A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. III. Quantifying the Energy Costs of Ion Transport in Salt-Stressed Roots of Arabidopsis.

Salt stress defense mechanisms in plant roots, such as active Na+ efflux and storage, require energy in the form of ATP. Understanding the energy required for these transport mechanisms is an important step toward achieving an understanding of salt tolerance. However, accurate measurements of the fluxes required to estimate these energy costs are difficult to achieve by experimental means. As a result, the magnitude of the energy costs of ion transport in salt-stressed roots relative to the available energy is unclear, as are the relative contributions of different defense mechanisms to the total cost. We used mathematical modeling to address three key questions about the energy costs of ion transport in salt-stressed Arabidopsis roots: are the energy requirements calculated on the basis of flux data feasible; which transport steps are the main contributors to the total energy costs; and which transport processes could be altered to minimize the total energy costs? Using our biophysical model of ion and water transport we calculated the energy expended in the trans-plasma membrane and trans-tonoplast transport of Na+, K+, Cl-, and H+ in different regions of a salt-stressed model Arabidopsis root. Our calculated energy costs exceeded experimental estimates of the energy supplied by root respiration for high external NaCl concentrations. We found that Na+ exclusion from, and Cl- uptake into, the outer root were the major contributors to the total energy expended. Reducing the leakage of Na+ and the active uptake of Cl- across outer root plasma membranes would lower energy costs while enhancing exclusion of these ions. The high energy cost of ion transport in roots demonstrates that the energetic consequences of altering ion transport processes should be considered when attempting to improve salt tolerance.

Energy costs of salt tolerance in crop plants.

Agriculture is expanding into regions that are affected by salinity. This review considers the energetic costs of salinity tolerance in crop plants and provides a framework for a quantitative assessment of costs. Different sources of energy, and modifications of root system architecture that would maximize water vs ion uptake are addressed. Energy requirements for transport of salt (NaCl) to leaf vacuoles for osmotic adjustment could be small if there are no substantial leaks back across plasma membrane and tonoplast in root and leaf. The coupling ratio of the H+ -ATPase also is a critical component. One proposed leak, that of Na+ influx across the plasma membrane through certain aquaporin channels, might be coupled to water flow, thus conserving energy. For the tonoplast, control of two types of cation channels is required for energy efficiency. Transporters controlling the Na+ and Cl- concentrations in mitochondria and chloroplasts are largely unknown and could be a major energy cost. The complexity of the system will require a sophisticated modelling approach to identify critical transporters, apoplastic barriers and root structures. This modelling approach will inform experimentation and allow a quantitative assessment of the energy costs of NaCl tolerance to guide breeding and engineering of molecular components.

Dynamics in plant roots and shoots minimize stress, save energy and maintain water and nutrient uptake.

Plants are inherently dynamic. Dynamics minimize stress while enabling plants to flexibly acquire resources. Three examples are presented for plants tolerating saline soil: transport of sodium chloride (NaCl), water and macronutrients is nonuniform along a branched root; water and NaCl redistribute between shoot and soil at night-time; and ATP for salt exclusion is much lower in thinner branch roots than main roots, quantified using a biophysical model and geometry from anatomy. Noninvasive phenotyping and precision agriculture technologies can be used together to harness plant dynamics, but analytical methods are needed. A plant advancing in time through a soil and atmosphere space is proposed as a framework for dynamic data and their relationship to crop improvement.

A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. II. Clarifying the Roles of SOS1 in the Salt-Stress Response in Arabidopsis.

SOS1 transporters play an essential role in plant salt tolerance. Although SOS1 is known to encode a plasma membrane Na+/H+ antiporter, the transport mechanisms by which these transporters contribute to salt tolerance at the level of the whole root are unclear. Gene expression and flux measurements have provided conflicting evidence for the location of SOS1 transporter activity, making it difficult to determine their function. Whether SOS1 transporters load or unload Na+ from the root xylem transpiration stream is also disputed. To address these areas of contention, we applied a mathematical model to answer the question: what is the function of SOS1 transporters in salt-stressed Arabidopsis roots? We used our biophysical model of ion and water transport in a salt-stressed root to simulate a wide range of SOS1 transporter locations in a model Arabidopsis root, providing a level of detail that cannot currently be achieved by experimentation. We compared our simulations with available experimental data to find reasonable parameters for the model and to determine likely locations of SOS1 transporter activity. We found that SOS1 transporters are likely to be operating in at least one tissue of the outer mature root, in the mature stele, and in the epidermis of the root apex. SOS1 transporter activity in the mature outer root cells is essential to maintain low cytosolic Na+ levels in the root and also restricts the uptake of Na+ to the shoot. SOS1 transporters in the stele actively load Na+ into the xylem transpiration stream, enhancing the transport of Na+ and water to the shoot. SOS1 transporters acting in the apex restrict cytosolic Na+ concentrations in the apex but are unable to maintain low cytosolic Na+ levels in the mature root. Our findings suggest that targeted, tissue-specific overexpression or knockout of SOS1 may lead to greater salt tolerance than has been achieved with constitutive gene changes. Tissue-specific changes to the expression of SOS1 could be used to identify the appropriate balance between limiting Na+ uptake to the shoot while maintaining water uptake, potentially leading to enhancements in salt tolerance.

A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. I. Clarifying the Roles of Endodermal Barriers in the Salt Stress Response.

