An updated model for nitrate uptake modelling in plants. I. Functional component: cross-combination of flow-force interpretation of nitrate uptake isotherms, and environmental and in planta regulation of nitrate influx

A mechanistic mathematical model for describing and predicting the dynamics of high-affinity nitrate intake into roots of maize and other plant species

A fully mechanistic dynamical model for plant nitrate uptake is presented. Based on physiological and regulatory pathways and based on physical laws, we form a dynamic system mathematically described by seven differential equations. The model evidences the presence of a short-term positive feedback on the high-affinity nitrate uptake, triggered by the presence of nitrate around the roots, which induces its intaking. In the long run, this positive feedback is overridden by two long-term negative feedback loops which drastically reduces the nitrate uptake capacity. These two negative feedbacks are due to the generation of ammonium and amino acids, respectively, and inhibit the synthesis and the activity of high-affinity nitrate transporters. This model faithfully predicts the typical spiking behavior of the nitrate uptake, in which an initial strong increase of nitrate absorption capacity is followed by a drop, which regulates the absorption down to the initial value. The model outcome was compared with experimental data and they fit quite nicely. The model predicts that after the initial exposure of the roots with nitrate, the absorption of the anion strongly increases and that, on the contrary, the intensity of the absorption is limited in presence of ammonium around the roots.

Combined Allosteric Responses Explain the Bifurcation in Non-Linear Dynamics of 15N Root Fluxes Under Nutritional Steady-State Conditions for Nitrate

With regard to thermodynamics out of equilibrium, seedlings are open systems that dissipate energy towards their environment. Accordingly, under nutritional steady-state conditions, changes in external concentrations of one single ion provokes instability and reorganization in the metabolic and structure/architecture of the seedling that is more favorable to the fluxes of energy and matter. This reorganization is called a bifurcation and is described in mathematics as a non-linear dynamic system. In this study, we investigate the non-linear dynamics of ¹⁵N fluxes among cellular compartments of B. napus seedlings in response to a wide range of external NO 3 - 15 concentrations (from 0.05 to 20 mM): this allows to determine whether any stationary states and bifurcations could be found. The biphasic behavior of the root NO 3 - 15 uptake rate (v_in ) was explained by the combined cooperative properties between the v_app (N uptake, storage and assimilation rate) and v_out (N translocation rate) ¹⁵N fluxes that revealed a unique and stable stationary state around 0.28 mM nitrate. The disappearance of this stationary state around 0.5 mM external nitrate concentrations provokes a dramatic bifurcation in ¹⁵N flux pattern. This bifurcation in the v_in and v_out ¹⁵N fluxes fits better with the increase of BnNPF6.3/NRT1.1 expression than BnNRT2.1 nitrate transporter genes, confirming the allosteric property of the BnNPF6/NRT1.1 transporter, as reported in the literature between low and high nitrate concentrations. Moreover, several statistically significant power-law equations were found between variations in the shoots tryptophan concentrations (i.e., IAA precursor) with changes in the v_app and v_out ¹⁵N fluxes as well as a synthetic parameter of plant N status estimated from the root/shoot ratio of total free amino acids concentrations. These relationships designate IAA as one of the major biological parameters related to metabolic and structural-morphological reorganization coupled with the N and water fluxes induced by nitrate. The results seriously challenge the scientific grounds of the concept of high- and low-affinity of nitrate transporters and are therefore discussed in terms of the ecological significance and physiological implications on the basis of recent agronomic, physiological and molecular data of the literature.

Targeting Root Ion Uptake Kinetics to Increase Plant Productivity and Nutrient Use Efficiency

Root system architecture has received increased attention in recent years; however, significant knowledge gaps remain for physiological phenes, or units of phenotype, that have been relatively less studied. Ion uptake kinetics studies have been invaluable in uncovering distinct nutrient uptake systems in plants with the use of Michaelis-Menten kinetic modeling. This review outlines the theoretical framework behind ion uptake kinetics, provides a meta-analysis for macronutrient uptake parameters, and proposes new strategies for using uptake kinetics parameters as selection criteria for breeding crops with improved resource acquisition capability. Presumably, variation in uptake kinetics is caused by variation in type and number of transporters, assimilation machinery, and anatomical features that can vary greatly within and among species. Critically, little is known about what determines transporter properties at the molecular level or how transporter properties scale to the entire root system. A meta-analysis of literature containing measures of crop nutrient uptake kinetics provides insights about the need for standardization of reporting, the differences among crop species, and the relationships among various uptake parameters and experimental conditions. Therefore, uptake kinetics parameters are proposed as promising target phenes that integrate several processes for functional phenomics and genetic analysis, which will lead to a greater understanding of this fundamental plant process. Exploiting this genetic and phenotypic variation has the potential to greatly advance breeding efforts for improved nutrient use efficiency in crops.

