On the mechanism of anion uptake by plant roots

Summary The effect of the valence of the associated cation on Cl^–-uptake by excised barley roots grown in CaSO₄ has been studied at 26°, 6° and 2°C. The uptake of Cl^– relative to that of the associated cation was found to increase in the order: trivalent > divalent > monovalent. This was explained on the expected effect of the cation on the negative charge and potential of root surfaces. A lyotropic order was observed in case of monovalent cations, whereas divalent cations showed no such order. The order observed in Cl^–-uptake from chloride solutions of monovalent cations is associated with the ability of the absorbed cation to remove Ca and Mg from the roots. Li⁺ behaved similar to divalent cations in affecting the relative Cl^–-uptake from LiCl.As to the effect of temperature on the uptake of Cl^– and associated cation, it appears that Cl^– is not taken up to any great extent at 2°C whereas cations are still adsorbed at this low temperature. This has been explained on the assumption of the presence of negative adsorption spots on the root surface which can hold cations but not anions. It appears that Cl^–-uptake by roots requires the expenditure of energy to overcome repulsion arising from the negative surface.This work is supported by AEC contract AT (11-1) — 34 project 55.     

Binding of Dissolved Strontium by Micrococcus luteus

Resting cells of Micrococcus luteus have been shown to remove strontium (Sr) from dilute aqueous solutions of SrCl₂ at pH 7. Loadings of 25 mg of Sr per g of cell dry weight were achieved by cells exposed to a solution containing 50 ppm (mg/liter) of Sr. Sr binding occurred in the absence of nutrients and did not require metabolic activity. Initial binding was quite rapid (<0.5 h), although a slow, spontaneous release of Sr was observed over time. Sr binding was inhibited in the presence of polyvalent cations but not monovalent cations. Ca and Sr were bound preferentially over all other cations tested. Sr-binding activity was localized on the cell envelope and was sensitive to various chemical and physical pretreatments. Bound Sr was displaced by divalent ions or by H⁺. Other monovalent ions were less effective. Bound Sr was also removed by various chelating agents. It was concluded that Sr binding by M. luteus is a reversible equilibrium process. Both ion exchange mediated by acidic cell surface components and intracellular uptake may be involved in this activity.     

Vanadium Uptake by Plants: Absorption Kinetics and the Effects of pH, Metabolic Inhibitors, and Other Anions and Cations

The kinetics of vanadium absorption by excised barley (Hordeum vulgare L., cv. Eire) roots were investigated with respect to ionic species of V in solution, time and concentration dependence, Ca sensitivity, and interaction with various anions, cations, and pH levels. The role of metabolism in V absorption was also studied using anaerobic treatment (N₂ gas) and chemical inhibitors (NaN₃, KCN, or 2,4-dinitrophenol). Approximately one-third of the labeled V initially taken up by excised roots was desorbed to a constant level after 45 min in unlabeled V solutions. The rate of absorption of labeled V from 5 μm NH₄VO₃ solutions containing 0.5 mm CaSO₄ was constant for at least 3 hours. Omission of Ca resulted in a 72% reduction in V uptake when compared to controls with 0.5 mm CaSO₄. The rate of uptake of V was highest at pH 4 but dropped to a very low level at pH 10. It was relatively constant between the pH levels of 5 and 8 at which the VO₃⁻ ion is the predominant ionic species in solution. The rate of absorption of V was followed as a function of concentrations from 0.5 to 100 μm NH₄VO₃. It was found to be a linear function of concentration and did not follow saturation kinetics. Absorption experiments carried out with labeled V from either N_aVO₃ or NH₄VO₃ sources gave similar results. No anion studied (i.e. HPO₄²⁻, HAsO₄²⁻, MoO₄²⁻, SeO₄²⁻, SeO₃²⁻, CrO₄²⁻, BO₃³⁻, No₃⁻, and Cl⁻) interfered appreciably (i.e. less than 30% inhibition) with the absorption of labeled V. Anaerobic treatment of absorption solution with N₂ gas did not inhibit V absorption by excised roots. The results obtained using chemical inhibitors were not consistent. It was concluded that V is not actively absorbed by excised barley roots.     

