Interactions of cell volume, membrane potential, and membrane transport parameters

Modeling cell volume regulation in nonexcitable cells: the roles of the Na+ pump and of cotransport systems

The purpose of this study is to contribute to understanding the role of Na+-K+-ATPase and of ionic cotransporters in the regulation of cell volume, by employing a model that describes the rates of change of the intracellular concentrations of Na+, K+, and Cl-, of the cell volume, and of the membrane potential. In most previous models of dynamic cellular phenomena, Na+-K+-ATPase is incorporated via phenomenological formulations; the enzyme is incorporated here via an explicit kinetic scheme. Another feature of the present model is the capability to perform short-term cell volume regulation mediated by cotransporters of KCl and NaCl. The model is employed to perform numerical simulations for a "typical" nonpolarized animal cell. Basically, the results are consistent with the view that the Na+ pump mainly plays a long-term role in the maintenance of the electrochemical gradients of Na+ and K+ and that short-term cell volume regulation is achieved via passive transport, exemplified in this case by the cotransport of KCl and NaCl.

Delayed increase of cell volume of single pyramidal cells in live rat hippocampal slices upon kainate application

Cell volume is an important physiologic parameter but is not directly accessible by conventional microscopy in vivo or in slice preparations. After staining of rat hippocampal slices with 1,1'-dioctadecyl-3,3,3',3'-tetramethylinso-carbocyanineperchlor ate (DiI), living single CA1 pyramidal cells were visualized by confocal microscopy while others in the illuminated area were recorded intracellularly. Resting membrane potential and action potentials were not affected by staining with DiI (4 microM) and repeated laser illumination (up to 600 times). A time- and dose-dependent increase of cell volume succeeds membrane depolarization upon bath application of kainate (40 microM and 100 microM) with a delay of several minutes indicating active regulation of cell volume. We conclude that cell swelling as visualized by confocal microscopy is a relatively late event of kainate excitotoxicity.

Analysis of volume regulation in an epithelial cell model

An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a previously developed model of the toad urinary bladder (Strieter et al., 1990, J. gen. Physiol. 96, 319-344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified model of the epithelium of the thick ascending limb of Henle.

Effects of selective cardiac denervation on collateral blood flow after coronary artery occlusion in conscious dogs

The extent to which cardiac nerves regulate responses to myocardial ischemia remains controversial. Our data in conscious dogs indicate that neither selective posterior left ventricular (LV) wall denervation nor selective ventricular denervation, leaving the atria intact, modifies the effects of coronary artery occlusion (for 24 h) on regional myocardial function and infarct size as compared to normally innervated dogs. Since hemodynamic changes were similar among the three groups after coronary artery occlusion, it is possible to speculate that responses of collateral blood flow to the ischemic zone were also not modified by chronic selective cardiac denervation. To address this, individual samples were selected and included in either the infarcted (TTC negative) or salvaged (TTC positive) group. The infarcted and salvaged samples were paired according to blood flow levels of 0.1-0.2, 0.2-0.3, or 0.3-0.4 ml/min/g at either 5 min, 1 h, 3 h, or 6 h after coronary artery occlusion. The results demonstrated similar patterns of myocardial blood flow in tissue samples within the area at risk after coronary artery occlusion in the animals, regardless of whether the ischemic zone was innervated or denervated. While blood flow rose in ischemic tissue that ultimately was salvaged, and tended not to rise over the 24 h monitoring period in tissue samples that became necrotic, no differences could be discerned on the basis of intact or absent innervation of the ischemic zone. Thus, chronic absence of cardiac nerves does not affect regulation of ischemic zone blood flow following coronary artery occlusion in conscious dogs.

Simultaneous imaging of cell and mitochondrial membrane potentials

The distribution of charged membrane-permeable molecular probes between intracellular organelles, the cytoplasm, and the outside medium is governed by the relative membrane electrical potentials of these regions through coupled equilibria described by the Nernst equation. A series of highly fluorescent cationic dyes of low membrane binding and toxicity (Ehrenberg, B., V. Montana, M.-D. Wei, J. P. Wuskell, and L. M. Loew, 1988. Biophys. J. 53:785-794) allows the monitoring of these equilibria through digital imaging video microscopy. We employ this combination of technologies to assess, simultaneously, the membrane potentials of cells and of their organelles in situ. We describe the methodology and optimal conditions for such measurements, and apply the technique to concomitantly follow, with good time resolution, the mitochondrial and plasma membrane potentials in several cultured cell lines. The time course of variations induced by chemical agents (ionophores, uncouplers, electron transport, and energy transfer inhibitors) in either or both these potentials is easily quantitated, and in accordance with mechanistic expectations. The methodology should therefore be applicable to the study of more subtle and specific, biologically induced potential changes in cells.

