Nutrient Uptake Model Research Articles

Growth rate as a link between microbial diversity and soil biogeochemistry.

Measuring the growth rate of a microorganism is a simple yet profound way to quantify its effect on the world. The absolute growth rate of a microbial population reflects rates of resource assimilation, biomass production and element transformation-some of the many ways in which organisms affect Earth's ecosystems and climate. Microbial fitness in the environment depends on the ability to reproduce quickly when conditions are favourable and adopt a survival physiology when conditions worsen, which cells coordinate by adjusting their relative growth rate. At the population level, relative growth rate is a sensitive metric of fitness, linking survival and reproduction to the ecology and evolution of populations. Techniques combining omics and stable isotope probing enable sensitive measurements of the growth rates of microbial assemblages and individual taxa in soil. Microbial ecologists can explore how the growth rates of taxa with known traits and evolutionary histories respond to changes in resource availability, environmental conditions and interactions with other organisms. We anticipate that quantitative and scalable data on the growth rates of soil microorganisms, coupled with measurements of biogeochemical fluxes, will allow scientists to test and refine ecological theory and advance process-based models of carbon flux, nutrient uptake and ecosystem productivity. Measurements of in situ microbial growth rates provide insights into the ecology of populations and can be used to quantitatively link microbial diversity to soil biogeochemistry.

Predicting chlorophyll and nitrogen content in rice using multiple regression models

Chlorophyll and nitrogen (N) content in rice at critical crop growth stages are important input parameters for crop growth and nutrient uptake models used to optimize N application. Hence, the study was conducted to predict chlorophyll and N content in rice using multiple regression-based models involving normalized difference vegetation index (NDVI), Soil Plant Analysis Development (SPAD), Customized leaf color chart (CLCC), chlorophyll and N content. An experiment was conducted with six varieties i.e. CR Dhan 312, CR Dhan 310, Lalat, Shatabdi, Swarna Shreya, CR Dhan 206 with four N levels (i.e. 0, 80, 100 and 120 kg N ha−1) in split plot design and replicated thrice. The NDVI, SPAD and CLCC readings were taken at 45, 49 and 54 days after transplanting (DAT). Plant sampling was done for estimating the chlorophyll and nitrogen content in laboratory following standard methodology. Multiple linear regressions were performed between NDVI, SPAD and CLCC readings and chlorophyll & N content in rice in different variables combinations. Multiple linear regression (MLR) models with two variables i.e. NDVI and SPAD predicted the chlorophyll and N content of rice varieties. The predicted values for nitrogen and chlorophyll were comparable to those obtained using models from individual varieties when combined data from six different varieties were used to create MLR models. The study concludes that variations in chlorophyll and N concentrations in rice can be estimated using data from optical sensors with notable accuracies.

Participatory design to investigate the effects of farmers’ fertilization practices under unsubmerged conditions toward efficient nutrient uptake in rainfed rice

Rainfed agriculture plays a vital role in providing food and livelihoods globally. However, its production is adversely affected due to uncertainty in rainfall patterns causing unsubmerged conditions during the dry period, which is increasing under the impact of climate change. Given that rice is a primarily grown crop in rainfed conditions and is the staple food of half the global population, it is under pressure to increase production due to the burgeoning population globally. Therefore, proper farming management such as balanced fertilization practices, irrigation etc. are required. Thus, we studied the effect of human-induced nutrient application quantity for nitrogen (N) and phosphorus (P), on production efficiency and assessed the nutrient budget in rainfed rice fields of Jamuna command area, Assam, India. A questionnaire was developed to know the farm management practices adopted by farmers and accordingly, applied N and P doses were ranked. Low, medium, high and very high doses for N are 40–60, 61–80, 81–100, 101 kg ha−1 and above, respectively, while for P are 0–4, 5–9, 10–19, 20 kg ha−1 and above respectively. Rice plants were sampled from farmers’ field of selected thirteen villages, at the maturity stage, soils were sampled after rice harvest to analyze Total Kjeldahl Nitrogen (TKN) and available Phosphorus (Pav). Nitrogen (N) balance was positive ranging from 33 kg ha−1 to 72 kg ha−1. Phosphorus (P) balance was ranging negative from 28 kg ha−1 to 129 kg ha−1. N uptake increased in order of low<medium<very high<high doses while P increased in order of high<very high<low<medium. The findings showed that plants uptook P efficiently under unsubmerged conditions. N uptake was consistent after a fertilizer dose of 100 kg ha−1. From the quantitative measurements of nutrient uptake and Cobb-Douglas model analysis validated farmer information on fertilizer and crop yield. Results also revealed that averaging across all the villages an amount of 71 kg ha−1 is needed for P replenishment to maintain the yield along with water for increased soil moisture in lateritic soil. Finally, it is concluded that involving farmers will prevent soil deterioration in rainfed rice areas and a policy shift to develop optimal N and P management strategies for sustainable agriculture under unsubmerged soil conditions.

