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.     

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.     

Nonequilibrium Statistical Model of Active Transport of Ions and ATP Production in Mitochondria

A model of the active transport of ions through internal membranes of mitochondria is proposed. If concentrations of ions in a cell are known, this model allows calculating concentrations of all main ions (H⁺, Ca⁺², K⁺, Mg²⁺, Na⁺, Cl⁻) in the mitochondrion matrix and the resting potential across the membrane. The theoretical values satisfactorily agree with available experimental data on the concentrations and the potentials, including different operating regimes of the adenosine triphosphate (ATP) synthetase (the main regime, short circuiting or ATP synthetase blocking). The active transport of Mg²⁺ ions in exchange for protons was assumed. In accordance with the model, the ATP synthetase operation is possible only if the stoichiometric coefficient of protons is 3.     

A Mathematical Model of Action Potential in Cells of Vascular Plants

A mathematical model of action potential (AP) in vascular plants cells has been worked out. The model takes into account actions of plasmalemma ion transport systems (K⁺, Cl^? and Ca²⁺ channels; H⁺- and Ca²⁺-ATPases; 2H⁺/Cl^? symporter; and H⁺/K⁺ antiporter), changes of ion concentrations in the cell and in the extracellular space, cytoplasmic and apoplastic buffer capacities and the temperature dependence of active transport systems. The model of AP simulates a stationary level of the membrane potential and ion concentrations, generation of AP induced by electrical stimulation and gradual cooling and the impact of external Ca²⁺ for AP development. The model supports a hypothesis about participation of H⁺-ATPase in AP generation.     

Involvement of protons in the ion transport cycle of Na<Superscript>+</Superscript>,K<Superscript>+</Superscript>-ATPase

The effect of pH on electrogenic sodium transport by the Na⁺,K⁺-ATPase has been studied. Experiments were carried out by admittance recording in a model system consisting of a bilayer lipid membrane with adsorbed membrane fragments containing purified Na⁺,K⁺-ATPase. Changes in the membrane admittance (capacitance and conductance increments in response to photo-induced release of ATP from caged ATP) were measured as function of AC voltage frequency, sodium ion concentration, and pH. In solutions containing 150 mM Na⁺, the frequency dependence of capacitance increments was not significantly dependent on pH in the range between 6 and 8. At a low NaCl concentration (3 mM), the capacitance increments at low frequencies decreased with the increasing pH. In the absence of NaCl, the frequency-dependent capacitance increment at low frequencies was similar to that measured in the presence of 3 mM NaCl. These results may be explained by involvement of protons in the Na⁺,K⁺-ATPase pump cycle, i.e., electroneutral exchange of sodium ions for protons under physiological conditions, electrogenic transport of sodium ions at high pH, and electrogenic transport of protons at low concentrations (and in the absence) of sodium ions.     

Optimization criteria of the mechanism governing the stability of the membrane potential

For small changes in ion concentration within the physiological range the membrane potential transients can be explained in terms of two linear models both for passive and active transport. Using frog sartorius muscle as a suitable model system the ion pump is considered to work within the steepest range of the flux-concentration characteristic. Further for the small perturbations the equations describing passive ion transport can be safely linearized. The conclusion appears inescapable that for the muscle membrane the intracellular ion concentration adjusts itself in some optimal manner to the level of the extracellular ions. The active ion transport represents a control parameter for the membrane potential. The model structure corresponds to a dynamic system, the control processes of which are optimized with respect to a quadratic integral-criterion function. Here, both the performance index of the control sequence in the membrane processes and the energy consumed by the ion fluxes have been considered for small perturbations of Na⁺, K⁺, and Cl^? in the neighbourhood of the physiological working point. As it is, the control system governing the active and passive ion transport processes is essentially optimized with respect to a minimal energy usage. The amount of energy consumed during the transients predicted by the model has been calculated.     

Effect of valinomycin on ion transport in bacterial cells and on bacterial growth

The antimicrobial action of valinomycin relative to the K⁺ and Na⁺ contents of the medium has been investigated in several species of bacteria, particularly in Streptococcus faecalis, which effects energy-linked transport exclusively via degradation of glycolytic ATP, Micrococcus lysodeikticus, effecting active ion transport by respiration and Staphylococcus aureus, the energy-dependent ion transport of which is due to both glycolytic ATP degradation and respiration. It was demonstrated that valinomycin does not act on K⁺ transport in the glycolysing cells in the same manner as it does on respiring cells under similar conditions. Addition of valinomycin to respiring cells leads to an increase in K⁺ influx against the concentrational gradient in both growing and resting cells. In contrast to this, antibiotic-treated glycolysing cells experience passive K⁺ outflow down the concentrational gradient. It was thus concluded that the electrical potential cannot be the driving force for the energy-linked K⁺ transport in glycolysing cells.     

