Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of proteins. Continuum electrostatic methods in combination with quantum chemical and molecular mechanical methods can help to analyze even very complex biochemical systems. In this article, applications of these methods to proteins involved in photosynthesis are reviewed. After giving a short introduction to the basic concepts of the continuum electrostatic model based on the Poisson-Boltzmann equation, we describe the application of this approach to the docking of electron transfer proteins, to the comparison of isofunctional proteins, to the tuning of absorption spectra, to the analysis of the coupling of electron and proton transfer, to the analysis of the effect of membrane potentials on the energetics of membrane proteins, and to the kinetics of charge transfer reactions. Simulations as those reviewed in this article help to analyze molecular mechanisms on the basis of the structure of the protein, guide new experiments, and provide a better and deeper understanding of protein functions.     

Histidine in continuum electrostatics protonation state calculations

A modification to the standard continuum electrostatics approach to calculate protein pK(a)s, which allows for the decoupling of histidine tautomers within a two-state model, is presented. Histidine with four intrinsically coupled protonation states cannot be easily incorporated into a two-state formalism, because the interaction between the two protonatable sites of the imidazole ring is not purely electrostatic. The presented treatment, based on a single approximation of the interrelation between histidine's charge states, allows for a natural separation of the two protonatable sites associated with the imidazole ring as well as the inclusion of all protonation states within the calculation.     

Protein docking using a genetic algorithm

A genetic algorithm (GA) for protein-protein docking is described, in which the proteins are represented by dot surfaces calculated using the Connolly program. The GA is used to move the surface of one protein relative to the other to locate the area of greatest surface complementarity between the two. Surface dots are deemed complementary if their normals are opposed, their Connolly shape type is complementary, and their hydrogen bonding or hydrophobic potential is fulfilled. Overlap of the protein interiors is penalized. The GA is tested on 34 large protein-protein complexes where one or both proteins has been crystallized separately. Parameters are established for which 30 of the complexes have at least one near-native solution ranked in the top 100. We have also successfully reassembled a 1,400-residue heptamer based on the top-ranking GA solution obtained when docking two bound subunits.     

Protein docking using spherical polar Fourier correlations

We present a new computational method of docking pairs of proteins by using spherical polar Fourier correlations to accelerate the search for candidate low-energy conformations. Interaction energies are estimated using a hydrophobic excluded volume model derived from the notion of "overlapping surface skins," augmented by a rigorous but "soft" model of electrostatic complementarity. This approach has several advantages over former three-dimensional grid-based fast Fourier transform (FFT) docking correlation methods even though there is no analogue to the FFT in a spherical polar representation. For example, a complete search over all six rigid-body degrees of freedom can be performed by rotating and translating only the initial expansion coefficients, many unfeasible orientations may be eliminated rapidly using only low-resolution terms, and the correlations are easily localized around known binding epitopes when this knowledge is available. Typical execution times on a single processor workstation range from 2 hours for a global search (5 x 10(8) trial orientations) to a few minutes for a local search (over 6 x 10(7) orientations). The method is illustrated with several domain dimer and enzyme-inhibitor complexes and 20 large antibody-antigen complexes, using both the bound and (when available) unbound subunits. The correct conformation of the complex is frequently identified when docking bound subunits, and a good docking orientation is ranked within the top 20 in 11 out of 18 cases when starting from unbound subunits. Proteins 2000;39:178-194.     

Protein docking prediction using predicted protein-protein interface

Background  

Many important cellular processes are carried out by protein complexes. To provide physical pictures of interacting proteins, many computational protein-protein prediction methods have been developed in the past. However, it is still difficult to identify the correct docking complex structure within top ranks among alternative conformations.     

Optimized atomic radii for protein continuum electrostatics solvation forces

Recently, we presented a Green's function approach for the calculation of analytic continuum electrostatic solvation forces based on numerical solutions of the finite-difference Poisson-Botzmann (FDPB) equation [Im et al., Comp. Phys. Comm. 111 (1998) 59]. In this treatment the analytic forces were explicitly defined as the first derivative of the FDPB continuum electrostatic free energy with respect to the coordinates of the solute atoms. A smooth intermediate region for the solute-solvent dielectric boundary needed to be introduced to avoid abrupt discontinuous variations in the solvation free energy and forces as a function of the atomic positions. In the present paper we extend the set of optimized radii, which was previously parametrized from molecular dynamics free energy simulations of the 20 standard amino acids with explicit solvent molecules [Nina et al., J. Phys. Chem. 101 (1997) 5239], to yield accurate solvation free energy by taking the influence of the smoothed dielectric region into account.     

