Conformational changes in the chaperonin GroEL: new insights into the allosteric mechanism

Protein Multiple Conformation Prediction Using Multi-Objective Evolution Algorithm

The breakthrough of AlphaFold2 and the publication of AlphaFold DB represent a significant advance in the field of predicting static protein structures. However, AlphaFold2 models tend to represent a single static structure, and multiple-conformation prediction remains a challenge. In this work, we proposed a method named MultiSFold, which uses a distance-based multi-objective evolutionary algorithm to predict multiple conformations. To begin, multiple energy landscapes are constructed using different competing constraints generated by deep learning. Subsequently, an iterative modal exploration and exploitation strategy is designed to sample conformations, incorporating multi-objective optimization, geometric optimization and structural similarity clustering. Finally, the final population is generated using a loop-specific sampling strategy to adjust the spatial orientations. MultiSFold was evaluated against state-of-the-art methods using a benchmark set containing 80 protein targets, each characterized by two representative conformational states. Based on the proposed metric, MultiSFold achieves a remarkable success ratio of 56.25% in predicting multiple conformations, while AlphaFold2 only achieves 10.00%, which may indicate that conformational sampling combined with knowledge gained through deep learning has the potential to generate conformations spanning the range between different conformational states. In addition, MultiSFold was tested on 244 human proteins with low structural accuracy in AlphaFold DB to test whether it could further improve the accuracy of static structures. The experimental results demonstrate the performance of MultiSFold, with a TM-score better than that of AlphaFold2 by 2.97% and RoseTTAFold by 7.72%. The online server is at http://zhanglab-bioinf.com/MultiSFold .

Comparative Natural History of Visual Function From Patients With Biallelic Variants in BBS1 and BBS10

Purpose

The purpose of this study was to compare the natural history of visual function change in cohorts of patients affected with retinal degeneration due to biallelic variants in Bardet-Biedl syndrome genes: BBS1 and BBS10.

Methods

Patients were recruited from nine academic centers from six countries (Belgium, Canada, France, New Zealand, Switzerland, and the United States). Inclusion criteria were: (1) female or male patients with a clinical diagnosis of retinal dystrophy, (2) biallelic disease-causing variants in BBS1 or BBS10, and (3) measures of visual function for at least one visit. Retrospective data collected included genotypes, age, onset of symptoms, and best corrected visual acuity (VA). When possible, data on refractive error, fundus images and autofluorescence (FAF), optical coherence tomography (OCT), Goldmann kinetic perimetry (VF), electroretinography (ERG), and the systemic phenotype were collected.

Results

Sixty-seven individuals had variants in BBS1 (n = 38; 20 female patients and 18 male patients); or BBS10 (n = 29; 14 female patients and 15 male patients). Missense variants were the most common type of variants for patients with BBS1, whereas frameshift variants were most common for BBS10. When ERGs were recordable, rod-cone dystrophy (RCD) was observed in 82% (23/28) of patients with BBS1 and 73% (8/11) of patients with BBS10; cone-rod dystrophy (CORD) was seen in 18% of patients with BBS1 only, and cone dystrophy (COD) was only seen in 3 patients with BBS10 (27%). ERGs were nondetectable earlier in patients with BBS10 than in patients with BBS1. Similarly, VA and VF declined more rapidly in patients with BBS10 compared to patients with BBS1.

Conclusions

Retinal degeneration appears earlier and is more severe in BBS10 cases as compared to those with BBS1 variants. The course of change of visual function appears to relate to genetic subtypes of BBS.

Analyses of displacements resulting from a point mutation in proteins

The effects of a single residue substitution on the protein backbone are frequently quite small and there are many other potential sources of structural variation for protein. We present here a methodology considering different sources of distortions in order to isolate the very effect of the mutation. To validate our methodology, we consider a well-studied family with many single mutants: the human lysozyme. Most of the perturbations are expected to be at the very localisation of the mutation, but in many cases the effects are propagated at long range. We show that the distances between the mutated residue and the 5% most disturbed residues exponentially decreases. One third of the affected residues are in direct contact with the mutated position; the remaining two thirds are potential allosteric effects. We confirm the reliability of the residues identified as significantly perturbed by comparing our results to experimental studies. We confirm with the present method all the previously identified perturbations. This study shows that mutations have long-range impact on protein backbone that can be detected, although the displacement of the affected atoms is small.

Stability of the chaperonin system GroEL-GroES under extreme environmental conditions

The chaperonin system GroEL-GroES is present in all kingdoms of life and rescues proteins from improper folding and aggregation upon internal and external stress conditions, including high temperatures and pressures. Here, we set out to explore the thermo- and piezostability of GroEL, GroES and the GroEL-GroES complex in the presence of cosolvents, nucleotides and salts employing quantitative FTIR spectroscopy and small-angle X-ray scattering. Owing to its high biological relevance and lack of data, our focus was especially on the effect of pressure on the chaperonin system. The experimental results reveal that the GroEL-GroES complex is remarkably temperature stable with an unfolding temperature beyond 70 °C, which can still be slightly increased by compatible cosolutes like TMAO. Conversely, the pressure stability of GroEL and hence the GroEL-GroES complex is rather limited and much less than that of monomeric proteins. Whereas GroES is pressure stable up to ∼5 kbar, GroEl and the GroEl-GroES complex undergo minor structural changes already beyond 1 kbar, which can be attributed to a dissociation-induced conformational drift. Quite unexpectedly, no significant unfolding of GroEL is observed even up to 10 kbar, however, i.e., the subunits themselves are very pressure stable. As for the physiological relevance, the structural integrity of the chaperonin system is retained in a relatively narrow pressure range, from about 1 to 1000 bar, which is just the pressure range encountered by life on Earth.

The Dynamic Behavior of the P2X4 Ion Channel in the Closed Conformation

We present the results of a detailed molecular dynamics study of the closed form of the P2X₄ receptor. The fluctuations observed in the simulations were compared with the changes that occur in the transition from the closed to the open structure. To get further insight on the opening mechanism, the actual displacements were decomposed into interchain motions and intrachain deformations. This analysis revealed that the iris-like expansion of the transmembrane helices mainly results from interchain motions that already take place in the closed conformation. However, these movements cannot reach the amplitude required for the opening of the channel because they are impeded by interactions occurring around the ATP binding pocket. This suggests that the union of ATP produces distortions in the chains that eliminate the restrictions on the interchain displacements, leading to the opening of the pore.

