Bridging between normal mode analysis and elastic network models

Normal mode analysis (NMA) has been a powerful tool for studying protein dynamics. Elastic network models (ENM), through their simplicity, have made normal mode computations accessible to a much broader research community and for many more biomolecular systems. The drawback of ENMs, however, is that they are less accurate than NMA. In this work, through steps of simplification that starts with NMA and ends with ENMs we build a tight connection between NMA and ENMs. In the process of bridging between the two, we have also discovered several high‐quality simplified models. Our best simplified model has a mean correlation with the original NMA that is as high as 0.88. In addition, the model is force‐field independent and does not require energy minimization, and thus can be applied directly to experimental structures. Another benefit of drawing the connection is a clearer understanding why ENMs work well and how it can be further improved. We discovered that can be greatly enhanced by including an additional torsional term and a geometry term. Proteins 2014; 82:2157–2168. © 2014 Wiley Periodicals, Inc.     

Analysis of peptides and proteins in their binding to GroEL

The GroEL–GroES is an essential molecular chaperon system that assists protein folding in cell. Binding of various substrate proteins to GroEL is one of the key aspects in GroEL‐assisted protein folding. Small peptides may mimic segments of the substrate proteins in contact with GroEL and allow detailed structural analysis of the interactions. A model peptide SBP has been shown to bind to a region in GroEL that is important for binding of substrate proteins. Here, we investigated whether the observed GroEL–SBP interaction represented those of GroEL–substrate proteins, and whether SBP was able to mimic various aspects of substrate proteins in GroE‐assisted protein folding cycle. We found that SBP competed with substrate proteins, including α‐lactalbumin, rhodanese, and malate dehydrogenase, in binding to GroEL. SBP stimulated GroEL ATP hydrolysis rate in a manner similar to that of α‐lactalbumin. SBP did not prevent GroES from binding to GroEL, and GroES association reduced the ATPase rates of GroEL/SBP and GroEL/α‐lactalbumin to a comparable extent. Binding of both SBP and α‐lactalbumin to apo GroEL was dominated by hydrophobic interaction. Interestingly, association of α‐lactalbumin to GroEL/GroES was thermodynamically distinct from that to GroEL with reduced affinity and decreased contribution from hydrophobic interaction. However, SBP did not display such differential binding behaviors to apo GroEL and GroEL/GroES, likely due to the lack of a contiguous polypeptide chain that links all of the bound peptide fragments. Nevertheless, studies using peptides provide valuable information on the nature of GroEL–substrate protein interaction, which is central to understand the mechanism of GroEL‐assisted protein folding. Copyright © 2010 European Peptide Society and John Wiley & Sons, Ltd.     

Harmonic and anharmonic aspects in the dynamics of BPTI: a normal mode analysis and principal component analysis.

A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distribution of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Mimicking the action of GroEL in molecular dynamics simulations: application to the refinement of protein structures

Bacterial chaperonin, GroEL, together with its co-chaperonin, GroES, facilitates the folding of a variety of polypeptides. Experiments suggest that GroEL stimulates protein folding by multiple cycles of binding and release. Misfolded proteins first bind to an exposed hydrophobic surface on GroEL. GroES then encapsulates the substrate and triggers its release into the central cavity of the GroEL/ES complex for folding. In this work, we investigate the possibility to facilitate protein folding in molecular dynamics simulations by mimicking the effects of GroEL/ES namely, repeated binding and release, together with spatial confinement. During the binding stage, the (metastable) partially folded proteins are allowed to attach spontaneously to a hydrophobic surface within the simulation box. This destabilizes the structures, which are then transferred into a spatially confined cavity for folding. The approach has been tested by attempting to refine protein structural models generated using the ROSETTA procedure for ab initio structure prediction. Dramatic improvements in regard to the deviation of protein models from the corresponding experimental structures were observed. The results suggest that the primary effects of the GroEL/ES system can be mimicked in a simple coarse-grained manner and be used to facilitate protein folding in molecular dynamics simulations. Furthermore, the results support the assumption that the spatial confinement in GroEL/ES assists the folding of encapsulated proteins.     

Principal component analysis for protein folding dynamics

Protein folding is considered here by studying the dynamics of the folding of the triple β-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.     

