Prediction of protein structure by simulating coarse-grained folding pathways: a preliminary report

A set of software tools designed to study protein structure and kinetics has been developed. The core of these tools is a program called Folding Machine (FM) which is able to generate low resolution folding pathways using modest computational resources. The FM is based on a coarse-grained kinetic ab initio Monte-Carlo sampler that can optionally use information extracted from secondary structure prediction servers or from fragment libraries of local structure. The model underpinning this algorithm contains two novel elements: (a) the conformational space is discretized using the Ramachandran basins defined in the local phi-psi energy maps; and (b) the solvent is treated implicitly by rescaling the pairwise terms of the non-bonded energy function according to the local solvent environments. The purpose of this hybrid ab initio/knowledge-based approach is threefold: to cover the long time scales of folding, to generate useful 3-dimensional models of protein structures, and to gain insight on the protein folding kinetics. Even though the algorithm is not yet fully developed, it has been used in a recent blind test of protein structure prediction (CASP5). The FM generated models within 6 A backbone rmsd for fragments of about 60-70 residues of alpha-helical proteins. For a CASP5 target that turned out to be natively unfolded, the trajectory obtained for this sequence uniquely failed to converge. Also, a new measure to evaluate structure predictions is presented and used along the standard CASP assessment methods. Finally, recent improvements in the prediction of beta-sheet structures are briefly described.     

Low resolution solution structure of the Apo form of Escherichia coli haemoglobin protease Hbp

We have studied the solution properties of the apo form of the haemoglobin protease or "haemoglobinase", Hbp, a principal component of an important iron acquisition system in pathogenic Escherichia coli. Experimental determination of secondary structure content from circular dichroism (CD) spectroscopy, obtained using synchrotron light, showed that the protein contains predominately beta-sheets in agreement with secondary structure prediction from the primary sequence. Next, the size and shape of the protein were probed using analytical ultracentrifugation (AUC) and small angle X-ray scattering (SAXS). These showed that Hbp is a monomer, with an extended conformation. Using ab initio reconstruction methods we have produced a model of Hbp, which shows that the protein adopts an extended crescent-shaped conformation. Analysis of the resulting model gives hydrodynamic parameters in good agreement with those observed experimentally. Thus we are able to construct a hydrodynamically rigorous model of apo-Hbp in solution, not only giving a greater level of confidence to the results of the SAXS reconstruction methods, but providing the first three-dimensional view of this intriguing molecule.     

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.     

Prediction of Protein Structure by Simulating Coarse-grained Folding Pathways: A Preliminary Report

Abstract

A set of software tools designed to study protein structure and kinetics has been developed. The core of these tools is a program called Folding Machine (FM) which is able to generate low resolution folding pathways using modest computational resources. The FM is based on a coarse-grained kinetic ab initio Monte-Carlo sampler that can optionally use information extracted from secondary structure prediction servers or from fragment libraries of local structure. The model underpinning this algorithm contains two novel elements: (a) the conformational space is discretized using the Ramachandran basins defined in the local φ-ψ energy maps; and (b) the solvent is treated implicitly by rescaling the pairwise terms of the non-bonded energy function according to the local solvent environments. The purpose of this hybrid ab initio/knowledge-based approach is threefold: to cover the long time scales of folding, to generate useful 3-dimensional models of protein structures, and to gain insight on the protein folding kinetics. Even though the algorithm is not yet fully developed, it has been used in a recent blind test of protein structure prediction (CASP5). The FM generated models within 6 Å backbone rmsd for fragments of about 60–70 residues of a-helical proteins. For a CASP5 target that turned out to be natively unfolded, the trajectory obtained for this sequence uniquely failed to converge. Also, a new measure to evaluate structure predictions is presented and used along the standard CASP assessment methods. Finally, recent improvements in the prediction of β-sheet structures are briefly described.     

Prediction of protein structure from ideal forms

For many years it has been accepted that the sequence of a protein can specify its three-dimensional structure. However, there has been limited progress in explaining how the sequence dictates its fold and no attempt to do this computationally without the use of specific structural data has ever succeeded for any protein larger than 100 residues. We describe a method that can predict complex folds up to almost 200 residues using only basic principles that do not include any elements of sequence homology. The method does not simulate the folding chain but generates many thousands of models based on an idealized representation of structure. Each rough model is scored and the best are refined. On a set of five proteins, the correct fold score well and when tested on a set of larger proteins, the correct fold was ranked highest for some proteins more than 150 residues, with others being close topological variants. All other methods that approach this level of success rely on the use of templates or fragments of known structures. Our method is unique in using a database of ideal models based on general packing rules that, in spirit, is closer to an ab initio approach.     