Predicting Protein Dynamics and Allostery Using Multi-Protein Atomic Distance Constraints

The related concepts of protein dynamics, conformational ensembles and allostery are often difficult to study with molecular dynamics (MD) due to the timescales involved. We present ExProSE (Exploration of Protein Structural Ensembles), a distance geometry-based method that generates an ensemble of protein structures from two input structures. ExProSE provides a unified framework for the exploration of protein structure and dynamics in a fast and accessible way. Using a dataset of apo/holo pairs it is shown that existing coarse-grained methods often cannot span large conformational changes. For T4-lysozyme, ExProSE is able to generate ensembles that are more native-like than tCONCOORD and NMSim, and comparable with targeted MD. By adding additional constraints representing potential modulators, ExProSE can predict allosteric sites. ExProSE ranks an allosteric pocket first or second for 27 out of 58 allosteric proteins, which is similar and complementary to existing methods. The ExProSE source code is freely available.

Opening and closing of a toroidal group II chaperonin revealed by a symmetry constrained elastic network model

Recently, the atomic structures of both the closed and open forms of Group 2 chaperonin protein Mm-cpn were revealed through crystallography and cryo-electron microscopy. This toroidal-like chaperonin is composed of two eightfold rings that face back-to-back. To gain a computational advantage, we used a symmetry constrained elastic network model (SCENM), which requires only a repeated subunit structure and its symmetric connectivity to neighboring subunits to simulate the entire system. In the case of chaperonin, only six subunits (i.e., three from each ring) were used out of the eight subunits comprising each ring. A smooth and symmetric pathway between the open and closed conformations was generated by elastic network interpolation (ENI). To support this result, we also performed a symmetry-constrained normal mode analysis (NMA), which revealed the intrinsic vibration features of the given structures. The NMA and ENI results for the representative single subunit were duplicated according to the symmetry pattern to reconstruct the entire assembly. To test the feasibility of the symmetry model, its results were also compared with those obtained from the full model. This study allowed the folding mechanism of chaperonin Mm-cpn to be elucidated by SCENM in a timely manner.

Specialized Dynamical Properties of Promiscuous Residues Revealed by Simulated Conformational Ensembles

The ability to interact with different partners is one of the most important features in proteins. Proteins that bind a large number of partners (hubs) have been often associated with intrinsic disorder. However, many examples exist of hubs with an ordered structure, and evidence of a general mechanism promoting promiscuity in ordered proteins is still elusive. An intriguing hypothesis is that promiscuous binding sites have specific dynamical properties, distinct from the rest of the interface and pre-existing in the protein isolated state. Here, we present the first comprehensive study of the intrinsic dynamics of promiscuous residues in a large protein data set. Different computational methods, from coarse-grained elastic models to geometry-based sampling methods and to full-atom Molecular Dynamics simulations, were used to generate conformational ensembles for the isolated proteins. The flexibility and dynamic correlations of interface residues with a different degree of binding promiscuity were calculated and compared considering side chain and backbone motions, the latter both on a local and on a global scale. The study revealed that (a) promiscuous residues tend to be more flexible than nonpromiscuous ones, (b) this additional flexibility has a higher degree of organization, and (c) evolutionary conservation and binding promiscuity have opposite effects on intrinsic dynamics. Findings on simulated ensembles were also validated on ensembles of experimental structures extracted from the Protein Data Bank (PDB). Additionally, the low occurrence of single nucleotide polymorphisms observed for promiscuous residues indicated a tendency to preserve binding diversity at these positions. A case study on two ubiquitin-like proteins exemplifies how binding promiscuity in evolutionary related proteins can be modulated by the fine-tuning of the interface dynamics. The interplay between promiscuity and flexibility highlighted here can inspire new directions in protein–protein interaction prediction and design methods.

The mechanism of allosteric coupling in choline kinase α1 revealed by the action of a rationally designed inhibitor

Applying a CHOK hold: Combined experimental and computational studies of the binding mode of a rationally designed inhibitor of the dimeric choline kinase α1 (CHOKα1) explain the molecular mechanism of negative cooperativity (see scheme) and how the monomers are connected. The results give insight into how the symmetry of the dimer can be partially conserved despite a lack of conservation in the static crystal structures.

Space warping order parameters and symmetry: application to multiscale simulation of macromolecular assemblies

Coarse-grained features of macromolecular assemblies are understood via a set of order parameters (OPs) constructed in terms of their all-atom configuration. OPs are shown to be slowly changing in time and capture the large-scale spatial features of macromolecular assemblies. The relationship of these variables to the classic notion of OPs based on symmetry breaking phase transitions is discussed. OPs based on space warping transformations are analyzed in detail as they naturally provide a connection between overall structure of an assembly and all-atom configuration. These OPs serve as the basis of a multiscale analysis that yields Langevin equations for OP dynamics. In this context, the characteristics of OPs and PCA modes are compared. The OPs enable efficient all-atom multiscale simulations of the dynamics of macromolecular assemblies in response to changes in microenvironmental conditions, as demonstrated on the structural transitions of cowpea chlorotic mottle virus capsid (CCMV) and RNA of the satellite tobacco mosaic virus (STMV).

Dynamics, flexibility and ligand-induced conformational changes in biological macromolecules: a computational approach

Biomolecules possess important dynamical properties that enable them to adapt and alternate their conformation as a response to environmental stimuli. Recent advancements in computational resources and methodology allow a higher capability to mimic in vitro conditions and open up the possibility of studying large systems over longer timescales. Here, we describe commonly used computational approaches for studying the dynamic properties of proteins. We review a selected set of simulation studies on ligand-induced changes in the chaperonin GroEL-GroES, a molecular folding machine, maltose-binding protein, a prototypical member of the periplasmic binding proteins, and the bacterial ribosomal A-site, focusing on aminoglycoside antibiotic recognition. We also discuss a recent quantitative reconstruction of the binding process of benzamidine and trypsin. These studies contribute to the understanding and further development of the medicinal regulation of large biomolecular systems.

