A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.     

Electrogenic ion transport by Na+,K+-ATPase

Experimental data on the ion electrogenic transport by Na+,K+-ATPase available in the literature are analyzed. Special attention is paid to the measurements of unsteady-state electric currents initiated by alternating voltage or rapid introduction of the substrate. In the final part, a physical model of the Na+,K+-ATPase functioning is discussed. According to this model, active transport is carried out by opening and closing of the access channels used for the sodium and potassium exchange between solutions on either side of the membrane. The model explains most of the experimental data, although some details (the channel size, rates of individual transport steps) need further refinement.     

Electrogenesis in a model of "boundary transport" in the sodium pump]

An equation of the membrane potential (MP) was developed for a model of sodium pump when it was assumed that a macromolecule-carrier operated on the interior boundary of the membrane exchaning Na+i for K+ of membrane. These ions then moved downhill the electrochemical gradient inside the membrane. There are factors in the equation which indicate energetical consumtions for the ionic exchange. In was shown that an exchange of 3Na+ for 2K+ required 9,0 kkal/mole. The equation satisfactorily describes experimental values of MP during the electrogenic active transport. After all it was shown that an alteration of MP for 100 mV did not affect the operation of sodium pump i.e. the influence of outer electrical field was not detected.     

Solute transport process in intestinal epithelial cells

In rat small intestine, the active transport of organic solutes results in significant depolarization of the membrane potential measured in an epithelial cell with respect to a grounded mucosal solution and in an increase in the transepithelial potential difference. According to the analysis with an equivalent circuit model for the epithelium, the changes in emf's of mucosal and serosal membranes induced by active solute transport were calculated using the measured conductive parameters. The result indicates that the mucosal cell membrane depolarizes while the serosal cell membrane remarkably hyperpolarizes on the active solute transport. Corresponding results are derived from the calculations of emf's in a variety of intestines, using the data that have hitherto been reported. The hyperpolarization of serosal membrane induced by the active solute transport might be ascribed to activation of the serosal electrogenic sodium pump. In an attempt to determine the causative factors in mucosal membrane depolarization during active solute transport, cell water contents and ion concentrations were measured. The cell water content remarkably increased and, at the same time, intracellular monovalent ion concentrations significantly decreased with glucose transport. Net gain of glucose within the cell was estimated from the restraint of osmotic balance between intracellular and extracellular fluids. In contrast to the apparent decreases in intracellular Na+ and K+ concentrations, significant gains of Na+ and K+ occurred with glucose transport. The quantitative relationships among net gains of Na+, K+ and glucose during active glucose transport suggest that the coupling ratio between glucose and Na+ entry by the carrier mechanism on the mucosal membrane is approximately 1:1 and the coupling ratio between Na+-efflux and K+-influx of the serosal electrogenic sodium pump is approximately 4:3 in rat small intestine. In addition to the electrogenic ternary complex inflow across the mucosal cell membrane, the decreases in intracellular monovalent ion concentrations, the temporary formation of an osmotic pressure gradient across the cell membrane and the streaming potential induced by water inflow through negatively charged pores of the cell membrane in the course of an active solute transport in intestinal epithelial cells are apparently all possible causes of mucosal membrane depolarization.     

Model for the cell biomembrane electric potential during active transport of various ions

A model of a stationary electrical potential on biomembrane was created. This model takes into account conformational changes in transport ATPase. N positive ions are transported simultaneously by the system of active transport. The model allows one to determine independently ion concentrations inside the cell and membrane electrical potential. It is shown that, to obtain the electrical potential, it is necessary to take into account organic negative intracellular ions. The effect of positive ions that are not transported by active transport systems on the potential value is discussed. The results obtained are in a good agreement with experimental data for various cells.     

Calmodulin can induce and control damping oscillations in the plasma membrane Ca2+ -ATPase activity: a kinetic model

Plasma membrane Ca2+-ATPase is the calcium pump that extrudes calcium ions from cells using ATP hydrolisis for the maintenance of low Ca2+ concentrations in the cell. Calmodulin stimulates Ca2+-ATPase by binding to the autoinhibitory enzyme domain, which allows the access of cytoplasmic ATP and Ca2+ to the active and transport cites. Our kinetic model predicts damped oscillations in the enzyme activity and interprets the known nonmonotonous kinetic behavior of the enzyme in the presence of calmodulin. For the parameters close to the experimental ones, the kinetic model explains the changes in frequency and damping factor of the oscillatory enzyme activity, as dependent on calmodulin concentration. The calculated pre-steady-state curves fit well the known experimental data. The kinetic analysis allows us to assign Ca2+-ATPase to the hysteretic enzymes exhibiting activity oscillations in open systems.     

