Ergodicity and model quality in template‐restrained canonical and temperature/Hamiltonian replica exchange coarse‐grained molecular dynamics simulations of proteins

Molecular simulations restrained to single or multiple templates are commonly used in protein‐structure modeling. However, the restraints introduce additional barriers, thus impairing the ergodicity of simulations, which can affect the quality of the resulting models. In this work, the effect of restraint types and simulation schemes on ergodicity and model quality was investigated by performing template‐restrained canonical molecular dynamics (MD), multiplexed replica‐exchange molecular dynamics, and Hamiltonian replica exchange molecular dynamics (HREMD) simulations with the coarse‐grained UNRES force field on nine selected proteins, with pseudo‐harmonic log‐Gaussian (unbounded) or Lorentzian (bounded) restraint functions. The best ergodicity was exhibited by HREMD. It has been found that non‐ergodicity does not affect model quality if good templates are used to generate restraints. However, when poor‐quality restraints not covering the entire protein are used, the improved ergodicity of HREMD can lead to significantly improved protein models. © 2017 Wiley Periodicals, Inc.     

Protein structure prediction: combining de novo modeling with sparse experimental data

Routine structure prediction of new folds is still a challenging task for computational biology. The challenge is not only in the proper determination of overall fold but also in building models of acceptable resolution, useful for modeling the drug interactions and protein-protein complexes. In this work we propose and test a comprehensive approach to protein structure modeling supported by sparse, and relatively easy to obtain, experimental data. We focus on chemical shift-based restraints from NMR, although other sparse restraints could be easily included. In particular, we demonstrate that combining the typical NMR software with artificial intelligence-based prediction of secondary structure enhances significantly the accuracy of the restraints for molecular modeling. The computational procedure is based on the reduced representation approach implemented in the CABS modeling software, which proved to be a versatile tool for protein structure prediction during the CASP (CASP stands for critical assessment of techniques for protein structure prediction) experiments (see http://predictioncenter/CASP6/org). The method is successfully tested on a small set of representative globular proteins of different size and topology, including the two CASP6 targets, for which the required NMR data already exist. The method is implemented in a semi-automated pipeline applicable to a large scale structural annotation of genomic data. Here, we limit the computations to relatively small set. This enabled, without a loss of generality, a detailed discussion of various factors determining accuracy of the proposed approach to the protein structure prediction.     

Folding of proteins with an all-atom Go-model

The Go-like potential at a residual level has been successfully applied to the folding of proteins in many previous works. However, taking into consideration more detailed structural information in the atomic level, the definition of contacts used in these traditional Go-models may not be suitable for all-atom simulations. Here, in this work, we develop a rational definition of contacts considering the screening effect in the crowded intramolecular environment. In such a scheme, a large amount of screened atom pairs are excluded and the number of contacts is decreased compared to the case of the traditional definition. These contacts defined by such a new definition are compatible with the all-atom representation of protein structures. To verify the rationality of the new definition of contacts, the folding of proteins CI2 and SH3 is simulated by all-atom molecular dynamics simulations. A high folding cooperativity and good correlation of the simulated Phi-values with those obtained experimentally, especially for CI2, are found. This suggests that the all-atom Go-model is improved compared to the traditional Go-model. Based on the comparison of the Phi-values, the roles of side chains in the folding are discussed, and it is concluded that the side-chain structures are more important for local contacts in determining the transition state structures. Moreover, the relations between side chain and backbone orderings are also discussed.     

Completely automated, highly error-tolerant macromolecular structure determination from multidimensional nuclear overhauser enhancement spectra and chemical shift assignments

The major rate-limiting step in high-throughput NMR protein structure determination involves the calculation of a reliable initial fold, the elimination of incorrect nuclear Overhauser enhancement (NOE) assignments, and the resolution of NOE assignment ambiguities. We present a robust approach to automatically calculate structures with a backbone coordinate accuracy of 1.0-1.5 A from datasets in which as much as 80% of the long-range NOE information (i.e., between residues separated by more than five positions in the sequence) is incorrect. The current algorithm differs from previously published methods in that it has been expressly designed to ensure that the results from successive cycles are not biased by the global fold of structures generated in preceding cycles. Consequently, the method is highly error tolerant and is not easily funnelled down an incorrect path in either three-dimensional structure or NOE assignment space. The algorithm incorporates three main features: a linear energy function representation of the NOE restraints to allow maximization of the number of simultaneously satisfied restraints during the course of simulated annealing; a method for handling the presence of multiple possible assignments for each NOE cross-peak which avoids local minima by treating each possible assignment as if it were an independent restraint; and a probabilistic method to permit both inactivation and reactivation of all NOE restraints on the fly during the course of simulated annealing. NOE restraints are never removed permanently, thereby significantly reducing the likelihood of becoming trapped in a false minimum of NOE assignment space. The effectiveness of the algorithm is demonstrated using completely automatically peak-picked experimental NOE data from two proteins: interleukin-4 (136 residues) and cyanovirin-N (101 residues). The limits of the method are explored using simulated data on the 56-residue B1 domain of Streptococcal protein G.     