Toward a detailed description of the pathways of allosteric communication in the GroEL chaperonin through atomistic simulation

GroEL, along with its coprotein GroES, is essential for ensuring the correct folding of unfolded or newly synthesized proteins in bacteria. GroEL is a complex, allosteric molecule, composed of two heptameric rings stacked back to back, that undergoes large structural changes during its reaction cycle. These structural changes are driven by the cooperative binding and subsequent hydrolysis of ATP, by GroEL. Despite numerous previous studies, the precise mechanisms of allosteric communication and the associated structural changes remain elusive. In this paper, we describe a series of all-atom, unbiased, molecular dynamics simulations over relatively long (50-100 ns) time scales of a single, isolated GroEL subunit and also a heptameric GroEL ring, in the presence and absence of ATP. Combined with results from a distance restraint-biased simulation of the single ring, the atomistic details of the earliest stages of ATP-driven structural changes within this complex molecule are illuminated. Our results are in broad agreement with previous modeling studies of isolated subunits and with a coarse-grained, forcing simulation of the single ring. These are the first reported all-atom simulations of the GroEL single-ring complex and provide a unique insight into the role of charged residues K80, K277, R284, R285, and E388 at the subunit interface in transmission of the allosteric signal. These simulations also demonstrate the feasibility of performing all-atom simulations of very large systems on sufficiently long time scales on typical high performance computing facilities to show the origins of the earliest events in biologically relevant processes.

Conformational sampling and nucleotide-dependent transitions of the GroEL subunit probed by unbiased molecular dynamics simulations

GroEL is an ATP dependent molecular chaperone that promotes the folding of a large number of substrate proteins in E. coli. Large-scale conformational transitions occurring during the reaction cycle have been characterized from extensive crystallographic studies. However, the link between the observed conformations and the mechanisms involved in the allosteric response to ATP and the nucleotide-driven reaction cycle are not completely established. Here we describe extensive (in total long) unbiased molecular dynamics (MD) simulations that probe the response of GroEL subunits to ATP binding. We observe nucleotide dependent conformational transitions, and show with multiple 100 ns long simulations that the ligand-induced shift in the conformational populations are intrinsically coded in the structure-dynamics relationship of the protein subunit. Thus, these simulations reveal a stabilization of the equatorial domain upon nucleotide binding and a concomitant “opening” of the subunit, which reaches a conformation close to that observed in the crystal structure of the subunits within the ADP-bound oligomer. Moreover, we identify changes in a set of unique intrasubunit interactions potentially important for the conformational transition.

Molecular machines convert chemical energy to mechanical work in the process of carrying out their specific tasks. Often these proteins are fueled by ATP binding and hydrolysis, enabling switching between different conformations. The ATP-dependent chaperone GroEL is a molecular machine that opens and closes its barrel-like structure in order to provide a folding cage for unfolded proteins. The quest to fully understand and control GroEL and other molecular machines is enhanced by complementing experimental work with computational approaches. Here, we provide a description of the molecular basis for the conformational changes in the GroEL subunit by performing extensive molecular dynamics simulations. The simulations sample the conformational population for the different nucleotide-free and bound states in the isolated subunit. The results reveal that the conformations of the subunit when isolated resemble those of the subunit integrated in the GroEL complex. Moreover, the molecular dynamics simulations allow following detailed changes in individual interatomic interactions brought about by ATP-binding.

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 of various 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, F(1) 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.

Procrustean rotation in concert with principal component analysis of molecular dynamics trajectories: Quantifying global and local differences between conformational samples

Given the principal component analysis (PCA) of a molecular dynamics (MD) conformational trajectory for a model protein, we perform orthogonal Procrustean rotation to "best fit" the PCA squared-loading matrix to that of a target matrix computed for a related but different molecular system. The sum of squared deviations of the elements of the rotated matrix from those of the target, known as the error of fit (EOF), provides a quantitative measure of the dissimilarity between the two conformational samples. To estimate precision of the EOF, we perform bootstrap resampling of the molecular conformations within the trajectories, generating a distribution of EOF values for the system and target. The average EOF per variable is determined and visualized to ascertain where, locally, system and target sample properties differ. We illustrate this approach by analyzing MD trajectories for the wild-type and four selected mutants of the beta1 domain of protein G.

Domain motions of hyaluronan lyase underlying processive hyaluronan translocation

Hyaluronan lyase (Hyal) is a surface enzyme occurring in many bacterial organisms including members of Streptococcus species. Streptococcal Hyal primarily degrades hyaluronan-substrate (HA) of the extracellular matrix. This degradation appears to facilitate the spread of this bacterium throughout host tissues. Unlike purely endolytic degradation of its other substrates, unsulfated chondroitin or some chondroitin sulfates, the degradation of HA by Hyal proceeds by processive exolytic cleavage of one disaccharide at a time following an initial endolytic cut. Molecular dynamics (MD) studies of Hyal from Streptococcus pneumoniae are presented that address the enzyme's molecular mechanism of action and the role of domain motions for processive functionality. The analysis of extensive sub-microsecond MD simulations of this enzyme action on HA-substrates of different lengths and the connection between the domain dynamics of Hyal and the translocation of the HA-substrate reveals that opening/closing and twisting domain motions of the Hyal are intimately linked to processive HA degradation. Enforced simulations confirmed this finding as the domain motions in SpnHyal were found to be induced by enforced substrate translocation. These results establish the dynamic interplay between Hyal flexibility and substrate translocation and provide insight into the processive mechanism of Hyal.

Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL

Identification of pathways involved in the structural transitions of biomolecular systems is often complicated by the transient nature of the conformations visited across energy barriers and the multiplicity of paths accessible in the multidimensional energy landscape. This task becomes even more challenging in exploring molecular systems on the order of megadaltons. Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases. Motivated by the utility of elastic network models for describing the collective dynamics of biomolecular systems and by the growing theoretical and experimental evidence in support of the intrinsic accessibility of functional substates, we introduce a new method, adaptive anisotropic network model (aANM), for exploring functional transitions. Application to bacterial chaperonin GroEL and comparisons with experimental data, results from action minimization algorithm, and previous simulations support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling potential transition pathways sampled by large complexes/assemblies. An important outcome is the assessment of the critical inter-residue interactions formed/broken near the transition state(s), most of which involve conserved residues.