Regulation of the electrogenic (Na+ + K+)-pump of Ehrlich cells by intracellular cation levels

Ehrlich cells actively accumulate neutral amino acids even if both the Na⁺ and K⁺ gradients are inverted. The seeming contradiction of this observation to the gradient hypothesis is, however, explained by the presence of a powerful electrogenic Na⁺ pump, which stongly raises the electrochemical potential gradient of Na⁺ under these conditions. Since the evidence of this pump has so far been found only during abnormal concentrations of alkali ions (low K⁺, high Na⁺) in these cells, the question arises whether the pump is equally powerful with completely normal cells, when the pump is not ‘needed’ for amino acid transport. Using the initial rate of uptake of the test amino acid (2-aminoisobutyrate) as a sensitive monitor of the electrical potential at constant cation distribution between cell and medium, a procedure has been devised to split the overall electrical potential into the diffusional and the pump component. With this procedure it could be shown that the electrogenic pump per se is most powerful in K⁺-depleted and Na⁺-rich cells but declines to a lower ‘resting’ value according as the electrolyte content of the cell approaches normality. A strong positive correlation between cellular Na⁺ content and the electrogenic pumping activity suggests that the intracellular activity of this ion regulates the rate of the electrogenic pump. The low activity of the pump under normal conditions may explain why the existance of this pump has rarely come to attention previously.     

Salicylic Acid Induced Salinity Tolerance Through Manipulation of Ion Distribution Rather than Ion Accumulation

In this research, the effect of different SA concentrations (0, 0.5, 1.0, 1.5, and 2.0 mM) on biological and grain yield as well as Na⁺, K⁺, Cl^?, Ca²⁺, and Mg²⁺ distribution and accumulation in barley plants was examined under nonsaline (2 dS m^?1) and saline (12 dS m^?1) conditions in a three-year field study (2012–2015 growing seasons). Storage factor (SF) was defined as the concentration of an ion in the root, as a proportion of total uptake of that ion, to quantify ion partitioning between root and shoot. Salt stress decreased SF for K⁺, Ca²⁺, and Mg²⁺ and enhanced it for Na⁺ and Cl^?, which led to reduce grain and biological yield. Nonetheless, foliar-applied SA in varying concentrations could lower some of these adverse effects on ion transport and accumulation. At the 2nd and 3rd years, unfavorable climatic conditions such as less precipitation and higher temperature intensified salt stress and decreased the alleviating impact of SA. Foliar application of SA at higher levels increased SF for Na⁺ and Cl^? ions and decreased that for K⁺ indicating that SA helped barley plants keep more Na⁺ and Cl^? and less K⁺ ions in the root system, which suggested the probable role of SA in altering ion transport within the plant in favor of salt stress tolerance. SF was found to be more correlated with grain yield under both nonsaline and saline conditions. Overall, SF might be considered as a potential criterion for salt tolerance in barley plants.     

The effect of potassium diffusion through the Schwann cell layer on potassium conductance of the squid axon

Summary The accumulation of K⁺ ions in the intermembranous spaces of the Schwann cell layer during K⁺ ion current flow may lead to appreciable changes of the K⁺ equilibrium potential. Thus, for an evaluation of the K⁺ conductance of the axolemma, the transport of K⁺ ions through the Schwann cell layer has to be characterized quantitatively. In the present work this is done for a simplified model of the geometrical arrangement of the slit-like channels traversing the Schwann cell region.The K⁺ transport through the slits is treated for two cases: (a) Assuming that electro-kinetic volume flow does not affect K⁺ transport. In this case, pure diffusion of K⁺ ions accounts for their removal from the intermembranous spaces. Estimates on electro-kinetic volume flow show that this case applies to axons ofLoligo forbesi in voltage clamps of fairly small depolarizations. (b) For the case of appreciable electro-kinetic volume flow, evidence is adduced that its main effect is a widening of the slits through the Schwann cell layer. This physical situation could be treated only for the steady-state of convective diffusion of K⁺ ions in the slits.This case is applied to experiments on large depolarizing voltage clamps forLoligo pealii axons. It is shown that a widening of the slits to up to eight times the resting width is to be expected.In both cases (a) and (b), marked deviations of the K⁺ conductance of the axolemma from the Hodgkin-Huxley conductance result. The series resistance of the Schwann cell layer and the decay of after-effects of trains of action potentials are described by the theory.     

