Models of active transport of ions in biomembranes of various types of cells

Nonequilibrium statistical models of the active transport of ions in biomembranes have been constructed. Differences of chemical potentials of the ATP-ADP reaction and the electrochemical potential of ions were taken as the thermodynamic forces responsible for the flow of ions through the membrane. The active transport of ions was viewed as a cross phenomenon arising from the chemical reaction of the ATP hydrolysis. These models provide independent calculations of the resting potential at the biomembrane and concentrations of ions in a cell on the assumption the free energy of the ATP-ADP reaction is fully (without the dissipation loss) converted to the free energy of transported ions. They take into account the presence of nonpenetrating ions in a cell. It was shown that different concentrations of nonpenetrating ions have a considerable effect on the resting potential. The proposed models were compared with experimental data obtained for different types of cells including neurons, muscular cells, bacteria, plants, and mitochondria. Calculated values of the membrane potential and ion concentrations were in good qualitative agreement with experimental data.     

Coupling of secondary active transport with\Delta \tilde \mu _{H^ + }

Most nutrients and ions in bacteria, yeasts, algae, and plants are transported uphill at the expense of a gradient of the electrochemical potential of protons deltamu-H+ (a type of secondary active transport). Diagnosis of such transports rests on the determination of the transmembrane electrical potential difference deltapsi and the difference of pH at the two membrane sides. The behavior of kinetic parameters K(T) (the half-saturation constant) and J(max), (the maximum rate of transport) upon changing driving ion concentrations and electrical potentials may be used to determine the molecular details of the transport reaction. Equilibrium accumulation ratios of driven solutes are expected to be in agreement with the deltapsi and deltapH measured independently, as well as with the Haldane-type expression involving K(T) and J(max). Different stoichiometries of H+/solute, as well as intramembrane effects of pH and deltapsi, may account for some of the observed inconsistencies.     

Electrical potential differences across salt transporting membranes

The electrical potential differences across membranes where active transport of ions occurs has been examined using the formalism of linear non-equilibrium thermodynamics, and can be represented as the arithmetic sum of a resistive term, a term directly dependent on metabolism (i.e. electrogenic) and terms appropriate for describing a diffusion potential. The Hittorf transport number for each ion in the latter terms is the ratio of the partial conductances of the membrane to that ion to the total membrane conductance, and the conductance to an ion consists of the arithmetic sum of conductance of active and passive pathways providing these are independent. The conductances of active transport mechanisms arise from variation of the rate of transport with the electrochemical potentials against which they operate. The electrogenic term arises from imbalance between anion and cation transport. If an ion is transported by an obligatorily electrically neutral exchange for some other ion such transport gives rise to no electrogenic effect. A membrane will transport salt most efficiently if there is no imbalance between anion and cation transport, when it will not be electrogenic, but modest deviations from this condition will not degrade the efficiency of active transport markedly.     

Active transport of potassium by insect midgut

Midguts isolated from fifth-instar larvae of the insert Hyalophora cecropia actively transport potassium in the hemolymph to lumen direction. No specific co- or counter-ion is required and other alkali ions are actively transported in the same direction as potassium. No specific inhibitor of K+ active transport has been found although most metabolic inhibitors reduce the net K+ flux, potential difference, and short-circuit current to zero. The site of the epithelial active transport of potassium has been identified by microelectrode measurements of intracellular resistance as the goblet cell, one of the two major cell types in the single-layered midgut. Under certain external conditions, the neighboring columnar cells are added to the goblet cell transport route through intercellular electrical coupling that occurs after application of external depolarizing current. Tracer influx kinetics were used to establish that the fraction of exchangeable K involved in the transport route under open-circuit conditions is small, corresponding to a goblet cell pathway. Under depolarizing current conditions, virtually all of the exchangeable midgut K is involved in the transport route, corresponding to a goblet and columnar cell pathway. These results and others are used to construct a model for rheogenic active transport of potassium in insect midgut.     

Characterization of orthophosphate-induced active cation transport in isolated liver mitochondria

The kinetics of the P_i-induced active transport of ions by isolated liver mitochondria were studied by monitoring photometrically mitochondrial volume changes. In a previous communication, these volume changes were shown to correlate quantitatively with the net uptake or release of ions. In the present study the specificity of the P_i role was further characterized. The data support the contention that cations are actively transported. Anions follow the transfer of cations to maintain electrical neutrality. The relationship of the transport system to oxidative phosphorylation was investigated by simultaneously monitoring both processes under different experimental conditions. The results of the experiments are quantitatively consistent with a model proposed for the P_i-induced active transport in isolated rat liver mitochondria. The model includes the following features. 1. P_i induces an inwardly directed, carrier-mediated active transport of cations. 2. The transport is coupled to the energy-conserving reactions of the cytochrome chain. 3. The efflux of ions accumulated in the presence of low P_i concentrations occurs by passive diffusion. 4. Net accumulation ceases when the rates of active transport and passive diffusion become equal. 5. The active transport competes with oxidative phosphorylation for a common, nonphosphorylated, high-energy intermediate.     