Most proteins are biomolecular machines. They perform their function by undergoing changes between different structures. Understanding the mechanism of transition between these structures is of major importance to design methods for controlling such transitions, and thereby modulating protein function. Although there are many computational methods for exploring the transitions of small proteins, the task of exploring the transition pathways becomes prohibitively expensive in the case of supramolecular systems. The bacterial chaperonin GroEL is such a supramolecular machine. It plays an important role in assisting protein folding. During its function, GroEL undergoes structural transitions between multiple forms. Here, we are introducing a new methodology, based on elastic network models, for elucidating the transition mechanisms in such supramolecular systems. Application to GroEL provides us with biologically significant information on critical interactions and sequence of events occurring during the chaperonin machinery and key contacts that make and break at the transition. The method can be readily applied to other supramolecular machines.

Dynamical characterization of the heme NO oxygen binding (HNOX) domain. Insight into soluble guanylate cyclase allosteric transition

Since the discovery of soluble guanylate cyclase (sGC) as the mammalian receptor for nitric oxide (NO), numerous studies have been performed in order to understand how sGC transduces the NO signal. However, the structural basis of sGC activation is still not completely elucidated. Spectroscopic and kinetic studies showed that the key step in the activation mechanism was the NO-induced breaking of the iron proximal histidine bond in the so-called 6c-NO to 5c-NO transition. The main breakthrough in the understanding of sGC activation mechanism came, however, from the elucidation of crystal structures for two different prokaryotic heme NO oxygen (HNOX) domains, which are homologues to the sGC heme domain. In this work we present computer simulation results of Thermoanaerobacter tencogensis HNOX that complement these structural studies, yielding molecular explanations to several poorly understood properties of these proteins. Specifically, our results explain the differential ligand binding patterns of the HNOX domains according to the nature of proximal and distal residues. We also show that the natural dynamics of these proteins is intimately related with the proposed conformational dependent activation process, which involves mainly the alphaFbeta1 loop and the alphaA-alphaC distal subdomain. The results from the sGC models also support this view and suggest a key role for the alphaFbeta1 loop in the iron proximal histidine bond breaking process and, therefore, in the sGC activation mechanism.

Exploring the molecular basis of heme coordination in human neuroglobin

Neuroglobin (Ngb), a recently discovered ancient heme protein, presents the typical globin fold and is around 20% identical to myoglobin (Mb). In contrast with Mb, however, its heme is hexacoordinated (6c). It is expressed in the nervous system and has been the subject of numerous investigations in the last years, but its function is still unclear. The proposed roles include oxygen transport, reactive oxygen species (ROS) detoxification, hypoxia protection, and redox state sensing. All proposed functions require distal histidine dissociation from the heme to yield a reactive iron. With the aim of understanding the 6c to 5c transition, we have performed molecular dynamics simulations for ferrous Ngb in the 6c, 5c, and oxy states. We also computed free energy profiles associated with the transition employing an advanced sampling technique. Finally, we studied the effect of the redox state of CysCD7 and CysD5, which are known to form a disulfide bridge. Our results show that protein oxidation promotes a stabilization of the pentacoordinated species, thus favoring the protein to adopt the more reactive state and supporting the existence of a molecular mechanism whereby O2 would be released under hypoxic conditions, thereby suggesting an O(2) storage function for Ngb. Taken together, our results provide structural information not available experimentally which may shed light on the protein proposed functions, particularly as a redox sensor.

Normal modes and essential dynamics

Normal mode analysis and essential dynamics analysis are powerful methods used for the analysis of collective motions in biomolecules. Their application has led to an appreciation of the importance of protein dynamics in function and the relationship between structure and dynamical behavior. In this chapter, the methods and their implementation are introduced and recent developments such as elastic networks and advanced sampling techniques are described.

Structure, flexibility, and mechanism of the Bacillus stearothermophilus RecU Holliday junction resolvase

Here we report a high resolution structure of RecU-Holliday junction resolvase from Bacillus stearothermophilus. The functional unit of RecU is a homodimer that contains a "mushroom" like structure with a rigid cap and two highly flexible loops extending outwards. These loops appear to be highly flexible/dynamic, and presumably are directly involved in DNA binding and holding it for catalysis. Structural modifications of both the protein and DNA upon their interaction are essential for catalysis. An Mg2+ ion is present in each of the two active sites in this homodimeric enzyme, and two water molecules are coordinated with each Mg2+ ion. Our data are consistent with one of these water molecules acting as a nucleophile and the other as a general acid. The identities of the general base and general acid involved in catalysis and the Lewis acid that stabilizes the pentacovalent transition state phosphate ion are proposed. A model for the RecU-Holliday junction DNA complex is also proposed and discussed in the context of DNA binding and cleavage.

Flooding in GROMACS: accelerated barrier crossings in molecular dynamics

The major bottleneck of today's atomistic molecular dynamics (MD) simulations is that because of the enormous computational effort involved, only processes at nanoseconds to microseconds time scales or faster can be studied directly. Unfortunately, apart from a few exceptions, relevant processes, such as chemical reactions or many large scale conformational transitions in proteins, occur at slower time scales and therefore are currently far out of reach for conventional MD. The flooding technique addresses this problem by inclusion of a flooding potential into the force field. This flooding potential locally destabilizes the educt state and thereby significantly accelerates the escape from the initial energy well without affecting the reaction pathway. Here, we summarize the theory and method for the computational chemistry community and detail the implementation within the official version 3.3 of the freely available MD program package GROMACS. Two examples shall demonstrate the application of flooding to accelerate conformational transitions and chemical reactions. The second example was carried out within a QM/MM framework.

Allosteric transitions in the chaperonin GroEL are captured by a dominant normal mode that is most robust to sequence variations

The Escherichia coli chaperonin GroEL, which helps proteins to fold, consists of two heptameric rings stacked back-to-back. During the reaction cycle GroEL undergoes a series of allosteric transitions triggered by ligand (substrate protein, ATP, and the cochaperonin GroES) binding. Based on an elastic network model of the bullet-shaped double-ring chaperonin GroEL-(ADP)(7)-GroES structure (R''T state), we perform a normal mode analysis to explore the energetically favorable collective motions encoded in the R''T structure. By comparing each normal mode with the observed conformational changes in the R''T --> TR'' transition, a single dominant normal mode provides a simple description of this highly intricate allosteric transition. A detailed analysis of this relatively high-frequency mode describes the structural and dynamic changes that underlie the positive intra-ring and negative inter-ring cooperativity. The dynamics embedded in the dominant mode entails highly concerted structural motions with approximate preservation of sevenfold symmetry within each ring and negatively correlated ones between the two rings. The dominant normal mode (in comparison with the other modes) is robust to parametric perturbations caused by sequence variations, which validates its functional importance. Response of the dominant mode to local changes that mimic mutations using the structural perturbation method technique leads to a wiring diagram that identifies a network of key residues that regulate the allosteric transitions. Many of these residues are located in intersubunit interfaces, and may therefore play a critical role in transmitting allosteric signals between subunits.

