Noncontact dipole effects on channel permeation. I. Experiments with (5F-indole)Trp13 gramicidin A channels.

Gramicidin A (gA), with four Trp residues per monomer, has an increased conductance compared to its Phe replacement analogs. When the dipole moment of the Trp13 side chain is increased by fluorination at indole position 5 (FgA), the conductance is expected to increase further. gA and FgA conductances to Na+, K+, and H+ were measured in planar diphytanoylphosphatidylcholine (DPhPC) or glycerylmonoolein (GMO) bilayers. In DPhPC bilayers, Na+ and K+ conductances increased upon fluorination, whereas in GMO they decreased. The low ratio in the monoglyceride bilayer was not reversed in GMO-ether bilayers, solvent-inflated or -deflated bilayers, or variable fatty acid chain monoglyceride bilayers. In both GMO and DPhPC bilayers, fluorination decreased conductance to H+ but increased conductance in the mixed solution, 1 M KCl at pH 2.0, where K+ dominates conduction. Eadie-Hofstee plot slopes suggest similar destabilization of K+ binding in both lipids. Channel lifetimes were not affected by fluorination in either lipid. These observations indicate that fluorination does not change the rotameric conformation of the side chain. The expected difference in the rate-limiting step for transport through channels in the two bilayers qualitatively explains all of the above trends.     

Noncontact dipole effects on channel permeation. III. Anomalous proton conductance effects in gramicidin

Proton transport on water wires, of interest for many problems in membrane biology, is analyzed in side-chain analogs of gramicidin A channels. In symmetrical 0.1 N HCl solutions, fluorination of channel Trp(11), Trp-(13), or Trp(15) side chains is found to inhibit proton transport, and replacement of one or more Trps with Phe enhances proton transport, the opposite of the effects on K(+) transport in lecithin bilayers. The current-voltage relations are superlinear, indicating that some membrane field-dependent process is rate limiting. The interfacial dipole effects are usually assumed to affect the rate of cation translocation across the channel. For proton conductance, however, water reorientation after proton translocation is anticipated to be rate limiting. We propose that the findings reported here are most readily interpreted as the result of dipole-dipole interactions between channel waters and polar side chains or lipid headgroups. In particular, if reorientation of the water column begins with the water nearest the channel exit, this hypothesis explains the negative impact of fluorination and the positive impact of headgroup dipole on proton conductance.     

Gramicidin channels that have no tryptophan residues.

In order to understand how aromatic residues modulate the function of membrane-spanning proteins, we examined the role of the four tryptophans in gramicidin A (gA) in determining the average duration and permeability characteristics of membrane-spanning gramicidin channels; the tryptophan residues were replaced by tyrosine (gramicidin T, gT), tyrosine O-benzyl ether [gramicidin T(Bzl), gT(Bzl)], naphthylalanine (gramicidin N, gN), and phenylalanine (gramicidin M enantiomer, gM-). These analogues form channels with durations and conductances that differ some 10- and 16-fold, respectively. The single-channel conductance was invariably decreased by the Trp----Yyy replacement, and the relative conductance alterations were similar in phosphatidylcholine (DPhPC) and monoglyceride (GMO) bilayers. The duration variations exhibited a more complex pattern, which was quite different in the two membrane environments: in DPhPC bilayers, gN channels have an average duration that is approximately 2-fold longer than that of gA channels; in GMO bilayers, the average duration of gN channels is about one-tenth that of gA channels. The sequence-dependent alterations in channel function do not result from alterations in the channels' peptide backbone structure, because heterodimers can form between the different analogues and gramicidine A, and there is no energetic cost associated with heterodimer formation [cf. Durkin, J. T., Koeppe, R. E., II, & Andersen, O. S. (1990) J. Mol. Biol. 211, 221]. The alterations in permeability properties are consistent with the notion that Trp residues alter the energy profile for ion permeation through long-range electrostatic interactions.     

