Deposition rates in growing tissue: Implications for physiology, molecular biology, and response to environmental variation
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Net rates of biosynthesis and mineral deposition are needed to understand the physiology and molecular biology of growth and plant responses to environmental variation. Many popular models ignore cell expansion and displacement. In contrast, the continuity equation, used with empirical data on growth velocity and concentration, allows computation of biosynthesis and deposition rates in growing tissue.
This article describes data and methods needed to calculate deposition rates and reviews some insights into environmental physiology and molecular biology.
Growth zones actively and strongly deposit mineral elements, even though local concentrations may not be changing in time. Deposition rate profiles give important insight into the mechanism of plant responses to drought and salinity, and they clarify many aspects of nitrogen metabolism in roots and leaves. This approach is also essential to understand molecular regulation of growth. A pioneering study determined transcript densities and calculated rates of change in gene expression; this study revealed how Actin 11 is highly regulated by a balance of transcription and decay during growth of roots. New technologies (in planta cytometry, coupled with powerful computational routines and real-time confocal microscopy) will allow determination of deposition rates in growing organs and advancement in understanding of gene regulation.
KeywordsGrowth Kinematics Continuity equation Deposition rates Plant-environment interactions Regulation of gene expression
Plants grow throughout most of their lives, and they use growth to acquire light, nutrients, and water. Organic compounds are metabolized and mineral elements are deposited in plant cells throughout the cellular development, maturation, and senescence. Net rates of biosynthesis and mineral deposition are needed to understand physiology and the response to environmental variation. Particularly in growing tissue it is necessary to consider expansion and displacement of cells relative to observed concentration patterns. This is because, in contrast to mature tissues, growing tissue has concentration profiles that are produced by cell expansion as well as nutrient import, catabolism and anabolism, thus, quantitative analyses of morphogenesis are required.
Plant computational morphodynamics is now a popular field of study. The classical literature on plant growth analysis is well cited. Landmark papers include an analysis of cell division rates based on a form of the continuity equation (Goodwin and Stepka 1945), the use of streak photographs by Erickson and Sax (1956) to quantify the one-dimensional growth rate pattern in corn roots, and a quantitative two-dimensional analysis of leaf growth (Erickson 1966). The important distinction between spatial and material (cell-specific) aspects of plant development was clarified three decades ago (Silk and Erickson 1978, 1979; Gandar 1983a, b). More recently Kwiatkowska and Dumais (2003) provided a quantitative analysis of apical morphogenesis, while improved computer-assisted tracking of natural marks has facilitated high-throughput growth analysis at high resolution (Walter et al. 2002; Grandjean et al. 2004; Reddy et al. 2004; Miller et al. 2007). At a recent workshop scientists showed time-lapse images from confocal microscopy of living tissue and described how image analysis is facilitated by genetic transformation to introduce fluorescent markers into plant cells (reviewed in Cunha et al. 2012, images viewable at http://www.computableplant.org/).
And yet in 2012, many computational models are time dependent but neglect to consider growth. Perhaps this is the heritage of the influential Turing model (1952) for morphogenesis. Turing showed that when two or three reactants with different diffusivities are involved in a common chain of chemical reactions, then a small amount of noise leads to stable, inhomogeneous patterns that are suggestive of biological patterning. This has been an appealing approach for theoretical biologists; by 2012 Turing’s paper had 3428 citations. However, the Turing models do not include expansion or active sinks both of which characterize growing plant organs. Another popular model, often used for mineral uptake in plants, is based on the Michaelis-Menten equations (1913) for enzyme kinetics. The Michaelis-Menten model assumes a well-stirred beaker: The system is seen to vary in time and to lack spatial gradients. This is not an appropriate pair of assumptions for a plant. The simplest model plant, in an appropriate (moving) reference frame, has spatial patterns of growth, anatomy, and biochemistry that may not change in time. The model plant must however have spatial variation associated with the developmental gradient, that is, the variation in tissue age at different positions.
When the deposition rate is positive, the location is a sink for the material of interest. The material can be imported or be produced by local metabolism. A negative deposition rate means the location is losing material by catabolism or by export either to the environment or to other plant tissues. The local deposition rate is a net accumulation rate, the result of synthesis, import, degradation, and/or export.