Can principal components yield a dimension reduced description of protein dynamics on long time scales?

The suitability of principal component analysis (PCA) to yield slow collective coordinates for use within a dimension reduced description of conformational motions in proteins is evaluated. Two proteins are considered, T4 lysozyme and crambin. We present a quantitative evaluation of the convergence of conformational coordinates obtained with principal component analysis. Detailed analyses of (>200 ns) molecular dynamics trajectories and crystallographic data suggests that simulations of a few nanoseconds should generally provide a stable and statistically reliable definition of the essential and near constraints subspaces. Moreover, a systematic assessment of the density of states of the dynamics of all principal components showed that for an optimal separation of time scales it is crucial to include also side chain atoms in the PCA.

Insights into molecular plasticity of choline binding proteins (pneumococcal surface proteins) by SAXS

Phosphocholine moieties decorating the pneumococcal surface are used as a docking station for a family of modular proteins, the so-called choline binding proteins or CBPs. Choline recognition is essential for CBPs function and may also be a determinant for their quaternary structure. There is little knowledge about modular arrangement or oligomeric structures in this family. Therefore, we have used the small angle X-ray scattering (SAXS) technique combined with analytical ultracentrifugation in order to model the three-dimensional envelope of two highly different CBPs: the phage encoded Cpl-1 lysozyme and the pneumococcal phosphorylcholine esterase Pce. Both enzymes have an N-terminal catalytic module and a C-terminal choline-binding module (CBM) that attaches them to the bacterial surface and comprises six and ten sequence repeats in Cpl-1 and Pce, respectively. SAXS experiments have shown an inherent conformational plasticity in Cpl-1 that accounts for the different relative position of these regions in the solution and crystal structures. Dimerization of Cpl-1 upon choline binding has been also visualised for the first time, and monomer-monomer interactions take place through the first CBR where a non-canonical choline binding site has now been identified. This mode of association seems to be independent of the absence or presence of the Cpl-1 catalytic module and reveals that the arrangement of the monomers differs from that previously found in the isolated CBM dimer of pneumococcal LytA amidase. In contrast, Pce displays the same modular disposition in the solution and crystal structures, and remains almost invariant upon choline binding. The present results suggest that protein dimerization and duplication of CBRs may be alternative but not equivalent ways of improving cell wall recognition by CBPs, since they provide different interaction geometries for choline residues present in (lipo)teichoic acids.

Markov propagation of allosteric effects in biomolecular systems: application to GroEL-GroES

We introduce a novel approach for elucidating the potential pathways of allosteric communication in biomolecular systems. The methodology, based on Markov propagation of 'information' across the structure, permits us to partition the network of interactions into soft clusters distinguished by their coherent stochastics. Probabilistic participation of residues in these clusters defines the communication patterns inherent to the network architecture. Application to bacterial chaperonin complex GroEL-GroES, an allostery-driven structure, identifies residues engaged in intra- and inter-subunit communication, including those acting as hubs and messengers. A number of residues are distinguished by their high potentials to transmit allosteric signals, including Pro33 and Thr90 at the nucleotide-binding site and Glu461 and Arg197 mediating inter- and intra-ring communication, respectively. We propose two most likely pathways of signal transmission, between nucleotide- and GroES-binding sites across the cis and trans rings, which involve several conserved residues. A striking observation is the opposite direction of information flow within cis and trans rings, consistent with negative inter-ring cooperativity. Comparison with collective modes deduced from normal mode analysis reveals the propensity of global hinge regions to act as messengers in the transmission of allosteric signals.

Alternate structural conformations of Streptococcus pneumoniae hyaluronan lyase: insights into enzyme flexibility and underlying molecular mechanism of action

Streptococcus pneumoniae hyaluronan lyase is a surface enzyme of this Gram-positive bacterium. The enzyme degrades several biologically important, information-rich linear polymeric glycans: hyaluronan, unsulfated chondroitin, and some chondroitin sulfates. This degradation facilitates spreading of bacteria throughout the host tissues and presumably provides energy and a carbon source for pneumococcal cells. Its beta-elimination catalytic mechanism is an acid/base process termed proton acceptance and donation leading to cleavage of beta-1,4 linkages of the substrates. The degradation of hyaluronan occurs in two stages, initial endolytic cuts are followed by processive exolytic cleavage of one disaccharide at a time. In contrast, the degradation of chondroitins is purely endolytic. Structural studies together with flexibility analyses of two streptococcal enzymes, from S.pneumoniae and Streptococcus agalactiae, allowed for insights into this enzyme's molecular mechanism. Here, two new X-ray crystal structures of the pneumococcal enzyme in novel conformations are reported. These new conformations, complemented by molecular dynamics simulation results, directly confirm the predicted domain motions presumed to facilitate the processive degradative process. One of these new structures resembles the S.agalactiae enzyme conformation, and provides evidence of a uniform mechanistic/dynamic behavior of this protein across different bacteria.

Cation-mediated interplay of loops in chaperonin-10

The ubiquitously occurring chaperonins consist of a large tetradecameric Chaperonin-60, forming a cylindrical assembly, and a smaller heptameric Chaperonin-10. For a functional protein folding cycle, Chaperonin-10 caps the cylindrical Chaperonin-60 from one end forming an asymmetric complex. The oligomeric assembly of Chaperonin-10 is known to be highly plastic in nature. In Mycobacterium tuberculosis, the plasticity has been shown to be modulated by reversible binding of divalent cations. Binding of cations confers rigidity to the metal binding loop, and also promotes stability of the oligomeric structure. We have probed the conformational effects of cation binding on the Chaperonin-10 structure through fluorescence studies and molecular dynamics simulations. Fluorescence studies show that cation binding induces reduced exposure and flexibility of the dome loop. The simulations corroborate these results and further indicate a complex landscape of correlated motions between different parts of the molecule. They also show a fascinating interplay between two distantly spaced loops, the metal binding "dome loop" and the GroEL-binding "mobile loop", suggesting an important cation-mediated role in the recognition of Chaperonin-60. In the presence of cations the mobile loop appears poised to dock onto the Chaperonin-60 structure. The divalent metal ions may thus act as key elements in the protein folding cycle, and trigger a conformational switch for molecular recognition.