Model of active transport of ions in biomembranes based on ATP-dependent change of height of diffusion barriers to ions

A closed model of the active transport was constructed taking into account ATP-dependent opening and closing of barriers to ions and the relationship between the membrane potential and the work of ionic pumps under the condition of electroneutrality inside the cell. The internal consistency of the model was verified by the fulfillment of Onsager's reciprocity relation. It was demonstrated that at the limit of large energy barriers the operation of the system of the active transport is equivalent to the "turning segment" model, which was proposed by the authors earlier. Values of the resting potential and the intracellular concentration of ions were obtained for different types of cells. These results were in qualitative agreement with relevant experimental data.     

A pathway separate from the central channel through the nuclear pore complex for inorganic ions and small macromolecules

Nuclear pore complexes (NPCs) are supramolecular nanomachines that mediate the exchange of macromolecules and inorganic ions between the nucleus and the cytosol. Although there is no doubt that large cargo is transported through the centrally located channel, the route of ions and small molecules remains debatable. We thus tested the hypothesis that there are two separate pathways by imaging NPCs using atomic force microscopy, NPC electrical conductivity measurements, and macromolecule permeability assays. Our data indicate a spatial separation between the active transport of macromolecules through the central channel and the passive transport of ions and small macromolecules through the pore periphery.     

Model of active transport of ions in cardiac cell

A model of the active transport of ions in a cardiac muscle cell, which takes into account the active transport of Na⁺, K⁺, Ca²⁺, Mg²⁺, HCO₃⁻ and Cl⁻ ions, has been constructed. The model allows independent calculations of the resting potential at the biomembrane and concentrations of basic ions (sodium, potassium, chlorine, magnesium and calcium) in a cell. For the analysis of transport processes in cardiac cell hierarchical algorithm “one ion-one transport system” was offered. The dependence of the resting potential on concentrations of the ions outside a cell has been established. It was shown, that ions of calcium and magnesium, despite their rather small concentration, play an essential role in maintenance of resting potential in cardiac cell. The calculated internal concentrations of ions are in good agreement with the corresponding experimental values.     

Metabolic cost of sodium transport in toad urinary bladder.

The metabolic cost of active sodium transport was determined in toad bladder at different gradients of transepithelial potential. Deltapsi, by continuous and simultaneous measurements of CO2 production and of transepithelial electric current. Amiloride was used to block active sodium transport in order to assess the nontransport-linked, basal, production of CO2 and the passive permeability of the tissue. From these determinations active sodium transport, Jna, and suprabasal CO2 production, Jsb CO2, were calculated. Since large transients in Jna and Jsb CO2 frequently accompanied any abrupt change in deltapsi, steady state conditions were carefully defined. Some 20 to 40 min were required after a change in deltapsi before steady state of transport activity and of CO2 production were achieved. The metabolic cost of sodium transport proved to be the same whether the bladder expended energy moving sodium against a transepithelial electrical potential grandient of +50 mV or whether sodium was being pulled through "the active transport pathway" by an electrical gradient of -50 mV. In both cases the value of the ratio Jna/Jsb CO2 averaged some 20 sodium ions transported per molecule of CO2 produced. When the Na pump was blocked by 10(-2) M ouabain, the perturbations of the transepithelial electrical potential did not elicit changes of Jna nor, consequently of Jsb CO2. The independence of the ratio Jna/Jsb CO2 from deltapsi over the range+/-50 mV indicates a high degree of coupling between active sodium transport and metabolism.     

