Modelling of root growth and bending in two dimensions

A special co-ordinate system is developed for modelling the gravitropic bending of plant roots. It is based on the Local Theory of Curves in differential geometry and describes, in one dimension, growth events that may actually occur in two, or even three, dimensions. With knowledge of the spatial distributions of relative elemental growth rates (RELELs) for the upper and lower flanks of a gravistimulated root, and also their temporal dependencies, it is possible to compute the development of curvature along the root and hence describe the time-course of gravitropic bending. In addition, the RELEL distributions give information about the velocity field and the basipetal displacement of points along the root's surface. According to the Fundamental Theorem of Local Curve Theory, the x and y co-ordinates of the root in its bending plane are then determined from the associated values of local curvature and local velocity. With the aid of this model, possible mathematical growth functions that correspond to biological mechanisms involved in differential growth can be tested. Hence, the model can help not only to distinguish the role of various physiological or biophysical parameters in the bending process, but also to validate hypotheses that make assumptions concerning their relative importance. However, since the model is constructed at the level of the organ and treats the root as a fluid continuum, none of the parameters relate to cellular behaviour; the parameters must instead necessarily apply to properties that impinge on the behaviour of the external boundary of the root.     

The growth of root systems — A numerical computer simulation model

Summary A simulation model of the growth of the plant root system is described. Firstly, the numbers and lengths of the laterals derived from a single axis are obtained from specified rates of elongation and branching. Secondly, the vertical distribution of filament lengt his obtained, after specifying the rate of initiation of axes at the crown of the plant and the orientation of successive, short straight segments representing the curved roots. Diagrams of the network can be produced using the graph-plotting facility of computer, and other properties such as the distribution of length of filament of given age and the distribution of apices can be computed. The model has sufficient flexibility to incorporate information on the temporal variation or local spatial variation in rates of growth found under non-uniform conditions.The utility of the model in agronomic studies is illustrated by using it to calculate the effects of fertilizer treatments on the root distribution, given certain growth responses expressed in terms of rates of elongation and branching. The examples considered pertain to (a) the enrichment of a layer in the soil with a fertilizer supplying a scarce nutrient and (b) a deferred application of a fertilizer supplying a scarce nutrient     

Distribution and redistribution of extension growth along vertical and horizontal gravireacting maize roots

Horizontal primary roots of Zea mays L. were photographed during the course of their gravireaction and during a preceding growth period in the vertical orientation. The displacement, by root elongation, of marker particles on the root surface was recorded. The particle-displacement rates were used to estimate the distribution of elemental elongation rates along opposite sides of the growing root apex. In the temperature range 21–25°C there was a stimulation of local elongation rates along the upper side of a gravireacting root and a reduction (and sometimes a cessation) of elongation along the lower side. Elemental elongation rates have been related to the development of root curvature, and the magnitude of the differential growth between upper and lower sides required for a particular rate of bending has also been estimated. The results complement, and are compatible with, findings relating to the distribution of certain endogenous growth regulators believed to participate in the gravireaction.Abbreviation RELEL relative elemental rate of elongation     

Root apical diameter and root elongation rate of rubber seedlings (Hevea brasiliensis) show parallel responses to photoassimilate availability

The hypothesis that root apical diameter may be used to evaluate root growth potential was tested. Temporal variations in the apical diameter of individual roots of rubber seedlings ( Hevea brasiliensis ) were studied together with their elongation patterns, using root observation boxes under controlled conditions. This study confirmed the overall positive correlation between apical diameter and growth rale. Moreover, the two parameters, varied in the same way during the life of a given root. For roots with short growth duration, there was a parallel quick decrease in both apical diameter and elongation rate, whereas roots that grew for longer periods showed synchronous fluctuations for both parameters. Since the mean values for the secondary roots within a root system exhibited the same trends, variations in apical diameter and elongation rates should depend on factors influencing the whole root system. When related to shoot rhythmic growth, both apical diameter and elongation rates were depressed during the periods of leaf growth. These effects were enhanced and/or prolonged by shading, hence reinforcing the hypothesis that this development depends on assimilate availability. Such results can be interpreted in terms of a source-sink relationship within the whole plant by considering the apical diameter, representing the size of the meristem related to the number of rneristematic cells, as an indicator of each root's growth potential.     

