Simulating convergent extension by way of anisotropic differential adhesion.

Simulations using the Extended Potts Model suggest that anisotropic differential adhesion can account for convergent extension, as observed during embryonic development of the frog Xenopus laevis for example. During gastrulation in these frogs, convergent extension produces longitudinal tissue growth from latitudinal elongation and migration of aligned constituent cells. The Extended Potts Model employs clustered points on a grid to represent subdivided cells with probabilistic displacement of cell boundaries such that small changes in energy drive gradual tissue development. For modeling convergent extension, simulations include anisotropic differential adhesion: the degree of attachment between adjacent elongated cells depends on their relative orientation. Without considering additional mechanisms, simulations based on anisotropic differential adhesion reproduce the hallmark stages of convergent extension in the correct sequence, with random fluctuations as sufficient impetus for cell reorganization.

[1]  R. Keller,et al.  Gastrulation : movements, patterns, and molecules , 1991 .

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

[3]  K D Irvine,et al.  Cell intercalation during Drosophila germband extension and its regulation by pair-rule segmentation genes. , 1994, Development.

[4]  J. McCaskill,et al.  Monte Carlo approach to tissue-cell populations. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  J. Shih,et al.  Cell motility driving mediolateral intercalation in explants of Xenopus laevis. , 1992, Development.

[6]  N S Goel,et al.  Computer simulation of cellular movements: cell-sorting, cellular migration through a mass of cells and contact inhibition. , 1978, Journal of theoretical biology.

[7]  A. Huttenlocher,et al.  Adhesion in cell migration. , 1995, Current opinion in cell biology.

[8]  N. Britton,et al.  Stochastic simulation of benign avascular tumour growth using the Potts model , 1999 .

[9]  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.

[10]  G. Odell,et al.  Polarized basolateral cell motility underlies invagination and convergent extension of the ascidian notochord. , 2002, Development.

[11]  M Ycas,et al.  Self-sorting of isotropic cells. , 1970, Journal of theoretical biology.

[12]  Malcolm S. Steinberg,et al.  Reconstruction of Tissues by Dissociated Cells , 1963 .

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

[14]  H. C. Corben,et al.  Classical Mechanics (2nd ed.) , 1961 .

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

[16]  M. Koehl,et al.  Cellular mechanism underlying neural convergent extension in Xenopus laevis embryos. , 1997, Developmental biology.

[17]  Glazier,et al.  Simulation of biological cell sorting using a two-dimensional extended Potts model. , 1992, Physical review letters.

[18]  J. Shih,et al.  The epithelium of the dorsal marginal zone of Xenopus has organizer properties. , 1992, Development.

[19]  P. Agarwal,et al.  Cell-based Computer Models in Developmental Biology , 1993 .

[20]  J. Shih,et al.  Cell Motility, Control and Function of Convergence and Extension during Gastrulation in Xenopus , 1991 .

[21]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[22]  N S Goel,et al.  Computer simulation of engulfment and other movements of embryonic tissues. , 1978, Journal of theoretical biology.

[23]  M. S. Steinberg,et al.  On the mechanism of tissue reconstruction by dissociated cells. I. Population kinetics, differential adhesiveness. and the absence of directed migration. , 1962, Proceedings of the National Academy of Sciences of the United States of America.

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

[25]  Glazier,et al.  Simulation of the differential adhesion driven rearrangement of biological cells. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Mombach,et al.  Mitosis and growth in biological tissues. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[28]  R. Winklbauer,et al.  Directional mesoderm cell migration in the Xenopus gastrula. , 1991, Developmental biology.

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

[30]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[31]  G. Oster,et al.  Notochord morphogenesis in Xenopus laevis: simulation of cell behavior underlying tissue convergence and extension. , 1991, Development.

[32]  E. J. Dean,et al.  Computational Physics--Fortran Version. , 1990 .

[33]  Pankaj Agarwal,et al.  The Cell Programming Language , 1994, Artificial Life.

[34]  Louis Y. Cheng,et al.  The mechanisms and mechanics of archenteron elongation during sea urchin gastrulation , 1986 .

[35]  Yi Jiang.  Cellular pattern formation , 1998 .

[36]  M. S. Cooper,et al.  Cell intercalation during notochord development in Xenopus laevis. , 1989, The Journal of experimental zoology.

[37]  Pankaj Agarwal,et al.  Simulation of aggregation in Dictyostelium using the Cell Programming Language , 1994, Comput. Appl. Biosci..

[38]  D. Fristrom,et al.  Apical cell shape changes during Drosophila imaginal leg disc elongation: a novel morphogenetic mechanism. , 1991, Development.

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

[40]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[41]  P. Armstrong,et al.  Cell sorting out: the self-assembly of tissues in vitro. , 1989, Critical reviews in biochemistry and molecular biology.

[42]  M. S. Steinberg,et al.  ON THE MECHANISM OF TISSUE RECONSTRUCTION BY DISSOCIATED CELLS, III. FREE ENERGY RELATIONS AND THE REORGANIZATION OF FUSED, HETERONOMIC TISSUE FRAGMENTS. , 1962, Proceedings of the National Academy of Sciences of the United States of America.

[43]  J. Moury,et al.  Tissue boundaries and cell behavior during neurulation. , 1995, Developmental Biology.

[44]  François Graner,et al.  Can Surface Adhesion Drive Cell-rearrangement? Part I: Biological Cell-sorting , 1993 .

[45]  P Agarwal.  Cellular segregation and engulfment simulations using the cell programming language. , 1995, Journal of theoretical biology.

[46]  D. Lauffenburger,et al.  Cell Migration: A Physically Integrated Molecular Process , 1996, Cell.

[47]  George D. Mostow,et al.  Mathematical models for cell rearrangement , 1975 .