Improving the accuracy of protein stability predictions with multistate design using a variety of backbone ensembles

Multistate computational protein design (MSD) with backbone ensembles approximating conformational flexibility can predict higher quality sequences than single‐state design with a single fixed backbone. However, it is currently unclear what characteristics of backbone ensembles are required for the accurate prediction of protein sequence stability. In this study, we aimed to improve the accuracy of protein stability predictions made with MSD by using a variety of backbone ensembles to recapitulate the experimentally measured stability of 85 Streptococcal protein G domain β1 sequences. Ensembles tested here include an NMR ensemble as well as those generated by molecular dynamics (MD) simulations, by Backrub motions, and by PertMin, a new method that we developed involving the perturbation of atomic coordinates followed by energy minimization. MSD with the PertMin ensembles resulted in the most accurate predictions by providing the highest number of stable sequences in the top 25, and by correctly binning sequences as stable or unstable with the highest success rate (≈90%) and the lowest number of false positives. The performance of PertMin ensembles is due to the fact that their members closely resemble the input crystal structure and have low potential energy. Conversely, the NMR ensemble as well as those generated by MD simulations at 500 or 1000 K reduced prediction accuracy due to their low structural similarity to the crystal structure. The ensembles tested herein thus represent on‐ or off‐target models of the native protein fold and could be used in future studies to design for desired properties other than stability. Proteins 2014; 82:771–784. © 2013 Wiley Periodicals, Inc.     

Insights into equilibrium dynamics of proteins from comparison of NMR and X-ray data with computational predictions

For a representative set of 64 nonhomologous proteins, each containing a structure solved by NMR and X-ray crystallography, we analyzed the variations in atomic coordinates between NMR models, the temperature (B) factors measured by X-ray crystallography, and the fluctuation dynamics predicted by the Gaussian network model (GNM). The NMR and X-ray data exhibited a correlation of 0.49. The GNM results, on the other hand, yielded a correlation of 0.59 with X-ray data and a distinctively better correlation (0.75) with NMR data. The higher correlation between GNM and NMR data, compared to that between GNM and X-ray B factors, is shown to arise from the differences in the spectrum of modes accessible in solution and in the crystal environment. Mainly, large-amplitude motions sampled in solution are restricted, if not inaccessible, in the crystalline environment of X-rays. Combined GNM and NMR analysis emerges as a useful tool for assessing protein dynamics.     

Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: application to alpha-amylase inhibitor

The dynamics of alpha-amylase inhibitors has been investigated using molecular dynamics (MD) simulations and two analytical approaches, the Gaussian network model (GNM) and anisotropic network model (ANM). MD simulations use a full atomic approach with empirical force fields, while the analytical approaches are based on a coarse-grained single-site-per-residue model with a single-parameter harmonic potential between sufficiently close (r 相似文献   

Cooperative fluctuations of unliganded and substrate-bound HIV-1 protease: a structure-based analysis on a variety of conformations from crystallography and molecular dynamics simulations

The dynamics of HIV-1 protease, both in unliganded and substrate-bound forms have been analyzed by using an analytical method, Gaussian network model (GNM). The method is applied to different conformations accessible to the protein backbone in the native state, observed in crystal structures and snapshots from fully atomistic molecular dynamics (MD) simulation trajectories. The modes of motion obtained from GNM on different conformations of HIV-1 protease are conserved throughout the MD simulations. The flaps and 40's loop of the unliganded HIV-1 protease structure are identified as the most mobile regions. However, in the liganded structure these flaps lose mobility, and terminal regions of the monomers become more flexible. Analysis of the fast modes shows that residues important for stability are in the same regions of all the structures examined. Among these, Gly86 appears to be a key residue for stability. The contribution of residues in the active site region and flaps to the stability is more pronounced in the substrate-bound form than in the unliganded form. The convergence of modes in GNM to similar regions of HIV-1 protease, regardless of the conformation of the protein, supports the robustness of GNM as a potentially useful and predictive tool.     