The RCN1-encoded A subunit of protein phosphatase 2A increases phosphatase activity in vivo

Protein phosphatase 2A (PP2A), a heterotrimeric serine/threonine-specific protein phosphatase, comprises a catalytic C subunit and two distinct regulatory subunits, A and B. The RCN1 gene encodes one of three A regulatory subunits in Arabidopsis thaliana. A T-DNA insertion mutation at this locus impairs root curling, seedling organ elongation and apical hypocotyl hook formation. We have used in vivo and in vitro assays to gauge the impact of the rcn1 mutation on PP2A activity in seedlings. PP2A activity is decreased in extracts from rcn1 mutant seedlings, and this decrease is not due to a reduction in catalytic subunit expression. Roots of mutant seedlings exhibit increased sensitivity to the phosphatase inhibitors okadaic acid and cantharidin in organ elongation assays. Shoots of dark-grown, but not light-grown seedlings also show increased inhibitor sensitivity. Furthermore, cantharidin treatment of wild-type seedlings mimics the rcn1 defect in root curling, root waving and hypocotyl hook formation assays. In roots of wild-type seedlings, RCN1 mRNA is expressed at high levels in root tips, and accumulates to lower levels in the pericycle and lateral root primordia. In shoots, RCN1 is expressed in the apical hook and the basal, rapidly elongating cells in etiolated hypocotyls, and in the shoot meristem and leaf primordia of light-grown seedlings. Our results show that the wild-type RCN1-encoded A subunit functions as a positive regulator of the PP2A holoenzyme, increasing activity towards substrates involved in organ elongation and differential cell elongation responses such as root curling.     

Arabidopsis cytokinin receptor mutants reveal functions in shoot growth, leaf senescence, seed size, germination, root development, and cytokinin metabolism

We used loss-of-function mutants to study three Arabidopsis thaliana sensor histidine kinases, AHK2, AHK3, and CRE1/AHK4, known to be cytokinin receptors. Mutant seeds had more rapid germination, reduced requirement for light, and decreased far-red light sensitivity, unraveling cytokinin functions in seed germination control. Triple mutant seeds were more than twice as large as wild-type seeds. Genetic analysis indicated a cytokinin-dependent endospermal and/or maternal control of embryo size. Unchanged red light sensitivity of mutant hypocotyl elongation suggests that previously reported modulation of red light signaling by A-type response regulators may not depend on cytokinin. Combined loss of AHK2 and AHK3 led to the most prominent changes during vegetative development. Leaves of ahk2 ahk3 mutants formed fewer cells, had reduced chlorophyll content, and lacked the cytokinin-dependent inhibition of dark-induced chlorophyll loss, indicating a prominent role of AHK2 and, particularly, AHK3 in the control of leaf development. ahk2 ahk3 double mutants developed a strongly enhanced root system through faster growth of the primary root and, more importantly, increased branching. This result supports a negative regulatory role for cytokinin in root growth regulation. Increased cytokinin content of receptor mutants indicates a homeostatic control of steady state cytokinin levels through signaling. Together, the analyses reveal partially redundant functions of the cytokinin receptors and prominent roles for the AHK2/AHK3 receptor combination in quantitative control of organ growth in plants, with opposite regulatory functions in roots and shoots.     

