Assembly of protein structure from sparse experimental data: An efficient Monte Carlo model

A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Cαs. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 Å from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 Å are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 Å. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints. Proteins 32:475–494, 1998. © 1998 Wiley-Liss, Inc.     

Testing a new Monte Carlo algorithm for protein folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.     

Lattice simulations of cotranslational folding of single domain proteins

We use lattice protein models and Monte Carlo simulations to study cotranslational folding of small single domain proteins. We show that the assembly of native structure begins during late extrusion stages, but final formation of native state occurs during de novo folding, when all residues are extruded. There are three main results in our study. First, for the sequences displaying two-state refolding mechanism de novo cotranslational folding pathway differs from that sampled in in vitro refolding. The change in folding pathways is due to partial assembly of native interactions during extrusion that results in different starting conditions for in vitro refolding and for de novo cotranslational folding. For small single domain proteins cotranslational folding is slower than in vitro refolding, but is generally fast enough to be completed before the release from a ribosome. Second, we found that until final stages of biosynthesis cotranslational folding is essentially equilibrium. This observation is explained by low stability of structured states for partially extruded chains. Finally, our data suggest that the proteins, which refold in vitro slowly via intermediates, complete their de novo folding after the release from a ribosome. Comparison of our lattice cotranslational simulations with recent experimental and computational studies is discussed.     

Monte carlo simulations of protein folding. II. Application to protein A,ROP, and crambin

The hierarchy of lattice Monte Carlo models described in the accompanying paper (Kolinski, A., Skolnick, J. Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Proteins 18:338–352, 1994) is applied to the simulation of protein folding and the prediction of 3-dimensional structure. Using sequence information alone, three proteins have been successfully folded: the B domain of staphylococcal protein A, a 120 residue, monomeric version of ROP dimer, and crambin. Starting from a random expanded conformation, the model proteins fold along relatively well-defined folding pathways. These involve a collection of early intermediates, which are followed by the final (and rate-determining) transition from compact intermediates closely resembling the molten globule state to the native-like state. The predicted structures are rather unique, with native-like packing of the side chains. The accuracy of the predicted native conformations is better than those obtained in previous folding simulations. The best (but by no means atypical) folds of protein A have a coordinate rms of 2.25 Å from the native Cα trace, and the best coordinate rms from crambin is 3.18 Å. For ROP monomer, the lowest coordinate rms from equivalent Cαs of ROP dimer is 3.65 Å. Thus, for two simple helical proteins and a small α/β protein, the ability to predict protein structure from sequence has been demonstrated. © 1994 John Wiley & Sons, Inc.     

Domains in folding of model proteins.

By means of Monte Carlo simulation, we investigated the equilibrium between folded and unfolded states of lattice model proteins. The amino acid sequences were designed to have pronounced energy minimum target conformations of different length and shape. For short fully compact (36-mer) proteins, the all-or-none transition from the unfolded state to the native state was observed. This was not always the case for longer proteins. Among 12 designed sequences with the native structure of a fully compact 48-mer, a simple all-or-none transition was observed in only three cases. For the other nine sequences, three states of behavior-the native, denatured, and intermediate states-were found. The contiguous part of the native structure (domain) was conserved in the intermediate state, whereas the remaining part was completely unfolded and structureless. These parts melted separately from each other.     

On the origin of the cooperativity of protein folding: Implications from model simulations

There is considerable experimental evidence that the cooperativity of protein folding resides in the transition from the molten globule to the native state. The objective of this study is to examine whether simplified models can reproduce this cooperativity and if so, to identify its origin. In particular, the thermodynamics of the conformational transition of a previously designed sequence (A. Kolinski, W. Galazka, and J. Skolnick, J. Chem. Phys. 103: 10286–10297, 1995), which adopts a very stable Greek-key β-barrel fold has been investigated using the entropy Monte Carlo sampling (ESMC) technique of Hao and Scheraga (M.-H. Hao and H.A. Scheraga, J. Phys. Chem. 98: 9882–9883, 1994). Here, in addition to the original potential, which includes one body and pair interactions between side chains, the force field has been supplemented by two types of multi-body potentials describing side chain interactions. These potentials facilitate the proteinlike pattern of side chain packing and consequently increase the cooperativity of the folding process. Those models that include an explicit cooperative side chain packing term exhibit a well-defined all-or-none transition from a denatured, random coil state to a high-density, well-defined, nativelike low-energy state. By contrast, models lacking such a term exhibit a conformational transition that is essentially continuous. Finally, an examination of the conformations at the free-energy barrier between the native and denatured states reveals that they contain a substantial amount of native-state secondary structure, about 50% of the native contacts, and have an average root mean square radius of gyration that is about 15% larger than native. © 1996 Wiley-Liss, Inc.     