In this paper, we present a detailed and comprehensive mathematical model of active and passive ion and water transport in plant roots. Two key features are the explicit consideration of the separate, but interconnected, apoplastic, and symplastic transport pathways for ions and water, and the inclusion of both active and passive ion transport mechanisms. The model is used to investigate the respective roles of the endodermal Casparian strip and suberin lamellae in the salt stress response of plant roots. While it is thought that these barriers influence different transport pathways, it has proven difficult to distinguish their separate functions experimentally. In particular, the specific role of the suberin lamellae has been unclear. A key finding based on our simulations was that the Casparian strip is essential in preventing excessive uptake of Na+ into the plant via apoplastic bypass, with a barrier efficiency that is reflected by a sharp gradient in the steady-state radial distribution of apoplastic Na+ across the barrier. Even more significantly, this function cannot be replaced by the action of membrane transporters. The simulations also demonstrated that the positive effect of the Casparian strip of controlling Na+ uptake, was somewhat offset by its contribution to the osmotic stress component: a more effective barrier increased the detrimental osmotic stress effect. In contrast, the suberin lamellae were found to play a relatively minor, even non-essential, role in the overall response to salt stress, with the presence of the suberin lamellae resulting in only a slight reduction in Na+ uptake. However, perhaps more significantly, the simulations identified a possible role of suberin lamellae in reducing plant energy requirements by acting as a physical barrier to preventing the passive leakage of Na+ into endodermal cells. The model results suggest that more and particular experimental attention should be paid to the properties of the Casparian strip when assessing the salt tolerance of different plant varieties and species. Indeed, the Casparian strip appears to be a more promising target for plant breeding and plant genetic engineering efforts than the suberin lamellae for the goal of improving salt tolerance.

Modeling Root Zone Effects on Preferred Pathways for the Passive Transport of Ions and Water in Plant Roots.

We extend a model of ion and water transport through a root to describe transport along and through a root exhibiting a complexity of differentiation zones. Attention is focused on convective and diffusive transport, both radially and longitudinally, through different root tissue types (radial differentiation) and root developmental zones (longitudinal differentiation). Model transport parameters are selected to mimic the relative abilities of the different tissues and developmental zones to transport water and ions. For each transport scenario in this extensive simulations study, we quantify the optimal 3D flow path taken by water and ions, in response to internal barriers such as the Casparian strip and suberin lamellae. We present and discuss both transient and steady state results of ion concentrations as well as ion and water fluxes. We find that the peak in passive uptake of ions and water occurs at the start of the differentiation zone. In addition, our results show that the level of transpiration has a significant impact on the distribution of ions within the root as well as the rate of ion and water uptake in the differentiation zone, while not impacting on transport in the elongation zone. From our model results we infer information about the active transport of ions in the different developmental zones. In particular, our results suggest that any uptake measured in the elongation zone under steady state conditions is likely to be due to active transport.

Toward a biophysical understanding of the salt stress response of individual plant cells.

We present and explore a kinetic model of ion transport across and between the membranes of an isolated plant cell with an emphasis on the cell's response to salt (Na(+)) stress. The vacuole, cytoplasm and apoplast are treated as concentric regions separated by tonoplast and plasma membranes. The model includes the transport of Na(+), K(+), Cl(-) and H(+) across both membranes via primary active proton pumps, secondary active antiporters and symporters, as well as passive ion channels. In addition, water transport is included, allowing us to investigate both the osmotic and ionic components of salt stress. The model's predictions of steady state and transient cytosolic pH and Na(+) concentrations were found to be quantitatively comparable to measured experimental values. Through an extensive simulation study we have identified and characterized scenarios in which individual transport processes (H(+) pumps, Na(+)/H(+) antiporters and channels involved in the transport of Na(+)) and their combinations have major effects on the level of Na(+) in each of the cell compartments. This systematic study emulates the effects of overexpressing and inhibiting transporter genes by genetic modification and hence we have compared our simulations with observations from experiments conducted on transgenic plants. The simulations suggest that overexpressing tonoplast Na(+)/H(+) antiporter genes and tonoplast H(+) pump genes lead to an increase in the storage of Na(+) in the vacuole (helping the cell to maintain water uptake under salt stress), with only a transient influence on the cytoplasmic Na(+) concentration. The model predicts effects of varying the expression of transporter genes (individually or in combination) which have yet to be investigated in experiments. For example, our findings indicate that simultaneously overexpressing plasma membrane and tonoplast Na(+)/H(+) antiporter genes would lead to improvements in both ionic and osmotic stress tolerance. The results demonstrate the importance of simultaneously modelling the transport of Na(+) across both the tonoplast and plasma membrane, a task not undertaken previously.

On the competitive uptake and transport of ions through differentiated root tissues.

We simulate the competitive uptake and transport of a mixed salt system in the differentiated tissues of plant roots. The results are based on a physical model that includes both forced diffusion and convection by the transpiration stream. The influence of the Casparian strip on regulating apoplastic flow, the focus of the paper, is modelled by varying ion diffusive permeabilities, hydraulic reflection coefficients and water permeability for transport across the endodermis-pericycle interface. We find that reducing diffusive permeabilities leads to significantly altered ion concentration profiles in the pericycle and vascular cylinder regions, while increased convective reflectivities affect predominantly ion concentrations in the cortex and endodermis tissues. The self-consistent electric field arising from ion separation is a major influence on predicted ion fluxes and accumulation rates.

Mathematical modelling of the uptake and transport of salt in plant roots.

In this paper, we present and discuss a mathematical model of ion uptake and transport in roots of plants. The underlying physical model of transport is based on the mechanisms of forced diffusion and convection. The model can take account of local variations in effective ion and water permeabilities across the major tissue regions of plant roots, represented through a discretized coupled system of governing equations including mass balance, forced diffusion, convection and electric potential. We present simulation results of an exploration of the consequent enormous parameter space. Among our findings we identify the electric potential as a major factor affecting ion transport across, and accumulation in, root tissues. We also find that under conditions of a constant but realistic level of bulk soil salt concentration and plant-soil hydraulic pressure, diffusion plays a significant role even when convection by the water transpiration stream is operating.