Mechanistic simulation models of nutrient uptake: A review

Mechanistic models of nutrient uptake consider diffusion and mass flow acting simultaneously to supply nutrients to the sorbing root surface. Plant parameters that determine nutrient uptake include those describing changes in root geometry and size due to root growth and others describing kinetics of the nutrient uptake process. Mechanistic models generally assume that nutrient uptake occurs evenly along the roots that are uniformly distributed in homogeneous and isotropic soil having no temporal and spatial gradients in volumetric moisture content. Uptake of immobile nutrients (like P and K) is mainly determined by the soil-supply parameters and is well predicted by the simulation models. In contrast, uptake of mobile nutrients (e.g. Ca and Mg) that usually accumulate at the root surface is determined mainly by the plant-uptake parameters; prediction of uptake of those nutrients is subject to a much wider error due to uncertainties of applying kinetic parameters measured on hydroponically-grown plants to soil-grown plants. Comparison of model-predicted and experimentally-observed uptake values should be done by calculating the mean squares of deviates instead of performing regression analysis, especially if data that encompass a relatively wide range in root length are considered. Complementary-ion effects occurring at the soil-root interface raise the need for developing a multi-nutrient uptake model that will simultaneously calculate uptake of several essential nutrients taking into account interactions among them.     

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.     

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.     

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.     

An improved model of root growth in structured soil

Summary The growth of roots of maize, sorghum and soybean is modelled through beds of spherical aggregates. Effects of aggregate size and strength, and effects of the spread or distribution of aggregate strengths are investigated.This is achieved by a combination of a statistical model for soil structure with a statistical model for the penetration behaviour of a root at a void/aggregate interface. It is shown that the behaviour of a root at such an interfac is dependent on the previous history of the root in its passage through the soil.It is concluded that the smaller the aggregate size, the greater is the nutrient availability per unit length of root. The influence of aggregate size decreases with increasing soil strength.An increase in aggregate strength reduces the availability of nutrients per unit length of root. However, the rate of nutrient uptake per root axis goes through a minimum at a strength (for maize) of around 80 per cent of the maximum limiting aggregate strength for root penetration. An increase in the spread of aggregate strengths usually results in a proportional increase in nutrient availability. This effect is more pronounced with smaller aggregate sizes.     

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.     

Simulation of nutrient uptake by a growing root system considering increasing root density and inter-root competition

A simulation model is presented which describes uptake of a growth limiting nutrient from soil by a growing root system. The root surface is supposed to behave like a zero-sink. 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 assigning to each root a finite cylindrical soil volume that delivers nutrients. The radius of these cylinders declines with increasing root density. Experiments with rape plants grown on quartz sand were used to evaluate the model. Simulated nitrogen uptake agreed well with observed uptake under nitrogen limiting conditions. In case no nitrogen limitation occurred nitrogen uptake was overestimated by the model, probably because the roots did not behave like a zero-sink any more.     

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.     

增温、施肥与种内竞争的交互作用对云杉根系属性的影响

增温、施肥与种内竞争的交互作用对云杉根系属性的影响 物种竞争、气温和土壤养分是青藏高原东部高寒地区影响树木生长的重要因素。虽然已开展了大量关于物种竞争、气温、施肥单因素对树木生长的影响研究,但关于这三者的交互作用对根系生长的影响还知之甚少。因此,本研究拟通过测量根系属性(细根长、根表面积、比根长、比表面积、根尖数、根系分支数等)、根生物量,以及根系养分吸收,研究施肥和增温对物种竞争的影响,并进一步探讨施肥、增温与物种竞争的交互作用对云杉(Picea asperata)生长的影响机制以及所采取的适应策略。研究结果表明,增温、施肥和竞争均提高了细根的氮、钾浓度,但并未影响细根生物量和根长、根表面积、根尖数和根分支数等根系特征。然而,无论是增温、施肥,或是它们的联合作用,与物种竞争进行交互时,均增加了根长、根表面积、根尖数、根系分支数和养分吸收。此外,施肥降低了根比表面积、比根长和单位面积的根尖数和根分支数,增温和竞争的交互作用使根比表面积、比根长下降,其他参数不受温度和竞争的影响。该结果表明,云杉在物种竞争、气候变暖、施肥及其交互作用下保持着保守的营养策略。该研究加强了对树木应对全球变化的生理和生态适应性的理解。     

