Wendy K. Silk

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.

Moving with climbing plants from Charles Darwin’s time into the 21st century

We provide an overview of research on climbing plants from Charles Darwin to the present day. Following Darwins interests, this review will focus on functional perspectives including attachment mechanisms and stem structure and function. We draw attention to a number of unsolved problems inviting future research. These include the mechanism for establishment of the twining habit, a quantitative description following the development of a tissue element through space and time, the chemistry of sticky exudates, the microstructure of xylem and the capacity for water storage, the vulnerability to embolism, and the mechanism for embolism repair. In conclusion we cite evidence that, in response to increasing CO(2) concentration, anthropic perturbation and/ or increasing forest fragmentation, lianas are increasing relative to tree species. In the 21st century, we are returning to the multiscale, multidisciplinary approach taken by Darwin to understand natural history.

To duckweeds (Landoltia punctata), nanoparticulate copper oxide is more inhibitory than the soluble copper in the bulk solution.

CuO nanoparticles (CuO-NP) were synthesized in a hydrogen diffusion flame. Particle size and morphology were characterized using scanning mobility particle sizing, Brunauer-Emmett-Teller analysis, dynamic light scattering, and transmission electron microscopy. The solubility of CuO-NP varied with both pH and presence of other ions. CuO-NP and comparable doses of soluble Cu were applied to duckweeds, Landoltia punctata. Growth was inhibited 50% by either 0.6 mg L(-1) soluble copper or by 1.0 mg L(-1) CuO-NP that released only 0.16 mg L(-1) soluble Cu into growth medium. A significant decrease of chlorophyll was observed in plants stressed by 1.0 mg L(-1) CuO-NP, but not in the comparable 0.2 mg L(-1) soluble Cu treatment. The Cu content of fronds exposed to CuO-NP is four times higher than in fronds exposed to an equivalent dose of soluble copper, and this is enough to explain the inhibitory effects on growth and chlorophyll content.

Effect of Water Stress on Cortical Cell Division Rates within the Apical Meristem of Primary Roots of Maize.

We characterized the effect of water stress on cell division rates within the meristem of the primary root of maize (Zea mays L.) seedlings. As usual in growth kinematics, cell number density is found by counting the number of cells per small unit length of the root; growth velocity is the rate of displacement of a cellular particle found at a given distance from the apex; and the cell flux, representing the rate at which cells are moving past a spatial point, is defined as the product of velocity and cell number density. The local cell division rate is estimated by summing the derivative of cell density with respect to time, and the derivative of the cell flux with respect to distance. Relatively long (2-h) intervals were required for time-lapse photography to resolve growth velocity within the meristem. Water stress caused meristematic cells to be longer and reduced the rates of cell division, per unit length of tissue and per cell, throughout most of the meristem. Peak cell division rate was 8.2 cells mm-1 h-1 (0.10 cells cell-1 h-1) at 0.8 mm from the apex for cells under water stress, compared with 13 cells mm-1 h-1 (0.14 cells cell-1 h-1) at 1.0 mm for controls.

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: possible role of some mineral elements in growth inhibition

Elongating leaf tissue, which in monocotyledonous species is a small region located near the leaf base, requires a continuous supply of nutrients to maintain cell expansion and is, therefore, highly susceptible to nutrient disturbances. The objective of this work was to investigate the effects of salinity on the availability of nutrient elements within the elongating region of sorghum (Sorghum bicolor [L.] Moench, cv. ‘NK 265’) leaves, in order to assess their possible role in salt-induced growth inhibition. Plants grown in complete nutrient solution were exposed to 1 or 100 mol·m−3 NaCl salinity. Spatial distributions of biomass and bulk tissue K, Na, Ca, and Mg were determined on a millimeter scale in the growth zone of leaf 6, while it was growing rapidly just after emergence from the encircling whorl of older leaf sheaths. Spatial patterns of net rates of element deposition were also calculated. Potassium, Ca, Mg, and Na exhibit along the leaf growing zone, distinct spatial concentration patterns which are changed by exposure to saline stress. Salinity induces a decrease in K concentration and deposition rate throughout the elongation zone. The inhibition of K deposition rate due to salinity increases with distance from the leaf base, as did the inhibition of growth. Salinity induces a dramatic decrease in Ca that could also be responsible for leaf growth inhibition. The concentration of Mg is lower under salt stress in the basal part of the growing region, where Na is preferentially accumulated. Since the base of the growth zone is where growth is least affected by salinity, high levels of Na are not the cause of growth inhibition in this salt-affected leaf tissue.

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 uncouples the synchrony between growth and cell division to produce longer cells at the base of the meristem and shorter cells at the base of the growth zone. The longer cells near the root apex probably facilitate transport of metabolites from the phloem to the dividing cells in stressed roots. In general, patterns of cell size may affect the selection of plants for environmental adaptation.

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.

Hydraulics of plant growth

Multicellular plants rely on growth in localised regions that contain small, undifferentiated cells and may be many millimetres from the nearest differentiated xylem and phloem. Water and solutes must move to these small cells for their growth. Increasing evidence indicates that after exiting the xylem and phloem, water and solutes are driven to the growing cells by gradients in water potential and solute potential or concentration. The gradients are much steeper than in the vascular transport system and can change in magnitude or suffer local disruption with immediate consequences for growth. Their dynamics often obscure how turgor drives wall extension for growth, and different flow paths for roots and shoots have different dynamics. In this review, the origins of the gradients, their mode of action and their consequences are discussed, with emphasis on how their dynamics affect growth processes.

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.