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 model for radial water transport across plant roots

Summary A model based on the canal theory (Katou andFurumoto 1986 a, b) is proposed for the absorption of solute and water at the root periphery. The present canal model in the periphery and the model which was previously proposed for the exudation in the stele (Katou et al. 1987), are organized into a model for radial transport across excised plant roots, in the light of anatomical and physiological knowledge of maize roots. The canal equations for both canals are numerically solved to give quite a good explanation for the observed exudation of maize roots. It is found that the regulation of solute transport has a primary importance in the regulation of water transport across excised roots. The internal cell pressure of the symplast adjusts the water absorption at the root periphery to the water secretion into the vessels. There seems no need for this explanation of the radial water transport across roots to assume cell membranes with low reflection coefficient or variable water permeability. It would seem that the apoplast wall layers play a crucial role in metabolic control of water transport in roots as well as in hypocotyls.Abbreviations J _s ^ex* the theoretically estimated rate of solute exudation per unit surface area of model maize roots - J that of volume exudation per unit surface area of model maize roots - the reflection coefficient of the cell membrane against solutes     

Mechanism of pressure-induced water flow across plant roots

Summary Pressure-induced non-linear water flow across plant roots was analyzed theoretically. The double-canal model of radial water transport shown lately explained accurately the observed non-linear water flow in maize roots. The driving force rather than the hydraulic permeability caused the non-linear flow of water. The conclusion was drawn that non-linearity in pressure-induced water flow was an inherent property of the apoplast canal system in roots. Net solute transport plays a primary part for water transport.     

A model for water transport in the stele of plant roots

Summary The mechanism of water movement across roots is, as yet, not well understood. Some workable black box theories have already been proposed. They, however, assumed unrealistic cell membranes with low values of , or were based on a poor anatomical knowledge of roots. The role of root stele in solute and water transport seems to be especially uncertain. An attempted explanation of the nature of root exudation and root pressure by applying the apoplast canal theory (Katou andFurumoto 1986 a, b) to transport in the root stele is given. The canal equations are solved for boundary conditions based on anatomical and physiological knowledge of the root stele. It is found that the symplast cell membrane, cell wall and net solute transport into the wall apoplast are the essential constituents of the canal system. Numerical analysis shows that the canal system enables the coupled transport of solutes and water into a xylem vessel, and the development of root pressure beyond the level predicted by the osmotic potential difference between the ambient medium and the exudate. Observations on root exudation and root pressure previously reported seem to be explained quite well. It is concluded that the movement of water in the root stele although apparently active is essentially osmotic.Abbreviations J _v ^ex volume exudation per root surface - J₀ non-osmotic exudation - L^r overall radial hydraulic conductivity of an excised root - reflection coefficient - C_s difference in the osmotic concentration between the bathing medium and the exudate - R gas constant - T absolute temperature - C_K molar concentration of K⁺ - C_Cl molar concentration of Cl^– - C_j molar concentration of ion species j - P_j membrane permeability of ion j - z_j valence of ion j - F Faraday constant - V_ix intracellular electric potential with reference to the canal     

A theoretical study of the distribution of substances around roots resulting from simultaneous diffusion and mass flow

Summary The change in concentration of a solute in soil, moving near the surface of a root by both mass flow and diffusion, has been calculated by a numerical method with a computer. The effect of change in the plant controlled variables v₀ (the solvent flux at the root surface) and k (the root absorbing power), and the soil variables b (the buffer power) and D (the diffusion coefficient) are described in turn.The concentration at the root surface, relative to the undisturbed soil solution, approaches a limiting value v₀/k. As v₀ is increased, the limiting value is approached more rapidly, and the zone of disturbance is more compressed. A steady state is reached if r₀v₀/bD>2, but if r₀v₀/bD<2 the disturbance continues to spread outwards even though the concentration at the root surface has nearly attained its limiting value.As k is increased, other factors being constant, the limiting relative concentration at the root surface is approached more rapidly, but the spread of the disturbance away from the root is little affected.As Db is decreased, corresponding to a decrease in soil moisture, the concentration at the root surface reaches its limit more rapidly and the zone of disturbance is compressed.If, because of increase in the concentration at the root surface, the efficiency of root absorption declines, the relative concentration will exceed v₀/k, and may reach no limit — at least until the assumptions of the model used break down.     

Amphiphile diffusion in model membrane systems studied by pulsed NMR

The translational diffusion of the amphiphilic molecules in a number of lyotropic liquid crystalline phases has been measured with the pulsed NMR pulsed magnetic field gradient method. The amphiphiles studied were soaps, monoglycerids and lecithins. Measurements were performed both for oriented lamellar and for cubic phases. The order of magnitude of the diffusion coefficients was found to be the same as in neat liquids of analogous compounds. It was also found that the difussion coefficient depend markedly on the amphiphile end group in a way that parallels the area per polar head group as determined in X-ray studies. When corrections for geometrical factors has been made the diffusion rate is approximately equal in cubic and lamellar phases containing the same amphiphile.     

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.     

The supply of nutrient ions by diffusion to plant roots in soil

Summary Observation of soil grown roots of rye-grass shows that an approximately cylindrical volume of soil, the root hair cylinder, is densely occupied by root hairs. Estimates are given of the concentration of labile and solution potassium within the root hair cylinder during experiments measuring potassium uptake from two soils by single roots. Calculations, using a diffusion model, suggest that labile potassium concentrations may be reduced to between 99.3 and 53 per cent of the initial, depending on the diffusion characteristics of the soil and nutrient demand by the root. Of the total potassium absorbed by a root in 4 days, the proportion which is supplied from within the root hair cylinder is small (0.8 to 6.3 per cent) indicating that diffusion to the root from the soil outside the root hair cylinder is of paramount importance. When root demand is high, diffusion appears to limit uptake to between 71 and 59 per cent of that which roots of comparable physiology would be expected to absorb from stirred solution of the same concentration. Nevertheless, the presence of root hairs is calculated to have enhanced uptake by up to 77 per cent compared with roots without hairs because they virtually increase the root diameter. Diffusion does not appear to be a limiting factor when root demand is low and hairs can then add little to the efficiency of the root system in potassium absorption.     

