Coupling in secondary transport. Effect of electrical potentials on the kinetics of ion linked co-transport.

In a previous paper kinetic equations of secondary active transport by cotransport have been derived. In the present paper these equations have been expanded by including the effect of an electrical potential difference in order to make them applicable to the more realistic systems of secondary active transport driven by the gradients of Na+ or H+. Thermodynamically an electrical potential difference is as a driving force fully exchangeable with an equivalent chemical potential difference. This is not necessarily so for the kinetics of co-transport. It is not always the same whether a given difference in electrochemical activity of the driver ion is mainly osmotic, i.e. due to difference in concentration, or electric, i.e. due to a difference in the electrochemical activity coefficient. In most cases a difference in concentration is more effective in driving co-transport than is an equivalent difference in electrical potential leading to the same difference in electrical activity. The effectiveness of the latter highly depends on the model, whether it is of the affinity type or of the velocity type, but also on whether the loaded or the unloaded carrier bears an electrical charge. With the same electrical potential difference co-transport is as a rule faster if the ternary complex rather than the empty carrier is charged. Also the "standard parameters", (see Glossary, page 62) Jmax and Km, of the overall transport respond differently to the introduction of an electrical potential difference, depending on the model. So an electrical potential difference will mostly affect Km if the loaded carrier is ionic, and mostly Jmax if the empty carrier is ionic, provided that the mobility of the loaded carrier is greater than that of the empty one. On the other hand, distinctive criteria between affinity type and velocity type models are partly affected by an electrical potential difference. If the translocation steps of loaded and unloaded carrier are no longer rate limiting for the overall transport, electrical effects on the transport rate are bound to vanish as does the activation by co-transport.     

Apparent cooperativity of amino acid transport in Halobacterium halobium: Effect of electrical potential

Active serine accumulation in cell envelope vesicles from Halobacterium halobium proceeds by co-transport with Na⁺ and can be induced by either transmembrane electrical potential or transmembrane Na⁺ concentration difference. It was shown earlier that in the former case the initial transport rate is a fourth-power function of the magnitude of the electrochemical potential difference of sodium ions, and in the latter, a second-power function. A possible interpretation of this finding is cooperativity of sodium-transporting sites in the transport carrier. When both kinds of driving force are imposed simultaneously on the vesicles, fourth-power dependence on the total potential difference of sodium ions is obtained, suggesting that the transport carrier is regulated by the electrical potential. Heat treatment of the vesicles at 48 ° partially inactivates transport and abolishes this effect of the electrical potential.     

Potassium activation of Na+-dependent leucine transport in brush-border membrane vesicles from rat jejunum

Na⁺-dependent leucine uptake was greater in potassium loaded brush-border membrane vesicles compared with controls. This effect was not mediated by an electrical potential difference, since it was still present in voltage-clamped conditions. Inhibition experiments indicate the same Na⁺-dependent leucine transport activity in the presence or in the absence of potassium. The affinity of sodium for the cotransporter was identical at 10 or 100 mM potassium. Leucine kinetics at different potassium concentrations showed a maximum 2.4-fold increase in V_max, while K_m was unaffected. The secondary plots of the kinetic results were not linear. This kinetic behaviour suggests that K⁺ acts as a non-essential activator of Na⁺-dependent leucine cotransport. A charge compensation of sodium-leucine influx is most probably a component of the potassium effect in the presence of valinomycin.     

