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Determining how cell-scale processes lead to tissue-scale patterns is key to understanding how hormones and morphogens are distributed within biological tissues and control developmental processes. In this article, we use multiscale asymptotic analysis to derive a continuum approximation for hormone transport in a long file of cells to determine how subcellular compartments and cell growth and division affect tissue-scale hormone transport. Focusing our study on plant tissues, we begin by presenting a discrete multicellular ODE model tracking the hormone concentration in each cell’s cytoplasm, subcellular vacuole, and surrounding apoplast, represented by separate compartments in the cell-file geometry. We allow the cells to grow at a rate that can depend both on space and time, accounting for both cytoplasmic and vacuolar expansion. Multiscale asymptotic analysis enables us to systematically derive the corresponding continuum model, obtaining an effective reaction–advection–diffusion equation and revealing how the effective diffusivity, effective advective velocity, and the effective sink term depend on the parameters in the cell-scale model. The continuum approximation reveals how subcellular compartments, such as vacuoles, can act as storage vessels, that significantly alter the effective properties of hormone transport, such as the effective diffusivity and the induced effective velocity. Furthermore, we show how cell growth and spatial variance across cell lengths affect the effective diffusivity and the induced effective velocity, and how these affect the tissue-scale hormone distribution. In particular, we find that cell growth naturally induces an effective velocity in the direction of growth, whereas spatial variance across cell lengths induces effective velocity due to the presence of an extra compartment, such as the apoplast and the vacuole, and variations in the relative sizes between the compartments across the file of cells. It is revealed that hormone transport is faster across cells of decreasing lengths than cells with increasing lengths. We also investigate the effect of cell division on transport dynamics, assuming that each cell divides as soon as it doubles in size, and find that increasing the time between successive cell divisions decreases the growth rate, which enhances the effect of cell division in slowing hormone transport. Motivated by recent experimental discoveries, we discuss particular applications for transport of gibberellic acid (GA), an important growth hormone, within the Arabidopsis root. The model reveals precisely how membrane proteins that mediate facilitated GA transport affect the effective tissue-scale transport. However, the results are general enough to be relevant to other plant hormones, or other substances that are transported in a similar way in any type of cells. [ABSTRACT FROM AUTHOR]

In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells' lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics. [ABSTRACT FROM AUTHOR]

The role of gibberellins (GAs) during germination and early seedling growth is examined by following the metabolism and transport of radiolabeled GAs in cotyledon, shoot, and root tissues of pea ( Pisum sativum L.) using an aseptic culture system. Mature pea seeds have significant endogenous GA levels that fall during germination and early seedling growth, a period when the seedling develops the capacity to transport GA from the cotyledon to the shoot and root of the seedling. Even though cotyledons at 0-2 days after imbibition have appreciable amounts of GA, the cotyledons retain the ability to metabolize labeled GA to GA and express significant levels of PsGA20ox2 message (which encodes a GA biosynthesis enzyme, GA 20-oxidase). The large pool of cotyledonary GA likely provides substrate for GA synthesis in the cotyledons during germination, as well as for shoots and roots during early seedling growth. The shoots and roots express GA metabolism genes ( PsGA3ox genes which encode GA 3-oxidases for synthesis of bioactive GA, and PsGA2ox genes which encode GA 2-oxidases for deactivation of GAs to GA and GA), and they develop the capacity to metabolize GAs as necessary for seedling establishment. Auxins also show an interesting pattern during early seedling growth, with higher levels of 4-chloro-indole-3-acetic acid (4-Cl-IAA) in mature seeds and higher levels of indole-3-acetic acid (IAA) in young root and shoot tissues. This suggests a changing role for auxins during early seedling development. [ABSTRACT FROM AUTHOR]

This review highlights the generation of various types of short forms of membrane hormonal receptors and the mode of regulation of their tissue-specific patterns. The short forms of membrane receptors are classified on the basis of localization of missing functional fragments. The review provides examples of tissues for which expression of short forms may serve as a marker of changes of ontogenetic stage, physiological state, or the development of pathological process. The short forms of receptors are shown to participate in determining tissue-specificity and efficacy of hormonal signal transduction, as well as in transport of hormones within cell, through physiological barriers, and in blood circulation. Peculiarities of signal transduction pathways for short receptor forms and potential physiological significance of these forms are analyzed. It is concluded that the ratio of long and short receptor forms may serve as a key marker of dynamic changes of differentiation stage and alterations of metabolic and proliferative activity of tissues under normal and pathologic conditions, and thus to be an important indicator of therapeutic effect for many pathological processes. [ABSTRACT FROM AUTHOR]

