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Proton Transfer Dynamics at the Membrane/Water Interface: Dependence on the Fixed and Mobile pH Buffers, on the Size and Form of Membrane Particles, and on the Interfacial Potential Barrier

Dmitry A. Cherepanov ^* , Wolfgang Junge ^* and Armen Y. Mulkidjanian ^* 

^* Division of Biophysics, Faculty of Biology/Chemistry, University of Osnabrück, D-49069 Osnabrück, Germany; A. N. Frumkin Institute of Electrochemistry, Russian Academy of Sciences, 117071 Moscow, Russia; and A. N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Moscow, 119899, Russia

Correspondence: Address reprint requests to Armen Y. Mulkidjanian, Abteilung Biophysik, Fachbereich Biologie/Chemie, Universität Osnabrück, D-49069 Osnabrück, Germany. Tel.: +49-0541-9692871; Fax: +49-0541-9692870; E-mail: mulkidjanian{at}biologie.uni-osnabrueck.de.

	ABSTRACT

TOP ABSTRACT INTRODUCTION RESULTS AND DISCUSSION OUTLOOK AND CONCLUSIONS APPENDIX A APPENDIX B ACKNOWLEDGEMENTS REFERENCES

 
Crossing the membrane/water interface is an indispensable step in the transmembrane proton transfer. Elsewhere we have shown that the low dielectric permittivity of the surface water gives rise to a potential barrier for ions, so that the surface pH can deviate from that in the bulk water at steady operation of proton pumps. Here we addressed the retardation in the pulsed proton transfer across the interface as observed when light-triggered membrane proton pumps ejected or captured protons. By solving the system of diffusion equations we analyzed how the proton relaxation depends on the concentration of mobile pH buffers, on the surface buffer capacity, on the form and size of membrane particles, and on the height of the potential barrier. The fit of experimental data on proton relaxation in chromatophore vesicles from phototropic bacteria and in bacteriorhodopsin-containing membranes yielded estimates for the interfacial potential barrier for H⁺/OH^- ions of 120 meV. We analyzed published data on the acceleration of proton equilibration by anionic pH buffers and found that the height of the interfacial barrier correlated with their electric charge ranging from 90 to 120 meV for the singly charged species to >360 meV for the tetra-charged pyranine.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION RESULTS AND DISCUSSION OUTLOOK AND CONCLUSIONS APPENDIX A APPENDIX B ACKNOWLEDGEMENTS REFERENCES

 
The transmembrane difference in electrochemical potential of hydrogen ion plays a key role in biological energy transduction. This difference is generated by redox- or light-driven proton pumps in the energy-transducing membranes of bacteria, chloroplasts, and mitochondria. After Mitchell (1961), the protonmotive force (pmf) is written as

(1)

where is the transmembrane electric potential difference and pH is the transmembrane pH difference.

In bacteria, protons are extruded by pumps out of the cell. Without constraints on proton diffusion, as first noted by Williams, the ejected protons would be diluted in the infinite external solution and the entropic component of pmf would be lost; see, e.g., Williams (1978) and references therein. This argument is crucial for alkaliphilic bacteria, such as Bacillus firmus, which clamp their internal pH by 3 pH units more acidic than the ambient one (see Krulwich et al. (1996) for a review). As in these bacteria hardly increases above 200 mV (Guffanti et al., 1984), the application of Eq. 1 yields a pmf value of about zero. A wealth of data obtained with other bacteria revealed a poor correlation between the magnitude of pmf, which was calculated as the sum of pH (between two water phases) and , and the efficiency of various pmf consumers, the ATP synthase in the first line (see, e.g., Michel and Oesterhelt (1980) and Elferink et al. (1983) for original data and Kell (1979), Ferguson (1985), and Cramer and Knaff (1991) for the surveys). To account for these kinds of observations, Kell (1979) hypothesized that the ejected protons spread at the membrane surface but were somehow hindered from the prompt equilibration with the bulk. Michel and Oesterhelt (1980) came to the same conclusion based on the poor correlation between the adenosine tri-phosphate (ATP) yield as measured in whole cells of halobacteria and the magnitude of pmf, defined as a sum of and pH. If proton exchange is retarded, the local pH at the membrane surface might differ from the pH in the bulk at steady state, leading to reasonably large values of pmf even in the case of alkaliphilic bacteria (see also discussion in Guffanti and Krulwich (1984)).

In the previous work we argued that the diffusion of charged molecules across the membrane/water interface might be restricted by the low dielectric permittivity () of water at negatively charged membrane surface (Cherepanov et al., 2003). Using the permittivity profile as obtained by the atomic force microscopy at the negatively charged mica surface at low (1 mM) ionic strength (Teschke et al., 2001), we extrapolated the dielectric properties to the higher ionic strength of 0.1 M and calculated the potential energy profile for probe ions at the membrane/water interface. We found that the decreased dielectric permittivity of the surface water gave rise to a potential barrier that peaked 0.5–1 nm away from the surface. The height of barrier depended on the charge and the size of probe ions. It was on the order of 100–200 meV for monovalent spherical ions with radius of 0.25 nm, being higher for anions than for cations. At steady operation of proton pumps, such a barrier could raise up the proton concentration at the membrane surface by 10^-6 M over the value in the bulk. This finding might explain how alkaliphilic bacteria synthesize ATP at the expense of the surface-to-surface pmf.