Numerical study of some age-dependent parameters in root nutrient uptake

Computer simulation of root nutrient uptake has become a very powerfull tool in the analysis of plant and soil characteristics. One of the shortcomings of earlier numerical models is the lack of a proper accounting for age-dependent root parameters. In this article we present an algorithm that not only allows for time-and/or space-varying root growth rates, convective moisture uptake, root density, initial distribution of nutrient, effective diffusion coefficients, and buffer power; but also accounts for time-varying root efflux, root absorption power and maximum nutrient influxive rate.Several elementary numerical examples of NH ₄ ⁺ , NO ₃ ^– , P and K uptake for roots with temporally varying characteristics are presented.Contribution from the Purdue Agric. Exp. Stn., W. Lafayette, IN. Journal Paper No. 9476.     

Relationships between physiological and morphological attributes related to phosphate uptake in 25 genotypes of Arabidopsis thaliana

The degree of genetic integration among morphological and physiological characters associated with phosphate uptake in impoverished versus fertile sites was studied among 25 inbred homozygous lines of Arabidopsis thaliana (L.) Heynh. The characters recorded were initial uptake rates, C_min (which reflects the ability to deplete phosphate to low concentrations), SRL (specific root length), and root: shoot allocation variables. Highly significant genotypic differentiation was detected for all of the variables (P<0.001). Cmin was correlated with influx per cm or mg of root; the lines better able to pick up Pi at low concentrations generally had slower initial uptake rates per cm or mg of root. This suggests an evolutionary divergence between a character important for nutrient uptake under fertile conditions, and one important for nutrient uptake under impoverished conditions. This relationship however, may not be valid due to the non-proportional relationship between root length or mass and influx. With a measure of influx that took this non-proportionality into account, the relationship became nonsignificant. SRL was negatively correlated (P<0.05) with influx per unit length of root. This suggests that there is an allocation-based trade-off between root length and diameter among Arabidopsis thaliana genotypes. Lower uptake rates per unit length of root for genotypes with thin roots may simply be a consequence of lower root surface area.     

Nutrient Relations of Groundsel (Senecio vulgaris) Infected by Rust (Puccinia lagenophorae) at a Range of Nutrient Concentrations II. Uptake of N, P and K and Shoot-Root Interactions

Groundsel (Senecio vulgaris), healthy or infected with rust,Puccinia lagenophorae, was grown at a range of nutrient concentrationsin sand culture. Specific absorption rates calculated on thebasis of root dry weight (SAR_W) were greater in rusted thancontrol groundsel for nitrogen, potassium and phosphorus. Whilethe magnitudes of these stimulations varied, they occurred acrossthe whole range of nutrient concentrations. By contrast, specificabsorption rate on the basis of root length (SAR_L) were littlechanged by rust at any external nutrient concentration; SAR_Lfor phosphate and potassium were slightly reduced when nutrientswere freely available. Water flux per unit dry root weight and length was stimulatedby rust because transpiration per unit leaf area was more rapidin infected plants after fungal sporulation. However, water-fluxand the rate of uptake of nutrients were correlated only whenexpressed on the basis of root weight and increased transpirationdid not appear to be the mechanism underlying increased rootactivity. Rather, increased SAR_W for N, P and K could very largelybe attributed to increased shoot demand per unit root, whichresulted from the higher shoot: root (S: R) ratios of infectedindividuals. Changes in S: R accounted for 92, 81 and 57% oftotal variation in SAR_W for K, P and N respectively. Greatervalues for SAR_W were possible because specific root length (SRL)increased, producing more functional root per unit root weight.The lack of stimulation in SAR_L in response to rust could beexplained since the higher SRL of infected plants resulted instable values of shoot weight per unit root length, i.e. shootdemand was not increased by infection on this basis. Senecio vulgaris, Puccinia lagenophorae, rust infection, nutrient uptake, water uptake, shoot: root interactions     

