Comparing different approaches to calculate the effects of heterogeneous root distribution on nutrient uptake: a case study on subsoil nitrate uptake by a barley root system

Simulation models of nutrient uptake of root systems starting with one-dimensional single root approaches up to complex three-dimensional models are increasingly used for examining the interacting of root distribution and nutrient uptake. However, their accuracy was seldom systematically tested. The objective of the study is to compare one-dimensional and two-dimensional modelling approaches and to test their applicability for simulation of nutrient uptake of heterogeneously distributed root systems giving particular attention to the impact of spatial resolution. Therefore, a field experiment was carried out with spring barley (Hordeum vulgare L. cv. Barke) in order to obtain data of in situ root distribution patterns as model input. Results indicate that a comparable coarse spatial resolution can be used with sufficient modelling results when a steady state approximation is applied to the sink cells of the two-dimensional model. Furthermore, the accuracy of the model was clearly improved compared to a simple zero sink approach assuming both near zero concentrations within the sink cell and a linear gradient between the sink cell and its adjacent neighbours. However, for modelling nitrate uptake of a heterogeneous root system a minimum number of grid cells is still necessary. The tested single root approach provided a computational efficient opportunity to simulate nitrate uptake of an irregular distributed root system. Nevertheless, two-dimensional models are better suited for a number of applications (e.g. surveys made on the impact of soil heterogeneity on plant nutrient uptake). Different settings for the suggested modelling techniques are discussed.     

A mathematical model for water and nutrient uptake by plant root systems

This article deals with modelling the simultaneous uptake of water and highly buffered nutrient, such as phosphate, by root branching structures from partially saturated soil. We use the simultaneous water and nutrient uptake model to investigate the effect that water movement has on nutrient uptake. With the aid of this model we are also able to show that the previous models by Barber and Tinker and Nye systematically underestimated the phosphate uptake, due to the oversimplified approach in dealing with root branching structure. In this article we show how this discrepancy can be remedied and the root branching structure included in the models of plant nutrient uptake. We will also discuss the differences in the results for continuous and spot fertilization combined with variable rainfall.     

Uptake and long-distance transport of phosphate,potassium and chloride in relation to internal ion concentrations in barley: evidence of non-allosteric regulation

The extent to which uptake and transport of either phosphate, potassium or chloride are controlled by the concentration of these ions within the root, perhaps through an allosteric mechanism, was investigated with young barley plants in nutrient solution culture. Plants were grown with their roots divided between two containers, such that a single seminal root was continuously supplied with all the required nutrient ions, while the remaining four or five seminal roots were either supplied with the same solution (controls) or, temporarily, a solution lacking a particular nutrient ion (nutrient-deficient treatment). Compared with controls, there was a marked stimulation of uptake and transport of labelled ions by the single root following 24 h or more of nutrient dificiency to the remainder of the root system. This stimulation, which comprised an increased transport to the shoot and, for all ions except Cl^-, increased transport to the remainder of the root system, took place without appreciable change in the concentration of particular ions within the single root. However, nutrient deficiency quickly caused a lower concentration of ions in the shoot and the remaining roots. The results are discussed in relation to various mechanisms, proposed in the literature, by which the coordination of ion uptake and transport may be maintained within the plant. We suggest that under our conditions any putative allosteric control of uptake and transport by root cortical cells was masked by an alternative mechanism, in which ion influx appears to be regulated by ion efflux to the xylem, perhaps controlled by the concentration of particular ions recycled in the phloem to the root from the shoot.     

Modelling Nutrient Uptake by Individual Hyphae of Arbuscular Mycorrhizal Fungi: Temporal and Spatial Scales for an Experimental Design

Arbuscular mycorrhizas, associations between plant roots and soil fungi, are ubiquitous among land plants. Arbuscular mycorrhizas can be beneficial for plants by overcoming limitations in nutrient supply. Hyphae, which are long and thin fungal filaments extending from the root surface into the soil, increase the volume of soil accessible for plant nutrient uptake. However, no models so far specifically consider individual hyphae. We developed a mathematical model for nutrient uptake by individual fungal hyphae in order to assess suitable temporal and spatial scales for a new experimental design where fungal uptake parameters are measured on the single hyphal scale. The model was developed based on the conservation of nutrients in an artificial cylindrical soil pore (capillary tube) with adsorbing wall, and analysed based on parameter estimation and non-dimensionalisation. An approximate analytical solution was derived using matched asymptotic expansion. Results show that nutrient influx into a hypha from a small capillary tube is characterized by three phases: Firstly, uptake rapidly decreases as the hypha takes up nutrients, secondly, the depletion zone reaches the capillary wall and thus uptake is sustained by desorption of nutrients from the capillary wall, and finally, uptake goes to zero after nutrients held on the capillary wall have been completely depleted. Simulating different parameter regimes resulted in recommending the use of capillaries filled with hydrogel instead of water in order to design an experiment operating over measurable time scales.     