A question might arise to what extent the smooth mica surface can represent the irregular interface of biological membranes. Here we scrutinized the properties of interfacial water at the surface of biological membranes by the quantitative analysis of a variety of experimental data on the proton transfer dynamics as obtained in pulse experiments at moderate ionic strength close to the physiological conditions. In experiments of this kind, the equilibrium was perturbed by a rapid ejection (uptake) of protons at the membrane surface, with the subsequent proton relaxation being monitored by different techniques. The surface/bulk proton relaxation in different membrane preparations and membrane enzymes was found to be substantially slower than the proton equilibration at the surface proper. The relatively fast rate of lateral proton equilibration along the membrane surface is apparently due to the high density of pH-buffering groups at the membrane surface (see Georgievskii et al. (2002), Zhang and Unwin (2002), and Serowy et al. (2003) for the recent quantitative analysis of this issue and relevant references). Several teams have shown independently that hydrophilic pH indicators, when added to a suspension of unsealed bacteriorhodopsin (BR) membranes, picked the BR-ejected protons at 1 ms, by order of magnitude slower than they arrived and equilibrated at the surface (Drachev et al., 1984, 1992; Heberle and Dencher, 1992; Heberle et al., 1994; Alexiev et al., 1995; Dioumaev et al., 1998; Porschke, 2002). Analogously, it has been shown that protons appeared at the surface of the cells and spheroplasts of purple phototrophic bacteria Rhodobacter sphaeroides and Rhodobacter capsulatus at < 5 ms as followed by electrochromic shift of carotenoid pigments (which correlate with the absorbance changes of an amphiphilic, membrane-bound pH indicator neutral red (Mulkidjanian and Junge, 1994)) but were sensed in the bulk phase by hydrophilic pH indicators only at 30–70 ms (Arata et al., 1987; Jones and Jackson, 1989, 1990). A retardation has been also shown for the proton uptake: i), by the photosystem II of green plants (Haumann and Junge, 1994b), and ii), by the photosynthetic reaction centers (RC) of Rb. sphaeroides (Maroti and Wraight, 1997; Gopta et al., 1999).

The slow rate of proton transfer between the surface of biological membranes and the bulk water phase has been commonly attributed to the damping effect of fixed pH buffer at the surface (Junge and Polle, 1986; Junge and McLaughlin, 1987; Jones and Jackson, 1989). However, if the surface pH buffers were alone responsible for the retardation, the rate of proton equilibration had to depend on the concentration of mobile pH buffers or pH indicators (see discussion by Junge and McLaughlin (1987), Gopta et al. (1999), and Georgievskii et al. (2002)). Such a dependence was indeed observed with the pH indicator p-nitrophenol added to BR membranes (Drachev et al., 1984). Contrastingly, the response time of another hydrophilic pH indicator pyranine, which was added to the similar BR membranes, remained independent of its concentration in the range of 10–150 µM (Heberle, 1991; Porschke, 2002).

These apparently contradictory observations could be rationalized if one takes into account that the height of the above-noted potential barrier in the interfacial water layer depends on the charge of penetrating ion (Cherepanov et al., 2003). Because the charge of pyranine in the deprotonated state is -4 and the charge of p-nitrophenol is -1, one expects a much higher barrier in the former case, in agreement with the experimental observations. Qualitatively it looks like the retardation of proton transfer in pulse experiments resulted both from the damping effect of the surface pH buffers and from the influence of the dielectric barrier.

Aiming at a quantitative analysis of the above-cited kinetic data on proton relaxation at the biological interfaces, we modeled here, by numeric integration of the diffusion equations, the proton equilibration between membrane particles of various form and the surrounding bulk solution. In our previous modeling (Cherepanov et al., 2003), we considered only the mobile proton carriers, but neglected the fixed buffers at the membrane surface because the latter do not affect the proton flux at steady state. In the case of pulse experiments, the participation of fixed pH buffers at the membrane surface cannot be neglected (Junge and Polle, 1986; Junge and McLaughlin, 1987). Therefore here we treated the dependence of proton relaxation on the surface buffer capacity explicitly. Besides this, we analyzed the dependence on the concentration of mobile buffer, on the form and the size of membrane particles, and on the height of the interfacial potential barrier. The comparison of model results with published experimental data allowed to obtain a consistent picture where differences in the ability of various mobile pH buffers to accelerate the proton equilibration between the surface and the bulk water were explained by the difference in their electric charge. The latter largely determined the energy barrier as seen by these buffers. The estimated barrier height varied between 90 meV for the singly charged p-nitrophenol and >360 meV for pyranine, which carries four negative charges in the deprotonated state.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION RESULTS AND DISCUSSION OUTLOOK AND CONCLUSIONS APPENDIX A APPENDIX B ACKNOWLEDGEMENTS REFERENCES

 
Proton transfer dynamics at the outer surface of spherical vesicles
As a starting point, we considered the proton equilibration between the membrane surface and the bulk buffer solution in the absence of any barrier at the surface, i.e., under the assumption that the dielectric properties of water at the interface do not differ from those in the bulk phase. This assumption corresponds to the discontinuous model of the membrane/water interface, where the membrane phase with the dielectric constant 4 borders abruptly the bulk water phase with 78, as commonly used when modeling interfacial and membrane phenomena (see, e.g., Israelachvili (1992)). To simplify the calculations, we considered spherical vesicles of radius R surrounded by an infinite bulk solution (R < r < ). The solvent in a typical experiment contains several mobile acids and bases (pH buffers, pH indicators, neutral water, H₃O⁺, and OH^-), which interact by bimolecular collision with each other and with fixed pH buffers at the membrane surface. The latter are believed to be coupled to each other by water molecules forming a proton-conducting continuum, which allows fast proton transfer along the surface (see Georgievskii et al. (2002), Serowy et al. (2003), and references therein). For simplicity, we considered only one species of a fixed buffer, B, at the surface of membrane and a single species of a mobile buffer, C, in the bulk solution, with pK values determined by the respective equilibrium dissociation constants K_B and K_C: and

Let us assume that a short light impulse triggers the rapid turnover of proton pumps and perturbs the preexisting proton equilibrium at the membrane surface in 100 µs, a typical time of proton equilibration at the surface of biological membranes. Let _B be the density of fixed buffer at the membrane surface (mol m^-2), K_B be the dissociation constant of this buffer (mol m^-3). The density of the protonated form of the surface buffer _BH is therefore

(2)

where [H⁺] is the equilibrium concentration of free proton (mol m^-3) near the surface (in the absence of surface potential [H⁺] is equal to the bulk concentration of proton).

