Relative Elemental Growth Rate Research Articles

Kinematics and Dynamics of Sorghum (Sorghum bicolor L.) Leaf Development at Various Na/Ca Salinities (I. Elongation Growth).

In many salt-sensitive species, elevated concentrations of Ca in the root growth media ameliorate part of the shoot growth reduction caused by NaCl stress. The physiological mechanisms by which Ca exerts protective effects on leaf growth are still not understood. Understanding growth inhibition caused by a stress necessitates locating the leaf expansion region and quantifying the profile of the growth reduction. This will enable comparisons and correlations with spatial gradients of probable physiologically inhibiting factors. In this work we applied the methods of growth kinematics to analyze the effects of elevated Ca concentrations on the spatial and temporal distributions of growth within the intercalary expanding region of salinized sorghum (Sorghum bicolor [L.] Moench, cv NK 265) leaves. NaCl (100 mM) caused a decrease in leaf elongation rate by shortening the leaf growing zone by 20%, as well as reducing the peak value of the longitudinal relative elemental growth rate (REG rate). Increasing the Ca concentrations from 1 to 10 mM restored the length of the growing zone of both emerged and unemerged salinized leaves and increased the peak value of the REG rate. The beneficial effects of supplemental Ca were, however, more pronounced in leaves after their appearance above the whorl of encircling older leaf sheaths. Elevated Ca then resulted in a peak value of REG rate higher than in the salinized leaves. The peak value of unemerged leaves was not increased, although it was maintained over a longer distance. The duration of elongation growth associated with a cell during its displacement from the leaf base was longer in salinized than control leaves, despite the fact that the elongation zone was shorter in salinity. Although partially restoring the length of the elongation region, supplemental Ca had no effect on the age of cessation of growth. Elongation of a tissue element, therefore, ceased when a cellular element reached a certain age and not a specific distance from the leaf base.

Growth and development of sorghum leaves under conditions of NaCl stress

Elevated concentrations of NaCl in plant growth media cause a reduction in leaf growth. In grasses, where the leaf growth zone is a small part of the entire leaf, it is important to locate the expanding region and spatially quantify the extent of growth reduction under stress. This will allow comparisons and correlations with possible physiologically important factors. We studied the spatial distribution of growth within the intercalary growth zone of sorghum (Sorghum bicolor [L.] Moench, cv. NK 265) leaves. Salinity (100 mM NaCl) shortened the length of the growth zone from 30 mm in the controls to about 24 mm, and reduced the maximal relative elemental growth rate (REG rate). The extent of growth inhibition varied with spatial location along the elongation region. The growth in the basal 3–9 mm of salinized plants was not affected. Young leaves, while still enclosed in the protected whorl of older sheaths and elongating rapidly, were affected more severely by the stress than emerged leaves. The distribution of growth along the leaf growth zone was not steady throughout the elongation period. The length of the elongation region of young nonemerged leaves increased with leaf age and reached a maximum of about 30 mm at leaf emergence. Toward the end of the elongation period, the growth zone shortened for both the control and salinized leaves, and was confined to more basal regions. The maximal REG rate increased after leaf emergence, the increase being larger in control than salinized leaves. Toward the end of the elongation period, when growth was no longer linear with respect to time, the maximum REG rate decreased and its position shifted closer to the leaf base. Growth profiles of leaves 8, 9 and 10 were similar in both control and salinized plants. This suggests that within that time frame of plant development, successive leaves are similarly affected by the stress, and that the length of time the plant was exposed to a steady level of salinity plays no role in specific leaf inhibition.

