The tensor-based model for growth and cell divisions of the root apex. II. Lateral root formation

In this work, the formation of the virtual lateral root (VLR) is shown. The VLR is formed using the 2D simulation model of growth and cell divisions based on the concept of growth tensor, specified for radish. Growth is generated by the field of growth rates of an unsteady type (GT field). Principal directions of growth (PDGs) are assumed to define the orientation of cell divisions. Temporal sequences of the VLR formation are a result of an application of the GT field to the polygon meshwork representing cell pattern of already initiated primordium. The computer-generated lateral root (LR) develops realistically, and its cell pattern is vivid and similar to that observed in anatomical sections. The real and virtual LRs show similar cellular organization, both originate from a small group of cells situated in two-cell layers of the pericycle and both layers are engaged in the LR development. The LR formation seems to be controlled at the tensor level and individual cells presumably detect PDGs and obey them in the course of the cell divisions. PDGs are postulated to affect the cellular organization of the LR. Using the method of computer simulations, cellular aspects of the LR morphogenesis are discussed.     

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 trajectories 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.     

Principal directions of growth and the generation of cell patterns in wild-type and gib-1 mutant roots of tomato (Lycopersicon esculentum Mill.) grown in vitro

The patterns of cell growth and division characteristic of the apex of tomato roots grown in vitro were simulated by computer using a growth tensor (GT). The GT was used to clarify the basis of the altered cell patterns found within apices of roots whose gibberellin levels had been depressed by mutation (at the GIB-1 locus) or through application of the gibberellin-biosynthesis inhibitor, 2S,3S paclobutrazol. At the pole of wild-type roots, where the cell files of the cortex converge, there are commonly only one or two tiers of cortical cells sandwiched between the pole of the stele and the cap initials. By contrast, root apices of the gib-1 mutant contain additional tiers in this region. The development of these additional tiers is suppressed when roots of the mutant are grown in the presence of gibberellic acid (GA₃), but could be induced in wild-type roots when they are grown in 2S,3S paclobutrazol. The wild-type cell pattern can be simulated using the GT and by the application of appropriate rules that govern cell growth and division. The induced variations in cell pattern are interpreted as being due to displacements, within the apex, of the principal directions of growth (PDGs), which are represented, in part, by the set of periclines and anticlines seen in the cell wall network; these, in turn, are utilized in the specification of the GT. During normal (wild-type) root growth, the PDGs maintain a stable pattern and the corresponding cell pattern is also stable. However, in order to interpret the cellular behaviour found in wild-type roots grown in 2S, 3S paclobutrazol, simulation using the GT shows that, if the pattern of PDGs is destabilized and displaced distally along the root axis, the cell pattern reorganizes into that typical of gib-1 mutant roots. Conversely, the cell pattern of gib-1 roots, which reverts to wild-type upon exposure to GA₃, can be simulated if the PDGs are displaced proximally to the inside of the apex whereupon the number of cortical tiers at the root pole decreases. These results suggest a link between endogenous gibberellin level and the specification of the PDGs in the growing tomato root apex. Furthermore, the evidence of cell patterns from gib-1 roots suggests that, in order to achieve stability of PDGs with concomitant stable cellular patterning, an optimal gibberellin level is necessary. In practice, this can be attained by culturing the mutant roots in medium containing 1 M GA₃.Abbreviations GA₃ gibberellic acid - GT growth tensor - NCS natural coordinate system - PDG principal direction of growth - QC quiescent centre - RERG relative elemental rate of growth We are grateful to the former Agricultural and Food Research Council for financial support under the International Scientific Interchange Scheme to enable J.N. to work at Long Ashton Research Station, and to K. Kurczyski (Silesian University, Katowice, Poland) for help in writing a computer program for cell proliferation. Preparation of the model for growth and division was supported in part by a grant from the Committee for Scientific Research, Poland.     

