Physicochemical evaluation of protein folds predicted by threading

Protein structure prediction remains an unsolved problem. Since prediction of the native structure seems very difficult, one usually tries to predict the correct fold of a protein. Here the "fold" is defined by the approximate backbone structure of the protein. However, physicochemical factors that determine the correct fold are not well understood. It has recently been reported that molecular mechanics energy functions combined with effective solvent terms can discriminate the native structures from misfolded ones. Using such a physicochemical energy function, we studied the factors necessary for discrimination of correct and incorrect folds. We first selected correct and incorrect folds by a conventional threading method. Then, all-atom models of those folds were constructed by simply minimizing the atomic overlaps. The constructed correct model representing the native fold has almost the same backbone structure as the native structure but differs in side-chain packing. Finally, the energy values of the constructed models were compared with that of the experimentally determined native structure. The correct model as well as the native structure showed lower energy than misfolded models. However, a large energy gap was found between the native structure and the correct model. By decomposing the energy values into their components, it was found that solvent effects such as the hydrophobic interaction or solvent shielding and the Born energy stabilized the correct model rather than the native structure. The large energetic stabilization of the native structure was attained by specific side-chain packing. The stabilization by solvent effects is small compared to that by side-chain packing. Therefore, it is suggested that in order to confidently predict the correct fold of a protein, it is also necessary to predict correct side-chain packing.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

A correlation-based method for the enhancement of scoring functions on funnel-shaped energy landscapes

A correlation-based approach is introduced for enhancing the ability of structure-scoring methods to identify and distinguish native-like conformations. The proposed method relies on a funnel-shaped scoring function that decreases steadily toward the native state. It takes advantage of the idea that the structure from a given ensemble that is closest to the native basin leads to the highest correlation coefficient between a given score and distance to that structure as an approximation of the native state for the entire ensemble. The method is applied successfully to a number of different test cases that demonstrate substantial improvements in the correlation of the score with the distance from the true native state but also result in the selection of more native-like structures compared to the original score.     

Radial distributions of water—water distances in protein crystals

An accurate protein crystallographic structure determination requires a knowledge of the solvent contribution to the diffraction pattern. As resolutions improve, research groups are reporting coordinates of large numbers of water molecules. We examine the accuracy of these coordinates by presenting radial distributions of water—water distances from refinements at different stages and interpreting them in terms of preferred hydrogen-bonding distances and problems in solvent electron density map interpretation. Marked differences between the distributions suggest that wide variations exist in the water molecule selection and refinement criteria employed by different research groups which mask possible real differences in solvent structure.     

Computational protein design is a challenge for implicit solvation models

Increasingly complex schemes for representing solvent effects in an implicit fashion are being used in computational analyses of biological macromolecules. These schemes speed up the calculations by orders of magnitude and are assumed to compromise little on essential features of the solvation phenomenon. In this work we examine this assumption. Five implicit solvation models, a surface area-based empirical model, two models that approximate the generalized Born treatment and a finite difference Poisson-Boltzmann method are challenged in situations differing from those where these models were calibrated. These situations are encountered in automatic protein design procedures, whose job is to select sequences, which stabilize a given protein 3D structure, from a large number of alternatives. To this end we evaluate the energetic cost of burying amino acids in thousands of environments with different solvent exposures belonging, respectively, to decoys built with random sequences and to native protein crystal structures. In addition we perform actual sequence design calculations. Except for the crudest surface area-based procedure, all the tested models tend to favor the burial of polar amino acids in the protein interior over nonpolar ones, a behavior that leads to poor performance in protein design calculations. We show, on the other hand, that three of the examined models are nonetheless capable of discriminating between the native fold and many nonnative alternatives, a test commonly used to validate force fields. It is concluded that protein design is a particularly challenging test for implicit solvation models because it requires accurate estimates of the solvation contribution of individual residues. This contrasts with native recognition, which depends less on solvation and more on other nonbonded contributions.     