Xyloglucan Endotransglycosylase Activity, Microfibril Orientation and the Profiles of Cell Wall Properties Along Growing Regions of Maize Roots

A series of physical and chemical analyses were made on the expanding zone of maize seedling roots grown in hydroponics. Comparison of longitudinal profiles of local relative elemental growth rate and turgor pressure indicated that cell walls become looser in the apical 5 mm and then tighten 5-10 mm from the root tip. Immersion of roots in 200 mol m-3 mannitol (an osmotic stress of 0-48 MPa) rapidly and evenly reduced turgor pressure along the whole growing region. Growth was reduced to a greater extent in the region 5-10 mm from the root tip than in the apical region. This indicated rapid wall-loosening in the root tip, but not in the more basal regions. Following 24 h immersion in 400 mol m-3 mannitol (an osmotic stress of 0-96 MPa) turgor had recovered to pre-stressed values. Under this stress treatment, growth was reduced in the region 4-10 mm from the root tip, despite the recovery of turgor, indicating a tightening of the wall. In the root apex, local relative elemental growth rate was unchanged in comparison to control tissue, showing that wall properties here were similar to the control values. Cellulose microfibrils on the inner face of cortical cell walls became increasingly more parallel to the root axis along the growth profile of both unstressed and stressed roots. Orientation did not correlate with the wall loosening in the apical region of unstressed roots, or with the tightening in the region 5-10 mm from the root tip following 24 h of osmotic stress. Longitudinal profiles of the possible wall-loosening enzyme xyloglucan endotransglycosylase (XET) had good correspondence with an increase in wall loosening during development. In the zone of wall tightening following osmotic stress, XET activity was decreased per unit dry weight (compared with the unstressed control), but not per unit fresh weight.

Use of a flexible logistic function to describe axial growth of plants

A sigmoid curve with three fitting parameters is proposed as a descriptive model for the spatial velocity field in one-dimensional growth of plant organs. Analytic expressions are derived for the relative elemental growth (REG) rate, the position and value of the REG rate maximum, the length of the growth zone, the inverse of the growth trajectory and cell length in the “elongation only” zone. The expressions are fit to published data to characterize the effects of environmental variation on growth of monocotyledonous roots. The simple expressions for growth may prove useful in mechanistic models. The fitted curves summarize more than a decade of observations and thus provide a challenge to theorists.

Steady Form from Changing Cells

The analysis of longitudinal growth is reviewed in terms of growth trajectories and fields of velocity and relative elemental growth (REG) rate. Then the relationships among cell division rate, cell size, and growth rate are reviewed. A careful distinction is made between spatial (site specific) and material (cellparticle specific) aspects of growth and cell division. The equations indicate the experimental design and numerical analysis needed to assess the physiological importance of gene products recently proposed to regulate cell cycle activity. Effects of temperature and water stress on growth and cell division in seedling roots of maize are described. Temperature changes REG rates and cell production rates in synchrony, so the cell length pattern is unchanged by temperature perturbation between 19 and 29 C. In contrast, water stress has no effect on REG rate in apical regions but shortens the length of the growth zone. Water stress also causes a decrease in the cell production rate. Thus water stress...

Growth and Deposition of Inorganic Nutrient Elements in Developing Leaves of Zea mays L.

Spatial distributions of growth and of the concentration of some inorganic nutrient elements were analyzed in developing leaves of maize (Zea mays L.). Growth was analyzed by pinprick experiments with numerical analysis to characterize fields of velocity and relative elemental elongation rate. Inductively coupled plasma and atomic emission spectroscopy were used to measure nutrients extracted from segments of leaf tissue collected by position. Leaves 7 and 8, both elongating 3 millimeters per hour had maximum relative elemental growth rates of 0.06 to 0.08 millimeters per hour with maximum rates 20 to 50 millimeters from the node and cessation of growth by 90 millimeters from the node. Spatial distribution of dry weight density revealed that the rate of biomass deposition was maximum in the most rapidly expanding region and continued beyond the elongation zone. The nutrient elements K, Cl, Ca, Mg, and P showed different distribution patterns of ion density (on a dry weight basis). K and Cl had minimal density in the leaf tips; K density was maximum in the growing region, whereas Cl density was maximum at the region of growth cessation. Ca, Mg, and P had relatively high densities at the base of the elongation zone near the node and also in the tip regions. Near the node, P and Mg densities were higher in the young, growing leaves, whereas Ca density near the node was higher in older leaves that had completed elongation. Deposition rates of all nutrients were greatest in the region of maximum elongation rate.