Root gravitropism

When a plant root is reoriented within the gravity field, it responds by initiating a curvature which eventually results in vertical growth. Gravity sensing occurs primarily in the root tip. It may involve amyloplast sedimentation in the columella cells of the root cap, or the detection of forces exerted by the mass of the protoplast on opposite sides of its cell wall. Gravisensing activates a signal transduction cascade which results in the asymmetric redistribution of auxin and apoplastic Ca²⁺ across the root tip, with accumulation at the bottom side. The resulting lateral asymmetry in Ca²⁺ and auxin concentration is probably transmitted to the elongation zone where differential cellular elongation occurs until the tip resumes vertical growth. The Cholodny-Went theory proposes that gravity-induced auxin redistribution across a gravistimulated plant organ is responsible for the gravitropic response. However, recent data indicate that the gravity-induced reorientation is more complex, involving both auxin gradient-dependent and auxin gradient-independent events.     

Epidermal Patterning Genes Impose Non-cell Autonomous Cell Size Determination and have Additional Roles in Root Meristem Size Control

The regulation of cellular growth is of vital importance for embryonic and postembryonic patterning. Growth regulation in the epidermis has importance for organ growth rates in roots and shoots, proposing epidermal cells as an interesting model for cellular growth regulation. Here we assessed whether the root epidermis is a suitable model system to address cell size determination. In Arabidopsis thaliana L., root epidermal cells are regularly spaced in neighbouring tricho- (root hair) and atrichoblast (non-hair) cells, showing already distinct cell size regulation in the root meristem. We determined cell sizes in the root meristem and at the onset of cellular elongation, revealing that not only division rates but also cellular shape is distinct in tricho- and atrichoblasts. Intriguingly, epidermal-patterning mutants, failing to define differential vacuolization in neighbouring epidermal cell files, also display non-differential growth. Using these epidermal-patterning mutants, we show that polarized growth behaviour of epidermal tricho- and atrichoblast is interdependent, suggesting non-cell autonomous signals to integrate tissue expansion. Besides the interweaved cell-type-dependent growth mechanism, we reveal an additional role for epidermal patterning genes in root meristem size and organ growth regulation. We conclude that epidermal cells represent a suitable model system to study cell size determination and interdependent tissue growth.     

Spatio-temporal quantification of differential growth processes in root growth zones based on a novel combination of image sequence processing and refined concepts describing curvature production

Differential growth processes in root and shoot growth zones are governed by the transport kinetics of auxin and other plant hormones. While gene expression and protein localization of hormone transport facilitators are currently being unraveled using state-of-the-art techniques of live cell imaging, the quantitative analysis of growth reactions is lagging behind because of a lack of suitable methods. A noninvasive technique, based on digital image sequence processing, for visualizing and quantifying highly resolved spatio-temporal root growth processes was applied in the model plant Arabidopsis thaliana and was adapted to provide precise information on differential curvature production activity within the root growth zone. Comparison of root gravitropic curvature kinetics in wild-type and mutant plants altered in a facilitator for auxin translocation allowed the determination of differences in the location and in the temporal response of curvature along the growth zone between the investigated plant lines. The findings of the quantitative growth analysis performed here confirm the proposed action of the investigated transport facilitator. The procedure developed here for the investigation of differential growth processes is a valuable tool for characterizing the phenomenology of a wide range of shoot and root growth movements and hence facilitates elucidation of their molecular characterization.     

Plant development: slowing root growth naturally

What determines organ size? A screen for plant strains showing natural variation in root length has identified a novel gene that modulates root growth rate by controlling cell division and elongation at the root tip.     

Root growth in Arabidopsis requires gibberellin/DELLA signalling in the endodermis

Gibberellins (GAs) are key regulators of plant growth and development. They promote growth by targeting the degradation of DELLA repressor proteins; however, their site of action at the cellular, tissue or organ levels remains unknown. To map the site of GA action in regulating root growth, we expressed gai, a non-degradable, mutant DELLA protein, in selected root tissues. Root growth was retarded specifically when gai was expressed in endodermal cells. Our results demonstrate that the endodermis represents the primary GA-responsive tissue regulating organ growth and that endodermal cell expansion is rate-limiting for elongation of other tissues and therefore of the root as a whole.     