Let _H be the surface density of ejected protons (mol m^-2), which is equal to the density of operating proton pumps if they turn over only once. After the fast equilibration of ejected protons with the buffer B at the surface, which precedes the ultimate equilibration with the bulk solution, the local equilibrium at the membrane surface can be written as

(3)

where _BH is the change in the density of the protonated form of the surface buffer, and [H⁺] is the change in the local concentration of free proton in the vicinity of the interface. In the experiments considered below, the local capacity of fixed buffer at the surface (the effective volume concentration has order of 0.1 M) greatly exceeds the capacity of mobile buffers (the maximal used concentration of the latter was 1 mM). In such a case, almost all ejected protons would reside at the surface buffer, so _{BH H}. Combining Eqs. 2 and 3, one gets the relation between the number of ejected protons and the change in the local concentration of free proton near the surface:

(4)

If the concentration of mobile buffer C₀ greatly exceeds the concentration of free protons (the usual condition in biological experiments), the change in concentration of the protonated form of mobile buffer at the surface is

In the following we assume that pK values of mobile and surface buffers match so that the latter relation simplifies to:

(5)

The rate of equilibration for a spherical vesicle of radius R in infinite solution can be calculated by the steady-state flux assuming a constant concentration of diffusing species at the surface (see e.g. Berry et al. (1980); the accuracy of such approximation is discussed below after comparison with the respective numerical solution). The steady-state concentration around the vesicle, c(r), can be then written as

and the total steady-state flux across a surface of radius r is

The rate of relaxation therefore reads

This equation can be generalized for the case when several different fixed buffers are present at the membrane surface. If ₀ is the total surface buffer capacity and the solution contains N mobile buffers (i = 1...N) with the respective buffer capacities and diffusion coefficients D_i, the relaxation rate constant reads

(6)

Here we treated explicitly the diffusion of H⁺ and OH^- (the neutral water is present in great excess, so its diffusion does not limit the total flux).

According to Eq. 6, the rate of proton relaxation around a spherical vesicle is proportional to the weighted sum of the concentrations of all mobile species (including H⁺ and OH^-) times their respective diffusion coefficients, and it is reciprocal to the surface buffer capacity and to the radius of vesicles. Equation 6 states that the proton relaxation is accelerated by mobile pH buffers but slows down with the increase of: i), the surface buffer capacity, and ii), the geometrical size of vesicles. The dependence of the proton equilibration rate on the concentration of mobile and fixed buffers has been discussed previously (Junge and Polle, 1986; Junge and McLaughlin, 1987; Jones and Jackson, 1989; Gopta et al., 1999; Georgievskii et al., 2002). The dependence of proton relaxation on the size of membrane particles vesicles has not been noted so far.

Published data on proton relaxation in various membrane preparations are summarized in Table 1. On one hand, these data corroborate the notion that the proton relaxation time increases with the geometrical size of membrane particles (see also below). On the other hand, the model predicts a rather straightforward dependence of the proton relaxation on the concentration of mobile pH buffers/indicators. Indeed, because the diffusion coefficient of common buffers is one order of magnitude smaller than that of H⁺ and OH^-, one could expect that a mobile pH buffer added to a buffer-free suspending medium would accelerate the proton equilibration when its concentration exceeds the concentration of predominant proton carrier (H⁺ or OH^-, depending on pH) by one order of magnitude. At neutral pH the "threshold" concentration of mobile pH buffer is then expected to be on the order of 5 x 10^-6 M. As already noted in Introduction (see also below), the observed "threshold" concentrations, at which pH buffers started to accelerate pH relaxation, were often much higher and correlated with the electric net charge of buffer molecules. This behavior cannot be described by Eq. 6.

Proton relaxation in the presence of a potential barrier: comprehensive model of interfacial proton transfer
We developed a detailed model of proton transfer dynamics at the membrane/water interface to analyze the experimental data quantitatively. On modeling we considered the protolytic interactions and diffusion of four chemical species: 1), a fixed pH buffer at the membrane surface B; 2), a soluble pH buffer (pH dye) in the bulk phase C; 3), the hydrated proton H⁺; and 4), the hydroxyl anion OH^-. The protolytic interactions in the system were described by the following reactions:

Because of the small buffer capacity of water, we did not consider the direct interaction of H⁺ and OH^- ions in the presence of other buffers. The rate constants used for the reactions in the bulk phase are listed in Table 2 (the concentration of neutral water was included in the pseudo-first-order rate constants); other details are given in Appendix A.

(7)

The function contains two adjustable parameters: the characteristic length of the interfacial region L (taken equal to 2 nm for all species) and the height of the barrier Beyond a distance of 2L from the surface the potential was zero. The barrier height might depend on the electric charge, the size and geometrical form and on the chemical properties (like polarity and hydrogen bonding structure) of the mobile species. To reduce the number of fit parameters, we assumed the same height of the potential barrier both for the protonated and deprotonated form of a mobile buffer. Indeed, the total proton flux mediated by a mobile buffer includes two equal contributions: the protonated form of buffer moves in one direction and the deprotonated one moves in the opposite direction. Even if the protonated and deprotonated forms have different mobility at the interface, the total kinetic competence of the buffer in establishing proton equilibrium is determined by the slowest form. The patched distribution of positive and negative charges on the surface, which has been considered in our previous article (Cherepanov et al., 2003), was ignored for simplicity.

The evolution in time was described by the system of diffusion equations with the source terms responsible for the chemical interconversions of the species. For spherical membrane vesicles, the equations had the following form:

Here the first term is the one-dimensional Smoluchowski equation in spherical coordinates, c_i is the concentration, D_i the diffusion coefficient, and k_BT the thermal energy; the exact form of chemical terms was determined in accordance with the scheme of chemical interconversions (see Appendix A for details). The system of five partial differential equations was solved numerically by the algorithm described in Blom and Zegeling (1994). The size of the bulk phase was limited in such a way that the total amount of soluble buffer was at least 10-fold greater than the total amount of the fixed buffer on the membrane surface. The typical grid size was 20-fold greater than the radius of particles R, and the grid spacing was 20-fold smaller than the length of the interfacial region L; the boundaries were considered as impermeable for all kinds of particles.

The membrane sheets were approximated by flat horizontal cylinders. In cylindrical coordinates the respective diffusion equations had the form

The numeric solution was obtained by the adaptive grid solver for parabolic partial differential equations VLUGR2 (Blom et al., 1996) analogously to the solution in spherical coordinates.

