Automated use of mutagenesis data in structure prediction

In the absence of experimental structural determination, numerous methods are available to indirectly predict or probe the structure of a target molecule. Genetic modification of a protein sequence is a powerful tool for identifying key residues involved in binding reactions or protein stability. Mutagenesis data is usually incorporated into the modeling process either through manual inspection of model compatibility with empirical data, or through the generation of geometric constraints linking sensitive residues to a binding interface. We present an approach derived from statistical studies of lattice models for introducing mutation information directly into the fitness score. The approach takes into account the phenotype of mutation (neutral or disruptive) and calculates the energy for a given structure over an ensemble of sequences. The structure prediction procedure searches for the optimal conformation where neutral sequences either have no impact or improve stability and disruptive sequences reduce stability relative to wild type. We examine three types of sequence ensembles: information from saturation mutagenesis, scanning mutagenesis, and homologous proteins. Incorporating multiple sequences into a statistical ensemble serves to energetically separate the native state and misfolded structures. As a result, the prediction of structure with a poor force field is sufficiently enhanced by mutational information to improve accuracy. Furthermore, by separating misfolded conformations from the target score, the ensemble energy serves to speed up conformational search algorithms such as Monte Carlo-based methods.     

A new method for building protein conformations from sequence alignments with homologues of known structure

We describe a largely automatic procedure for building protein structures from sequence alignments with homologues of known structure. This procedure uses simple rules by which multiple sequence alignments can be translated into distance and chirality constraints, which are then used as input for distance geometry calculations. By this means one obtains an ensemble of conformations for the unknown structure that are compatible with the rules employed, and the differences among these conformations provide an indication of the reliability of the structure prediction. The overall approach is demonstrated here by applying it to several Kazal-type trypsin inhibitors, for which experimentally determined structures are available. On the basis of our experience with these test problems, we have further predicted the conformation of the human pancreatic secretory trypsin inhibitor, for which no experimentally determined structure is presently available.     

New strategies for the determination of macromolecular structure in solution

Non-crystallographic approaches to the determination of protein structure must solve the problem of insufficient and low information content experimental data. Most successful methods augment experimentation with theoretical constraints (for example, potential energy functions or optimization error metrics). We believe it is important to separate the contributions of experimentation and theory in the construction of protein structure. The PROTEAN system defines protein topology on the basis of experimental data alone. Its performance on three data sets, derived from the lac-repressor headpiece of E. coli, sperm whale myoglobin, and domain 1 of bacteriophage T4 lysozyme, indicates that there may be families of related conformations that are consistent with the experimental data. These conformations provide insight into the strengths and weaknesses in the data sets. They also provide a set of structures with which to begin theoretical refinements. We outline here a strategy which maintains a clear distinction between refinements based on theory and those based on experiment, and thus allows a careful analysis of the properties of such refinement methods.     

Folding of the villin headpiece subdomain from random structures. Analysis of the charge distribution as a function of pH

The structure of the 36 residue villin headpiece subdomain is investigated with the electrostatically driven Monte Carlo method. The ECEPP/3 (Empirical Conformational Energy Program for Peptides) force field, plus two different continuum solvation models, were used to describe the conformational energy of the chain with both blocked and unblocked N and C termini. A statistical analysis of an ensemble of ab initio generated conformations was carried out, based on a comparison with a set of ten native-like structures derived from published experimental data, by using rigid geometry and NMR-derived constraints obtained at pH 3.7. The ten native-like structures satisfy the NMR-derived constraints. The whole ensemble of conformations of the terminally unblocked villin headpiece sub-domain, generated by using ECEPP/3 with a continuum solvation model, were subsequently evaluated at pH 3.7 with a potential function that includes ECEPP/3 combined with a fast multigrid boundary element method. At pH 3.7, the lowest-energy conformation found during the conformational search satisfies approximately 70% of both the distance and the dihedral-angle constraints, and possesses the characteristic packing of three phenylalanine residues that constitute the main part of the hydrophobic core of the molecule. On the other hand, computations at pH 3.7 and pH 7.0 for the ten native-like structures satisfying the NMR-derived constraints indicate a substantial change in the charge distribution for each type of amino acid residue with the change in pH. The results of this study provide a basis to understand the effect of the interactions, such as hydrophobicity, charge-charge interaction and solvent polarization, on the stability of this small alpha-helical protein.     