Distinguishing foldable proteins from nonfolders: When and how do they differ?

When a denatured polypeptide is put into refolding conditions, it undergoes conformational changes on a variety of times scales. We set out here to distinguish the fast events that promote productive folding from other processes that may be generic to any non-folding polypeptide. We have apply an ab initio folding algorithm to model the folding of various proteins and their compositionally identical, random-sequence analogues. In the earliest stages, proteins and their scrambled-sequence counterparts undergo indistinguishable reductions in the extent to which they explore conformation space. For both polypeptides, an early contraction occurs but does not involve the formation of a distinct intermediate. Following this phase, however, the naturally-occurring sequences are distinguished by an increase in the formation of three-body correlations wherein a hydrophobic group desolvates and protects an intra-molecular hydrogen bond. These correlations are manifested in a mild but measurable reduction of the accessible configuration space beyond that of the random-sequence peptides, and portend the folding to the native structure. Hence, early events reflect a generic response of the denatured ensemble to a change in solvent condition, but the wild-type sequence develops additional correlations as its structure evolves that can reveal the protein's foldability.     

Ab initio folding simulation of the Trp-cage mini-protein approaches NMR resolution

Here, we report a 100 ns molecular dynamics simulation of the folding process of a recently designed autonomous-folding mini-protein designated as tc5b with a new AMBER force field parameter set developed based on condensed-phase quantum mechanical calculations and a Generalized Born continuum solvent model. Starting from its fully extended conformation, our simulation has produced a final structure resembling that of NMR native structure to within 1A main-chain root mean square deviation. Remarkably, the simulated structure stayed in the native state for most part of the simulation after it reached the state. Of greater significance is that our simulation has not only reached the correct main-chain conformation, but also a very high degree of accuracy in side-chain packing conformation. This feat has traditionally been a challenge for ab initio simulation studies. In addition to characterization of the trajectory, comparison of our results to experimental data is also presented. Analysis of the trajectory suggests that the rate-limiting step of folding of this mini-protein is the packing of the Trp side-chain.     

Generalized comparative modeling (GENECOMP): a combination of sequence comparison, threading, and lattice modeling for protein structure prediction and refinement

An improved generalized comparative modeling method, GENECOMP, for the refinement of threading models is developed and validated on the Fischer database of 68 probe-template pairs, a standard benchmark used to evaluate threading approaches. The basic idea is to perform ab initio folding using a lattice protein model, SICHO, near the template provided by the new threading algorithm PROSPECTOR. PROSPECTOR also provides predicted contacts and secondary structure for the template-aligned regions, and possibly for the unaligned regions by garnering additional information from other top-scoring threaded structures. Since the lowest-energy structure generated by the simulations is not necessarily the best structure, we employed two structure-selection protocols: distance geometry and clustering. In general, clustering is found to generate somewhat better quality structures in 38 of 68 cases. When applied to the Fischer database, the protocol does no harm and in a significant number of cases improves upon the initial threading model, sometimes dramatically. The procedure is readily automated and can be implemented on a genomic scale.     

Dynamic Monte Carlo simulations of a new lattice model of globular protein folding, structure and dynamics

A long-standing problem of molecular biology is the prediction of globular protein tertiary structure from the primary sequence. In the context of a new, 24-nearest-neighbor lattice model of proteins that includes both alpha and beta-carbon atoms, the requirements for folding to a unique four-member beta-barrel, four-helix bundles and a model alpha/beta-bundle have been explored. A number of distinct situations are examined, but the common requirements for the formation of a unique native conformation are tertiary interactions plus the presence of relatively small (but not irrelevant) intrinsic turn preferences that select out the native conformer from a manifold of compact states. When side-chains are explicitly included, there are many conformations having the same or a slightly greater number of side-chain contacts as in the native conformation, and it is the local intrinsic turn preferences that produce the conformational selectivity on collapse. The local preference for helix or beta-sheet secondary structure may be at odds with the secondary structure ultimately found in the native conformation. The requisite intrinsic turn populations are about 0.3% for beta-proteins, 2% for mixed alpha/beta-proteins and 6% for helix bundles. In addition, an idealized model of an allosteric conformational transition has been examined. Folding occurs predominantly by a sequential on-site assembly mechanism with folding initiating either at a turn or from an isolated helix or beta-strand (where appropriate). For helical and beta-protein models, similar folding pathways were obtained in diamond lattice simulations, using an entirely different set of local Monte Carlo moves. This argues strongly that the results are universal; that is, they are independent of lattice, protein model or the particular realization of Monte Carlo dynamics. Overall, these simulations demonstrate that the folding of all known protein motifs can be achieved in the context of a single class of lattice models that includes realistic backbone structures and idealized side-chains.     

