I. INTRODUCTION

Top Previous Next References

Voltage-gated proton channels are unique ion channels in several respects. They are called proton channels because they behave like ion channels and are highly selective for protons. Although protons exist in solution almost entirely in the form of hydronium ions, H₃O⁺, all proton-selective channels conduct protons as H⁺, rather than H₃O⁺. This is true even for water-filled pores like gramicidin. It remains a matter of some contention whether proton channels should be considered to be ion channels at all, although this designation seems more appropriate than any alternative and is becoming accepted (444). Proton channels differ from carriers and unequivocally are not pumps. Protons are unique ions with respect to their behavior in bulk solutions, their interactions with proteins, and the mechanism by which they traverse ion channels and other molecules. The unique chemical properties of protons explain why proton channels hold the records for both the largest and smallest single-channel currents. Thus there is an introductory discussion of selected aspects of proton chemistry. For a detailed discussion of the methods of pH measurement, the reader is referred to the superb review by Roos and Boron (850).

This review includes what I as a student of voltage-gated proton channels consider to be useful and relevant. Although the main focus is voltage-gated proton channels, there is substantial coverage of salient properties of a number of other proton-conducting molecules, for several reasons. First, the structure and even the molecular identity of voltage-gated proton channels is essentially unknown, whereas the structures of a number of other proton-conducting molecules are known to within a few Angstroms. Second, certain features that differentiate proton channels from other ion channels may be shared among molecules whose function involves proton translocation. Once nature discovers a solution to a design problem, this solution tends to recur (245). Proton conduction through the prototypical ion channel, gramicidin, provides a frame of reference with respect to which we interpret many results (deuterium and temperature effects, pH dependence, unitary conductance, etc.). It is possible to distinguish two broad classes of proton-permeable molecules. Some molecules couple the flux of protons to a bioenergetic or enzymatic goal, such as photosynthesis or CO₂ hydrolysis. Other molecules are simple proton channels that apparently exist for the sole purpose of mediating proton flux across membranes. In both cases, proton flux is tightly regulated, either by coupling to events central to the function of the molecule or by a gating mechanism that turns proton flux on and off at appropriate times. A premise of this review is that the molecular details of proton movement through all types of proton-conducting molecules are likely to display similarities with general applicability.

The properties common to all voltage-gated proton channels are described in detail. Then the properties and proposed functions of H⁺ channels in specific cells are discussed. There is a strong emphasis on proton channel function in phagocytes, because much more is known about function in these cells than in any other. Evidence for and against the proposal that part of the phagocyte NADPH oxidase complex functions as a proton channel (427) is summarized.

I do not expect more than a handful of people to read the entire review. For those who study any of the numerous molecules with proton pathways, I hope to present a synopsis of their molecule from the vantage point of an electrophysiologist interested in proton conduction. I feel that it is useful to have information specifically regarding proton conduction in various channels/molecules assembled in one place. Those who study "normal" ion channels and are curious about H⁺ channels will want to know their biophysical properties, which will appear esoteric and tedious to others. Phagocyte biologists will be interested mainly in the section on H⁺ channels in phagocytes. For everyone else, the review should be a resource enabling a particular bit of information to be located in the table of contents.

	II. CHEMISTRY OF PROTONS

Top Previous Next References

Protons in aqueous solution almost always exist in hydrated form as hydronium ions, H₃O⁺ (or H₃O⁺ · nH₂O, including waters of hydration), also called oxonium (605) or hydroxonium ions (1070). Protons exist as H⁺ <1% of the time during transfer from one water to another (184). The three protons in H₃O⁺ are equivalent, and each is equally likely to jump to a neighboring water molecule (84). The proton is unique among cations in being interchangeable with the protons that form water molecules. This capability is significant in light of the tiny concentration of "free protons" (H₃O⁺) in physiological solutions, ~40 nM, and the enormous total concentration of H in water, 110 M. Only one proton in a billion is part of H₃O⁺ at any moment. The average lifetime of the H₃O⁺ ion is ~1 ps in liquid water at room temperature: estimates in chronological order include 0.65 ps (84), 0.24 ps (184), 3.0 ps (287), 1.7 ps (636), 1.1 ps (11), 1.3 ps (1095), 0.95 ps (1050), and 0.5-0.79 ps (890). The proton is also unique as a monovalent cation in having no electrons, giving it a radius 10⁵ smaller than other ions, which greatly facilitates proton transfer reactions (80) and electrostatic interactions with nearby molecules (696).

The quintessential feature of water and other proton conduction pathways is the hydrogen bond (80, 84, 287, 361, 380, 469, 470, 592, 605, 799, 800, 967, 1101). Huggins appears to have originated the concept of the hydrogen bond while in the laboratory of Latimer and Rodebush. Huggins conceived the idea of a hydrogen "kernel" held between two atoms in organic compounds, which he did not publish until 1922 (468); several earlier investigators discussed interactions that in retrospect could be considered examples of hydrogen bonds (490). In 1920, Latimer and Rodebush (592) adopted this idea and applied it to water, foreseeing the existence of networks of water molecules, and used hydrogen bonding to explain the high mobility of protons in water as "a sort of Grotthuss chain effect, rather than ... a rapid motion of any one H₃O⁺ ion."

"Water ... shows tendencies both to add and give up hydrogen, which are nearly balanced. Then, in terms of the Lewis theory, a free pair of electrons on one water molecule might be able to exert sufficient force on a hydrogen held by a pair of electrons on another water molecule to bind the two molecules together. Structurally this may be represented as

View larger version (7K): [in this window] [in a new window]

Such combination need not be limited to the formation of double or triple molecules. Indeed, the liquid may be made up of large aggregates of molecules, continually breaking and reforming under the influence of thermal agitation. Such an explanation amounts to saying that the hydrogen nucleus held between 2 octets constitutes a weak `bond' ¹ " (592).

Linus Pauling coined the term hydrogen bond in a general paper on chemical bonds (798) and developed and popularized the idea in a chapter of his book, The Nature of the Chemical Bond (800).

