Kinematics of plant growth.

Abstract Many of the concepts and equations which have been used in the study of compressible fluids can be applied to problems of plant development. Growth field variables, i.e. functions of position in the plant and of time, can be specified in either Eulerian (spatial) or Lagrangian (material) terms. The two specifications coincide only when the spatial distribution of the variable is steady, and steady patterns are most likely to emerge when an apex is chosen as origin of the co-ordinate system. The growth field itself can be described locally by the magnitude and orientation of the principal axes of the rate of strain tensor and by the vorticity tensor. Material derivatives can be calculated if the temporal and spatial variation in both growth velocity, u (rate of displacement from a material origin), and the variable of interest are known. The equation of continuity shows the importance of including both growth velocity, u, and growth rate, ▽ ·u in estimates of local biosynthesis and transport rates in expanding tissue, although the classical continuity equation must be modified to accommodate the compartmentalized distributions characteristic of plant tissue. Relatively little information on spatial variation in plant organs can be found in the botanical literature, but the current availability of interactive computer graphics equipment suggests that analysis of the spatial distribution of growth rates at least is no longer difficult.

[1]  P B Green,et al.  Metabolic and physical control of cell elongation rate: in vivo studies in nitella. , 1971, Plant physiology.

[2]  R. O. Erickson.  Integration of Plant Growth Processes , 1959, The American Naturalist.

[3]  E. B. Matzke.  In the Twinkling of an Eye , 1950 .

[4]  R. Archer,et al.  REACTION WOOD: INDUCTION AND MECHANICAL ACTION! , 1977 .

[5]  R. Archer,et al.  Mechanics of the compression wood response: I. Preliminary analyses. , 1970, Plant physiology.

[6]  R. O. Erickson.  Modeling of Plant Growth , 1976 .

[7]  Richard H. Goodwin,et al.  STUDIES ON ROOTS. III. AN ANALYSIS OF ROOT GROWTH IN PHLEUM PRATENSE USING PHOTOMICROGRAPHIC RECORDS , 1956 .

[8]  Oscar W. Richards,et al.  The Analysis of the Relative Growth Gradients and Changing Form of Growing Organisms: Illustrated by the Tobacco Leaf , 1943, The American Naturalist.

[9]  R. Brown,et al.  The Development of the Enzyme Complement in Growing Root Cells , 1952 .

[10]  A. Sievers,et al.  Mathematical Model of Geotropically Bending Chara Rhizoids , 1971 .

[11]  M. Probine.  Cell Growth and the Structure and Mechanical Properties of the Wall in Internodal Cells of Nitella opaca: III. SPIRAL GROWTH AND CELL WALL STRUCTURE , 1963 .

[12]  A. Turing.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[13]  R. Cleland.  Cell Wall Extension , 1971 .

[14]  J. Metraux,et al.  Transverse viscoelastic extension in nitella: I. Relationship to growth rate. , 1978, Plant physiology.

[15]  E. S. Castle.  THE TOPOGRAPHY OF TIP GROWTH IN A PLANT CELL , 1958, The Journal of general physiology.

[16]  R. H. Goodwin,et al.  GROWTH AND DIFFERENTIATION IN THE ROOT TIP OF PHLEUM PRATENSE , 1945 .

[17]  F. Skoog,et al.  DISTRIBUTIONS OF GROWTH, NUCLEIC ACIDS, AND NUCLEIC‐ACID SYNTHESIS IN SEEDLING ROOTS OF ZEA MAYS , 1962 .

[18]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[19]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[20]  R. O. Erickson,et al.  KINEMATICS OF HYPOCOTYL CURVATURE , 1978 .

[21]  P. Green.  Growth and Cell Pattern Formation on an Axis: Critique of Concepts, Terminology, and Modes of Study , 1976, Botanical Gazette.

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