Refinement of NMR structures using implicit solvent and advanced sampling techniques

NMR biomolecular structure calculations exploit simulated annealing methods for conformational sampling and require a relatively high level of redundancy in the experimental restraints to determine quality three-dimensional structures. Recent advances in generalized Born (GB) implicit solvent models should make it possible to combine information from both experimental measurements and accurate empirical force fields to improve the quality of NMR-derived structures. In this paper, we study the influence of implicit solvent on the refinement of protein NMR structures and identify an optimal protocol of utilizing these improved force fields. To do so, we carry out structure refinement experiments for model proteins with published NMR structures using full NMR restraints and subsets of them. We also investigate the application of advanced sampling techniques to NMR structure refinement. Similar to the observations of Xia et al. (J.Biomol. NMR 2002, 22, 317-331), we find that the impact of implicit solvent is rather small when there is a sufficient number of experimental restraints (such as in the final stage of NMR structure determination), whether implicit solvent is used throughout the calculation or only in the final refinement step. The application of advanced sampling techniques also seems to have minimal impact in this case. However, when the experimental data are limited, we demonstrate that refinement with implicit solvent can substantially improve the quality of the structures. In particular, when combined with an advanced sampling technique, the replica exchange (REX) method, near-native structures can be rapidly moved toward the native basin. The REX method provides both enhanced sampling and automatic selection of the most native-like (lowest energy) structures. An optimal protocol based on our studies first generates an ensemble of initial structures that maximally satisfy the available experimental data with conventional NMR software using a simplified force field and then refines these structures with implicit solvent using the REX method. We systematically examine the reliability and efficacy of this protocol using four proteins of various sizes ranging from the 56-residue B1 domain of Streptococcal protein G to the 370-residue Maltose-binding protein. Significant improvement in the structures was observed in all cases when refinement was based on low-redundancy restraint data. The proposed protocol is anticipated to be particularly useful in early stages of NMR structure determination where a reliable estimate of the native fold from limited data can significantly expedite the overall process. This refinement procedure is also expected to be useful when redundant experimental data are not readily available, such as for large multidomain biomolecules and in solid-state NMR structure determination.     

Performance assessment of different constraining potentials in computational structure prediction for disulfide-bridged proteins

The presence of disulfide bonds in proteins has very important implications on the three-dimensional structure and folding of proteins. An adequate treatment of disulfide bonds in de-novo protein simulations is therefore very important. Here we present a computational study of a set of small disulfide-bridged proteins using an all-atom stochastic search approach and including various constraining potentials to describe the disulfide bonds. The proposed potentials can easily be implemented in any code based on all-atom force fields and employed in simulations to achieve an improved prediction of protein structure. Exploring different potential parameters and comparing the structures to those from unconstrained simulations and to experimental structures by means of a scoring function we demonstrate that the inclusion of constraining potentials improves the quality of final structures significantly. For some proteins (1KVG and 1PG1) the native conformation is visited only in simulations in presence of constraints. Overall, we found that the Morse potential has optimal performance, in particular for the β-sheet proteins.     

A GRID-derived water network stabilizes molecular dynamics computer simulations of a protease

Structural water molecules are crucial for the stability and function of proteins. Recently, we presented a molecular dynamics (MD) study on blood coagulation factor Xa (fXa) to investigate the effect of water molecules on the flexibility of the protein structure. We showed that neglecting important water positions at the outset of the simulation leads to severe structural distortions during the MD simulations: A stable trajectory was obtained with a water set that was derived from all 73 X-ray structures of the protein. However, for many proteins of interest, only limited structural data is available, which precludes the merging of information from many X-ray structures. Here, we show that an in silico assembled water network, derived from molecular interaction fields generated with the GRID program, is a viable alternative to X-ray data. MD simulations with the GRID water set show a significantly improved stability over alternative setups without water or the X-ray resolved water molecules in the starting structure. The performance is comparable to a water setup derived from a recently presented clustering approach.     