Analytical solution of Nye–Tinker–Barber model by Laplace transform

The Nye–Tinker–Barber model is a classical convection–diffusion model for nutrient uptake by plant roots in cylindrical coordinates and has one nonlinear left Robin boundary condition with Michaelis–Menten function of concentration. First the Michaelis–Menten function is fitted into a function of time by numerical concentration at root surface from difference scheme, and then the Laplace and numerical inverse Laplace transforms — Zakian inversion method are taken to obtain the approximate analytical solution. Compared with other solutions made by difference scheme, Stehfest inversion method and previous analytical methods, it is found that the analytical solution obtained by Laplace and Zakian inversion transforms has higher accuracy and computation efficiency. This analytical method can be extended to other nutrient uptake models with Michaelis–Menten function.

How Much Phosphorus Uptake Is Required for Achieving Maximum Maize Grain Yield? Part 1: Luxury Consumption and Implications for Yield

Development of a more precise and process-based tool for making phosphorus (P) recommendations requires detailed understanding of plant P uptake needs. Future adaptation of a nutrient uptake model for this purpose must utilize a mass-balance approach. The objectives of this study were to determine the minimum P uptake mass required for achieving maximum grain yield of maize and to evaluate plant P partitioning over a range of P uptake. Three maize hybrids were grown under optimal conditions using sand-culture hydroponics for precise control of the root environment. Plants were grown to maturity with six different P concentrations followed by biomass and nutrient partitioning analysis of various maize parts. Phosphorus uptake occurred in three phases with two steps of luxury consumption; (i) increased uptake with increased grain yield and total biomass until maximum grain yield was attained at 580 mg P uptake, (ii) further P uptake with increase in total biomass until 730 mg P uptake, but with decrease in grain yield; and (iii) additional P uptake with little to no increase in total biomass and continued decrease in grain yield. Luxury consumption of P implies that excess P fertility is an economic drag for grain production.

Analytical solutions of the nitrogen uptake model with Michaelis-Menten flux

In this paper, we describe the application of the generalized finite Hankel transform method to the convection diffusion problems of nitrogen in soil subject to Robin boundary conditions and the right-hand side of the left Robin boundary condition is the classic nonlinear Michaelis-Menten flux. If the Michaelis-Menten flux is taken as a function of time, the analytical solution of series form can be derived by the generalized finite Hankel transform. In the calculation, the Michaelis-Menten flux is evaluated by the numerical concentration at the root surface and the number of terms of the partial sum is determined after adequately approximating the numerical solution. Therefore, we improve and develop the analytical method built by Garg et al., and exemplify and verify it by the nitrogen uptake model for roots. The investigated model has a representatively and completely mathematical structure among most nutrient uptake models, and then the analytical method and the solutions developed here can also be used to nutrient uptake problems in soil subject to homogeneous or inhomogeneous Dirichlet or Neumann boundary conditions.

Simple Growth-Metabolism Relations Are Revealed by Conserved Patterns of Heat Flow from Cultured Microorganisms.

