Does the Na channel conduct ions through a water-filled pore or a condensed-state pathway?

Many investigators assert that the ion-conducting pathway of the Na channel is a water-filled pore. This assertion must be reevaluated to clear the way for more productive approaches to channel gating. The hypothesis of an aqueous pore leaves the questions of voltage-dependent gating and ion selectivity unexplained because a column of water can neither serve as a switch nor provide the necessary selectivity. The price of believing in an aqueous pore therefore is a futile search for separate ad hoc mechanisms for gating and selectivity. The fallacy is to assume that only water is available to carry ions rapidly, ignoring the role of the glycoprotein, which can form an elastomeric phase with water. The elastomer is a state of matter, neither liquid nor solid, in which the molecules of a liquid are threaded together with cross-linked polymer chains; it supports fast ion motion (Owen, 1989). An alternative hypothesis for channel gating, based on condensed-state materials science, already exists (Leuchtag, 1988, 1991a). The ferroelectric-superionic transition hypothesis (FESITH) postulates that the Na channel exists in a metastable ordered (closed) state at resting potential and, on threshold depolarization, undergoes a reversible order-disorder phase transition to a less-ordered, ion-conducting (open) state. The ordered state is ferroelectric; the disordered state is a fast ion conductor selective for Li+ and Na+. The basis of the voltage dependence is elevation of transition temperature with electric field, well established in ferroelectrics. FESITH is consistent with single-channel transitions, gating currents, heat and cold block, and other phenomena observed at channel or membrane level.(ABSTRACT TRUNCATED AT 250 WORDS)     

Ammonium ion transport—a cause of cell death

Ammonium can be transported into the cell by ion pumps in the cytoplasmic membrane. Ammonia then diffuse out through the cell membrane. A futile cycle is created that results in cytoplasmic acidification and extracellular alkalinisation. Ammonium transport can be quantified by measuring the extracellular pH changes occurring in a cell suspension (in PBS) after addition of ammonium. By using this technique, in combination with specific inhibitors of various ion pumps, it was shown that ammonium ions are transported across the cytoplasmic membrane by the Na⁺K⁺2Cl^--cotransporter in both hybridoma and myeloma cells. Further, the Na⁺/H⁺ exchanger, which regulates intracellular pH by pumping out protons, was shown to be active during ammonium exposure. The viability of hybridoma cells suspended in PBS and exposed to NH _inf4 ^sup+ for only 90 min, was reduced by 11% (50% necrosis and 50% apoptosis). A control cell suspension did not loose viability during this time. Turning off the activity of the Na⁺/H⁺ exchanger (by amiloride) during ammonium exposure decreased viability further, while inhibiting transport itself (by bumetanide) restored viability to the same level as for the control experiment with bumetanide alone. These results show that one effect of ammonia/ammonium on cell physiology is specifically related to the inward transport of ammonium ions by membrane bound ion pumps.Abbreviations q _pH specific rate of pH increase (pH units per min and 10⁶ cells per ml)     

Multinuclear NMR studies of the Langendorff perfused rat heart

The quantitation of intracellular sodium ion concentration [Na+]in perfused organs using NMR spectroscopy requires a knowledge of the extent of visibility of the 23Na resonance and of the intracellular volume of the organ. We have used a multinuclear NMR approach, in combination with the extracellular shift reagent dysprosium (III) tripolyphosphate, to determine the NMR visibility of intra- and extracellular 23Na and 35Cl ions, intracellular volume, and [Na+]in in the isolated Langendorff perfused rat heart. Based on a comparison of the extracellular volumes calculated using 2H and 23Na, 35Cl, or 59Co NMR of the perfused heart we conclude that resonances of extracellular sodium and chloride ions (including ions in interstitial spaces) are fully visible, contrary to assumptions in the literature. Furthermore, prolonged hypoxia or ischemia caused a dramatic increase in intracellular Na+ and [Na+] in rose to approach that in the external medium indicating full visibility of the intracellular 23Na resonance. Resonance intensities of intra- and extracellular 23Na ions, along with a knowledge of the extracellular space as a fraction of the total organ water space, yielded an average [Na+] in of about 10 mM (10 +/- 1.5 mM) for the rat heart at 37 degrees C. Double-quantum filtered 23Na NMR of the perfused rat heart in the absence and presence of paramagnetic reagents revealed, contrary to assumptions in the literature, that both intra- and extracellular sodium ions contribute to the detected signal.     