NMR-pseudoenergy approach to the solution structure of acyl carrier protein

A method for protein structure determination from two-dimensional NMR cross-relaxation data is presented and explored by using short amino acid segments from acyl carrier protein as a test case. The method is based on a molecular mechanics program and incorporates NMR distance constraints in the form of a pseudoenergy term that accurately reflects the distance-dependent precision of NMR cross-relaxation data. When it is used in an indiscriminant fashion, the method has a tendency to produce structures representing local energy minima near starting structures, rather than structures representing a global energy minimum. However, stepwise inclusion of energy terms, beginning with a function heavily weighted by backbone distance constraints, appears to simplify the potential energy surface to a point where convergence to a common backbone structure from a variety of starting structures is possible. In the case of the segment from residues 3 to 15 in acyl carrier protein, a nearly perfect alpha-helix is produced starting with a linear chain, an alpha-helical chain, or a chain having residues with alternating linear and alpha-helical backbone torsional angles. In the case of the segment from residues 26 to 36 a structure having a right-handed loop is produced.     

Relationship between protein structure and geometrical constraints.

We evaluate to what extent the structure of proteins can be deduced from incomplete knowledge of disulfide bridges, surface assignments, secondary structure assignments, and additional distance constraints. A cost function taking such constraints into account was used to obtain protein structures using a simple minimization algorithm. For small proteins, the approximate structure could be obtained using one additional distance constraint for each amino acid in the protein. We also studied the effect of using predicted secondary structure and surface assignments. The constraints used in this approach typically may be obtained from low-resolution experimental data. When using a cost function based on distances, half of the resulting structures will be mirrored, because the resulting structure and its mirror image will have the same cost. The secondary structure assignments were therefore divided into chirality constraints and distance constraints. Here we report that the problem of mirrored structures, in some cases, can be solved by using a chirality term in the cost function.     

Optimal mutation sites for PRE data collection and membrane protein structure prediction

Nuclear magnetic resonance paramagnetic relaxation enhancement (PRE) measures long-range distances to isotopically labeled residues, providing useful constraints for protein structure prediction. The method usually requires labor-intensive conjugation of nitroxide labels to multiple locations on the protein, one at a time. Here a computational procedure, based on protein sequence and simple secondary structure models, is presented to facilitate optimal placement of a minimum number of labels needed to determine the correct topology of?a helical transmembrane protein. Tests on DsbB (four helices) using just one label lead to correct topology predictions in four of five cases, with the predicted structures <6 ? to the native structure. Benchmark results using simulated PRE data show that we can generally predict the correct topology for five and six to seven helices using two and three labels, respectively, with an average success rate of 76% and structures of similar precision. The results show promise in facilitating experimentally constrained structure prediction of membrane proteins.     

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.     

Rapid sampling of local minima in protein energy surface and effective reduction through a multi-objective filter

Background

Many problems in protein modeling require obtaining a discrete representation of the protein conformational space as an ensemble of conformations. In ab-initio structure prediction, in particular, where the goal is to predict the native structure of a protein chain given its amino-acid sequence, the ensemble needs to satisfy energetic constraints. Given the thermodynamic hypothesis, an effective ensemble contains low-energy conformations which are similar to the native structure. The high-dimensionality of the conformational space and the ruggedness of the underlying energy surface currently make it very difficult to obtain such an ensemble. Recent studies have proposed that Basin Hopping is a promising probabilistic search framework to obtain a discrete representation of the protein energy surface in terms of local minima. Basin Hopping performs a series of structural perturbations followed by energy minimizations with the goal of hopping between nearby energy minima. This approach has been shown to be effective in obtaining conformations near the native structure for small systems. Recent work by us has extended this framework to larger systems through employment of the molecular fragment replacement technique, resulting in rapid sampling of large ensembles.