This article reviews deposition rates in plant tissue and some implications for physiology, ecology and molecular biology. The use of this approach to quantify cell division rates and the molecular regulation of cell division has been reviewed elsewhere (Fiorani and Beemster 2006); environmental effects on coordination between division and elongation have been reviewed by Tardieu et al. (2011). The article concludes by citing some recent computational advances that have the potential to greatly extend understanding of biochemistry and molecular biology of growing tissue.
Non-growing tissue—seeds and mature tissue
Equation 1C tells us the deposition rate equals the observed rate of change in concentration. It would be assayed for instance in a spectrophotometric assay by a change in color intensity. In the Bradford assay using Coomassie Brilliant Blue dye, an increase in blue color would indicate protein production; a decrease in blue color would indicate destruction of the protein. Seeds and non-growing tissue producing or degrading protein without changes in volume can be characterized in this way.
One-dimensional, steady cases—growing roots and monocot leaves
This equation is derived from the assumption of conservation of matter (e.g. Boas 2005). Here the deposition rate, perhaps in ng per mm of tissue along a plant axis, is a local rate ascribed to a particular position. The equation is in terms of changes in concentration with respect to time, t, and distance, z. We see that the equation needs data on both concentration and growth. To find the spatial pattern of growth velocity, vz, it is convenient to use the reference frame with origin at a root or shoot apex, or the base of a monocot leaf. That is, z = 0 and vz = 0 at the origin and vz increases with z to reach a maximum displacement velocity at the base of the growth zone (Erickson and Sax 1956). The velocity gradient is the “relative elemental growth rate” (“REGR”) quantifying the local expansion. In this moving reference frame, in the simplest case, growth patterns may be steady (unchanging in time), while cells are formed and displaced through the growth zone (Erickson and Sax 1956; Boffey et al. 1980). In growing roots and monocot leaves the spatial pattern in mineral content may also be steady (Silk and Erickson 1979). The gradient terms may be evaluated in spreadsheets using Erickson’s midpoint differentiation formulas (Erickson 1976), or cubic splines may be fit to the data and numerically differentiated, for instance using MATLAB (The MathWorks, Inc.).
The growth dilution term is always positive in growing tissue. The convective rate of change is negative if the concentration decreases with position (a negative gradient as in Fig. 1), and positive if concentration increases with position so that the tissue element increases in concentration during its displacement (as suggested in Fig. 2). The experimental design used to obtain Fig. 1 gives results per mm of root or leaf. These results can be made more universal if they are divided by the weight or cross-sectional area of the segments used for the chemical assay, to give deposition rates on the basis of tissue weight or volume (Silk et al. 1984).
Sampling and time intervals
The continuity equations show that the spatial patterns of growth velocity and metabolite concentration are the basic data required to find the metabolite deposition rates. Tissue sampling should provide adequate resolution through the growth zone. Indeed linear growth zones show a large range of length. Determining metabolite concentration profiles is easier in long growth zones without needing to pool samples. Recently, Nelissen et al. (2012) used the 65 mm-long growth zone of the maize (Zea mays L.) leaf to facilitate the determination of several hormone concentrations. The ~30 mm-long growth zone of grasses such as tall fescue (Festuca arundinacea Schreb.) leaf offer also a good model (Schnyder and Nelson 1988; Gastal and Nelson 1994). A mm-scale resolution is required for plant roots whose growth zone is around 10 mm such as maize (Sharp et al. 1988) or poplar (Populus deltoïdes × nigra cv. ‘Soligo’) (Merret et al. 2010). The shorter root growth zone of the model plant Arabidopsis thaliana (L.) Heynh. (~2.5 mm, Beemster and Baskin 1998) requires much higher resolution, using microdissection or imaging of quantitative and sufficiently short-lived reporters. At the other end of the size scale, the giant blades of bull kelp (Nereocystis luetkeana (K. Mertens) Postels & Ruprecht) have growth zones almost one meter long and can be sampled on the 5-cm scale (Koehl et al. 2008).