Noncontact dipole effects on channel permeation. VI. 5F- and 6F-Trp gramicidin channel currents

Fluorination of peptide side chains has been shown to perturb gramicidin channel conductance without significantly changing the average side chain structure, which, it is hoped, will allow detailed analysis of electrostatic modulation of current flow. Here we report a 1312-point potassium current-voltage-concentration data set for homodimeric channels formed from gramicidin A (gA) or any of eight fluorinated Trp analogs in both lecithin and monoglyceride bilayers. We fit the data with a three-barrier, two-site, two-ion (3B2S) kinetic model. The fluorination-induced changes in the rate constants were constrained by the same factor in both lipids. The rate constant changes were converted to transition-state free-energy differences for comparison with previous electrostatic potential energy differences based on an ab initio force field. The model allowed a reasonably good fit (chi = 8.29 with 1271 degrees of freedom). The measured changes were subtle. Nevertheless, the fitted energy perturbations agree well with electrostatic predictions for five of the eight peptides. For the other three analogs, the fitted changes suggested a reduced translocation barrier rather than the reduced exit barrier as predicted by electrostatics.     

Noncontact dipole effects on channel permeation. V. Computed potentials for fluorinated gramicidin

Experimental and theoretical calculations indicate that the dipole moment of the four Trp side chains in gramicidin A (gA) channels modify channel conductance through long-range electrostatic interactions. Electrostatic ion/side-chain interaction energies along the channel were computed with CHARMM using ab initio atom charges for native and 4-, 5-, or 6-fluorinated Trp side chains. The bulk water reaction to the polar side chains was included using the method of images as implemented by, and channel waters in idealized structures were included. Ion/Trp interaction energies were approximately -0.6 kcal/mol throughout the channel for all four of the native Trp pairs. Channel waters produced a modest reduction in the magnitude of interactions, essentially offsetting images representing the bulk water outside the channel. The effects of side-chain fluorination depended on ring position and, to a lesser extent, residue number. Compared with native Trp, 5-fluorination reduces the translocation barrier with minor effects on the exit barrier. In contrast, 6-fluorination primarily reduces exit barrier. 4-Fluorination produces a more complex double-well energy profile. Effects of measured side-chain movements resulting from fluorination or change in lipid bilayer were negligible whereas thermal side chain librations cause large effects, especially in the region of the ion-binding sites.     

Proton conduction in gramicidin A and in its dioxolane-linked dimer in different lipid bilayers.

Gramicidin A (gA) molecules were covalently linked with a dioxolane ring. Dioxolane-linked gA dimers formed ion channels, selective for monovalent cations, in planar lipid bilayers. The main goal of this study was to compare the functional single ion channel properties of natural gA and its covalently linked dimer in two different lipid bilayers and HCl concentrations (10-8000 mM). Two ion channels with different gating and conductance properties were identified in bilayers from the product of dimerization reaction. The most commonly observed and most stable gramicidin A dimer is the main object of this study. This gramicidin dimer remained in the open state most of the time, with brief closing flickers (tau(closed) approximately 30 micros). The frequency of closing flickers increased with transmembrane potential, making the mean open time moderately voltage dependent (tau(open) changed approximately 1.43-fold/100 mV). Such gating behavior is markedly different from what is seen in natural gA channels. In PEPC (phosphatidylethanolamine-phosphatidylcholine) bilayers, single-channel current-voltage relationships had an ohmic behavior at low voltages, and a marked sublinearity at relatively higher voltages. This behavior contrasts with what was previously described in GMO (glycerylmonooleate) bilayers. In PEPC bilayers, the linear conductance of single-channel proton currents at different proton concentrations was essentially the same for both natural and gA dimers. g(max) and K(D), obtained from fitting experimental points to a Langmuir adsorption isotherm, were approximately 1500 pS and 300 mM, respectively, for both the natural gA and its dimer. In GMO bilayers, however, proton affinities of gA and the dioxolane-dimer were significantly lower (K(D) of approximately 1 and 1.5 M, respectively), and the g(max) higher (approximately 1750 and 2150 pS, respectively) than in PEPC bilayers. Furthermore, the relationship between single-channel conductance and proton concentration was linear at low bulk concentrations of H+ (0.01-2 M) and saturated at concentrations of more than 3 M. It is concluded that 1) The mobility of protons in gramicidin A channels in different lipid bilayers is remarkably similar to proton mobilities in aqueous solutions. In particular, at high concentrations of HCl, proton mobilities in gramicidin A channel and in solution differ by only 25%. 2) Differences between proton conductances in gramicidin A channels in GMO and PEPC cannot be explained by surface charge effects on PEPC membranes. It is proposed that protonated phospholipids adjacent to the mouth of the pore act as an additional source of protons for conduction through gA channels in relation to GMO bilayers. 3) Some experimental results cannot be reconciled with simple alterations in access resistance to proton flow in gA channels. Said differences could be explained if the structure and/or dynamics of water molecules inside gramicidin A channels is modulated by the lipid environment and by modifications in the structure of gA channels. 4) The dioxolane ring is probably responsible for the closing flickers seen in the dimer channel. However, other factors can also influence closing flickers.     