Current status of the thiol redox model for the regulation of hexose transport by insulin.

Data obtained over the last two years pertinent to the thiol redox model for the modulation of hexose transport activity by insulin is summarized. The model proposes that activation of hexose transport in fat cells involves sulfhydryl oxidation to the disulfide form in a key protein component of the fat cell surface membrane. Theoretically, the rapid activation of transport by insulin may involve either the conversion of inactive membrane carriers to the active form as originally proposed, or the conversion of a low Vmax transport system to a high Vmax form. The present experiments showed that the percent inhibition of insulin-activated transport rates by submaximal levels of cytochalasin B was decreased compared to its effects on basal transport. Treatment of fat cells with N-ethylmaleimide inhibited cytochalasin B action but not transport activity. When insulin or the oxidant vitamin K5 was added to cells 5 minutes before the N-ethylmaleimide, the elevated transport activity was also resistant to the sulfhydryl reagent, but cytochalasin B retained its potent inhibitory effect on transport. The data demonstrate that unique properties characterize basal versus insulin-activated transport activity with respect to the sensitivity of cytochalasin B action to sulfhydryl blockade in isolated fat cells. The data are consistent with the concept that activation of transport activity reflects the conversion of a reduced (sulfhydryl) system characterized by a low Vmax to an oxidized (disulfide), high Vmax transport system.     

The use of membrane vesicles in transport studies

Transport-competent plasma membrane vesicles isolated from mammalian cells provide a system to investigate mechanisms and regulation of nutrient and ion transport systems. The characteristics of membrane vesicle systems to study transport in erythrocytes, renal and epithelial membranes, Ehrlich ascites cells, and mouse fibroblasts are discussed. Studies of Na+-stimulated and Na+-independent amino acid and glucose transport in these systems are evaluated, with emphasis on experimental verification of concepts stated in the Na+ gradient hypothesis. Nucleoside, phosphate, and calcium transport systems in plasma membrane vesicles from mouse fibroblast cultures are discussed. Also, current biochemical approaches to investigate mechanisms of regulation of nutrient transport systems by hormones or cellular proliferative state are described.     

The relationship between the electrochemical proton gradient and active transport in Escherichia coli membrane vesicles.

In the previous paper [ramos, S., and Kaback, H.R. (1977), Biochemistry 16 (preceding paper in this issue)], it was demonstrated that Escherichia coli membrane vesicles generate a large electrochemical proton gradient (delta-muH+) under appropriate conditions, and some of the properties of delta-muH+ and its component forces [i.e., the membrane potential (delta psi) and the chemical gradient of protons (deltapH)] were described. In this paper, the relationship between delta-muH+, delta psi, and deltapH and the active transport of specific solutes is examined. Addition of lactose or glucose 6-phosphate to membrane vesicles containing the appropriate transport systems results in partial collapse of deltapH, providing direct evidence for the suggestion that respiratory energy can drive active transport via the pH gradient across the membrane. Titration studies with valinomycin and nigericin lead to the conclusion that, at pH 5.5, there are two general classes of transport systems: those that are driven primarily by delta-muH+ (lactose, proline, serine, glycine, tyrosine, glutamate, leucine, lysine, cysteine, and succinate) and those that are driven primarily by deltapH (glucose 6-phosphate, D-lactate, glucuronate, and gluconate). Importantly, however, it is also demonstrated that at pH 7.5, all of these transport systems are driven by delta psi which comprises the only component of delta-muH+ at this external pH. In addition, the effect of external pH on the steady-state levels of accumulation of different solutes is examined, and it is shown that none of the pH profiles correspond to those observed for delta-muH+, delta psi, or deltapH. Moreover, at external pH values above 6.0-6.5, delta-muH+ is insufficient to account for the concentration gradients established for each substrate unless the stoichiometry between protons and accumulated solutes is greater than unity. The results confirm many facets of the chemiosmotic hypothesis, but they also extend the concept in certain important respects and allow explanations for some earlier observations which seemed to preclude the involvement of chemiosmotic phenomena in active transport.     