Sodium chloride transport by rabbit gallbladder. Direct evidence for a coupled NaCl influx process

The results of the present study that NaCl transport by in vitro rabbit gallbladder must be a consequence of a neutral coupled carrier-mediated mechanism that ultimately results in the active absorption of both ions; pure electrical coupling between the movements of Na and Cl can be excluded on the grounds of electrphysiologic considerations. Studies on the unidirectional influxes of Na and Cl have localized the site of this coupled mechanism to the mucosal membranes. Studies on the intracellular ion concentrations and the intracellular electrical potential are consistent with the notion that (a) the coupled NaCl influx process results in the movement of Cl from the mucosal solution into the cell against an apparent electrochemical potential difference; (b) the energy for the uphill movement of Cl is derived from the Na gradient across the mucosal membrane which is maintained by an active Na extrusion mechanism located at the basolateral membranes; and (c) Cl exit from the cell across the basolateral membranes is directed down an electrochemical potential gradient and may be diffusional. Finally, as for the case of rabbit ileum, the coupled NaCl influx process is inhibited by elevated intracellular levels of cyclic 3',5'-adenosine monophosphate. A working model for transcellular and paracellular NaCl transport by in vitro rabbit gallbladder is proposed.     

On the mechanism of generation of electrical potential differences in cell biomembranes]

A statistical model of active ion transport in biomembranes was developed. The model makes it possible to calculate both the value of membrane potential phi zero and the rate of ion concentrations inside and outside the cell. These values depend on the difference of chemical potentials of the ATP-ADP system and the permeability of the biomembrane for ions being transported. The calculated phi zero value approximately 200-250 mV is consistent with the data on proton pumps.     

Modification of ion transport in lipid bilayer membranes in the presence of 2,4-dichlorophenoxyacetic acid. I. Enhancement of cationic conductance and changes of the kinetics of nonactin-mediated transport of potassium.

We have found that herbicide 2,4-dichlorophenoxyacetic acid (2,4-D) has the ability to increase the rate of transport of positive ions of several kinds, and to inhibit transport of negatively charged tetraphenylborate ions in lipid bilayer membranes. It has been found that only the neutral form of 2,4-D is transport active, whereas the ionized from of 2,4-D does not modify transport of ions, and does not by itself permeate through lipid membranes. The results suggest that the enhancement of transport of positively charged ions such as tetraphenylarsonium + and nonactin-K+ is dominated by the increase of the ion translocation rate constant. It has been shown that the enhancement of nonactin-mediated transport of K+ by 2,4-D can be accounted for by a simple carrier model. We have observed that a 2,4-D concentration above 3 X 10(-4) M the potassium ion transport in phosphatidylcholine-cholesterol as well as in cholesterol-free glycerolmonooleate membranes is enhanced to such a degree that, depending upon the concentration of potassium ions, it becomes limited by the rate of recombination of K+ with nonactin, and/or by backdiffusion of unloaded nonactin molecules. Furthermore, the effect of 2,4-D is enhanced by ionic strength of aqueous solution. From the changes of kinetic parameters of nonactin-K+ transport, as well as from the changes of membranes conductance due to tetraphenylarsonium + ions, we have estimated the changes of the electrical potential of the membrane interior. We have found that the potential of the interior of the membrane becomes more negative in the presence of 2,4-D, and that its change is proportional to the aqueous concentration of 2,4-D. The effect of 2,4-D on ion transport has been attributed to a layer of 2,4-D molecules absorbed within the interfacial region, and having a dipole moment directed toward the aqueous medium. The results of kinetic studied of nonactin-K+ transport suggest that this layer is located on the hydrocarbon side of the interface.     

Light-activated amino acid transport in Halobacterium halobium envelope vesicles.

Vesicles prepared from Halobacterium halobium cell envelopes accumulate amino acids in response to light-induced electrical and chemical gradients. Nineteen of 20 commonly occurring amino acids have been shown to be actively accumulated by these vesicles in response to illumination or in response to an artificially created Na-gradient. Sodium-activated amino acid transport for 18 of these amino acids has been shown to occur in direct response to the protonmotive force generated. Glutamate is transported only in response to a sodium gradient. Michaelis constants for the uptake of these amino acids are close or identical whether the amino acids are accumulated in response to a sodium gradient or a protonmotive force (i.e., electrical gradient). On the basis of shared common carriers the transport systems can be divided into eight classes, each responsible for the transport of one or several amino acids, i.e., arginine, lysine, histidine; asparagine, glutamine; alanine, glycine, threonine, serine; leucine, valine, isoleucine, methionine; phenylalanine, tyrosine, tryptophan; aspartate; glutamate; proline. Available evidence suggests that these carriers are symmetrical in that amino acids can be transported equally well in both directions across the vesicle membranes. A tentative working model to account for these observations is presented.     

A double (series) pump model for transporting epithelia

This paper considers the behaviour of an epithelial structure in which the opposite faces of the tissue are able to actively transport sodium ions in the same direction, thus affecting a net transfer of sodium across the tissue. The short circuit current of an electrical equivalent circuit under steady-state and transient conditions is considered. This latter condition represents the behaviour of an epithelium when sodium is removed from the side from which it is transported. The behaviour of the electrical model is compared to that of actual epithelia under experimental conditions.     