Intracellular pH of canine subendocardial Purkinje cells surviving in 1-day-old myocardial infarcts

A large reduction of intracellular potassium activity in depolarized subendocardial Purkinje fibers 24 hours after coronary artery ligation is accompanied by a much smaller increase in intracellular sodium activity. Similar intracellular ionic changes also occur during acute ischemia in ventricular muscle and are consistent with mechanisms based on intracellular acidification, which is known to occur in acutely ischemic muscle. To determine if canine subendocardial Purkinje cells 24 hours after myocardial infarction are also acidic, their intracellular pH, surface pH, and maximum diastolic potential (MDP) were measured with double-barrel pH-sensitive microelectrodes and compared with control fibers in noninfarcted hearts. In 12 mM bicarbonate Tyrode's solution (5% CO2-95% O2), the average intracellular pH was not significantly different (p greater than 0.25) for normal tissue (6.83 +/- 0.08, SD, MDP = -83.5 +/- 3.2 mV), for depolarized Purkinje fibers in infarct preparations during the first hour of superfusion (6.88 +/- 0.11, MDP = -47.8 +/- 11.8 mV), and for partially recovered Purkinje fibers in infarcts averaged over the third to sixth hours of superfusion (6.85 +/- 0.12, MDP = -74.5 +/- 9.6 mV). In 24 mM bicarbonate Tyrode's solution, infarct intracellular pH during both the first hour of superfusion (7.08 +/- 0.13, MDP = -57.6 +/- 15.7 mV) and during the third to sixth hours of superfusion (7.06 +/- 0.15, MDP = -76.5 +/- 9.6 mV) was significantly alkaline (p less than 0.0005) compared with average control pH (6.92 +/- 0.12, MDP = 82.1 +/- 3.7 mV). In 24 mM bicarbonate Tyrode's solution, the intracellular pH did vary with MDP (0.0032 pH units/mV). During superfusion of normal Purkinje fibers with hypoxic Tyrode's solution, intracellular pH acidified by 0.22 pH units as they depolarized. Therefore, intracellular acidification does not seem to be a cause of the depolarization of subendocardial Purkinje cells 24 hours after myocardial infarction.

Kinetic model of the effects of electrogenic enzymes on the membrane potential

Electrogenic enzymes contribute to the electrical field existing across biological membranes by using a source of free energy to generate an ionic current. The model introduced here permits one to evaluate this contribution. Since the model incorporates the electrogenic enzyme in the form of a sequential kinetic diagram, it permits one to study the kinetic effects of the concentration of the enzyme, the substrates and the different ligands on the membrane potential. Ionic electrodiffusion is expressed in terms of a chemical reaction; ionic permeabilities are thus treated as voltage-dependent rate constants. We use the condition of global electroneutrality to obtain an expression for the electrical potential difference across the membrane; such expression constitutes an extension of the Goldman-Hodgkin-Katz equation. The enzyme-related terms appear in the equation as functions of the rate constants and the diverse concentrations. The model is used to analyze the case of a cell membrane traversed by Na+ and K+ by simple diffusion, and by electrogenic transport mediated by a Na+-K+ ATPase. The enzyme reaction is represented by the six-step scheme proposed by Chapman et al. (1983, J. membr. Biol. 74, 139-153). The main results of the numerical calculations are that, within a certain interval, the membrane potential difference depends linearly on the enzyme density and hyperbolically on the ATP concentration. A similar behavior has been experimentally observed for the electrogenic proton pump of Neurospora crassa. Thus, the model here can be useful in the explanation and prediction of effects of electrogenic enzymes on the membrane potential.

New insights into maitotoxin action

Maitotoxin (3 ng/mol) induced a massive uptake of 45Ca2+ into BC3H1 cells. This effect exhibits a lag phase of 3 min. Inositol diphosphate formation occurred concomittantly with the 45Ca2+ uptake but inositol monophosphate formation was found only after a 5-min delay following toxin addition. Maitotoxin-induced 45Ca2+ influxes could not be blocked by either 1 microM verapamil, 1 microM nifedipine or 1 mM La3+ but was blocked by Zn2+ (IC50 = 41 microM). In addition to inositol phosphate formation and 45Ca2+ uptake, maitotoxin stimulated a large uptake of Na+ and a great loss of K+ in BC3H1 cells. In the absence of Ca2+ (1 mM EGTA) none of the four maitotoxin effects could be detected. After restoration of Ca2+, the maitotoxin effects reappeared even when the toxin itself was no longer present. The divalent cation, Co2+ (1 mM), inhibited ion movements induced by maitotoxin and also digitonin (8.1 microM). The toxin action showed a very pronounced pH dependence. At low pH, maitotoxin was inactive. The dose-response curves for H+ ion inhibition of maitotoxin-induced Ca2+ uptake showed a shift to the right when determined in the absence of HCO3- and HCO3-/Cl- ions. It was concluded that the primary action of maitotoxin in BC3H1 cells was a pore-forming or channel-forming activity of a non-classical type. Some properties of maitotoxin resemble those of alpha-latrotoxin, others those of pore-forming agents such as melittin or alpha-toxin of Staphylococcus aureus.