Computational study of the conformational preferences of the (R)-8-amino-pentacyclo[5.4.0.0(2,6).0(3,10).0(5,9)]undecane-8-carboxylic acid monopeptide.

alpha-Amino acids are important building blocks for the synthesis of a large number of bioactive compounds and pharmaceutical drugs. However, a literature survey revealed that no theoretical conformational study of alpha-amino acids with cage carbon frameworks has been performed to date. This paper reports the results of a conformational study on the (R)-8-amino-pentacyclo[5.4.0.0(2,6).0(3,10).0(5,9)]undecane-8-carboxylic acid monopeptide (cage monopeptide), using molecular mechanics and ab initio methods. The in vacuo Ramachandran maps computed using the different parameterizations of the AMBER force field show the C7eq structure as the most favourable conformation, in contrast to the C7ax structure, that is the lowest energy conformation at the ab initio level. Analysis of these maps reveals the helical preference for the monopeptide and provides the potential for the cage residue to be incorporated into constrained peptide analogues.     

Contact order and ab initio protein structure prediction

Although much of the motivation for experimental studies of protein folding is to obtain insights for improving protein structure prediction, there has been relatively little connection between experimental protein folding studies and computational structural prediction work in recent years. In the present study, we show that the relationship between protein folding rates and the contact order (CO) of the native structure has implications for ab initio protein structure prediction. Rosetta ab initio folding simulations produce a dearth of high CO structures and an excess of low CO structures, as expected if the computer simulations mimic to some extent the actual folding process. Consistent with this, the majority of failures in ab initio prediction in the CASP4 (critical assessment of structure prediction) experiment involved high CO structures likely to fold much more slowly than the lower CO structures for which reasonable predictions were made. This bias against high CO structures can be partially alleviated by performing large numbers of additional simulations, selecting out the higher CO structures, and eliminating the very low CO structures; this leads to a modest improvement in prediction quality. More significant improvements in predictions for proteins with complex topologies may be possible following significant increases in high-performance computing power, which will be required for thoroughly sampling high CO conformations (high CO proteins can take six orders of magnitude longer to fold than low CO proteins). Importantly for such a strategy, simulations performed for high CO structures converge much less strongly than those for low CO structures, and hence, lack of simulation convergence can indicate the need for improved sampling of high CO conformations. The parallels between Rosetta simulations and folding in vivo may extend to misfolding: The very low CO structures that accumulate in Rosetta simulations consist primarily of local up-down beta-sheets that may resemble precursors to amyloid formation.     

Improving the performance of Rosetta using multiple sequence alignment information and global measures of hydrophobic core formation

This study explores the use of multiple sequence alignment (MSA) information and global measures of hydrophobic core formation for improving the Rosetta ab initio protein structure prediction method. The most effective use of the MSA information is achieved by carrying out independent folding simulations for a subset of the homologous sequences in the MSA and then identifying the free energy minima common to all folded sequences via simultaneous clustering of the independent folding runs. Global measures of hydrophobic core formation, using ellipsoidal rather than spherical representations of the hydrophobic core, are found to be useful in removing non-native conformations before cluster analysis. Through this combination of MSA information and global measures of protein core formation, we significantly increase the performance of Rosetta on a challenging test set. Proteins 2001;43:1-11.     

All-atom ab initio folding of a diverse set of proteins

Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins by using a minimalist transferable-energy model that consists of two-body atom-atom interactions, hydrogen bonding, and a local sequence-energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native-in the range of 2-6 A root-mean-square deviation (rmsd). Our results demonstrate that the successful folding of a protein chain to its native state is governed by only a few crucial energetic terms.     

Ab initio quantum mechanical models of peptide helices and their vibrational spectra

Structural parameters for standard peptide helices (alpha, 3(10), 3(1) left-handed) were fully ab initio optimized for Ac-(L-Ala)(9)-NHMe and for Ac-(L-Pro)(9)-NHMe (poly-L-proline-PLP I and PLP II-forms), in order to better understand the relative stability and minimum energy geometries of these conformers and the dependence of the ir absorption and vibrational CD (VCD) spectra on detailed variation in these conformations. Only the 3(10)-helical Ala-based conformation was stable in vacuum for this decaamide structure, but both Pro-based conformers minimized successfully. Inclusion of solvent effects, by use of the conductor-like screening solvent model (COSMO), enabled ab initio optimizations [at the DFT/B3LYP/SV(P) level] without any constraints for the alpha- and 3(10)-helical Ala-based peptides as well as the two Pro-based peptides. The geometries obtained compare well with peptide chain torsion angles and hydrogen-bond distances found for these secondary structure types in x-ray structures of peptides and proteins. For the simulation of VCD spectra, force field and intensity response tensors were obtained ab initio for the complete Ala-based peptides in vacuum, but constrained to the COSMO optimized torsional angles, due to limitations of the solvent model. Resultant spectral patterns reproduce well many aspects of the experimental spectra and capture the differences observed for these various helical types.     

