pK(a) Calculations suggest storage of an excess proton in a hydrogen-bonded water network in bacteriorhodopsin.

Calculations of protonation states and pK(a) values for the ionizable groups in the resting state of bacteriorhodopsin have been carried out using the recently available 1.55 A resolution X-ray crystallographic structure. The calculations are in reasonable agreement with the available experimental data for groups on or near the ion transport chain (the retinal Schiff base; Asp85, 96, 115, 212, and Arg82). In contrast to earlier studies using lower-resolution structural data, this agreement is achieved without manipulations of the crystallographically determined heavy-atom positions or ad hoc adjustments of the intrinsic pK(a) of the Schiff base. Thus, the theoretical methods used provide increased reliability as the input structural data are improved. Only minor effects on the agreement with experiment are found with respect to methodological variations, such as single versus multi-conformational treatment of hydrogen atom placements, or retaining the crystallographically determined internal water molecules versus treating them as high-dielectric cavities. The long-standing question of the identity of the group that releases a proton to the extracellular side of the membrane during the L-to-M transition of the photocycle is addressed by including as pH-titratable sites not only Glu204 and Glu194, residues near the extracellular side that have been proposed as the release group, but also an H(5)O(2)(+) molecule in a nearby cavity. The latter represents the recently proposed storage of the release proton in an hydrogen-bonded water network. In all calculations where this possibility is included, the proton is stored in the H(5)O(2)(+) rather than on either of the glutamic acids, thus establishing the plausibility on theoretical grounds of the storage of the release proton in bacteriorhodopsin in a hydrogen-bonded water network. The methods used here may also be applicable to other proteins that may store a proton in this way, such as the photosynthetic reaction center and cytochrome c oxidase.

Optimization of the electrostatic interactions between ionized groups and peptide dipoles in proteins.

The three-dimensional optimization of the electrostatic interactions between the charged amino acid residues and the peptide partial charges was studied by Monte-Carlo simulations on a set of 127 nonhomologous protein structures with known atomic coordinates. It was shown that this type of interaction is very well optimized for all proteins in the data set, which suggests that they are a valuable driving force, at least for the native side-chain conformations. Similar to the optimization of the charge-charge interactions (Spassov VZ, Karshikoff AD, Ladenstein R, 1995, Protein Sci 4:1516-1527), the optimization effect was found more pronounced for enzymes than for proteins without enzymatic function. The asymmetry in the interactions of acidic and basic groups with the peptide dipoles was analyzed and a hypothesis was proposed that the properties of peptide dipoles are a factor contributing to the natural selection of the basic amino acids in the chemical composition of proteins.

The optimization of protein-solvent interactions: thermostability and the role of hydrophobic and electrostatic interactions.

Protein-solvent interactions were analyzed using an optimization parameter based on the ratio of the solvent-accessible area in the native and the unfolded protein structure. The calculations were performed for a set of 183 nonhomologous proteins with known three-dimensional structure available in the Protein Data Bank. The dependence of the total solvent-accessible surface area on the protein molecular mass was analyzed. It was shown that there is no difference between the monomeric and oligomeric proteins with respect to the solvent-accessible area. The results also suggested that for proteins with molecular mass above some critical mass, which is about 28 kDa, a formation of domain structure or subunit aggregation into oligomers is preferred rather than a further enlargement of a single domain structure. An analysis of the optimization of both protein-solvent and charge-charge interactions was performed for 14 proteins from thermophilic organisms. The comparison of the optimization parameters calculated for proteins from thermophiles and mesophiles showed that the former are generally characterized by a high degree of optimization of the hydrophobic interactions or, in cases where the optimization of the hydrophobic interactions is not sufficiently high, by highly optimized charge-charge interactions.

Optimization of the electrostatic interactions in proteins of different functional and folding type.

The 3-dimensional optimization of the electrostatic interactions between the charged amino acid residues was studied by Monte Carlo simulations on an extended representative set of 141 protein structures with known atomic coordinates. The proteins were classified by different functional and structural criteria, and the optimization of the electrostatic interactions was analyzed. The optimization parameters were obtained by comparison of the contribution of charge-charge interactions to the free energy of the native protein structures and for a large number of randomly distributed charge constellations obtained by the Monte Carlo technique. On the basis of the results obtained, one can conclude that the charge-charge interactions are better optimized in the enzymes than in the proteins without enzymatic functions. Proteins that belong to the mixed alpha beta folding type are electrostatically better optimized than pure alpha-helical or beta-strand structures. Proteins that are stabilized by disulfide bonds show a lower degree of electrostatic optimization. The electrostatic interactions in a native protein are effectively optimized by rejection of the conformers that lead to repulsive charge-charge interactions. Particularly, the rejection of the repulsive contacts seems to be a major goal in the protein folding process. The dependence of the optimization parameters on the choice of the potential function was tested. The majority of the potential functions gave practically identical results.