Annealing function of GroEL: structural and bioinformatic analysis

The Escherichia coli chaperonin system, GroEL–GroES, facilitates folding of substrate proteins (SPs) that are otherwise destined to aggregate. The iterative annealing mechanism suggests that the allostery-driven GroEL transitions leading to changes in the microenvironment of the SP constitutes the annealing action of chaperonins. To describe the molecular basis for the changes in the nature of SP–GroEL interactions we use the crystal structures of GroEL (T state), GroEL–ATP (R state) and the GroEL–GroES–(ADP)₇ (R″ state) complex to determine the residue-specific changes in the accessible surface area and the number of tertiary contacts as a result of the T→R→R″ transitions. We find large changes in the accessible area in many residues in the apical domain, but relatively smaller changes are associated with residues in the equatorial domain. In the course of the T→R transition the microenvironment of the SP changes which suggests that GroEL is an annealing machine even without GroES. This is reflected in the exposure of Glu386 which loses six contacts in the T→R transition. We also evaluate the conservation of residues that participate in the various chaperonin functions. Multiple sequence alignments and chemical sequence entropy calculations reveal that, to a large extent, only the chemical identities and not the residues themselves important for the nominal functions (peptide binding, nucleotide binding, GroES and substrate protein release) are strongly conserved. Using chemical sequence entropy, which is computed by classifying aminoacids into four types (hydrophobic, polar, positively charged and negatively charged) we make several new predictions that are relevant for peptide binding and annealing function of GroEL. We identify a number of conserved peptide binding sites in the apical domain which coincide with those found in the 1.7 Å crystal structure of ‘mini-chaperone’ complexed with the N-terminal tag. Correlated mutations in the HSP60 family, that might control allostery in GroEL, are also strongly conserved. Most importantly, we find that charged solvent-exposed residues in the T state (Lys 226, Glu 252 and Asp 253) are strongly conserved. This leads to the prediction that mutating these residues, that control the annealing function of the SP, can decrease the efficacy of the chaperonin function.     

Comparison of intrinsic dynamics of cytochrome p450 proteins using normal mode analysis

Cytochrome P450 enzymes are hemeproteins that catalyze the monooxygenation of a wide‐range of structurally diverse substrates of endogenous and exogenous origin. These heme monooxygenases receive electrons from NADH/NADPH via electron transfer proteins. The cytochrome P450 enzymes, which constitute a diverse superfamily of more than 8,700 proteins, share a common tertiary fold but < 25% sequence identity. Based on their electron transfer protein partner, cytochrome P450 proteins are classified into six broad classes. Traditional methods of protein classification are based on the canonical paradigm that attributes proteins’ function to their three‐dimensional structure, which is determined by their primary structure that is the amino acid sequence. It is increasingly recognized that protein dynamics play an important role in molecular recognition and catalytic activity. As the mobility of a protein is an intrinsic property that is encrypted in its primary structure, we examined if different classes of cytochrome P450 enzymes display any unique patterns of intrinsic mobility. Normal mode analysis was performed to characterize the intrinsic dynamics of five classes of cytochrome P450 proteins. The present study revealed that cytochrome P450 enzymes share a strong dynamic similarity (root mean squared inner product > 55% and Bhattacharyya coefficient > 80%), despite the low sequence identity (< 25%) and sequence similarity (< 50%) across the cytochrome P450 superfamily. Noticeable differences in C_α atom fluctuations of structural elements responsible for substrate binding were noticed. These differences in residue fluctuations might be crucial for substrate selectivity in these enzymes.     

A kinetic analysis of the nucleotide-induced allosteric transitions in a single-ring mutant of GroEL

The function of GroE requires a complex system of allosteric communication driven by protein-nucleotide interactions. These rearrangements couple the binding and hydrolysis of ATP to an overall reaction cycle in which substrate proteins are bound, encapsulated and released. Positive cooperativity with respect to ATP binding occurs within one heptameric ring of GroEL, while negative cooperativity between the two rings generates an inherent asymmetry between the two rings. A previously engineered mutant of GroEL in which the ring-ring contacts are broken gives rise to a single-ring version of the wild-type chaperonin (SR1). We have studied the kinetics of the nucleotide-induced conformational changes in a single-tryptophan variant of SR1 (Y485W-SR1) and compared the resulting data with those we reported previously for the double-ring, single-tryptophan variant of wild-type GroEL (Y485W-GroEL). Remarkably, the parting of the rings does not have a major effect on the conformational changes occurring within the heptameric ring and a kinetic model is presented to describe the sequence of structural rearrangements that occur upon ATP binding to the SR1 molecule. The observation that both the ATP-induced and ADP-induced conformational rearrangements occur more rapidly in the SR1 than they do in wild-type GroEL, indicates that intra-ring conformational changes in the double-ring structure must overcome conformational constraints provided by the presence of the second ring. Lastly, the data presented here imply a role for inter-ring allostery in controlling the dissociation-association behaviour of the GroES co-protein in the overall reaction cycle.     