Intracellular K+ activities in Aplysia gut: effects of transport inhibitors on the Na+ pump

Na+ absorption by the Aplysia californica foregut is affected through an active Na+ transport mechanism located in the basolateral membrane of the epithelial absorptive cells. Since Cl- absorption by the Aplysia gut has been shown to be very different from that demonstrated in vertebrate gut, the present study was undertaken to discern if Na+ transport was also different from that observed in vertebrate preparations. Utilizing microelectrode technique, it was demonstrated that intracellular K+ activity is above electrochemical equilibrium in the Aplysia absorptive cells and that serosal ouabain, Ba2+ or Cd2+ abolished this asymmetry in K+ electrochemical potential. Neither bumetanide nor furosemide had any effect on intracellular K+ activities, mucosal membrane potentials or transepithelial potentials in the Aplysia gut preparation. These results are consistent with the operation of a basolateral Na+/K+ pump.     

Characterization of sodium transport in Acholeplasma laidlawii B cells and in lipid vesicles containing purified A. laidlawii (Na+-Mg2+)-ATPase by using nuclear magnetic resonance spectroscopy and 22Na tracer techniques.

The active transport of sodium ions in live Acholeplasma laidlawii B cells and in lipid vesicles containing the (Na+-Mg2+)-ATPase from the plasma membrane of this microorganism was studied by 23Na nuclear magnetic resonance spectroscopic and 22Na tracer techniques, respectively. In live A. laidlawii B cells, the transport of sodium was an active process in which metabolic energy was harnessed for the extrusion of sodium ions against a concentration gradient. The process was inhibited by low temperatures and by the formation of gel state lipid in the plasma membrane of this organism. In reconstituted proteoliposomes containing the purified (Na+-Mg2+)-ATPase, the hydrolysis of ATP was accompanied by the transport of sodium ions into the lipid vesicles, and the transport process was impaired by reagents known to inhibit ATPase activity. At the normal growth temperature (37 degrees C), this transport process required a maximum of 1 mol of ATP per mol of sodium ion transported. Together, these results provide direct experimental evidence that the (Na+-Mg2+)-ATPase of the Acholeplasma laidlawii B membrane is the cation pump which maintains the low levels of intracellular sodium characteristic of this microorganism.     

Properties of the stochastic energization-relaxation channel model for vectorial ion transport

A model for the primary active transport by an ion pump protein is proposed. The model, the "energization-relaxation channel model," describes an ion pump as a multiion channel that undergoes stochastic transitions between two conformational states by external energy supply. When the potential profile along ion transport pathway is asymmetrical, a net ion flux is induced by the transitions. In this model, the coupling of the conformational change and ion transport is stochastic and loose. The model qualitatively reproduces known properties of active transport such as the effect of ion concentration gradient and membrane potential on the rate of transport and the inhibition of ion transport at high ion concentration. We further examined the effect of various parameters on the ion transport properties of this model. The efficiency of the coupling was almost 100% under some conditions.     

Testing the polar auxin transport model with a selective plasma membrane H+-ATPase inhibitor

Auxin is unique among plant hormones in that its function requires polarized transport across plant cells. A chemiosmotic model was proposed to explain how polar auxin transport is derived by the H⁺ gradient across the plasma membrane (PM) established by PM H⁺-adenosine triphosphatases (ATPases). However, a classical genetic approach by mutations in PM H⁺-ATPase members did not result in the ablation of polar auxin distribution, possibly due to functional redundancy in this gene family. To confirm the crucial role of PM H⁺-ATPases in the polar auxin transport model, we employed a chemical genetic approach. Through a chemical screen, we identified protonstatin-1 (PS-1), a selective small-molecule inhibitor of PM H⁺-ATPase activity that inhibits auxin transport. Assays with transgenic plants and yeast strains showed that the activity of PM H⁺-ATPases affects auxin uptake as well as acropetal and basipetal polar auxin transport. We propose that PS-1 can be used as a tool to interrogate the function of PM H⁺-ATPases. Our results support the chemiosmotic model in which PM H⁺-ATPase itself plays a fundamental role in polar auxin transport.     