Effects of hydrostatic pressure on lipid bilayer membranes. I. Influence on membrane thickness and activation volumes of lipophilic ion transport.

Measurements of membrane capacitance, Cm, were performed on lipid bilayers of different lipidic composition (diphytanoyl phosphatidylcholine PPhPC, dioleoyl phosphatidylcholine DOPE, glycerylmonooleate GMO) and containing n-decane as solvent. In the same membranes, the absorption of the lipophilic ions dipicrylamine (DPA-) and tetraphenylborate (TPhB-), and the kinetics of their translocation between the two membrane faces have been studied. The data were obtained from charge pulse relaxation measurements. Upon increasing pressure the specific capacity Cm increased in a fully reversible and reproducible way reflecting a thinning of the membrane that is attributed to extrusion of n-decane from the black membrane area. High pressure decreased the rate constant, ki, for lipophilic ion translocation. After correcting for changes in the height of the energy barrier for translocation due to membrane thinning the pressure dependence of ki yields an apparent activation volume for translocation of approximately 14 cm3/mol both for DPA- and TPhB-. Changes in lipophilic ion absorption following a step of pressure developed with a rather slow time course due to diffusion limitations in solution. The stationary concentration of membrane absorbed lipophilic ions increased with pressure according to an apparent volume of absorption of about -10 cm3/mol. The relevance of the results for the interpretation of the effects of pressure on nerve membrane physiology is discussed.     

Ion movement through gramicidin A channels. Single-channel measurements at very high potentials

The patch-clamp technique of Mueller (1975, Ann. N.Y. Acad. Sci., 274:247-264) and Neher and Sakmann (1976, Nature (Lond.), 260:799-802) was modified to be suitable for single-channel measurements in lipid bilayers at potentials up to 500 mV. This method was used to study gramicidin A single-channel current-voltage characteristics. It was found that the sublinear current-voltage behavior normally observed at low permeant ion concentrations and rather low potentials (V less than or equal to 200 mV) continues to be seen all the way up to 500 mV. This phenomenon is characteristic of the low permeant ion situation in which the channel is far from saturation, and implies that the overall rate constant for association between ion and channel is very weakly, if at all, voltage dependent. The magnitude of the single channel currents at 500 mV is consistent with the notion that the aqueous convergence conductance is a significant factor in determining the permeability characteristics of the gramicidin A channel.     

The interaction of dipole modifiers with amphotericin-ergosterol complexes. Effects of phospholipid and sphingolipid membrane composition

The influence of agents, known to affect the membrane dipole potential, phloretin and RH 421, on the multi channel activity of amphotericin B in lipid bilayers of various compositions, was studied. It was shown that the effects were dependent on the membrane’s phospholipid and sphingolipid type. Phloretin enhanced amphotericin B induced steady-state transmembrane current through bilayers made from binary mixtures of POPC (DOPC) and ergosterol and ternary mixture of DPhPC, ergosterol and stearoylphytosphingosine. RH 421 increased steady-state polyene induced transmembrane current through membranes made from binary mixtures of DPhPC (DPhPS) and ergosterol and ternary mixture of DPhPS, ergosterol and stearoylphytosphingosine. It was proposed that the observed effects reflect the fine balance of the interactions between the various components present: amphotericin B, ergosterol, phospholipid, sphingolipid and dipole modifier. The shape of lipid molecules seems to be an important factor impacting the responses of amphotericin B modified bilayers to dipole modifiers. The influence of different phospholipids and sphingolipids on the physical and structural properties of ordered lipid microdomains, enriched in AmB, was also discussed. It was also shown that RH 421 enhanced the antifungal activity of amphotericin B in vitro.     