Water molecules tend to form tetrahedral hydrogen bonded structures, at least ideally (84). In ice the tetrahedral structure exists (799) and is evidently so rigid at very low temperature (i.e., the dielectric constant drops drastically) that proton conduction is limited (188, 261, 313). In liquid water, however, the tetrahedral ideal is not achieved, and the actual coordination number decreases with increasing temperature (300, 366), which likely accounts for the greater decrease in activation energy at higher temperatures for proton transport than for other ions (319, 605, 784, 786). Water can be considered a "broken down ice structure" with continual formation and breaking of hydrogen bonds (707). Although protons in water are formally considered to exist as H₃O⁺ molecules, it has long been recognized that larger molecular groupings exist and are central to the understanding of proton conduction. As early as 1936, Huggins (470) explicitly postulated the existence of H₅O, showed that proton conduction can occur by shifts in the identities of the water molecules that comprise the cation, and suggested that the rapidity of such shifts accounts for the high mobility of protons in water. The two main larger species are the so-called "Zundel cation," two waters sharing an excess proton as H₅O (470, 1102, 1103), and the "Eigen cation," four waters sharing an excess proton as H₉O (80, 287, 1070), although a transitional H₁₃O structure has also been proposed (1049). These quasi-molecules are in a sense fictitious, in that they are idealizations that exist only transiently along with many undefined intermediate or alternative states (664, 890). Quantum molecular dynamics simulations show that a proton in water sometimes shuttles back and forth between two neighboring water molecules many times per picosecond, behavior that defines a Zundel (or Huggins) cation, but also spends time associated with a single water (which is hydrogen bonded to three first shell waters) as an Eigen cation (890, 1050). Eigen thought that the proton in H₉O was essentially delocalized (288) and shared among three of the waters surrounding the H₃O⁺ molecule; the fourth water is oriented incorrectly for rapid proton transfer (605). Ab initio molecular dynamics calculations indicate that a proton in water is affiliated with one oxygen atom as H₃O⁺ (H₉O, including the primary hydration shell) 60% of the time, and 40% of the time it is intermediate between two oxygens as H₅O (1025). Although the proton spends blocks of time as H₉O (i.e., associated with a single oxygen), these events occur within bursts of oscillations between the same pair of oxygens as though the proton remembers its former partner (1050), and hence, appearances to the contrary, was never truly delocalized.

That there is a fundamental difference between protons and other cations is clear from the fivefold higher conductivity of H⁺ in water than other cations like K⁺ (84, 217). In fact, considering its degree of hydration (based on solution density) H⁺ might be expected to have a low mobility like Li⁺ (84, 845) but has nine times higher mobility (845). It has long been appreciated that protons are conducted by a special mechanism in which they hop from one water molecule to the next, which is often called the Grotthuss mechanism, although de Grotthuss' proposal (254a) differs from current views. The Grotthuss mechanism is also called "prototropic" transfer (605), to distinguish it from ordinary "hydrodynamic" diffusion of H₃O⁺ as an intact cation. Danneel (217) suggested that a proton in an electric field might bind to one side of a water molecule and that another proton could leave the far side of the molecule, thus saving the time it would have taken to diffuse that distance. A key distinction from other ions is that during proton conduction the identity of the conducted proton changes (84). Except for Hückel's theory (467a), the equivalence of the three protons in H₃O⁺ is generally considered to be essential to the special prototropic conduction mechanism. Danneel further proposed in 1905 (217) that proton conduction by a Grotthuss mechanism requires two processes: proton hopping from one water molecule to the next, and also a reorientation of water molecules. Glasstone, Laidler, and Eyring (366) concluded that proton transfer was rate-limiting and that water rotation was rapid. Conway, Bockris, and Linton (184) concluded that the proton transfer step was rapid and proposed that the rate-determining step was the reorientation of the recipient water molecule in the electrical field of the donor H₃O⁺ (184, 448). More recent theories growing out of Eigen and co-workers' views agree that the proton transfer step is rapid, but ascribe the rate-limiting step to reorganization of the hydrogen-bonded network through which H⁺ conduction occurs (10a, 11, 221, 479, 664, 1024, 1025, 1050).

The special prototropic conduction mechanism appears to require a hydrogen-bonded structure (361, 469, 605). Water is an ideal medium for prototropic conduction because of its propensity to form hydrogen bonds; water has a higher viscosity compared with other solvents due to hydrogen bonding (300). Proton conduction occurs essentially by means of changes in the identity of the water molecules that participate in the hydrogen-bonded network that includes the excess proton. The mechanism of proton conduction in water has been described as "structural diffusion," which was felt to reflect the delocalized nature of the solvated proton within a hydrogen-bonded network (287, 319, 1070). The concept of structural diffusion of protons in water is supported by ab initio molecular dynamics simulation (1024). Proton conduction occurs as a result of isomerization between Zundel and Eigen cations (10a, 11, 1024). The rate-determining step appears to be the breaking of a second shell hydrogen bond, which allows the replacement of one of the waters by a different one (10a, 287, 288, 664). This process has been called the "Moses mechanism," with second shell hydrogen bonds breaking in the path of the proton and reforming behind (10a, 11a), just as the Red Sea parted to allow Moses and his companions to cross (Exodus 14:21-27). At this point the modern view (10a) diverges from most earlier models in which the water molecule immediately adjacent to H₃O⁺ is required to rotate into an appropriate configuration to accept the proton (80, 184, 448, 467a). The three first shell hydrogen bonds are too strong to be easily broken (10a), whereas the second shell hydrogen bonds are expected to be of normal strength, 2.6 kcal/mol, consistent with empirical measurements of proton mobility (636, 678). In Agmon's view, the widely used traditional method of estimating the "abnormal" component of H⁺ mobility by subtracting the mobility of a "normal" cation such as Na⁺ or K⁺ from the total H⁺ mobility (319, 361, 366, 467a, 605, 628, 636, 678, 845) is incorrect. Because the H₃O⁺ ion is tightly hydrogen bonded to its first shell neighbors, it is effectively immobilized. Consequently, essentially all of the mobility of protons in solution is of the abnormal (Grotthuss type) variety (11). Another difference is that in contrast to Eigen's delocalized proton that could move freely within the H₉O complex (287, 319, 1070), in the current view the proton is mainly associated with a single oxygen or vascillates rapidly between two oxygens, and eventually transfers successfully as a result of second shell hydrogen bond rearrangement (10a, 890, 1024, 1025, 1095).