A multiple ion-uptake phenotyping platform reveals shared mechanisms affecting nutrient uptake by roots

Nutrient uptake is critical for crop growth and is determined by root foraging in soil. Growth and branching of roots lead to effective root placement to acquire nutrients, but relatively little is known about absorption of nutrients at the root surface from the soil solution. This knowledge gap could be alleviated by understanding sources of genetic variation for short-term nutrient uptake on a root length basis. A modular platform called RhizoFlux was developed for high-throughput phenotyping of multiple ion-uptake rates in maize (Zea mays L.). Using this system, uptake rates were characterized for the crop macronutrients nitrate, ammonium, potassium, phosphate, and sulfate among the Nested Association Mapping (NAM) population founder lines. The data revealed substantial genetic variation for multiple ion-uptake rates in maize. Interestingly, specific nutrient uptake rates (nutrient uptake rate per length of root) were found to be both heritable and distinct from total uptake and plant size. The specific uptake rates of each nutrient were positively correlated with one another and with specific root respiration (root respiration rate per length of root), indicating that uptake is governed by shared mechanisms. We selected maize lines with high and low specific uptake rates and performed an RNA-seq analysis, which identified key regulatory components involved in nutrient uptake. The high-throughput multiple ion-uptake kinetics pipeline will help further our understanding of nutrient uptake, parameterize holistic plant models, and identify breeding targets for crops with more efficient nutrient acquisition.

A platform for quantifying root uptake rates of multiple, simultaneous nutrients reveals these rates are correlated among nutrients, are heritable, and may have a common genetic basis.     

The effect of the nutrient intensity and buffering power of a soil,and the absorbing power,size and root hairs of a root,on nutrient absorption by diffusion

Summary A portion of a single plant root is treated as an absorbing cylindrical sink to which nutrients move by diffusion. Assuming that the rate of uptake of nutrient is proportional to its concentration at the root surface, and that the nutrient, though reacting with the solid, moves only through the soil solution, standard diffusion equations are used to calculate the effect of soil and plant characteristics on the rate of uptake. The treatment is applicable to phosphorus and potassium. Among soil properties uptake should increase directly with the soil solution concentration. It should also increase, but only slowly, with increasing buffering power. It increases with increasing soil moisture. Among plant characteristics, uptake should increase with the root absorbing power until diffusion through the soil becomes limiting. Absorption by unit surface area of root increases as the root radius decreases. A root hair is shown to interfere quickly with the uptake of adjacent hairs. The hairs increase absorption by the root because they can exploit rapidly the soil between the hairs, and they have the effect of extending the effective root surface to their tips.     

A model for water uptake by plant roots

We present a model for water uptake by plant roots from unsaturated soil. The model includes the simultaneous flow of water inside the root network and in the soil. It is constructed by considering first the water uptake by a single root, and then using the parameterized results thereby obtained to build a model for water uptake by the developing root network. We focus our model on annual plants, in particular the model will be applicable to commercial monocultures like maize, wheat, etc. The model is solved numerically, and the results are compared with approximate analytic solutions. The model predicts that as a result of water uptake by plant roots, dry and wet zones will develop in the soil. The wet zone is located near the surface of the soil and the depth of it is determined by a balance between rainfall and the rate of water uptake. The dry zone develops directly beneath the wet zone because the influence of the rainfall at the soil surface does not reach this region, due to the nonlinear nature of the water flow in the partially saturated soil. We develop approximate analytic expressions for the depth of the wet zone and discuss briefly its ecological significance for the plant. Using this model we also address the question of where water uptake sites are concentrated in the root system. The model indicates that the regions near the base of the root system (i.e. close to the ground surface) and near the root tips will take up more water than the middle region of the root system, again due to the highly nonlinear nature of water flow in the soil.     