Identification and characterization of a GroEL homologue in Rhodobacter sphaeroides

A protein closely related to the Escherichia coli GroEL protein has been isolated from Rhodobacter sphaeroides. Native and SDS-polyacrylamide gel electrophoresis of this protein have shown that it is present in the cell as a multimeric complex of Mr 670,000 which is composed of a monomer of Mr 58,000. Antisera raised against the Mr 58,000 polypeptide have been shown to cross-react with GroEL and the alpha subunit of the pea plastid chaperonin. The N-terminal amino acid sequence of the Mr 58,000 polypeptide is identical to that of GroEL at 15 of 19 residues and is also closely related to the alpha subunit of the pea plastid chaperonin, though less so to the beta subunit.     

Probing structurally altered and aggregated states of therapeutically relevant proteins using GroEL coupled to bio-layer interferometry

The ability of a GroEL-based bio-layer interferometry (BLI) assay to detect structurally altered and/or aggregated species of pharmaceutically relevant proteins is demonstrated. Assay development included optimizing biotinylated-GroEL immobilization to streptavidin biosensors, combined with biophysical and activity measurements showing native and biotinylated GroEL are both stable and active. First, acidic fibroblast growth factor (FGF-1) was incubated under conditions known to promote (40°C) and inhibit (heparin addition) molten globule formation. Heat exposed (40°C) FGF-1 exhibited binding to GroEL-biosensors, which was significantly diminished in the presence of heparin. Second, a polyclonal human IgG solution containing 6–8% non-native dimer showed an increase in higher molecular weight aggregates upon heating by size exclusion chromatography (SEC). The poly IgG solution displayed binding to GroEL-biosensors initially with progressively increased binding upon heating. Enriched preparations of the IgG dimers or monomers showed significant binding to GroEL-biosensors. Finally, a thermally treated IgG1 monoclonal antibody (mAb) solution also demonstrated increased GroEL-biosensor binding, but with different kinetics. The bound complexes could be partially to fully dissociated after ATP addition (i.e., specific GroEL binding) depending on the protein, environmental stress, and the assay’s experimental conditions. Transmission electron microscopy (TEM) images of GroEL-mAb complexes, released from the biosensor, also confirmed interaction of bound complexes at the GroEL binding site with heat-stressed mAb. Results indicate that the GroEL-biosensor-BLI method can detect conformationally altered and/or early aggregation states of proteins, and may potentially be useful as a rapid, stability-indicating biosensor assay for monitoring the structural integrity and physical stability of therapeutic protein candidates.     

Denaturation and reassembly of chaperonin GroEL studied by solution X-ray scattering

We measured the denaturation and reassembly of Escherichia coli chaperonin GroEL using small-angle solution X-ray scattering, which is a powerful technique for studying the overall structure and assembly of a protein in solution. The results of the urea-induced unfolding transition show that GroEL partially dissociates in the presence of more than 2 M urea, cooperatively unfolds at around 3 M urea, and is in a monomeric random coil-like unfolded structure at more than 3.2 M urea. Attempted refolding of the unfolded GroEL monomer by a simple dilution procedure is not successful, leading to formation of aggregates. However, the presence of ammonium sulfate and MgADP allows the fully unfolded GroEL to refold into a structure with the same hydrodynamic dimension, within experimental error, as that of the native GroEL. Moreover, the X-ray scattering profiles of the GroEL thus refolded and the native GroEL are coincident with each other, showing that the refolded GroEL has the same structure and the molecular mass as the native GroEL. These results demonstrate that the fully unfolded GroEL monomer can refold and reassemble into the native tetradecameric structure in the presence of ammonium sulfate and MgADP without ATP hydrolysis and preexisting chaperones. Therefore, GroEL can, in principle, fold and assemble into the native structure according to the intrinsic characteristic of its polypeptide chain, although preexisting GroEL would be important when the GroEL folding takes place under in vivo conditions, in order to avoid misfolding and aggregation.     