Effect of theophylline and Na+ on methionine influx in Na+-depleted intestine

The unidirectional influx of methionine into the brush border epithelium of chicken jejunum has been studied. Tissues leached of Na⁺ transport methionine from a medium devoid of Na⁺ with reduced apparent affinity (K_t) and maximal flux (J_max). Addition of Na⁺ to the medium during a 1-min incubation with substrate, or during a 30-min preincubation, restored K_t but affected J_max slightly. Theophylline was found to maintain J_max in the absence of Na⁺. Essentially complete restoration of K_t and J_max could be attained when theophylline-treated tissue was exposed to Na⁺ for 30 min. Influx from a Na⁺ medium was unaffected by theophylline pretreatment in Na⁺-containing buffer. K_t was increased without an effet upon J_max when influx was studied from choline medium following preincubation in Na⁺.Modifiers of tissue cyclic AMP levels were investigated in conjunction with theophylline. Histamine and carbachol were found to inhibit theophylline-stimulated transport. Secretin was found to stimulate influx in Na⁺-leached tissue, but did not potentiate the theophylline effect. Amino acids in the incubation medium inhibited theophylline-stimulated influx, whereas preloaded lysine or methionine had no effect.The results are interpreted in terms of a model which envisions roles for cellular and external Na⁺ and for cyclic AMP in the activation and regulation of amino acid transport in intestine.     

Interaction of glycylglycine and Na+ at the mucosal border of Guinea-pig small intestine: A non-mutual stimulation of transport

Sodium-dependence of glycylglycine (Gly-Gly) influx and stimulation of Na⁺ transport by Gly-Gly were studied in everted sacs, sheet preparations and brush-border membrane vesicles isolated from guinea-pig ileum. Gly-Gly influx was found to be independent of the presence of Na⁺, while Na⁺ transport was stimulated by Gly-Gly as evidenced by increases in transmural potential difference (PD_t), short-circuit current (I_sc) and Na⁺ influx. The change in PD_t (ΔPD_t) induced by Gly-Gly was a saturable function of Gly-Gly concentration, showing a Michaelis-Menten type relationship. The half-saturation concentration for Gly-Gly estimated from the electrical data was nearly identical with that estimated from influx data. At a constant Gly-Gly concentration the relationship between I_sc and Na⁺ concentration was sigmoid, and the Hill coefficient was 1.5. Kinetic analysis according to Garay Garrahan indicates that each Gly-Gly carrier has two equivalent non-interacting binding sites for Na⁺, and that translocation of Na⁺ occurs when the two Na⁺ sites on the carrier loaded with Gly-Gly are occupied by Na⁺. However, our results indicate that the resultant Na⁺ flow is not capable of stimulating Gly-Gly translocation.     

Evidence for amino Acid-h co-transport in oat coleoptiles

Microelectrode and tracer techniques were used to test for possible amino acid-H⁺ co-transport in coleoptiles of Avena sativa L. cv. “Garry.” The amino acid analogue α-aminoisobutyric acid (AIB) caused transient depolarization of the membrane potential. The absolute magnitude of the maximum depolarization was affected by the same factors that affected AIB transport. Both increased with higher concentrations of AIB, increased with higher acidities in the medium, and were enhanced by indoleacetic acid (which hyperpolarized the membrane potential). AIB transport was reduced as K⁺ concentrations in the medium were increased and by the metabolic inhibitor NaN₃, both of which reduce membrane potentials. Our data fit an amino acid-H⁺ co-transport model in which transport is controlled by both the membrane potential and proton concentration components of the chemical potential difference of protons across the coleoptile cell membrane.     

l-leucine, l-methionine, and l-phenylalanine share a Na+/K+-dependent amino acid transporter in shrimp hepatopancreas