Because waters inside proton channels may be bound or constrained in some way, proton movement through water-filled channels is often considered to be more analogous to proton transport in ice than in water (732, 733). Proton conduction in ice is fundamentally different from that in liquid water (288, 552, 771, 783). The extensive hydrogen bond rearrangement that characterizes proton transfer in water cannot occur in ice (552, 771). Liquid water is mainly three-coordinated, but the ice structure enforces four-coordination. Repulsion from the fourth water pushes the H₃O⁺ closer to its neighbors, decreasing the energy barrier for proton transfer (552, 771). Historically, the question of proton conduction in ice has proven to be difficult and controversial (42, 44, 96, 157, 188, 288, 294, 380, 500, 808). Eigen and colleagues reported that the mobility of H⁺ in ice was extremely high (289), 1-2 orders of magnitude higher than in water (288), and differing "from that of conduction band electrons in metals by only about 2 orders of magnitude" (287). Subsequently, the general consensus has been that these measurements were contaminated by conduction through melted water at the surface and that the true mobility is much lower, 3 × 10⁴ to 6.4 × 10³ cm² · V¹ · s¹, typically ~10³ cm² · V¹ · s¹ (142, 157, 294, 575, 734, 782, 808, 809). The mobility of H⁺ in water is 3.6 × 10³ cm² · V¹ · s¹ (845). It is a major problem to determine the number of defects (ionic or bonding) in ice, which must be known to calculate mobility. "Pure" ice almost invariably contains enough impurities to dominate attempts to measure the mobility of ionic defects, which are present at only ~1 per 10¹³ H₂O molecules at 20°C (808). This problem can be overcome by "doping" the ice with carriers so that their concentration is known and the signal is larger and thus more accurately measurable (380). In ice studies, it is important to distinguish events at the surface from events occurring within the bulk phase, although the former can be useful in dissecting elementary processes that contribute to proton mobility (260, 356, 357, 1028, 1083).

The only ions that carry current in ice are H⁺ and OH, and both move as a consequence of proton or proton defect movement (783). Both protons and Bjerrum defects (see sect. IIID) must move for sustained current (380); movement of L defects (or protons) alone simply produces (or eliminates) polarization (782). In pure ice at moderate temperatures, the dominant charge carrier is the Bjerrum L defect (the conduction of which occurs by rotation of water molecules), and thus for DC conduction the motion of the ionic defect (H₃O⁺) is rate determining (809). Protons tend to become shallowly "trapped" by the more abundant Bjerrum L defects, but above 110 K they escape at a significant rate and are mobile until they encounter the next trap (1083). Data on H₃O⁺ "soft-landed" onto the surface of ice were interpreted to mean that at temperatures below 190 K proton conductance in ice is essentially absent (188). One danger that must be considered in such studies is that protons can be trapped at the ice surface (1028), probably because the 4-coordinated state that is enforced inside ice is less favorable than the less stringent coordination at the surface (552). Earlier studies of isotope exchange in pure and in doped ice had indicated that Bjerrum defect and proton migration occurred to a similar extent in ice in the 135-150 K range, although OH lacked mobility (181). A recent study of isotope exchange in pure ice nanocrystals at 145 K revealed clear evidence of mobility of both Bjerrum L defects and protons, based on the distinctive infrared spectra of D₂O, coupled HDO molecules, and isolated HDO (1028). Most evidence indicates that protons are mobile in ice at least down to 110 K (1083), and possibly as low as 72 K (808), that proton mobility in ice is practically temperature independent (782, 808), and that the mobility of H₃O⁺ at ~100 K is within an order of magnitude of that in liquid water (808).

The hydroxide anion (OH) also has anomalously high conductivity compared with other anions, ~198 cm² · S/eq (218, 845, 943), although not quite so extreme as H⁺ at ~350 cm² · S/eq (786, 845, 921). In addition, the activation energy for OH conductivity is higher than for H⁺ (288, 623, 636). The high mobility is believed to reflect OH migration by a Grotthuss-like mechanism in which the OH moves from one water to the next by virtue of a proton hopping in the opposite direction (80, 84, 184, 217, 469, 605, 845). Protons move via prototropic transfers between H₃O⁺ and H₂O, whereas OH migrates by prototropic transfers between H₂O and OH. The rate-determining step in OH mobility may be the same as for H⁺ mobility, the breaking of a second shell hydrogen bond (11b), although a recent proposal invokes the crucial breaking of a first-shell hydrogen bond (1026). That OH mobility is less than H⁺ mobility in spite of the similarity of mechanism has been explained in several ways. Bernal and Fowler (84) proposed that the two protons in the donor H₂O are held more tightly than the three protons in the donor H₃O⁺ molecule, thus reducing the likelihood of the former proton transfer. Conway et al. (184) felt the critical difference was the electrostatic facilitation by the extra proton in H₃O⁺ of the prerequisite and rate-limiting water rotation that precedes proton transfer. Gierer and Wirtz (361) suggested a charge mechanism: for H⁺ transfer the proton hops between neutral H₂O molecules, whereas for OH the proton hops between two residual negative charges (288, 361). Agmon (11b) proposed that contraction of the O-O bond distance adds an extra 0.5 kcal/mol to OH transfer. Onsager proposed that H⁺ mobility is higher because the additional kinetic energy of the excess proton increases the energy of H₃O⁺ and favors subsequent proton transfer, whereas in OH conduction the energy of the proton is transferred from OH to H₂O and thus does not contribute to the next transfer (J. F. Nagle, personal communication).

Eigen (287) studied proton transfer reactions extensively and formulated general rules that govern such reactions. Proton transfer reactions tend to be very rapid and are described as "diffusion controlled" because the rate of the reaction is determined by the frequency of molecular encounters resulting from diffusion (287). The rate of proton transfer in normal proton transfer reactions depends on the pK_a difference between donor and acceptor, as illustrated in Figure 1.² When pK_acceptor > pK_donor, the forward reaction is rapid and independent of the pK_a difference. Protonation of various bases occurs with a rate constant >10¹⁰ M¹ · s¹, with the electrostatically favorable recombination of H⁺ and OH clocking in at 1.4 × 10¹¹ M¹ · s¹ (287). When the forward reaction is diffusion controlled, the reverse reaction will occur at a rate that is linearly related to the pK difference (Fig. 1A). By definition, log k_f  log k_r  pK_acceptor  pK_donor = pK (290). If the reaction is asymmetrical with respect to charge (e.g., HX + Y = X + HY⁺), then the diffusion-controlled limit will be different for the forward and backward reactions (Fig. 1B). A Brönsted plot (123a) provides similar information (787). A more thorough theoretical development of the kinetics of proton transfer invokes Marcus rate theory (654), as has been applied successfully to carbonic anhydrase (931).

