A New Theory about Interfacial Proton Diffusion Revisited: The Commonly Accepted Laws of Electrostatics and Diffusion Prevail

Abstract

The high propensity of protons to stay at interfaces has attracted much attention over the decades. It enables long-range interfacial proton diffusion without relying on titratable residues or electrostatic attraction. As a result, various phenomena manifest themselves, ranging from spillover in material sciences to local proton circuits between proton pumps and ATP synthases in bioenergetics. In an attempt to replace all existing theoretical and experimental insight into the origin of protons' preference for interfaces, TELP, the "Transmembrane Electrostatically-Localized Protons" hypothesis, has been proposed. The TELP hypothesis envisions static H⁺ and OH^- layers on opposite sides of interfaces that are up to 75 µm thick. Yet, the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy is more than two orders of magnitude smaller and, as a result, the H⁺ and OH^- layers cannot mutually stabilize each other, rendering proton accumulation at the interface energetically unfavorable. We show that (i) the law of electroneutrality, (ii) Fick's law of diffusion, and (iii) Coulomb's law prevail. Using them does not hinder but helps to interpret previously published experimental results, and also helps us understand the high entropy release barrier enabling long-range proton diffusion along the membrane surface.

Keywords: PMF; TELP; interfacial water; proton diffusion; surface proton.

Figure 1

The surface and bulk proton concentrations differ: (A) $\Delta G^{‡}$, the activation free energy of proton surface-to-bulk release accounts for the retarded release of excess protons (i.e., protons not accounted for by an equilibrium description). Such barriers are not specific to biological membranes, as long-range diffusion has also been observed adjacent to inorganic substrates [76] and at the water–nonpolar liquid interface. $\Delta G^{‡}$ cannot be used to predict the difference between interfacial and bulk pH values since it characterizes an out-of-equilibrium state (in contrast to B). Importantly, ΔG^‡ does not permit estimating the equilibrium proton concentration difference between the membrane surface and the bulk phase. Such assessments require knowledge of ΔG. (B) At equilibrium, the higher proton concentration at the lipid membrane–water interface may be due to the negative surface potential of natural lipid membranes, as described by the Gouy–Chapman theory. The H⁺ concentration decreases exponentially with increasing distance from the surface with the Debye length, ${\lambda }_D$ [38]. Titratable residues at the interface, such as ethanolamine lipid headgroups, may provide a surface buffer for protons [77,78]. However, proton release kinetics have only a tiny effect on the migration kinetics between the proton source and sink. The purple line sketches the free energy profile of protons normal to the interface. Solid lines indicate which part of the profile was measured experimentally. The yellow line shows the corresponding equilibrium proton concentration profile. (C) Lee’s TELP hypothesis postulates that the proton concentration adjacent to the outer surface of the inner mitochondrial membrane is governed by the transmembrane potential, $\Delta \psi$. The TELP hypothesis assumes that hydroxide anions adsorb on the matrix side of the membrane. The protons in the surface layer of thickness l have no counterions and do not form a double layer—in contrast to the Gouy–Chapman theory. The TELP hypothesis does not explain why protons do not interact with hydroxides from the same side or why $\Delta \psi$ does not alter the concentration of other ions in the immediate membrane vicinity. We plot the equilibrium concentration and energy profiles for H⁺ using Lee’s estimations of interfacial pH drop [70].

Figure 2

Origin of the potential at the inner mitochondrial membrane. (A) $\Delta \psi$ is generated by proton pumps [83]. Complexes I, III, and IV transfer positively charged protons from the matrix to the intermembrane space, thereby causing charge separation. The protons then may travel between these pumps and a proton sink, e.g., uncoupling proteins or the ATP synthase, along the outer membrane surface. After being subsequently released at the N surface, interfacial proton migration may occur again, i.e., the protons may travel in the opposite direction. (B) Lee’s TELP hypothesis stipulates that proton pumping into the intermembrane space produces excess protons there and leaves excess hydroxide anions in the matrix. Mutual repulsion of the excess charges in both compartments results in their accumulation at both sides of the inner membrane, where they are supposedly stabilized by mutual attraction across the membrane. The accumulated ions represent the charges on capacitor plates giving rise to $\Delta \psi$.

Figure 3

Proton migration along the decane–water interface. (A) In an effort to find a minimalistic system that would enable interfacial proton diffusion, we injected protons at a small spot at the decane–water monolayer interface [52]. Observing the proton concentration change at a distant detection site allowed the calculation of the diffusion coefficient and the surface-to-bulk release constant. (B) Lee’s TELP hypothesis stipulates that only protons deprived of counter-charges may enter the interfacial layer and that these protons are stabilized by an equal number of OH⁻ in the opposite interfacial layer (dotted lines and letters). Yet, in our experiments, all protons have counterions (Cl⁻), and the stabilizing OH⁻ are missing—as is the second interface. The lack of a second capacitator plate renders the capacitator model inapplicable. As indicated by the arrow, the absence of $\Delta \psi$ allows all protons to leave the membrane in a barrier-free fashion. (C) In contrast to the predictions of the TELP hypothesis, we observed long-range interfacial proton migration [52]. Consequently, a significant energy barrier that prevents proton surface-to-bulk release must exist. Later experiments showed that the barrier is mainly entropic in nature [54].

Figure 4

The proton surface-to-bulk release barrier. Mounting evidence indicates that the peculiar structure of water at interfaces generates an entropic barrier (E_a,3) that constitutes the major contribution to $\Delta G^{‡}$ (∑E_a). Minor enthalpic contributions come from hydrogen bonding (E_a,1) and electrostatic interactions with charged interfacial residues (E_a,2). Accordingly, the proton surface-to-bulk release constant k_off scales with $\Delta G^{‡}$, i.e., E_a,1 + E_a,2 + E_a,3. Proton diffusion along the membrane surface is favored by the fact that the barrier E_a for moving from one water molecule at the surface to the next is much smaller than that for releasing the surface proton into the bulk phase.