Conditions for Reversible Na Intercalation in Graphite: Theoretical Studies on the Interplay Among Guest Ions,Solvent, and Graphite Host

Graphite is the most widely used anode material for Li‐ion batteries and is also considered a promising anode for K‐ion batteries. However, Na⁺, a similar alkali ion to Li⁺ or K⁺, is incapable of being intercalated into graphite and thus, graphite is not considered a potential electrode for Na‐ion batteries. This atypical behavior of Na has drawn considerable attention; however, a clear explanation of its origin has not yet been provided. Herein, through a systematic investigation of alkali metal graphite intercalation compounds (AM‐GICs, AM = Li, Na, K, Rb, Cs) in various solvent environments, it is demonstrated that the unfavorable local Na‐graphene interaction primarily leads to the instability of Na‐GIC formation but can be effectively modulated by screening Na ions with solvent molecules. Moreover, it is shown that the reversible Na intercalation into graphite is possible only for specific conditions of electrolytes with respect to the Na‐solvent solvation energy and the lowest unoccupied molecular orbital level of the complexes. It is believed that these conditions are applicable to other electrochemical systems involving guest ions and an intercalation host and hint at a general strategy to tailor the electrochemical intercalation between pure guest ion intercalation and cointercalation.     

Ion movements in cell death: from protection to execution

Cell death is preceded by severe disruption of inorganic ion homeostasis. Seconds to minutes after an injury, calcium, protons, sodium, potassium and chloride are exchanged between the cell and its environment. Simultaneously, ions are shifted between membrane compartments inside the cell, whereby mitochondria and endoplasmic reticulum play a crucial role. Depending of the type and severity of injury, two mutually exclusive metastable states can be reached, which predict the final outcome. Cells characterized by large increases in cytosolic [Ca2+], [Na+] and [Mg2+] swell and die by necrosis; alternatively, cells characterized by high [H+] and low [K+], with normal [Na+] and normal to moderate [Ca2+] increases die by apoptosis. The levels of these ions represent central determinants in signaling events leading to cell death. Their movements are explained mechanistically by specific modulation of membrane transport proteins including channels, pumps and carriers.     

The two C-terminal tyrosines stabilize occluded Na/K pump conformations containing Na or K ions

Interactions of the three transported Na ions with the Na/K pump remain incompletely understood. Na/K pump crystal structures show that the extended C terminus of the Na,K–adenosine triphosphatase (ATPase) α subunit directly contacts transmembrane helices. Deletion of the last five residues (KETYY in almost all Na/K pumps) markedly lowered the apparent affinity for Na activation of pump phosphorylation from ATP, a reflection of cytoplasmic Na affinity for forming the occluded E1P(Na3) conformation. ATPase assays further suggested that C-terminal truncations also interfere with low affinity Na interactions, which are attributable to extracellular effects. Because extracellular Na ions traverse part of the membrane’s electric field to reach their binding sites in the Na/K pump, their movements generate currents that can be monitored with high resolution. We report here electrical measurements to examine how Na/K pump interactions with extracellular Na ions are influenced by C-terminal truncations. We deleted the last two (YY) or five (KESYY) residues in Xenopus laevis α1 Na/K pumps made ouabain resistant by either of two kinds of point mutations and measured their currents as 10-mM ouabain–sensitive currents in Xenopus oocytes after silencing endogenous Xenopus Na/K pumps with 1 µM ouabain. We found the low affinity inhibitory influence of extracellular Na on outward Na/K pump current at negative voltages to be impaired in all of the C-terminally truncated pumps. Correspondingly, voltage jump–induced transient charge movements that reflect pump interactions with extracellular Na ions were strongly shifted to more negative potentials; this signals a several-fold reduction of the apparent affinity for extracellular Na in the truncated pumps. Parallel lowering of Na affinity on both sides of the membrane argues that the C-terminal contacts provide important stabilization of the occluded E1P(Na3) conformation, regardless of the route of Na ion entry into the binding pocket. Gating measurements of palytoxin-opened Na/K pump channels additionally imply that the C-terminal contacts also help stabilize pump conformations with occluded K ions.     