The influence of membrane geometry on the proton relaxation dynamics
In the following sections, we analyzed experimental data on proton relaxation as obtained with membrane particles of different form: i), spherical membrane vesicles from phototrophic bacteria (chromatophores), and ii), bacteriorhodopsin containing flat membrane sheets (purple membranes). To check how the difference in membrane geometry affects the rate of proton relaxation, we calculated the latter for: i), spherical vesicles of radius R_sph = 354 nm, and ii), flat cylindrical membrane sheets of radius R_cyl = 500 nm (typical for BR membranes). The full surface area of both types of particles (including both sides for unsealed membrane sheets) was identical and equal to 1.57 x 10⁶ nm². In calculations we used, here quite arbitrary, the surface buffer capacity for BR membrane sheets of 7.4 x 10^-8 mol m^-2 estimated from the data of Grzesiek and Dencher (1986) as described below. We calculated the proton relaxation dynamics in the presence of 100 µM of a mobile pH buffer (pK_C = 7.2) with a diffusion coefficient D_C = 2 x 10^-6 cm²/s. The effect of interfacial potential barrier was not considered in these calculations.

The system was shifted out of the equilibrium by a fast and uniformly distributed ejection of protons on the membrane surface, after which the relaxation dynamics was calculated by numerical integration of the system of diffusion equations. The amount of protons transferred at a given time was calculated from the distribution of the protonated form of mobile buffer. The dynamics of surface/bulk equilibration for the cylindrical membrane sheet and for the spherical vesicle of the same area are shown in Fig. 1 by squares and circles, respectively. The rate of equilibration did not depend on the quantity of ejected protons. The dynamics of proton transfer in the flat sheet was somewhat faster during the first few microseconds after the ejection, but the general kinetic patterns became very similar already after 10 µs. The acceleration of proton transfer in the case of flat membrane sheet as compared to the spherical vesicle could be explained by a more dispersed volume distribution of fixed buffer in the former case. The calculated difference in the proton relaxation rate constant (by a factor of 1.5) was minor and of the same order as the scatter of data as measured by pH dyes (see, e.g., Heberle (1991)). Because of this reason, we used the spherical model throughout our further calculations as a more handy one.

View larger version (15K): [in this window] [in a new window]   FIGURE 1  Calculated time course of surface/bulk proton equilibration in flat cylindrical membrane sheets () and spherical vesicles () of the same surface area. The radius of sheets and vesicles was 500 and 354 nm, respectively; the surface capacity of fixed buffer was 7.4 x 10-8 mol m-2; the concentration of mobile buffer (pK = 7.2) was 100 µM; the diffusion coefficient of mobile buffer was 2 x 10-6 cm2 s-1, pH 7.2. The dashed line represents the monoexponential kinetics with the time constant calculated for the same parameters as Eq. 6.

Dependence of the proton relaxation time on the vesicle size
Fig. 2 shows the dependence of the relaxation time on the concentration of mobile pH buffer as calculated for vesicles of various size (their radii are indicated at the plot; the diffusion coefficient of H₃O⁺/OH^- ions and of the mobile buffer were assumed to be 10^-4 cm² s^-1 and 2 x 10^-6 cm² s^-1, respectively; the potential barrier was assumed to be 60 meV both for H₃O⁺/OH^- and for the mobile pH buffer). The plot in Fig. 2 shows that the proton relaxation time depends linearly on the radius of vesicles at concentrations of mobile buffer below 10^-4 M, in agreement with the asymptotically derived Eq. 6. At high buffer concentrations (>10^-3 M) the relaxation time becomes independent of the radius because the depletion layer is then thinner than the radius of the vesicles.

View larger version (20K): [in this window] [in a new window]   FIGURE 2  Dependence of proton relaxation time on the concentration of added mobile pH buffer as calculated for vesicles of various size. The radii in nm are indicated at the left of the curves; the diffusion coefficients of H+/OH- ions and of the mobile buffer were 10-4 cm2 s-1 and 2 x 10-6 cm2 s-1, respectively; the potential barrier was 60 meV, both for the H+/OH- ions and for the mobile pH buffer.

A qualitatively similar behavior was observed also for the proton release by flat BR membranes and for the proton binding by photosynthetic reaction centers of Rb. sphaeroides. In both cases, the rate of proton relaxation was faster in preparations of the detergent-solubilized enzymes as compared with membrane preparations (see Table 1 for time constants and references). One has to take into account, however, that in these cases the transition to the detergent-solubilized preparation was likely to be coupled with the change in the surface buffering capacity, which can be hardly quantified.

Proton relaxation in chromatophores from purple bacteria
As shown in our previous work (Cherepanov et al., 2003), the height of the potential barrier in the interfacial layer with the low dielectric permittivity is determined largely by the electric charge and the effective radius of penetrating ions. The macroscopic approach is, however, rather imprecise in the treatment of molecular interactions at very short distances, so the effective radius of ions in the Born theory can significantly differ from the apparent geometrical radius calculated by the van der Waals volume of the molecule. Especially difficult is the case of H₃O⁺ and OH^- ions because of strong hydrogen bonding in the first solvation layer of these species. Because of this uncertainty, we estimated the height of the potential barrier for H₃O⁺ and OH^- ions by using our own experimental data on proton equilibration in preparations of chromatophore vesicles from Rb. sphaeroides and Rb. capsulatus (Gopta et al., 1999).

Chromatophores are sealed membrane vesicles of a radius of 15–30 nm. They are obtained from native invaginations of the plasma membrane after the disruption of bacterial cell. Excitation of chromatophores by a flash of light causes a charge separation in the photosynthetic reaction center followed by the reduction of the secondary quinone acceptor Q_B (see Okamura et al. (2000) for a review of the RC operation). The reduction of Q_B causes a proton transfer from the protein surface to the buried binding site at <100 µs. pH indicators in the bulk respond to this event only with delay; depending on the pH, the response time varied between 450 µs and 1 ms at 6.2 < pH < 8.1 in the presence of 300 mM KCl (see Gopta et al. (1999) for further details). At pH 6.2, the response time of the pH indicator bromocresol purple (BCP) was independent of its concentration up to 100 µM. The addition of the mobile pH buffer MES gradually diminished the extent of the BCP response. From the dependence of the extent of BCP response on the concentration of MES the buffer capacity of washed chromatophores at pH 6.2 could be estimated as 12 µM (Gopta et al., 1999), that corresponds to 100 buffer groups with pK 6.2 per one RC. This was an upper estimate for two reasons. First, 10–20 µM of residual HEPES (pK = 7.5), which was used as pH buffer during the chromatophore preparation, was expected to remain even after a double washing of chromatophores in a buffer-free medium and to contribute, together with the fixed surface buffers, to the overall buffer capacity of the sample. Second, as long as the suspension medium was not degassed, a certain pH-buffering contribution from the dissolved carbon dioxide could be expected. Because the hydrolytic reaction of carbon dioxide is slow (the time constant is about 0.3 s^-1 (Drachev et al., 1984)), the latter contribution should be rather small on the timescale of pulsed measurements (1 ms).