For the growth analysis, the movement of natural or applied marks should be followed on a time scale long enough for mark displacement, but short enough that marks do not move too far from their initial, ascribed positions (Silk 1984). A rule of thumb is that the time interval for observation should be chosen so that marks do not move more than 15 % of the length of the growth zone. To capture the growth near the origin (where growth velocity is small), it may be useful to follow the marks over a longer time scale than that used to analyze the faster moving marks. Ideally, the sampling time scale should be adequately designed to also assess shorter temporal variations-hourly oscillations and circadian rhythms (Merret et al. 2010).
Comparison to radiolabel experiments
Lagrangian (cell-particle-specific) description
Most of the time, concentration and net deposition rate are given as a function of position in the growth zone and describe “what happens” in each particle or cell disposed along the growth zone. It is also interesting to get a temporal and spatial description of these variables in a single particle or cell cohort crossing the growth zone as time goes on (Green 1976; Silk and Erickson 1979; Gandar 1983a, b). This cell-specific description is called a Lagrangian specification as opposed to the spatial (site-specific) or Eulerian specification (Silk and Erickson 1979). If data are given as spatial patterns of a developmental variable, to follow a cell requires determining the Eulerian specifications of growth and of the variable over the time necessary for a particle to cross the growth zone. In non-steady state this requires extensive data on spatial and temporal patterns of the variable and the growth velocity. In steady state (that is, if spatial patterns of both growth velocity and density are not changing with time), the spatial specification can be interpreted as descriptions of “what happens” in a single particle as it is moved through the growth zone. In steady state it is also possible to use a single growth velocity curve to determine the growth trajectory, that is the relationship between particle position and time, from the temporal integration of the velocity field following the particle (Silk and Erickson 1979; Gandar 1983a) or by counting cells outside the meristem (Silk et al. 1989). Then the spatial coordinates can be converted into temporal coordinates to provide the Lagrangian specification.
Biological outcomes: Regulation of metabolite concentration in growth zones
In this section we describe some basic patterns that emerged during early applications of the continuity equation to analyse metabolite production in growing tissue. A later section on biological outcomes then quantifies impacts of environmental variation.
The pattern of metabolite density may be unchanging with time in primary growth zones while the cellular population of the zone is replaced several times
Even when the concentration of a mineral element is decreasing in developing tissue, large deposition of the element is occurring. Growth zones are often the largest sink for metabolites and mineral elements
Deposition rates of nutrients in developing corn leaves
Leaf Serial #
Elongation Rate (mm h−1)
Length of growth zone (mm)
Element deposition rate
45 mm from node (rapid growth)
100 mm from tip (not growing)
Regulation of metabolite concentration depends on net deposition rate, not concentration
In the example above (Fig. 7), an experimenter seeking to understand potassium transport should look for carrier activity or up-regulation of gene expression associated with deposition rate. On the other hand, the physiological importance of potassium (as osmoticum for instance) is related to the concentration itself.
N is deposited rapidly into dividing and elongating leaf cells of fescue; RuBisCO in maturing tissue is formed by cannibalization of previously formed metabolites
Comparison of endogenous deposition rates and exogenous influx reveals contrasting import/export patterns for ammonium and nitrate in growth zones of maize roots
Bloom et al. (2012) then were able to infer the patterns of import and export of different forms of nitrogen by calculating endogenous nitrogen deposition rates and comparing these to the previously determined exogenous uptake rates (Fig. 9). Where local deposition exceeds local influx, the tissue must be importing endogenous nitrogen. Under Ca(NO3)2 supply, root NO3– influx was adequate to account for pools found in the growth zone and provided twice as much as was deposited locally throughout the non-growing tissue. Some NH4+ was deposited and must have been imported from the seed or shoot. In contrast, under NH4NO3 supply, NO3– influx was less than the local deposition of NO3– in the growth zone, indicating that additional NO3– was imported or metabolically produced. Yet the profile of NO3– in the growth zone was similar for the plants receiving Ca(NO3)2 or NH4NO3 (Bloom et al. 2012). For both N supplies, tissue nitrate levels increased from the meristem through the growth zone and all of the apical 60 mm. Xylem sap NH4+ concentrations were indifferent to the presence of NO3– in the medium. Since the exogenous uptake of NO3– in the root apex is highly dependent on the presence of NH4+ in the medium, when NH4+ is present, all the NO3– absorbed near the apex is stored as free NO3– in the tissues, and additional nitrate is imported or metabolically produced. When NO3– is the sole N-source, the roots store similar amounts of free NO3– and they absorb additional NO3– that is assimilated or translocated to the shoot. These results show that NO3– deposition, whether exogenously supplied or imported, is important for supporting root elongation in the basal part of the growth zone and maintaining root function in the young mature tissues.