Approximate nutrient flux and concentration solutions of the Nye-Tinker-Barber model by the perturbation expansion method

The Nye-Tinker-Barber model is a basic and representative one for single-ion nutrient uptake by plant root from the soil and we aim to derive its approximate analytical solutions of flux and concentration. We divide the rhizosphere into the inner and the outer fields, match the inner and the outer solutions near the root surface, and then obtain the approximate analytical solutions of nutrient uptake flux at the root surface and global nutrient concentration of the diffusion or the convection-diffusion Nye-Tinker-Barber model. The analytical and numerical fluxes of K⁺ and [Formula: see text] decay quickly to 0 in less than 3 days while [Formula: see text] and Cd²⁺ gradually decrease in more than 15 days; the depletion profile spread of [Formula: see text] is apparently narrower than [Formula: see text] and K⁺ in 24 days. The different flux and concentration patterns of 4 nutrients result from their mobility and solubility in the rhizosphere. In comparison with the numerical simulations and the previous analytical results, we find that the analytical flux will overestimate the numerical flux of [Formula: see text] and Cd²⁺ while the analytical concentration can accurately predict the numerical concentration; the flux and the concentration solutions of the convection-diffusion Nye-Tinker-Barber model can be simplified to the diffusion versions by the Péclet number, and they can more widely describe the transport of nutrients of different attributes in soils of different textures with different levels of saturation, conductivity and permeability.

Developmental and physiological responses of Brachypodium distachyon to fluctuating nitrogen availability

The Nitrogen Use Efficiency (NUE) of grain cereals depends on nitrate (NO3-) uptake from the soil, translocation to the aerial parts, nitrogen (N) assimilation and remobilization to the grains. Brachypodium distachyon has been proposed as a model species to identify the molecular players and mechanisms that affects these processes, for the improvement of temperate C3 cereals. We report on the developmental, physiological and grain-characteristic responses of the Bd21-3 accession of Brachypodium to variations in NO3- availability. As previously described in wheat and barley, we show that vegetative growth, shoot/root ratio, tiller formation, spike development, tissue NO3- and N contents, grain number per plant, grain yield and grain N content are sensitive to pre- and/or post-anthesis NO3- supply. We subsequently described constitutive and NO3--inducible components of both High and Low Affinity Transport Systems (HATS and LATS) for root NO3- uptake, and BdNRT2/3 candidate genes potentially involved in the HATS. Taken together, our data validate Brachypodium Bd21-3 as a model to decipher cereal N nutrition. Apparent specificities such as high grain N content, strong post-anthesis NO3- uptake and efficient constitutive HATS, further identify Brachypodium as a direct source of knowledge for crop improvement.

Changes in 15NO3 - Availability and Transpiration Rate Are Associated With a Rapid Diurnal Adjustment of Anion Contents as Well as 15N and Water Fluxes Between the Roots and Shoots

Background and Aims: Understanding interactions between water and nitrate fluxes in response to nitrate availability and transpiration rate is crucial to select more efficient plants for the use of water and nitrate. Methods: Some of these interactions were investigated in intact Brassica napus plants by combining a non-destructive gravimetric device with ¹⁵NO₃ ^- labeling. The set-up allowed high-resolution measurement of the effects of a cross-combination of two concentrations of KNO₃ or KCl (0.5 and 5 mM) with two different rates of transpiration controlled by the relative humidity during a day-night cycle. Key Results: Results show that (1) high external nitrate concentrations increased root water uptake significantly whatever the transpiration rate, (2) nitrate translocation depended both on the rate of nitrate uptake and loading into xylem (3) dilution-concentration effect of nitrate in the xylem was mainly modulated by both external nitrate availability and transpiration rate, (4) dynamic changes in ¹⁵N translocation in the xylem modified shoot growth and capacitance, and (5) variations in tissue concentrations of NO₃ ^- induced by the experimental conditions were balanced by changes in concentrations of chloride and sulfate ions. These effects were even more amplified under low transpiration condition and 0.5 mM external nitrate concentration. Conclusion: Taken together, these results highlight the fine and rapid adjustment of anion contents, nitrate and water flows to changes in transpiration rate and nitrate availability during a day-night cycle. The use of this non-invasive gravimetric device is therefore a powerful tool to assess candidates genes involved in nitrogen and water use efficiency.

Nitrate Reductase Regulates Plant Nitric Oxide Homeostasis

Nitrate reductase (NR) is a key enzyme for nitrogen acquisition by plants, algae, yeasts, and fungi. Nitrate, its main substrate, is required for signaling and is widely distributed in diverse tissues in plants. In addition, NR has been proposed as an important enzymatic source of nitric oxide (NO). Recently, NR has been shown to play a role in NO homeostasis by supplying electrons from NAD(P)H through its diaphorase/dehydrogenase domain both to a truncated hemoglobin THB1, which scavenges NO by its dioxygenase activity, and to the molybdoenzyme NO-forming nitrite reductase (NOFNiR) that is responsible for NO synthesis from nitrite. We review how NR may play a central role in plant biology by controlling the amounts of NO, a key signaling molecule in plant cells.