Thallous ion movements through gramicidin channels incorporated in lipid monolayers supported by mercury.

The potential independent limiting flux of hydrated Tl(+) ions through gramicidin (GR) channels incorporated in phospholipid monolayers self assembled on a hanging mercury-drop electrode is shown to be controlled both by diffusion and by a dehydration step. Conversely, the potential independent limiting flux of dehydrated Tl(+) ions stemming from Tl amalgam electro-oxidation is exclusively controlled by diffusion of thallium atoms within the amalgam. Modulating the charge on the polar heads of dioleoylphosphatidylserine (DOPS) by changing pH affects the limiting flux of hydrated Tl(+) ions to a notable extent, primarily by electrostatic interactions. The dipole potential of DOPS and dioleoylphosphatidylcholine (DOPC), positive toward the hydrocarbon tails, does not hinder the translocation step of Tl(+) ions to such an extent as to make it rate limiting. Consequently, incorporation in the lipid monolayer of phloretin, which decreases such a positive dipole potential, does not affect the kinetics of Tl(+) flux through GR channels. In contrast, the increase in the positive dipole potential produced by the incorporation of ketocholestanol causes the translocation step to contribute to the rate of the overall process. A model providing a quantitative interpretation of the kinetics of diffusion, dehydration-hydration, translocation, and charge transfer of the Tl(+)/Tl(0)(Hg) couple through GC channels incorporated in mercury-supported phospholipid monolayers is provided. A cut-off disk model yielding the profile of the local electrostatic potential created by an array of oriented dipoles located in the lipid monolayer along the axis of a cylindrical ion channel is developed.     

Procedure using voltage-sensitive spin-labels to monitor dipole potential changes in phospholipid vesicles: The estimation of phloretin-induced conductance changes in vesicles

Summary Voltage-sensitive membrane potential probes were used to monitor currents resulting from positive or negative charge movement across small and large unilamellar phosphatidylcholine (PC) vesicles. Positive currents were measured for the paramagnetic phosphonium ion or for K⁺-valinomycin. Negative currents were indirectly measured for the anionic proton carriers CCCP and DNP by monitoring transmembrane proton currents. Phloretin, a compound that is believed to decrease dipole fields in planar bilayers, increases positive currents and decreases negative currents when added to egg PC vesicles. In these vesicles, positive currents are increased by phloretin addition to a much larger degree than CCCP currents are reduced. This asymmetry, with respect to the sign of the charge carrier, is apparently not the result of changes in the membrane dielectric constant. It is most easily explained by deeper binding minima at the membrane-solution interface for the CCCP anion, when compared to the phosphonium. The measured asymmetry and the magnitudes of the current changes are consistent with the predictions of a point dipole model. The use of potential-sensitive probes to estimate positive and negative currents, provides a methodology to monitor changes in the membrane dipole potential in vesicle systems.     

Asymmetry of the gramicidin channel in bilayers of asymmetric lipid composition: I. Single channel conductance

Summary Gramicidin-doped asymmetric bilayers made by the Montal-Mueller method exhibited an asymmetric current-voltage relationship. The asymmetric conductance was shown to be the product of two components, a rectifying single-channel conductance and an asymmetric voltage dependence of the reaction which leads to the conducting channel. The single-channel conductance was asymmetric in both asymmetric bilayers made of charged lipids and asymmetric bilayers made only of neutral lipids. The single-channel asymmetry decreased with increasing ion concentration. From the comparison of the singlechannel conductance in symmetric and asymmetric bilayers and the dependence of the asymmetry on the solution ion concentrations, it was concluded that (1) the rate of ion entry into the channel is dependent on the lipid composition of the membrane and is asymmetric in asymmetric bilayers; (2) the entry step is rate determining at low ion concentrations; and (3) at higher ion concentrations the rate-determining step is the translocation across the main barrier in the membrane; and this translocation appears insensitive to lipid asymmetry.     