Hepatopancreatic brush border membrane vesicles (BBMV), made from Atlantic White shrimp (Litopenaeus setiferus), were used to characterize the transport properties of ³H-l-leucine influx by these membrane systems and how other essential amino acids and the cations, sodium and potassium, interact with this transport system. ³H-l-leucine uptake by BBMV was pH-sensitive and occurred against transient transmembrane concentration gradients in both Na⁺- and K⁺-containing incubation media, suggesting that either cation was capable of providing a driving force for amino acid accumulation. ³H-l-leucine uptake in NaCl or KCl media were each three times greater in acidic pH (pH 5.5) than in alkaline pH (pH 8.5). The essential amino acid, l-methionine, at 20 mM significantly (p < 0.0001) inhibited the 2-min uptakes of 1 mM ³H-l-leucine in both Na⁺- and K⁺-containing incubation media. The residual ³H-l-leucine uptake in the two media were significantly greater than zero (p < 0.001), but not significantly different from each other (p > 0.05) and may represent an l-methionine- and cation-independent transport system. ³H-l-leucine influxes in both NaCl and KCl incubation media were hyperbolic functions of [l-leucine], following the carrier-mediated Michaelis–Menten equation. In NaCl, ³H-l-leucine influx displayed a low apparent K _M (high affinity) and low apparent J _max, while in KCl the transport exhibited a high apparent K _M (low affinity) and high apparent J _max. l-methionine or l-phenylalanine (7 and 20 mM) were competitive inhibitors of ³H-l-leucine influxes in both NaCl and KCl media, producing a significant (p < 0.01) increase in ³H-l-leucine influx K _M, but no significant response in ³H-l-leucine influx J _max. Potassium was a competitive inhibitor of sodium co-transport with ³H-l-leucine, significantly (p < 0.01) increasing ³H-l-leucine influx K _M in the presence of sodium, but having negligible effect on ³H-l-leucine influx J _max in the same medium. These results suggest that shrimp BBMV transport ³H-l-leucine by a single l-methionine- and l-phenylalanine-shared carrier system that is enhanced by acidic pH and can be stimulated by either Na⁺ or K⁺ acting as co-transport drivers binding to shared activator sites.     

Phloem Loading of Sucrose: pH Dependence and Selectivity

Autoradiographic, plasmolysis, and ¹⁴C-metabolite distribution studies indicate that the majority of exogenously supplied ¹⁴C-sucrose enters the phloem directly from the apoplast in source leaf discs of Beta vulgaris. Phloem loading of sucrose is pH-dependent, being markedly inhibited at an apoplast pH of 8 compared to pH 5. Kinetic analyses indicate that the apparent K_m of the loading process increases at the alkaline pH while the maximum velocity, V_max, is pH-independent. The pH dependence of sucrose loading into source leaf discs translates to phloem loading in and translocation of sucrose from intact source leaves. Studies using asymmetrically labeled sucrose ¹⁴C-fructosyl-sucrose, show that sucrose is accumulated intact from the apoplast and not hydrolyzed to its hexose moieties by invertase prior to uptake. The results are discussed in terms of sucrose loading being coupled to the co-transport of protons (and membrane potential) in a manner consistent with the chemiosmotic hypothesis of nonelectrolyte transport.     

Co-transport of anions and neutral solutes with cations across charged biological membranes. Effects of surrface potential on uptake kinetics

General rate equations have been developed for the co-transport of an anion with one or two cations across a negatively charged biological membrane. The effects of surface potential on the kinetical parameters of co-transport of monovalent anions with monovalent cations have been investigated in more detail. The influence of changes in the surface potential on ion uptake kinetics appears to be markedly affected by the properties of the co-transport system. This can be shown by investigating boundary cases of the general model, namely (a) random order of binding of the ions, (b) anion binds before cations, (c) cations bind before anion. Since the effects of the surface potential are different for these three cases, these effects might serve as (additional) discrimination criteria.The effect of the surface potential on anion uptake kinetics via a co-transport system to which two cations can bind is rather complex: maxima or minima of the apparent affinity constant K_m of anion uptake may occur. Not only the magnitude of the effect of changes in the surface potential, but also its direction (stimulation, inhibition), is influenced by the co-substrate (cation) concentration. Such effects may also occur if only one cation can bind to the translocator, provided that OH^? ions compete for the anion transport site.In addition, the case of co-transport of a neutral solute with a monovalent cation has been investigated. It has been shown, that monovalent cation has been investigated. It has been shown, that also in this case, the effect of changes in the surfaces potential is affected by the order of binding of the substrates to the translocator.     