Quantitative analyses of cell replication address the connection between metabolism and growth. Various growth models approximate time-dependent cell numbers in culture media, but physiological implications of the parametrizations are vague. In contrast, isothermal microcalorimetry (IMC) measures with unprecedented sensitivity the heat (enthalpy) release via chemical turnover in metabolizing cells. Hence, the metabolic activity can be studied independently of modeling the time-dependence of cell numbers. Unexpectedly, IMC traces of various origins exhibit conserved patterns when expressed in the enthalpy domain rather than the time domain, as exemplified by cultures of Lactococcus lactis (prokaryote), Trypanosoma congolese (protozoan) and non-growing Brassica napus (plant) cells. The data comply extraordinarily well with a dynamic Langmuir adsorption reaction model of nutrient uptake and catalytic turnover generalized here to the non-constancy of catalytic capacity. Formal relations to Michaelis–Menten kinetics and common analytical growth models are briefly discussed. The proposed formalism reproduces the “life span” of cultured microorganisms from exponential growth to metabolic decline by a succession of distinct metabolic phases following remarkably simple nutrient–metabolism relations. The analysis enables the development of advanced enzyme network models of unbalanced growth and has fundamental consequences for the derivation of toxicity measures and the transferability of metabolic activity data between laboratories.

Diversity of Growth Rates Maximizes Phytoplankton Productivity in an Eddying Ocean

AbstractIn the subtropical gyres, phytoplankton rely on eddies for transporting nutrients from depth to the euphotic zone. But, what controls the rate of nutrient supply for new production? We show that vertical nutrient flux both depends on the vertical motion within the eddying flow and varies nonlinearly with the phytoplankton growth rate. Flux is maximized when the growth rate matches the inverse of the decorrelation timescale for vertical motion. Using a three‐dimensional ocean model and a linear nutrient uptake model, we find that phytoplankton productivity is maximized for a growth rate of 1/3 day−1, which corresponds to the timescale of submesoscale dynamics. Variability in the frequency of vertical motion across different physical features of the flow favors phytoplankton production with different growth rates. Such a growth‐transport feedback can generate diversity in the phytoplankton community structure at submesoscales and higher net productivity in the presence of community diversity.

Mechanistic model of nutrient uptake explains dichotomy between marine oligotrophic and copiotrophic bacteria.

Marine bacterial diversity is immense and believed to be driven in part by trade-offs in metabolic strategies. Here we consider heterotrophs that rely on organic carbon as an energy source and present a molecular-level model of cell metabolism that explains the dichotomy between copiotrophs—which dominate in carbon-rich environments—and oligotrophs—which dominate in carbon-poor environments—as the consequence of trade-offs between nutrient transport systems. While prototypical copiotrophs, like Vibrios, possess numerous phosphotransferase systems (PTS), prototypical oligotrophs, such as SAR11, lack PTS and rely on ATP-binding cassette (ABC) transporters, which use binding proteins. We develop models of both transport systems and use them in proteome allocation problems to predict the optimal nutrient uptake and metabolic strategy as a function of carbon availability. We derive a Michaelis–Menten approximation of ABC transport, analytically demonstrating how the half-saturation concentration is a function of binding protein abundance. We predict that oligotrophs can attain nanomolar half-saturation concentrations using binding proteins with only micromolar dissociation constants and while closely matching transport and metabolic capacities. However, our model predicts that this requires large periplasms and that the slow diffusion of the binding proteins limits uptake. Thus, binding proteins are critical for oligotrophic survival yet severely constrain growth rates. We propose that this trade-off fundamentally shaped the divergent evolution of oligotrophs and copiotrophs.

Modeling the Carbon Cost of Plant Nitrogen and Phosphorus Uptake Across Temperate and Tropical Forests