The Na/H antiport of eukaryotic cells: Relationship between the kinetic properties of the system and its physiological function

The Na+/H+ antiport is present in the plasma membrane of virtually all vertebrate cells and it plays a central role in cell homeostasis. The pharmacological properties and the characteristics of the interaction of extracellular Na+, Li+, H+ and of intracellular H+ with the Na+/H+ antiport are reviewed herein. The kinetic properties of the system are shown to be essential for defining its four main physiological functions: transepithelial ion transport, control of the pHi, control of the intracellular Na+ concentration, and control of the cell volume. The activity of the Na+/H+ antiport can be modulated by a large number of effectors which are thought to act via protein kinases. At least three mechanisms of activation of the Na+/H+ exchanger are defined from the analysis of the kinetic properties of the system. Activation of the Na+/H+ antiport leads to very different consequences, depending upon the activity of other ion transporting systems in the membrane.     

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.     

Na/K pump-induced [Na](i) gradients in rat ventricular myocytes measured with two-photon microscopy

Via the Na/Ca and Na/H exchange, intracellular Na concentration ([Na](i)) is important in regulating cardiac Ca and contractility. Functional data suggest that [Na](i) might be heterogeneous in myocytes that are not in steady state, but little direct spatial information is available. Here we used two-photon microscopy of SBFI to spatially resolve [Na](i) in rat ventricular myocytes. In vivo calibration yielded an apparent K(d) of 27 +/- 2 mM Na. Similar resting [Na](i) was found using two-photon or single-photon ratiometric measurements with SBFI (10.8 +/- 0.7 vs. 11.1 +/- 0.7 mM). To assess longitudinal [Na](i) gradients, Na/K pumps were blocked at one end of the myocyte (locally pipette-applied K-free extracellular solution) and active in the rest of the cell. This led to a marked increase in [Na](i) at sites downstream of the pipette (where Na enters the myocyte and Na/K pumps are blocked). [Na](i) rise was smaller at upstream sites. This resulted in sustained [Na](i) gradients (up to approximately 17 mM/120 microm cell length). This implies that Na diffusion in cardiac myocytes is slow with respect to trans-sarcolemmal Na transport rates, although the mechanisms responsible are unclear. A simple diffusion model indicated that such gradients require a Na diffusion coefficient of 10-12 microm(2)/s, significantly lower than in aqueous solutions.     

Two functionally different Na/K pumps in cardiac ventricular myocytes

The whole-cell patch-clamp technique was used to voltage clamp acutely isolated myocytes at -60 mV and study effects of ionic environment on Na/K pump activity. In quiescent guinea pig myocytes, normal intracellular Na+ is approximately 6 mM, which gives a total pump current of 0.25 +/- 0.09 pA/pF, and an inward background sodium current of 0.75 +/- 0.26 pA/pF. The average capacitance of a cell is 189 +/- 61 pF. Our main conclusion is the total Na/K pump current comprises currents from two different types of pumps, whose functional responses to the extracellular environment are different. Pump current was reversibly blocked with two affinities by extracellular dihydro-ouabain (DHO). We determined dissociation constants of 72 microM for low affinity (type-1) pumps and 0.75 microM for high affinity (type-h) pumps. These dissociation constants did not detectably change with two intracellular Na+ concentrations, one saturating and one near half- saturating, and with two extracellular K+ concentrations of 4.6 and 1.0 mM. Ion effects on type-h pumps were therefore measured using 5 microM DHO and on total pump current using 1 mM DHO. Extracellular K+ half- maximally activated the type-h pumps at 0.4 mM and the type-1 at 3.7 mM. Extracellular H+ blocked the type-1 pumps with half-maximal blockade at a pH of 7.71 whereas the type-h pumps were insensitive to extracellular pH. Both types of pumps responded similarly to changes in intracellular-Na+, with 9.6 mM causing half-maximal activation. Neither changes in intracellular pH between 6.0 and 7.2, nor concentrations of intracellular K+ of 140 mM or below, had any effect on either type of pump. The lack of any effect of intracellular K+ suggests the dissociation constants are in the molar range so this step in the pump cycle is not rate limiting under normal physiological conditions. Changes in intracellular-Na+ did not affect the half-maximal activation by extracellular K+, and vice versa. We found DHO-blockade of Na/K pump current in canine ventricular myocytes also occurred with two affinities, which are very similar to those from guinea pig myocytes or rat ventricular myocytes. In contrast, isolated canine Purkinje myocytes have predominantly the type-h pumps, insofar as DHO-blockade and extracellular K+ activation are much closer to our type-h results than type-1. These observations suggest for mammalian ventricular myocytes: (a) the presence of two types of Na/K pumps may be a general property. (b) Normal physiological variations in extracellular pH and K+ are important determinants of Na/K pump current. (c) Normal physiological variations in the intracellular environment affect Na/K pump current primarily via the Na+ concentration. Lastly, Na/K pump current appears to be specifically tailored for a tissue by expression of a mix of functionally different types of pumps.     