Allosteric regulation of chaperonins

Chaperonins are molecular machines that facilitate protein folding by undergoing energy (ATP)-dependent movements that are coordinated in time and space by complex allosteric regulation. Recently, progress has been made in describing the various functional (allosteric) states of these machines, the pathways by which they interconvert, and the coupling between allosteric transitions and protein folding reactions. However, various mechanistic issues remain to be resolved.

Molecular motions of human cyclin-dependent kinase 2

We present a comprehensive description of the dynamic behavior of CDK2 in complex with cyclin A, arrived at by analysis of a total of 0.25 micros of solvated molecular dynamics trajectories and 42 deposited CDK2 structures, and refined using other protein simulation algorithms. The CDK2-cyclin A dimer is a dynamic complex of 6 subdomains. Thermal motions are dominated by a relative twisting of the two monomers. The predominant motion within CDK2 is a "breathing" of the N-terminal and C-terminal lobes. The N-terminal lobe of cyclin A is tightly linked to the "PSTAIRE" helix of CDK2 to provide a rigid nucleus to the complex. By contrast, the "CDK-insert" region (residues 219-251) sometimes becomes highly mobile, a behavior that is observed in crystallographic analyses of CDK2 structures and that may relate to its role in recognizing diverse binding partners. We find that the three arginines that anchor phosphothreonine 160 of fully active CDK2 do not contribute equally to structural stabilization. This observation is supported by a survey of protein kinase sequences. We have also explored the physical basis of the role of the phosphate moiety in signaling by artificially modifying the charge of phosphothreonine 160 in molecular dynamics simulations. We find that phosphothreonine binding involves an active process of attraction in which both the receptor site (the arginine triad), and the phosphothreonine have a higher charge than is required to maintain an active conformation once formed. We have deposited our dynamics data to aid protein kinase inhibitor design.

The role of dynamics in allosteric regulation

The biomolecular conformational changes often associated with allostery are, by definition, dynamic processes. Recent publications have disclosed the role of pre-existing equilibria of conformational substates in this process. In addition, the role of dynamics as an entropic carrier of free energy of allostery has been investigated. Recent work thus shows that dynamics is pivotal to allostery, and that it constitutes much more than just the move from the 'T'-state to the 'R'-state. Emerging computational studies have described the actual pathways of allosteric change.

Crystal structures of the group II chaperonin from Thermococcus strain KS-1: steric hindrance by the substituted amino acid, and inter-subunit rearrangement between two crystal forms

The crystal structures of the group II chaperonins consisting of the alpha subunit with amino acid substitutions of G65C and/or I125T from the hyperthermophilic archaeum Thermococcus strain KS-1 were determined. These mutants have been shown to be active in ATP hydrolysis but inactive in protein folding. The structures were shown to be double-ring hexadecamers in an extremely closed form, which was consistent with the crystal structure of native alpha8beta8-chaperonin from Thermoplasma acidophilum. Comparisons of the present structures with the atomic structures of the GroEL14-GroES7-(ADP)7 complex revealed that the deficiency in protein-folding activity with the G65C amino acid substitution is caused by the steric hindrance of the local conformational change in an equatorial domain. We concluded that this mutant chaperonin with G65C substitution is deprived of the smooth conformational change in the refolding-reaction cycle. We obtained a new form of crystal with a distinct space group at a lower concentration of sulfate ion in the presence of nucleotide. The crystal structure obtained at the lower concentration of sulfate ion tilts outward, and has much looser inter-subunit contacts compared with those in the presence of a higher concentration of sulfate ion. Such subunit rotation has never been characterized in group II chaperonins. The crystal structure obtained at the lower concentration of sulfate ion tilts outward, and has much looser inter-subunit contacts compared with those in the presence of a higher concentration of sulfate ion.

Conformational sampling for the impatient

Several new methods for sampling conformations of biomolecules have appeared recently. A brief review thereof is presented, with particular emphasis on applications that have been published, and suitability for different kinds of systems. Four methods (namely: RESPA, replica-exchange molecular dynamics, CONCOORD and Gaussian network method) are readily applicable for biomolecular systems.

Insights into the catalytic mechanism of cofactor-independent phosphoglycerate mutase from X-ray crystallography, simulated dynamics and molecular modeling

Phosphoglycerate mutases catalyze the isomerization of 2 and 3-phosphoglycerates, and are essential for glucose metabolism in most organisms. Here, we further characterize the 2,3-bisphosphoglycerate-independent phosphoglycerate mutase (iPGM) from Bacillus stearothermophilus by determination of a high-resolution (1.4A) crystal structure of the wild-type enzyme and the crystal structure of its S62A mutant. The mutant structure surprisingly showed the replacement of one of the two catalytically essential manganese ions with a water molecule, offering an additional possible explanation for its lack of catalytic activity. Crystal structures invariably show substrate phosphoglycerate to be entirely buried in a deep cleft between the two iPGM domains. Flexibility analyses were therefore employed to reveal the likely route of substrate access to the catalytic site through an aperture created in the enzyme's surface during certain stages of the catalytic process. Several conserved residues lining this aperture may contribute to orientation of the substrate as it enters. Factors responsible for the retention of glycerate within the phosphoenzyme structure in the proposed mechanism are identified by molecular modeling of the glycerate complex of the phosphoenzyme. Taken together, these results allow for a better understanding of the mechanism of action of iPGMs. Many of the results are relevant to a series of evolutionarily related enzymes. These studies will facilitate the development of iPGM inhibitors which, due to the demonstrated importance of this enzyme in many bacteria, would be of great potential clinical significance.