Methods

This paper investigates the algorithmic components in Basin Hopping to both understand and control their effect on the sampling of near-native minima. Realizing that such an ensemble is reduced before further refinement in full ab-initio protocols, we take an additional step and analyze the quality of the ensemble retained by ensemble reduction techniques. We propose a novel multi-objective technique based on the Pareto front to filter the ensemble of sampled local minima.

Results and conclusions

We show that controlling the magnitude of the perturbation allows directly controlling the distance between consecutively-sampled local minima and, in turn, steering the exploration towards conformations near the native structure. For the minimization step, we show that the addition of Metropolis Monte Carlo-based minimization is no more effective than a simple greedy search. Finally, we show that the size of the ensemble of sampled local minima can be effectively and efficiently reduced by a multi-objective filter to obtain a simpler representation of the probed energy surface.

     

Exploring the dynamic information content of a protein NMR structure: Comparison of a molecular dynamics simulation with the NMR and X‐ray structures of Escherichia coli ribonuclease HI

The multiconformer nature of solution nuclear magnetic resonance (NMR) structures of proteins results from the effects of intramolecular dynamics, spin diffusion and an uneven distribution of structural restraints throughout the molecule. A delineation of the former from the latter two contributions is attempted in this work for an ensemble of 15 NMR structures of the protein Escherichia coli ribonuclease HI (RNase HI). Exploration of the dynamic information content of the NMR ensemble is carried out through correlation with data from two crystal structures and a 1.7‐ns molecular dynamics (MD) trajectory of RNase HI in explicit solvent. Assessment of the consistency of the crystal and mean MD structures with nuclear Overhauser effect (NOE) data showed that the NMR ensemble is overall more compatible with the high‐resolution (1.48 Å) crystal structure than with either the lower‐resolution (2.05 Å) crystal structure or the MD simulation. Furthermore, the NMR ensemble is found to span more conformational space than the MD simulation for both the backbone and the sidechains of RNase HI. Nonetheless, the backbone conformational variability of both the NMR ensemble and the simulation is especially consistent with NMR relaxation measurements of two loop regions that are putative sites of substrate recognition. Plausible side‐chain dynamic information is extracted from the NMR ensemble on the basis of (i) rotamericity and syn‐pentane character of variable torsion angles, (ii) comparison of the magnitude of atomic mean‐square fluctuations (msf) with those deduced from crystallographic thermal factors, and (iii) comparison of torsion angle conformational behavior in the NMR ensemble and the simulation. Several heterogeneous torsion angles, while adopting non‐rotameric/syn‐pentane conformations in the NMR ensemble, exist in a unique conformation in the simulation and display low X‐ray thermal factors. These torsions are identified as sites whose variability is likely to be an artifact of the NMR structure determination procedure. A number of other torsions show a close correspondence between the conformations sampled in the NMR and MD ensembles, as well as significant correlations among crystallographic thermal factors and atomic msf calculated from the NMR ensemble and the simulation. These results indicate that a significant amount of dynamic information is contained in the NMR ensemble. The relevance of the present findings for the biological function of RNase HI, protein recognition studies, and previous investigations of the motional content of protein NMR structures are discussed. Proteins 1999;36:87–110. © 1999 Wiley‐Liss, Inc.     