Cellular Growth in Roots of a Gibberellin-Deficient Mutant of Tomato (Lycopersicon esculentumMill.) and its Wild-type

The role of gibberellins in regulating the growth of tomato roots was investigated by comparing various cellular parameters in cultured roots of the gibberellin-deficient mutant gib-l/gib-l with those in roots of the near-isogenic wild-type. In addition, wild-type roots treated with 0·1 μM 2S,3S paclobutrazol, an inhibitor of gibberellin biosynthesis, and mutant roots treated with 0·1 μM GA3 were also compared: the former roots constitute a phenocopy of the mutant, whereas the latter roots appear to be ‘normalized’ and similar to wild-type. The elongation of mutant and phenocopied roots were similar, their maximum elongation rates being about half or two-thirds that of wild-type or GA3-treated mutant roots, respectively. These rates were interpreted in terms of the numbers and lengths of cells within the meristematic and non-meristematic portions of the elongation zone. Mean meristem length tended to be shorter in both the mutant and the 2S,3S paclobutrazol-treated wild-type roots than in the other two types of root. A major difference between the two pairs of mutant and normal roots was their mean final cell lengths: mean lengths of cortical cells of the mutant and 2S,3S paclobutrazol-treated roots were, respectively, 39% and 25% shorter than the mean length of wild-type roots. Final cell length in the GA3-treated mutant roots were similar to wild-type. By contrast, the diameters of mature cortical cells of the mutant and phenocopy were about 20% greater than the diameters of equivalent wild-type or ‘normalized’ mutant cells. The mean volumes of cortical cells in all four types of roots showed no significant differences. Knowledge of the distribution of cortical cell lengths, widths and volumes along the root axis, together with information about the rate of root elongation, permitted comparisons of the relative elemental growth rates of each of these three cellular parameters. The available evidence suggests that the level of endogenous gibberellins in mutant roots is lower than in wild-type roots. The present results, therefore, suggest that endogenous gibberellins are necessary for normal growth of cultured tomato roots and that they regulate the relative amounts of growth at the longitudinal and transverse walls of the cells which, in turn, affects the shape of the elongating cells.

Spatial distribution of growth rates and of epidermal cell lengths in the elongation zone during leaf development in Lolium perenne L.

Relative elemental growth rates (REGR) and lengths of epidermal cells along the elongation zone of Lolium perenne L. leaves were determined at four developmental stages ranging from shortly after emergence of the leaf tip to shortly before cessation of leaf growth. Plants were grown at constant light and temperature. At all developmental stages the length of epidermal cells in the elongation zone of both the blade and sheath increased from 12 μm at the leaf base to about 550 μm at the distal end of the elongation zone, whereas the length of epidermal cells within the joint region only increased from 12 to 40 μm. Throughout the developmental stages elongation was confined to the basal 20 to 30 mm of the leaf with maximum REGR occurring near the center of the elongation zone. Leaf elongation rate (LER) and the spatial distributions of REGR and epidermal cell lengths were steady to a first approximation between emergence of the leaf tip and transition from blade to sheath growth. Elongation of epidermal cells in the sheath started immediately after the onset of elongation of the most proximal blade epidermal cells. During transition from blade to sheath growth the length of the blade and sheath portion of the elongation zone decreased and increased, respectively, with the total length of the elongation zone and the spatial distribution of REGR staying near constant, with exception of the joint region which elongated little during displacement through the elongation zone. Leaf elongation rate decreased rapidly during the phase when only the sheath was growing. This was associated with decreasing REGR and only a small decrease in the length of the elongation zone. Data on the spatial distributions of growth rates and of epidermal cell lengths during blade elongation were used to derive the temporal pattern of epidermal cell elongation. These data demonstrate that the elongation rate of an epidermal cell increased for days and that cessation of epidermal cell elongation was an abrupt event with cell elongation rate declining from maximum to zero within less than 10 h.