Hidden order in the GroEL-GroES-(ADP)7 chaperonin: forms, folding, and ADP-binding sites

A molecular crystallography approach reveals the existence of a hidden order in GroEL-GroES-(ADP)(7). The new crystallographic symmetry concepts required are first illustrated for a hypothetical planar molecule. Their application to the chaperonin complex leads to molecular forms with vertices having integral coordinates (the indices) with respect to a symmetry-adapted basis and to folding points approximated by ideal C(alpha) positions with rational indices connected by integral scale-rotations, just as for the vertices of the molecular forms. The Mg(+2)-ions at nucleotide binding sites are symmetry-related in a similar way to C(alpha)'s folding points.

On the evaluation and optimization of protein X-ray structures for pKa calculations

The calculation of the physical properties of a protein from its X-ray structure is of importance in virtually every aspect of modern biology. Although computational algorithms have been developed for calculating everything from the dynamics of a protein to its binding specificity, only limited information is available on the ability of these methods to give accurate results when used with a particular X-ray structure. We examine the ability of a pKa calculation algorithm to predict the proton-donating residue in the catalytic mechanism of hen egg white lysozyme. We examine the correlation between the ability of the pKa calculation method to obtain the correct result and the overall characteristics of 41 X-ray structures such as crystallization conditions, resolution, and the output of structure validation software. We furthermore examine the ability of energy minimizations (EM), molecular dynamics (MD) simulations, and structure-perturbation methods to optimize the X-ray structures such that these give correct results with the pKa calculation algorithm. We propose a set of criteria for identifying the proton donor in a catalytic mechanism, and demonstrate that the application of these criteria give highly accurate prediction results when using unmodified X-ray structures. More specifically, we are able to successfully identify the proton donor in 85% of the X-ray structures when excluding structures with crystal contacts near the active site. Neither the use of the overall characteristics of the X-ray structures nor the optimization of the structure by EM, MD, or other methods improves the results of the pKa calculation algorithm. We discuss these results and their implications for the design of structure-based energy calculation algorithms in general.

Structure and flexibility of Streptococcus agalactiae hyaluronate lyase complex with its substrate. Insights into the mechanism of processive degradation of hyaluronan

Streptococcus agalactiae hyaluronate lyase degrades primarily hyaluronan, the main polysaccharide component of the host connective tissues, into unsaturated disaccharide units as the end product. Such function of the enzyme destroys the normal connective tissue structure of the host and exposes the tissue cells to various bacterial toxins. The crystal structure of hexasaccharide hyaluronan complex with the S. agalactiae hyaluronate lyase was determined at 2.2 A resolution; the mechanism of the catalytic process, including the identification of specific residues involved in the degradation of hyaluronan, was clearly identified. The enzyme is composed structurally and functionally from two distinct domains, an alpha-helical alpha-domain and a beta-sheet beta-domain. The flexibility of the protein was investigated by comparing the crystal structures of the S. agalactiae and the Streptococcus pneumoniae enzymes, and by using essential dynamics analyses of CONCOORD computer simulations. These revealed important modes of flexibility, which could be related to the protein function. First, a rotation/twist of the alpha-domain relative to the beta-domain is potentially related to the mechanism of processivity of the enzyme; this twist motion likely facilitates shifting of the ligand along the catalytic site cleft in order to reposition it to be ready for further cleavage. Second, a movement of the alpha- and beta-domains with respect to each other was found to contribute to a change in electrostatic characteristics of the enzyme and appears to facilitate binding of the negatively charged hyaluronan ligand. Third, an opening/closing of the substrate binding cleft brings a catalytic histidine closer to the cleavable substrate beta1,4-glycosidic bond. This opening/closing mode also reflects the main conformational difference between the crystal structures of the S. agalactiae and the S. pneumoniae hyaluronate lyases.

Mapping pathways of allosteric communication in GroEL by analysis of correlated mutations

An interesting example of an allosteric protein is the chaperonin GroEL. It undergoes adenosine 5'-triphosphate-induced conformational changes that are reflected in binding of adenosine 5'-triphosphate with positive cooperativity within rings and negative cooperativity between rings. Herein, correlated mutations in chaperonins are analyzed to unravel routes of allosteric communication in GroEL and in its complex with its co-chaperonin GroES. It is shown that analysis of correlated mutations in the chaperonin family can provide information about pathways of allosteric communication within GroEL and between GroEL and GroES. The results are discussed in the context of available structural, genetic, and biochemical data concerning short- and long-range interactions in the GroE system.

Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic

We investigated protein motions using normal modes within a database framework, determining on a large sample the degree to which normal modes anticipate the direction of the observed motion and were useful for motions classification. As a starting point for our analysis, we identified a large number of examples of protein flexibility from a comprehensive set of structural alignments of the proteins in the PDB. Each example consisted of a pair of proteins that were considerably different in structure given their sequence similarity. On each pair, we performed geometric comparisons and adiabatic-mapping interpolations in a high-throughput pipeline, arriving at a final list of 3,814 putative motions and standardized statistics for each. We then computed the normal modes of each motion in this list, determining the linear combination of modes that best approximated the direction of the observed motion. We integrated our new motions and normal mode calculations in the Macromolecular Motions Database, through a new ranking interface at http://molmovdb.org. Based on the normal mode calculations and the interpolations, we identified a new statistic, mode concentration, related to the mathematical concept of information content, which describes the degree to which the direction of the observed motion can be summarized by a few modes. Using this statistic, we were able to determine the fraction of the 3,814 motions where one could anticipate the direction of the actual motion from only a few modes. We also investigated mode concentration in comparison to related statistics on combinations of normal modes and correlated it with quantities characterizing protein flexibility (e.g., maximum backbone displacement or number of mobile atoms). Finally, we evaluated the ability of mode concentration to automatically classify motions into a variety of simple categories (e.g., whether or not they are "fragment-like"), in comparison to motion statistics. This involved the application of decision trees and feature selection (particular machine-learning techniques) to training and testing sets derived from merging the "list" of motions with manually classified ones.