Protein docking using surface matching and supervised machine learning

Computational prediction of protein complex structures through docking offers a means to gain a mechanistic understanding of protein interactions that mediate biological processes. This is particularly important as the number of experimentally determined structures of isolated proteins exceeds the number of structures of complexes. A comprehensive docking procedure is described in which efficient sampling of conformations is achieved by matching surface normal vectors, fast filtering for shape complementarity, clustering by RMSD, and scoring the docked conformations using a supervised machine learning approach. Contacting residue pair frequencies, residue propensities, evolutionary conservation, and shape complementarity score for each docking conformation are used as input data to a Random Forest classifier. The performance of the Random Forest approach for selecting correctly docked conformations was assessed by cross-validation using a nonredundant benchmark set of X-ray structures for 93 heterodimer and 733 homodimer complexes. The single highest rank docking solution was the correct (near-native) structure for slightly more than one third of the complexes. Furthermore, the fraction of highly ranked correct structures was significantly higher than the overall fraction of correct structures, for almost all complexes. A detailed analysis of the difficult to predict complexes revealed that the majority of the homodimer cases were explained by incorrect oligomeric state annotation. Evolutionary conservation and shape complementarity score as well as both underrepresented and overrepresented residue types and residue pairs were found to make the largest contributions to the overall prediction accuracy. Finally, the method was also applied to docking unbound subunit structures from a previously published benchmark set.     

Protein structure classification using geometric invariants and dynamic programming

Classification of newly determined protein structures is important in understanding their function and mechanism of action. Currently available methods employ a global structure alignment strategy and are computationally expensive. We propose a two-step methodology with a quick screen to significantly reduce the number of candidate structures followed by global structure alignment of the query structure with the reduced set. We represent a protein structure as a sequence of local structures, codified in the form of geometric invariants. Geometric invariants are quantities that remain unchanged under transformations such as translation and rotation. Protein structures represented as multi-attribute sequences are aligned via dynamic programming to identify close neighbors of the query structure. The query structure is then compared with this reduced dataset using conventional structure comparison methods to predict its functional class. For a typical protein structure, the screening method was able to reduce the protein data bank to mere 200 proteins while preserving structurally closest neighbor in the reduced set. This has resulted in 30 to 60 fold improvement in the execution time. We present the results of leave-one-out classification experiment on ASTRAL-95 domains and comparison with SCOP classification hierarchy.     

Protein docking and complementarity

Predicting the structures of protein-protein complexes is a difficult problem owing to the topographical and thermodynamic complexity of these structures. Past efforts in this area have focussed on fitting the interacting proteins together using rigid body searches, usually with the conformations of the proteins as they occur in crystal structure complexes. Here we present work which uses a rigid body docking method to generate the structures of three known protein complexes, using both the bound and unbound conformations of the interacting molecules. In all cases we can regenerate the geometry of the crystal complexes to high accuracy. We also are able to find geometries that do not resemble the crystal structure but nevertheless are surprisingly reasonable both mechanistically and by some simple physical criteria. In contrast to previous work in this area, we find that simple methods for evaluating the complementarity at the protein-protein interface cannot distinguish between the configurations that resemble the crystal structure complex and those that do not. Methods that could not distinguish between such similar and dissimilar configurations include surface area burial, solvation free energy, packing and mechanism-based filtering. Evaluations of the total interaction energy and the electrostatic interaction energy of the complexes were somewhat better. Of the techniques that we tried, energy minimization distinguished most clearly between the "true" and "false" positives, though even here the energy differences were surprisingly small. We found the lowest total interaction energy from amongst all of the putative complexes generated by docking was always within 5 A root-mean-square of the crystallographic structure. There were, however, several putative complexes that were very dissimilar to the crystallographic structure but had energies that were close to that of the low energy structure. The magnitude of the error in energy calculations has not been established in macromolecular systems, and thus the reliability of the small differences in energy remains to be determined. The ability of this docking method to regenerate the crystallographic configurations of the interacting proteins using their unbound conformations suggests that it will be a useful tool in predicting the structures of unsolved complexes.     

