Guiding probabilistic search of the protein conformational space with structural profiles

The roughness of the protein energy surface poses a significant challenge to search algorithms that seek to obtain a structural characterization of the native state. Recent research seeks to bias search toward near-native conformations through one-dimensional structural profiles of the protein native state. Here we investigate the effectiveness of such profiles in a structure prediction setting for proteins of various sizes and folds. We pursue two directions. We first investigate the contribution of structural profiles in comparison to or in conjunction with physics-based energy functions in providing an effective energy bias. We conduct this investigation in the context of Metropolis Monte Carlo with fragment-based assembly. Second, we explore the effectiveness of structural profiles in providing projection coordinates through which to organize the conformational space. We do so in the context of a robotics-inspired search framework proposed in our lab that employs projections of the conformational space to guide search. Our findings indicate that structural profiles are most effective in obtaining physically realistic near-native conformations when employed in conjunction with physics-based energy functions. Our findings also show that these profiles are very effective when employed instead as projection coordinates to guide probabilistic search toward undersampled regions of the conformational space.     

Sampling realistic protein conformations using local structural bias

The prediction of protein structure from sequence remains a major unsolved problem in biology. The most successful protein structure prediction methods make use of a divide-and-conquer strategy to attack the problem: a conformational sampling method generates plausible candidate structures, which are subsequently accepted or rejected using an energy function. Conceptually, this often corresponds to separating local structural bias from the long-range interactions that stabilize the compact, native state. However, sampling protein conformations that are compatible with the local structural bias encoded in a given protein sequence is a long-standing open problem, especially in continuous space. We describe an elegant and mathematically rigorous method to do this, and show that it readily generates native-like protein conformations simply by enforcing compactness. Our results have far-reaching implications for protein structure prediction, determination, simulation, and design.     

Loop modeling: Sampling, filtering, and scoring

We describe a fast and accurate protocol, LoopBuilder, for the prediction of loop conformations in proteins. The procedure includes extensive sampling of backbone conformations, side chain addition, the use of a statistical potential to select a subset of these conformations, and, finally, an energy minimization and ranking with an all-atom force field. We find that the Direct Tweak algorithm used in the previously developed LOOPY program is successful in generating an ensemble of conformations that on average are closer to the native conformation than those generated by other methods. An important feature of Direct Tweak is that it checks for interactions between the loop and the rest of the protein during the loop closure process. DFIRE is found to be a particularly effective statistical potential that can bias conformation space toward conformations that are close to the native structure. Its application as a filter prior to a full molecular mechanics energy minimization both improves prediction accuracy and offers a significant savings in computer time. Final scoring is based on the OPLS/SBG-NP force field implemented in the PLOP program. The approach is also shown to be quite successful in predicting loop conformations for cases where the native side chain conformations are assumed to be unknown, suggesting that it will prove effective in real homology modeling applications.     

Native atomic burials, supplemented by physically motivated hydrogen bond constraints, contain sufficient information to determine the tertiary structure of small globular proteins

We investigate the possibility that atomic burials, as measured by their distances from the structural geometrical center, contain sufficient information to determine the tertiary structure of globular proteins. We report Monte Carlo simulated annealing results of all-atom hard-sphere models in continuous space for four small proteins: the all-beta WW-domain 1E0L, the alpha/beta protein-G 1IGD, the all-alpha engrailed homeo-domain 1ENH, and the alpha + beta engineered monomeric form of the Cro protein 1ORC. We used as energy function the sum over all atoms, labeled by i, of |R(i) - R(i) (*)|, where R(i) is the atomic distance from the center of coordinates, or central distance, and R(i) (*) is the "ideal" central distance obtained from the native structure. Hydrogen bonds were taken into consideration by the assignment of two ideal distances for backbone atoms forming hydrogen bonds in the native structure depending on the formation of a geometrically defined bond, independently of bond partner. Lowest energy final conformations turned out to be very similar to the native structure for the four proteins under investigation and a strong correlation was observed between energy and distance root mean square deviation (DRMS) from the native in the case of all-beta 1E0L and alpha/beta 1IGD. For all alpha 1ENH and alpha + beta 1ORC the overall correlation between energy and DRMS among final conformations was not as high because some trajectories resulted in high DRMS but low energy final conformations in which alpha-helices adopted a non-native mutual orientation. Comparison between central distances and actual accessible surface areas corroborated the implicit assumption of correlation between these two quantities. The Z-score obtained with this native-centric potential in the discrimination of native 1ORC from a set of random compact structures confirmed that it contains a much smaller amount of native information when compared to a traditional contact Go potential but indicated that simple sequence-dependent burial potentials still need some improvement in order to attain a similar discriminability. Taken together, our results suggest that central distances, in conjunction to physically motivated hydrogen bond constraints, contain sufficient information to determine the native conformation of these small proteins and that a solution to the folding problem for globular proteins could arise from sufficiently accurate burial predictions from sequence followed by minimization of a burial-dependent energy function.     