Ab initio protein structure prediction using pathway models

Ab initio prediction is the challenging attempt to predict protein structures based only on sequence information and without using templates. It is often divided into two distinct sub-problems: (a) the scoring function that can distinguish native, or native-like structures, from non-native ones; and (b) the method of searching the conformational space. Currently, there is no reliable scoring function that can always drive a search to the native fold, and there is no general search method that can guarantee a significant sampling of near-natives. Pathway models combine the scoring function and the search. In this short review, we explore some of the ways pathway models are used in folding, in published works since 2001, and present a new pathway model, HMMSTR-CM, that uses a fragment library and a set of nucleation/propagation-based rules. The new method was used for ab initio predictions as part of CASP5. This work was presented at the Winter School in Bioinformatics, Bologna, Italy, 10-14 February 2003.     

Prediction of protein local structures and folding fragments based on building-block library

In recent years, protein structure prediction using local structure information has made great progress. In this study, a novel and effective method is developed to predict the local structure and the folding fragments of proteins. First, the proteins with known structures are split into fragments. Second, these fragments, represented by dihedrals, are clustered to produce the building blocks (BBs). Third, an efficient machine learning method is used to predict the local structures of proteins from sequence profiles. Finally, a bi-gram model, trained by an iterated algorithm, is introduced to simulate the interactions of these BBs. For test proteins, the building-block lattice is constructed, which contains all the folding fragments of the proteins. The local structures and the optimal fragments are then obtained by the dynamic programming algorithm. The experiment is performed on a subset of the PDB database with sequence identity less than 25%. The results show that the performance of the method is better than the method that uses only sequence information. When multiple paths are returned, the average classification accuracy of local structures is 72.27% and the average prediction accuracy of local structures is 67.72%, which is a significant improvement in comparison with previous studies. The method can predict not only the local structures but also the folding fragments of proteins. This work is helpful for the ab initio protein structure prediction and especially, the understanding of the folding process of proteins.     

Amino acid code of protein secondary structure

The calculation of protein three-dimensional structure from the amino acid sequence is a fundamental problem to be solved. This paper presents principles of the code theory of protein secondary structure, and their consequence--the amino acid code of protein secondary structure. The doublet code model of protein secondary structure, developed earlier by the author (Shestopalov, 1990), is part of this theory. The theory basis are: 1) the name secondary structure is assigned to the conformation, stabilized only by the nearest (intraresidual) and middle-range (at a distance no more than that between residues i and i + 5) interactions; 2) the secondary structure consists of regular (alpha-helical and beta-structural) and irregular (coil) segments; 3) the alpha-helices, beta-strands and coil segments are encoded, respectively, by residue pairs (i, i + 4), (i, i + 2), (i, i = 1), according to the numbers of residues per period, 3.6, 2, 1; 4) all such pairs in the amino acid sequence are codons for elementary structural elements, or structurons; 5) the codons are divided into 21 types depending on their strength, i.e. their encoding capability; 6) overlappings of structurons of one and the same structure generate the longer segments of this structure; 7) overlapping of structurons of different structures is forbidden, and therefore selection of codons is required, the codon selection is hierarchic; 8) the code theory of protein secondary structure generates six variants of the amino acid code of protein secondary structure. There are two possible kinds of model construction based on the theory: the physical one using physical properties of amino acid residues, and the statistical one using results of statistical analysis of a great body of structural data. Some evident consequences of the theory are: a) the theory can be used for calculating the secondary structure from the amino acid sequence as a partial solution of the problem of calculation of protein three-dimensional structure from the amino acid sequence, and the calculated secondary structure and codon strength distribution can be used for simulating the next step of protein folding; b) one can propose that the same secondary structures can be folded into different tertiary structures and, vice versa, different secondary structures can be folded into the same tertiary structures, provided codon distributions are considered also; c) codons can be considered as first elements of protein three-dimensional structure language.     