The simulation model of growth and cell divisions for the root apex with an apical cell in application to Azolla pinnata

In contrast to seed plants, the roots of most ferns have a single apical cell which is the ultimate source of all cells in the root. The apical cell has a tetrahedral shape and divides asymmetrically. The root cap derives from the distal division face, while merophytes derived from three proximal division faces contribute to the root proper. The merophytes are produced sequentially forming three sectors along a helix around the root axis. During development, they divide and differentiate in a predictable pattern. Such growth causes cell pattern of the root apex to be remarkably regular and self-perpetuating. The nature of this regularity remains unknown. This paper shows the 2D simulation model for growth of the root apex with the apical cell in application to Azolla pinnata. The field of growth rates of the organ, prescribed by the model, is of a tensor type (symplastic growth) and cells divide taking principal growth directions into account. The simulations show how the cell pattern in a longitudinal section of the apex develops in time. The virtual root apex grows realistically and its cell pattern is similar to that observed in anatomical sections. The simulations indicate that the cell pattern regularity results from cell divisions which are oriented with respect to principal growth directions. Such divisions are essential for maintenance of peri-anticlinal arrangement of cell walls and coordinated growth of merophytes during the development. The highly specific division program that takes place in merophytes prior to differentiation seems to be regulated at the cellular level.     

A method to determine the displacement velocity field in the apical region of the Arabidopsis root

In angiosperms, growth of the root apex is determined by the quiescent centre. All tissues of the root proper and the root cap are derived from initial cells that surround this zone. The diversity of cell lineages originated from these initials suggests an interesting variation of the displacement velocity within the root apex. However, little is known about this variation, especially in the most apical region including the root cap. This paper shows a method of determination of velocity field for this region taking the Arabidopsis root apex as example. Assuming the symplastic growth without a rotation around the root axis, the method combines mathematical modelling and two types of empirical data: the published velocity profile along the root axis above the quiescent centre, and dimensions of cell packet originated from the initials of epidermis and lateral root cap. The velocities, calculated for points of the axial section, vary in length and direction. Their length increases with distance from the quiescent centre, in the root cap at least twice slower than in the root proper, if points at similar distance from the quiescent centre are compared. The vector orientation depends on the position of a calculation point, the widest range of angular changes, reaching almost 90°, in the lateral root cap. It is demonstrated how the velocity field is related to both distribution of growth rates and growth-resulted deformation of the cell wall system. Also changes in the field due to cell pattern asymmetry and differences in slope of the velocity profile are modelled.     

The tensor-based model of plant growth applied to leaves of Arabidopsis thaliana: A two-dimensional computer model

Plant organs grow in coordinated and continuous way. Such growth is of a tensor nature, hence there is an infinite number of different directions of growth rate in each point of the growing organ. Three mutually orthogonal directions of growth can be recognized in which growth achieves extreme values (principal directions of growth [PDGs]). Models based on the growth tensor have already been successfully applied to the root and shoot apex. This paper presents the 2D model of growth applied to the arabidopsis leaf. The model employs the growth tensor method with a non-stationary velocity field. The postulated velocity functions are confirmed by growth measurements with the aid of the replica method.     

Influence of a weak DC electric field on root meristem architecture

BACKGROUND AND AIMS: Electric fields are an important environmental factor that can influence the development of plants organs. Such a field can either inhibit or stimulate root growth, and may also affect the direction of growth. Many developmental processes directly or indirectly depend upon the activity of the root apical meristem (RAM). The aim of this work was to examine the effects of a weak electric field on the organization of the RAM. METHODS: Roots of Zea mays seedlings, grown in liquid medium, were exposed to DC electric fields of different strengths from 0.5 to 1.5 V cm(-1), with a frequency of 50 Hz, for 3 h. The roots were sampled for anatomical observation immediately after the treatment, and after 24 and 48 h of further undisturbed growth. KEY RESULTS: DC fields of 1 and 1.5 V cm(-1) resulted in noticeable changes in the cellular pattern of the RAM. The electric field activated the quiescent centre (QC): the cells of the QC penetrated the root cap junction, disturbing the organization of the closed meristem and changing it temporarily into the open type. CONCLUSIONS: Even a weak electric field disturbs the pattern of cell divisions in plant root meristem. This in turn changes the global organization of the RAM. A field of slightly higher strength also damages root cap initials, terminating their division.     