Nutrient limitation is a key source of uncertainty in predicting terrestrial carbon (C) uptake. Models have begun to include nitrogen (N) dynamics; however, phosphorus (P), which can also limit or co-limit net primary production (NPP) in many ecosystems, is currently absent in most models. To meet this challenge, we integrated P dynamics into a cutting-edge plant nutrient uptake model (Fixation and Uptake of Nitrogen: FUN 2.0) that mechanistically tracks the C cost of N uptake from soil based on the cost of allocating C to leaf resorption and root/root-microbial uptake, and the availability of N in soil. We incorporated the direct C cost of P uptake, as well as a N cost of synthesizing phosphatase enzymes to extract P from soil, into a new model formulation (Fixation and Uptake of Nutrients: FUN 3.0). We confronted and validated FUN 3.0 against empirical estimates of canopy, root, and soil P pools from 45 temperate forest plots in Indiana, USA and 18 tropical dry forest plots located in Guanacaste, Costa Rica that vary in P availability and distribution of arbuscular mycorrhizal- (AM) and ectomycorrhizal- (ECM) associated trees. FUN 3.0 was able to accurately predict N and P retranslocation across the temperate and tropical forest sites (slopes of 0.95 and 0.92 for P and N retranslocation, respectively). Carbon costs for acquiring P were three times higher in tropical forest sites compared to temperate forest sites, driving overall higher C costs in tropical sites. In addition, the N costs for acquiring P in tropical forest sites lead to a substantial increase in N fixation to support phosphatase enzyme production. Sensitivity analyses showed that tropical sites appeared to be severely P limited, while the temperate sites showed evidence for co-limitation by N and P. Collectively, FUN 3.0 provides a novel framework for predicting coupled N and P limitation that earth system models can leverage to enhance predictions of ecosystem response to global change.

Modelling Nitrogen Uptake in Plants and Phytoplankton: Advantages of Integrating Flexibility into the Spatial and Temporal Dynamics of Nitrate Absorption

Under field conditions, plants need to optimize nutrient ion and water acquisition in their fluctuating environment. One of the most important variables involved in variations of ion uptake processes is temperature. It modifies the thermodynamic processes of root uptake and ion diffusion in soil throughout day–night and ontogenetic cycles. Yet, most models of nitrogen (N) uptake in plants are built from set values of microscopic kinetic parameters, Vm and Km, derived from a Michaelis–Menten (MM) interpretation of nutrient isotherms. An isotherm is a curve depicting the response of root nitrate influx to external nitrate concentrations at a given temperature. Models using the MM formalism are based on several implicit assumptions that do not always hold, such as homothetic behavior of the kinetic parameters between the different root biological scales, i.e., the epidermis cell, root segments, root axes, and the whole root system. However, in marine phytoplankton, it has been clearly demonstrated that the macroscopic behavior in the nutrient uptake of a colony cannot be confounded with the microscopic behavior of individual cells, due to the cell diffusion boundary layer. The same is also true around plant root segments. Improved N uptake models should either take into account the flexibility of the kinetic parameters of nitrate uptake at the cellular level (porter–diffusion approach) or use the more realistic macroscopic kinetic parameters proposed by the flow–force approach. Here we present recent solutions proposed in marine phytoplankton and plant nutrient uptake models to make a more flexible description of the nutrient ion uptake process. Use of the mechanistic porter–diffusion approach developed in marine phytoplankton introduces more flexibility in response to cell characteristics and physical processes driven by temperature (diffusion and convection). The thermodynamic flow–force interpretation of plant-based nutrient uptake isotherms introduces more flexibility in response to environmental cues and root aging. These two approaches could help solve many problems that modelers encounter in these two research areas.

Significance of P influx and Root Growth in P Acquisition at Different Growth Stages of Maize, Wheat and Groundnut Grown in a P-Deficient Alfisol