Multiple helical conformations of the helix‐turn‐helix region revealed by NOE‐restrained MD simulations of tryptophan aporepressor,TrpR

The nature of flexibility in the helix‐turn‐helix region of E. coli trp aporepressor has been unexplained for many years. The original ensemble of nuclear magnetic resonance (NMR structures showed apparent disorder, but chemical shift and relaxation measurements indicated a helical region. Nuclear Overhauser effect (NOE) data for a temperature‐sensitive mutant showed more helical character in its helix‐turn‐helix region, but nevertheless also led to an apparently disordered ensemble. However, conventional NMR structure determination methods require all structures in the ensemble to be consistent with every NOE simultaneously. This work uses an alternative approach in which some structures of the ensemble are allowed to violate some NOEs to permit modeling of multiple conformational states that are in dynamic equilibrium. Newly measured NOE data for wild‐type aporepressor are used as time‐averaged distance restraints in molecular dynamics simulations to generate an ensemble of helical conformations that is more consistent with the observed NMR data than the apparent disorder in the previously reported NMR structures. The results indicate the presence of alternating helical conformations that provide a better explanation for the flexibility of the helix‐turn‐helix region of trp aporepressor. Structures representing these conformations have been deposited with PDB ID: 5TM0. Proteins 2017; 85:731–740. © 2016 Wiley Periodicals, Inc.     

Identification and removal of nitroxide spin label contaminant: impact on PRE studies of α-helical membrane proteins in detergent

NMR paramagnetic relaxation enhancement (PRE) provides long‐range distance constraints (～15–25 Å) that can be critical to determining overall protein topology, especially where long‐range NOE information is unavailable such as in the case of larger proteins that require deuteration. However, several challenges currently limit the use of NMR PRE for α‐helical membrane proteins. One challenge is the nonspecific association of the nitroxide spin label to the protein‐detergent complex that can result in spurious PRE derived distance restraints. The effect of the nitroxide spin label contaminant is evaluated and quantified and a robust method for the removal of the contaminant is provided to advance the application of PRE restraints to membrane protein NMR structure determination.     

Fast gap‐free enumeration of conformations and sequences for protein design

Despite significant successes in structure‐based computational protein design in recent years, protein design algorithms must be improved to increase the biological accuracy of new designs. Protein design algorithms search through an exponential number of protein conformations, protein ensembles, and amino acid sequences in an attempt to find globally optimal structures with a desired biological function. To improve the biological accuracy of protein designs, it is necessary to increase both the amount of protein flexibility allowed during the search and the overall size of the design, while guaranteeing that the lowest‐energy structures and sequences are found. DEE/A*‐based algorithms are the most prevalent provable algorithms in the field of protein design and can provably enumerate a gap‐free list of low‐energy protein conformations, which is necessary for ensemble‐based algorithms that predict protein binding. We present two classes of algorithmic improvements to the A* algorithm that greatly increase the efficiency of A*. First, we analyze the effect of ordering the expansion of mutable residue positions within the A* tree and present a dynamic residue ordering that reduces the number of A* nodes that must be visited during the search. Second, we propose new methods to improve the conformational bounds used to estimate the energies of partial conformations during the A* search. The residue ordering techniques and improved bounds can be combined for additional increases in A* efficiency. Our enhancements enable all A*‐based methods to more fully search protein conformation space, which will ultimately improve the accuracy of complex biomedically relevant designs. Proteins 2015; 83:1859–1877. © 2015 Wiley Periodicals, Inc.     

Rapid generation of a representative ensemble of N-glycan conformations

Glycosylated proteins are ubiquitous components of extracellular matrices and cellular surfaces where their oligosaccharide moieties are implicated in a wide range of cell-cell and cell-matrix recognition events. Glycans constitute highly flexible molecules. Only a small number of glycan X-ray structures is available for which sufficient electron density for an entire oligosaccharide chain has been observed. An unambiguous structure determination based on NMR-derived geometric constraints alone is often not possible. Time consuming computational approaches such as Monte Carlo calculations and molecular dynamics simulations have been widely used to explore the conformational space accessible to complex carbohydrates. The generation of a comprehensive data base for N-glycan fragments based on long time molecular dynamics simulations is presented. The fragments are chosen in such a way that the effects of branched N-glycan structures are taken into account. The prediction database constitutes the basis of a procedure to generate a complete set of all possible conformations for a given N-glycan. The constructed conformations are ranked according to their energy content. The resulting conformations are in reasonable agreement with experimental data. A web interface has been established (http://www.dkfz.de/spec/glydict/), which enables to input any N-glycan of interest and to receive an ensemble of generated conformations within a few minutes.     

