Low dielectric permittivity of water at the membrane interface: effect on the energy coupling mechanism in biological membranes

Abstract

Protonmotive force (the transmembrane difference in electrochemical potential of protons, ) drives ATP synthesis in bacteria, mitochondria, and chloroplasts. It has remained unsettled whether the entropic (chemical) component of relates to the difference in the proton activity between two bulk water phases (deltapH(B)) or between two membrane surfaces (deltapH(S)). To scrutinize whether deltapH(S) can deviate from deltapH(B), we modeled the behavior of protons at the membrane/water interface. We made use of the surprisingly low dielectric permittivity of interfacial water as determined by O. Teschke, G. Ceotto, and E. F. de Souza (O. Teschke, G. Ceotto, and E. F. de Sousa, 2001, PHYS: Rev. E. 64:011605). Electrostatic calculations revealed a potential barrier in the water phase some 0.5-1 nm away from the membrane surface. The barrier was higher for monovalent anions moving toward the surface (0.2-0.3 eV) than for monovalent cations (0.1-0.15 eV). By solving the Smoluchowski equation for protons spreading away from proton "pumps" at the surface, we found that the barrier could cause an elevation of the proton concentration at the interface. Taking typical values for the density of proton pumps and for their turnover rate, we calculated that a potential barrier of 0.12 eV yielded a steady-state pH(S) of approximately 6.0; the value of pH(S) was independent of pH in the bulk water phase under neutral and alkaline conditions. These results provide a rationale to solve the long-lasting problem of the seemingly insufficient protonmotive force in mesophilic and alkaliphilic bacteria.

FIGURE 1

Dielectric characteristics of the membrane/water interface. (A) The distance dependence of the dielectric permittivity at the mica/water interface. The profile was calculated based on data from Teschke et al. (2001) for an ionic strength of 0.1 M (λ = 1 nm) as described in the text. (B) The potential energy of a cation (solid line) and of an anion (dashed line) and the respective Born solvation energy (dotted line) at the charged membrane/water interface. The calculations by the Poisson-Boltzmann equation were performed for the ionic strength of 0.1 M using the effective radius of probe charges of 0.25 nm. The negative and the positive membrane charges were treated as described in the text.

FIGURE 2

Steady-state pH-profiles at the surface of a proton-ejecting membrane. (A) Proton distribution along a planar membrane containing only one proton pump. The cylindrical axis z is perpendicular to the membrane plane, and the axis r is directed along the membrane. The protons ejected by the pump are spread initially along the membrane surface and then escape through the interfacial barrier (no proton sinks in the membrane were considered). The turnover rate of the pump was 5 × 10² s⁻¹, the height of the potential barrier was 0.12 eV, the surface potential was −0.06 V, the bulk diffusion coefficient of protons was 10⁻⁴ cm²/s, and the other details of the model are described in the text. (B) Steady-state pH profile at the surface of sealed membrane vesicles with the radius of 1 μm and the surface pump density of 2 × 10¹¹ cm⁻². The potential barrier as calculated for the ionic strength of 0.1 M in Fig. 1 B (solid line) was used on modeling. The dashed line shows the proton concentration as calculated without potential barrier.

FIGURE 3

Schematic presentation of the topology of different energy-transducing membrane structures. The p-side of coupling membrane is marked by darker color. (Top) A bacterial cell and two types of subbacterial particles. (Bottom) A schematic presentation of a coupling membrane with protons moving along the p-surface from pumps to the ATP synthase.