In a related study, Walter and colleagues (2003) determined the endogenous fluxes and deposition rates of metabolites in the seedling roots of maize. They showed that nitrates, but not other nutrients, were exported to a great extent from the root growth zone to the mature tissue. Overall, their results show that a careful analysis of growth kinematics allows quantifying and interpreting a number of important flux parameters in the growing organ.
Biological outcomes: Metabolite deposition rate and growth response to environment
Under water stress, if maize roots do not experience a change in mechanical impedance, osmotic adjustment occurs with decreased rates of solute deposition coupled to larger decreases in radial growth rates
Similar conclusions were found in growing leaves of tall fescue after water was withheld (Spollen and Nelson 1994). The increasing levels of water deficit reduced the relative elemental elongation rates and shortened the growing zone in proportion to the duration of water withholding. When the water deficit exceeded a threshold, the dry matter content per unit length was increased by more than 20 % over the whole growing zone while leaf elongation rate was decreased by approximately 50 %, indicating that net dry matter import rate must have been decreased in this growing zone. Further analyses of water soluble carbohydrates content suggested that the hydrolysis of fructan stored in the distal part of the elongation zone could account for an increased content in hexoses in the apical part. It is clear that the accumulation of water soluble carbohydrates leads to osmotic adjustment.
We note that these effects of drought occurred only in the absence of changes in soil hardness. In contrast roots often grow thicker in those soils that become hard to penetrate as they dry. (reviewed in Bengough et al. 2006). Work remains to analyze the growth kinematics and metabolism as the root adapts to increased soil impedance.
In salt-affected sorghum leaves, decreases in potassium deposition rates parallel decreases in growth rates
Aphid infestation of alfalfa transforms apical nitrate sink tissue to a nitrate source
Molecular biology: Utility and outcomes
In mature tissues, where cells do not enlarge, the transcriptional regulation of gene expression (e.g., environmental induction) is computed as the temporal change of transcript density in a stationary reference frame. In practice, gene induction or repression is inferred from the ratio of the gene expression in treated plants relative to controls. When focusing on development, gene expression is compared in samples collected in different positions representative of successive time points. For instance, highly accurate maps of gene expression in the root apex have been produced, highlighting coordinated gene expression networks (Birnbaum et al. 2003; Brady et al. 2007). Since longitudinal profiles describe the different developmental stages undergone by a cell during growth, one could be tempted to deduce regulation of gene expression from variations of gene expression along the growing zone. However, this would be misleading since cells expand at varying rates while being displaced along the root. The continuity equation can be used with growth trajectories to get an unbiased view of the spatio-temporal regulation of gene expression.
Actin11 is highly regulated by a balance of transcription and decay during growth of poplar roots
While gene expression is usually normalized in order to get rid of sampling error and to eliminate differences of biological activity among samples, the continuity equation must be applied to absolute quantities, thus on transcript densities. Since the density of nuclei and presumably the cellular activity are heterogeneous along the root growth zone, net accumulation rates must be compared to the net accumulation rate of a standard entity, either the expression of reference genes or cell density. Merret and co-authors used total RNA content as an estimate of cell density (2010). As expected, the net accumulation rate of total RNA was null, except in the meristem supporting the significance of the conclusions about the regulation of Actin 11 expression (Merret et al. 2010).