Preparation and properties of soluble-insoluble immobilized proteases

In order to carry out an effective enzyme reaction, the preparation of soluble-insoluble immobilized enzyme was investigated. Proteases were selected as model enzymes, and their immobilization was carried out by using an enteric coating polymer as a carrier. Among the polymers tested, methacrylic acid-methylacrylate-methylmethacrylate copolymer (MPM-06) gave the most active soluble-insoluble immobilized papain. This immobilized papain showed insoluble from below pH 4.8 and soluble form above pH 5.8; it was also soluble in water-miscible organic solvent. It was reusable and more stable with heat and water-miscible organic solvents than native proteases. Furthermore, various proteases could be immobilized by using MPM-06 with high activity. Chymotrypsin immobilized by this method catalyzed the effective peptide synthesis in a heterogeneous reaction system containing water-miscible organic solvent.     

Hydrophobic potential of mean force as a solvation function for protein structure prediction

We have developed a solvation function that combines a Generalized Born model for polarization of protein charge by the high dielectric solvent, with a hydrophobic potential of mean force (HPMF) as a model for hydrophobic interaction, to aid in the discrimination of native structures from other misfolded states in protein structure prediction. We find that our energy function outperforms other reported scoring functions in terms of correct native ranking for 91% of proteins and low Z scores for a variety of decoy sets, including the challenging Rosetta decoys. This work shows that the stabilizing effect of hydrophobic exposure to aqueous solvent that defines the HPMF hydration physics is an apparent improvement over solvent-accessible surface area models that penalize hydrophobic exposure. Decoys generated by thermal sampling around the native-state basin reveal a potentially important role for side-chain entropy in the future development of even more accurate free energy surfaces.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

Enhanced specificity against misfolding in a thermostable mutant of the Tetrahymena ribozyme

Structured RNAs encode native conformations that are more stable than the vast ensembles of alternative conformations, but how this specificity is evolved is incompletely understood. Here we show that a variant of the Tetrahymena group I intron ribozyme that was generated previously by in vitro selection for enhanced thermostability also displays modestly enhanced specificity against a stable misfolded structure that is globally similar to the native state, despite the absence of selective pressure to increase the energy gap between these structures. The enhanced specificity for native folding arises from mutations in two nucleotides that are close together in space in the native structure, and additional experiments show that these two mutations do not affect the stability of the misfolded conformation relative to the largely unstructured transition state ensemble for interconversion between the native and misfolded conformers. Thus, they selectively stabilize the native state, presumably by strengthening a local tertiary contact network that cannot form in the misfolded conformation. The stabilization is larger in the presence of the peripheral element P5abc, suggesting that cooperative tertiary structure formation plays a key role in the enhanced stability. The increased specificity in the absence of explicit selection suggests that the large energy gap in the wild-type RNA may have arisen analogously, a consequence of selective pressure for stability of the functional structure. More generally, the structural rigidity and intricate networks of contacts in structured RNAs may allow them to evolve substantial structural specificity without explicit negative selection, even against closely related alternative structures.     

Comparison of energy components of proteins from thermophilic and mesophilic organisms

In order to infer the energetic determinants of thermophilic proteins, molecular mechanics calculations were applied to five proteins from thermophilic eubacteria and their mesophilic homologs. The energy function includes a hydration term as well as the electrostatic contribution from the solvent in addition to the usual conformational energy terms. We calculated energy values for three different states of each protein: the native, near-native, and unfolded structures. The energy difference and its components between pairs of these states were compared. The hypothetical near-native structures have almost the same backbone conformation as the native structure but with largely distorted side-chain packing, thus enabling us to extract the energy components important for stabilizing the native backbone topology itself, irrespective of structural details. It was found that the sum of the electrostatic and hydration energies, although of large positive values, were consistently lower for the thermophilic proteins than for their mesophilic counterparts. This trend was observed in the energy difference not only between the native and unfolded structures, but also between the near-native and unfolded structures. In contrast, the energy components regarding side-chain packing did not show any clear tendency. These results suggest that the thermophilic proteins are stabilized so that the precise packing of the native structure does not significantly affect the stability. Implications of this conclusion are also discussed.     