Identification of Electric-Field-Dependent Steps in the Na,K-Pump Cycle

The charge-transporting activity of the Na⁺,K⁺-ATPase depends on its surrounding electric field. To isolate which steps of the enzyme’s reaction cycle involve charge movement, we have investigated the response of the voltage-sensitive fluorescent probe RH421 to interaction of the protein with BTEA (benzyltriethylammonium), which binds from the extracellular medium to the Na⁺,K⁺-ATPase’s transport sites in competition with Na⁺ and K⁺, but is not occluded within the protein. We find that only the occludable ions Na⁺, K⁺, Rb⁺, and Cs⁺ cause a drop in RH421 fluorescence. We conclude that RH421 detects intramembrane electric field strength changes arising from charge transport associated with conformational changes occluding the transported ions within the protein, not the electric fields of the bound ions themselves. This appears at first to conflict with electrophysiological studies suggesting extracellular Na⁺ or K⁺ binding in a high field access channel is a major electrogenic reaction of the Na⁺,K⁺-ATPase. All results can be explained consistently if ion occlusion involves local deformations in the lipid membrane surrounding the protein occurring simultaneously with conformational changes necessary for ion occlusion. The most likely origin of the RH421 fluorescence response is a change in membrane dipole potential caused by membrane deformation.     

Intracellular compartmentation of Na+, K+ and Cl− in the Ehrlich ascites tumor cell: Correlation with the membrane potential

Summary The intracellular distribution of Na⁺, K⁺, Cl^– and water has been studied in the Ehrlich ascites tumor cell. Comparison of the ion and water contents of whole cells with those of cells exposed to La³⁺ and mechanical stress indicated that La³⁺ treatment results in selective damage to the cell membrane and permits evaluation of cytoplasmic and nuclear ion concentrations. The results show that Na⁺ is sequestered within the nucleus, while K⁺ and Cl^– are more highly concentrated in the cell cytoplasm. Reduction of the [Na⁺] of the incubation medium by replacement with K⁺ results in reduced cytoplasmic [Na⁺], increased [Cl^–] and no change in [K⁺]. Nuclear concentrations of these ions are virtually insensitive to the cation composition of the medium. Concomitant measurements of the membrane potential were made. The potential in control cells was –13.7 mV. Reduction of [Na⁺] in the medium caused significant depolarization. The measured potential is describable by the Cl^– equilibrium potential and can be accounted for in terms of cation distributions and permeabilities. The energetic implications of the intracellular compartmentation of ions are discussed.     

Identification of Electric-Field-Dependent Steps in the Na+,K+-Pump Cycle

The charge-transporting activity of the Na⁺,K⁺-ATPase depends on its surrounding electric field. To isolate which steps of the enzyme’s reaction cycle involve charge movement, we have investigated the response of the voltage-sensitive fluorescent probe RH421 to interaction of the protein with BTEA (benzyltriethylammonium), which binds from the extracellular medium to the Na⁺,K⁺-ATPase’s transport sites in competition with Na⁺ and K⁺, but is not occluded within the protein. We find that only the occludable ions Na⁺, K⁺, Rb⁺, and Cs⁺ cause a drop in RH421 fluorescence. We conclude that RH421 detects intramembrane electric field strength changes arising from charge transport associated with conformational changes occluding the transported ions within the protein, not the electric fields of the bound ions themselves. This appears at first to conflict with electrophysiological studies suggesting extracellular Na⁺ or K⁺ binding in a high field access channel is a major electrogenic reaction of the Na⁺,K⁺-ATPase. All results can be explained consistently if ion occlusion involves local deformations in the lipid membrane surrounding the protein occurring simultaneously with conformational changes necessary for ion occlusion. The most likely origin of the RH421 fluorescence response is a change in membrane dipole potential caused by membrane deformation.     