The chromatophores from Rb. sphaeroides with mean radius of 18 nm were shown to carry 11 RC per vesicle, on average (with an error of ±30%); see Packham et al. (1978). Taking into account the uncertainties in the number of RC per vesicle and in the contribution from residual pH buffers, the surface buffer capacity of the external side of the membrane could be estimated to lie in the range between 1.2 x 10^-7 mol m^-2 and 2.8 x 10^-7 mol m^-2. We calculated the time of proton equilibration for different potential barriers (varied in the range of 0–240 meV). The respective curves are plotted in Fig. 3. The open circles correspond to the lower estimate of the surface capacity (1.2 x 10^-7 mol m^-2), and the solid circles correspond to the upper one (2.8 x 10^-7 mol m^-2). The experimentally determined proton relaxation time range of 450 ± 50 µs is shown by two dashed horizontal lines. The intersection of the theoretical and experimental curves gives an estimate for the potential barrier of 65–125 meV (shown by vertical lines).

View larger version (16K): [in this window] [in a new window]   FIGURE 3  Estimation of the interfacial potential barrier for H+/OH- ions from the rate of BCP protonation in chromatophores of Rb. sphaeroides. The dependence of the proton relaxation time on the barrier height was calculated as described in the text using the surface buffer capacity of 1.2 x 10-7 mol m-2 () and 2.8 x 10-7 mol m-2 (•) and taking the thickness of the interfacial layer of 2 nm and the diffusion coefficient of H+/OH- ions of 10-4 cm2s-1. The chromatophore radius of 18 nm was assumed at calculations. The experimentally determined time constant of proton relaxation in chromatophores from Rb. sphaeroides (450 ± 50 µs) is shown by dashed horizontal lines. Vertical lines mark the interval for the estimated potential barrier of 65–125 meV consistent with the experimental data.

The "threshold" concentration depends on the ratio between the diffusional mobility of the buffer and the one of H⁺/OH^- ions in the interfacial water layer. The mobility is determined in turn by the diffusion coefficient and the height of the potential barrier for the respective mobile species. Because the diffusion coefficients of mobile pH buffers/dyes in water vary in a rather narrow range being 10–50 times smaller than the diffusion coefficient of the proton (Baur and Wightman, 1991; Culbertson et al., 2002), the height of the potential barrier can be inferred from the threshold concentration. It is noteworthy that the "threshold" concentration is essentially independent of the surface buffer capacity and of the size of the vesicles. Moreover, it is even possible to compare data obtained at different experimental conditions after their normalization (i.e., multiplication of the rate by a constant factor).

The proton relaxation has been extensively studied with BR membrane sheets (reviewed by Heberle (2000)). The circles in Fig. 4, A and B, show the time of proton relaxation as measured at different concentrations of pH indicator pyranine, which was the only mobile proton carrier in the experimental system (the solid circles show the data of Porschke (2002) whereas the open circles the data of Heberle (1991)); the data sets were shifted along the y-axis to match the theoretical curves). The rate of proton relaxation was almost independent of the concentration of pyranine, apparently because of poor ability of the highly charged pyranine anions (total charge -4) to penetrate the interfacial layer. Fig. 4 shows sets of theoretical curves, which were calculated for two different heights of the potential barrier for H⁺ ions, and for different heights of the potential barrier for mobile buffer, Because the difference between proton relaxation dynamics as calculated for flat sheets and spherical vesicles was minor (see Fig. 1), and because the computation for the flat sheets was more involved, especially in the presence of a potential barrier, the curves were calculated for spherical vesicles of 100 nm radius and a surface buffer capacity of 7.4 x 10^-8 mol m^-2 (pH 7.2). The value of the latter was estimated as follows: the total buffer capacity of the suspension of purple membranes, which contained 10 µM bacteriorhodopsin and 50 µM pyranine, can be estimated as 37 µM at pH 7 from data of Grzesiek and Dencher (1986). Subtracting the buffer capacity of pyranine at given pH (27 µM), we obtained a total surface buffer capacity for both sides of membrane of 1.0 mol/mol of BR. Taking the surface area of 11 nm² per monomer of BR (Essen et al., 1998) and assuming that both sides of membrane have similar capacity, we got the surface buffer capacity of 7.4 x 10^-8 mol m^-2. This is the upper estimate because the membrane suspension might contain some residual extrinsic buffers besides pyranine (see above).

View larger version (22K): [in this window] [in a new window]   FIGURE 4  Dependence of proton relaxation time on the concentration of added mobile buffer. Each set of seven theoretical curves was calculated for various heights of potential barrier for mobile buffer, (the values = 0, 60, 120, 150, 180, 240, and 360 meV correspond to the curves plotted sequentially from the left to the right) at a given value of the potential barrier for H+ ions. All curves were calculated for vesicles of 100 nm radius and for the surface buffer capacity of 7.4 x 10-8 mol m-2, pH 7.2. The time constants of experimentally measured pyranine protonation by the BR-ejected protons are shown by circles (solid circles represent the data from Porschke (2002) and open circles correspond to data from Heberle (1991)). (A) . The response time of p-nitrophenol (Drachev et al., 1984) is shown by stars, the acceleration of proton relaxation (as measured by pyranine) by added MES (Porschke, 2002) and phosphate (Grzesiek and Dencher, 1986) is shown by squares and triangles, respectively. In the case of MES, the effective buffer capacity at the ambient pH of 7.45 was recalculated by using the buffer pK value of 6.2. The diffusion coefficient of H3O+/OH- ions and of the mobile buffer were assumed to be 10-4 cm2 s-1 and 2 x 10-6 cm2 s-1, respectively. The response time of indicators in the bulk was recalculated from the experimental kinetics by accounting for the time needed by BR to eject a proton under given experimental conditions.