A coarse-grained protein force field for folding and structure prediction

We have revisited the protein coarse-grained optimized potential for efficient structure prediction (OPEP). The training and validation sets consist of 13 and 16 protein targets. Because optimization depends on details of how the ensemble of decoys is sampled, trial conformations are generated by molecular dynamics, threading, greedy, and Monte Carlo simulations, or taken from publicly available databases. The OPEP parameters are varied by a genetic algorithm using a scoring function which requires that the native structure has the lowest energy, and the native-like structures have energy higher than the native structure but lower than the remote conformations. Overall, we find that OPEP correctly identifies 24 native or native-like states for 29 targets and has very similar capability to the all-atom discrete optimized protein energy model (DOPE), found recently to outperform five currently used energy models.     

Improved strategies for the determination of protein structures from NMR data: the solution structure of acyl carrier protein

The hybrid method that combines the early stages of a distance geometry program with simulated annealing in the presence of NMR constraints was optimized to obtain structures fully consistent with the observed NMR data. This was achieved by using more restrictive bounds of the NOE constraints than those usually used in the literature and by grouping the NOEs into classes dependent on the quality of the experimental NOE data. The 'floating' stereospecific assignment introduced at the simulated annealing stage of the calculations further improved the definition of the local conformation. An improved sampling and convergence property of the hybrid method was obtained by means of fitting the substructure obtained from the distance geometry program to different conformations. Compared to the standard hybrid methods, this procedure gave superior structures for a 77 amino acid protein, acyl carrier protein from Escherichia coli.     

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for ¹⁵N relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.     

Distance geometry and related methods for protein structure determination from NMR data

Computational tools have been developed in the last few years, to allow a direct determination of protein structures from NMR data. Numerical calculations with simulated and experimental NMR constraints for distances and torsional angles show that data sets available with present NMR techniques carry enough information to determine reliably the global fold of a small protein. The maximum size of a protein for which the direct method can be applied is not limited by the computational tools but rather by the resolution of the two-dimensional spectra. A general estimate of the maximum size would be a molecular weight of about 10,000 (Markley et al. 1984), but parts of larger proteins might be accessible with the method. Effort for improvement of the NMR structures should be concentrated more on the local conformation rather than the global features. The r.m.s. D values for variations of the polypeptide backbone fold are on the order of 1.5-2 A for several of the studied proteins, indicating that the global structure is well determined by the present NMR data and their interpretation. The local structures are sometimes rather poor, with standard deviations for the backbone torsion angles of about 50 degrees. Possible improvements would be stereospecific resonance assignments of individual methylene protons and individual assignments of the methyl groups of the branched side-chains. Accurate estimates of the short-range NOE distance constraints by calibrating the distance constraints, including segmental flexibility effects, and combined use of distance geometry, energy minimization and molecular dynamics calculations, are further tools for improving the structures.     

Selective refinement and selection of near‐native models in protein structure prediction

In recent years in silico protein structure prediction reached a level where fully automated servers can generate large pools of near‐native structures. However, the identification and further refinement of the best structures from the pool of models remain problematic. To address these issues, we have developed (i) a target‐specific selective refinement (SR) protocol; and (ii) molecular dynamics (MD) simulation based ranking (SMDR) method. In SR the all‐atom refinement of structures is accomplished via the Rosetta Relax protocol, subject to specific constraints determined by the size and complexity of the target. The best‐refined models are selected with SMDR by testing their relative stability against gradual heating through all‐atom MD simulations. Through extensive testing we have found that Mufold‐MD, our fully automated protein structure prediction server updated with the SR and SMDR modules consistently outperformed its previous versions. Proteins 2015; 83:1823–1835. © 2015 Wiley Periodicals, Inc.