A theoretical explanation of the Piper-Steenbjerg effect

The relation between plant yield and plant nutrient concentration is sometimes found to be negative, a phenomenon called the Piper-Steenbjerg (PS) effect. A model was used to examine the underlying causes of the PS effect, and the conditions under which it is most likely to occur. The model uses the nutrient productivity concept for plant growth and a nutrient uptake equation in which root growth rate and external nutrient concentration determine the uptake rate. The study suggests that the PS effect occurs when the fast growth of plants grown in an initially higher nutrient medium eventually leads to a more rapid depletion of external nutrients than the slow growth of plants grown in an initially lower nutrient medium. The fast growth of plants combined with a rapid decrease of nutrient uptake leads to a fall in plant nutrient concentration. When these large plants with very low nutrient concentrations are compared with the smaller, slow-growing plants, a PS effect may be found depending on the time at which the plants are harvested, and on the range of initial values of the external nutrient content. When it occurs, the effect is greatest when the depletion volume per unit new root (V_d) is lowest, and when the mobility of nutrients in the medium is highest (α=1). The results are sufficiently general to apply to a variety of nutrients, plant species and growth media.     

Modeling magnesium,phosphorus and potassium uptake by loblolly pine seedlings using a Barber-Cushman approach

The Barber-Cushman mechanistic nutrient uptake model, which has been utilized extensively to describe and predict nutrient uptake by crop plants, was evaluated for its ability to predict K, Mg, and P uptake by loblolly pine (Pinus taeda L.) seedlings. Sensitivity analyses were also used to investigate the impact of changes in soil nutrient supply, root morphological, and root uptake kinetics parameters on simulated nutrient uptake. Established experimental techniques were utilized to define the 11 parameters needed to model uptake by 1-0 seedlings of K, Mg, and P from a modified A horizon soil (Lilly series). Model predictions of K and P uptake over a 180-d growth period were underestimated by 6 and 11%, respectively. Estimates of Mg uptake were underestimated by 62%. While the level of agreement between predicted and observed K and P values was quite acceptable, analysis of parameter values and results of sensitivity analyses both indicated that the model underestimation of Mg uptake was the result of applying an I_max value developed under relatively low Mg concentration to a situation in which the functional I_max would be much higher due to the dominance of passive versus active uptake. Overall results of sensitivity analyses indicate that under the circumstances investigated, I_max, was the primary variable controlling plant uptake of K, Mg, and P. The dominance of this term over others was due to the relatively high C_li values for all three nutrients. Reducing (-50%) or increasing (+ 100%) other soil supply, root morphological, and remaining root uptake kinetics values did not substantially alter model estimates of nutrient uptake.     

硝态氮(NO-3)对水稻侧根生长及其氮吸收的影响

侧根是植物吸收利用土壤养分的重要器官,其生长发育受内部遗传因子和外部环境矿质养分的影响.通过琼脂分层培养发现:局部供应NO-3可以诱导水稻( Oryza sativa L.)主根或不定根上侧根的生长.为研究旱种条件下NO-3对水稻侧根发育及其N吸收的影响,设置了3个蛭石培养实验:分根处理、全株缺N、全株供N处理.分根处理(一半根系供应3 mmol/L KNO3,另一半根系供应3 mmol/L KCl)结果表明:局部供应NO-3 能够促进水稻侧根生长.而在全株处理下,N饥饿诱导了侧根的伸长.水稻根系对NO-3的这两种反应都存在着显著的基因型差异.同时对地上部N浓度、可溶性总糖含量及N含量分析表明,这些生理指标在分根处理与全株加N处理中的差异均不显著,表明分根处理也能基本满足植株正常生长对N的需求.在分根处理中,水稻的N含量与分根处理中供N一侧的平均侧根长度存在显著正相关,这表明在养分不均一的介质中,侧根长度对水稻N素吸收具有十分重要的作用.而在N素充足的条件下,两者之间的相关性并不显著,这暗示在养分充足的环境下,侧根长度可能并不是决定根系吸收N素的主要因素.     

Relationships between root morphology and nitrogen availability in a recent theoretical model describing nitrogen uptake from soil

Abstract. The effect upon potential maximum nitrogen uptake rate of root morphology and nitrogen availability in soil was investigated using a simple nutrient transport model. Parameter values appropriate to an ecological or an agricultural context were introduced from the literature. The model predicted that the maximum uptake rate of nitrate was morphology-dependent only at extremely low concentrations. For ammonium, this was so for all realistic concentrations, assuming a high potential maximum uptake rate. The important concentration range for ammonium was two orders of magnitude greater than that for nitrate. With a lower potential maximum uptake rate of ammonium, root morphology was important below 15/igNg' soil, the concentration range in this case being a single order of magnitude greater than that for nitrate. The effects of root hairs were to decrease the threshold concentration for morphology-dependence, and to minimize root dry weight per unit volume of soil needed to maintain maximum nitrogen uptake rate. The effects of simultaneous mass flow of solution were negligible. The possible significance of these effects upon plant growth are discussed in relation to nitrogen availability.     