The Thermodynamic Flow-Force Interpretation of Root Nutrient Uptake Kinetics: A Powerful Formalism for Agronomic and Phytoplanktonic Models

The ion influx isotherms obtained by measuring unidirectional influx across root membranes with radioactive or stable tracers are mostly interpreted by enzyme-substrate-like modeling. However, recent analyses from ion transporter mutants clearly demonstrate the inadequacy of the conventional interpretation of ion isotherms. Many genetically distinct carriers are involved in the root catalytic function. Parameters Vmax and Km deduced from this interpretation cannot therefore be regarded as microscopic parameters of a single transporter, but are instead macroscopic parameters (Vmapp and Kmapp, apparent maximum velocity and affinity constant) that depend on weighted activities of multiple transporters along the root. The flow-force interpretation based on the thermodynamic principle of irreversible processes is an alternative macroscopic modeling approach for ion influx isotherms in which macroscopic parameters L_j (overall conductance of the root system for the substrate j) and π_j (thermodynamic parameter when J_j = 0) have a straightforward meaning with respect to the biological sample studied. They characterize the efficiency of the entire root catalytic structure without deducing molecular characteristics. Here we present the basic principles of this theory and how its use can be tested and improved by changing root pre- and post-wash procedures before influx measurements in order to come as close as possible to equilibrium conditions. In addition, the constant values of Vm and Km in the Michaelis-Menten (MM) formalism of enzyme-substrate interpretation do not reflect variations in response to temperature, nutrient status or nutrient regimes. The linear formalism of the flow-force approach, which integrates temperature effect on nutrient uptake, could usefully replace MM formalism in the 1-3-dimension models of plants and phytoplankton. This formalism offers a simplification of parametrization to help find more realistic analytical expressions and numerical solution for root nutrient uptake.

Breaking conceptual locks in modelling root absorption of nutrients: reopening the thermodynamic viewpoint of ion transport across the root

BACKGROUND

The top-down analysis of nitrate influx isotherms through the Enzyme-Substrate interpretation has not withstood recent molecular and histochemical analyses of nitrate transporters. Indeed, at least four families of nitrate transporters operating at both high and/or low external nitrate concentrations, and which are located in series and/or parallel in the different cellular layers of the mature root, are involved in nitrate uptake. Accordingly, the top-down analysis of the root catalytic structure for ion transport from the Enzyme-Substrate interpretation of nitrate influx isotherms is inadequate. Moreover, the use of the Enzyme-Substrate velocity equation as a single reference in agronomic models is not suitable in its formalism to account for variations in N uptake under fluctuating environmental conditions. Therefore, a conceptual paradigm shift is required to improve the mechanistic modelling of N uptake in agronomic models.

SCOPE

An alternative formalism, the Flow-Force theory, was proposed in the 1970s to describe ion isotherms based upon biophysical 'flows and forces' relationships of non-equilibrium thermodynamics. This interpretation describes, with macroscopic parameters, the patterns of N uptake provided by a biological system such as roots. In contrast to the Enzyme-Substrate interpretation, this approach does not claim to represent molecular characteristics. Here it is shown that it is possible to combine the Flow-Force formalism with polynomial responses of nitrate influx rate induced by climatic and in planta factors in relation to nitrate availability.

CONCLUSIONS

Application of the Flow-Force formalism allows nitrate uptake to be modelled in a more realistic manner, and allows scaling-up in time and space of the regulation of nitrate uptake across the plant growth cycle.

An updated model for nitrate uptake modelling in plants. II. Assessment of active root involvement in nitrate uptake based on integrated root system age: measured versus modelled outputs

Background and Aims An updated version of a mechanistic structural-functional model was developed to predict nitrogen (N) uptake throughout the growth cycle by a crop of winter oilseed rape, Brassica napus, grown under field conditions. Methods The functional component of the model derives from a revisited conceptual framework that combines the thermodynamic Flow-Force interpretation of nitrate uptake isotherms and environmental and in planta effects on nitrate influx. Estimation of the root biomass (structural component) is based upon a combination of root mapping along the soil depth profile in the field and a relationship between the specific root length and external nitrate concentration. The root biomass contributing actively to N uptake was determined by introduction of an integrated root system age that allows assignment of a root absorption capacity at a specific age of the root. Key Results Simulations were well matched to measured data of N taken up under field conditions for three levels of N fertilization. The model outputs indicated that the two topsoil layers (0-30 and 30-60 cm) contained 75-88 % of the total root length and biomass, and accounted for 90-95 % of N taken up at harvest. Conclusions This conceptual framework provides a model of nitrate uptake that is able to respond to external nitrate fluctuations at both functional and structural levels.