Plant growth modelling and applications: the increasing importance of plant architecture in growth models

Background

Modelling plant growth allows us to test hypotheses and carry out virtual experiments concerning plant growth processes that could otherwise take years in field conditions. The visualization of growth simulations allows us to see directly and vividly the outcome of a given model and provides us with an instructive tool useful for agronomists and foresters, as well as for teaching. Functional–structural (FS) plant growth models are nowadays particularly important for integrating biological processes with environmental conditions in 3-D virtual plants, and provide the basis for more advanced research in plant sciences.

Scope

In this viewpoint paper, we ask the following questions. Are we modelling the correct processes that drive plant growth, and is growth driven mostly by sink or source activity? In current models, is the importance of soil resources (nutrients, water, temperature and their interaction with meristematic activity) considered adequately? Do classic models account for architectural adjustment as well as integrating the fundamental principles of development? Whilst answering these questions with the available data in the literature, we put forward the opinion that plant architecture and sink activity must be pushed to the centre of plant growth models. In natural conditions, sinks will more often drive growth than source activity, because sink activity is often controlled by finite soil resources or developmental constraints.

PMA06

This viewpoint paper also serves as an introduction to this Special Issue devoted to plant growth modelling, which includes new research covering areas stretching from cell growth to biomechanics. All papers were presented at the Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06), held in Beijing, China, from 13–17 November, 2006. Although a large number of papers are devoted to FS models of agricultural and forest crop species, physiological and genetic processes have recently been included and point the way to a new direction in plant modelling research.Key words: Biomechanics, carbon allocation, functional–structural plant models, meristem, nitrogen, phenotypic plasticity, root architecture, simulation, sink, source, PMA06     

On valuing patches: estimating contributions to metapopulation growth with reverse-time capture-recapture modelling

Metapopulation ecology has historically been rich in theory, yet analytical approaches for inferring demographic relationships among local populations have been few. We show how reverse-time multi-state capture-recapture models can be used to estimate the importance of local recruitment and interpopulation dispersal to metapopulation growth. We use 'contribution metrics' to infer demographic connectedness among eight local populations of banner-tailed kangaroo rats, to assess their demographic closure, and to investigate sources of variation in these contributions. Using a 7 year dataset, we show that: (i) local populations are relatively independent demographically, and contributions to local population growth via dispersal within the system decline with distance; (ii) growth contributions via local survival and recruitment are greater for adults than juveniles, while contributions involving dispersal are greater for juveniles; (iii) central populations rely more on local recruitment and survival than peripheral populations; (iv) contributions involving dispersal are not clearly related to overall metapopulation density; and (v) estimated contributions from outside the system are unexpectedly large. Our analytical framework can classify metapopulations on a continuum between demographic independence and panmixia, detect hidden population growth contributions, and make inference about other population linkage forms, including rescue effects and source-sink structures. Finally, we discuss differences between demographic and genetic population linkage patterns for our system.     

Effect of soil volume and plant density on mycorrhizal infection and growth response

Summary The effect of soil volume and plant density on mycorrhizal infection and growth response was studied with onion. There was a significant negative correlation between percentage vesicular-arbuscular mycorrhizal infection and root density. The growth response due to mycorrhiza decreased when less soil was available for the plant. The root: shoot ratio decreased with increasing plant density in both mycorrhizal and non-mycorrhizal plants. Pot size did not affect the root: shoot ratio.     

On the analysis of competition at the level of the individual plant

Summary The extent to which some measure of local crowding can account for the performance of individual plants is examined with reference to populations of two species of annual plant. Only a relatively small proportion of the variation in individual plant yield could be accounted for by measures of local crowding. These included the number of close neighbours, an estimate of the area available to each plant and competitive pressure. A multiple regression that took account of both emergence time and local crowding increased the proportion of variance that could be accounted for up to 50%. Computer simulations of the growth of indivudual plants in monoculture were then caried out in order to determine whether the unexplained variation resulted from fundamental flaws in the models or from unaccounted for sources of variation in the field. The results from the simulations again indicated that only a relatively low proportion of the variation in individual plant yield could be accounted for by emergence time and local density, even though these were known to be the only variables present. These findings are discussed in relation to the relative importance of one-sided and two-sided competition, and the complex cross-correlations that occur between individuals in plant populations. These two factors will make it very difficult for field workers to determine accurately what factors determine individual plant yield and in particular to predict the effects of local crowding on the performance of individual plants.     

On the composition of the nucleolus with special reference to its filamentous structure

Summary Different staining procedures, various digestion methods and autoradiographic techniques were employed to study the structure and composition of the nucleolus and of the nucleolonema, after unmasking the latter by adenosine treatment. The presence of DNA, RNA, protein and lipid in these structures has been shown. It has been demonstrated that the filamentous structure within the nucleolus — the nucleolonema— has a core of DNA, around which RNA and protein have accumulated. The structure of the nucleolonema suggests that it is in a highly active state, in synthesizing ribosomal RNA and protein.We take the opportunity to express our gratefulness to the Director, Prof. Dr. Hans Lettré, for providing facilities to work in this Institute. We like to thank our other colleagues, particularly Dr. N. Paweletz, for their valuable help during the course of the investigations.     

