Glazier,et al.  Model of convergent extension in animal morphogenesis. , 1999, Physical review letters.

[67]  C. Parent,et al.  A cell's sense of direction. , 1999, Science.

[68]  W. Godwin Article in Press , 2000 .

[69]  W Alt,et al.  Cytoplasm dynamics and cell motion: two-phase flow models. , 1999, Mathematical biosciences.

[70]  D. Soll,et al.  Dictyostelium amebae alter motility differently in response to increasing versus decreasing temporal gradients of cAMP , 1985, The Journal of cell biology.

[71]  M. Dembo,et al.  Stresses at the cell-to-substrate interface during locomotion of fibroblasts. , 1999, Biophysical journal.

[72]  Bretschneider,et al.  A Model for Cell Movement During Dictyostelium Mound Formation , 1997, Journal of theoretical biology.

[73]  T. Mitchison,et al.  Actin-Based Cell Motility and Cell Locomotion , 1996, Cell.

[74]  P. Janmey,et al.  Mechanical properties of cytoskeletal polymers. , 1991, Current opinion in cell biology.

[75]  Erik Sahai,et al.  Differing modes of tumour cell invasion have distinct requirements for Rho/ROCK signalling and extracellular proteolysis , 2003, Nature Cell Biology.

[76]  R Skalak,et al.  Passive deformations and active motions of leukocytes. , 1990, Journal of biomechanical engineering.

[77]  Micah Dembo,et al.  Separation of Propulsive and Adhesive Traction Stresses in Locomoting Keratocytes , 1999, The Journal of cell biology.

[78]  J. Condeelis,et al.  Relationship of pseudopod extension to chemotactic hormone‐induced actin polymerization in amoeboid cells , 1988, Journal of cellular biochemistry.

[79]  Hermann E. Gaub,et al.  Discrete interactions in cell adhesion measured by single-molecule force spectroscopy , 2000, Nature Cell Biology.

[80]  Alan C. Hindmarsh,et al.  Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations , 1993 .

[81]  P. Hogeweg,et al.  Modelling Morphogenesis: From Single Cells to Crawling Slugs. , 1997, Journal of theoretical biology.

[82]  S. Zimmer,et al.  Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation. , 1991, Biorheology.