First observation of diffusion-limited plant root phosphorus uptake from nutrient solution

Diffusion towards the root surface has recently been shown to control the uptake of metal ions from solutions. The uptake flux of phosphorus (P) from solutions often approaches the maximal diffusion flux at low external concentrations, suggesting diffusion-controlled uptake also for P. Potential diffusion limitation in P uptake from nutrient solutions was investigated by measuring P uptake of Brassica napus from solutions using P-loaded Al(2) O(3) nanoparticles as mobile P buffer. At constant, low free phosphate concentration, plant P uptake increased up to eightfold and that of passive, diffusion-based samplers up to 40-fold. This study represents the first experimental evidence of diffusion-limited P uptake by plant roots from nutrient solution. The Michaelis constant of the free phosphate ion obtained in unbuffered solutions (K(m) = 10.4 μmol L(-1) ) was 20-fold larger than in the buffered system (K(m) ～0.5 μmol L(-1) ), indicating that K(m) s determined in unbuffered solutions do not represent the transporter affinity. Increases in the P uptake efficiency of plants by increasing the carrier affinity are therefore unlikely, while increased root surface area or exudation of P-solubilizing compounds are more likely to enhance P uptake. Furthermore, our results highlight the important role natural nanoparticles may have in plant P nutrition.     

Leaf senescence and N uptake parameters as selection traits for nitrogen efficiency of oilseed rape cultivars

The cultivation of N-efficient oilseed rape cultivars could contribute to a reduction of the large N balance surpluses of this crop. To facilitate the breeding process of N-efficient cultivars, the identification of secondary plant traits correlating with N efficiency is necessary. The objectives of this study were to investigate leaf senescence and N uptake parameters of oilseed rape cultivars and doubled haploid (DH) lines with contrasting N efficiency in a short-term nutrient solution experiment and to relate these results to their performance in field experiments. In the nutrient solution experiment, genotypes differed in leaf senescence of fully expanded leaves and maximum N uptake rate per unit root length under low N supply. A high maximum N uptake rate seemed to have contributed to delayed leaf senescence by enhancing N accumulation in leaves. Also in the field experiments, genotypes differed in leaf senescence after flowering at limiting N supply. Additionally, the most N-efficient DH line was able to adapt leaf photosynthetic capacity to the low-light conditions in the canopy during flowering. N efficiency (grain yield at limiting N supply) was positively correlated with delayed leaf senescence both in nutrient solution and field experiments. It is concluded that important leaf and root traits of N-efficient cultivars are expressed in short-term nutrient solution experiments, which may facilitate the selection of N-efficient cultivars.     

Growth of a root system described as diffusion. II. Numerical model and application

In simulation models for water movement and nutrient transport, uptake of water and nutrients by roots forms an essential part. As roots are spatially distributed, prediction of root growth and root distribution is crucial for modelling water and nutrient uptake. In a preceding paper, De Willigen et al. (2002; Plant and Soil 240, 225–234) presented an analytical solution for describing root length density distribution as a diffusion-type process. In the current paper, we present a numerical model that does the same, but which is more flexible with respect to where root input can occur. We show that the diffusion-type root growth model can describe well observed rooting patterns. We used rooting patterns for different types of crops: maize, gladiolus, eastern white cedar, and tomato. For maize, we used data for two different types of fertiliser application: broadcast and row application. In case of row application, roots extend more vertically than horizontally with respect to the broadcast application situation. This is reflected in a larger ratio of diffusion coefficients in vertical versus horizontal direction. For tomato, we considered tomatoes grown on an artificial rooting medium, i.e. rockwool. We have shown that, in principle, the model can be extended by including reduction functions on the diffusion coefficient in order to account for environmental conditions.     