Characterization of a partly folded protein by NMR methods: studies on the molten globule state of guinea pig alpha-lactalbumin

NMR spectroscopy has been used to investigate the structure of a partially folded state of a protein, the molten globule or A-state of alpha-lactalbumin. The 1H NMR spectrum of this species differs substantially from those of both the native and fully unfolded states, reflecting the intermediate level of order. The resolution in the spectrum is limited by the widespread overlap and substantial line widths of many of the resonances. Methods have therefore been developed that exploit the well-resolved spectrum of the native protein to probe indirectly the A-state. A number of resonances of the A-state have been found to be substantially shifted from their positions in the spectrum of the unfolded state and have been identified through magnetization transfer with the native state, under conditions where the two states are interconverting. The most strongly perturbed residues in the A-state were found to be among those that form a hydrophobic core to the native structure. A number of amides were found to be highly protected from solvent exchange in the A-state. These have been identified through pH-jump experiments, which label them in the spectrum of the native protein. They were found to occur mainly in segments that are helical in the native structure. These results enable a model of the A-state to be proposed in which significant conformational freedom exists but where specific elements of native-like structure are preserved.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

Molecular dynamics simulations of folding processes of a beta-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.     

Phasing macromolecular structures with UV-induced structural changes

Experimental phasing of macromolecular crystal structures relies on the accurate measurement of two or more sets of reflections from isomorphous crystals, where the scattering power of a few atoms is different for each set. Recently, it was demonstrated that X-ray-induced intensity differences can also contain phasing information, exploiting specific structural changes characteristic of X-ray damage. This method (radiation damage-induced phasing; RIP) has the advantage that it can be performed on a single crystal of the native macromolecule. However, a drawback is that X-rays introduce many small changes to both solvent and macromolecule. In this study, ultraviolet (UV) radiation has been used to induce specific changes in the macromolecule alone, leading to a larger contrast between radiation-susceptible and nonsusceptible sites. Unlike X-ray RIP, UV RIP does not require the use of a synchrotron. The method has been demonstrated for a series of macromolecules.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

To keep or not to keep? the question of crystallographic waters for enzyme simulations in organic solvent

The use of enzymes in non-aqueous solvents expands the use of biocatalysts to hydrophobic substrates, with the ability to tune selectivity of reactions through solvent selection. Non-aqueous enzymology also allows for fundamental studies on the role of water and other solvents in enzyme structure, dynamics, and function. Molecular dynamics simulations serve as a powerful tool in this area, providing detailed atomic information about the effect of solvents on enzyme properties. However, a common protocol for non-aqueous enzyme simulations does not exist. If you want to simulate enzymes in non-aqueous solutions, how many and which crystallographic waters do you keep? In the present work, this question is addressed by determining which crystallographic water molecules lead most quickly to an equilibrated protein structure. Five different methods of selecting and keeping crystallographic waters are used in order to discover which crystallographic waters lead the protein structure to reach an equilibrated structure more rapidly in organic solutions. It is found that buried waters contribute most to rapid equilibration in organic solvent, with slow-diffusing waters giving similar results.     

Modifications generated by fast photochemical oxidation of proteins reflect the native conformations of proteins

Hydroxyl radical footprinting (HRF) is a nonspecific protein footprinting method that has been increasingly used in recent years to analyze protein structure. The method oxidatively modifies solvent accessible sites in proteins, which changes upon alterations in the protein, such as ligand binding or a change in conformation. For HRF to provide accurate structural information, the method must probe the native structure of proteins. This requires careful experimental controls since an abundance of oxidative modifications can induce protein unfolding. Fast photochemical oxidation of proteins (FPOP) is a HRF method that generates hydroxyl radicals via photo‐dissociation of hydrogen peroxide using an excimer laser. The addition of a radical scavenger to the FPOP reaction reduces the lifetime of the radical, limiting the levels of protein oxidation. A direct assay is needed to ensure FPOP is probing the native conformation of the protein. Here, we report using enzymatic activity as a direct assay to validate that FPOP is probing the native structure of proteins. By measuring the catalytic activity of lysozyme and invertase after FPOP modification, we demonstrate that FPOP does not induce protein unfolding.     