Plant growth and architectural modelling and its applications. Preface

Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels.     

Bioprocess strategies for mass multiplication of and metabolite synthesis by plant growth promoting pseudomonads for agronomical applications

The exponential substrate feeding (open-loop) and automated feedback substrate feeding (closed loop) strategies were developed to obtain high cell densities of fluorescent pseudomonad strains R62 and R81 and enhanced production of antifungal compound 2,4-diacetylphloroglucinol (DAPG) from glycerol as a sole carbon source. The exponential feeding strategy resulted in increased glycerol accumulation during the fed-batch cultivation when the predetermined specific growth rate (μ) was set at 0.10 or 0.20 h^?1 (<μ_m = 0.29 h^?1). Automated feeding strategies using dissolved oxygen (DO) or pH as feedback signals resulted in minimal to zero accumulation of glycerol for both the strains. In case of DO-based feeding strategy, biomass productivity of 0.24 g/(L h) and 0.29 g/(L h) was obtained for R62 and R81, respectively. Using pH-based feeding strategy, biomass productivity could be increased to a maximum of 0.51 and 0.54 g/(L h), for the strains R62 and R81, respectively, whereas the DAPG concentration was enhanced to 298 mg/L for R62 and 342 mg/L for R81 strains. These yields of DAPG are thus far the highest reported from GRAS organisms.     

Turbidimetric measurement of plant cell culture growth

Turbidimetric measurement of cultures grown in sidearm flasks was used to measure the growth of plant cells. The turbidity was shown to vary proportionally with cell number and dry weight over time. The effect of different freezing conditions on the growth of the culture was presented to demonstrate the application of the sidearm-turbidity method.     

Absolute measurement of cell expansion in plant cell suspension cultures

A method is described for the measurement of intracellular volume (V_i) in cell cultures. In principle, any stable compound that neither penetrates the plasma membrane nor binds to the cells can be used to trace the total extracellular (apoplastic) volume and hence to estimate the intracellular volume. No suitable coloured or UV-absorbing compound could be found among those tested; the main problems were binding to the cell surface and/or instability in the medium. However, [¹⁴C]mannitol was an acceptable apoplastic marker, by use of which we showed that 21–47% of total packed cell volume (PCV) was intracellular, and 14–33% of total settled cell volume (SCV) was intracellular. Therefore, measurements of PCV and SCV misrepresent cell expansion to a variable extent. Cultures of Acer, Rosa, Spinacia and Zea achieved final symplastic volumes of only 9, 14, 6 and 6%, respectively, of the total suspension culture volume.     

On the measurement of cytokinetics by continuous labeling with bromodeoxyuridine with applications to chick wing buds.

The cytokinetic properties, specifically the phase-transit times, TG1, TS, and TG2+M, of chick wing bud cells were estimated using data obtained from continuous labeling of stage 20 embryos with bromodeoxyuridine (BrdUrd). The presence of BrdUrd was detected with monoclonal antibodies, and the amount of DNA in the cells was determined with propidium iodide. The fraction of cells in each cell cycle phase, the fraction of labeled cells, and the relative movement, a measure of the mean DNA content, of all labeled cells were evaluated using bivariate flow cytometry at successive times following introduction of the label. Equations are presented to describe the fraction of unlabeled cells in G2 + M, which gives a direct estimate of TG2+M; the fraction of all labeled cells, which can then be used to estimate TG1; and, finally, the relative movement, which provides an estimate of TS. Thus, the data measured in these experiments together provide estimates of the progression through the cell cycle of limb mesoderm cells.     

Wall extensibility: its nature, measurement and relationship to plant cell growth

Expansive growth of plant cells is controlled principally by processes that loosen the wall and enable it to expand irreversibly. The central role of wall relaxation for cell expansion is reviewed. The most common methods for assessing the extension properties of plant cell walls ( wall extensibility') are described, categorized and assessed critically. What emerges are three fundamentally different approaches which test growing cells for their ability (a) to enlarge at different values of turgor, (b) to induce wall relaxation, and (c) to deform elastically or plastically in response to an applied tensile force. Analogous methods with isolated walls are similarly reviewed. The results of these different assays are related to the nature of plant cell growth and pertinent biophysical theory. I argue that the extensibilities' measured by these assays are fundamentally different from one another and that some are more pertinent to growth than others.     