Resolution-adapted recombination of structural features significantly improves sampling in restraint-guided structure calculation

Recent work has shown that NMR structures can be determined by integrating sparse NMR data with structure prediction methods such as Rosetta. The experimental data serve to guide the search for the lowest energy state towards the deep minimum at the native state which is frequently missed in Rosetta de novo structure calculations. However, as the protein size increases, sampling again becomes limiting; for example, the standard Rosetta protocol involving Monte Carlo fragment insertion starting from an extended chain fails to converge for proteins over 150 amino acids even with guidance from chemical shifts (CS-Rosetta) and other NMR data. The primary limitation of this protocol--that every folding trajectory is completely independent of every other--was recently overcome with the development of a new approach involving resolution-adapted structural recombination (RASREC). Here we describe the RASREC approach in detail and compare it to standard CS-Rosetta. We show that the improved sampling of RASREC is essential in obtaining accurate structures over a benchmark set of 11 proteins in the 15-25 kDa size range using chemical shifts, backbone RDCs and HN-HN NOE data; in a number of cases the improved sampling methodology makes a larger contribution than incorporation of additional experimental data. Experimental data are invaluable for guiding sampling to the vicinity of the global energy minimum, but for larger proteins, the standard Rosetta fold-from-extended-chain protocol does not converge on the native minimum even with experimental data and the more powerful RASREC approach is necessary to converge to accurate solutions.     

Protein structure evaluation using an all-atom energy based empirical scoring function

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions--energy based or statistical--have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp.     

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28–110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the α-helices. The method fails to predict the native 3-D structure of proteins with a predominantly β secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from β-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment. Proteins 31:74–96, 1998. © 1998 Wiley-Liss, Inc.     

Homology modelling of protein-protein complexes: a simple method and its possibilities and limitations

Background  

Structure-based computational methods are needed to help identify and characterize protein-protein complexes and their function. For individual proteins, the most successful technique is homology modelling. We investigate a simple extension of this technique to protein-protein complexes. We consider a large set of complexes of known structures, involving pairs of single-domain proteins. The complexes are compared with each other to establish their sequence and structural similarities and the relation between the two. Compared to earlier studies, a simpler dataset, a simpler structural alignment procedure, and an additional energy criterion are used. Next, we compare the Xray structures to models obtained by threading the native sequence onto other, homologous complexes. An elementary requirement for a successful energy function is to rank the native structure above any threaded structure. We use the DFIRE _β energy function, whose quality and complexity are typical of the models used today. Finally, we compare near-native models to distinctly non-native models.     

A simple reference state makes a significant improvement in near-native selections from structurally refined docking decoys

Near-native selections from docking decoys have proved challenging especially when unbound proteins are used in the molecular docking. One reason is that significant atomic clashes in docking decoys lead to poor predictions of binding affinities of near native decoys. Atomic clashes can be removed by structural refinement through energy minimization. Such an energy minimization, however, will lead to an unrealistic bias toward docked structures with large interfaces. Here, we extend an empirical energy function developed for protein design to protein-protein docking selection by introducing a simple reference state that removes the unrealistic dependence of binding affinity of docking decoys on the buried solvent accessible surface area of interface. The energy function called EMPIRE (EMpirical Protein-InteRaction Energy), when coupled with a refinement strategy, is found to provide a significantly improved success rate in near native selections when applied to RosettaDock and refined ZDOCK docking decoys. Our work underlines the importance of removing nonspecific interactions from specific ones in near native selections from docking decoys.     