The N terminus of the head protein of T4 bacteriophage directs proteins to the GroEL chaperonin

The head protein of T4 bacteriophage requires the GroEL chaperonin for its insertion into a growing T4 head. Hundreds of thousands of copies of this protein must pass through the chaperonin in a limited time later in infection, indicating that the protein must use GroEL very efficiently and may contain sequences that bind tightly to GroEL. We show that green fluorescent protein (GFP) fused to the N terminus of the head protein can fold at temperatures higher than those at which the GFP protein can fold well by itself. We present evidence that this folding is promoted by the strong binding of N-terminal head protein sequences to GroEL. This binding is so strong that some fusion proteins can apparently deplete the cell of the GroEL needed for other cellular functions, altering the cellular membranes and slowing growth.     

Isolation and characterisation of mutants of GroEL that are fully functional as single rings

A key aspect of the reaction mechanism for the molecular chaperone GroEL is the transmission of an allosteric signal between the two rings of the GroEL complex. Thus, the single-ring mutant SR1 is unable to act as a chaperone as it cannot release bound substrate or GroES. We used a simple selection procedure to identify mutants of SR1 that restored chaperone activity in vivo. A large number of single amino acid changes, mapping at diverse positions throughout the protein, enabled SR1 to regain its ability to act as a chaperone while remaining as a single ring. In vivo assays were used to identify the proteins that had regained maximal activity. In some cases, no difference could be detected between strains expressing wild-type GroEL and those expressing the mutated proteins. Three of the most active proteins where the mutations were in distinct parts of the protein were purified to homogeneity and characterised in vitro. All were capable of acting efficiently as chaperones for two different GroES-dependent substrates. All three proteins bound nucleotide as effectively as did GroEL, but the binding of GroES in the presence of ATP or ADP was reduced significantly relative to the wild-type. These active single rings should provide a useful tool for studying the nature of the allosteric changes that occur in the GroEL reaction cycle.     

Principal component analysis applied to bacterial cell behaviour in the presence of organic solvents

The behaviour of cells of Rhodococcus erythropolis DCL14, Xanthobacter Py2, Arthrobacter simplex and Mycobacterium sp. NRRL B-3805, in biphasic systems containing different organic solvents was evaluated and compared. The data, obtained mainly by fluorescence microscopy and image analysis, was interpreted using principal components analysis (PCA). With this technique, the variability of the data could be summarised in 7 components, representing 75.8% of the variance of the data. Over a third of the variance could be explained by the first two principal components which represent solvent toxicity. Apparently this is the major factor influencing cell behaviour in an organic:aqueous system. However, factors such as substrate concentration, cell adaptation ability (resulting in morphological changes and aggregation or separation of cells) and membrane composition (specific to each strain) also play an important role in cell resistance to solvent toxicity. The results regarding cell shape indicate that loss of viability occurs, in the tested bacterial strains, after incorporation of molecules of solvent in the cellular membrane. This should result in an increase in membrane fluidity, and thus, in an alteration of cell shape. The ability to form “self-defence” clusters was observed to be different amongst the four strains. X. Py2 showed, in general, a low tendency to form aggregates under the tested conditions; A. simplex and R. erythropolis aggregated mainly in the presence of low log P solvents; and Mycobacterium. sp. cells showed a high ability to aggregate.     

Principal component analysis applied to bacterial cell behaviour in the presence of organic solvents

The behaviour of cells of Rhodococcus erythropolis DCL14, Xanthobacter Py2, Arthrobacter simplex and Mycobacterium sp. NRRL B-3805, in biphasic systems containing different organic solvents was evaluated and compared. The data, obtained mainly by fluorescence microscopy and image analysis, was interpreted using principal components analysis (PCA). With this technique, the variability of the data could be summarised in 7 components, representing 75.8% of the variance of the data. Over a third of the variance could be explained by the first two principal components which represent solvent toxicity. Apparently this is the major factor influencing cell behaviour in an organic:aqueous system. However, factors such as substrate concentration, cell adaptation ability (resulting in morphological changes and aggregation or separation of cells) and membrane composition (specific to each strain) also play an important role in cell resistance to solvent toxicity. The results regarding cell shape indicate that loss of viability occurs, in the tested bacterial strains, after incorporation of molecules of solvent in the cellular membrane. This should result in an increase in membrane fluidity, and thus, in an alteration of cell shape. The ability to form “self-defence” clusters was observed to be different amongst the four strains. X. Py2 showed, in general, a low tendency to form aggregates under the tested conditions; A. simplex and R. erythropolis aggregated mainly in the presence of low log P solvents; and Mycobacterium. sp. cells showed a high ability to aggregate.     