X‐ray vs. NMR structures as templates for computational protein design

Certain protein‐design calculations involve using an experimentally determined high‐resolution structure as a template to identify new sequences that can adopt the same fold. This approach has led to the successful design of many novel, well‐folded, native‐like proteins. Although any atomic‐resolution structure can serve as a template in such calculations, most successful designs have used high‐resolution crystal structures. Because there are many proteins for which crystal structures are not available, it is of interest whether nuclear magnetic resonance (NMR) templates are also appropriate. We have analyzed differences between using X‐ray and NMR templates in side‐chain repacking and design calculations. We assembled a database of 29 proteins for which both a high‐resolution X‐ray structure and an ensemble of NMR structures are available. Using these pairs, we compared the rotamericity, χ₁‐angle recovery, and native‐sequence recovery of X‐ray and NMR templates. We carried out design using RosettaDesign on both types of templates, and compared the energies and packing qualities of the resulting structures. Overall, the X‐ray structures were better templates for use with Rosetta. However, for ～20% of proteins, a member of the reported NMR ensemble gave rise to designs with similar properties. Re‐evaluating RosettaDesign structures with other energy functions indicated much smaller differences between the two types of templates. Ultimately, experiments are required to confirm the utility of particular X‐ray and NMR templates. But our data suggest that the lack of a high‐resolution X‐ray structure should not preclude attempts at computational design if an NMR ensemble is available. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Calculation of protein ionization equilibria with conformational sampling: pK(a) of a model leucine zipper, GCN4 and barnase.

The use of conformational ensembles provided by nuclear magnetic resonance (NMR) experiments or generated by molecular dynamics (MD) simulations has been regarded as a useful approach to account for protein motions in the context of pK(a) calculations, yet the idea has been tested occasionally. This is the first report of systematic comparison of pK(a) estimates computed from long multiple MD simulations and NMR ensembles. As model systems, a synthetic leucine zipper, the naturally occurring coiled coil GCN4, and barnase were used. A variety of conformational averaging and titration curve-averaging techniques, or combination thereof, was adopted and/or modified to investigate the effect of extensive global conformational sampling on the accuracy of pK(a) calculations. Clustering of coordinates is proposed as an approach to reduce the vast diversity of MD ensembles to a few structures representative of the average electrostatic properties of the system in solution. Remarkable improvement of the accuracy of pK(a) predictions was achieved by the use of multiple MD simulations. By using multiple trajectories the absolute error in pK(a) predictions for the model leucine zipper was reduced to as low as approximately 0.25 pK(a) units. The validity, advantages, and limitations of explicit conformational sampling by MD, compared with the use of an average structure and a high internal protein dielectric value as means to improve the accuracy of pK(a) calculations, are discussed.     

Self‐assembling study of sarcolipin and its mutants in multiple molecular dynamic simulations

The Sarcolipin (SLN) is a single trans‐membrane protein that can self‐assembly to dimer and oligomer for playing importantphysiological function. In this work, we addressed the dimerization of wild type SLN (wSLN) and its mutants (mSLNs) – I17A and I20A, using both coarse‐grained (CG) and atomistic (AT) molecular dynamics (MD) simulations. Our results demonstrated that wSLN homodimer assembled as a left‐handed helical complex, while mSLNs heterodimers assembled as right‐handed complexes. Analysis of residue‐residue contacts map indicated that isoleucine (Ile)‐leucione (Leu) zipper domain played an important role in dimerization. The potential of mean force (PMF) demonstrated that wSLN homodimer was more stable than mSLNs heterodimers. Meanwhile, the mSLNs heterodimers preferred right‐handed rather than left‐handed helix. AT‐MD simulations for wSLN and mSLNs were also in line with CG‐MD simulations. These results provided the insights for understanding the mechanisms of SLNs self‐assembling. Proteins 2017; 85:1065–1077. © 2017 Wiley Periodicals, Inc.     