Ab initio folding of terminal segments with secondary structures reveals the fine difference between two closely related all-atom statistical energy functions

One of the common methods for assessing energy functions of proteins is selection of native or near-native structures from decoys. This is an efficient but indirect test of the energy functions because decoy structures are typically generated either by sampling procedures or by a separate energy function. As a result, these decoys may not contain the global minimum structure that reflects the true folding accuracy of the energy functions. This paper proposes to assess energy functions by ab initio refolding of fully unfolded terminal segments with secondary structures while keeping the rest of the proteins fixed in their native conformations. Global energy minimization of these short unfolded segments, a challenging yet tractable problem, is a direct test of the energy functions. As an illustrative example, refolding terminal segments is employed to assess two closely related all-atom statistical energy functions, DFIRE (distance-scaled, finite, ideal-gas reference state) and DOPE (discrete optimized protein energy). We found that a simple sequence-position dependence contained in the DOPE energy function leads to an intrinsic bias toward the formation of helical structures. Meanwhile, a finer statistical treatment of short-range interactions yields a significant improvement in the accuracy of segment refolding by DFIRE. The updated DFIRE energy function yields success rates of 100% and 67%, respectively, for its ability to sample and fold fully unfolded terminal segments of 15 proteins to within 3.5 A global root-mean-squared distance from the corresponding native structures. The updated DFIRE energy function is available as DFIRE 2.0 upon request.     

Are structural biases at protein termini a signature of vectorial folding?

Experimental investigations of the biosynthesis of a number of proteins have pointed out that part of the native structure may be acquired already during translation. We carried out a comprehensive statistical analysis of some average structural properties of proteins that have been put forward as possible signatures of this progressive buildup process. Contrary to a widespread belief, we found that there is no major propensity of the amino acids to form contacts with residues that are closer to the N-terminus. Moreover, we found that the C-terminus is significantly more compact and locally organized than the N-terminus. This bias, though, is unlikely to be related to vectorial effects, since it correlates with subtle differences in the primary sequence. These findings indicate that even if proteins acquire their structure vectorially, no signature of this seems to be detectable in their average structural properties.     

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.     

Protein Structure Evaluation using an All-Atom Energy Based Empirical Scoring Function

Abstract

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions—energy based or statistical—have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp     

Effective scoring function for protein sequence design

We have developed an effective scoring function for protein design. The atomic solvation parameters, together with the weights of energy terms, were optimized so that residues corresponding to the native sequence were predicted with low energy in the training set of 28 protein structures. The solvation energy of non-hydrogen-bonded hydrophilic atoms was considered separately and expressed in a nonlinear way. As a result, our scoring function predicted native residues as the most favorable in 59% of the total positions in 28 proteins. We then tested the scoring function by comparing the predicted stability changes for 103 T4 lysozyme mutants with the experimental values. The correlation coefficients were 0.77 for surface mutations and 0.71 for all mutations. Finally, the scoring function combined with Monte Carlo simulation was used to predict favorable sequences on a fixed backbone. The designed sequences were similar to the natural sequences of the family to which the template structure belonged. The profile of the designed sequences was helpful for identification of remote homologues of the native sequence.     