The set of curves in Fig. 4 A demonstrates how the increasing potential barrier for mobile buffer slows down the proton equilibration (the values = 0, 60, 120, 150, 180, 240, and 360 meV correspond to the curves plotted sequentially from the left to the right, respectively). Qualitatively, the higher is the potential barrier the weaker is the dependence on the buffer concentration. It is remarkable, however, that the impact of the barrier is relatively small and has a tendency to saturate: proton relaxation at is almost as slow as at 360 meV. The underlying mechanism can be described as follows: the high potential barrier suppresses the direct interaction of the mobile buffer with the surface, so that the proton flux in the interfacial layer of 1 nm thickness is mediated mainly by the diffusion of H⁺ ions proper. Therefore the further increase in the barrier height for buffer, starting from a certain value, has only a minor effect on the H⁺ flux across the interfacial layer. Beyond the interfacial layer, however, the mobile buffer, the concentration of which greatly exceeds the concentration of H⁺ ions, mediates the proton flux accounting for the residual weak dependence of proton relaxation rate on the concentration of the buffer. The experimental dependence for pyranine is shown in Fig. 4 A by circles. It is essentially flatter than the theoretical curve calculated with the maximal barrier .

Apparently, the negligible dependence of proton relaxation on concentration of pyranine cannot be explained by the effect of potential barrier for pyranine alone and indicates the presence of a potential barrier for H⁺/OH^- ions as well. In such case, the total proton flux would be limited by the H⁺ diffusion through the interfacial layer and not by the diffusion in the bulk phase, where it can be accelerated by addition of pyranine. We calculated the analogous set of curves with the potential barrier (not documented). The barrier made the dependence on the concentration of mobile buffer less steep, but this was not sufficient to explain the negligible dependence on the concentration of pyranine. Only when the barrier for H⁺/OH^- ions was increased up to 120 meV, the slowest theoretical curve calculated for the barrier with became consistent with the experimental data (see Fig. 4 B). It is noteworthy that the calculated time of pyranine protonation of 800 µs in Fig. 4 B matches the experimentally measured one (700–1000 µs depending on conditions (Grzesiek and Dencher, 1986; Heberle, 1991; Porschke, 2002)). Thus, the quantitative consideration of proton relaxation in the preparations of BR membranes at different concentrations of pyranine provided the estimates of the barrier height for H⁺/OH^- ions of 120 meV and for pyranine of 360 meV.

Several sets of experimental data for other pH buffers/mediators as obtained with the BR membranes are superimposed on the theoretical curves in Fig. 4 B. Because the experimental data were obtained at slightly varying conditions, each data set was shifted in the vertical direction to the position where its slope was equal to the slope of the respective theoretical curve. The stars represent the time of proton equilibration at different concentrations of pH indicator p-nitrophenol as measured by Drachev and co-workers (1984). Contrary to the pyranine case, the proton relaxation was accelerated already when the concentration of p-nitrophenol was increased from 25 µM to 50 µM. Two more data sets, which describe the acceleration of pyranine response in the bulk by added pH buffers, are plotted in Fig. 4 B: the triangles show the dependence of the pyranine response time on added phosphate (Grzesiek and Dencher, 1986) and the squares document the acceleration by added MES (Porschke, 2002). Because pyranine apparently could not get across the interfacial layer, these data allowed to estimate the height of the interfacial barrier for phosphate and MES, respectively. The height of the potential barrier was acquired from the shape of the curves in Fig. 4 B by assuming the same diffusion coefficient of 2 x 10^-6 cm² s^-1 for all mobile buffers. This procedure yielded the figure of 90 meV for p-nitrophenol and MES, 150 meV for phosphate, and 360 meV for pyranine, respectively.

We made analogous calculations for the acceleration of proton relaxation by mobile buffers in chromatophores from Rb. sphaeroides (shown in Fig. 5). The response times of BCP as function of its concentration (Gopta et al., 1999) are plotted in Fig. 5 by diamonds. One can see that at <100 µM the response of BCP was almost independent of its concentration. The response could be, however, accelerated by the addition of MES. Correspondingly, the open squares show the dependence of the proton relaxation time on the concentration of MES as revealed from the kinetics of 20 µM BCP protonation (data from Gopta et al. (1999)). The comparison with the theoretical curves (the respective barrier heights in meV are indicated near the curves) yielded the potential barrier height of 120 meV for MES and 180 meV for BCP, respectively. The estimate for MES is in agreement with the estimate of 90 meV as obtained above for the BR membranes. The figure of 180 meV for BCP (the deprotonated form of which has the electric charge of -2) is consistent with the barrier of 150 meV as obtained above for the similarly charged phosphate.

View larger version (19K): [in this window] [in a new window]   FIGURE 5  Acceleration of the proton relaxation in chromatophores from Rb. sphaeroides by mobile buffers. The response time of BCP is shown by circles and the acceleration of the 20-µM BCP response by MES is shown by squares (the experimental data were taken from Gopta et al. (1999) and corrected for the time of proton transfer from the surface to QB of 100 µs); the set of seven curves was calculated for the various heights of the potential barrier for mobile buffer = 0, 60, 120, 150, 180, 240, and 360 meV correspond to the curves plotted sequentially from the left to the right) using the potential barrier for H+/OH- ions .

View larger version (9K): [in this window] [in a new window]   FIGURE 6  The height of interfacial barrier for five anionic pH buffers/indicators as function of their electric net charge in the deprotonated state. The barrier height was determined from the ability of buffers to accelerate proton equilibration at the membrane surface as described in the text. The symbols match those used in Figs. 4 B and 5.

The solvent accessible volume of p-nitrophenol (calculated by taking the van der Waals volume of molecule plus 0.14-nm-thick solvating shell) is 0.4 nm³. Approximating the ellipsoidal molecule by a sphere of the same volume, one gets the effective radius of 0.46 nm. As long as the Born self-energy contribution to the potential barrier is expected to be proportional to the inverse radius of penetrating ions, the simple scaling of the barrier height calculated earlier for a sphere of 0.25 nm radius gives the estimate of 80–110 meV for the barrier height in the case of p-nitrophenol (method b), in agreement with the value of 90 meV as obtained by the data fit (method a). The solvent accessible volume of the sulfate group in MES, calculated in the same way, is 0.3 nm³, so the barrier height as estimated by the primitive model comes in the range of 90–120 meV, again in agreement with the found value of 90–120 meV. It is noteworthy that a similar barrier height of 120 meV was revealed here for the singly charged H⁺/OH^- ions.