Characteristics of Sodium Flux from Serosa to Mucosa in Rabbit Ileum

Sodium flux from serosa to mucosa, J_sm^Na in rabbit ileum in vitro has been studied as a function of applied electrical potential at equal sodium concentrations in the bathing solutions. The results indicate that J_sm^Na involves two pathways, a diffusional flux through a paracellular shunt pathway and a flux that is independent of applied potential and presumably involves a transcellular pathway. The latter pathway comprises approximately 25 % of J_sm^Na in Ringer's solution containing 10 mM glucose and 25 mM bicarbonate. It is stimulated significantly by theophylline unaffected by removal of glucose or addition of ouabain but is reduced to negligible values by anoxia, dinitrophenol, and replacement of all chloride and bicarbonate by isethionate. Thus this component of J_sm^Na has a number of characteristics consistent with involvement in a specific secretory process mediating an electrically neutral secretory transport of sodium plus anion from serosa to mucosa. In addition to stimulating this process, theophylline significantly reduced the permeability of the paracellular shunt pathway to sodium.     

Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data

The temperature dependence of C₃ photosynthesis is known to vary with growth environment and with species. In an attempt to quantify this variability, a commonly used biochemically based photosynthesis model was parameterized from 19 gas exchange studies on tree and crop species. The parameter values obtained described the shape and amplitude of the temperature responses of the maximum rate of Rubisco activity (V_cmax) and the potential rate of electron transport (J_max). Original data sets were used for this review, as it is shown that derived values of V_cmax and its temperature response depend strongly on assumptions made in derivation. Values of J_max and V_cmax at 25 °C varied considerably among species but were strongly correlated, with an average J_max : V_cmax ratio of 1·67. Two species grown in cold climates, however, had lower ratios. In all studies, the J_max : V_cmax ratio declined strongly with measurement temperature. The relative temperature responses of J_max and V_cmax were relatively constant among tree species. Activation energies averaged 50 kJ mol^?1 for J_max and 65 kJ mol^?1 for V_cmax, and for most species temperature optima averaged 33 °C for J_max and 40 °C for V_cmax. However, the cold climate tree species had low temperature optima for both J_max(19 °C) and V_cmax (29 °C), suggesting acclimation of both processes to growth temperature. Crop species had somewhat different temperature responses, with higher activation energies for both J_max and V_cmax, implying narrower peaks in the temperature response for these species. The results thus suggest that both growth environment and plant type can influence the photosynthetic response to temperature. Based on these results, several suggestions are made to improve modelling of temperature responses.     

The relationship of leaf photosynthetic traits – Vcmax and Jmax – to leaf nitrogen,leaf phosphorus,and specific leaf area: a meta‐analysis and modeling study

Great uncertainty exists in the global exchange of carbon between the atmosphere and the terrestrial biosphere. An important source of this uncertainty lies in the dependency of photosynthesis on the maximum rate of carboxylation (V_cmax) and the maximum rate of electron transport (J_max). Understanding and making accurate prediction of C fluxes thus requires accurate characterization of these rates and their relationship with plant nutrient status over large geographic scales. Plant nutrient status is indicated by the traits: leaf nitrogen (N), leaf phosphorus (P), and specific leaf area (SLA). Correlations between V_cmax and J_max and leaf nitrogen (N) are typically derived from local to global scales, while correlations with leaf phosphorus (P) and specific leaf area (SLA) have typically been derived at a local scale. Thus, there is no global-scale relationship between V_cmax and J_max and P or SLA limiting the ability of global-scale carbon flux models do not account for P or SLA. We gathered published data from 24 studies to reveal global relationships of V_cmax and J_max with leaf N, P, and SLA. V_cmax was strongly related to leaf N, and increasing leaf P substantially increased the sensitivity of V_cmax to leaf N. J_max was strongly related to V_cmax, and neither leaf N, P, or SLA had a substantial impact on the relationship. Although more data are needed to expand the applicability of the relationship, we show leaf P is a globally important determinant of photosynthetic rates. In a model of photosynthesis, we showed that at high leaf N (3 gm⁻²), increasing leaf P from 0.05 to 0.22 gm⁻² nearly doubled assimilation rates. Finally, we show that plants may employ a conservative strategy of J_max to V_cmax coordination that restricts photoinhibition when carboxylation is limiting at the expense of maximizing photosynthetic rates when light is limiting.     