Crop species differ in their phosphorus (P) efficiency i.e. their ability to grow well in low P supplying soils. To test this hypothesis, field experiments were carried out in a low P soil to study P efficiency of wheat (Triticum aestium L.), maize (Zea mays L.) and groundnut (Arachis hypogaea L.) during the whole growing season and the possible reasons of variation in P efficiency of these crops. Treatments replicated four times consisted of P-0 (no P), P-50 (50 mg P kg−1 soil) and P-400 (400 mg P kg−1 soil). Four harvests were made to cover whole growing season of all the crops. At each harvest, different soil and plant parameters were determined. Plot size varied from 10 m2 for the first three harvests and 16 m2 for the last harvest (at maturity). Taking the relative yield as measure of P efficiency (expressed by the yield at P-0 relative to the yield at P-400), maize was most efficient, yielding more than 80%, followed by groundnut, 75%, and wheat, 65% of their maximum yields. Total P uptake of maize was twice to those of wheat and groundnut. The variation in uptake efficiency was not related to size of root systems but mainly to the P influx. At P-0, although the root system of groundnut was only 50% of that of wheat, P uptake was the same; and maize had the same root length as wheat but P uptake was twice. Wheat was of intermediate P efficiency during the whole growing season while maize was inefficient in early growth stages and very efficient later. In contrast, groundnut was very efficient at the beginning and less efficient later. The efficiency of wheat was mainly based on its root system whereas maize and groundnut relied on a large P influx. The P influx was the major factor determining differences in P efficiency among the species as well as for the same species during the growing season under field conditions. To separate the influence of root and soil properties, model calculation of P influx were carried out by employing the nutrient uptake model. Measured influx was much higher than the calculated influx at low P level. Sensitivity analysis shows that at low P level the CLi (initial soil solutions P concentration) was the most sensitive parameter for all the three crops. Among the physiological parameters Imax and Km was found to play negligible role in P uptake at low P level. But at higher P level (P-400) Imax was the most sensitive parameters followed by r0 for P uptake of three crop species. The higher measured than calculated influx indicated that plant possesses mechanisms that enhance P transport to the root from soil. Possible reason for this enhanced transport may be through root exudates that increase P solubility in the rhizosphere or mycorrhizae symbiosis.

Continuum multiscale model of root water and nutrient uptake from soil with explicit consideration of the 3D root architecture and the rhizosphere gradients

Although modelling of water and nutrient uptake by root systems has advanced considerably in recent years, steep local gradients of nutrient concentration near the root-soil interface in the rhizosphere are still a central challenge for accurate simulation of water and nutrient uptake at the root system scale. Conventionally, mesh refinement is used to resolve these gradients. However, it results in excessive computational costs. The object of the study is to present a multiscale approach which resolves the steep gradient of nutrient concentrations at rhizosphere scale and simulates nutrient and water fluxes within the entire root zone at macroscale scale in a computationally efficient way. We developed a 3D water and nutrient transport model of the root-soil system with explicit consideration of the 3D root architecture. To capture the nutrient gradients at root surfaces, 1D axisymmetric soil models at rhizosphere scale were constructed and coupled to the coarse 3D root-system-scale simulations using a mass conservative approach. The multiscale model was investigated under different scenarios for water and potassium (K+) uptake of a single root, multiple roots, and whole 3D architecture of a Zea mays L. root system in conditions of dynamic soil water and different soil buffer capacity of K+. The steep gradients of K+ concentrations were efficiently resolved in the multiscale simulations thanks to the 1D model at the rhizosphere scale. In comparison with the refinement method, the multiscale model achieved a significant accuracy of K+ uptake prediction with a relative error below 5%. Meanwhile, the simulation at macroscale with coarse mesh could overestimate the K+ uptake in one order of magnitude. Moreover, the computational cost of multiscale simulations was decreased considerably by using coarse soil mesh. The newly developed model can describe the effect of the drying and nutrient transport in the root zone on nutrient uptake. It also allows to simulate processes in larger and complex root systems because of the considerable reduction in computational cost.

The Extended Monod Model for Microalgae Growth and Nutrient Uptake in Different Wastewaters

Water pollution is a serious issue which always being concerned by public. Microalgae for wastewater treatment is an effective way to solve the problem due to its eco-friendly and apparently low cost. This research aims to investigate the efficiency of the mathematical model to estimate the microalgae growth and nutrient uptake by microalgae in wastewaters. The extended Monod model is applied in the Verhulst model to describe the microalgae growth and nutrient uptake by microalgae whereas microalgae Botryococcus sp. is the species of microalgae used in this research. The microalgae Botryococcus sp. growth and nutrient uptake in domestic, agricultural and industrial wastewater are estimated and the results reveal that the extended Monod model is suitable for the estimation of microalgae growth and nutrient uptake by microalgae. In addition, microalgae Botryococcus sp. is promising for treating domestic, agricultural and industrial wastewater.