Modulating dipoles for structure-function correlations in the gramicidin A channel.

Dipoles of the tryptophan indole side chains have a direct impact on ion conductance in the gramicidin channel. Here, fluorination of the indoles (both 5- and 6-fluoro) is used to manipulate both the orientations and the magnitudes of the dipoles. The orientations and positions with respect to the channel axis were determined using (2)H solid state NMR of uniformly aligned lipid bilayer preparations. By exchange of the remaining four protons in the indole ring for deuterium, comparison could be made to d(5)-indole spectra that have previously been recorded for each of the four indoles of gramicidin A. After making the assignments which were aided by the observation of (19)F-(2)H dipolar interactions, we found that fluorination caused only minor changes in side chain conformation. With the high-resolution structural characterization of the fluorinated indoles in position 11, 13, and 15, the electrostatic interactions with a cation at the channel and bilayer center can be predicted and the influence of the modified dipoles on ion conductance estimated. The importance of the long-range electrostatic interaction was recently documented with the observation of alpha-helical dipoles oriented toward the bilayer center on the ion conductance pathway for the Streptomyces K(+) channel. We present direct measurements of the orientation of gramicidin channel F-Trp positions for use in analysis of dipole effects on channel permeation.     

Formation and characterization of planar lipid bilayer membranes from synthetic phytanyl-chained glycolipids

The formability, current-voltage characteristics and stability of the planar lipid bilayer membranes from the synthetic phytanyl-chained glycolipids, 1, 3-di-O-phytanyl-2-O-(beta-glycosyl)glycerols (Glc(Phyt)(2), Mal(N)(Phyt)(2)) were studied. The single bilayer membranes were successfully formed from the glycolipid bearing a maltotriosyl group (Mal(3)(Phyt)(2)) by the folding method among the synthetic glycolipids examined. The membrane conductance of Mal(3)(Phyt)(2) bilayers in 100 mM KCl solution was significantly lower than that of natural phospholipid, soybean phospholipids (SBPL) bilayers, and comparable to that of 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC) bilayers. From the permeation measurements of lipophilic ions through Mal(3)(Phyt)(2) and DPhPC bilayers, it could be presumed that the carbonyl groups in glycerol backbone of the lipid molecule are not necessarily required for the total dipole potential barrier against cations in Mal(3)(Phyt)(2) bilayer. The stability of Mal(3)(Phyt)(2) bilayers against long-term standing and external electric field change was rather high, compared with SBPL bilayers. Furthermore, a preliminary experiment over the functional incorporation of membrane proteins was demonstrated employing the channel proteins derived from octopus retina microvilli vesicles. The channel proteins were functionally incorporated into Mal(3)(Phyt)(2) bilayers in the presence of a negatively charged glycolipid. From these observations, synthetic phytanyl-chained glycolipid bilayers are promising materials for reconstitution and transport studies of membrane proteins.     

The effects of bilayer thickness and tension on gramicidin single-channel lifetime

Measurements have been made of gramicidin single-channel lifetimes in monoacylglycerol bilayers chosen so that their thickness ranged from above to below the length of the gramicidin channel. Contact angles, electrical capacities and bulk-phase interfacial tensions have also been determined for these systems. The mean channel lifetime decreased with the hydrocarbon thickness of the membrane until the latter reached 2.2 nm, after which the lifetime was relatively constant. A theoretical model has been proposed which relates the mean channel lifetime (or dissociation constant) to both the thickness and the tension of the bilayers. The analysis of the present results and of those of previous studies has led to the idea that aggregates of water molecules may play an important r?le in the dissociation of the gramicidin channel.     