Relationship between Rapid, Firm Adhesion and Long-Term Colonization of Roots by Bacteria

For rhizobacteria to exert physiological effects on plant growth, the bacteria must first effectively colonize the root surface. To examine the relationship between long-term colonization of root systems and adherence to roots in the short term, a binding assay was developed. Adherence was determined by incubating roots of intact radish seedlings with bacteria, washing and homogenizing the roots, and dilution plating the resulting homogenate. Irreversible binding of bacteria was rapid, reaching half-maximum by 5 min. All of the rhizosphere bacteria tested showed similar, concentration-dependent binding (ranging from 10⁴ to 10⁸ CFU/ml), as well as long-term colonization of radish roots under sterile conditions. Escherichia coli, which is not a root colonizer, showed about 10-fold less binding, but still demonstrated concentration-dependent binding and rapid kinetics of adherence at high concentrations (10⁶ to 10⁸ CFU/ml). The bacteria tested were very different with respect to source or habitat and plant response, yet they showed similar concentration-dependent binding. There was no correlation between the relative hydrophobicities of the cell surfaces of strains and the adherence of the strains to roots. Binding of Pseudomonas fluorescens E6-22 was promoted by divalent cations (Ca²⁺ and Mg²⁺) at concentrations of 5 to 10 mM, whereas monovalent cations (Na⁺ and K⁺) had little effect; electrostatic phenomena may partially explain adherence in the short term, an important prelude to long-term colonization of root surfaces.     

Temporal Variation of Denitrification Activity in Plant-Covered, Littoral Sediment from Lake Hampen, Denmark

Diel and seasonal variations in denitrification were determined in a littoral lake sediment colonized by the perennial macrophyte Littorella uniflora (L.) Aschers. In the winter, the activity was low (5 μmol of N m⁻² h⁻¹) and was restricted to the uppermost debris layer at a depth of 0 to 1 cm. By midsummer, the activity increased to 50 μmol of N m⁻² h⁻¹ and was found throughout the root zone to a depth of 10 cm. The root zone accounted for as much as 50 to 70% of the annual denitrification. A significant release of organic substrates from the roots seemed to determine the high activities of root zone denitrification in the summer. The denitrification in the surface layer and in the root zone formed two distinct activity zones in the summer, when the root zone also contained nitrification activity, as indicated from the accumulations of NO₃⁻. Light conditions inhibited denitrification in both the surface layer and the upper part of the root zone, suggesting that a release of O₂ by benthic algae and from the roots of L. uniflora controlled a diel variation of denitrification. In midsummer, the rate of denitrification in both the surface layer and the upper part of the root zone was limited by NO₃⁻. In the growth season, there was evidence for a significant population of denitrifiers closely associated with the root surface.     

Cation Penetration through Isolated Leaf Cuticles

The rates of penetration of various cations through isolated apricot Prunus armeniaca L. leaf cuticles were determined. Steady state rates were measured by using a specially constructed flow-through diffusion cell. The penetration rates of the monovalent cations in group IA followed a normal lyotropic series, i.e., CS⁺ ≥ Rb⁺ > K⁺ > Na⁺ > Li⁺. The divalent cations all penetrated through the cuticle more slowly than the monovalent cations. Comparison of the relative values of k (permeability coefficient) and D (diffusion coefficient) indicates that the penetration of ions through isolated cuticles took place by diffusion and was impeded by charge interactions between the solute and charge sites in the penetration pathway. Cuticular penetration rates of K⁺ and H₂O at pH above 9 were of similar magnitude. At pH 5.5 H₂O penetration was not affected but that of K⁺ was greatly reduced. From this observation and from data on cuticle titration and ion adsorption studies, we hypothesize that cuticular pores are lined with a substance (perhaps a protein) which has exposed positively charged sites.     

Effects of monovalent cations and anions on ADP-induced aggregation of bovine platelets, and mechanism thereof

The effects of monovalent cations - inorganic alakali metal cations and organic quanternary ammonium cations - and monovalent inorganic anions on ADP-induced aggregation of bovine platelets were investigated. In the presence of K⁺, Rb⁺, Cs⁺, choline or tetramethylammonium, aggeregation proceeded. However, aggregation was markedly restricted in media containing Li⁺, Na⁺, tetrabutylammonium or dimethyldibenzylammonium. With anions, aggregation proceeded in the order Cl⁻ > Br⁻ > I⁻ > Clo₄⁻ > SCN⁻. The effects of cations significantly depended on Ca²⁺ concentration, whereas those of the anions depended little of Ca²⁺. Anions such as SCN⁻ and ClO₄⁻ markedly decreased the fluorescence of the surface charge probe 2-p-tuluidinylnaphthalene-6-sulfonate, whereas cations had less pronouced effects. The relative effects of the anions on the fluorescence were consistent with their relative inhibitory effects on aggregation. These results suggest that inhibition of platelet aggregation by the anions is due to a change in the surface change of the platelet plasma membrane. On the other hand, kinetic analysis suggests that the effects of monovalent cations on platelet aggregation are due to their competition with Ca²⁺ during the process of aggregation.     