Methyl proton contacts obtained using heteronuclear through-bond transfers in solid-state NMR spectroscopy

A two-dimensional proton-mediated carbon-carbon correlation experiment that relies on through-bond heteronuclear magnetization transfers is demonstrated in the context of solid-state NMR of proteins. This new experiment, dubbed J-CHHC by analogy to the previously developed dipolar CHHC techniques, is shown to provide selective and sensitive correlations in the methyl region of 2D spectra of crystalline organic compounds. The method is then demonstrated on a microcrystalline sample of the dimeric protein Crh (2 x 10.4 kDa). A total of 34 new proton-proton contacts involving side-chain methyl groups were observed in the J-CHHC spectrum, which had not been observed with the conventional experiment. The contacts were then used as additional distance restraints for the 3D structure determination of this microcrystalline protein. Upon addition of these new distance restraints, which are in large part located in the hydrophobic core of the protein, the root-mean-square deviation with respect to the X-ray structure of the backbone atom coordinates of the 10 best conformers of the new ensemble of structures is reduced from 1.8 to 1.1 A.     

Precision of free energies calculated by molecular dynamics simulations of peptides in solution

Errors in free energies for molecular replacement and for conformation change of a small model peptide have been determined empirically by repeated simulations from different starting points. All calculations have been done using thermodynamic integration, in which the system's potential energy is coupled to a parameter λ, that is increased or decreased by a small amount at each step of the simulation. The effects of several factors that may alter the precision are evaluated. These factors include: the length of the simulation, the dependence of the potential energy on λ, the use of conformational restraints, and their magnitude and form. The methods used for restraint and conformational forcing are described in detail. The free energy change, calculated as the mean from several successive simulations with alternately increasing and decreasing λ, is found to be independent of the length of the simulations. As expected, longer simulations produce more precise results. The variation of the calculated free energies is found to consist of two parts, a random error and a systematic hysteresis, i.e., a dependence on the direction in which λ changes. The hysteresis varies as the inverse of the length of the simulation and the random error as the inverse square root The advantage of the use of a different (nonlinear) dependence of the attractive and repulsive parts of the nonbonded potential energy on the coupling parameter when “creating” particles in solution is found to be very large. This nonlinear coupling was found to be superior to the use of linear coupling and a nonlinear change of the coupling parameter with the simulation time. The hysteresis in conformational free energy calculations is found to increase markedly if too weak a forcing restraint is chosen. It is shown how to deconvolute the contribution of a torsional restraint from the dependence of the free energy on a torsion angle.     

Stereospecific assignments of protein NMR resonances based on the tertiary structure and 2D/3D NOE data

In many cases of protein structure determination by NMR a high-quality structure is required. An important contribution to structural precision is stereospecific assignment of magnetically nonequivalent prochiral methylene and methyl groups, eliminating the need for introducing pseudoatoms and pseudoatom corrections in distance restraint lists. Here, we introduce the stereospecific assignment program that uses the resonance assignment, a preliminary 3D structure and 2D and/or 3D nuclear Overhauser effect spectroscopy peak lists for stereospecific assignment. For each prochiral group the algorithm automatically calculates a score for the two different stereospecific assignment possibilities, taking into account the presence and intensity of the nuclear Overhauser effect (NOE) peaks that are expected from the local environment of each prochiral group (i.e., the close neighbors). The performance of the algorithm has been tested and used on NMR data of alpha-helical and beta-sheet proteins using homology models and/or X-ray structures. The program produced no erroneous stereospecific assignments provided the NOEs were carefully picked and the 3D model was sufficiently accurate. The set of NOE distance restraints produced by nmr2st using the results of the SSA module was superior in generating good-quality ensembles of NMR structures (low deviations from upper limits in conjunction with low root-mean-square-deviation values) in the first round of structure calculations. The program uses a novel approach that employs the entire 3D structure of the protein to obtain stereospecific assignment; it can be used to speed up the NMR structure refinement and to increase the quality of the final NMR ensemble even when no scalar or residual dipolar coupling information is available.     