23Na multiple quantum filtered NMR characterisation of Na+ binding and dynamics in animal cells: a comparative study and effect of Na+/Li+ competition

Double quantum and triple quantum filtered ²³Na nuclear magnetic resonance techniques were used to characterise in detail the isotropic and anisotropic binding and dynamics of intra- and extracellular Na⁺ in different cellular systems, in the absence and presence of Li⁺. The kinetics of Li⁺ influx by different cell types was evaluated. At steady state, astrocytes accumulated more Li⁺ than red blood cells (RBCs), while a higher intracellular Li⁺ concentration was found in chromaffin than in SH-SY5Y cells. Anisotropic and isotropic motions were detected for extracellular Na⁺ in all cellular systems studied. Isotropic intracellular Na⁺ motions were observed in all types of cells, while anisotropic Na⁺ motions in the intracellular compartment were only detected in RBCs. ²³Na triple quantum signal efficiency for intracellular Na⁺ was SH-SY5Y > chromaffin > RBCs, while the reverse order was observed for the extracellular ions. ²³Na double quantum signal efficiency for intracellular Na⁺ was non-zero only in RBCs, and for extracellular Na⁺ the order RBCs > chromaffin > SH-SY5Y cells was observed. Li⁺ loading generally decreased intracellular Na⁺ isotropic movements in the cells, except for astrocytes incubated with a low Li⁺ concentration and increased anisotropic intracellular Na⁺ movements in RBCs. Li⁺ effects on the extracellular signals were more complex, reflecting Li⁺/Na⁺ competition for isotropic and anisotropic binding sites at the extracellular surface of cell membranes and also at the surface of the gel used for cell immobilisation. These results are relevant and contribute to the interpretation of the in vivo pharmacokinetics and sites of Li⁺ action.     

Calcium-dependent sodium current in the marine ciliateEuplotes vannus

Summary Ca and Na inward currents were recorded upon depolarizations inEuplotes after the blockage of K outward currents with intracellular Cs ions. The Na current was analyzed under voltage clamp and had the following properties: it activated to a maximum within 150 msec and partly inactivated during sustained voltage steps. It had a positive equilibrium potential between 25 and 30 mV and could be carried by Na or Li ions but not by K, choline or Tris ions. The current revealed a prominent associated inward tail current which deactivated with a single-exponential time constant of 118 msec. Both the current and its tail were strongly reduced after reduction of the extracellular Na concentration. Externally applied K channel blocker tetraethylammonium chloride did not block the current. Either EGTA injection into the cell or nonlethal deciliation with ethanol eliminated the current and its tail. These results indicate the existence of a Na conductance within the membrane ofEuplotes which is activated by the intracellular level of free Ca²⁺.     

Ionic Partition between Surface and Bulk Water in a Silica Gel: A Biological Model

Distribution of the biologically important ions between two aqueous phases of different structure has been used as a model for ionic distribution in living tissue. When other sources of specificity had been eliminated or corrected for, surface-oriented water in a silica gel was found to have increased solvent power for water-structure-breaking ions and decreased solvent power for water-structure-making ions; and the relative solubility of an ion in the phase of enhanced structure increased regularly with the water-structure-breaking powers of the ion. The ionic selectivity was decreased in the presence of urea. The selectivity of the gel water for potassium relative to sodium increased to a maximum when the gel surface was partially ionized so that distribution of cations was not linked to distribution of anions, and then decreased as the surface changed from a hydrogen bonding to an ionic surface. It is pointed out that the distribution of ions across most living cell membranes is qualitatively the same as that found in this silica gel, and it is suggested that the membrane separates two aqueous phases of different structure, and that the enhanced structure of cell water contributes to the observed ionic distributions.     