Coming to poly-charged species one had to take into account the actual shape of molecules, which can strongly deviate from the spherical form used in the previous calculations. It was especially important for the cases of BCP and pyranine. Indeed, the molecule of BCP has a complicated shape where the negatively charged sulfate and hydroxy groups are separated by 0.8 nm from each other. The solvation energy of such distinct groups is roughly equal to the sum of two terms corresponding to the independent singly charged moieties. The respective estimate by the Born approach (method b) yielded the figure of 240–320 meV, somewhat exceeding the value of 180 meV as obtained from the concentration dependence (method a). Independent contributions are also expected for the case of pyranine anion carrying three sulfate and one hydroxy group. These charged groups are separated by 0.5–0.8 nm and can be considered as rather independent, so the height of potential barrier calculated by the Born theory is 360–480 meV, that is in agreement with the above estimate of 360 meV. Parted charges, however, cannot be invoked in the case of phosphate ion. It is a rather compact, almost spherical molecule having a solvent accessible volume of 0.28 nm³. The Born approximation (method b) gave an estimate of 360–480 meV, exceeding more than twice the value of 150 meV, which was obtained by method a. The deviation might be due to several reasons. One possibility is that phosphate might adsorb at the membrane surface. Actually, some of the mobile buffers, as tested by Porschke (2002), showed an abnormally high ability to accelerate the proton equilibration between the BR surface and the bulk. Particularly, the data on boric acid and imidazole, when treated by the approach described above, could be described only under an assumption that their mobility in the interfacial water layer exceeded their mobility in bulk phase. Most likely these data indicate a nonspecific adsorption of these species in the interfacial layer. In the case of imidazole, its adsorption to thylakoid membranes and an unusually high ability to accelerate the proton relaxation has been amply documented (Junge et al., 1978; Hong and Junge, 1983; Polle and Junge, 1989; Haumann and Junge, 1994a). Correspondingly, the phosphate adsorption at the surface would decrease the height of an apparent potential barrier. Another reason for the discrepancy might be the higher mobility of small phosphate anions as compared to other pH buffers/dyes under consideration. Because the same diffusion coefficient of 2 x 10^-6 cm² s^-1 was taken for all mobile buffers on analyzing the data in Fig. 4 B, the barrier height for phosphate could be underestimated. One has also to take into account the general inaccuracy of the Poisson-Boltzmann approach when applied to inhomogeneous interfacial systems. For example, the activity coefficient of K⁺ ions is 0.76 when calculated by the Debye-Hückel theory for a homogeneous solution with the ionic strength of 0.1 M. However, in the interfacial water layer with the dielectric constant of 8, the activity coefficient of K⁺ would be as small as 0.003. The low coefficient of activity is just another notion of the low affinity of interfacial water for ions (in terms of chemical potential). It is known that the primitive models work poorly in solutions with low coefficient of activity because of strong intermolecular correlations (Varela et al., 2003). Moreover, the free energy of a charge near the interface is not simply proportional to the electrostatic potential (as it is assumed in the primitive self-consistent Poisson-Boltzman and Debye-Hückel theories) but includes also other contributions, particularly the change of self-energy in the low-dielectric medium, and various nonelectrostatic interactions (like hydrophobic and hydrogen bonding forces). It is noteworthy that the strong molecular organization of interfacial water has been established by direct measurements of forces between mica surfaces, which revealed up to 10 strong oscillations with a period of 0.25 nm propagating up to 3 nm from the interface (Israelachvili and Pashley, 1983). Such oscillating forces cannot be described in the framework of the primitive solvent model and require a more sophisticated microscopic consideration. Unless an adequate description of interfacial phenomena is developed, it seems reasonable to consider the interfacial potential barrier not as a rigorously defined physical term but rather as a phenomenological parameter, the magnitude of which could be inferred from the analysis of experimental data.

Summarizing, we conclude that the apparent height of the potential barrier, which was estimated from the ability of mobile pH buffers to accelerate the proton equilibrium at the membrane/water interface, revealed an almost linear correlation with the maximal electric charge characterizing the buffer at a given pH. The observed dependence might be rationalized in terms of the Poisson-Boltzmann theory under the assumption of the low dielectric permittivity of interfacial water.

Relation to the pH-jump experiments
We showed above that a wealth of data on proton relaxation at the membrane/water interface (see review by Heberle (2000) and the above cited references) could be understood in terms of an energy barrier arising in the surface water layer with altered dielectric properties. Despite numerous evidence indicating the presence of such a barrier (see citations above), the concept of anisotropic proton relaxation at the membrane surface has remained controversial, mainly because of the counter-argumentation based on pH-jump experiments (reviewed by Gutman and Nachliel (1995) and Brandsburg-Zabary et al. (2000)). These authors used short laser pulses to trigger photo-deprotonation of pyranine in the absence and in the presence of membrane preparations. In pure water, the photo-deprotonation of pyranine (at < 1 ns) was followed by its reprotonation at few µs. In the presence of submitochondrial particles, however, the reprotonation became essentially biphasic: besides the major fast component, a new slower component with of 30 µs appeared (Gutman et al., 1993). The authors explained the retardation of pyranine reprotonation by the transient interaction of the photo-ejected protons with the membrane surface. Based on these and similar observations it has been concluded that the diffusion of protons between the membrane surface and the bulk occurs at tens of microseconds and that such a fast proton transfer excludes functionally relevant kinetic barriers at the interface (Gutman et al., 1993; Kotlyar et al., 1994; Gutman and Nachliel, 1995).