Development of the quiescent center in maturing embryonic radicles of pea (Pisum sativum L. cv. Alaska)

Maturing embryos of pea (Pisum sativum L. cv. Alaska) were treated with an aqueous solution of tritiated thymidine for 1 h, sectioned, and processed for autoradiography. An analysis of the distribution of labelled nuclei and mitotic figures demonstrated the presence of a quiescent center (QC) in the radicles of developing embryos. The QC developed in the radicle during the growth of the embryo. Immature radicles that did not contain a well-formed zone of root-cap initials did not show a QC. In the latter stages of seed ripening, the pattern of arrest of DNA synthesis and mitosis was tissue-specific. Cells within the QC remained inactive. The region lacking labelled nuclei and mitotic figures progressively expanded to include the root cap initials and then the provascular cylinder. Mitosis was arrested before DNA synthesis in the embryonic cortex. Cells within the QC synthesized DNA during the first stages of seed germination.Abbreviations [³H]TdR tritiated thymidine - QC quiescent center     

MODELING OF MERISTEMATIC GROWTH OF ROOT APICES IN A NATURAL COORDINATE SYSTEM

A curvilinear, orthogonal coordinate system, which resembles the pattern of periclines and anticlines in the cellular network of root apices, is presented. The system makes possible an analysis of the dynamics of apical growth: the relationship between growth rates and tensile stresses in cell walls. In this paper the coordinate system is used in modeling the growth and cell partitioning in the apical domes. The symplastic growth is described by means of the growth tensor which is assumed to have diagonal form in the system, so its coordinate lines represent the principal directions of growth rate. The coordinate system and the growth tensor in diagonal form assure temporal stability of form and cellular structure of the modeled apex including transition from the dome to the cylindrical part of the apex. The spatial and temporal aspects of the dome part of two types of root apices—one with maximum of volumetric relative growth rate at the center region of the apex, and another with minimum of the rate (quiescent center)—are described. The maximum of the rate at the center results in the cellular pattern with an apical cell and merophytes, the minimum results in ribs of cells (inside the root proper) converging toward the quiescent center.     

Regeneration of the Root Cap of Zea mays L. and Pisum sativum L.: A Study with the Scanning Electron Microscope

Removal of the root cap from a root apex initiates regenerationof a new cap. The process has been followed using scanning electronmicroscopy. Quantitative data have been obtained for the growthin area of the exposed acroscopic surface of the quiescent centre(QC) and the increase in volume of the regenerating cap tissue.In Zea the surface of the QC shows an initial rapid increasein area followed by a slower increase. In Pisum the surfacearea increases uniformly, a rapid initial phase being absent.Together with observations on the behaviour of an incision atthe exposed surface, the results indicate that in Zea the capnormally imposes a constraint upon radial growth at the acroscopicsurface of the QC; in Pisum the QC appears not to be so constrained.The different responses may be related to the different arrangementsof cells at the apex of the meristem of these two species. Zea mays, Pisum sativum, maize, peao, scanning electron microscopy, root apex, regeneration     

The quiescent center in roots of maize: initiation,maintenance and role in organization of the root apical meristem

Summary Using roots of maize, we tested the hypothesis that the origin and maintenance of the quiescent center (QC) are a consequence of polar auxin supply. Exposing roots to the polar auxin transport inhibitor 2,3,5-triiodobenzoic acid (TIBA), or to low temperature (4 °C, with subsequent return to 24 °C), enhances mitotic frequency within the QC. In both treatments, the QC most typically is activated at its distal face, and the protoderm/dermatogen undergoes several periclinal divisions. As a result, the root body penetrates and ruptures the root cap junction and the characteristic closed apical organization changes to open. A QC persists during these changes in apical organization, but it is diminished in size. The data from the TIBA-treated roots suggest a role for auxin in the origin and maintenance of the QC, and further, that alterations in QC dimensions are a consequence of polar auxin supply. We hypothesize that the root cap, and specifically the root cap initials, are important in regulating polar auxin movements towards the root apex, and hence are important in determining the status of the QC.Abbreviations QC quiescent center - TIBA 2,3,5-triiodobenzoic acid Dedicated to the memory of Professor John G. Torrey     

Origin of the concept of the quiescent centre of plant roots

Concepts in biology feed into general theories of growth, development and evolution of organisms and how they interact with the living and non-living components of their environment. A well-founded concept clarifies unsolved problems and serves as a focus for further research. One such example of a constructive concept in the plant sciences is that of the quiescent centre (QC). In anatomical terms, the QC is an inert group of cells maintained within the apex of plant roots. However, the evidence that established the presence of a QC accumulated only gradually, making use of strands of different types of observations, notably from geometrical-analytical anatomy, radioisotope labelling and autoradiography. In their turn, these strands contributed to other concepts: those of the mitotic cell cycle and of tissue-related cell kinetics. Another important concept to which the QC contributed was that of tissue homeostasis. The general principle of this last-mentioned concept is expressed by the QC in relation to the recovery of root growth following a disturbance to cell proliferation; the resulting activation of the QC provides new cells which not only repair the root meristem but also re-establish a new QC.     