Adenosine triphosphatase from soybean callus and root cells

The ATPase activity of a membrane fraction from soybean (Glycine max L.) root and callus cells, presumed to be enriched in plasma membrane, has been characterized with respect to ion stimulation, pH requirement, and nucleotide specificity. The enzyme from both sources was activated by divalent cations (Mg²⁺ > Mn²⁺ > Zn²⁺ > Ca²⁺ > Sr²⁺) and further stimulated by monovalent salts. Preparations from root cells were stimulated by monovalent ions according to the sequence: K⁺ > Rb⁺ > Choline⁺ > Na⁺ > Li⁺ > NH₄⁺ > Cs⁺ > tris⁺. Membrane preparations from callus cells showed similar stimulatory patterns except for a slight preference for Na⁺ over K⁺. No synergism between K⁺ and Na⁺ was found with preparations from either cell source.     

Properties of the kainate channel in rat brain mRNA injected Xenopus oocytes: ionic selectivity and blockage

The properties of kainate receptor/channels were studied in Xenopus oocytes injected with mRNA that was isolated from adult rat striatum and cerebellum and partially purified by sucrose gradient fractionation. Kainate (3–1000 µ.M) induced a smooth inward current that was competitively inhibted by gamma-D-glutamyl-aminomethanesulfonate (GAMS, 300 µM). In striatal mRNA-injected oocytes, the kainate current displayed nearly linear voltage-dependence and mean reversal potential (E_r) of -6.1 ± 0.5 mV In cerebellar mRNA-injected oocytes; E_r was nearly identical (-5.1 ± 1.2 mV) but there was marked inward rectification of the kainate current. Ion replacement studies reveal that the kainate channel is selective for cations over anions, but relatively non-selective among small monovalent cations. Large monovalent cations such as tetrabutylammonium are impermeant and induce a non-competitive block of kainate current that is strongly voltage-dependent. Divalent cations are relatively impermeant in the kainate channel and Cd⁺⁺ and other polyvalent metals were shown to block kainate current by a mechanism that is only weakly voltage-dependent. A model of the kainate channel is proposed based upon these observations.     

Localization of Nitrate Absorption and Translocation within Morphological Regions of the Corn Root

The absorption of NO₃⁻ was characterized in six regions of a 7-d-old corn root (Zea mays L. cv W64A × W182E) growing in a complete nutrient solution. Based on changing rates of ¹⁵N accumulation during 15-min time courses, translocation of the concurrently absorbed N through each region of the intact root was calculated and distinguished from direct absorption from the medium. Of the ¹⁵N accumulated in the 5-mm root tip after 15 min, less than 15 and 35% had been absorbed directly from the external solution at 0.1 and 10 mm NO₃⁻ concentration of the external solution, respectively. The characterization of the apical portion of the primary root as a sink for concurrently absorbed N was conconfirmed in a pulse-chase experiment that showed an 81% increase of ¹⁵N in the 5-mm root tip during a 12-min chase (subsequent to a 6-min labeling period). The lateral roots alone accounted for 60% of root influx and 70% of 15-min whole root ¹⁵N accumulation at either 0.1 or 10 mm. NO₃⁻ concentration of the external solution. Because relatively steady rates of ¹⁵N accumulation in the shoot were reached after 6 min, the rapidly exchanging pools in lateral roots must have been involved in supplying ¹⁵N to the shoot. The laterals and the basal primary root also showed large decreases (24 and 17%) in ¹⁵N during the chase experiment, confirming their role in rapid translocation.     