Dipolar chemical shift correlation spectroscopy for homonuclear carbon distance measurements in proteins in the solid state: application to structure determination and refinement

High-resolution solid-state NMR spectroscopy has become a promising tool for protein structure determination. Here, we describe a new dipolar-chemical shift correlation experiment for the measurement of homonuclear 13C-13C distances in uniformly 13C,15N-labeled proteins and demonstrate its suitability for protein structure determination and refinement. The experiments were carried out on the beta1 immunoglobulin binding domain of protein G (GB1). Both intraresidue and interresidue distances between carbonyl atoms and atoms in the aliphatic side chains were collected using a three-dimensional chemical shift correlation spectroscopy experiment that uses homogeneously broadened rotational resonance recoupling for carbon mixing. A steady-state approximation for the polarization transfer function was employed in data analysis, and a total of 100 intramolecular distances were determined, all in the range 2.5-5.5 A. An additional 41 dipolar contacts were detected, but the corresponding distances could not be accurately quantified. Additional distance and torsional restraints were derived from the proton-driven spin diffusion measurements and from the chemical shift analysis, respectively. Using all these restraints, it was possible to refine the structure of GB1 to a root-mean square deviation of 0.8 A. The approach is of general applicability for peptides and small proteins and can be easily incorporated into a structure determination and refinement protocol.     

Solution structure of a peptide nucleic acid duplex from NMR data: features and limitations

This paper describes the results of a 1D and 2D NMR spectroscopy study of a palindromic 8-base pair PNA duplex GGCATGCC in H2O and H2O-D2O solutions. The (1)H NMR peaks have been assigned for most of the protons of the six central base pairs, as well as for several amide protons of the backbone. The resulting 36 interbase and base-backbone distance restraints were used together with Watson-Crick restraints to generate the PNA duplex structure in the course of 10 independent simulated annealing runs followed by restrained molecular dynamics (MD) simulations in explicit water. The resulting PNA structures correspond to a P-type helix with helical parameters close to those observed in the crystal structures of PNA. Based on the current limited number of restraints obtained from NMR spectra, alternative structures obtained by MD from starting PNA models based on DNA cannot be ruled out and are also discussed.     

Structure determination by restrained molecular dynamics using NMR pseudocontact shifts as experimentally determined constraints

The structure of a DNA octamer d(TTGGCCAA)(2) complexed to chromomycin-A(3) and a single divalent cobalt ion has been solved by using the pseudocontact shifts due to the unpaired electrons on the cobalt. A protocol was developed and critically evaluated for using the pseudocontact shifts in structure determination. The pseudocontact shifts were input as experimental restraints in molecular dynamics simulations with or without NOE constraints. Both the magnitude and orientation of the susceptibility anisotropy tensor required for the shift calculations were determined during the simulations by iterative refinement. The pseudocontact shifts could be used to define the structure to a very high precision and accuracy compared with a corresponding NOE-determined structure. Convergence was obtained from different starting structures and tensors. A structure determination using both NOE's and pseudocontact shifts revealed a general agreement between the two data sets. However, some evidence for a discrepancy between NOE's and pseudocontact shifts was observed in the backbone and terminal base pairs of the DNA. Violations in shift or NOE restraints remaining in the final structures were examined and may be a reflection of motional averaging of the constraints and evidence for flexibility. This work demonstrates that pseudocontact shifts are a powerful tool for NMR structure determination.     

Protein Folding with a Reduced Model and Inaccurate Short‐Range Restraints

Summary: A reduced high‐coordination lattice protein model and the Replica Exchange Monte Carlo sampling were employed in de novo folding simulations of a set of representative small proteins. Three distinct situations were analyzed. In the first series of simulations, the folding was controlled purely by the generic force field of the model. In the second, a bias was introduced towards the theoretically predicted secondary structure. Finally, we superimposed soft restraints towards the native‐like local conformation of the backbone. The short‐range restraints used in these simulations are based on approximate values of ϕ and ψ dihedral angles, which may simulate restraints derived from inaccurate experimental measurements. Incorporating such data into the reduced model required developing a procedure, which transforms the ϕ and ψ coordinates into coordinates of the protein alpha carbon trace. It has been shown that such limited data are sufficient for de novo determination of three‐dimensional structures of small and topologically not too complex proteins.

Protein folding based on secondary structure prediction and simulated torsion angles data.     

Determination of an ensemble of structures representing the denatured state of the bovine acyl-coenzyme a binding protein

The denatured state of a protein contains important information about the determinants of the folding process. By combining site-directed spin-labeling NMR experiments and restrained computer simulations, we have determined ensembles of conformations that represent the denatured state of the bovine acyl-coenzyme A binding protein (ACBP) at three different concentrations of guanidine hydrochloride. As the experimentally determined distance information corresponds to weighted averages over a broad ensemble of structures, we applied the experimental restraints to a system of noninteracting replicas of the protein by using a Monte Carlo sampling scheme. This procedure permits us to sample ensembles of conformations that are compatible with the experimental data and thus to obtain information regarding the distribution of structures in the denatured state. Our results show that the denatured state of ACBP is highly heterogeneous. The high sensitivity of the computational method that we present, however, enabled us to identify long-range interactions between two regions, located near the N- and C-termini, that include both native and non-native elements. The preferential formation of these contacts suggests that the sequence-dependent patterns of helical propensity and hydrophobicity are important determinants of the structure in the denatured state of ACBP.     