View larger version (16K): [in this window] [in a new window]   Fig. 1. Idealized dependence of the normalized rates of proton transfer reactions on the pKa difference between donor and acceptor molecules participating in the reaction. In A, the transfer is symmetrical with respect to charge (e.g., HX+ + Y = X + HY+), whereas in B, the reaction results in charge neutralization. The slopes of the forward reaction () and backward reaction () limit at 0 or 1 at large pK. The limiting rate constant (kmax) is 109 to 1010 M1 · s1 for a diffusion-controlled reaction. [From Eigen and Hammes (290), copyright 1963 John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons.]

In terms of a proton conduction pathway that is composed of a series of protonation sites, proton hops may not obey the same rules as proton transfer reactions in diffusion-controlled reactions, due to steric constraints, etc. However, the general principles of the pK dependence of transfer rates are likely to apply. Continuous prototropic transfer is most efficient when the donor and acceptor are symmetrical, as in water to water transfer (605). In solvent mixtures, the solvent with higher affinity traps the proton (605). Ab initio molecular orbital method calculations indicate that in a long water wire, multiple proton transfers (hops) can occur simultaneously (i.e., energetically coupled to each other) using the energy cost associated with a single transfer event (882). An example of coherent proton tunneling has been observed directly in a network of four coupled hydrogen bonds (465).

There is long-standing debate over the suggestion that protons may diffuse laterally at the surface of the membrane at a higher rate than they diffuse in bulk solution. The question has been discussed extensively in the context of bioenergetic membranes (404, 418, 527, 530, 706, 724, 731, 820, 821, 1002, 1079). This question has arisen in several instances in which the apparent single proton channel current is larger than the maximum rate at which protons can diffuse to the channel, as predicted by simple diffusion models. To some extent, surface enhancement may be ascribed to geometric factors, i.e., the difference between diffusion in two and three dimensions (353) without specifying the mechanism by which protons would bind to the surface. A proton trapped at the membrane surface will diffuse into a proton channel if it does not first desorb, whereas a proton in three-dimensional bulk solution has a low probability of diffusing into the channel. In unbuffered solutions, surface conduction dominates; in buffered solutions, the dominant pathway depends on protonated buffer concentration and the effective size of the proton collecting antenna (353) (see below).

One general way that surface conduction could enhance proton fluxes through a channel is by the "antenna effect" (400, 867). Rather than requiring a proton to diffuse directly to the channel entrance, the entire membrane surface, by virtue of its many negatively charged groups, might collect protons, which then travel in the plane of the membrane surface to the channel. Detailed experimental and computational studies have been done on this question (155, 353, 400, 653, 867). Protonation reactions are often extremely rapid and limited only by diffusion, with rate constants typically 1-6 × 10¹⁰ M¹ · s¹ (287, 290, 400, 653, 867). One of the most rapid reactions known is the recombination of H⁺ and OH with a rate constant 1.4 × 10¹¹ M¹ · s¹ (287). However, occasionally higher rate constants are observed. An anomalously high protonation rate measured for a site on a Ca²⁺ channel, 4 × 10¹¹ M¹ · s¹, was explained by proposing the site to be negatively charged and located in the channel vestibule, which would funnel the electric field lines and enhance the electrostatic attraction (823). If two negatively charged groups (e.g., at the surface of a membrane) are close enough together that their Coulomb cages overlap, the "virtual second-order" rate constant governing the transfer of a proton from one group to the other can be 10¹² M¹ · s¹ or greater (400), with the current record being 6 × 10¹² M¹ · s¹ (867). The probability that a proton that is bound to a site with 1 charge at the interface between membrane and aqueous solution will transfer to a neighboring site, also with 1 charge, rather than entering bulk phase, calculated with the Debye-Smoluchowski equation, is close to 100% for a 12-Å separation, decreasing with distance to ~40% for a 60-Å separation (867). It seems clear that rapid proton transfer in the plane of the membrane is possible.

On the other hand, the extent to which rapid surface conduction might play a significant role must be established in each specific situation. In a study on proton transfer rates between superficial amino acid groups on tuna cytochrome c oxidase, all of the virtual second-order rate constants were <10⁹ except for one that was as large as 10¹¹, which was between groups within 10 Å of each other (652). A cluster of three carboxylates on bacteriorhodopsin acts as a proton-collecting antenna, each with a high protonation rate of 5.8 × 10¹⁰ M¹ · s¹, but the dimensions of the antenna are smaller than those of the molecule. Long-range proton migration occurs along a protein monolayer, but depends critically on molecular packing, and is abolished at low or high protein densities (331). Molecular dynamics simulation indicates that proton transport near the surface of a dipalmitoylphosphatidylcholine membrane is inhibited rather than enhanced (953). Finally, de Godoy and Cukierman (253a) explored the effects of bilayer composition on H⁺ currents through gramicidin channels. The limiting H⁺ conductance at low pH was the same in bilayers formed from protonatable phospholipids that presumably should be capable of mediating lateral H⁺ conduction and bilayers formed from covalently modified phospholipids that cannot be protonated. Furthermore, differences in the H⁺ conductance at higher pH were fully accounted for by electrostatically induced changes in local H⁺ concentration near the membrane, providing no evidence of significant lateral H⁺ conduction (253a). In summary, it appears that rapid proton transfer at the membrane surface may occur under specialized conditions but cannot be assumed to occur generally.