A comparison of the effects of ouabain and 2-deoxy-d-glucose on the thermodynamic variables of the frog skin

Previous studies support the validity of a linear thermodynamic formalism relating the rates of active Na⁺ transport and oxygen consumption J_r to the electrical potential difference ΔΨ an the affinity α (negative free energy) of the metabolic driving reaction. The formulation was further tested in paired control and experimental hemiskins by the use of two inhibitors of Na⁺ transport. Ouabain, a specific inhibitor of the Na⁺ pump, might be expected to diminish the dependence of J_r on ΔΨ without affecting α, whereas 2-deoxy-d-glucose, a competitive inhibitor of glucose metabolism, should be expected to diminish α. Both inhibitors were used at concentrations adequate to depress Na⁺ transport (i.e. short-circuit current J_o) to some 50°_o of control level. Measurements were made of I_o and $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$, and the apparent value of the affinity α_app was calculated according to the thermodynamic formulation. Ouabain depressed $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$ without affecting α_app whereas 2-deoxy-d-glucose depressed α_app without affecting $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(αΨ)}$. The demonstration of these effects indicates the utility of the formalism.     

Accelerative exchange diffusion kinetics of glucose between blood and brain and its relation to transport during anoxia

An earlier study showed that unidirectional glucose transport from blood to brain decreases during perfusion with anoxic blood (Betz, A.L., Gilboe, D.D. and Drewes, L.R. (1974) Brain Res. 67, 307–316). Brain glucose levels also decrease during anoxia. Therefore, the present study was designed to investigate whether the decreased transport might be the result of decreased accelerative exchange diffusion when brain glucose levels are low.The rate of unidirectional transport into brain (v) of d-[6-³H]glucose was studied in 22 isolated, perfused dog brains by means of an indicator dilution technique using ²²Na as the intravascular reference. The kinetics of transport were determined over a range of blood glucose concentrations (S₁) at each of live different brain glucose levels (S₂). The existence of accelerative exchange diffusion for glucose was indicated by a decrease in the intercept (increase of apparent V) of a double reciprocal plot ($\text{1}\text{v}$ versus $\text{1}\text{S}{}_1$) as S₂ increased. This phenomenon is consistent with a model for facilitated diffusion in which the mobility of the loaded carrier is greater than that of the unloaded carrier. Although the data predict a decrease in glucose transport during anoxia, the predicted decrease (5%) is less than the observed decrease (35%). It is concluded that the simple mobile-carrier model for facilitated diffusion cannot, by itself, describe all properties of blood-brain glucose transport.     

The hypoxanthine transporter of Novikoff rat hepatoma cells exhibits directional symmetry and equal mobility when empty or substrate-loaded

The kinetics of hypoxanthine transport were measured in hypoxanthine phosphoribosyltransferase-deficient Novikoff cells by rapid kinetic techniques applying both zero-trans and equilibrium exchange protocols. The data indicate operation of a simple carrier with directional symmetry and equal mobility when substrate loaded and empty. Zero-trans influx and efflux were about equivalent and so were zero-trans influx and equilibrium exchange flux. The apparent Michaelis-Menten constant and maximum velocity were about 500 μM and 100 pmol/s per μl cell H₂O, respectively. The time courses of accumulation of radioactively labeled hypoxanthine at a concentration above the Michaelis-Menten constant differed noticeably in zero-trans and equilibrium exchange mode, but computer simulations showed that the difference is predicted by the symmetrical carrier model and does not reflect trans-stimulation.     