Structural Alphabets for Protein Structure Classification: A Comparison Study

Finding structural similarities between proteins often helps reveal shared functionality, which otherwise might not be detected by native sequence information alone. Such similarity is usually detected and quantified by protein structure alignment. Determining the optimal alignment between two protein structures, however, remains a hard problem. An alternative approach is to approximate each three-dimensional protein structure using a sequence of motifs derived from a structural alphabet. Using this approach, structure comparison is performed by comparing the corresponding motif sequences or structural sequences. In this article, we measure the performance of such alphabets in the context of the protein structure classification problem. We consider both local and global structural sequences. Each letter of a local structural sequence corresponds to the best matching fragment to the corresponding local segment of the protein structure. The global structural sequence is designed to generate the best possible complete chain that matches the full protein structure. We use an alphabet of 20 letters, corresponding to a library of 20 motifs or protein fragments having four residues. We show that the global structural sequences approximate well the native structures of proteins, with an average coordinate root mean square of 0.69 Å over 2225 test proteins. The approximation is best for all α-proteins, while relatively poorer for all β-proteins. We then test the performance of four different sequence representations of proteins (their native sequence, the sequence of their secondary-structure elements, and the local and global structural sequences based on our fragment library) with different classifiers in their ability to classify proteins that belong to five distinct folds of CATH. Without surprise, the primary sequence alone performs poorly as a structure classifier. We show that addition of either secondary-structure information or local information from the structural sequence considerably improves the classification accuracy. The two fragment-based sequences perform better than the secondary-structure sequence but not well enough at this stage to be a viable alternative to more computationally intensive methods based on protein structure alignment.     

Extracting knowledge from protein structure geometry

Protein structure prediction techniques proceed in two steps, namely the generation of many structural models for the protein of interest, followed by an evaluation of all these models to identify those that are native‐like. In theory, the second step is easy, as native structures correspond to minima of their free energy surfaces. It is well known however that the situation is more complicated as the current force fields used for molecular simulations fail to recognize native states from misfolded structures. In an attempt to solve this problem, we follow an alternate approach and derive a new potential from geometric knowledge extracted from native and misfolded conformers of protein structures. This new potential, Metric Protein Potential (MPP), has two main features that are key to its success. Firstly, it is composite in that it includes local and nonlocal geometric information on proteins. At the short range level, it captures and quantifies the mapping between the sequences and structures of short (7‐mer) fragments of protein backbones through the introduction of a new local energy term. The local energy term is then augmented with a nonlocal residue‐based pairwise potential, and a solvent potential. Secondly, it is optimized to yield a maximized correlation between the energy of a structural model and its root mean square (RMS) to the native structure of the corresponding protein. We have shown that MPP yields high correlation values between RMS and energy and that it is able to retrieve the native structure of a protein from a set of high‐resolution decoys. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Development of a physics-based force field for the scoring and refinement of protein models

The minimal requirements of a physics-based potential that can refine protein structures are the existence of a correlation between the energy with native similarity and the scoring of the native structure as the lowest in energy. To develop such a force field, the relative weights of the Amber ff03 all-atom potential supplemented by an explicit hydrogen-bond potential were adjusted by global optimization of energetic and structural criteria for a large set of protein decoys generated for a set of 58 nonhomologous proteins. The average correlation coefficient of the energy with TM-score significantly improved from 0.25 for the original ff03 potential to 0.65 for the optimized force field. The fraction of proteins for which the native structure had lowest energy increased from 0.22 to 0.90. Moreover, use of an explicit hydrogen-bond potential improves scoring performance of the force field. Promising preliminary results were obtained in applying the optimized potentials to refine protein decoys using only an energy criterion to choose the best decoy among sampled structures. For a set of seven proteins, 63% of the decoys improve, 18% get worse, and 19% are not changed.     

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 reduced protein model with accurate native-structure identification ability

A protein model that is simple enough to be used in protein-folding simulations but accurate enough to identify a protein native fold is described. Its geometry consists of describing the residues by one, two, or three pseudoatoms, depending on the residue size. Its energy is given by a pairwise, knowledge-based potential obtained for all the pseudoatoms as a function of their relative distance. The pseudoatomic potential is also a function of the primary chain separation and residue order. The model is tested by gapless threading on a large, representative set of known protein and decoy structures obtained from the "Decoys 'R' Us" database. It is also tested by threading on gapped decoys generated for proteins with many homologs. The gapless threading tests show near 98% native-structure recognition as the lowest energy structure and almost 100% as one of the three lowest energy structures for over 2200 test proteins. In decoy threading tests, the model recognized the majority of the native structures. It is also able to recognize native structures among gapped decoys, in spite of close structural similarities. The results indicate that the pseudoatomic model has native recognition ability similar to comparable atomic-based models but much better than equivalent residue-based models.