Spatial optimization of electrostatic interactions between the ionized groups in globular proteins.

A model approach is suggested to estimate the degree of spatial optimization of the electrostatic interactions in protein molecules. The method is tested on a set of 44 globular proteins, representative of the available crystallographic data. The theoretical model is based on macroscopic computation of the contribution of charge-charge interactions to the electrostatic term of the free energy for the native proteins and for a big number of virtual structures with randomly distributed on protein surface charge constellations (generated by a Monte-Carlo technique). The statistical probability of occurrence of random structures with electrostatic energies lower than the energy of the native protein is suggested as a criterion for spatial optimization of the electrostatic interactions. The results support the hypothesis that the folding process optimizes the stabilizing effect of electrostatic interactions, but to very different degree for different proteins. A parallel analysis of ion pairs shows that the optimization of the electrostatic term in globular proteins has increasingly gone in the direction of rejecting the repulsive short contacts between charges of equal sign than of creating of more salt bridges (in comparison with the statistically expected number of short-range ion pairs in the simulated random structures). It is observed that the decrease in the spatial optimization of the electrostatic interactions is usually compensated for by an appearance of disulfide bridges in the covalent structure of the examined proteins.

Structural modeling and electrostatic properties of aspartate transcarbamylase from Saccharomyces cerevisiae.

In Saccharomyces cerevisiae the first two reactions of the pyrimidine pathway are catalyzed by a multifunctional protein which possesses carbamylphosphate synthetase and aspartate transcarbamylase activities. Genetic and proteolysis studies suggested that the ATCase activity is carried out by an independently folded domain. In order to provide structural information for ongoing mutagenesis studies, a model of the three-dimensional structure of this domain was generated on the basis of the known X-ray structure of the related catalytic subunit from E. coli ATCase. First, a model of the catalytic monomer was built and refined by energy minimization. In this structure, the conserved residues between the two proteins were found to constitute the hydrophobic core whereas almost all the mutated residues are located at the surface. Then, a trimeric structure was generated in order to build the active site as it lies at the interface between adjacent chains in the E. coli catalytic trimer. After docking a bisubstrate analog into the active site, the whole structure was energy minimized to regularize the interactions at the contact areas between subunits. The resulting model is very similar to that obtained for the E. coli catalytic trimer by X-ray crystallography, with a remarkable conservation of the structure of the active site and its vicinity. Most of the interdomain and intersubunit interactions that are essential for the stability of the E. coli catalytic trimer are maintained in the yeast enzyme even though there is only 42% identity between the two sequences. Free energy calculations indicate that the trimeric assembly is more stable than the monomeric form. Moreover an insertion of four amino acids is localized in a loop which, in E. coli ATCase, is at the surface of the protein. This insertion exposes hydrophobic residues to the solvent. Interestingly, such an insertion is present in all the eukaryotic ATCase genes sequences so far, suggesting that this region is interacting with another domain of the multifunctional protein.

Urea unfolding and stability of gamma-II crystallin.

The conformational stability of gamma-II crystallin at pH 7.0 was estimated by studying its urea denaturation at isothermal conditions. The conformational states were monitored by far UV-CD and fluorescence measurements. Gamma-II crystallin shows sigmoidal order-disorder transition curves by both methods. The presence of more than one intermediate was confirmed but at neutral pH. The experiment results were critically analyzed in terms of both linear extrapolation and Tanford's models. The Gibbs free energy of unfolding delta G u,H2O = -36 kcal mol-1 was obtained. This value corresponds to the high conformational stability of the protein predicted qualitatively by its crystal structure.

Theoretical model and computer simulation of excitation-contraction coupling of mammalian cardiac muscle.

A mathematical model is developed to investigate the kinetics of electrical, mechanical and molecular processes in mammalian cardiac muscle. Isometric contractions at different muscle length and frequency of stimulation in response to a rhythmically applied clamp pulse or artificial action potential are simulated. Numerical results show that concentration of Ca2+ ions, bound to Ca(2+)-specific sites on protein troponin C, could be a regulatory factor in actin-myosin interactions and subsequent production of force in Huxley's mathematical approach for the sliding mechanism. The behavior of the model is compared to that of living cardiac muscle.