CABS‐NMR—De novo tool for rapid global fold determination from chemical shifts,residual dipolar couplings and sparse methyl‐methyl noes

Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low‐cost global protein fold determination. Here, we present CABS‐NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C‐Alpha‐Beta‐Side‐group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge‐based force field. Its versatile structure enables a variety of protein‐modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS‐NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low‐energy structures obtained from chemical shifts by CABS‐NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl‐methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post‐experiment processing of various kinds of NMR data or fast and low‐cost structural analysis in the still challenging field of new fold predictions. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Protein structure prediction aided by geometrical and probabilistic constraints

Database-assisted ab initio protein structure prediction methods have exhibited considerable promise in the recent past, with several implementations being successful in community-wide experiments (CASP). We have employed combinatorial optimization techniques toward solving the protein structure prediction problem. A Monte Carlo minimization algorithm has been employed on a constrained search space to identify minimum energy configurations. The search space is constrained by using radius of gyration cutoffs, the loop backbone dihedral probability distributions, and various secondary structure packing conformations. Simulations have been carried out on several sequences and 1000 conformations have been initially generated. Of these, 50 best candidates have then been selected as probable conformations. The search for the optimum has been simplified by incorporating various geometrical constraints on secondary structural elements using distance restraint potential functions. The advantages of the reported methodology are its simplicity, and modifiability to include other geometric and probabilistic restraints.     

The elastic net algorithm and protein structure prediction

Predicting protein structures from their amino acid sequences is a problem of global optimization. Global optima (native structures) are often sought using stochastic sampling methods such as Monte Carlo or molecular dynamics, but these methods are slow. In contrast, there are fast deterministic methods that find near-optimal solutions of well-known global optimization problems such as the traveling salesman problem (TSP). But fast TSP strategies have yet to be applied to protein folding, because of fundamental differences in the two types of problems. Here, we show how protein folding can be framed in terms of the TSP, to which we apply a variation of the Durbin-Willshaw elastic net optimization strategy. We illustrate using a simple model of proteins with database-derived statistical potentials and predicted secondary structure restraints. This optimization strategy can be applied to many different models and potential functions, and can readily incorporate experimental restraint information. It is also fast; with the simple model used here, the method finds structures that are within 5-6 A all-Calpha-atom RMSD of the known native structures for 40-mers in about 8 s on a PC; 100-mers take about 20 s. The computer time tau scales as tau approximately n, where n is the number of amino acids. This method may prove to be useful for structure refinement and prediction.     

Bioconjugation of Proteins with a Paramagnetic NMR and Fluorescent Tag

Site‐specific labeling of proteins with lanthanide ions offers great opportunities for investigating the structure, function, and dynamics of proteins by virtue of the unique properties of lanthanides. Lanthanide‐tagged proteins can be studied by NMR, X‐ray, fluorescence, and EPR spectroscopy. However, the rigidity of a lanthanide tag in labeling of proteins plays a key role in the determination of protein structures and interactions. Pseudocontact shift (PCS) and paramagnetic relaxation enhancement (PRE) are valuable long‐range structure restraints in structural‐biology NMR spectroscopy. Generation of these paramagnetic restraints generally relies on site‐specific tagging of the target proteins with paramagnetic species. To avoid nonspecific interaction between the target protein and paramagnetic tag and achieve reliable paramagnetic effects, the rigidity, stability, and size of lanthanide tag is highly important in paramagnetic labeling of proteins. Here 4′‐mercapto‐2,2′: 6′,2′′‐terpyridine‐6,6′′‐dicarboxylic acid (4MTDA) is introduced as a a rigid paramagnetic and fluorescent tag which can be site‐specifically attached to a protein by formation of a disulfide bond. 4MTDA can be readily immobilized by coordination of the protein side chain to the lanthanide ion. Large PCSs and RDCs were observed for 4MTDA‐tagged proteins in complexes with paramagnetic lanthanide ions. At an excitation wavelength of 340 nm, the complex formed by protein–4MTDA and Tb³⁺ produces high fluorescence with the main emission at 545 nm. These interesting features of 4MTDA make it a very promising tag that can be exploited in NMR, fluorescence, and EPR spectroscopic studies on protein structure, interaction, and dynamics.