Changes in the shape of the developing vertebrate nervous system analyzed experimentally, mathematically and by computer simulation.

Two forces are necessary and sufficient to produce the transformation of the newt neural plate from a hemispheric sheet of cells one cell thick to a keyhole shape. These forces are: (1) a regionally programmed shrinkage of the surface of the neural plate (accomplished by contraction of the apical surfaces of the neural plate cells and elongation of these cells perpendicular to the plate); and (2) displacement of the whole sheet caused by elongation of either the notochord or the overlying neural plate cells in the antero-posterior direction. A computer simulation and mathematical analysis ("morphodynamics"), together with experiments and observations on embryos, were used to deduce the morphogenesis of the neural plate from these forces.

[1]  B. Burnside,et al.  Microtubules and microfilaments in newt neuralation. , 1971, Developmental biology.

[2]  B. Lipton,et al.  Experimental analysis of the mechanisms of somite morphogenesis. , 1974, Developmental biology.

[3]  R Gordon.  On stochastic growth and form. , 1966, Proceedings of the National Academy of Sciences of the United States of America.

[4]  T. E. Schroeder,et al.  Cytoplasmic filaments and morphogenetic movement in the amphibian neural tube. , 1967, Developmental biology.

[5]  M B Burnside,et al.  Analysis of morphogenetic movements in the neural plate of the newt Taricha torosa. , 1968, Developmental biology.

[6]  N. K. Wessells,et al.  Microfilaments in Cellular and Developmental Processes , 1971, Science.

[7]  Computer modelling of hyphal tip growth in fungi , 1972 .

[8]  E. Witschi.  Development of vertebrates , 1956 .

[9]  Richard Morris Holman,et al.  A Textbook of General Botany: for Colleges and Universities , 1934, Nature.

[10]  B. Burnside.  Microtubules and Microfilaments in Amphibian Neurulation , 1973 .

[11]  T. M. Harris.  PREGASTRULAR MECHANISMS IN THE MORPHOGENESIS OF THE SALAMANDER AMBYSTOMA MACULATUM. , 1964, Developmental biology.

[12]  B. Lipton,et al.  Analysis of normal somite development. , 1974, Developmental biology.

[13]  Olli Lehto,et al.  Quasiconformal mappings in the plane , 1973 .

[14]  R. Gillette.  Cell number and cell size in the ectoderm during neurulation (Amblystoma maculatum) , 1944 .

[15]  R. O. Erickson,et al.  Relative Elemental Rates and Anisotropy of Growth in Area: a Computer Programme , 1966 .

[16]  C. Waddington.  Observations on the Forces of Morphogenesis in the Amphibian Embryo , 1942 .

[17]  O. Tietjens,et al.  Fundamentals of hydro- and aeromechanics , 1934 .

[18]  D. Potter,et al.  Chapter 4 Low-Resistance Junctions Between Cells in Embryos and Tissue Culture , 1968 .

[19]  G. S. Avery,.  STRUCTURE AND DEVELOPMENT OF THE TOBACCO LEAF , 1933 .

[20]  A. Jacobson.  Inductive processes in embryonic development. , 1966, Science.

[21]  J. Holtfreter.  Structure, motility and locomotion in isolated embryonic amphibian cells , 1946, Journal of morphology.

[22]  J. Holtfreter.  A study of the mechanics of gastrulation. Part I , 1943 .

[23]  R. Tomkins,et al.  The cortex of Xenopus laevis embryos: regional differences in composition and biological activity. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[24]  J. Holtfreter.  Observations on the migration, aggregation and phagocytosis of embryonic cells , 1947, Journal of morphology.

[25]  L. Kantorovich,et al.  Functional analysis in normed spaces , 1952 .

[26]  N S Goel,et al.  A rheological mechanism sufficient to explain the kinetics of cell sorting. , 1972, Journal of theoretical biology.

[27]  A. Jacobson.  The roles of neural and non‐neural tissues in lens induction , 1958 .

[28]  P Karfunkel,et al.  The mechanisms of neural tube formation. , 1974, International review of cytology.

[29]  O. Glaser.  THE THEORY OF AUTONOMOUS FOLDING IN EMBRYOGENESIS. , 1916, Science.

[30]  O. Glaser.  On the mechanism of morphological differentiation in the nervous system. I. The transformation of a neural plate into a neural tube , 1914 .

[31]  D'arcy W. Thompson.  On Growth and Form , 1945 .

[32]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[33]  C. Waddington,et al.  The ultrastructure of the developing urodele notochord , 1962, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[34]  J. Milnor.  Topology from the differentiable viewpoint , 1965 .

[35]  C. Waddington.  Organisers and genes. , 1943 .