Structure,dynamics, and interactions of jacalin. Insights from molecular dynamics simulations examined in conjunction with results of X‐ray studies

Molecular dynamics simulations have been carried out on all the jacalin–carbohydrate complexes of known structure, models of unliganded molecules derived from the complexes and also models of relevant complexes where X‐ray structures are not available. Results of the simulations and the available crystal structures involving jacalin permit delineation of the relatively rigid and flexible regions of the molecule and the dynamical variability of the hydrogen bonds involved in stabilizing the structure. Local flexibility appears to be related to solvent accessibility. Hydrogen bonds involving side chains and water bridges involving buried water molecules appear to be important in the stabilization of loop structures. The lectin–carbohydrate interactions observed in crystal structures, the average parameters pertaining to them derived from simulations, energetic contribution of the stacking residue estimated from quantum mechanical calculations, and the scatter of the locations of carbohydrate and carbohydrate‐binding residues are consistent with the known thermodynamic parameters of jacalin–carbohydrate interactions. The simulations, along with X‐ray results, provide a fuller picture of carbohydrate binding by jacalin than provided by crystallographic analysis alone. The simulations confirm that in the unliganded structures water molecules tend to occupy the positions occupied by carbohydrate oxygens in the lectin–carbohydrate complexes. Population distributions in simulations of the free lectin, the ligands, and the complexes indicate a combination of conformational selection and induced fit. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

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.     

Coarse‐grained and all‐atom modeling of structural states and transitions in hemoglobin

Hemoglobin (Hb), an oxygen‐binding protein composed of four subunits (α1, α2, β1, and β2), is a well‐known example of allosteric proteins that are capable of cooperative ligand binding. Despite decades of studies, the structural basis of its cooperativity remains controversial. In this study, we have integrated coarse‐grained (CG) modeling, all‐atom simulation, and structural data from X‐ray crystallography and wide‐angle X‐ray scattering (WAXS), aiming to probe dynamic properties of the two structural states of Hb (T and R state) and the transitions between them. First, by analyzing the WAXS data of unliganded and liganded Hb, we have found that the structural ensemble of T or R state is dominated by one crystal structure of Hb with small contributions from other crystal structures of Hb. Second, we have used normal mode analysis to identify two distinct quaternary rotations between the α1β1 and α2β2 dimer, which drive the transitions between T and R state. We have also identified the hot‐spot residues whose mutations are predicted to greatly change these quaternary motions. Third, we have generated a CG transition pathway between T and R state, which predicts a clear order of quaternary and tertiary changes involving α and β subunits in Hb. Fourth, we have used the accelerated molecular dynamics to perform an all‐atom simulation starting from the T state of Hb, and we have observed a transition toward the R state of Hb. Further analysis of crystal structural data and the all‐atom simulation trajectory has corroborated the order of quaternary and tertiary changes predicted by CG modeling. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Folding and stability of helical bundle proteins from coarse‐grained models

We develop a coarse‐grained model where solvent is considered implicitly, electrostatics are included as short‐range interactions, and side‐chains are coarse‐grained to a single bead. The model depends on three main parameters: hydrophobic, electrostatic, and side‐chain hydrogen bond strength. The parameters are determined by considering three level of approximations and characterizing the folding for three selected proteins (training set). Nine additional proteins (containing up to 126 residues) as well as mutated versions (test set) are folded with the given parameters. In all folding simulations, the initial state is a random coil configuration. Besides the native state, some proteins fold into an additional state differing in the topology (structure of the helical bundle). We discuss the stability of the native states, and compare the dynamics of our model to all atom molecular dynamics simulations as well as some general properties on the interactions governing folding dynamics. Proteins 2013; 81:1200–1211. © 2013 Wiley Periodicals, Inc.     

Crystal contact-free conformation of an intrinsically flexible loop in protein crystal: Tim21 as the case study

BackgroundIn protein crystals, flexible loops are frequently deformed by crystal contacts, whereas in solution, the large motions result in the poor convergence of such flexible loops in NMR structure determinations. We need an experimental technique to characterize the structural and dynamic properties of intrinsically flexible loops of protein molecules.MethodsWe designed an intended crystal contact-free space (CCFS) in protein crystals, and arranged the flexible loop of interest in the CCFS. The yeast Tim 21 protein was chosen as the model protein, because one of the loops (loop 2) is distorted by crystal contacts in the conventional crystal.ResultsYeast Tim21 was fused to the MBP protein by a rigid α-helical linker. The space created between the two proteins was used as the CCFS. The linker length provides adjustable freedom to arrange loop 2 in the CCFS. We re-determined the NMR structure of yeast Tim21, and conducted MD simulations for comparison. Multidimensional scaling was used to visualize the conformational similarity of loop 2. We found that the crystal contact-free conformation of loop 2 is located close to the center of the ensembles of the loop 2 conformations in the NMR and MD structures.ConclusionsLoop 2 of yeast Tim21 in the CCFS adopts a representative, dominant conformation in solution.General significanceNo single powerful technique is available for the characterization of flexible structures in protein molecules. NMR analyses and MD simulations provide useful, but incomplete information. CCFS crystallography offers a third route to this goal.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Identification of specificity and promiscuity of PDZ domain interactions through their dynamic behavior