Computer simulations aimed at structure prediction of supersecondary motifs in proteins

It is well established that protein structures are more conserved than protein sequences. One-third of all known protein structures can be classified into ten protein folds, which themselves are composed mainly of alpha-helical hairpin, beta hairpin, and betaalphabeta supersecondary structural elements. In this study, we explore the ability of a recent Monte Carlo-based procedure to generate the 3D structures of eight polypeptides that correspond to units of supersecondary structure and three-stranded antiparallel beta sheet. Starting from extended or misfolded compact conformations, all Monte Carlo simulations show significant success in predicting the native topology using a simplified chain representation and an energy model optimized on other structures. Preliminary results on model peptides from nucleotide binding proteins suggest that this simple protein folding model can help clarify the relation between sequence and topology.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

Configuration and validation of an analytical model predicting secondary neutron radiation in proton therapy using Monte Carlo simulations and experimental measurements

PurposeThis study focuses on the configuration and validation of an analytical model predicting leakage neutron doses in proton therapy.MethodsUsing Monte Carlo (MC) calculations, a facility-specific analytical model was built to reproduce out-of-field neutron doses while separately accounting for the contribution of intra-nuclear cascade, evaporation, epithermal and thermal neutrons. This model was first trained to reproduce in-water neutron absorbed doses and in-air neutron ambient dose equivalents, H*(10), calculated using MCNPX. Its capacity in predicting out-of-field doses at any position not involved in the training phase was also checked. The model was next expanded to enable a full 3D mapping of H*(10) inside the treatment room, tested in a clinically relevant configuration and finally consolidated with experimental measurements.ResultsFollowing the literature approach, the work first proved that it is possible to build a facility-specific analytical model that efficiently reproduces in-water neutron doses and in-air H*(10) values with a maximum difference less than 25%. In addition, the analytical model succeeded in predicting out-of-field neutron doses in the lateral and vertical direction. Testing the analytical model in clinical configurations proved the need to separate the contribution of internal and external neutrons. The impact of modulation width on stray neutrons was found to be easily adjustable while beam collimation remains a challenging issue. Finally, the model performance agreed with experimental measurements with satisfactory results considering measurement and simulation uncertainties.ConclusionAnalytical models represent a promising solution that substitutes for time-consuming MC calculations when assessing doses to healthy organs.     

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.     

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.     

Tertiary structure prediction of the KIX domain of CBP using Monte Carlo simulations driven by restraints derived from multiple sequence alignments

Using a recently developed protein folding algorithm, a prediction of the tertiary structure of the KIX domain of the CREB binding protein is described. The method incorporates predicted secondary and tertiary restraints derived from multiple sequence alignments in a reduced protein model whose conformational space is explored by Monte Carlo dynamics. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that was modified for the presence of predicted U-turns, i.e., regions where the chain reverses global direction. Tertiary restraints are obtained via a two-step process: First, seed side-chain contacts are identified from a correlated mutation analysis, and then, a threading-based algorithm expands the number of these seed contacts. Blind predictions indicate that the KIX domain is a putative three-helix bundle, although the chirality of the bundle could not be uniquely determined. The expected root-mean-square deviation for the correct chirality of the KIX domain is between 5.0 and 6.2 Å. This is to be compared with the estimate of 12.9 Å that would be expected by a random prediction, using the model of F. Cohen and M. Sternberg (J. Mol. Biol. 138:321–333, 1980). Proteins 30:287–294, 1998. © 1998 Wiley-Liss, Inc.     