Nutrient uptake and allocation at steady-state nutrition

Ingestad, T. and Ågren, G. I. 1988. Nutrient uptake and allocation at steady-state nutrition. - Physiol. Plant. 72: 450–459. Net nutrient uptake and translocation rates are discussed for conditions of steady-state nutrition and growth. Under these conditions, the relative uptake rate is equal to the relative growth rate, for whole plants as well as for plant parts, since the root/shoot ratio and internal concentrations remain stable. The nutrient productivity and the minimum internal concentration are parameters characteristic for the plant and the nutrient. A conceptual, mathematical model, based on these two fundamental parameters is used for calculation and prediction of the net nutrient uptake rate, which is required to maintain steady-state nutrition at a specified internal nutrient concentration or relative growth rate. When uptake rate is expressed on the basis of the root growth rate, there is, up to optimum, a strong linear relationship between uptake rate and the internal concentration of the limiting nutrient. More complicated and less consistent relationships are obtained when uptake rate is related to root biomass. The limiting factor for suboptimum uptake is the amount of nutrients becoming available at the root surface. When replenishment is efficient, e.g. with vigorous stirring, the concentration requirement at the root surface appears to be extremely low, even at optimum. In the suboptimum range of nutrition, the effect of nutrient status on root growth rate is a critical factor with a strong feed-back on nutrition, growth and allocation. At supraoptimum conditions, the uptake mechanism is interpreted as a protection against too high uptake rates and internal concentrations at high external concentration. In birch (Betula pendula Roth.), the allocation of nitrogen to the shoots is high compared to that of potassium and also to that of phosphorus at low nitrogen or phosphorus status. With decreasing stress, phosphorus allocation becomes more and more similar to nitrogen allocation. The formulation of a mathematical model for calculation of allocation of biomass and nutrients requires more exact information on the quantitative dependence of the growth-regulating processes on nutrition.     

硝态氮（NO3^—）对水稻侧根生长及其氮吸收的影响

侧根是植物吸收利用土壤养分的重要器官 ,其生长发育受内部遗传因子和外部环境矿质养分的影响。通过琼脂分层培养发现 :局部供应NO-3 可以诱导水稻 (OryzasativaL .)主根或不定根上侧根的生长。为研究旱种条件下NO-3 对水稻侧根发育及其N吸收的影响 ,设置了 3个蛭石培养实验 :分根处理、全株缺N、全株供N处理。分根处理 (一半根系供应 3mmol/LKNO3,另一半根系供应 3mmol/LKCl)结果表明 :局部供应NO-3 能够促进水稻侧根生长。而在全株处理下 ,N饥饿诱导了侧根的伸长。水稻根系对NO-3 的这两种反应都存在着显著的基因型差异。同时对地上部N浓度、可溶性总糖含量及N含量分析表明 ,这些生理指标在分根处理与全株加N处理中的差异均不显著 ,表明分根处理也能基本满足植株正常生长对N的需求。在分根处理中 ,水稻的N含量与分根处理中供N一侧的平均侧根长度存在显著正相关 ,这表明在养分不均一的介质中 ,侧根长度对水稻N素吸收具有十分重要的作用。而在N素充足的条件下 ,两者之间的相关性并不显著 ,这暗示在养分充足的环境下 ,侧根长度可能并不是决定根系吸收N素的主要因素     

Fall in nutrient demand per unit root length during the linear phase of plant growth

If root length increases in proportion to plant weight, growth is expolinear, and plant composition is constant, then there is fundamental drop in nutrient demand per unit root length during the linear growth phase. This is in contrast to the exponential phase, when increments of growth and hence of nutrient demand are proportional to plant size and thus to root length: in the linear growth phase, they are constant despite increasing root length. For nutrient uptake models in which demand is based on growth and uptake is based on root length, this would suggest a tendency for nutrients to accumulate in the plant as it grows.     

Modelling zinc uptake by rice crop using a Barber-Cushman approach

The Barber-Cushman mechanistic nutrient uptake model which has been utilized extensively to describe and predict nutrient uptake by crop plants at different stages of crop growth was evaluated for its ability to predict the Zn uptake by rice seedlings. Uptake of the nutrient is, therefore, determined by the rate of nutrient supply to the root surface by mass flow and diffusion. Inter root competition and time dependent root density are accounted for by soil volume that delivers nutrients. The radii of these cylinders decline with increasing density. Since mass flow and diffusion each supply zinc to the root, the process can be described mathematically using the model of Barber-Cushman (1984). The 11 parameters of the model for the uptake by rice cultivars were measured by established experimental techniques. Zinc uptake at different growth stages predicted by the model was compared to measured zinc uptake by rice cultivars grown on sandy loam soil in a green house. Predicted zinc uptake was significantly correlated with observed uptake r ²=0.99^**. Sensitivity analysis was also used to investigate the impact of changes in soil nutrient supply, root morphological and root uptake kinetic parameters on simulated nutrient uptake. Overall results of sensitivity analysis indicate that the half distance between root axes, rate of root growth and water flux affect the uptake of zinc particularly at their higher values rather than at lower values and DaZn is the most sensitive parameter for zinc uptake at its lower values.     