The role of calcium ions in the maintenance of resting potentials and ionic gradients of mollusk neurons

We studied on apple snail neurons the connection between K⁺ and Na⁺ concentration gradients, transmembrane difference of potentials, and concentrations of Ca²⁺ in the external medium. Sensitivity of the resting potential (RP) of neurons to the influence of temperature and to metabolic poisons rose considerably with a decrease of Ca²⁺ concentration in the solution surrounding a ganglion. An excess of Ca²⁺ in the external medium did not affect the RP or ion concentration in nerve cells. Removal of Na²⁺ from this solution causes hyperpolarization of the membrane which disappears when active transport of sodium ions through the membrane is suppressed. Sodium enrichment and potassium impoverishment of the neurons are observed in potassium-free solutions at 4°C. Reaccumulation of K⁺ and exclusion of Na⁺ from the solutions of 21°C depends on the concentration of Ca²⁺ in the medium. The ionic composition of the neurons is not restored upon removal of Ca²⁺ from the solution. Upon increasing the amount of Ca²⁺, movement of ions against the concentration gradients is intensified. Thus, it may be concluded that Ca²⁺ ions on the one hand participate in the maintenance of normal passive permeability of ions through the membrane, and on the other accelerate active transport of K⁺ and Na⁺ against the concentration gradients. The mechanisms of these processes are discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 1, No. 3, pp. 323–330, November–December, 1969.     

Identification of the Third Na Site and the Sequence of Extracellular Binding Events in the Glutamate Transporter

The transport cycle in the glutamate transporter (GlT) is catalyzed by the cotransport of three Na⁺ ions. However, the positions of only two of these ions (Na1 and Na2 sites) along with the substrate have been captured in the crystal structures reported for both the outward-facing and the inward-facing states of Glt_ph. Characterizing the third ion binding site (Na3) is necessary for structure-function studies attempting to investigate the mechanism of transport in GlTs at an atomic level, particularly for the determination of the sequence of the binding events during the transport cycle. In this study, we report a series of molecular dynamics simulations performed on various bound states of Glt_ph (the apo state, as well as in the presence of Na⁺, the substrate, or both), which have been used to identify a putative Na3 site. The calculated trajectories have been used to determine the water accessibility of potential ion-binding residues in the protein, as a prerequisite for their ion binding. Combined with conformational analysis of the key regions in the protein in different bound states and several additional independent simulations in which a Na⁺ ion was randomly introduced to the interior of the transporter, we have been able to characterize a putative Na3 site and propose a plausible binding sequence for the substrate and the three Na⁺ ions to the transporter during the extracellular half of the transport cycle. The proposed Na3 site is formed by a set of highly conserved residues, namely, Asp³¹², Thr⁹², and Asn³¹⁰, along with a water molecule. Simulation of a fully bound state, including the substrate and the three Na⁺ ions, reveals a stable structure—showing closer agreement to the crystal structure when compared to previous models lacking an ion in the putative Na3 site. The proposed sequence of binding events is in agreement with recent experimental models suggesting that two Na⁺ ions bind before the substrate, and one after that. Our results, however, provide additional information about the sites involved in these binding events.     

Bioelectric effects of ions microinjected into the giant axon of Loligo

1. A technique is described for recording the bioelectric activity of the squid giant axon during and following alteration of the internal axonal composition with respect to ions or other substances. 2. Experimental evidence indicates that the technique as described is capable of measuring changes in local bioelectric activity with an accuracy of 10 to 15 per cent or higher. 3. Alterations of the internal K⁺ or Cl^- concentrations do not cause the change in resting potential expected on the basis of a Donnan mechanism. 4. The general effect of microinjection of K⁺ Rb⁺, Na⁺, Li⁺, Ba⁺⁺, Ca⁺⁺, Mg⁺⁺, or Sr⁺⁺ is to cause decrease in spike amplitude, followed by propagation block. 5. The resting potential decreases when the amplitude of the spike becomes low and block is incipient. 6. The decrease in resting potential and spike amplitude may be confined to the immediate vicinity of the injection. 7. At block, the resting potential decreases up to 50 per cent, but injection of small quantities of divalent cations may cause much larger localized depolarization. 8. The blocking effectiveness of K⁺, Na⁺, and Ca⁺⁺ expressed as reciprocals of the relative amounts needed to cause block is approximately 1:5:100. Rb⁺ has the same low effectiveness as does K⁺. Li⁺ resembles Na⁺. Ba⁺⁺ and Mg⁺⁺ are approximately as effective as Ca⁺⁺. 9. Microinjection of Na⁺ may cause marked prolongation of the spike at the injection site as well as decrease in its amplitude. 10. The anions used (Cl^-, HCO₃^-, NO₃^-, SO₄^-, aspartate, and glutamate) do not seem to exert specific effects. 11. A tentative explanation is offered for the insensitivity of the resting potential to changes in the axonal ionic composition. 12. New data are presented on the range of variation, in a large sample, of the magnitude of the resting potential and spike amplitude.     