Use of quantitative structure-property relationships to predict the folding ability of model proteins

We investigate the folding of a 125-bead heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice. Detailed study of a few sequences revealed a folding mechanism consisting of a rapid collapse followed by a slow search for a stable core that served as the transition state for folding to a near-native intermediate. Rearrangement from the intermediate to the native state slowed folding further because it required breaking native-like local structure between surface monomers so that those residues could condense onto the core. We demonstrate here the generality of this mechanism by a statistical analysis of a 200 sequence database using a method that employs a genetic algorithm to pick the sequence attributes that are most important for folding and an artificial neural network to derive the corresponding functional dependence of folding ability on the chosen sequence attributes [quantitative structure-property relationships (QSPRs)]. QSPRs that use three sequence attributes yielded substantially more accurate predictions than those that use only one. The results suggest that efficient search for the core is dependent on both the native state's overall stability and its amount of kinetically accessible, cooperative structure, whereas rearrangement from the intermediate is facilitated by destabilization of contacts between surface monomers. Implications for folding and design are discussed. Proteins 33:177–203, 1998. © 1998 Wiley-Liss, Inc.     

In silico profiling of tyrosine kinases binding specificity and drug resistance using Monte Carlo simulations with the ensembles of protein kinase crystal structures

The molecular basis of the tyrosine kinases binding specificity and drug resistance against cancer drugs Imatinib and Dasatinib is elucidated using Monte Carlo simulations of the inhibitor-receptor binding with the ensembles of protein kinase crystal structures. In silico proteomics analysis unravels mechanisms by which structural plasticity of the tyrosine kinases is linked with the conformational preferences of Imatinib and Dasatinib in achieving effective drug binding with a distinct spectrum of the tyrosine kinome. The differences in the inhibitor sensitivities to the ABL kinase mutants are rationalized based on variations in the binding free energy profiles with the conformational states of the ABL kinase. While Imatinib binding is highly sensitive to the activation state of the enzyme, the computed binding profile of Dasatinib is remarkably tolerant to the conformational state of ABL. A comparative analysis of the inhibitor binding profiles with the clinically important ABL kinase mutants has revealed an excellent agreement with the biochemical and proteomics data. We have found that conformational adaptability of the kinase inhibitors to structurally different conformational states of the tyrosine kinases may have pharmacological relevance in acquiring a specific array of potent activities and regulating a scope of the inhibitor resistance mutations. This study outlines a useful approach for understanding and predicting the molecular basis of the inhibitor sensitivity against potential kinase targets and drug resistance.     

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56?Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.     

Failures of inverse folding and threading with gapped alignment

To calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has some of the features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we show that even the given contact potential, which by definition is used to identify the folding sequences and their unique native conformations, cannot always correctly select which sequences will fold to a given structure. Second, we demonstrate that the given contact potential is not always able to favor the native alignment of a native sequence on its own native conformation over other gapped alignments of different folding sequences onto that same conformation. Because of these shortcomings, even in this simple model system in which all conformations and all native sequences are known and determined directly by the given potential, we must reexamine our expectations for empirical potentials used for inverse folding and gapped alignment on more realistic representations of proteins. © 1996 Wiley-Liss, Inc.     

Exhaustive enumeration of protein conformations using experimental restraints.

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of alpha-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1,000 conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.     

A pH-dependent variation in alpha-helix structure of the S-peptide of ribonuclease A studied by Monte Carlo simulated annealing.

Low-energy conformations of the S-peptide fragment (20 amino acid residues long) of ribonuclease A were studied by Monte Carlo simulated annealing. The obtained lowest-energy structures have alpha-helices with different size and location, depending distinctively on the ionizing states of acidic amino acid residues. The simulation started from completely random initial conformation and was performed without any bias toward a particular structure. The most conspicuous alpha-helices arose from the simulation when both Glu 9 and Asp 14 were assumed to be electrically neutral, whereas the resulting conformations became much less helical when Asp 14 rather than Glu 9 was allowed to have a negative charge. Together with experimental evidence that the alpha-helix in the S-peptide is most stable at pH 3.8, we consider the helix formation need the carboxyl group of Asp 14 to be electrically neutral in this weakly acidic condition. In contrast, a negative charge at Asp 14 appears to function in support of a view that this residue is crucial to helix termination owing to its possibility to form a salt bridge with His 12. These results indicate that the conformation of the S-peptide depends considerably on the ionizing state of Asp 14.