Cytochrome c oxidase is a transmembrane proton pump that builds an electrochemical gradient using chemical energy from the reduction of O 2 . Ionization states of all residues were calculated with Multi-Conformation Continuum Electrostatics (MCCE) in seven anaerobic oxidase redox states ranging from fully oxidized to fully reduced. One long-standing problem is how proton uptake is coupled to the reduction of the active site binuclear center (BNC). The BNC has two cofactors: heme a 3 and Cu B . If the protein needs to maintain electroneutrality, then 2 protons will be bound when the BNC is reduced by 2 electrons in the reductive half of the reaction cycle. The effective pK a s of ionizable residues around the BNC are evaluated in Rhodobacter sphaeroides cytochrome c oxidase. At pH 7, only a hydroxide coordinated to Cu B shifts its pK a from below 7 to above 7 and so picks up a proton when heme a 3 and Cu B are reduced. Glu I-286, Tyr I-288, His I-334, and a second hydroxide on heme a 3 all have pK a s above 7 in all redox states, although they have only 1.6-3.5 ∆pK units energy cost for deprotonation. Thus, at equilibrium, they are protonated and cannot serve as proton acceptors. The propionic acids near the BNC are deprotonated with pK a s well below 7. They are well stabilized in their anionic state and do not bind a proton upon BNC reduction. This suggests that electroneutrality in the BNC is not maintained during the anaerobic reduction. Proton uptake on reduction of Cu A , heme a, heme a 3 , and Cu B shows ≈2.5 protons bound per 4 electrons, in agreement with prior experiments. One proton is bound by a hydroxyl group in the BNC and the rest to groups far from the BNC. The electrochemical midpoint potential (E m ) of heme a is calculated in the fully oxidized protein and with 1 or 2 electrons in the BNC. The E m of heme a shifts down when the BNC is reduced, which agrees with prior experiments. If the BNC reduction is electroneutral, then the heme a E m is independent of the BNC redox state.Heme-copper oxidases are the terminal electron acceptors in anaerobic organisms. These transmembrane proteins reduce dioxygen and convert the released chemical energy into an electrochemical gradient, across the eukaryotic mitochondrial membrane or the bacterial cell membrane (1-4). Cytochrome c oxidases are the most prevalent hemecopper oxidases. In this protein 4 electrons, provided by 4 cytochromes c, are used to reduce dioxygen to water. The 4 protons needed to make water are taken from the negative cytoplasmic side of the membrane, adding to the electrochemical gradient. Four additional protons are pumped across the membrane (5). Thus, each dioxygen molecule reduced by cytochrome c oxidase is coupled to the transfer of 8 charges across the membrane.The first step of electron transfer is from cytochrome c to Cu A , a dicopper center in subunit II which extends beyond the membrane on the proton release side of the protein (Figure 1). After receiving the electron, Cu A reduces the 6-coordinate, low-spin, bis-Hi...

In this paper a two-state, two-component, Ising-type model is used to simulate the lateral distribution of the components and gel/fluid state acyl chains in dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers. The same model has been successful in calculating the excess heat capacity curves, the fluorescence recovery after photobleaching (FRAP) threshold temperatures, the most frequent center-to-center distances between DSPC clusters, and the fractal dimensions of gel clusters (Sugar, I. P., T. E. Thompson, and R. L. Biltonen, 1999. Biophys. J. 76:2099-2110). Depending on the temperature and mole fraction the population of the cluster size is either homogeneous or inhomogeneous. In the inhomogeneous population the size of the largest cluster scales with the size of the system, while the rest of the clusters remain small with increasing system size. In a homogeneous population, however, every cluster remains small with increasing system size. For both compositional and fluid/gel state clusters, threshold temperatures-the so-called percolation threshold temperatures-are determined where change in the type of the population takes place. At a given mole fraction, the number of percolation threshold temperatures can be 0, 1, 2, or 3. By plotting these percolation threshold temperatures on the temperature/mole fraction plane, the diagrams of component and state separation of DMPC/DSPC bilayers are constructed. In agreement with the small-angle neutron scattering measurements, the component separation diagram shows nonrandom lateral distribution of the components not only in the gel-fluid mixed phase region, but also in the pure gel and pure fluid regions. A combined diagram of component and state separation is constructed to characterize the lateral distribution of lipid components and gel/fluid state acyl chains in DMPC/DSPC mixtures. While theoretical phase diagrams of two component mixtures can be constructed only in the case of first-order transitions, state and component separation diagrams can be constructed whether or not the system is involved in first-order transition. The effects of interchain interactions on the component and state separation diagrams are demonstrated on three different models. The influences of state and component separation on the in-plane and off-plane membrane reactions are discussed.

In this paper the geometrical properties of gel and fluid clusters of equimolar dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers are calculated by using an Ising-type model (Sugar, I. P., T. E. Thompson, and R. L. Biltonen. 1999. Biophys. J. 76:2099-2110). The model is able to predict the following properties in agreement with the respective experimental data: the excess heat capacity curves, fluorescence recovery after photobleaching (FRAP) threshold temperatures at different mixing ratios, the most frequent center-to-center distance between DSPC clusters, and the fractal dimension of gel clusters. In agreement with the neutron diffraction and fluorescence microscopy data, the simulations show that below the percolation threshold temperature of gel clusters many nanometer-size gel clusters co-exist with one large gel cluster of size comparable with the membrane surface area. With increasing temperature the calculated effective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the region of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the cluster perimeter linearly increases with the number of cluster arms at a rate of 8.2 nm/arm; 2) the average number of inner islands in a cluster increases with increasing cluster size, S, according to a power function of 0.00427 x S(1.3); 3) the following exponential function describes the average size of an inner island versus the size of the host cluster, S: 1 + 1.09(1 - e(-0.0072xS)). By means of the equations describing the average geometry of the clusters the process of the association of clusters is investigated.

Proteins and lipid components are organized into domains in many biological membranes. With different experimental techniques vastly different cluster sizes have been measured in an equimolar mixture of a DMPC/ DSPC two-component lipid bilayer: very small ones in the nanometer range and very large ones of size comparable with the size of the bilayer. In this paper the lateral distribution of gel and fluid lipid molecules in a DMPC/DSPC bilayer is simulated by using a two-state, Ising type model with the application of Monte Carlo methods. The same model has been able to predict the excess heat capacity curves, FRAP threshold temperatures, average coherence length between DSPC clusters, and the fractal dimension of gel clusters, in agreement with the respective experimental data. In this work, similarly to the experimental results, the calculated equilibrium distributions of cluster size show that, between the onset temperature of the gel-tofluid transition and the percolation threshold temperature of the gel clusters, nanometer size gel clusters coexist with a gel cluster of size comparable to the bilayer's size itself. The calculated upper bound for the size of the small clusters, 8 ( 1.5 nm is very close to the experimental estimate of 10 nm. More than one large gel clusters might be present in the case of nonequilibrium lateral distributions. By means of the calculated temperature dependence of three different cluster size averages we can get insight into the process of cluster growth.