Reaction space, proton diffusion between membranes

The manner in which protons diffuse is a reflection of the physical properties of the environment, the geometry of the diffusion space, and the chemical composition of the surface that defines the reaction space. The biomembrane, with heterogeneous surface composition and dielectric discontinuity normal to the surface, markedly alters the dynamics of proton transfer reactions that proceed close to its surface. Time-resolved measurements of fast, diffusion-controlled reactions of protons with chromophores and fluorophores allow us to gauge the physical, chemical, and geometric characteristics of thin water layers enclosed between phospholipid membranes. Combination of the experimental methodology and the mathematical formalism for analysis renders this procedure an accurate tool for evaluating the properties of the special environment of the water-membrane interface, where the proton-coupled energy transformation takes place. 

The reaction space pertinent to our system is depicted in Figure 4. The proton is assumed to dissociate in the aqueous layer and diffuse in a three-dimensional space until its diffusion sphere contacts both membranes. At that point the diffusion loses its three-dimensional property and assumes a cylindrical configuration that, with respect to the volume increment between two shells, is identical to a two-dimensional diffusion. The shift from a three-to a two-dimensional space has a marked effect on the diffusion dynamics In the three-dimensional space the density of a particle in a concentric shell varies as r-3, whereas in the two-dimensional space the density varies as r-2. Consequently the concentration gradient in three-dimensional space is larger and drives a better diffusion away from the center. 

Figure 4. Schematic presentation of the reaction space for proton-excited pyranine anion recombination in the thin water layer between phospholipid membranes of multilamellar vesicles. The proton release is depicted at the center of the layer and diffuses in concentric shells. When the diffusion radius exceeds the distance to the membrane (dw/2), the shape of the diffusion space deviates from spherical symmetry and approaches cylindrical symmetry. R0 is the reaction radius, R is the unscreened Debye radius of pyranine (R d = 28.3 A ). in this scheme is 30 A, and the size of the water molecules is drawn to...

The discussion so far centered on proton diffusion in an infinite space. Hence, a spherically symmetric diffusion (Smoluchowski) equation in three dimensional space has been employed in the data analysis. An inner boundary condition (at the contact distance) has been imposed to describe reaction, but no outer boundary condition. Almost all of the interesting biological applications [4] involve proton diffusion in cavities and restricted geometries. These may include the inner volume of an organelle, the water layers between membranes or pores within a membrane. 

After the primary electron acceptor, Qb, in the bacterial reaction center accepts one electron, forming Qb , it accepts a second electron from the same reaction-center chlorophyll following its absorption of a second photon. The quinone then binds two protons from the cytosol, forming the reduced quinone (QHb), which is released from the reaction center (see Figure 8-36). QHb diffuses within the bacterial membrane to the Qo site on the exoplasmic face of a cytochrome bci complex, where it releases its two protons into the periplasmic space (the space between the plasma membrane and the bacterial cell wall). This process moves protons from the cytosol to the outside of the cell, generating a proton-motive force across the plasma membrane. Simultaneously, QHb releases its two electrons, which move through the cytochrome bci complex exactly as depicted for the mito-... 

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