The usual way to control pH is with buffered solutions. Because the control of pH is never perfect, recognizing systematic sources of error is useful. Voltage-gated proton channels appear to be perfectly selective for protons over all other ions besides deuterium, as discussed in section VE, and hence act as local pH meters (237). Selectivity is evaluated by measuring the reversal potential (V_rev) in solutions of various pH, and comparing the result with the Nernst potential for H⁺ (E_H)

(1)

Although reasonable agreement between the measured V_rev and E_H is often obtainable, the agreement is rarely perfect. If we tentatively accept the conclusion that voltage-gated proton channels are perfectly H⁺ selective (see sect. VE), then any deviation of V_rev from E_H indicates that the true pH differs from the nominal pH. The primary cause of this deviation in patch-clamp experiments is imbalance between the rate that proton equivalents cross the cell membrane and the rate the buffer from the pipette replenishes the cytoplasmic compartment. The intracellular compartment is a large unstirred volume, and proton efflux such as that occurring during H⁺ currents will deplete protonated buffer from the cell. For example, a 10-µm-diameter cell has a volume of 524 fl, and if it is filled with a pipette solution that has 100 mM buffer at its pK_a, the entire cell will contain 1.6 × 10¹⁰ protonated buffer molecules. During a modest sustained outward H⁺ current of 100-pA amplitude, 6.25 × 10⁸ H⁺ leave the cell each second, deprotonating 4% of the total protonated buffer. Even at intracellular pH (pH_i) 6 there are only 315,000 free protons in the entire cell, all of which would be consumed during 0.5 ms of H⁺ current. Thus, essentially the entire H⁺ current is carried by protons that immediately previously were bound to buffer molecules. Replenishment of buffer occurs by diffusion from the pipette solution and requires the diffusion of these rather large molecules through a small <1-µm-diameter pipette tip into the cell.

Calculations based on Pusch and Neher's empirical determination of diffusion rates (827) predict a time constant of 19 s for the equilibration of 250-Da buffer molecules from a pipette with 5-M tip resistance into a 15-µm-diameter cell. This time constant is proportional to cell volume (776). The rate of equilibration of pH_i will be slower than that for simple buffer diffusion, due to the effective slowing of H⁺ diffusion by fixed (immobile) intracellular buffers (514). Direct estimates of the time constant of equilibration of pH_i in HL-60 cells and macrophages of unspecified size were 11 s (258) and 58 s or 97 s (519), respectively, representing at least qualitative agreement.

The presence and action of any membrane transporter that moves proton equivalents across the cell membrane will alter V_rev. Thus, when Na⁺ is present only in the external solution and pH_i is low, the inward Na⁺ gradient and outward H⁺ gradient both conspire to activate Na⁺/H⁺ antiport. H⁺ extrusion by the antiporter is rapid enough to raise pH_i substantially (i.e., by 0.5 unit or more) in alveolar epithelial cells studied in whole cell patch-clamp configuration, in spite of the presence of 119 mM buffer in the pipette solution (237). H⁺ is extruded by the antiporter faster than the supply is replenished by diffusion of protonated buffer from the pipette. Geometrical factors influence this balance, with smaller cells or larger pipette openings attenuating the change in pH_i due to antiport activity. Thus manifestations of Na⁺/H⁺ antiport were less pronounced in human neutrophils (237) or murine microglia (546) than in the larger rat alveolar epithelial cells, but obviously differences in the expression of Na⁺/H⁺ antiport molecules could also play a role. Any other mechanism that results in net movement of H⁺ equivalents across the membrane will alter pH_i. Several mechanisms of membrane H⁺ flux are discussed in section IIIA, of which the shuttle mechanism in particular could cause attenuation of the pH gradient across the membrane (see sect. IIIA3).

A systematic deviation arises when V_rev is measured by the conventional tail current protocol. A depolarizing prepulse activates the H⁺ conductance (g_H) and then the voltage is repolarized to various levels, and the direction of the tail current (the decaying current waveform that reflects the progressive closing of H⁺ channels) is observed. The necessity to activate a substantial g_H during the prepulse to elicit an interpretable tail current, combined with the extremely slow activation kinetics of voltage-gated proton channels in mammalian cells, inevitably causes significant depletion of intracellular protonated buffer during the prepulse. If a comparable H⁺ current is elicited during the prepulse in solutions of varying pH, the error will be a relatively constant addition of a few millivolts to the measured V_rev. This systematic error may explain why the vast majority of V_rev measurements in the literature are more positive than E_H. On the other hand, V_rev measurements that encompass negative pH [pH_i > extracellular pH (pH_o)] indicate deviation in the opposite direction in this range (166, 519, 886), suggesting that an element of dissipation of any pH gradient may also play a role. As a result, measurement of the change in V_rev at several pH rather than the absolute V_rev often provides a cleaner estimate, which explains the fondness that many experimentalists have for this way of expressing their data. Direct measurements of V_rev using prepulses that elicit smaller or larger currents have been shown to raise pH_i and hence shift V_rev positively roughly in proportion to the integral of the outward H⁺ current during the prepulse (70, 232, 372, 473, 519, 709), although this effect is not apparent in large cells (134). It is important to recognize that the deviation of V_rev from E_H is not an error, but instead accurately reflects the effects of the pulse protocol on pH_i. We consider voltage-gated proton channels to be perfect pH meters (see sect. VE).

An expedient way to estimate V_rev is to activate the g_H and then ramp the membrane voltage "downward" from positive to negative (372). If enough channels open at positive voltages and the ramp is rapid enough that the channels remain open, then V_rev can be taken as the zero current voltage, although any leak conductance and capacity current must be either negligibly small or corrected. The problem remains that it is first necessary to activate the g_H to observe V_rev, so this approach does not avoid the problem of depletion. Another clever way to estimate V_rev is simply to interpolate between the H⁺ current at the end of a depolarizing pulse and that at the start of the subsequent tail current (473). One required assumption is that the instantaneous current-voltage relationship be approximately linear. This method is useful in certain situations, particularly if one suspects that significant depletion has occurred. The advantage is that both required data points are obtained by applying a single pulse, and they are measured at nearly the same time. Again, this approach does not avoid the effects of depletion. In fact, its originators used this approach to demonstrate that H⁺ efflux during large depolarizing pulses alkalinized the cytoplasm significantly.

H⁺ currents increase pH_i in proportion to the amount of H⁺ extruded. For small currents, the change in pH_i may be negligible, but for large currents, depletion of protonated buffer will noticeably increase pH_i. These effects are less pronounced in large cells (134) because they reflect the area-to-volume ratio. Restoration of pH_i is determined by the geometrical factors already discussed, and typically requires tens of seconds up to several minutes. A useful rule of thumb is that because voltage-gated proton channels do not inactivate, when the H⁺ current peaks and then droops during a sustained depolarization, this always reflects an increase in pH_i. Experimentally, this phenomenon can be annoying, but it is simply a manifestation of the ability of the H⁺ conductance to do its job, namely, to extrude acid at a rate adequate to alkalinize the cytoplasm rapidly.