A kinetic study of phosphorus absorption by excised maize roots from flowing solutions influenced by 2,4 dinitrophenol and viscosity of solution

The effect of 2,4 dinitrophenol and increased viscosity of the absorption solution on the absorption of phosphorus by excised roots of maize plants was investigated. The concentration of the solution was 0.1 mM KH₂PO₄, the activity of³²P was 52 µCi l^-1. The temperature of the absorption solution was 26 °C, pH 5.5, aeration prior to the experiment. There was 11 of solution for every 1 g of roots. Two basic variants were used for comparison: with non-flowing solution and with solution flow (circulation) of 0.162 cm s^-1, respectively. In all cases, 2,4 dinitrophenol reduced the rate of phosphorus absorption by the roots regardless of the mechanism of phosphorus supply to the roots (diffusion, mass flow). If it is proved that 2,4 dinitrophenol inhibits the active uptake of phosphorus, then the uptake of phosphorus by the roots increased under the influence of mass flow will be active,i.e., connected with energy metabolism. Raising the viscosity of the absorption solution 3.3 times over that of water by means of potato starch substantially reduced the absorption of the phosphorus transported to the absorption zone by diffusion and practically did not affect the rate of absorption, or the amount of anions transported to the absorption area by mass flow.     

Studies on molybdenum absorption and transport in bean and rice

The patterns of molybdenum (MoO₄²⁻) absorption and transport were investigated in intact bean (Phaseolus vulgaris L.) and rice (Oryza sativa L. cv. I.R.8) plants. The mobility of MoO₄²⁻ absorbed by roots and by leaves was compared with that of a freely mobile element, Rb⁺. Although MoO₄²⁻ absorption by bean roots was nearly as high as that of Rb⁺, its transport to the shoot was considerably less. When MoO₄²⁻ was fed to one of the primary leaves, most of it was transported to the stem and root. Evidence obtained here showed that MoO₄²⁻ was mobile. Experiments with intact rice seedlings revealed large differences in the absorption and transport of MoO₄²⁻ between the plants grown in CaSO₄ and those in Hoagland solution. Molybdate uptake by excised rice roots was suggested to be an active process since it was greatly inhibited by a metabolic inhibitor. The presence of Mn²⁺, Zn²⁺, Cu²⁺, CI⁻, or SO₄²⁻ in the absorption medium reduced MoO₄²⁻ uptake which was markedly enhanced by the presence of Fe²⁺.     

Determination of cation exchange capacity of ryegrass roots by summing exchangeable cations

Cations were desorbed from root exchange sites of ryegrass (Lolium multiflorum Lam. cvs. Gulf, Marshall, Urbana, and Wilo) using BaCl₂, BaCl₂-triethanolamine, NH₄OAc, and KCl. Results were analysed using multivariate analysis of variance. Ba²⁺-containing desorbents displaced more Ca²⁺ while monovalent desorbents displaced more exchangeable monovalent cations. The sum of adsorbed cations was significantly correlated with root exchange capacity (CEC) as determined by the H⁺ titration procedure, although slightly larger values were obtained with all desorbents. Lower CEC values were obtained for ryegrass cultivars less sensitive to Al.     

Electrostatic Changes in Lycopersicon esculentum Root Plasma Membrane Resulting from Salt Stress

Salinity-induced alterations in tomato (Lypersicon esculentum Mill. cv Heinz 1350) root plasma membrane properties were studied and characterized using a membrane vesicle system. Equivalent rates of MgATP-dependent H⁺-transport activity were measured by quinacrine fluorescence (ΔpH) in plasma membrane vesicles isolated from control or salt-stressed (75 millimolar salt) tomato roots. However, when bis-[3-phenyl-5-oxoisoxazol-4-yl] pentamethine was used to measure MgATP-dependent membrane potential (ΔΨ) formation, salt-stressed vesicles displayed a 50% greater initial quench rate and a 30% greater steady state quench than control vesicles. This differential probe response suggested a difference in surface properties between control and salt-stressed membranes. Fluorescence titration of vesicles with the surface potential probe, 8-anilino-1-napthalenesulphonic acid (ANS) provided dissociation constants (K_d) of 120 and 76 micromolar for dye binding to control and salt-stressed vesicles, respectively. Membrane surface potentials (Ψ_o) of−26.0 and −13.7 millivolts were calculated for control and salt-stressed membrane vesicles from the measured K_d values and the calculated intrinsic affinity constant, K_i. The concentration of cations and anions at the surface of control and salt-stressed membranes was estimated using Ψ_o values and the Boltzmann equation. The observed difference in membrane surface electrostatic properties was consistent with the measured differences in K⁺-stimulated kinetics of ATPase activity between control and salt-stressed vesicles and by the differential ability of Cl⁻ ions to stimulate H⁺-transport activity. Salinity-induced changes in plasma membrane electrostatic properties may influence ion transport across the plasma membrane.     