Recent findings on auxin-gibberellin interactions in pea are reviewed, and related to those from studies conducted in the 1950s and 1960s. It is now clear that in elongating internodes, auxin maintains the level of the bioactive gibberellin, GA[sub1], by promoting GA[sub1] biosynthesis and by inhibiting GA[sub1] deactivation. These effects are mediated by changes in expression of key GA biosynthesis and deactivation genes. In particular, auxin promotes the step GA[sub20] to GA[sub1], catalyzed by a GA 3-oxidase encoded by Mendel's LE gene. We have used the traditional system of excised stem segments, in which auxin strongly promotes elongation, to investigate the importance for growth of auxin-induced GA[sub1]. After excision, the level of GA[sub1] in wild-type (LE) stem segments rapidly drops, but the auxin indole-3-acetic acid (IAA) prevents this decrease. The growth response to IAA was greater in internode segments from LE plants than in segments from the le-1 mutant, in which the step GA2[sub20] to GA[sub1] is impaired. These results indicate that, at least in excised segments, auxin partly promotes elongation by increasing the content of GA[sub1]. We also confirm that excised (light-grown) segments require exogenous auxin in order to respond to GA. On the other hand, decapitated internodes typically respond strongly to GA[sub1] application, despite being auxin-deficient. Finally, unlike the maintenance of GA[sub1] content by auxin, other known relationships among the growth-promoting hormones auxin, brassinosteroids, and GA do not appear to involve large changes in hormone level. [ABSTRACT FROM AUTHOR]

A mathematical model of the diffusive transport of abscisic acid (ABA) and gibberellins (GAs) through the aleurone layer of barley (Hordeum vulgare L.) grain is presented. The model consists of two partial differential equations describing the accumulation of phytohormone in the apoplastic and symplasmic compartments of the aleurone layer, both spatially and temporally. The mathematical model contains the morphology of the barley grain and the physicochemical properties of the two phytohormones. A mathematical derivation of the accumulation ratios for the two phytohormones between the symplast and apoplast under equilibrium conditions resulted in different distribution mechanisms for GAs and ABA. A sensitivity analysis of the accumulation ratio for GAs indicated high sensitivity to the apoplastic pH and the membrane potential, whereas the accumulation ratio for ABA proved to be most sensitive to the pH difference between the apoplast and symplast. The diffusive transport time for GAs to the basal site of the aleurone layer as calculated with the mathematical model is within a physiologically plausible timescale according to experimental data from the literature. Abscisic acid cannot be transported by diffusion to the end of the aleurone layer as quickly as GAs, according to model simulations. Therefore, the functional role of ABA in germination is likely to be in the vicinity of the embryo. [ABSTRACT FROM AUTHOR]

Abscisic acid (ABA) in lanolin, applied to the internode of decapitated runner bean plants enhances the outgrowth of lateral buds. The optimum concentration of the paste is 10 M. The effect of ABA is counteracted by indoleacetic acid (IAA) but not by gibberellic acid (GA). There is no effect when ABA is applied to the apical bud or lateral buds of intact plants. However, 13.2 ng given to the lateral buds of decapitated plants stimulate their growth, whereas higher concentrations are inhibitory. Consequently, ABA enhances growth of lateral buds directly, but only when apical dominance is already weakened. The growth of the decapitated 2 internode was not affected by ABA. Radioactivity from [2-C] ABA, applied to nonelongating 2 internode stumps of decapitated runner bean plants moves to the lateral buds, whereas [1-C]IAA-and [H]GA-translocation is much weaker. ABA transport is inhibited if IAA or [H]GA is applied simultaneously. In elongating internodes [C]ABA is almost completely immobile. [C]IAA-and [H]GA-translocation is not affected by ABA. The amount of radioactivity from labelled ABA, translocated to the lateral buds, is highest during the early stages of bud outgrowth. [ABSTRACT FROM AUTHOR]