EMBRYOGENY AND HISTOGENESIS IN NERIUM OLEANDER II. ORIGIN AND DEVELOPMENT OF THE NON-ARTICULATED LATICIFER

Mahlberg , P. G. (U. Pittsburgh, Pittsburgh, Pa.) Embryogeny and histogenesis in Nerium oleander. II. Origin and development of the non-articulated Iaticifer. Amer. Jour. Bot. 48(1): 90–99. Illus. 1961.—Laticifer initials, collectively considered as a laticifer system, are differentiated in the globular embryo from meristematic cells which occupy a position within the potential procambial tissue. A total of usually 28 initials, in Nerium oleander, arise as an irregular ring of cells directly below the embryonic shoot apex, during initiation of the cotyledonary primordia. No anastomoses occur between laticifer initials. During subsequent development of the embryo, the laticifer initials grow in a bi-directional manner and penetrate into the root, cotyledons and toward the shoot apex. Upon enlargement the initials bifurcate repeatedly, many branches penetrate into the cotyledons, others grow into the cortex of the hypocotyl or penetrate between cells of the procambium. Repeated nuclear divisions within each initial result in the formation of a multinucleated protoplast in this cell type. The tips of laticifers occupy intercellular spaces during their growth; they do not penetrate into or through adjacent cells. A plexus of laticifer branches is formed within the cotyledonary node of the mature embryo. No new initials are formed during subsequent growth of the plant, rather certain branches from the cotyledonary nodal plexus penetrate into the enlarging shoot system. The nature of their growth habit and branching suggests that the tips of laticifer initials exhibit an intrusive form of growth.     

THE ROOT APEX OF LINUM

Several developmental stages of primary roots of 13 species of Linum were studied. The basic pattern of root apex organization in three species consisted of a single tier of cortical initials. Ten species had a basic pattern of two tiers of cortical initials. Variations, manifested by either an increase or a decrease in the tiers of cortical initials, were observed in some roots in those species that had a basic pattern of two tiers of cortical initials. Although these variations were interpreted as being ontogenetic, there was no total reorganization of the root apex. There was anatomical and cytological evidence that a quiescent center is established in Linum roots.     

Modeling the formation of root apices

The formation of new root apices from small groups of cells with different cellular patterns has been simulated using an existing model based on growth tensors. To generate an apex, a steady growth field was used. The pattern of cells evolved to approach the steady state. Two extreme types of progressions have been obtained : one leading to an apex with a single or a few apical cells, and the other to an apex with a quiescent centre. The change of structure while applying a steady growth tensor indicates that development may involve a succession of discrete growth tensors.     

Structure and Cytogenesis of the Shoot Apex of Syringa oblata var. affinis Lingelsh

The structure, growth and mitotic activity of 211 shoot apices of developing sprouts of Syringa oblata var. affinis Lingelsh. in longitudinal sections and 67 in transverse sections have been studied with the view to understanding the nature of zonation patterns and cytogenesis of the apical meristems during a double plastochron. The external morphology and the anatomical structure of the apices in 4 plastochronic stage-early, middle, late Ⅰ and late Ⅱ stages are described. In the shoot apices examined, especially those at late plastochronic stage, the following zones may be delimited: Zone of tunica initials, zone of corpus initials, peripheral zone and zone of rib meristem. The location and orientation of mitotic figures observed in longisections of the apices in 4 plastochronic stages are plotted in diagrams and the mitotic frequency has been calculated. Information obtained from these investigations reveals that the tunica and corpus inititals constitute an active region of the apex, but their mitotic activity changes periodically within the double plastochron. In the middle plastochronic stage when the apex is at its minimal area and the cells of peripheral zone and rib meristem zone have been completely transformed into constituent parts of foliar primordia and the subjacent tissues of the stem and the pith mother cells respectively, the mitotic frequency of the initials is at its maximium and its intensity of mitotic activity is not much lower than that of any other meristematic zone at any stage. When the apical dome is reformed by the activity of these initials in late plastochronic stages, the mitotic frequency of the initials gradually drops and the region of high mitotic frequency shifts to the flank of the apex, the peripheral zone. Anticlinal divisions are predominant in this zone. On the other hand, those cells directly left behind by the corpus initials, which constitute the rib meristem, are vacuolated and marked by the pre- dominance of transverse divisions. Thus the entire zonation pattern reappears. In the next early plastochronic stage, the mitotic frequency of the tunica and corpus initials drops to its mimimium, but other regions of the apex still maintain a high mitotic frequency. It may be concluded that the tunica and corpus initials form a cytogenerative center of the shoot, and the cytohistological zonation is actually a result of the fact that different regions of apical meristems are different in mitotic activety, different in state of cell differentiation and different in their function in morphogenesis.     