Conformer selection and induced fit in flexible backbone protein-protein docking using computational and NMR ensembles

Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein-protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue-residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.     

pyDock: electrostatics and desolvation for effective scoring of rigid-body protein-protein docking

The accurate scoring of rigid-body docking orientations represents one of the major difficulties in protein-protein docking prediction. Other challenges are the development of faster and more efficient sampling methods and the introduction of receptor and ligand flexibility during simulations. Overall, good discrimination of near-native docking poses from the very early stages of rigid-body protein docking is essential step before applying more costly interface refinement to the correct docking solutions. Here we explore a simple approach to scoring of rigid-body docking poses, which has been implemented in a program called pyDock. The scheme is based on Coulombic electrostatics with distance dependent dielectric constant, and implicit desolvation energy with atomic solvation parameters previously adjusted for rigid-body protein-protein docking. This scoring function is not highly dependent on specific geometry of the docking poses and therefore can be used in rigid-body docking sets generated by a variety of methods. We have tested the procedure in a large benchmark set of 80 unbound docking cases. The method is able to detect a near-native solution from 12,000 docking poses and place it within the 100 lowest-energy docking solutions in 56% of the cases, in a completely unrestricted manner and without any other additional information. More specifically, a near-native solution will lie within the top 20 solutions in 37% of the cases. The simplicity of the approach allows for a better understanding of the physical principles behind protein-protein association, and provides a fast tool for the evaluation of large sets of rigid-body docking poses in search of the near-native orientation.     

Guiding protein docking with geometric and evolutionary information

Structural modeling of molecular assemblies promises to improve our understanding of molecular interactions and biological function. Even when focusing on modeling structures of protein dimers from knowledge of monomeric native structure, docking two rigid structures onto one another entails exploring a large configurational space. This paper presents a novel approach for docking protein molecules and elucidating native-like configurations of protein dimers. The approach makes use of geometric hashing to focus the docking of monomeric units on geometrically complementary regions through rigid-body transformations. This geometry-based approach improves the feasibility of searching the combined configurational space. The search space is narrowed even further by focusing the sought rigid-body transformations around molecular surface regions composed of amino acids with high evolutionary conservation. This condition is based on recent findings, where analysis of protein assemblies reveals that many functional interfaces are significantly conserved throughout evolution. Different search procedures are employed in this work to search the resulting narrowed configurational space. A proof-of-concept energy-guided probabilistic search procedure is also presented. Results are shown on a broad list of 18 protein dimers and additionally compared with data reported by other labs. Our analysis shows that focusing the search around evolutionary-conserved interfaces results in lower lRMSDs.     

Protein decoy assembly using short fragments under geometric constraints

A small set of protein fragments can represent adequately all known local protein structure. This set of fragments, along with a construction scheme that assembles these fragments into structures, defines a discrete (relatively small) conformation space, which approximates protein structures accurately. We generate protein decoys by sampling geometrically valid structures from this conformation space, biased by the secondary structure prediction for the protein. Unlike other methods, secondary structure prediction is the only protein-specific information used for generating the decoys. Nevertheless, these decoys are qualitatively similar to those found by others. The method works well for all-alpha proteins, and shows promising results for alpha and beta proteins.     

Energy functions for protein design I: efficient and accurate continuum electrostatics and solvation

Electrostatics and solvation energies are important for defining protein stability, structural specificity, and molecular recognition. Because these energies are difficult to compute quickly and accurately, they are often ignored or modeled very crudely in computational protein design. To address this problem, we have developed a simple, fast, and accurate approximation for calculating Born radii in the context of protein design calculations. When these approximate Born radii are used with the generalized Born continuum dielectric model, energies calculated by the 10(6)-fold slower finite difference Poisson-Boltzmann model are faithfully reproduced. A similar approach can be used for estimating solvent-accessible surface areas (SASAs). As an independent test, we show that these approximations can be used to accurately predict the experimentally determined pK(a)s of >200 ionizable groups from 15 proteins.     

Protein stability and surface electrostatics: a charged relationship

Engineering proteins to withstand a broad range of conditions continues to be a coveted objective, holding the potential to advance biomedicine, industry, and our understanding of disease. One way of achieving this goal lies in elucidating the underlying interactions that define protein stability. It has been shown that the hydrophobic effect, hydrogen bonding, and packing interactions between residues in the protein interior are dominant factors that define protein stability. The role of surface residues in protein stability has received much less attention. It has been believed that surface residues are not important for protein stability particularly because their interactions with the solvent should be similar in the native and unfolded states. In the case of surface charged residues, it was sometimes argued that solvent exposure meant that the high dielectric of the solvent will further decrease the strength of the charge-charge interactions. In this paper, we challenge the notion that the surface charged residues are not important for protein stability. We computationally redesigned sequences of five different proteins to optimize the surface charge-charge interactions. All redesigned proteins exhibited a significant increase in stability relative to their parent proteins, as experimentally determined by circular dichroism spectroscopy and differential scanning calorimetry. These results suggest that surface charge-charge interactions are important for protein stability and that rational optimization of charge-charge interactions on the protein surface can be a viable strategy for enhancing protein stability.     