Relationships between Root Temperature and the Transport of Ammonium and Nitrate Ions by Italian and Perennial Ryegrass (Lolium multiflorum and Lolium perenne)

At root temperature below 14 C the absorption of ¹⁵N from NH₄⁺ greatly exceeded that from NO₂⁻ by tillers of Lolium multiflorum and Lolium perenne under conditions where pH, external concentration, plant N status, and pretreatment temperature were varied. There was a marked increase in the temperature sensitivity of NO₃⁻ transport below 14 C, irrespective of the temperature at which plants were grown previously. A marked increase in the temperature sensitivity was also seen for NH₄⁺ transport, but this occurred at the lower temperature of 10 C. Pretreatment of roots at 8 C lowered this still further to 5 C. Above and below these transition temperatures the Q₁₀ values for NO₃⁻ and NH₄⁺ transport were similar. Thus, the increased absorption of NH₄⁺ relative to NO₃⁻ at low temperatures seems to be related primarily to the difference in transition temperatures.     

Interactive effects of Al, h, and other cations on root elongation considered in terms of cell-surface electrical potential

The rhizotoxicities of Al³⁺ and of La³⁺ to wheat (Triticum aestivum L.) were similarly ameliorated by cations in the following order of effectiveness: H⁺ ≈ C³⁺ > C²⁺ > C¹⁺. Among tested cations of a given charge, ameliorative effectiveness was similar except that Ca²⁺ was slightly more effective than other divalent cations and H⁺ was much more effective than other monovalent cations. H⁺ rhizotoxicity was also ameliorated by cations in the order C³⁺ > C²⁺ > C¹⁺. These results suggest a role for cell-surface electrical potential in the rhizotoxicity of Al³⁺, La³⁺, H⁺, and other toxic cations: negatively charged cell surfaces of the root accumulate the toxic cations, and amelioration is effected by treatments that reduce the negativity of the cell-surface electrical potential by charge screening or cation binding. Membrane-surface activities of free Al³⁺ or La³⁺ computed according to a Gouy-Chapman-Stern model correlated well with growth inhibition, which correlated only poorly with Al³⁺ or La³⁺ activities in the external medium. The similar responses of Al-intoxicated and La-intoxicated roots to ameliorative treatments provide evidence that Al³⁺, rather than AlOH²⁺ or Al(OH)₂⁺, is the principal toxic species of mononuclear Al. Comparisons of the responses of Al-sensitive and Al-tolerant wheats to Al³⁺ and to La³⁺ did not support the hypothesis that varietal sensitivity to Al³⁺ is based upon differences in cell-surface electrical potential.     

A kinetic study of phosphorus absorption by excised maize roots from flowing solutions with different phosphorus concentrations

The effect of two different mechanisms of phosphorus ion transport from the nutrient solution volume to the surface areas of excised maize roots was studied under concentrations ranging from 0.01 mM to 50.0 mM KH₂PO₄. A modified technique of study of kinetic ion absorption was used. In the control series, the roots were placed in absorption solution without flow (the dominant mechanism of ion transport to the roots being diffusion), while in the experimental series the absorption solution was flowing round the roots at a rate of 0.162 cm s^?1 (the dominant mechanism of ion transport to the roots being mass flow). The rate of phosphorus absorption by the roots from flowing solutions was highly significantly increased at all concentrations of absorption solution except for the 50.0 mM KH₂PO₄ concentration. The increase in phosphorus absorption in the case of 50.0 mM KH₂PO₄ concentration was non-significant due to the fact that the high concentration of phosphorus together with the diffusion of phosphorus ions ensured a sufficient supply of phosphorus to the roots, covering the requirement for their uptake. The results point to the need for an analysis of environmental factors to be carried out in studying ion absorption kinetics, and reveal the inadequacy of methods usually employed in such investigations, in particular with respect to the homogeneity of the nutrient solution in the whole of its volume and especially round the roots.     