On the botanic model of plant growth with intermediate vegetative-reproductive stage

The application of dynamic optimization to mathematical models of ontogenic biological growth has been the subject of much research [see e.g. . J. Theor. Biol. 33, 299-307]. Koz?owsky and Zió?ko [1988. Thor. Popul. Biol. 34, 118-129] and Zió?ko and Koz?owski [1995. IEEE Trans. Automat. Contr. 40(10), 1779-1783] presented a model with gradual transition from vegetative to reproductive growth. The central point of their model is a mixed state-control constraint on the rate of reproductive growth, which leads to a mixed vegetative-reproductive growth period. Their model is modified here in order to take into account the difference of photosynthesis use efficiency when energy is accumulated in the vegetative and in the reproductive organs of a plant, respectively. The simple assumption on correlation between photosynthesis and temperature permits us to modify the model in a form that is useful for changing climate. Unfortunately, the mathematical solution of the optimal control problem in Koz?owsky and Zió?ko (1988) and Zió?ko and Koz?owski (1995) is incorrect. The strict mathematical solution is presented here, the numerical example from is solved, and the results are compared. The influence of the length of the season and the relative photosynthesis use efficiency, as well as of the potential sink demand of the reproductive organs, on the location and duration of the mixed vegetative-reproduction period of growth is investigated numerically. The results show that the mixed growth period is increased and shifted toward the end of the season when the lengths of the season is increased. Additional details of the sensitivity analysis are also presented.     

Trends and applications in plant volatile sampling and analysis

Volatile organic compounds (VOCs) released by plants serve as information and defense chemicals in mutualistic and antagonistic interactions and mitigate effects of abiotic stress. Passive and dynamic sampling techniques combined with gas chromatography–mass spectrometry analysis have become routine tools to measure emissions of VOCs and determine their various functions. More recently, knowledge of the roles of plant VOCs in the aboveground environment has led to the exploration of similar functions in the soil and rhizosphere. Moreover, VOC patterns have been recognized as sensitive and time-dependent markers of biotic and abiotic stress. This focused review addresses these developments by presenting recent progress in VOC sampling and analysis. We show advances in the use of small, inexpensive sampling devices and describe methods to monitor plant VOC emissions in the belowground environment. We further address latest trends in real-time measurements of volatilomes in plant phenotyping and most recent developments of small portable devices and VOC sensors for non-invasive VOC fingerprinting of plant disease. These technologies allow for innovative approaches to study plant VOC biology and application in agriculture.     

Chemical modelling applications to experimental recirculating streams

Chemical models describing the precipitation of calcium carbonate, coprecipitation of inorganic phosphate, carbon dioxide and oxygen transfer through the air-water interface have been applied to results from a recirculating experimental stream. The transfer velocities for carbon dioxide and oxygen transfer for the experimental stream were determined as 1.00 × 10^–4 m s^–1 and 0.0058 m min^–1 (at 20°C) respectively. During a 24-hour long experiment the stream, containing a varied biota dominated by the macro-algae Zygnema, was monitored to evaluate changes in the water chemistry. The calcite precipitation rate varied during the experiment reflecting changes in temperature, supersaturation of the water and local variation in the solution chemistry at the growth sites. The rate constant was evaluated from a chemical mechanistic model as 516.7 ± 27.2 mol h^–1 at 10 °C. The coprecipitation of inorganic phosphate, which accompanied calcite growth, accounted for < 6% of the total phosphorus loss. The constant uptake of phosphorus by plants and algae was estimated as 0.22 mol h^–1 g^–1 dry weight). The rates of production of oxygen and consumption of inorganic carbon in the experimental stream, after taking account of gas transfer and calcite precipitation, were also computed and found to be in good agreement during the experiment. The maximum rate of production of oxygen was 3.5 × 10^–4 mol h^–1 g^–1 (dry weight).     

Limitations associated with conductivity measurement for monitoring growth in plant tissue culture

The suitability of conductivity measurement for monitoring growth in plant cell culture has been tested using suspended cells and genetically-transformed hairy roots of Atropa belladonna, and aggregated cells of Solanum aviculare. Other researchers have proposed that a constant ratio exists between increase in cell concentration (x) and decrease in medium conductivity (C). In all cases studied in this work, x/C was not constant over a wide range of cell densities tested in batch culture. With cell suspensions, x/C decreased continuously during the growth phase from 3.4 to 2.5 g cm l^–1 mS^–1. For the hairy roots, the ratio between x and C varied by as much as 4-fold during growth. The relationship between conductivity and growth for S. aviculare aggregates was found to vary depending on inoculum density. No simple correlation between conductivity change and cell growth was apparent for the plant-cell systems studied.     

种群密度和培养体积对发头裸腹溞生长和繁殖的影响

研究了不同培养密度(D1=100 ind·L-1,D2=150 ind·L-1,D3 =300 ind·L-1)和培养体积(V1 =50 mL,V2=100 mL,V3 =400 mL)对发头裸腹溞生长和生殖的影响.结果表明:在相同培养密度下,发头裸腹溞首次怀卵体长、雌体第一窝幼溞数和后代总数均随着培养体积的增大而减少,而雌体所产后代的性比(雄体∶雌体)随着培养体积的增大而增大.在相同培养体积下,雌体产出后代总数随着培养密度的增加而减少.雌体最大首次怀卵体长(0.95±0.10 mm)和最大后代总数(171.3±19.8 ind)均出现在D1V1组合,最大性比(0.54±0.05)出现在D3V2组合.培养密度和培养体积及其协同作用对发头裸腹溞雌体后代总数、后代性比均具有显著影响(P＜0.001).