Analogous results as obtained with BR membranes were rationalized in a similar way (Nachliel et al., 1996; Checover et al., 1997). In the latter case, however, it has remained unexplained how it could happen that the protons, ejected by pyranine in the bulk phase, could reach the BR membrane and return back to the bulk phase at 20–30 µs (making a full roundtrip), whereas the protons, which were ejected to the membrane surface by BR proper, needed as long as 1 ms for their one way trip to pyranine in the bulk (this behavior has been reported by several research groups (Heberle and Dencher, 1992; Drachev et al., 1992; Heberle et al., 1994; Alexiev et al., 1995; Dioumaev et al., 1998; Porschke, 2002)). Further on, the collision of protons ejected by pyranine in the bulk phase with the surface of membrane particle could occur only if pyranine resides in the surrounding water layer not farther than 20 nm from the surface (the average distance between pyranine molecules in solution). One can easily calculate, taking the actual size of membrane particles and their usual concentration of a few nanomoles, that the probability of such reaction is <2 x 10^-3. Correspondingly, the extent of the slow kinetic component of pyranine reprotonation is expected to be smaller than the extent of the fast component by three orders of magnitude, and not by a factor of 10, as it has been reported.

Fernandez and Politi (1997) asked whether the pyranine molecules, the reprotonation of which proceeded at 10–30 µs in such pH-jump experiments, were indeed dissolved in the bulk and not adsorbed at the membrane surface. They noted that if the negatively charged pyranine binds both to liposomes, even the negatively charged ones (Kano and Fendler, 1978; Clement and Gould, 1981), and to proteins (Sedgwick and Bragg, 1990; Gutman, 1986; Yam et al., 1991; Gutman et al., 1992), it might bind to the protein-containing membranes as well. And indeed, Ziegler and Penefsky (1993) have convincingly demonstrated that submitochondrial particles, similar to those used by Gutman and co-workers, retained significant amounts of pyranine at their outer surface even after they were passed through a Sephadex column. The presence of a membrane-absorbed/bound fraction of pyranine would affect the kinetics of its protolytic reactions in a quite predictable way. The pyranine in the water phase would be reprotonated at a few µs. The protons released by the fraction of pyranine adsorbed at the membrane surface would be transiently retained by surface buffers. In this fraction the reprotonation of pyranine would proceed in tens of microseconds. The kinetic trace of pyranine reprotonation would contain thereby two components with the characteristic time of few microseconds (in the bulk) and tens of microseconds (at the surface), as it was actually observed (Gutman et al., 1993; Kotlyar et al., 1994; Gutman and Nachliel, 1995; Nachliel et al., 1996; Checover et al., 1997). The relative extent of the slower component is expected to be roughly proportional to the relative amount of pyranine adsorbed at the membrane surface. Because the relaxation in both fractions completes at tens of microseconds, the proton transfer between the surface and the bulk, which has a characteristic time of 1 ms (Heberle et al., 1994, 2000), could not be revealed from the kinetics of pyranine reprotonation.

If some pyranine could adsorb at the BR surface, it was expected to be protonated by the BR-ejected protons faster than the major fraction in the bulk. In Appendix B we demonstrate that the published kinetic traces of pyranine protonation by the BR-ejected protons indeed contain a minor fast component with a rise time of 300 µs matching the response time of fluorescein, which was covalently bound to BR. (One has to keep in mind that the proton ejection by BR proper takes 100 µs as compared to the proton ejection by photoexcited pyranine, which proceeds at <1 ns). The relative extent of the fast component is 10–20%, in good correspondence with the relative amplitude of the slower component in the pH-jump experiments.

Thus, the striking controversy between the time constants of pyranine protonation by the BR-ejected protons (1 ms) and of its reprotonation in the pH-jump experiments (tens of microseconds for the slower component) could be resolved by attributing the latter reaction to the surface adsorbed fraction of pyranine. Based on this consideration, we suggest that the data obtained in the pH-jump experiments do not contain information about proton exchange between the membrane surface and the bulk water phase and therefore cannot be considered as evidence against the slow rate of the proton equilibration between the membrane surface and the bulk water phase.

	OUTLOOK AND CONCLUSIONS

TOP ABSTRACT INTRODUCTION RESULTS AND DISCUSSION OUTLOOK AND CONCLUSIONS APPENDIX A APPENDIX B ACKNOWLEDGEMENTS REFERENCES

 
The analysis presented in this work complements two previous reports. In the first one we have studied the repletion from the bulk of proton vacancies (holes) formed at the surface of chromatophore vesicles of Rb. sphaeroides and Rb. capsulatus in response to a light flash. We found that proton donation by bimolecular collision with soluble pH buffers was impeded at their concentration below 100 µM. The high activation energy of the proton relaxation (30–50 kJ at neutral pH) provided evidence for proton donation by neutral water (Gopta et al., 1999).

The possible nature of the potential barrier, which impeded the interaction of mobile pH buffers with the surface, was elucidated in the next article (Cherepanov et al., 2003), where we have shown that potential barrier could result from the low dielectric permittivity of surface water, a phenomenon well known in electrochemistry (Bockris and Reddy, 1977) and recently corroborated by atomic force microscopy at the mica surface (Teschke et al., 2001).

It has remained an open question whether the properties of water at the mica surface apply to biological membranes. Elucidation of this question was the main goal of the present work. We attempted to "extract" the properties of the interfacial barrier by a comparative analysis of data obtained with various biological membranes and various pH buffers/indicators. We obtained a consistent picture where the ability of various mobile buffers to accelerate the proton equilibration between the surface and the bulk phase was correlated with their electric charge, which determined the height of the interfacial energy barrier as felt by these buffers.

Modeling showed that the rate of proton exchange between the surface of a membrane particle and the bulk is determined by the pH-buffering capacity of the surface, the size of the particle, and the height of the potential barrier. The importance of the surface buffering capacity for explaining the proton relaxation dynamics is well recognized (Junge and Polle, 1986; Junge and McLaughlin, 1987; Jones and Jackson, 1989). The dependence on the geometrical size of membrane particles and on the height of the interfacial potential barrier was revealed for the first time. It is noteworthy that the surface buffering capacity does not matter at steady state (Junge and Polle, 1986), so that only the height of the potential barrier and the size of membrane particles determine the surface proton activity. Because the potential barrier for proton proper is only on the order of 120 meV, the dependence on the size is especially relevant for understanding bioenergetics of bacteria, particularly of the alkaliphilic ones. The steric effects are expected to be minimal for the spherical particles, which we have considered on modeling; for membraneous structures with negative curvature (e.g., invaginati