Tryptophan contributions to the empirical free-energy profile in gramicidin A/M heterodimer channels

Gramicidin A/gramicidin M heterodimer conductances were measured in planar lipid bilayers and found to form two distinguishable populations about halfway between the gramicidin A and gramicidin M homodimer conductances. This implies that the principle difference in the gramicidin A and gramicidin M transport free-energy profiles occurs at the channel center, where it would produce similar effects on the rate-limiting barrier for the two heterodimers. Kinetic analysis based on this and nearly all previously published homodimer conductance data for both gramicidin A and gramicidin M channels confirms this conclusion, indicating that the translocation step is approximately 100-fold slower in gramicidin M homodimers than in gramicidin A homodimers and that first- and second-ion exit-rate constants are higher by factors of 24 and 10, respectively. Assuming that the ratios of rate constants are related to the free-energy difference between gramicidin A and gramicidin M, we construct an effective ion-Trp free-energy interaction profile that has a minimum at the channel center.     

Dielectric relaxation studies of ionic processes in lysolecithin-packaged gramicidin channels

Summary Dielectric permittivities have been determined for suspensions of lysolecithin packaged malonyl gramicidin channels over the frequency range of 5kHz to 900 MHz and under conditions of approximately equimolar concentrations (10mM) of channels and salts. The salts were lithium chloride, sodium chloride and thallium acetate. A relaxation process unique to the thallium acetate-channel system was observed which on analysis gave rise to a relaxation time at 25⁰ of 120 nsec. The permittivity data, as well as a comparison of binding constants, indicate that the relaxation process results from Tl⁺ being bound within the channel and more specifically from an intrachannel ion translocation with a rate constant of approximately 4×10⁶ sec^–1 and with an energy of activation of less than 6.7 kcal/mole. These data compare favorably with data from conductance studies on planar bilayers and with ion and carbon-13 nuclear magnetic studies on the lysolecithin packaged malonyl gramicidin channels which combine to indicate that the relaxation process is due to the jump of the thallium ion across a central barrier.     

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath.

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.     

The membrane dipole potential in a total membrane potential model. Applications to hydrophobic ion interactions with membranes.

The total potential energy profile for hydrophobic ion interactions with lipid bilayers can be written as the sum of four terms: the electrical Born, image and dipole contributions, and a neutral energy term. We introduce a specific model for the membrane dipole potential, treating it as a two-dimensional array of point dipoles located near each membrane-water interface. Together with specific theoretical models for the other energy terms, a total potential profile is developed that successfully describes the complete set of thermodynamic parameters for binding and translocation for the two hydrophobic ion structural analogues, tetraphenylphosphonium (TPP+) and tetraphenylboron (TPB-). A reasonable fit to the data is possible if the dipole potential energy has a magnitude of 5.5 + 0.5 kcal/mol (240 + 20 mV), positive inside, and if the neutral energy contribution for TPP+ and TPB- is -7.0 + 1.0 kcal/mol. These results may also have important implications for small ion interactions with membranes and the energetics of charged groups in membrane proteins.     

Modulation of gramicidin A open channel lifetime by ion occupancy.

The hypothesis that the gramicidin A channel stability depends on the level of ion occupancy of the channel was used to derive a mathematical model relating channel lifetime to channel occupancy. Eyring barrier permeation models were examined for their ability to fit the zero-voltage conductance, current-voltage, as well as lifetime data. The simplest permeation model required to explain the major features of the experimental data consists of three barriers and four sites (3B4S) with a maximum of two ions occupying the channel. The average lifetime of the channel was calculated from the barrier model by assuming the closing rate constant to be proportional to the probability of the internal channel sites being empty. The link between permeation and lifetime has as its single parameter the experimentally determined averaged lifetime of gramicidin A channels in the limit of infinitely dilute solutions and has therefore no adjustable parameters. This simple assumption that one or more ions inside the channel completely stabilize the dimer conformation is successful in explaining the experimental data considering the fact that this model for stabilization is independent of ion species and configurational occupancy. The model is used to examine, by comparison with experimental data, the asymmetrical voltage dependence of the lifetime in asymmetrical solutions, the effects of blockers, and the effects of elevated osmotic pressure.