Protein structure prediction

Current methods developed for predicting protein structure are reviewed. The most widely used algorithms of Chou and Fasman and Garnier et al for predicting secondary structure are compared to the most recent ones including sequence similarity methods, neural network, pattern recognition or joint prediction methods. The best of these methods correctly predict 63-65% of the residues in the database with cross-validation for 3 conformations, helix, beta strand and coli with a standard deviation of 6-8% per protein. However, when a homologous protein is already in the database, the accuracy of prediction by the similarity peptide method of Levin and Garnier reaches about 90%. Some conclusions can be drawn on the mechanism of protein folding. As all the prediction methods only use the local sequence for prediction (+/- 8 residues maximum) one can infer that 65% of the conformation of a residue is dictated on average by the local sequence, the rest is brought by the folding. The best predicted proteins or peptide segments are those for which the folding has less effect on the conformation. Presently, prediction of tertiary structure is only of practical use when the structure of a homologous protein is already known. Amino acid alignment to define residues of equivalent spatial position is critical for modelling of the protein. We showed for serine proteases that secondary structure prediction can help to define a better alignment. Non-homologous segments of the polypeptide chain, such as loops, libraries of known loops and/or energy minimization with various force fields, are used without yet giving satisfactory solutions. An example of modelling by homology, aided by secondary structure prediction on 2 regulatory proteins, Fnr and FixK is presented.     

Accuracy of side-chain prediction upon near-native protein backbones generated by ab initio folding methods

The ab initio folding problem can be divided into two sequential tasks of approximately equal computational complexity: the generation of native-like backbone folds and the positioning of side chains upon these backbones. The prediction of side-chain conformation in this context is challenging, because at best only the near-native global fold of the protein is known. To test the effect of displacements in the protein backbones on side-chain prediction for folds generated ab initio, sets of near-native backbones (≤ 4 Å Cα RMS error) for four small proteins were generated by two methods. The steric environment surrounding each residue was probed by placing the side chains in the native conformation on each of these decoys, followed by torsion-space optimization to remove steric clashes on a rigid backbone. We observe that on average 40% of the χ1 angles were displaced by 40° or more, effectively setting the limits in accuracy for side-chain modeling under these conditions. Three different algorithms were subsequently used for prediction of side-chain conformation. The average prediction accuracy for the three methods was remarkably similar: 49% to 51% of the χ1 angles were predicted correctly overall (33% to 36% of the χ1+2 angles). Interestingly, when the inter-side-chain interactions were disregarded, the mean accuracy increased. A consensus approach is described, in which side-chain conformations are defined based on the most frequently predicted χ angles for a given method upon each set of near-native backbones. We find that consensus modeling, which de facto includes backbone flexibility, improves side-chain prediction: χ1 accuracy improved to 51–54% (36–42% of χ1+2). Implications of a consensus method for ab initio protein structure prediction are discussed. Proteins 33:204–217, 1998. © 1998 Wiley-Liss, Inc.     

Single proline residues can dictate the oxidative folding pathways of cysteine-rich peptides

The cysteine-rich N and C-terminal domains of minicollagen-1 from Hydra nematocysts fold with excesses of oxidized/reduced glutathione (10:1) into globular structures with distinct cystine frameworks despite their identical cysteine sequence pattern. An additional main difference is the cis conformation of a conserved proline residue in the N-terminal and the trans conformation of this residue in the C-terminal domain. Comparative analysis of the oxidative folding revealed for the C-terminal domain a fast and highly cooperative formation of a single disulfide isomer. Conversely, oxidation of the N-terminal domain proceeds mainly via an intermediate that results from the fast quasi-stochastic disulfide formation according to the proximity rule. The rate of conversion of the bead-like isomer into the globular end-product is largely dominated by the trans-to-cis isomerization of the critical proline residue as well assessed by its replacement with (4R)- and (4S)-fluoroproline known to exhibit distinct propensities for the trans and cis conformation, respectively. Independently, whether the trans or cis conformation is favored by these substitutions, both analogues retain sufficient sequence-encoded information to fold almost quantitatively into the identical cystine framework and thus spatial structure of the parent peptide with the critical proline residue as cis isomer, but at rates significantly lower for the (4R) than for the (4S)-fluoroproline analogue. Correspondingly, other sequence-encoded structural elements have to act as a driving force for these unidirectional folding pathways despite the rather simple sequence composition consisting only of aliphatic residues, some proline and only one aromatic residue (tyrosine) in the core parts of the C and N-terminal domains. The two cysteine-rich domains of minicollagen-1 may well represent ideal targets for ab initio structure calculations in order to learn more about the elementary information encoded in such primordial molecules.