Molecular Model of a Cell Plasma Membrane With an Asymmetric Multicomponent Composition: Water Permeation and Ion Effects

We present molecular dynamics simulations of a multicomponent, asymmetric bilayer in mixed aqueous solutions of sodium and potassium chloride. Because of the geometry of the system, there are two aqueous solution regions in our simulations: one mimics the intracellular region, and one mimics the extracellular region. Ion-specific effects are evident at the membrane/aqueous solution interface. Namely, at equal concentrations of sodium and potassium, sodium ions are more strongly adsorbed to carbonyl groups of the lipid headgroups. A significant concentration excess of potassium is needed for this ion to overwhelm the sodium abundance at the membrane. Ion-membrane interactions also lead to concentration-dependent and cation-specific behavior of the electrostatic potential in the intracellular region because of the negative charge on the inner leaflet. In addition, water permeation across the membrane was observed on a timescale of ∼100 ns. This study represents a step toward the modeling of realistic biological membranes at physiological conditions in intracellular and extracellular environments.     

Energetic cooperation via ion-permeable junctions in mixed animal cell cultures

Low ouabain concentration (1 x 10(-6) M) is shown to decrease intracellular K+ (K+in) and to increase intracellular Na+ (Na+in) in human fibroblast cell cultures. The same ouabain concentration was without effect upon K+in ad Na+in in rodent cultures such as BHK-21, mouse fibroblasts and rat glyoma C6 cells. K+in and Na+in in the mixed cultures of human and BHK-21 fibroblasts or human and mouse fibroblasts were found to be resistant to 1 x 10(-6) M ouabain whereas that of the mixtures of human and rat glyoma C6 cells proved to be ouabain-sensitive. The gap-junction-mediated dye transfer was revealed between human and BHK-21 cells. Such an effect was very small in the human-C6 cell mixed culture. It is concluded that cells with active ion pumps can support the maintenance of K+ and Na+ gradients in cells with inactive pumps, provided that effective ion transport via gap junctions takes place.     

Measurement of a wide range of intracellular sodium concentrations in erythrocytes by 23Na nuclear magnetic resonance.

The accuracy of the 23Na nuclear magnetic resonance (NMR) method for measuring the sodium concentration in erythrocytes was tested by comparing the NMR results to those obtained by emission-flame photometry. Comparisons were made on aqueous solutions, hemolysates, gels, ghosts, and intact erythrocytes. The intra- and extracellular 23Na NMR signals were distinguished by addition of the dysprosium tripolyphosphate [Dy(PPP)7-2] shift reagent to the extracellular fluid. The intra- and extracellular volumes of ghosts and cells were determined by the isotope dilution method. Our results indicate that greater than 20% of the intracellular signal remains undetected by NMR in ghosts and cells. When the cells are hemolyzed, the amount of NMR-detectable sodium varies depending on the importance of gel formation. In hemolysates prepared by water addition, the NMR and flame photometry results are identical. The loss of signal in ghosts, cells, and undiluted hemolysates is attributed to partial binding of the Na+ ion to intracellular components, this binding being operative only when these components exist in a gel state. In a second part, 31P NMR was used to monitor the penetration of the shift reagent into the cells during incubation. Our data demonstrate that free Dy3+ can slowly accumulate inside the red cell.     

Role of water in some biological processes.

The state of intracellular water has been a matter of controversy for a long time for two reasons. First, experiments have often given conflicting results. Second, hitherto, there have been no plausible grounds for assuming that intracellular water should be significantly different from bulk water. A collective behavior of water molecules is suggested here as a thermodynamically inevitable mechanism for generation of appreciable zones of abnormal water. At a highly charged surface, water molecules move together, generating a zone of water perhaps 6 nm thick, which is weakly hydrogen bonded, fluid, and reactive and selectively accumulates small cations, multivalent anions, and hydrophobic solutes. At a hydrophobic surface, molecules move apart and local water becomes strongly bonded, inert, and viscous and accumulates large cations, univalent anions, and compatible solutes. Proteins and many other biopolymers have patchy surfaces which therefore induce, by the two mechanisms described, patchy interfacial water structures, which extended appreciable distances from the surface. The reason for many conflicting experimental results now becomes apparent. Average values of properties of water measured in gels, cells, or solutions of proteins are often not very different from the same properties of normal water, giving no indication that they are averages of extreme values. To detect the operation of this phenomenon, it is necessary to probe selectively a single abnormal population. Examples of such experiments are given. It is shown that this collective behavior of water molecules amounts to a considerable biological force, which can be equivalent to a pressure of 1,000 atm (1.013 x 10(5) kPa). It is suggested that cells selectively accumulate K+ ions and compatible solutes to avoid extremes of water structure in their aqueous compartments, but that cation pumps and other enzymes exploit the different solvent properties and reactivities of water to perform work of transport or synthesis.     

