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QUANTITATIVE PATTERNS OF LEAF EXPANSION: COMPARISON OF NORMAL AND MALFORMED LEAF GROWTH IN VITIS VINIFERA CV. RUBY RED
Authors:Sue D. Wolf  Wendy Kuhn Silk  Richard E. Plant
Affiliation:1. Department of Land, Air and Water Resources;2. Department of Mathematics, University of California, Davis, California, 95616

Department of Land, Air and Water Resources

Abstract:Developmental patterns produced during normal expansion of the leaf of Vitis vinifera cv. Ruby Red are quantitatively characterized from the distribution of relative growth rates and growth velocity vectors and are compared to patterns produced during the development of an abnormally shaped leaf. The bilateral symmetry of the V. vinifera leaf, which is present in the normal leafand absent in the malformed leaf, is shown during growth by the patterns of velocity isolines. Ellipses formed by the isolines around the midrib during normal development are distorted during development of the malformed leaf. During normal growth, tissue elements are displaced in rather straight lines, resulting in streamlines which radiate outward from the petiole. Element motion in the abnormally developing leaf causes curving of streamlines. Relative growth in area of elements located in an area in the normal leaf are higher than those in the malformed leaf. The most frequently observed category of relative area growth in the normal leaf is 40%-59% d~1, while 20%–39% d−-1 predominates in the abnormal leaf. A spatial gradient in growth appears during normal development with lowest relative growth (20%–39% d−-1) present in the tip region, intermediate values (40%–59% d−-1) in the midsection, and maximum growth (> 60% d−-1) appearing in the basal region. During development of the abnormally shaped leaf, the gradient along the midrib is disrupted with low magnitudes of growth (<20% d−-1) appearing in the midsection of the leaf where intermediate values are expected. The theoretical and numerical distinctions between two common expressions for relative growth (relative elemental growth and exponential growth rate) are discussed. Relative elemental growth is shown to become increasingly larger than the exponential growth rate as the magnitude of growth increases relative to initial size of the tissue element. Numerical methods for evaluating relative growth based on finite element areas are compared to methods based on displacement and velocity gradients and are shown to produce similar results.
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