Perhaps not surprisingly, variations in extracellular buffer from 1 to 100 mM had very little effect on voltage-gated proton currents (241). The bath solution represents an effectively infinite sink for protons. The situation for intracellular buffer is more complicated. Several whole cell patch-clamp studies in which pH_i was determined have revealed that including 5-10 mM buffer in the pipette solution does not control pH_i as well as higher buffer concentrations, e.g., 100-120 mM (232, 258, 519, 574). In addition, the time course of the H⁺ current during a single depolarizing pulse was shown to depend strongly on "internal" buffer concentration in excised inside-out patches of membrane (241). The initial turn on of H⁺ current was similar, but the longer the pulse, the more the current with 1 mM buffer drooped relative to that with 10 mM buffer. Nevertheless, decreasing internal buffer from 100 to 1 mM attenuated the H⁺ current by only ~50%; thus this effect is attributable to H⁺ current-associated pH changes, rather than a limitation of the conductance of the channel by buffer (241) (cf. sect. VJ).

In addition to buffers, application of an NH gradient has proven to be a useful way to control pH_i in patch-clamped cells (242, 248, 387) (see also sect. IIID). Control over pH_i is excellent and rapid when the NH gradient is symmetrical, becoming less effective for large NH (hence pH) gradients (248, 387). An advantage of this technique is that pH_i can be changed in a cell simply by altering the bathing solution.

Several issues related to buffers are relevant to the study of proton channels. Experimental control of pH requires adequate buffering, as just discussed in section IIE. Buffering power (or buffering capacity) is defined as dB/dpH (1036), i.e., the concentration of strong base required to change the pH of a solution by one unit. A more rigorous discussion of this and other definitions can be found elsewhere (849, 850). The reported buffering power of the cytoplasm in mammalian cells ranges from 18 to 77 mmol · pH¹ · liter¹ (850). The measured buffering power of most cells increases substantially at lower pH, typically three- to fivefold between pH_i 7.5 and pH_i 6.5 (24, 41, 92, 324, 603, 630, 840, 850, 1067). A similar observation has been made for the Golgi (153). The buffering power is maximal at the pK_a of the buffer (425, 1064), where it is (ln10)[B]/4 ~ 0.58[B], where [B] is the total buffer concentration (559, 849, 1036). Thus a cytoplasmic buffering power of 58 mmol · pH¹ · liter¹ would reflect the presence of the equivalent of at least 100 mM simple buffer in cytoplasm. To control pH experimentally, many investigators use solutions with 100 mM exogenous buffer near its pK_a. Under normal conditions, this is adequate to prevent pH changes large enough to alter H⁺ currents noticeably (240) (but see cautionary tales in sect. IIE).

When a cell is dialyzed with a pipette solution containing inadequate buffer, intrinsic cytoplasmic buffers override the attempts of the pipette solution to control pH_i. The larger the cell, the more difficult is the control of pH_i. Byerly and Moody (135) compared the rate of equilibration of pipette solutions containing K⁺ or highly buffered H⁺ with cytoplasm in large neurons (90-120 µm in diameter) studied with suction pipettes one-third the cell diameter. The effective equilibration of H⁺ even with high buffer concentrations (50-100 mM) was three to five times slower than that of K⁺, and with 20 mM buffer, little control over pH_i was achieved (135). Similarly, the effective diffusion coefficient of H⁺ in cytoplasm is five times slower than that of mobile buffers (15). In small cells studied with patch pipettes containing pH 5.5 solutions, pH_i deduced from the V_rev of H⁺ currents was ~5.7 for 119 mM MES buffer and ~6.3 for 5 mM MES (232). A pipette solution with 1 mM buffer appeared to have essentially no effect on pH_i (240).

Buffers have variable tendencies to chelate metal ions (805). Because we could not find much information on this property for normal pH buffers beyond the initial description of the Good buffers (370), we measured the binding constants of several buffers for Zn²⁺, Cd²⁺, Ni²⁺, and Ca²⁺ (163). Certain buffers bind Zn²⁺ avidly, including tricine and N-(2-acetamido)-2-iminodiacetic acid (ADA). The latter has been used to establish free Zn²⁺ concentrations in the nanomolar range (22, 792).

	III. MECHANISMS OF PROTON PERMEATION THROUGH MEMBRANES

Top Previous Next References

The Born self-energy cost of an ion permeating a pure lipid bilayer is prohibitive (794), ~58.6 kcal/mol for the H₃O⁺ (243). Therefore, a mechanism subtler than brute force is required to translocate protons across membranes. Four mechanisms that have been proposed to explain proton permeation through biological membranes are as follows: transient water wires (sect. IIIA2), weak base or acid shuttles (sect. IIIA3), phospholipid flip-flop (sect. IIIA4), and specific proteins (channels, carriers, and pumps) whose function is to transport protons. High "intrinsic" proton permeability must be explained by one of these mechanisms. As will become apparent however, the proton permeability of cell membranes that contain voltage-gated proton channels is several orders of magnitude higher than the highest estimate for simple phospholipid bilayers. In most cells with H⁺ channels, any proton permeability of the membrane itself is negligible in comparison (242).

It has been maintained widely and for some time that membrane proton permeability (P_H) is anomalous in two respects. First, P_H is many orders of magnitude higher (10⁴ to 10² cm/s) than the permeability of other cations (10¹² to 10¹⁰ cm/s) (227, 228, 390, 755, 797). Second, the proton conductance (G_H) is practically independent of pH (226, 395, 396, 755). These observations have been challenged on various counts, and some of the complications will be mentioned here.