Physiology of the tracheal epithelium

The mucosa that lines the airways is covered with a fluid film forming a hypophase between mucus and cell surface. To study the function of this epithelium aims at describing the mechanisms by which fluid is normally produced. Another goal to be pursued consists in looking for the origin of pathological situations, such as cystic fibrosis, in which the functioning of epithelial cell is altered. The elucidation of transport mechanisms present in the apical and in the basolateral membrane results in a conceptual model that illustrates the asymmetrical functioning of epithelial cells. Recent discoveries enlarge our understanding of membrane transport processes; in particular, a concerted, reciprocal regulation of the activity of both membranes was shown to be exerted via the intracellular composition. The tracheal epithelium absorbs Na+ and secretes Cl-. These two transports are active and electrogenic; their sum corresponds approximately to the short-circuit current measured in vitro. Na+ absorption is sensitive to amiloride from the luminal side and also to ouabain added to the serosal compartment. The process is a primary active transport, analogous to that found in amphibian epithelia or in mammalian colon. Cl- secretion is abolished by furosemide (or bumetanide), by ouabain or by Na+ suppression in the serosal incubation solution. The mechanism is a secondary active transport: Cl- influx across the basolateral membrane is coupled to Na+ (probably through Na+, K+, Cl- symport); energy is dissipated by the Na+-K+-ATPase localised in the basolateral membrane. Thus, Na+ is recirculated across that membrane by the pump activity, which maintains a favorable gradient for influx via the symport. Cl- efflux takes place by diffusion through the luminal membrane. This model applies to other epithelia in which Na+-coupled Cl- secretion was shown to take place. It is confirmed by isotopic fluxes measurements and by electrophysiologic properties of the apical and the basolateral membrane. Various agents are known to influence ion transports. In particular Cl- secretion is stimulated by substances that increase the intracellular concentration of cyclic AMP. At the membrane level, the number of active Cl- channels in the apical membrane is primarily controlled, then the basolateral membrane K+ permeability. Yet, species differences are worth to note: the trachea of the cow is barely sensitive to agents that exert a marked action on dog trachea. The tracheal epithelium is used as an experimental model for studying cystic fibrosis, a disease in which the apical membrane is almost devoid of functional Cl- channels, so that Cl- permeability is quite low.(ABSTRACT TRUNCATED AT 400 WORDS)     

Steady state analysis and experimental validation of a model for hepatic high-density lipoprotein transport

Transport of high-density lipoprotein (HDL) in the hepatocyte plays a fundamental role in reverse cholesterol transport and regulation of plasma HDL levels. On the basis of a recently developed kinetic model, the steady state distribution of HDL was analyzed. Fractional fluorescence of labeled HDL in the basolateral membrane, sorting endosomes (SE), the subapical compartment/ apical recycling compartment, the biliary canaliculus and in late endosomes and lysosomes (LE/LYS) including expected standard deviation is predicted. Improved parameter estimation was obtained by including kinetic data of apical endocytosis of fluorescent markers for LE/LYS, asialoorosomucoid and Rhodamine-dextran, in the regression. Predicted values using the refined kinetic parameters are in good agreement with experimental values of compartmental steady state fluorescence of Alexa488-HDL in polarized hepatic HepG2 cells. From calculated steady state fluxes, it is suggested that export of HDL from basolateral SE is the key step for determining the transport of HDL through the hepatocyte. The analysis provides testable predictions for high-throughput fluorescence microscopy screening experiments on potential inhibitors of hepatic HDL processing. By quantitative fluorescence imaging and model analysis, it is shown that the phosphoinositide kinase inhibitor wortmannin prevents apical transport of fluorescent HDL from basolateral SE. The results support that endosomes of polarized hepatic cells have different sorting functions and that apical endocytosis is an integrative trafficking step in hepatocytes.     

A model of active transport of ions in hepatocytes

A mathematical model of the transport of basic ions (K⁺, Na⁺, Cl⁻) across the hepatocyte membrane has been created using the previously constructed models of active ion transport in biomembranes. The dependence of the resting potential on extracellular ion concentration has been established. Using the model, it is possible to independently calculate the resting potential at the biomembrane and the concentrations of sodium, potassium, and chlorine ions in the cell. The calculated internal concentrations of the ions are in good agreement with the corresponding experimental values.     

Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane

The Kedem-Katchalsky-Zelman model equations for transmembrane transport in multicomponent, non-ionic and heterogeneous solutions have been modified. The validity of this model for binary and ternary solutions was verified, using a cell with a horizontally mounted membrane. In the cell, volume and solute fluxes were measured as a function of gravitational configuration. In the experimental set-up, water was placed on one side of the membrane. The opposite side of the membrane was exposed to aqueous solutions of densities greater than that of water, aqueous ethanol (less dense than water) or glucose/ethanol/water solutions. The experimental results presented herein illustrate pseudo-phase transitions which occur from a non-convectional to convectional state or in the reverse direction.     

A two population model of prion transport through a tunnelling nanotube

This article develops a two prion population model that simulates prion trafficking between an infected dendritic cell and a neuron. The situation when the two cells are connected by a tunnelling nanotube (TNT) is simulated. Two mechanisms of prion transport are considered: lateral diffusion in the TNT membrane and active actin-dependent transport inside endocytic vesicles that are propelled by myosin Va molecular motors. Analytical solutions describing prion concentrations and fluxes are obtained. Numerical results are compared with those predicted by a single prion population model that relies on a single reaction–diffusion equation and accounts for the two modes of prion transport in an effective way.     

Analysis of oxygen transport in a diffusion-limited model of engineered heart tissue

Cardiac tissue engineering has made notable progress in recent years with the advent of an experimental model based on neonatal cardiomyocytes entrapped in collage gels and purified basement membrane extract, known as "engineered heart tissues" (EHTs). EHTs are a formidable display of tissue-level contractile function and cellular-level differentiation, although they suffer greatly from mass transport limitations due to the high density of metabolically active cells and the diffusion-limited nature of the hydrogel. In this report, a mathematical model was developed to predict oxygen levels inside a one-dimensional, diffusion-limited model of EHT. These predictions were then compared to values measured in corresponding experiments with a hypoxia-sensitive stain (pimonidazole). EHTs were cast between two plastic discs, which allowed for mass transfer with the culture medium to occur in only the radial direction. EHTs were cultured for up to 36 h in the presence of pimonidazole, after which time they were snap-frozen, histologically sectioned, and stained for bound pimonidazole. Quantitative image analysis was performed to measure the distance from the culture medium at which hypoxia first occurs under various conditions. As tested by variation of simple design parameters, the trends in oxygen profiles predicted by the model are in reasonable agreement with those obtained experimentally, although a number of ambiguities related to the specific model parameters led to a general overprediction of oxygen concentrations. Based on the sensitivity analysis in the present study, it is concluded that diffusion-reaction models may offer relatively precise predictions of oxygen concentrations in diffusion-limited tissue constructs.     

Characterization of sodium-dependent and sodium-independent nucleoside transport systems in rabbit brush-border and basolateral plasma-membrane vesicles from the renal outer cortex.

The transport of uridine into rabbit renal outer-cortical brush-border and basolateral membrane vesicles was compared at 22 degrees C. Uridine was taken up into an osmotically active space in the absence of metabolism for both types of membrane vesicles. Uridine influx by brush-border membrane vesicles was stimulated by Na+, and in the presence of inwardly directed gradients of Na+ a transient overshoot phenomenon was observed, indicating active transport. Kinetic analysis of the saturable Na+-dependent component of uridine flux indicated that it was consistent with Michaelis-Menten kinetics (Km 12 +/- 3 microM, Vmax. 3.9 +/- 0.9 pmol/s per mg of protein). The sodium:uridine coupling stoichiometry was found to be consistent with 1:1 and involved the net transfer of positive charge. In contrast, uridine influx by basolateral membrane vesicles was not dependent on the cation present and was inhibited by nitrobenzylthioinosine (NBMPR). NBMPR-sensitive uridine transport was saturable (Km 137 +/- 20 microM, Vmax. 5.2 +/- 0.6 pmol/s per mg of protein). Inhibition of uridine flux by NBMPR was associated with high-affinity binding of NBMPR to the basolateral membrane (Kd 0.74 +/- 0.46 nM). Binding of NBMPR to these sites was competitively blocked by adenosine and uridine. These results indicate that uridine crosses the brush-border surface of rabbit proximal renal tubule cells by Na+-dependent pathways, but permeates the basolateral surface by NBMPR-sensitive facilitated-diffusion carriers.