Electrophoretic polyamine transport in rat liver mitochondria

Summary Naturally occurring polyamines (spermidine, putrescine, cadaverine), as the well studied spermine, are transported into rat liver mitochondrial matrix provided that mitochondria are energized and the electrical membrane potential has a value of about 180 mV. This condition is achieved by the presence of inorganic phosphate, or acetate, or nigericin in the incubation medium. Valinomycin plus K⁺ almost completely blocks polyamine transport.The obtained results clearly show that all naturally occurring polyamines are transported by an electrophoretic mechanism in responce to a high negative inner electrical potential.The distribution ratio of polyamines across the mitochondrial membrane is far from the thermodynamic equilibrium by many orders of magnitude. This result might suggest the existence of a different pathway for polyamine efflux.     

Model of Active Transport of Ions Through Diatom Cell Biomembrane

A model of the active transport of ions in the Cascinodiscus wailesii diatom cell is constructed taking into account the transport of H⁺, Na⁺, K⁺, Ca⁺², NO₃^-\mathrm{NO}_{3}^{-}, Cl⁻, and NH₄⁺\mathrm{NH}_{4}^{+} ions. This model allows calculating intracellular concentrations of basic ions and the biomembrane resting potential. A hierarchical algorithm “one ion—one transport system” is used in the model. The dependence of the resting potential on the extracellular concentration of potassium is plotted in terms of the model. The calculated values are in good agreement with the corresponding experimental data.     

A metabolic osmotic model of human erythrocytes

A metabolic osmotic model of red blood cells is presented which takes into account the main reaction steps of glycolysis and the passive and active fluxes of ions across the cell membrane. Cellular energy metabolism and osmotic behaviour are linked by the ATP consumption for the active transport of cations as well as by the osmotic action of the glycolytic intermediate 2,3-diphosphoglycerate (2,3-DPG). The model is based on a system of differential equations describing the metabolic reactions and transport processes. Further, two algebraic conditions for the osmotic equilibrium and the electroneutrality of the cell are considered. Using realistic system parameters the model allows the calculation of a great number of dependent variables, among them the cell volume, the concentrations of metabolites and ions and the transmembrane potential. Only stationary states are considered.The parameter dependence of important model variables is characterized by control coefficients. The main results are: (a) The volume of erythrocytes is mainly determined by the permeabilities of the leak fluxes of cations, the content of hemoglobin and the activity of the hexokinase-phosphofructokinase system of glycolysis; (b) Changes of volume affect the glycolytic rate mainly by changing the concentration of ATP which is a regulator of glycolysis; (c) A change in the membrane area may affect the other cell properties only if it is connected with variations of the number of active and leak sites of the membrane.     

Membrane potential and active transport--an information theory approach

A membrane potential stabilizing mechanism is proposed. Permeability is portrayed as controlled by a potential sensor. The active transport system is suggested to be a Maxwell demon able to recognize different ions, and modulate their passage into and out of the cell, without apparent reliance on energy. The idea that information is equivalent to entropy is used to resolve that paradox and construct a model of the active transport system. The non-steady ionic state of muscle cell is deduced; that ionic concentration may determine the condition of muscle is also suggested.     

Influence of cellular and paracellular conductance patterns on epithelial transport and metabolism

Theoretical analysis of transepithelial active Na transport is often based on equivalent electrical circuits comprising discrete parallel active and passive pathways. Recent findings show, however, that Na+ pumps are distributed over the entire basal lateral surface of epithelial cells. This suggests that Na+ that has been actively transported into paracellular channels may to some extent return to the apical (mucosal) bathing solution, depending on the relative conductances of the pathways via the tight junctions and the lateral intercellular spaces. Such circulation, as well as the relative conductance of cellular and paracellular pathways, may have an important influence on the relationships between parameters of transcellular and transepithelial active transport and metabolism. These relationships were examined by equivalent circuit analysis of active Na transport, Na conductance, the electromotive force of Na transport, the "stoichiometry" of transport, and the degree of coupling of transport to metabolism. Although the model is too crude to permit precise quantification, important qualitative differences are predicted between "loose" and "tight" epithelia in the absence and presence of circulation. In contrast, there is no effect on the free energy of metabolic reaction estimated from a linear thermodynamic formalism. Also of interest are implications concerning the experimental evaluation of passive paracellular conductance following abolition of active transport, and the use of the cellular voltage-divider ratio to estimate the relative conductances of apical and basal lateral plasma membranes.