Enzyme specificity under dynamic control II: Principal component analysis of α-lytic protease using global and local solvent boundary conditions

The contributions of conformational dynamics to substrate specificity have been examined by the application of principal component analysis to molecular dynamics trajectories of alpha-lytic protease. The wild-type alpha-lytic protease is highly specific for substrates with small hydrophobic side chains at the specificity pocket, while the Met190-->Ala binding pocket mutant has a much broader specificity, actively hydrolyzing substrates ranging from Ala to Phe. Based on a combination of multiconformation analysis of cryo-X-ray crystallographic data, solution nuclear magnetic resonance (NMR), and normal mode calculations, we had hypothesized that the large alteration in specificity of the mutant enzyme is mainly attributable to changes in the dynamic movement of the two walls of the specificity pocket. To test this hypothesis, we performed a principal component analysis using 1-nanosecond molecular dynamics simulations using either a global or local solvent boundary condition. The results of this analysis strongly support our hypothesis and verify the results previously obtained by in vacuo normal mode analysis. We found that the walls of the wild-type substrate binding pocket move in tandem with one another, causing the pocket size to remain fixed so that only small substrates are recognized. In contrast, the M190A mutant shows uncoupled movement of the binding pocket walls, allowing the pocket to sample both smaller and larger sizes, which appears to be the cause of the observed broad specificity. The results suggest that the protein dynamics of alpha-lytic protease may play a significant role in defining the patterns of substrate specificity. As shown here, concerted local movements within proteins can be efficiently analyzed through a combination of principal component analysis and molecular dynamics trajectories using a local solvent boundary condition to reduce computational time and matrix size.     

Probing the "annealing" mechanism of GroEL minichaperone using molecular dynamics simulations

Although the intact chaperonin machinery is needed to rescue natural substrate proteins (SPs) under non-permissive conditions the "minichaperone" alone, containing only the isolated apical domain of GroEL, can assist folding of a certain class of proteins. To understand the annealing function of the minichaperone, we have carried out molecular dynamics simulations in the NPT ensemble totaling 300ns for four systems; namely, the isolated strongly binding peptide (SBP), the minichaperone, and the SBP and a weakly binding peptide (WBP) in complex with the minichaperone. The SBP, which is structureless in isolation, adopts a beta-hairpin conformation in complex with the minichaperone suggesting that favorable non-specific interactions of the SPs confined to helices H and I of the apical domains can induce local secondary structures. Comparison of the dynamical fluctuations of the apo and the liganded forms of the minichaperone shows that the stability (needed for SP capture) involves favorable hydrophobic interactions and hydrogen bond network formation between the SBP and WBP, and helices H and I. The release of the SP, which is required for the annealing action, involves water-mediated interactions of the charged residues at the ends of H and I helices. The simulation results are consistent with a transient binding release (TBR) model for the annealing action of the minichaperone. According to the TBR model, SP annealing occurs in two stages. In the first stage the SP is captured by the apical domain. This is followed by SP release (by thermal fluctuations) that places it in a different region of the energy landscape from which it can partition rapidly to the native state with probability Phi or be trapped in another misfolded state. The process of binding and release can result in enhancement of the native state yield. The TBR model suggests "that any cofactor that can repeatedly bind and release SPs can be effective in assisting protein folding." By comparing the structures of the non-chaperone alpha-casein (which has no sequence similarity with the apical domain) and the minichaperone and the hydrophobicity profiles we show that alpha-casein has a pair of helices that have similar sequence and structural profiles as H and I. Based on this comparison we identify residues that stabilize (destabilize) alpha-casein-protein complexes. This suggests that alpha-casein assists folding by the TBR mechanism.