Ion transport through membrane-spanning nanopores studied by molecular dynamics simulations and continuum electrostatics calculations

Narrow hydrophobic regions are a common feature of biological channels, with possible roles in ion-channel gating. We study the principles that govern ion transport through narrow hydrophobic membrane pores by molecular dynamics simulation of model membranes formed of hexagonally packed carbon nanotubes. We focus on the factors that determine the energetics of ion translocation through such nonpolar nanopores and compare the resulting free-energy barriers for pores with different diameters corresponding to the gating regions in closed and open forms of potassium channels. Our model system also allows us to compare the results from molecular dynamics simulations directly to continuum electrostatics calculations. Both simulations and continuum calculations show that subnanometer wide pores pose a huge free-energy barrier for ions, but a small increase in the pore diameter to approximately 1 nm nearly eliminates that barrier. We also find that in those wider channels the ion mobility is comparable to that in the bulk phase. By calculating local electrostatic potentials, we show that the long range Coulomb interactions of ions are strongly screened in the wide water-filled channels. Whereas continuum calculations capture the overall energetics reasonably well, the local water structure, which is not accounted for in this model, leads to interesting effects such as the preference of hydrated ions to move along the pore wall rather than through the center of the pore.     

Simulation of electron-proton coupling with a Monte Carlo method: application to cytochrome c3 using continuum electrostatics.

A new method is presented for simulating the simultaneous binding equilibrium of electrons and protons on protein molecules, which makes it possible to study the full equilibrium thermodynamics of redox and protonation processes, including electron-proton coupling. The simulations using this method reflect directly the pH and electrostatic potential of the environment, thus providing a much closer and realistic connection with experimental parameters than do usual methods. By ignoring the full binding equilibrium, calculations usually overlook the twofold effect that binding fluctuations have on the behavior of redox proteins: first, they affect the energy of the system by creating partially occupied sites; second, they affect its entropy by introducing an additional empty/occupied site disorder (here named occupational entropy). The proposed method is applied to cytochrome c3 of Desulfovibrio vulgaris Hildenborough to study its redox properties and electron-proton coupling (redox-Bohr effect), using a continuum electrostatic method based on the linear Poisson-Boltzmann equation. Unlike previous studies using other methods, the full reduction order of the four hemes at physiological pH is successfully predicted. The sites more strongly involved in the redox-Bohr effect are identified by analysis of their titration curves/surfaces and the shifts of their midpoint redox potentials and pKa values. Site-site couplings are analyzed using statistical correlations, a method much more realistic than the usual analysis based on direct interactions. The site found to be more strongly involved in the redox-Bohr effect is propionate D of heme I, in agreement with previous studies; other likely candidates are His67, the N-terminus, and propionate D of heme IV. Even though the present study is limited to equilibrium conditions, the possible role of binding fluctuations in the concerted transfer of protons and electrons under nonequilibrium conditions is also discussed. The occupational entropy contributions to midpoint redox potentials and pKa values are computed and shown to be significant.     

Protein dynamics and electrostatics in the function of p-hydroxybenzoate hydroxylase

para-Hydroxybenzoate hydroxylase is a flavoprotein monooxygenase that catalyzes a reaction in two parts: reduction of the enzyme cofactor, FAD, by NADPH in response to binding p-hydroxybenzoate to the enzyme, then oxidation of reduced FAD by oxygen to form a hydroperoxide, which oxygenates p-hydroxybenzoate to form 3,4-dihydroxybenzoate. These diverse reactions all occur within a single polypeptide and are achieved through conformational rearrangements of the isoalloxazine ring and protein residues within the protein structure. In this review, we examine the complex dynamic behavior of the protein that enables regulated fast and specific catalysis to occur. Original research papers (principally from the past 15 years) provide the information that is used to develop a comprehensive overview of the catalytic process. Much of this information has come from detailed analysis of many specific mutants of the enzyme using rapid reaction technology, biophysical measurements, and high-resolution structures obtained by X-ray crystallography. We describe how three conformations of the enzyme provide a foundation for the catalytic cycle. One conformation has a closed active site for the conduct of the oxygen reactions, which must occur in the absence of solvent. The second conformation has a partly open active site for exchange of substrate and product, and the third conformation has a closed protein structure with the isoalloxazine ring rotated out to the surface for reaction with NADPH, which binds in a surface cleft. A fundamental feature of the enzyme is a H-bond network that connects the phenolic group of the substrate in the buried active site to the surface of the protein. This network serves to protonate and deprotonate the substrate and product in the active site to promote catalysis and regulate the coordination of conformational states for efficient catalysis.