Steady-state voltages, ion fluxes, and volume regulation in syncytial tissues

Equations are developed that describe the steady-state relationships among ion fluxes, solute fluxes, water flow, voltage, concentration of solute, and hydrostatic pressure in a spherically symmetrical syncytial tissue. Each cell of the syncytium is assumed to have membrane channels for Na, K, and Cl, a membrane pump for Na/K, and some concentration of intracellular protein of net negative charge. However, the surface cells and inner cells of the tissue are assumed to have different distributions of membrane transport properties, hence there is a radial circulation of fluxes and a radial distribution of forces. Some reasonable approximations are made that allow analytic solutions of the nonlinear differential equations. These solutions are used to analyze data from the frog lens and are shown to account for the known steady-state properties of this tissue. Moreover, these solutions are used to make predictions on other steady-state properties, which have not been directly measured, and graphical results on the circulation of water, ions and solute through the frog lens are presented.

Oxonol dyes as monitors of membrane potential: the effect of viruses and toxins on the plasma membrane potential of animal cells in monolayer culture and in suspension

Optical indicators of the cationic, cyanine and anionic oxonol classes were used to evaluate the plasma membrane potential of animal cells in suspension and in monolayer culture. The optical signals were calibrated by using diffusion potentials either of K+ (in the presence of valinomycin) or of H+ (in the presence of carbonyl cyanide p-trifluoromethoxyphenylhydrazone; FCCP); both classes of dye gave similar values of plasma membrane potential, in the range -40 to -90 mV for different cell types. Addition of haemolytic Sendai virus or Staphylococcus aureus alpha-toxin depolarizes cells and causes them to leak monovalent cations; these effects are antagonized by extracellular Ca2+. Cells infected with vesicular stomatitis or Semliki Forest virus become depolarized during an infectious cycle; infection with other viruses was without affect on plasma membrane potential.

Cellular ions in intact and denervated muscles of the rat

Tissue composition, membrane potentials and cellular activity of potassium, sodium and chloride have been measured in innervated and denervated rat skeletal muscles incubated in vitro. After denervation for 3 days, tissue water, sodium and chloride were increased but cellular potassium content and measured activity were little affected, despite a decrease of 16 mV in resting membrane potential which would have necessitated a decrease in cellular potassium activity of almost 50% were potassium distributed at electrochemical equilibrium. These findings, therefore, preclude a decreased electrochemical potential gradient for potassium as the cause of the membrane depolarization characteristic of denervated muscle fibers. Analysis of the data excludes an important contribution of rheogenic sodium transport to the resting potential of innervated muscles. These results strongly support the hypothesis that the decreased membrane potential in denervated fibers reflects a relative increase in the membrane permeability to sodium.

Reduced resistances of septal artery collateral channels after cardiac sympathectomy

We have shown that chronic cardiac sympathectomy reduces coronary collateral resistances. The present experiments in isolated dog hearts delineated the role of intramyocardial collateral channels from the septal (SEP) to the circumflex (CIRC), left anterior descending (LAD), and right (RT) coronary arteries in this phenomenon. In 11 controls and 8 2-wk sympathectomized hearts, a retrograde flow technique was used to determine collateral resistances between the epicardial arteries (CIRC, LAD, RT). Collateral resistances between the CIRC and LAD and between the LAD and RT were 42-68% less in sympathectomized hearts (P less than 0.05). Collateral resistances from the SEP to each epicardial artery were determined from retrograde flows simultaneously collected on each epicardial artery when the SEP was the only vessel perfused. Collateral resistances from the SEP to the CIRC and LAD were 51-59% less in the sympathectomized hearts (P less than 0.05). Thus, intramyocardial channels from the SEP to the left coronary arteries show reduced resistances after sympathectomy and can provide a substantial portion of the increased collateral flow to these vessels.