Mechanism of hyaluronan degradation by Streptococcus pneumoniae hyaluronate lyase. Structures of complexes with the substrate

Hyaluronate lyase enzymes degrade hyaluronan, the main polysaccharide component of the host connective tissues, predominantly into unsaturated disaccharide units, thereby destroying the normal connective tissue structure and exposing the tissue cells to various endo- and exogenous factors, including bacterial toxins. The crystal structures of Streptococcus pneumoniae hyaluronate lyase with tetra- and hexasaccharide hyaluronan substrates bound in the active site were determined at 1.52- and 2.0-A resolution, respectively. Hexasaccharide is the longest substrate segment that binds entirely within the active site of these enzymes. The enzyme residues responsible for substrate binding, positioning, catalysis, and product release were thereby identified and their specific roles characterized. The involvement of three residues in catalysis, Asn(349), His(399), and Tyr(408), is confirmed, and the details of proton acceptance and donation within the catalytic machinery are described. The mechanism of processivity of the enzyme is analyzed. The flexibility (allosteric) behavior of the enzyme may be understood in terms of the results of flexibility analysis of this protein, which identified two modes of motion that are also proposed to be involved in the hyaluronan degradation process. The first motion describes an opening and closing of the catalytic cleft located between the alpha- and beta-domains. The second motion demonstrates the mobility of a binding cleft, which may facilitate the binding of the negatively charged hyaluronan to the enzyme.

Inhibition of trypsin by cowpea thionin: characterization, molecular modeling, and docking

Higher plants produce several families of proteins with toxic properties, which act as defense compounds against pests and pathogens. The thionin family represents one family and comprises low molecular mass cysteine-rich proteins, usually basic and distributed in different plant tissues. Here, we report the purification and characterization of a new thionin from cowpea (Vigna unguiculata) with proteinase inhibitory activity. Cowpea thionin inhibits trypsin, but not chymotrypsin, binding with a stoichiometry of 1:1 as shown with the use of mass spectrometry. Previous annotations of thionins as proteinase inhibitors were based on their erroneous identification as homologues of Bowman-Birk family inhibitors. Molecular modeling experiments were used to propose a mode of docking of cowpea thionin with trypsin. Consideration of the dynamic properties of the cowpea thionin was essential to arrive at a model with favorable interface characteristics comparable with structures of trypsin-inhibitor complexes determined by X-ray crystallography. In the final model, Lys11 occupies the S1 specificity pocket of trypsin as part of a canonical style interaction.

Structure and mechanism of action of a cofactor-dependent phosphoglycerate mutase homolog from Bacillus stearothermophilus with broad specificity phosphatase activity

The crystal structure of Bacillus stearothermophilus PhoE (originally termed YhfR), a broad specificity monomeric phosphatase with a molecular mass of approximately 24 kDa, has been solved at 2.3 A resolution in order to investigate its structure and function. PhoE, already identified as a homolog of a cofactor-dependent phosphoglycerate mutase, shares with the latter an alpha/beta/alpha sandwich structure spanning, as a structural excursion, a smaller subdomain composed of two alpha-helices and one short beta-strand. The active site contains residues from both the alpha/beta/alpha sandwich and the sub-domain. With the exception of the hydrophilic catalytic machinery conserved throughout the cofactor-dependent phosphoglycerate mutase family, the active-site cleft is strikingly hydrophobic. Docking studies with two diverse, favored substrates show that 3-phosphoglycerate may bind to the catalytic core, while alpha-napthylphosphate binding also involves the hydrophobic portion of the active-site cleft. Combining a highly favorable phospho group binding site common to these substrate binding modes and data from related enzymes, a catalytic mechanism can be proposed that involves formation of a phosphohistidine intermediate on His10 and likely acid-base behavior of Glu83. Other structural factors contributing to the broad substrate specificity of PhoE can be identified. The dynamic independence of the subdomain may enable the active-site cleft to accommodate substrates of different sizes, although similar motions are present in simulations of cofactor-dependent phosphoglycerate mutases, perhaps favoring a more general functional role. A significant number of entries in protein sequence databases, particularly from unfinished microbial genomes, are more similar to PhoE than to cofactor-dependent phosphoglycerate mutases or to fructose-2,6-bisphosphatases. This PhoE structure will therefore serve as a valuable basis for inference of structural and functional characteristics of these proteins.

Molecular mechanisms of chaperonin GroEL-GroES function

The dynamics of the GroEL-GroES complex is investigated with a coarse-grained model. This model is one in which single-residue points are connected to other such points, which are nearby, by identical springs, forming a network of interactions. The nature of the most important (slowest) normal modes reveals a wide variety of motions uniquely dependent upon the central cavity of the structure, including opposed torsional rotation of the two GroEL rings accompanied by the alternating compression and expansion of the GroES cap binding region, bending, shear, opposed radial breathing of the cis and trans rings, and stretching and contraction along the protein assembly's long axis. The intermediate domains of the subunits are bifunctional due to the presence of two hinges, which are alternatively activated or frozen by an ATP-dependent mechanism. ATP binding stabilizes a relatively open conformation (with respect to the central cavity) and hinders the motion of the hinge site connecting the intermediate and equatorial domains, while enhancing the flexibility of the second hinge that sets in motion the apical domains. The relative flexibilities of the hinges are reversed in the nucleotide-free form. Cooperative cross-correlations between subunits provide information about the mechanism of action of the protein. The mechanical motions driven by the different modes provide variable binding surfaces and variable sized cavities in the interior to enable accommodation of a broad range of protein substrates. These modes of motion could be used to manipulate the substrate's conformations.

Bias-free separation of internal and overall motion of biomolecules

Collective internal motions are known to be important for the function of biological macromolecules. It has been discussed in the past whether the application of superimposing algorithms to remove the overall motion from a structural ensemble introduces artificial correlations between distant atoms. Here we present a new method to eliminate residual rotation and translation from cartesian modes derived from a normal mode analysis or from a principal component analysis. Bias-free separation is based on the idea that the addition of modes of pure rotation/translation can compensate the residual overall motion. Removal of overall motion must reduce the "total amount of motion" (TAM) in the mode. Our algorithm allows to back-calculate revised covariance matrices. The approach was applied to two model systems that show residual overall motion, when analyzed using all atoms as reference for the superimposing algorithm. In both cases, our algorithm was capable of eliminating residual covariances caused by the overall motion, while retaining internal covariances even for very distant atoms. A structural ensemble obtained for a 13-ns molecular dynamics simulation of the protein Ribonuclease T1 showed a covariance matrix of the corrected modes with significantly sharper contours after applying the bias-free separation.