A model shows the regulatory importance of hormone dilution by plant growth
Recently, a modelling approach has suggested that growth-induced dilution of gibberellins (GA) can explain the dynamics of cell elongation in the Arabidopsis thaliana root apex (Band et al. 2012). Assuming that all parameters are steady, the model uses cell diameter, cell length profile along the growing zone and root growth rate to describe the volume increase of a growing cell in space and time, that is, in a Lagrangian way. The model also takes into account the biochemical rules determining hormone transfer among four subcellular compartments: the vacuole, nucleus, cytoplasm and cell wall. Based on transcriptomics and reporter analysis, GA biosynthesis and degradation are supposed to be null in the elongation zone. So, the model estimates the GA concentration in the cell during its expansion and predicts a significant growth-induced dilution. In parallel, the concentration of components belonging to the signalling networks, including the gibberellin receptor GID1 and the well-known growth repressing DELLA proteins, are calculated from the corresponding measured mRNA levels and the cell dimensions. Then, the molecular mechanism regulating the amount of DELLA proteins are incorporated in the model (To simplify, each gene family is treated as a single representative species). The multiscale model shows that the declining GA concentration along the elongation zone affects the level of downstream signalling components, in particular increases the concentration of DELLA proteins, which in turn decreases the relative cell elongation, implying a feedback loop. These implications were tested and confirmed through the phenotyping of roots treated with paclobutrazol (inhibiting GA biosynthesis) and GA biosynthetic mutants. This study also reveals that even if DELLA expression level appears constant over the duration of cell elongation, the protein level can vary, controlled by its degradation rate, which depends on the GA concentration. Authors note the importance of growth-induced GA dilution as cells pass through the elongation zone as a key finding in the control of cell elongation.
Deposition rates of GA regulate growth of maize leaves
Deposition rates of gibberellins have recently been shown to have an important role in regulating growth of maize leaves. Nelissen et al. (2012) made direct measurements of endogeneous hormone concentrations in the maize leaf growth zone and showed that the bioactive GA1 peaks in the transition zone at the distal end of the cell division zone. Using the continuity equation they showed that GA1 accumulation rate is positive in the division zone and the proximal part of the transition zone but drops very rapidly to negative values at the entrance in the strictly-elongation zone, highlighting that, in this zone, catabolic activity and/or export take place in addition to dilution. The combined metabolic and transcriptomic profiling revealed that the GA maximum is established by GA biosynthesis in the division zone and active GA catabolism at the onset of the expansion-only zone. Use of mutants deficient in GA and transgenic plants that overproduce GA confirmed that the size of the cell division zone varies with the GA deposition rate.
Fluorescent tagging of cell membranes and nuclei combined with automated particle tracking may greatly facilitate calculation of deposition rates in plant organs
Recently, powerful computational techniques have been disseminated to allow automated particle tracking so that cell cohorts are followed through space and time. An exciting approach, which the authors have called in planta cytometry, allows automated, nondestructive analysis of both growth and spatial patterns of gene expression (Federici et al. 2012). Nuclei were labeled with one fluorescent protein, and membranes were labeled with another; cells imaged with confocal microscopy then had red nuclei and blue edges. Using a particle search algorithm index cells were followed in space and time. Federici and colleagues then wrote an active contour segmentation algorithm that allowed them to quantify cell and shape and hence growth strain rates. These numerical methods are now available for use with the Image J platform (maintained by NIH). Then cell-specific gene expression was quantified by ratiometric measurement of spectrally distinct nuclear fluorescent proteins expressed under the control of differently regulated promoters. This paper implies that automated high-throughput technology is now available to analyze many aspects of growth kinematics in experimental systems that can be genetically transformed. In particular, the coming decade should reveal many cell-specific (Lagrangian) descriptions of deposition rates and inclusion of dilutional and positional effects to identify gene regulation causing organ development.
The continuity equation, used with empirical data on growth velocity and concentration, allows computation of biosynthesis and deposition rates in growing tissue. These deposition rates give important insight into the mechanism of plant response to drought and salinity, and they clarify many aspects of nitrogen metabolism in roots and leaves. This approach is also essential to understand molecular regulation of growth. Models of the molecular biology underlying plant development are still dominated by time-dependent formulations that are inadequate because they neglect cell displacement and expansion. However several pioneering studies have incorporated growth analysis into well-designed experiments to discover the kinematics of gene regulation. And new technologies—in planta cytometry, coupled with powerful new computational routines and real-time confocal microscopy—promise advancement in understanding of gene regulation in growing organs, especially in those systems that can be transformed with fluorescent tags.