Electrical and biochemical properties of an enzyme model of the sodium pump

The electrochemical properties of a widely accepted six-step reaction scheme for the Na+, K+-ATPase have been studied by computer simulation. Rate coefficients were chosen to fit the nonvectorial biochemical data for the isolated enzyme and a current-voltage (I-V) relation consistent with physiological observations was obtained with voltage dependence restricted to one (but not both) of the two translocational steps. The vectorial properties resulting from these choices were consistent with physiological activation of the electrogenic sodium pump by intracellular and extracellular sodium (Na+) and potassium (K+) ions. The model exhibited K+/K+ exchange but little Na+/Na+ exchange unless the energy available from the splitting of adenosine triphosphate (ATP) was reduced, mimicking the behavior seen in squid giant axon. The vectorial ionic activation curves were voltage dependent, resulting in large shifts in apparent Km's with depolarization. At potentials more negative than the equilibrium or reversal potential transport was greatly diminished unless the free energy of ATP splitting was reduced. While the pump reversal potential is at least 100 mV hyperpolarized relative to the resting potential of most cells, the voltage-dependent distribution of intermediate forms of the enzyme allows the possibility of considerable slope conductance of the pump I-V relation in the physiological range of membrane potentials. Some of the vectorial properties of an electrogenic sodium pump appear to be inescapable consequences of the nonvectorial properties of the isolated enzyme. Future application of this approach should allow rigorous quantitative testing of interpretative ideas concerning the mechanism and stoichiometry of the sodium pump.

Active modulation of electrical coupling between cardiac cells of the dog. A mechanism for transient and steady state variations in conduction velocity

Propagation velocities of action potentials were measured simultaneously along the longitudinal and transverse axes of cardiac fibers in ventricular muscle. The anisotropic distribution of propagation velocities was found to be altered transiently and in the steady state by the rate and pattern of stimulation and by ouabain. The relative amount of velocity change varied with the direction of propagation and was greatest in the direction perpendicular to the long fiber axis. None of the variables usually associated with the membrane ionic mechanism of depolarization--resting potential, Vmax, and taufoot--showed enough variation to account for the observed changes in velocity. A simplified anisotropic propagation model representing the internal current pathway as an alternating sequence of cytoplasmic and junctional resistance is presented, taking into account the larger contribution to the internal resistance made by the cell couplings in the transverse direction than in the longitudinal direction. On the basis of this model, it was concluded that the observed changes in velocity were due to changes in cell coupling. Both transient and steady state velocity changes were found to correspond to changes in the action potential duration, suggesting that there is a common factor, such as the internal calcium and/or sodium concentrations, linking the control of the action potential duration and the coupling resistance between cardiac cells.

Cell volume regulation in goldfish intestinal mucosa

1. Ion and water content of goldfish intestinal mucosa, stripped free from muscular layers were measured under various incubation conditions. 2. Ouabain induces an increase in cation content that is electrically compensated for by chloride. The increase in solute content is accompanied by an increase in water content. 3. When extracellular chloride is partially replaced by sulphate, ouabain does induce cell shrinkage. 4. Anoxia induces a rapid increase in cell volume that is restored by oxygenation of the incubation solution. Ouabain prevents the restoration of volume. 5. It is concluded that the classical ouabain-sensitive Na/K pump participates in the maintenance of cellular volume. We suggest that the constancy in volume after ouabain poisoning as is reported for many tissues might be due to a low chloride conductance of its membranes. 6. Anisotonic media (range: 0.6-1.2 isotonicity), made by variation on mannitol concentration, induce changes in cell water content that deviates from the simplified van't Hoff equation by about 10%. No change in water content after the initial increase was found. 7. We conclude that goldfish enterocytes do not possess a mechanism for rapid volume readjustment.

The measurement of membrane potential using optical indicators

Conclusions

Optical methods have become established as a major experimental protocol for following membrane potential. They can provide a rapid, continuous record of the potential and have a very wide applicability. However, when used to make quantitative assertions about membrane potential, optical methods have a number of weaknesses. Even the most reliable calibration procedures depend on accurate evaluation of a small number, namely the internal ion concentration, in a large background, that is total ion levels. However, a consensus seems to be emerging that the plasma membrane potential of non-excitable cells nevertheless has considerable magnitude: typical values are −60 mV for lymphocytes (Rink et al., 1980), −20 to −100 mV, depending on metabolic load, for Ehrlich ascites tumour cells (Philo & Eddy, 1978; but see also Smith & Robinson, 1980), and −66 to −86 mV for neutrophils (Tatham et al., 1980). In our own experiments using monolayer cultures of cells grown to confluence (Bashford et al., 1981) the potential across the plasma membrane is of the order of −100 mV (see Fig. 2). Membrane potentials of similar magnitude have been found using ion-distribution methods and microelectrodes in neuroblastoma cells and lymphocytes (Deutsch et al., 1979a,b). In the latter studies ions of different charge were used to provide upper and lower estimates of the potential, the presumed effects of binding being very different for anions and cations. A similar approach, in this case the use of optical indicators of different charge, has been taken by Rink et al. (1980), and this would seem to be one way in which to diminish the uncertainties involved in dye calibration. Unfortunately many anions, particularly oxonols, form complexes with valinomycin (Lavie & Sonenberg, 1980; Rink et al., 1980), although we have found no evidence for such a complex with bis isoxazolone oxonols (J.C. Smith and C.L. Bashford, unpublished observations). It is apparent that calibration procedures not dependent on valinomycin should be sought in order to establish optical methods as a quantitative approach to the study of membrane potential.