The supply of nutrient ions by diffusion to plant roots in soil

Summary Measurements were made of the diffusion of P³²-labelled phosphate to single roots of onion, leek and rye-grass growing in an Upper Greensand sandy loam (UGS) and a Coral Rag Clay (CRC) to which different amounts of phosphate had been added. Concentration-dependent diffusion coefficients for phosphate ions in the soils were calculated from phosphate desorption isotherms in calcium chloride. The experimental uptake by roots of known dimensions was compared with supply expected by diffusion to a cylindrical model root of the same dimensions. Allowance was made for absorption by the root hairs on rye-grass roots. Phosphate absorption by a cm length of intact root was found to continue for at least 16 days for onion, 10 days for leek and 5 days for rye-grass. Over a wide range of conditions (phosphate concentrations, soils, plant species), experimental uptake was close to the maximum calculated to be possible for the diffusion model except on one soil at a high level of phosphate. Although the concentration of phosphate in the soil solution at the root boundary appeared to be reduced to a small fraction of the initial concentration, because of the extreme non-linear form of the desorption isotherm less than 1/2 of the P³² exchangeable pool of P was considered to contribute to diffusion. Phosphate uptake by rye grass could only be accounted for if the root hairs were active. Although only a small fraction of the uptake is derived from inside the root hair cylinder, this increases the efficiency of the central root 2.3 fold by providing a zone close to the central root through which phosphate moves very readily.     

Tuned in: plant roots use sound to locate water

It was recently suggested that beta diversity can be partitioned into contributions of single sites to overall beta diversity (LCBD) or into contributions of individual species to overall beta diversity (SCBD). We explored the relationships of LCBD and SCBD to site and species characteristics, respectively, in stream insect assemblages. We found that LCBD was mostly explained by variation in species richness, with a negative relationship being detected. SCBD was strongly related to various species characteristics, such as occupancy, abundance, niche position and niche breadth, but was only weakly related to biological traits of species. In particular, occupancy and its quadratic terms showed a very strong unimodal relationship with SCBD, suggesting that intermediate species in terms of site occupancy contribute most to beta diversity. Our findings of unravelling the contributions of sites or species to overall beta diversity are of high importance to community ecology, conservation and bioassessment using stream insect assemblages, and may bear some overall generalities to be found in other organism groups.     

Accounting for diffusion in agent based models of reaction-diffusion systems with application to cytoskeletal diffusion

Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface.     

Derivation of general equations describing tracer diffusion in any two-compartment tissue with application to ionic diffusion in cylindrical muscle bundles

A set of generalized diffusion equations have been derived which describe radioactive tracer movement in any tissue that can be modeled as a distributed two-compartment system. These equations have been applied to ionic tracer movement in cylindrical muscle bundles, and the boundary conditions used correspond to experimental conditions during various ionic tracer diffusion experiments on cardiac papillary muscles. Specifically, solutions were obtained for extra- and intracellular tracer washout as well as for the extra- and intracellular steady-state tracer diffusion experiments of Weidmann (1966). These solutions are presented in series form as well as in graphical form and are compared with the corresponding experimental data. A comparison of these solutions with those obtained using simple exponential kinetics is presented, and it is shown that there is a marked discrepancy between these two methods of analysis for bundles of any appreciable diameter.     

A gauge to measure the mass flow rate of water in trees

A gauge that measures the mass flow rate of water in a growing tree is described. The gauge consists of an electric band heater wrapped around a section of the stem, a temperature controller that switches the current to the heater on and off so as to maintain a constant temperature rise across the heated section, and a timer to record the total time for which the heater is switched on. An energy balance shows the mass flow of water to be proportional to the time of operation of the heater. The magnitude of measurement errors is estimated using dimensional analysis and a numerical model. Experimental measurements of the flow rate of water in a tree using the gauge agree well with its recorded loss of weight.     

Radial migration of DNA molecules in cylindrical flow. II. The non-draining model and possible application to fractionation

The radial-migration calculation of the preceding paper is extended to the non-draining polymer. The results show an inward radial velocity that depends on the 5/2 power of the molecular weight, assuming gaussian statistics for the chain. This sensitivity to size serves as the basis for a method of separating DNA molecules in solution according to their size. Normal stress (Weissenberg) effects are also discussed.     

The application of mass spectrometry to membrane proteomics

Membrane proteins perform some of the most important functions in the cell, including the regulation of cell signaling through surface receptors, cell-cell interactions, and the intracellular compartmentalization of organelles. Recent developments in proteomic strategies have focused on the inclusion of membrane proteins in high-throughput analyses. While slow and steady progress continues to be made in gel-based technologies, significant advances have been reported in non-gel shotgun methods using liquid chromatography coupled to mass spectrometry (LC/MS). These latter strategies facilitate the identification of large numbers of membrane proteins and modifications, and have the potential to provide insights into protein topology and orientation in membranes.     

Kinetics of partly diffusion controlled reactions XXIV: Unidimensionalization of diffusion in cylindrical symmetry systems: Applications to membranes

We show that it is possible to change the space of diffusion to determine the diffusion controlled apparent rate constant of reaction k_a (t). The most important result is that k_a (t) can be always expressed by a simple law which will be used for reactions in an infinite plane to an infinite 3D spherical space.