Localization of ascorbic acid, ascorbic acid oxidase, and glutathione in roots of Cucurbita maxima L

To understand the function of ascorbic acid (ASC) in root development, the distribution of ASC, ASC oxidase, and glutathione (GSH) were investigated in cells and tissues of the root apex of Cucubita maxima. ASC was regularly distributed in the cytosol of almost all root cells, with the exception of quiescent centre (QC) cells. ASC also occurred at the surface of the nuclear membrane and correspondingly in the nucleoli. No ASC could be observed in vacuoles. ASC oxidase was detected by immunolocalization mainly in cell walls and vacuoles. This enzyme was particularly abundant in the QC and in differentiating vascular tissues and was absent in lateral root primordia. Administration of the ASC precursor L-galactono-gamma-lactone markedly increased ASC content in all root cells, including the QC. Root treatment with the ASC oxidized product, dehydroascorbic acid (DHA), also increased ASC content, but caused ASC accumulation only in peripheral tissues, where DHA was apparently reduced at the expense of GSH. The different pattern of distribution of ASC in different tissues and cell compartments reflects its possible role in cell metabolism and root morphogenesis.     

3D analysis of mitosis distribution highlights the longitudinal zonation and diarch symmetry in proliferation activity of the Arabidopsis thaliana root meristem

To date CYCB1;1 marker and cortex cell lengths have been conventionally used to determine the proliferation activity of the Arabidopsis root meristem. By creating a 3D map of mitosis distribution we showed that these markers overlooked that stele and endodermis save their potency to divide longer than the cortex and epidermis. Cessation of cell divisions is not a random process, so that mitotic activity within the endodermis and stele shows a diarch pattern. Mitotic activity of all root tissues peaked at the same distance from the quiescent center (QC); however, different tissues stopped dividing at different distances, with cells of the protophloem exiting the cell cycle first and the procambial cells being the last. The robust profile of mitotic activity in the root tip defines the longitudinal zonation in the meristem with the proliferation domain, where all cells are able to divide; and the transition domain, where the cell files cease to divide. 3D analysis of cytokinin deficient and cytokinin signaling mutants showed that their proliferation domain is similar to that of the wild type, but the transition domain is much longer. Our data suggest a strong inhibitory effect of cytokinin on anticlinal cell divisions in the stele.     

An Automata-theoretical Model of Meristem Development as Applied to the Primary Root of Zea mays L.

Observations were made of the sequence of division within thecellular packets (groups of cells of common descent) which comprisethe cell files that run the length of the central cortex ofthe primary root meristem ofZea mays. These sequences, and alsothe relative lengths of the cells within the packets recordedat various times during root growth, indicate that cell-filedevelopment can be expressed using one, or a limited number,of deterministic ‘bootstrap’ L-systems which assigndifferent lifespans to sister cells of successive cell generations.The outcome is a regular pattern of divisions from which daughtercells emerge usually with unequal, but definite, lengths. Inthe immediately post-germination stage of root growth, one divisionpathway is especially common in the cortex and generates sequencesof unequal daughters having a particular basi-apical orientation.Later in root growth, the cellular pattern in the cortex indicatesthat this pathway is replaced by another where unequal divisionsare not so marked, but which nevertheless continues to maintaina regular arrangement of differently sized cells. This latterpathway is characteristic of a zone close to the initial cellsof the cortex. It is present at all stages of root growth andspreads along the length of the cortex as the descendants ofthese initials proliferate. The development of the whole corticalcell file can be simulated from knowledge of the growth functionsof the bootstrap systems. The files so generated contain allthe observed cell patterns. The growth functions also predictthe sequence in which cells cease dividing near the proximalmargin of the meristem, but for this it is necessary to incorporatea counter for the number of divisions that will be accomplishedin the cell file. Cytological requirements for the propagationof unequal divisions, together with a consideration of the natureof the division counter, as well as the significance of theswitch in division pathways encountered during early root growth,are discussed in the context of this deterministic model ofcell division. Cell division; root meristem; L-systems; Zea mays