A dual porosity model of nutrient uptake by root hairs

? The importance of root hairs in the uptake of sparingly soluble nutrients is understood qualitatively, but not quantitatively, and this limits efforts to breed plants tolerant of nutrient-deficient soils. ? Here, we develop a mathematical model of nutrient uptake by root hairs allowing for hair geometry and the details of nutrient transport through soil, including diffusion within and between soil particles. We give illustrative results for phosphate uptake. ? Compared with conventional 'single porosity' models, this 'dual porosity' model predicts greater root uptake because more nutrient is available by slow release from within soil particles. Also the effect of soil moisture is less important with the dual porosity model because the effective volume available for diffusion in the soil is larger, and the predicted effects of hair length and density are different. ? Consistent with experimental observations, with the dual porosity model, increases in hair length give greater increases in uptake than increases in hair density per unit main root length. The effect of hair density is less in dry soil because the minimum concentration in solution for net influx is reached more rapidly. The effect of hair length is much less sensitive to soil moisture.     

Root Development and Nutrient Uptake

Root system formation proceeds in close coordination with shoot growth. Accordingly, root growth and its functions are regulated tightly by the shoot through materials cycling between roots and shoots. A plant root system consists of different kinds of roots that differ in morphology and functions. The spatial configuration and distribution of these roots determine root system architecture in the soil, which in turn primarily regulates the acquisition of soil resources like nutrients and water. Morphological and physiological properties of each root and the concomitant tissues further affect nutrient uptake and transport, while the root traits that are related to such acquisition also depend on the kinds of nutrients and their mobility in the soil. In addition, mechanisms involved in the uptake and transport of mineral nutrients recently have been elucidated at the molecular level. A number of genes for acquisition and transport of various mineral nutrients have been identified in model plant systems such as Arabidopsis thaliana, and rice, and in other plant species. An integration of studies on nutrient behavior in soils and the morphological and physiological functions of root systems will further elucidate the mechanism of plant nutrient uptake and transport by roots, and offer a real possibility of genetically improving crop productivity in problem soils.

     

Functional aspects of root architecture and mycorrhizal inoculation with respect to nutrient uptake capacity

The aim of this research was to investigate the effect of arbuscular mycorrhizal (AM) colonisation on root morphology and nitrogen uptake capacity of carob ( Ceratonia siliqua L.) under high and low nutrient conditions. The experimental design was a factorial arrangement of presence/absence of mycorrhizal fungus inoculation ( Glomus intraradices) and high/low nutrient status. Percent AM colonisation, nitrate and ammonium uptake capacity, and nitrogen and phosphorus contents were determined in 3-month-old seedlings. Grayscale and colour images were used to study root morphology and topology, and to assess the relation between root pigmentation and physiological activities. AM colonisation lead to a higher allocation of biomass to white and yellow parts of the root. Inorganic nitrogen uptake capacity per unit root length and nitrogen content were greatest in AM colonised plants grown under low nutrient conditions. A better match was found between plant nitrogen content and biomass accumulation, than between plant phosphorus content and biomass accumulation. It is suggested that the increase in nutrient uptake capacity of AM colonised roots is dependent both on changes in root morphology and physiological uptake potential. This study contributes to an understanding of the role of AM fungi and root morphology in plant nutrient uptake and shows that AM colonisation improves the nitrogen nutrition of plants, mainly when growing at low levels of nutrients.     

植物根系向地性感应的分子机理与养分吸收

植物根系向地性是决定根系空间生长趋势的主要因素之一,对于养分吸收具有重要影响.认识根系向地性感应和根系生长变化的分子机理及其与养分吸收的关系,可为遗传改良根系性状、提高植物养分吸收效率提供理论依据.本文从重力感应、信号转导和生长素非对称分布等方面总结了植物根系向地性感应的分子机理,探讨了根系在养分胁迫下(特别是磷胁迫下)向地性变化的生理基础及其与养分吸收(特别是磷吸收)的关系,最后对根系向地性研究的若干问题进行了展望.