Predicting microbial growth dynamics in response to nutrient availability

Developing mathematical models to accurately predict microbial growth dynamics remains a key challenge in ecology, evolution, biotechnology, and public health. To reproduce and grow, microbes need to take up essential nutrients from the environment, and mathematical models classically assume that the nutrient uptake rate is a saturating function of the nutrient concentration. In nature, microbes experience different levels of nutrient availability at all environmental scales, yet parameters shaping the nutrient uptake function are commonly estimated for a single initial nutrient concentration. This hampers the models from accurately capturing microbial dynamics when the environmental conditions change. To address this problem, we conduct growth experiments for a range of micro-organisms, including human fungal pathogens, baker’s yeast, and common coliform bacteria, and uncover the following patterns. We observed that the maximal nutrient uptake rate and biomass yield were both decreasing functions of initial nutrient concentration. While a functional form for the relationship between biomass yield and initial nutrient concentration has been previously derived from first metabolic principles, here we also derive the form of the relationship between maximal nutrient uptake rate and initial nutrient concentration. Incorporating these two functions into a model of microbial growth allows for variable growth parameters and enables us to substantially improve predictions for microbial dynamics in a range of initial nutrient concentrations, compared to keeping growth parameters fixed.     

Modelling the uptake of nitrate by a growing plant with an adjustable root nitrate uptake capacity

A new model is presented to predict the plant uptake of nitrate supplied by diffusion and mass flow to its roots. Plant growth, root-shoot ratio and the plant's nitrate uptake capacity are all set dependent on the plant's N nutrition state. By thoroughly integrating processes occurring in both plant and soil, the model enables to control the relative importance of both under a wide range of different nutritional scenarios.Soil parameters D₀ diffusion coefficient in water (m² day^-1) - D_e diffusion coefficient in soil (m² day^-1) - C nitrate concentration in soil (mol m^-3) - f tortuosity (-) - volumetric moisture content (-) - R radial distance from root axis (m) Plant parameters b₁, b₂ parameters of biomass partitioning Equation (10) - IR interroot distance (m) - K_mU Michaelis-Menten constant of the uptake system (mol m^-3) - K_mNRA Michaelis-Menten constant of nitrogen reduction system (mol g^-1) - k₁, k₂, k₃ parameters of growth model Equation (9) - L_v Root length density (m m^-3) - NO_{3 set} ^- Set point of the cytoplasmatic nitrate pool (mol g^-1 dw) - NO_{3 c} ^- cytoplasmatic nitrate concentration (mol g^-1 dw) - NO_{3 v} ^- vacuolar nitrate concentration (mol g^-1 dw) - NRA_max maximum nitrate reductase activity (mol g^-1 dw day^-1) - N_re reduced nitrogen content (mol) - N_remax maximum reduced N concentration in the plant (mol g^-1 dw) - P partitioning coefficient of nitrate between cyplasm and vacuole - R(1) root radius (m) - RGR relative growth rate (day^-1) - U uptake rate (mol day^-1 m^-2) - U_max maximum uptake rate (Eq. 6) (day^-1 m^-2) - Vo water flux at root surface (m day^-1) - W_r root dry weight (g) - W_sh shoot dry weight (g) - X model parameter: number of root compartments - Y model parameter: number of nodes     

The possibility of predicting solute uptake and plant growth response from independently measured soil and plant characteristics

Summary A model of the way the rate of growth of a plant may be affected by the level of supply of a nutrient is presented. Growth rate is linked to the nutrient level of the photosynthetic tissues, which is assumed to control changes in the net assimilation rate, the leaf area per unit shoot weight, the shoot: root ratio, the root surface area, and the distribution of nutrient between root and shoot. The uptake of nutrient depends on the concentration of nutrient at the root surface, the root surface area and its absorbing power. All these relationships may be determined in stirred solution culture. A method of applying this information to soil grown plants is suggested.Soil Science Laboratory, Department of Agricultural Science, University of Oxford     

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.     

根表面养分吸收通量和根围溶质浓度的近似解析解

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。