Differential growth resulting in the specification of different types of cellular architecture in root meristems

Symplastic growth of plant organs may be described by a continuous growth tensor field. In tensorial analysis of meristems, the trajectoris of periclinal and anticlinal cell walls represent trajectories of the principal directions of growth ( PDGs); this follows from the maintenance of mutual orthogonality between periclinal and anticlinal wall trajectories during growth. Periclinal and anticlinal cell divisions are also oriented in the principal planes of growth. The growth tensor for the root apex is specified in such a way that the principal directions of the tensor fit the pattern of periclinal and anticlinal walls in the apex, and that the grid formed by material particles aligned along PDG trajectories preserve this alignment during growth. Two growth tensors are formulated—one giving a maximum and the other giving a minimum of the volumetric relative elemental growth rate at the region of the initial cell(s). Temporal sequences of deformation of a grid formed by lines coinciding with the principal directions of growth are shown. The formation of cellular patterns in root apices is simulated. Two types of patterns are obtained: one with an apical cell and merophytes, and another with files of cells converging towards a quiescent centre.

Quantitative Patterns of Leaf Expansion: Comparison of Normal and Malformed Leaf Growth in Vitis vinifera cv. Ruby Red

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.

QUANTITATIVE PATTERNS OF LEAF EXPANSION: COMPARISON OF NORMAL AND MALFORMED LEAF GROWTH IN VITIS VINIFERA CV. RUBY RED

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 (&gt; 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 (&lt;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.

Growth-sustaining Water Potential Distributions in the Primary Corn Root

An equation is derived from transport theory to relate local growth rate to local water potential in an expanding tissue. For a noncompartmented continuum model, the relative elemental growth rate (L) equals the divergence of the tensor product of hydraulic conductivity (K) and the gradient of water potential, psi, i.e. L = big dn tri, open * [K . big dn tri, open psi]. This equation is solved numerically using published values of L and K to show the water potential distribution which can sustain the observed growth pattern in the primary root of Zea mays L. The water potential required to sustain growth decreases from the outside to the inside of the root, and the longitudinal profile shows most negative values near the location of the highest growth rate. A cell originally located near the apex experiences a loss and then a gain in water potential as it is displaced through the growth zone.THE APPROACH DIFFERS FROM PREVIOUS FORMULATIONS IN TWO RESPECTS: the assumption of spatial heterogeneity in growth rate, and the solution for spatial (site-specific) rather than material (cell-specific) values of water potential. The role of air spaces and of components (wall and possibly cytoplasm) of the water-conducting pathway which do not accumulate water remains to be clarified; and, as in earlier work, the most uncertain aspects of the analysis are probably the values for hydraulic conductivity.

Kinematics of Hypocotyl Curvature

Time lapse photographs were analyzed for curvature, κ, of the plumular hook as a function of distance from the apex, s, of seedlings of lettuce. Lactuca sativa cv ‘Grand Rapids,‘ during hook maintenance (red light) and hook opening (white light). Curvature of the inner edge of the photographic projection of the hook increases from 0.14 mm–1 near the apex to 12.7 mm–1 at the hook bisector (about 1 mm from the apex) and decreases to approximately zero below the hook (2 mm from the apex). Using concepts from fluid dynamics we relate growth rates to curvature changes. For a material element of stem cross section located at s we predict that where M(s,o) and M(s,i) are the relative elemental growth rates at the outer and inner edges of the hypocotyl cross section, w is element width, t is time, and u(s) is velocity of departure of s from the apex. During hook maintenance ∂[ln(1 + κw)]/∂t is approximately zero if the apex is taken as origin. As each hypocotyl element is displaced from the apex it becomes increasingly curved; then, after displacement past the hook bisector, the element straightens. Growth rates, determined by measurements of the displacement of epidermal hairs, show the pattern expected from the equation: On the apical side of the hook, relative growth rates of the outer edge exceed growth of the inner edge, M(s,o) > M(s,i), while on the basal side of the hook. M(s,o) < M(s,i). The constraint for hook maintenance is that [L(s,o) – L(s,i)] /u(s) be constant in time, where L(s,o) and L(s,i) are the relative elemental growth rates at s. During hook opening ∂[ln(1 + κw)]/∂t becomes important.