Model of Active Transport of Ions in Archaea Cells

A mathematical model of the active transport of main ions in cells of archaebacteria has been constructed. A set of equations has been developed and solved for ion fluxes through the bacterium membrane. The model is based on the principle “one ion—one transport system.” Considering experimental data, the major transport mechanism was determined for each ion and the balance equation was written on the basis of this mechanism in the stationary state. This allowed calculating values of the membrane potential and intracellular concentrations of the ions independently. The calculated values of the intracellular concentrations and resting potential are in qualitative agreement with the corresponding experimental values for cells of extremely halophilic archaea.     

Determinants of cation transport selectivity: Equilibrium binding and transport kinetics

ConclusionThe equilibrium ion-binding properties of ion channels and transporters can be difficult to discern from crystal structures alone, as proteins often adopt different lowest energy states depending on the ions bound. In cases where transport is slow, their inherent ion-binding preferences can be used to infer their transport preferences. However, in cases where transport is fast, the transport selectivity can hide their equilibrium preferences by accentuating the kinetics of ions hopping through a channel over its inherent ion-binding preferences. Thus, depending on the arrangement of ion-binding sites in a channel’s selectivity filter, one can achieve either selective or nonselective ion transport.The equilibrium K⁺ selectivity of some nonselective channels suggests a potential mechanism whereby they could evolve into a fast K⁺-selective channel. K⁺ channels and nonselective channels like CNG and HCN are related to one another in both sequence and structure, suggesting an evolutionary link between them. Swap experiments show that only a few mutations separate a nonselective channel from a K⁺-selective channel. One might imagine an evolutionary path between these channels in which the equilibrium preference for a K⁺ ion in a nonselective channel evolves into a K⁺-selective channel through these few mutations to create the selective ion queue. Alternatively, a slow single-ion channel with an equilibrium and transport preference for K⁺ ions could be transformed into a fast multi-ion channel through mutations that create a queue of K⁺-selective ion-binding sites, as is seen in most K⁺ channels studied to date.In the case of multi-ion selectivity filters, such as those found in K⁺ channels, the selectivity filter can be viewed as the active site that interacts with different queues of ions and water molecules. At least three properties emerge from multi-ion queues: (1) high conductance by reducing the affinity of multiple bound ions versus single ions; (2) high selectivity by allowing disfavored ions time to dissociate back into solution; and, consequently, (3) robust selectivity in an environment where ion concentrations can change. For transporters and carriers, the equilibrium preference and slow transport naturally create robust selectivity. In all these cases, equilibrium-based ion selectivity is achieved by slowing transport enough so that the disfavored ion is able to dissociate back into solution before transport takes place.     

Graded and All-or-None Electrogenesis in Arthropod Muscle : II. The effects of alkali-earth and onium ions on lobster muscle fibers

Conversion of graded responsiveness of lobster muscle fibers to all-or-none activity by alkali-earth and tetraethylammonium (TEA) ions appears to be due to a combination of effects. The membrane is hyperpolarized, its resistance is increased, and its sensitivity to external K⁺ is diminished, all effects which indicate diminished K⁺ conductance. While the spikes are prolonged, the conductance is higher throughout the response than it is in the resting membrane. Repetitive activity becomes prominent. These effects indicate maintained high conductance for an ion which causes depolarization. This is normally Na⁺, since its presence in low concentrations potentiates the effects of Ba⁺⁺, but the alkali-earth ions and TEA can also carry inward charge. Ba⁺⁺, Sr⁺⁺, and TEA appear to be more effective than is Ca⁺⁺ in its normal role, which is probably to depress K⁺ conductance and Na inactivation. Thus, conversion of graded to all-or-none responsiveness appears to occur because of the relative increase of depolarizing inward ion flux and decrease of repolarizing outward flux.