Estimation of photosynthesis parameters for a modified Farquhar–von Caemmerer–Berry model using simultaneous estimation method and nonlinear mixed effects model

The aims of this paper was to modify the photosynthesis model of Farquhar, von Caemmerer and Berry (FvCB) to be able to predict light dependency of the carboxylation capacity (V_c) and to improve the prediction of temperature dependency of the maximum carboxylation capacity (V_cmax) and the maximum electron transport rate (J_max). The FvCB model was modified by adding a sub-model for Ribulose-1,5-bisphosphate carboxylase (Rubisco) activation and validating the parameters for temperature dependency of V_cmax and J_max. Values of parameters for temperature dependency of V_cmax and J_max were validated and adjusted based on data of the photosynthesis response to temperature. Parameter estimation was based on measurements under a wide range of environmental conditions, providing parameters with broad validity. The simultaneous estimation method and the nonlinear mixed effects model were applied to ensure the accuracy of the parameter estimation. The FvCB parameters, V_cmax, J_max, α (the efficiency of light energy conversion), θ (the curvature of light response of electron transport), and R_d (the non-photorespiratory CO₂ release) were estimated and validated on a dataset from two other years. Observations and predictions matched well (R² = 0.94). We conclude that incorporating a sub-model of Rubisco activation improved the FvCB model through predicting light dependency of carboxylation rate; and that estimating V_cmax, J_max, α, θ, and R_d requires data sets of both CO₂ and light response curves.     

Intestinal nutrient transport in coho salmon (Oncorhynchus kisutch) and the effects of development,starvation, and seawater adaptation

Summary Intestinal nutrient transport in yearling coho salmon was characterized and adaptive changes in nutrient transport were described in relation to development, starvation, and environmental salinity. Salmon intestine exhibits a small transepithelial potential difference (TEP: –1.4 to 2.0 mV, mucosa ground) and low resistance (41 to 181 ohms·cm²) that varied with the region along the intestine, with starvation, and with environmental salinity. Addition of glucose or proline to the mucosal side of intestine caused a rapid increase in short-circuit current. Isotopic mucosalto-serosal net fluxes of glucose and proline were achieved across salmon intestine in the absence of transepithelial chemical or electrical gradients. A sleeve technique for measuring proline influx (Karasov and Diamond 1983a) was validated for use in salmon intestine. Comparison of total proline influx in different intestinal regions showed the following order (from highest to lowest rates): pyloric caeca anterior intestine > posterior intestine. Total proline influx was highest in April during the parr-smolt transformation.The kinetics of Na-dependent proline influx were altered by starvation and seawater adaptation. Starved fish exhibited a lowerK _t but similarJ _max in anterior intestine compared with values in fed fish. The effect of seawater adaptation on the kinetics of proline influx varied with the timing of entry into seawater, with length of seawater residence, and with season. Growth-inhibited SW stunts showed a reducedJ _max of proline influx compared with that of normal SW smolts.Abbreviations FW freshwater (-adapted) - SW seawater (-adapted) - TEP transepithelial potential difference - R transepithelial resistance - I _sc short-circuit current - P _a apparent passive permeability coefficient - J _max maximal influx - K _t half-saturation constant     

On the Mechanism of Sodium Extrusion across the Irrigated Gill of Sea Water-Adapted Rainbow Trout (Salmo gairdneri)

Sodium efflux (J_out^Na) across the irrigated trout gill was rapid in sea water (SW), but only about 25 % as large in fresh water (FW). The difference correlated with a change in the potential difference across the gill (TEP). The latter was about +10 mV (blood positive) in SW, but –40 mV in FW. Both flux and electrical data indicated that gills in this fish are permeable to a variety of cations including Na⁺, K⁺, Mg²⁺, choline, and Tris. They are less permeable to anions; P_Na:P_K:P_Cl was estimated to be 1:10:0.3, and P_Cl > P_gluconate. The TEP was shown to be a diffusion potential determined by these permeabilities and the extant ionic gradients in SW, FW as well as in other media. J_out^Na appeared to be diffusive in all of the experiments undertaken. Exchange diffusion need not be posited, and the question of whether there is an active component remains open.     