KINEMATICS OF HYPOCOTYL CURVATURE

Time lapse photographs were analyzed for curvature, κ, of the plumular hook as a function of distance from the apex, s, of seedlings of lettuce. Lactuca sativa cv ‘Grand Rapids,‘ during hook maintenance (red light) and hook opening (white light). Curvature of the inner edge of the photographic projection of the hook increases from 0.14 mm–1 near the apex to 12.7 mm–1 at the hook bisector (about 1 mm from the apex) and decreases to approximately zero below the hook (2 mm from the apex). Using concepts from fluid dynamics we relate growth rates to curvature changes. For a material element of stem cross section located at s we predict that urn:x-wiley:00029122:ajb206072:equation:ajb206072-math-0001 where M(s,o) and M(s,i) are the relative elemental growth rates at the outer and inner edges of the hypocotyl cross section, w is element width, t is time, and u(s) is velocity of departure of s from the apex. During hook maintenance ∂[ln(1 + κw)]/∂t is approximately zero if the apex is taken as origin. As each hypocotyl element is displaced from the apex it becomes increasingly curved; then, after displacement past the hook bisector, the element straightens. Growth rates, determined by measurements of the displacement of epidermal hairs, show the pattern expected from the equation: On the apical side of the hook, relative growth rates of the outer edge exceed growth of the inner edge, M(s,o) &gt; M(s,i), while on the basal side of the hook. M(s,o) &lt; M(s,i). The constraint for hook maintenance is that [L(s,o) – L(s,i)] /u(s) be constant in time, where L(s,o) and L(s,i) are the relative elemental growth rates at s. During hook opening ∂[ln(1 + κw)]/∂t becomes important.

Mathematical Analysis of Plant Growth zea mays Primary Roots

A new mathematical treatment is given to the concept of relative elemental growth rate, the limiting value at a point of the relative rate of tissue growth. The new point of view requires consideration of a coordinate system in which each point on the root surface is defined by its initial position on the root axis. The resultant technique of plotting growth parameters provides the ability to distinguish between waves of growth propagating toward the root tip away from cells and waves which tend to propagate along with the cells. Thus it is possible to model the plant growth-regulatory process in terms of auxin and other regulators, considering both cell-associated maxima of regulator concentration and maxima which propagate through the tissue.

Studies on Roots. V. Effects of Indoleacetic Acid on the Standard Root Growth Pattern of Phleum pratense

The effects of indoleacetic acid (IAA) on the elongation of Phleum pratense roots have been analyzed using photomicrographic records of the epidermal cells taken during growth. Concentrations applied to the root ranged from 10-5 to 10-11 M; the duration of the experimental period was about 5 hr. Effects can be separated into two categories Cells in their accelerating phase of growth and located close to the meristem (Phase I of Burstrom) were immediately inhibited by the higher concentrations (10-5-10-7 M) but after 1 hr began to recover their relative elemental growth rate, the extent of the recovery depending upon the strength of the application At lower concentrations (e g, 10-9 M) there may be a stimulation of the relative elemental growth rate Cells in their decelerating phase of growth and located in the basal portion of the elongating zone (Phase II of Burstrom) were irreversibly inhibited at all concentrations employed.

The topography of tip growth in a plant cell.

Tips of young Phycomyces sporangiophores were dusted with starch grains, and growth photographically recorded. Rates of longitudinal displacement from the cell tip of individual markers were determined, also corresponding rates of change of cell diameter. From these the magnitude and spatial distribution of "relative elemental growth rates" along both longitudinal and circumferential axes of the cell were obtained. Growth rates in these two directions are functions of distance from the cell apex, and have different spatial distributions. In particular, rates of growth in cell circumference are complexly patterned. Relative elemental growth rates in length and in girth are approximately equal and maximal at the cell's apex, with a value of 2.4 mm. mm.(-1) hr.(-1). The characteristic shape of the tip is maintained constant in the face of its changing substance and position. This shape reflects a steady state of the cell's constituent growth patterns. At every point the growing membrane simultaneously expands in the two dimensions of its surface. The degree of polarization or directional preference of growth is measured by the ratio of longitudinal to circumferential relative elemental growth rate at any point. The ratio is not constant, but changes with position along the tip. This fact does not support the idea that membrane growth is based upon a quantal "growth event." Possible causal factors in oriented membrane growth are discussed.