Substrate flow in catalases deduced from the crystal structures of active site variants of HPII from Escherichia coli.

The active site of heme catalases is buried deep inside a structurally highly conserved homotetramer. Channels leading to the active site have been identified as potential routes for substrate flow and product release, although evidence in support of this model is limited. To investigate further the role of protein structure and molecular channels in catalysis, the crystal structures of four active site variants of catalase HPII from Escherichia coli (His128Ala, His128Asn, Asn201Ala, and Asn201His) have been determined at approximately 2.0-A resolution. The solvent organization shows major rearrangements with respect to native HPII, not only in the vicinity of the replaced residues but also in the main molecular channel leading to the heme distal pocket. In the two inactive His128 variants, continuous chains of hydrogen bonded water molecules extend from the molecular surface to the heme distal pocket filling the main channel. The differences in continuity of solvent molecules between the native and variant structures illustrate how sensitive the solvent matrix is to subtle changes in structure. It is hypothesized that the slightly larger H(2)O(2) passing through the channel of the native enzyme will promote the formation of a continuous chain of solvent and peroxide. The structure of the His128Asn variant complexed with hydrogen peroxide has also been determined at 2.3-A resolution, revealing the existence of hydrogen peroxide binding sites both in the heme distal pocket and in the main channel. Unexpectedly, the largest changes in protein structure resulting from peroxide binding are clustered on the heme proximal side and mainly involve residues in only two subunits, leading to a departure from the 222-point group symmetry of the native enzyme. An active role for channels in the selective flow of substrates through the catalase molecule is proposed as an integral feature of the catalytic mechanism. The Asn201His variant of HPII was found to contain unoxidized heme b in combination with the proximal side His-Tyr bond suggesting that the mechanistic pathways of the two reactions can be uncoupled.     

QBES: predicting real values of solvent accessibility from sequences by efficient, constrained energy optimization

Solvent accessibility, one of the key properties of amino acid residues in proteins, can be used to assist protein structure prediction. Various approaches such as neural network, support vector machines, probability profiles, information theory, Bayesian theory, logistic function, and multiple linear regression have been developed for solvent accessibility prediction. In this article, a much simpler quadratic programming method based on the buriability parameter set of amino acid residues is developed. The new method, called QBES (Quadratic programming and Buriability Energy function for Solvent accessibility prediction), is reasonably accurate for predicting the real value of solvent accessibility. By using a dataset of 30 proteins to optimize three parameters, the average correlation coefficients between the predicted and actual solvent accessibility are about 0.5 for all four independent test sets ranging from 126 to 513 proteins. The method is efficient. It takes only 20 min for a regular PC to obtain results of 30 proteins with an average length of 263 amino acids. Although the proposed method is less accurate than a few more sophisticated methods based on neural network or support vector machines, this is the first attempt to predict solvent accessibility by energy optimization with constraints. Possible improvements and other applications of the method are discussed.     

Protein structure refinement by optimization

Knowledge‐based protein potentials are simplified potentials designed to improve the quality of protein models, which is important as more accurate models are more useful for biological and pharmaceutical studies. Consequently, knowledge‐based potentials often are designed to be efficient in ordering a given set of deformed structures denoted decoys according to how close they are to the relevant native protein structure. This, however, does not necessarily imply that energy minimization of this potential will bring the decoys closer to the native structure. In this study, we introduce an iterative strategy to improve the convergence of decoy structures. It works by adding energy optimized decoys to the pool of decoys used to construct the next and improved knowledge‐based potential. We demonstrate that this strategy results in significantly improved decoy convergence on Titan high resolution decoys and refinement targets from Critical Assessment of protein Structure Prediction competitions. Our potential is formulated in Cartesian coordinates and has a fixed backbone potential to restricts motions to be close to those of a dihedral model, a fixed hydrogen‐bonding potential and a variable coarse grained carbon alpha potential consisting of a pair potential and a novel solvent potential that are b‐spline based as we use explicit gradient and Hessian for efficient energy optimization. Proteins 2015; 83:1616–1624. © 2015 Wiley Periodicals, Inc.