K-Cl cotransport in LK sheep erythrocytes: Kinetics of stimulation by cell swelling

Summary The effects of osmotic cell swelling were studied on the kinetics of Cl-dependent K⁺ influx, K–Cl cotransport, in erythrocytes from sheep of the low K⁺ (LK) phenotype. Swelling 25% stimulated transport by increasing maximum velocity (J _max) 1.5-fold and by increasing apparent affinity for external K (K _o ) nearly twofold. Dithiothreitol (DTT) was shown to be a partial, reversible inhibitor of K–Cl cotransport. It inhibited in cells of normal volume by reducingJ _max more than twofold: apparent affinity for K _o was increased by DTT, suggesting that DTT stabilizes the transporter-K _o complex. Cell swelling reduced the extent of inhibition by DTT:J _max was inhibited by only about one-third in swollen cells, and apparent affinity was only slightly affected. This result suggested that DTT does not act directly on the transporter, but on a hypothetical regulator, an endogenous inhibitor. Swelling relieves inhibition by the regulator, and reduces the effect of DTT. Reducing intracellular Mg²⁺, Mg _o , stimulated cotransport. Swelling of low-Mg²⁺ cells stimulated transport further, but only by raising apparent affinity for K _o nearly threefold:J _max was unaffected. Thus effects of swelling onJ _max and apparent affinity are separable processes. The inhibitory effects of Mg _o and DTT were shown to be additive, indicating separate modes of action. There appear to be two endogenous inhibitors: the hypothetical regulator, which holds affinity for K _o , low; and Mg _o , which affectsJ _max perhaps by holding some transporters in an inactive form. Swelling stimulates transport by relieving both types of inhibition.     

Energetics of Active Transport Processes

Discussions of active transport usually assume stoichiometry between the rate of transport J₊ and the metabolic rate J_r. However, the observation of a linear relationship between J₊ and J_r does not imply a stoichiometric relationship, i.e., complete coupling. Since coupling may possibly be incomplete, we examine systems of an arbitrary degree of coupling q, regarding stoichiometry as a limiting case. We consider a sodium pump, with J₊ and J_r linear functions of the electrochemical potential difference, -X₊, and the chemical affinity of the metabolic driving reaction, A. The affinity is well defined even for various complex reaction pathways. Incorporation of a series barrier and a parallel leak does not affect the linearity of the composite observable system. The affinity of some region of the metabolic chain may be maintained constant, either by large pools of reactants or by regulation. If so, this affinity can be evaluated by two independent methods. Sodium transport is conveniently characterized by the open-circuit potential (Δψ)_I=0 and the natural limits, level flow (J₊)_X+=0, and static head X⁰₊ = (X₊)_J+=0. With high degrees of coupling -X⁰₊/F approaches the electromotive force E_Na (Ussing); -X⁰₊/F cannot be identified with ((RT/F) ln f)_X+=0, where f is the flux ratio. The efficiency η = -J₊X₊/J_rA is of significance only when appreciable energy is being converted from one form to another. When either J₊ or -X₊ is small η is low; the significant parameters are then the efficacies ε_J+ = J₊/J_rA and ε_X+ = -X₊/J_rA, respectively maximal at level flow and static head. Leak increases both J₊ and ε_J+ for isotonic saline reabsorption, but diminishes -X⁰₊ and ε_X♀. Electrical resistance reflects both passive parameters and metabolism. Various fundamental relations are preserved despite coupling of passive ion and water flows.