Determination of plant resistance to carbamate herbicidal compounds inhibiting cell division and early growth by seed and plantlets bioassays

Herbicide-resistant plants can be generated by either traditional breeding procedures or genetic engineering. Analyses of plant responses to a newly developed herbicide or the tolerance level of a newly developed plant line to a given herbicide are based on various bioassays. Here, we describe several methods for quantitative measurements of plants' responses to propham application, as a model herbicide of the carbamate family. Dose-response assays include seed germination and analyses of shoot and root elongation on paper. To better reflect the natural interaction between the plant, the soil and the herbicide, a protocol for germination and root elongation on sand is described. Finally, a more sensitive bioassay is based on plant growth on agar medium. The described protocols are simple, reproducible and can be easily adopted for a variety of plant species and for various herbicides. Plants' response to a given herbicide can be determined within a few weeks.     

Spatio-temporal dynamics of expansion growth in roots: automatic quantification of diurnal course and temperature response by digital image sequence processing

A newly developed technique based on image sequence analysis allows automatic and precise quantification of the dynamics of the growth velocity of the root tip, the distribution of expansion growth rates along the entire growth zone and the oscillation frequencies of the root tip during growth without the need of artificial landmarks. These three major parameters characterizing expansion growth of primary roots can be analysed over several days with high spatial (20 microm) and temporal resolution (several minutes) as the camera follows the growing root by an image-controlled root tracking device. In combination with a rhizotron set up for hydroponic plant cultivation the impact of rapid changes of environmental factors can be assessed. First applications of this new system proved the absence of diurnal variation of root growth in Zea mays under constant temperature conditions. The distribution profile of relative elemental growth rate (REGR) showed two maxima under constant and varying growth conditions. Lateral oscillatory movements of growing root tips were present even under constant environmental conditions. Dynamic changes in velocity- and REGR-distribution within 1 h could be quantified after a step change in temperature from 21 degrees C to 26 degrees C. Most prominent growth responses were found in the zone of maximal root elongation.     

Inhibition of root elongation in microgravity by an applied electric field.

Roots grown in an applied electric field demonstrate a bidirectional curvature. To further understand the nature of this response and its implications for the regulation of differential growth, we applied an electric field to roots growing in microgravity. We found that growth rates of roots in microgravity were higher than growth rates of ground controls. Immediately upon application of the electric field, root elongation was inhibited. We interpret this result as an indication that, in the absence of a gravity stimulus, the sensitivity of the root to an applied electric stimulus is increased. Further space experiments are required to determine the extent to which this sensitivity is shifted. The implications of this result are discussed in relation to gravitropic signaling and the regulation of differential cell elongation in the root.     

Inhibition of root elongation in microgravity by an applied electric field.

Roots grown in an applied electric field demonstrate a bidirectional curvature. To further understand the nature of this response and its implications for the regulation of differential growth, we applied an electric field to roots growing in microgravity. We found that growth rates of roots in microgravity were higher than growth rates of ground controls. Immediately upon application of the electric field, root elongation was inhibited. We interpret this result as an indication that, in the absence of a gravity stimulus, the sensitivity of the root to an applied electric stimulus is increased. Further space experiments are required to determine the extent to which this sensitivity is shifted. The implications of this result are discussed in relation to gravitropic signaling and the regulation of differential cell elongation in the root.     

Differential growth in plants--a phenomenon that occurs at all levels of organization

Differential growth is a feature of cells, the organs which they construct and the whole plant itself. The control of differential growth at each of these three levels of organization resides in the level lower than that in which it is expressed. Thus, differential growth of cells is regulated by the patterns of intracellular microtubules and cellulose microfibrils of the walls, that of organs by the pattern of growth of their cells, and that of the organism by the relative rates of organ growth. The latter is, in turn, determined an all-pervading system of correlative interactions. Plant hormones by may play a role in each of these regulatory systems.