Roots Partially in Contact with Soil: Analytical Solutions and Approximation in Models of Nutrient and Water Uptake

Core Ideas Partial root–soil contact has an impact on uptake. For the radial situation, a steady‐rate solution can be used. For partial longitudinal contact, steady‐rate solutions cannot always be used. Root–soil contact entails a trade‐off between uptake opportunities and aeration requirements. A single root in the center of a cylinder of soil has been the standard geometry for which most root‐level water and nutrient uptake models have been derived. However, this implies assumptions about complete root–soil contact and regularly spaced, parallel roots that do not conform to the situation in the field. In reality, the frequency distribution of transport distances will differ from what the cylinder model assumes, both by partial root–soil contact and irregular three‐dimensional (3‐D) distribution. We derived analytical equations describing the transport of water and nutrients to and uptake by roots in partial contact with soil for two extremes: (i) part of each root in contact or (ii) part of all roots in full contact and the rest without. Solutions range from negligible impacts to proportionality of uptake to the part of roots in contact with soil.

Tracking Nitrogen in Arctic Plants

Prevailing nutrient uptake models do not fit Arctic plants. Scientists test a new option that overcomes older models’ shortcomings.

Plant roots: new challenges in a changing world

Plant roots: new challenges in a changing world

Image-based modelling of nutrient movement in and around the rhizosphere.

In this study, we developed a spatially explicit model for nutrient uptake by root hairs based on X-ray computed tomography images of the rhizosphere soil structure. This work extends our previous work to larger domains and hence is valid for longer times. Unlike the model used previously, which considered only a small region of soil about the root, we considered an effectively infinite volume of bulk soil about the rhizosphere. We asked the question: At what distance away from root surfaces do the specific structural features of root-hair and soil aggregate morphology not matter because average properties start dominating the nutrient transport? The resulting model was used to capture bulk and rhizosphere soil properties by considering representative volumes of soil far from the root and adjacent to the root, respectively. By increasing the size of the volumes that we considered, the diffusive impedance of the bulk soil and root uptake were seen to converge. We did this for two different values of water content. We found that the size of region for which the nutrient uptake properties converged to a fixed value was dependent on the water saturation. In the fully saturated case, the region of soil we needed to consider was only of radius 1.1mm for poorly soil-mobile species such as phosphate. However, in the case of a partially saturated medium (relative saturation 0.3), we found that a radius of 1.4mm was necessary. This suggests that, in addition to the geometrical properties of the rhizosphere, there is an additional effect of soil moisture properties, which extends further from the root and may relate to other chemical changes in the rhizosphere. The latter were not explicitly included in our model.

Mathematical Modelling for nutrient uptake by plant root which is considered as cylindrical

In this article, we drive mathematical model for nutrient uptake by the plant root which is considered as cylindrical, i.e, we obtain concentration of nutrient entering into the root surface by advection diffusion equation. The equation is written in the radial form and solved using Michal Menten boundary condition, which is nonlinear boundary condition. It is found that generally advection diffusion is solved taking Peclet number as zero, then equation reduces to the diffusion equation and solved by Laplace method[9]. But wesolve the advection diffusion equation without taking Plect number as zero and solved by re-scaling and using separation of variable which reduces it into Bessel’s equation. For particular solution, we use extreme parameters.

A receptor-like kinase mutant with absent endodermal diffusion barrier displays selective nutrient homeostasis defects.

The endodermis represents the main barrier to extracellular diffusion in plant roots, and it is central to current models of plant nutrient uptake. Despite this, little is known about the genes setting up this endodermal barrier. In this study, we report the identification and characterization of a strong barrier mutant, schengen3 (sgn3). We observe a surprising ability of the mutant to maintain nutrient homeostasis, but demonstrate a major defect in maintaining sufficient levels of the macronutrient potassium. We show that SGN3/GASSHO1 is a receptor-like kinase that is necessary for localizing CASPARIAN STRIP DOMAIN PROTEINS (CASPs)--major players of endodermal differentiation--into an uninterrupted, ring-like domain. SGN3 appears to localize into a broader band, embedding growing CASP microdomains. The discovery of SGN3 strongly advances our ability to interrogate mechanisms of plant nutrient homeostasis and provides a novel actor for localized microdomain formation at the endodermal plasma membrane.