P_H is difficult to measure, and reported values vary over many orders of magnitude, ranging from <10⁹ to 10¹ cm/s (153, 396, 585, 688, 755, 764, 766, 797, 804). Although various studies report no (124), moderate (585), or strong (i.e., up to ~100-fold) (228, 390, 396, 755, 764, 804, 1033) dependence of P_H on the composition of the membrane, this dependence does not come close to resolving the vast disparity in reported values. The idea that P_H is anomalously high was challenged by Nozaki and Tanford (766), who measured P_H 10⁹ cm/s in phospholipid vesicles and estimated the true value to be 5 × 10¹² cm/s. Deamer and Nichols (227) argued that these measurements were limited by development of a diffusion potential. Diffusion potentials can be avoided by allowing counterion flux (114). The finding that several cells have undetectably small P_H (185, 1054) suggests that proton permeability is not a general property of cell membranes.

Another source of variability may be differences between conductance and permeability measurements. Radioactive tracers reveal unidirectional flux, whereas electrical currents reflect only net flux, i.e., the difference between the unidirectional fluxes. For example, at E_H there is no net H⁺ current, but there still can be large bidirectional fluxes. Hence, permeability estimates based on fluxes may be higher than electrical estimates made near E_H. On the other hand, if H⁺ current is measured during a large driving voltage, fluxes will be practically unidirectional, so the two estimates should be reasonably consistent.

It has been suggested that both the high apparent P_H and the pH independence of G_H might be the result of proton accumulation near the negatively charged phospholipid head groups at the membrane-solution interface (342). In this view, P_H is high because its calculation assumes the bulk solution concentration and neglects the possibility that the local concentration of protons at the membrane surface may be proportionally much higher than other cations, due to the closer approach of H₃O⁺ than a hydrated cation to the negatively charged membrane. It has been known at least since 1937 that negative surface charges tend to lower the surface pH, by up to 2 pH units in physiological solutions (215, 378, 988). Numerous studies indicate that negative surface charges can concentrate protons and other cations near membranes, resulting in higher conductance than expected from bulk concentrations (32, 214, 531, 716). Higher P_H is measured in negatively charged phospholipid membranes (764). Furthermore, because the negative charges at the surface are essentially fully screened by protons, the local proton concentration is relatively independent of bulk pH, and thus the apparent insensitivity of proton flux to bulk pH is also explained (342).

A fundamental difficulty with measuring P_H is that in the physiological pH range, the [H⁺] is up to 10⁶ smaller than that of other cations. Because the calculation of P_H effectively normalizes the measured flux according to the nominal [H⁺], any error is magnified, and the error is amplified at higher pH. At least in electrical measurements, most errors tend to increase the apparent P_H. In alveolar epithelial cells studied by voltage clamp in solutions lacking small ions, P_H < 10⁴ cm/s, even assuming that the entire leak is carried by H⁺ (242). In fact, the "leak" current was insensitive to pH and the leak reversal potential did not change in a direction consistent with H⁺ selectivity, thus P_H 10⁴ cm/s by direct electrical measurement and any proton permeability was too small to detect (242). Similar observations were made in myelinated nerve (440). Also consistent with a low P_H, large changes in apical pH_o do not change pH_i in alveolar epithelial monolayers (510). From the viewpoint of a cell trying to maintain homeostasis, any proton leak is undesirable. In light of the >10⁴ increase in P_H that occurs when the cell membrane is depolarized and H⁺ channels open, the background level of proton leak is negligible for most purposes.

It is questionable whether the traditional permeability coefficient P_H is useful for H⁺ flux through either membranes or most channels. The Goldman-Hodgkin-Katz (GHK) model (368, 444, 456) assumes that permeation is a simple process that occurs at a rate proportional to the rate that the permeant ion species encounters the membrane, which in turn is proportional to the bulk concentration. P_H is thus predicted to be a constant that is independent of pH, and lowering the pH by one unit should increase the H⁺ flux (or g_H) 10-fold. In fact, deviations from this prediction are more the rule than the exception. To the extent that simple membrane H⁺ conductance is independent of [H⁺] (226, 395, 396, 755), the parameter P_H, far from being constant, increases 10-fold/unit increase in pH. The P_H of Golgi membranes increases 3.4-fold/unit increase in pH (153). P_H calculated in alveolar epithelial cells during maximal activation of H⁺ currents increases ~5-fold/unit increase in pH (166, 242). This type of behavior demonstrates that these systems do not operate within the assumptions built into the GHK permeability equations, and hence, permeability calculations have little meaning. In contrast, for gramicidin P_H is constant over a wide pH range; i.e., the single-channel H⁺ conductance increases 10-fold/unit decrease in pH (Fig. 13). This counter-example suggests that the pH dependence of P_H in other systems does not reflect something peculiar about the diffusion of protons to membranes, at least at pH <5. Instead, it more likely indicates that a rate-limiting step in the permeability process is slower than the diffusional approach of protons to the membrane. In the case of voltage-gated proton channels, permeation through the channels is thought to be rate determining (166, 234, 238-240, 242-245). The GHK equations provide a valuable frame of reference by predicting the behavior of a simple system. However, in the frequently occurring situations in which P_H depends strongly on pH, the parameter P_H is not a meaningful way to evaluate or compare proton fluxes.

A transient water wire might occur if, due to thermal fluctuations, a chain of water molecules happened to align across the membrane (225, 228, 755). Although fatty acid monolayers and cell membranes present a significant barrier that slows water diffusion by ~10⁴ (34, 147), water can permeate most cell membranes, and several waters might follow the same path once a trailblazer has led the way. A hydrogen-bonded chain of water molecules intercalated between membrane phospholipids might be imagined to conduct protons. A membrane-spanning chain would need to be ~20 water molecules long, and the Born energy cost of forcing a proton into the bilayer might be reduced by virtue of partial hydration by nearby waters (730). The proton flux could be independent of pH if the rate-determining step were the breaking of hydrogen bonds between neutral waters, which might initiate the turning step of the hop-turn mechanism (730) (see sect. IIID). A recent modification of this idea is the translocation of protons by small clusters of water molecules in the membrane (405).