PDZ domains (PDZs), the most common interaction domain proteins, play critical roles in many cellular processes. PDZs perform their job by binding specific protein partners. However, they are very promiscuous, binding to more than one protein, yet selective at the same time. We examined the binding related dynamics of various PDZs to have insight about their specificity and promiscuity. We used full atomic normal mode analysis and a modified coarse‐grained elastic network model to compute the binding related dynamics. In the latter model, we introduced specificity for each single parameter constant and included the solvation effect implicitly. The modified model, referred to as specific‐Gaussian Network Model (s‐GNM), highlights some interesting differences in the conformational changes of PDZs upon binding to Class I or Class II type peptides. By clustering the residue fluctuation profiles of PDZs, we have shown: (i) binding selectivities can be discriminated from their dynamics, and (ii) the dynamics of different structural regions play critical roles for Class I and Class II specificity. s‐GNM is further tested on a dual‐specific PDZ which showed only Class I specificity when a point mutation exists on the βA‐βB loop. We observe that the binding dynamics change consistently in the mutated and wild type structures. In addition, we found that the binding induced fluctuation profiles can be used to discriminate the binding selectivity of homolog structures. These results indicate that s‐GNM can be a powerful method to study the changes in binding selectivities for mutant or homolog PDZs. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

NMR-assisted protein structure prediction with MELDxMD

We describe the performance of MELD-accelerated molecular dynamics (MELDxMD) in determining protein structures in the NMR-data-assisted category in CASP13. Seeded from web server predictions, MELDxMD was found best in the NMR category, over 17 targets, outperforming the next-best groups by a factor of ~4 in z-score. MELDxMD gives ensembles, not single structures; succeeds on a 326-mer, near the current upper limit for NMR structures; and predicts structures that match experimental residual dipolar couplings even though the only NMR-derived data used in the simulations was NOE-based ambiguous atom–atom contacts and backbone dihedrals. MELD can use noisy and ambiguous experimental information to reduce the MD search space. We believe MELDxMD is a promising method for determining protein structures from NMR data.     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

An automated approach to network features of protein structure ensembles

Network theory applied to protein structures provides insights into numerous problems of biological relevance. The explosion in structural data available from PDB and simulations establishes a need to introduce a standalone‐efficient program that assembles network concepts/parameters under one hood in an automated manner. Herein, we discuss the development/application of an exhaustive, user‐friendly, standalone program package named PSN‐Ensemble, which can handle structural ensembles generated through molecular dynamics (MD) simulation/NMR studies or from multiple X‐ray structures. The novelty in network construction lies in the explicit consideration of side‐chain interactions among amino acids. The program evaluates network parameters dealing with topological organization and long‐range allosteric communication. The introduction of a flexible weighing scheme in terms of residue pairwise cross‐correlation/interaction energy in PSN‐Ensemble brings in dynamical/chemical knowledge into the network representation. Also, the results are mapped on a graphical display of the structure, allowing an easy access of network analysis to a general biological community. The potential of PSN‐Ensemble toward examining structural ensemble is exemplified using MD trajectories of an ubiquitin‐conjugating enzyme (UbcH5b). Furthermore, insights derived from network parameters evaluated using PSN‐Ensemble for single‐static structures of active/inactive states of β2‐adrenergic receptor and the ternary tRNA complexes of tyrosyl tRNA synthetases (from organisms across kingdoms) are discussed. PSN‐Ensemble is freely available from http://vishgraph.mbu.iisc.ernet.in/PSN‐Ensemble/psn_index.html .