Relationship of Cell Sap pH to Organic Acid Change During Ion Uptake

Excised roots of barley (Hordeum vulgare, var. Campana) were incubated in KCl, K₂SO₄, CaCl₂, and NaCl solutions at concentrations of 10⁻⁵ to 10⁻² n. Changes in substrate solution pH, cell sap pH, and organic acid content of the roots were related to differences in cation and anion absorption. The pH of expressed sap of roots increased when cations were absorbed in excess of anions and decreased when anions were absorbed in excess of cations. The pH of the cell sap shifted in response to imbalances in cation and anion uptake in salt solutions as dilute as 10⁻⁵ n. Changes in cell sap pH were detectable within 15 minutes after the roots were placed in 10⁻³ n K₂SO₄. Organic acid changes in the roots were proportional to expressed sap pH changes induced by unbalanced ion uptake. Changes in organic acid content in response to differential cation and anion uptake appear to be associated with the low-salt component of ion uptake.     

Characterization of a proton-translocating ATPase in microsomal vesicles from corn roots

Sealed microsomal vesicles were prepared from corn (Zea mays, Crow Single Cross Hybrid WF9-Mo17) roots by centrifugation of a 10,000 to 80,000g microsomal fraction onto a 10% dextran T-70 cushion. The Mg²⁺-ATPase activity of the sealed vesicles was stimulated by Cl⁻ and NH₄⁺ and by ionophores and protonophores such as 2 micromolar gramicidin or 10 micromolar carbonyl cyanide p-trifluoromethoxyphenyl hydrazone (FCCP). The ionophore-stimulated ATPase activity had a broad pH optimum with a maximum at pH 6.5. The ATPase was inhibited by NO₃⁻, was insensitive to K⁺, and was not inhibited by 100 micromolar vanadate or by 1 millimolar azide.

Quenching of quinacrine fluorescence was used to measure ATP-dependent acidification of the intravesicular volume. Quenching required Mg²⁺, was stimulated by Cl⁻, inhibited by NO₃⁻, was insensitive to monovalent cations, was unaffected by 200 micromolar vanadate, and was abolished by 2 micromolar gramicidin or 10 micromolar FCCP. Activity was highly specific for ATP. The ionophore-stimulated ATPase and ATP-dependent fluorescence quench both required a divalent cation (Mg²⁺ ≥ Mn²⁺ > Co²⁺) and were inhibited by high concentrations of Ca²⁺. The similarity of the ionophore-stimulated ATPase and quinacrine quench and the responses of the two to ions suggest that both represent the activity of the same ATP-dependent proton pump. The characteristics of the proton-translocating ATPase differed from those of the mitochondrial F₁F₀-ATPase and from those of the K⁺-stimulated ATPase of corn root plasma membranes, and resembled those of the tonoplast ATPase.

     

Effect of Phloem-Translocated Malate on NO(3) Uptake by Roots of Intact Soybean Plants

In soybean (Glycine max L. Merr. cv Kingsoy), NO₃⁻ assimilation in leaves resulted in production and transport of malate to roots (B Touraine, N Grignon, C Grignon [1988] Plant Physiol 88: 605-612). This paper examines the significance of this phenomenon for the control of NO₃⁻ uptake by roots. The net NO₃⁻ uptake rate by roots of soybean plants was stimulated by the addition of K-malate to the external solution. It was decreased when phloem translocation was interrupted by hypocotyl girdling, and partially restored by malate addition to the medium, whereas glucose was ineffective. Introduction of K-malate into the transpiration stream using a split root system resulted in an enrichment of the phloem sap translocated back to the roots. This treatment resulted in an increase in both NO₃⁻ uptake and C excretion rates by roots. These results suggest that NO₃⁻ uptake by roots is dependent on the availability of shoot-borne, phloem-translocated malate. Shoot-to-root transport of malate stimulated NO₃⁻ uptake, and excretion of HCO₃⁻ ions was probably released by malate decarboxylation. NO₃⁻ uptake rate increased when the supply of NO₃⁻ to the shoot was increased, and decreased when the activity of nitrate reductase in the shoot was inhibited by WO₄²⁻. We conclude that in situ, NO₃⁻ reduction rate in the shoot may control NO₃⁻ uptake rate in the roots via the translocation rate of malate in the phloem.