A possible mechanism for the Na,K-ATPase

A model previously described for the Ca²⁺ pump of sarcoplasmic reticulum has been modified in a thought experiment so that it has the properties of a Na,K-adenosinetriphosphatase (ATPase). When the two Ca²⁺-specific sites are changed into three Na⁺-specific sites, and the channel which opens in the actively transporting conformation made univalent- instead of divalent-cation-selective, the model has the properties of the Na-ATPase which is observed on red cell membranes in the absence of both Na⁺ and K⁺ externally. As in the model for the Ca-ATPase the driving force for transport is generated by a change in solvent structure so that a preformed ionic equilibrium is displaced in favour of less-highly hydrated species; in this case highly hydrated Mg²⁺ ions displace the less highly hydrated Na⁺ ions from binding sites; and Na⁺ diffuses out through a simultaneously opened channel. With the addition of three external K⁺-selective sites per α-polypeptide chain, and the constraint that pump units with their external sites occupied by any univalent cation cannot be phosphorylated by ATP, the model turns out to have the properties of a Na,K-ATPase. It operates in the $\text{Na}{}^{\mathrm{+}}\text{K}{}^{\mathrm{+}}$ exchange, $\text{Na}{}^{\mathrm{+}}\text{Na}{}^{\mathrm{+}}$ exchange, $\text{K}{}^{\mathrm{+}}\text{K}{}^{\mathrm{+}}$ exchange, K⁺-dependent phosphatase, uncoupled Na⁺ efflux and pump reversal modes. It is concluded that if the modified water in the cleft of the phospho-enzymes has properties similar to those of water at 5°C the pump is competent to exchange three intracellular Na⁺ ions for two extracellular K⁺ ions, and one intracellular Na⁺ ion but it is incapable of exchanging three Na⁺ ions for three K⁺ ions.     

An analytical model of ionic movements in airway epithelial cells.

A new mathematical model of ion movements in airway epithelia is presented, which allows predictions of ion fluxes, membrane potentials and ion concentrations. The model includes sodium and chloride channels in the apical membrane, a Na/K pump and a cotransport system for Cl- with stoichiometry Na+:K+:2Cl- in the basolateral membrane. Potassium channels in the basolateral membrane are used to regulate cell volume. Membrane potentials, ion fluxes and intracellular ion concentration are calculated as functions of apical ion permeabilities, the maximum pump current and the cotransport parameters. The major predictions of the model are: (1) Cl- concentration in the cell is determined entirely by the intracellular concentration of negatively charged impermeable ions and the osmotic conditions; (2) changes in intracellular Na+ and K+ concentrations are inversely related; (3) cotransport provides the major driving force for Cl- flux, increases intracellular Na+ concentration, decreases intracellular K+ concentration and hyperpolarizes the cell interior; (4) the maximum rate of the Na/K pump, by contrast, has little effect on Na+ or Cl- transepithelial fluxes and a much less pronounced effect on cell membrane polarization; (5) an increase in apical Na+ permeability causes an increase in intracellular Na+ concentration and a significant increase in Na+ flux; (6) an increase in apical Cl- permeability decreases intracellular Na+ concentration and Na+ flux; (7) assuming Na+ and Cl- permeabilities equal to those measured in human nasal epithelia, the model predicts that under short circuit conditions, Na+ absorption is much higher than Cl- secretion, in agreement with experimental measurements.     

How erythrocyte volume is regulated, or what mathematical models can and cannot do for biology

Modern concepts of the red blood cell (RBC) volume regulation are considered. It is shown that the system of ion pumps and channels in the cell membrane ensures the physiological value of volume with a precision of about 10% even at 5- to 7-fold variations of passive membrane permeability for ions. Particular attention is paid to mathematical models for evaluation of the role of different molecular mechanisms in the RBC volume control. It is shown that many questions, for example, ‘why the Na⁺,K⁺-ATPase pumps the ions in opposite directions’ or ‘what is the physiological role of Ca²⁺-activated K⁺-channels’, cannot be answered without adequate mathematical models of such complex control systems as cell volume control.