There are some difficulties with the transient water wire proposal. Although water permeability varies 27-fold in different synthetic membranes (309), and P_H varies ~100-fold in different membranes, there is no correlation between P_H and water permeability (396). Molecular dynamics simulations indicate that the free energy barrier to formation of a water wire in a membrane is 108 kJ/mol, and thus the likelihood of a membrane-spanning pore forming is very low (658). The lifetime of such a water wire was <10 ps in this study (long enough to transport no more than one proton) and averaged 36 ps in a later simulation study (1038). The H⁺ flux calculated for this mechanism could be made to agree with experimental estimates only by assuming that a proton permeates instantaneously and that the entry rate of protons into the water wire is 10⁸ faster than provided by diffusion (658). Furthermore, simulations of H⁺ permeation through optimal water wires indicate that ~100 ps is required for H⁺ to permeate a 30-Å channel (120), which is longer than the predicted lifetimes of the transient water wires (658, 1038). The mean interval between H⁺ permeation events through gramicidin during the largest H⁺ currents recorded through any ion channel (2.2 × 10⁹ H⁺/s in gramicidin at +160 mV and 5 M HCl) (207) is 455 ps, which may or may not represent the maximum conduction rate (see sect. IVA4). A spontaneous water wire would have to be narrow and transient, because otherwise other ions might permeate (730), violating the observation that P_H is 10⁶ greater than that of other ions (755). Paula et al. (797) reported that P_H decreased from ~10² to ~10⁴ cm/s as the bilayer thickness was increased from 20 to 38 Å, and concluded that protons were conducted via transient water wires in thin membranes and by a solubility-diffusion mechanism in thicker membranes. As pointed out by Deamer (225), if P_H measured in biological membranes was found to be lower than in model (5) membranes, then the latter would be poor models, because biological membranes may have a variety of additional transport mechanisms that would, if anything, increase H⁺ flux. If water wires conduct protons across ordinary cell membranes, then they do so at a rate that is negligibly low compared with the proton fluxes that occur when voltage-gated proton channels are active (242).

Protons can cross membranes via weak acids or weak bases that act as proton carriers (106, 169, 671). It has been suggested that contaminant weak acids might account for the high P_H reported in phospholipid bilayer membranes (396). The weak acid mechanism has long been recognized (486) and is illustrated in Figure 2. When a weak acid is added to the extracellular solution, the protonated form (HA) will be present at a concentration determined by its pK_a and the pH as described by the Henderson-Hasselbalch equation (415, 425). The protonated form can permeate the membrane far more readily than the anionic form (A), and thus the predominant result will be entry of HA down its gradient into the cell. Once inside, HA will dissociate into A and H⁺, to an extent determined by pH_i. The net result is that protons have been transported into the cell and released there, thus increasing pH_o and decreasing pH_i. The addition of a weak base will have the opposite effect. Again, the neutral form is far more permeant, but when B, a weak base, enters the cell, it leaves its proton behind, lowering pH_o, and once inside the cell it will tend to bind H⁺ thus increasing pH_i. The neutral form of the acid or base will continue to diffuse across the membrane until its concentration is the same inside and outside the cell.

View larger version (11K): [in this window] [in a new window]   Fig. 2. Diagram illustrating the effects on local pH when weak acids (A) or weak bases (B) are present. The neutral form of each molecule typically is many orders of magnitude more permeant than the charged form. If the acid or base is present on one side of the membrane, the neutral form will permeate and change the pH on both sides of the membrane. The protonated weak acid, HA, carries its proton across the membrane and then may dissociate inside the cell, lowering intracellular pH (pHi) and increasing extracellular pH (pHo). These pH changes will be buffered, and the extent of the change will depend on geometrical considerations. The deprotonated weak base will permeate, in effect leaving a proton behind, and will tend to pick up a proton inside the cell, increasing pHi and lowering pHo.

A corollary to this mechanism is that weak acids and bases tend to equilibrate across membranes according to the pH on each side, which is important for determining intracellular drug concentrations (e.g., Refs. 233, 443, 744). This mechanism has been exploited as a way to estimate the pH inside cells or organelles (e.g., Refs. 152, 703, 1045). Another application of this phenomenon is the NH prepulse technique (850), which is a standard method to study pH_i recovery from an acid load. This principle has been exploited to regulate pH_i in cells under whole cell voltage clamp (242, 248, 387). One can establish a known NH (or triethylammonium⁺, for example) gradient by including a known concentration in the pipette solution, and then adjusting the NH in the bathing solution. Ideally, the NH gradient will establish an equivalent H⁺ gradient. For example, 5 mM NH in the bath and 50 mM NH in the pipette (and thus in the cell) will lower pH_i by 1 unit relative to pH_o.

Because of their exquisite sensitivity to pH, voltage-gated proton channels are effective pH meters that can be used to report pH changes (237). Adding NH to the bath produces intracellular alkalinization, which greatly diminishes H⁺ currents (473). Conversely, addition of sodium lactate or sodium acetate to the external solution rapidly and effectively acidifies the cytoplasm, enhancing voltage-gated proton currents (473, 710).

As a practical consideration, if one wants strict control over pH_i, one must worry about the presence of weak acids or bases in the solutions. Obviously, small molecules with pK_a near ambient pH (e.g., HCO, NH, etc.) are perilous, but even larger molecules with pK_a >2 units from ambient may produce significant changes in pH_i by the proton shuttle mechanism. For example, N-methyl-D-glucamine (NMDG), a commonly used large "impermeant" cation with pK_a 9.6, can cause significant shunting of the pH gradient by the shuttle mechanism (938). Whether it does so quickly enough to affect H⁺ currents in a patch-clamped cell has not been reported, but deviations of V_rev from E_H appear somewhat greater in a study using NMDG solutions (232) than tetramethylammonium⁺ solutions in the same cells (166). Tetrabutylammonium⁺ is sufficiently lipophilic to permeate cell membranes (233) and has been shown to enhance proton flux (764).

Another mechanism that might allow net proton flux across a membrane is phospholipid flip-flop (396). This is a subset of the weak-acid mechanism just discussed, but does not require any molecules exogenous to the membrane. Membrane phospholipids might transport protons, acting effectively as carriers. The negatively charged phosphate groups may become protonated, neutralizing their charge, and then the molecule could flip-flop across the membrane, releasing the proton on the other side. Long-chain fatty acids can also transport protons across membranes by this mechanism (397). Biological long-chain fatty acids may transport protons across the membrane by a weak acid mechanism, although their slow intrinsic flip-flop rate makes them relatively inefficient (397). Although it seems likely that this mechanism can occur under some conditions (397, 547), it has been argued that it does occur only at relatively high concentrations of fatty acids, such as 300 µM oleic acid (327).