Protein conformational transitions explored by mixed elastic network models

We develop a mixed elastic network model (MENM) to study large-scale conformational transitions of proteins between two (or more) known structures. Elastic network potentials for the beginning and end states of a transition are combined, in effect, by adding their respective partition functions. The resulting effective MENM energy function smoothly interpolates between the original surfaces, and retains the beginning and end structures as local minima. Saddle points, transition paths, potentials of mean force, and partition functions can be found efficiently by largely analytic methods. To characterize the protein motions during a conformational transition, we follow "transition paths" on the MENM surface that connect the beginning and end structures and are invariant to parameterizations of the model and the mathematical form of the mixing scheme. As illustrations of the general formalism, we study large-scale conformation changes of the motor proteins KIF1A kinesin and myosin II. We generate possible transition paths for these two proteins that reveal details of their conformational motions. The MENM formalism is computationally efficient and generally applicable even for large protein systems that undergo highly collective structural changes.     

Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.     

A mass weighted chemical elastic network model elucidates closed form domain motions in proteins

An elastic network model (ENM), usually Cα coarse‐grained one, has been widely used to study protein dynamics as an alternative to classical molecular dynamics simulation. This simple approach dramatically saves the computational cost, but sometimes fails to describe a feasible conformational change due to unrealistically excessive spring connections. To overcome this limitation, we propose a mass‐weighted chemical elastic network model (MWCENM) in which the total mass of each residue is assumed to be concentrated on the representative alpha carbon atom and various stiffness values are precisely assigned according to the types of chemical interactions. We test MWCENM on several well‐known proteins of which both closed and open conformations are available as well as three α‐helix rich proteins. Their normal mode analysis reveals that MWCENM not only generates more plausible conformational changes, especially for closed forms of proteins, but also preserves protein secondary structures thus distinguishing MWCENM from traditional ENMs. In addition, MWCENM also reduces computational burden by using a more sparse stiffness matrix.     

A kinetic model for the internal motions of proteins: diffusion between multiple harmonic wells.

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics. Subsequently, the kinetics of the main (essential) collective protein motions were characterized. A dual-diffusion behavior was observed in which a fast type of diffusion switches to a much slower type in a typical time of about 1-3 ps. From these results, the large backbone conformational fluctuations of a protein may be considered as "hopping" between multiple harmonic wells on a basically flat free energy surface.     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.     

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.     

Comparison of mode analyses at different resolutions applied to nucleic acid systems

More than two decades of different types of mode analyses has shown that these techniques can be useful in describing large-scale motions in protein systems. A number of mode analyses are available and include quasiharmonics, classical normal mode, block normal mode, and the elastic network model. Each of these methods has been validated for protein systems and this variety allows researchers to choose the technique that gives the best compromise between computational cost and the level of detail in the calculation. These same techniques have not been systematically tested for nucleic acid systems, however. Given the differences in interactions and structural features between nucleic acid and protein systems, the validity of these techniques in the protein regime cannot be directly translated into validity in the nucleic acid realm. In this work, we investigate the usefulness of the above mode analyses as applied to two RNA systems, i.e., the hammerhead ribozyme and a guanine riboswitch. We show that classical normal-mode analysis can match the magnitude and direction of residue fluctuations from the more detailed, anharmonic technique, quasiharmonic analysis of a molecular dynamics trajectory. The block normal-mode approximation is shown to hold in the nucleic acid systems studied. Only the mode analysis at the lowest level of detail, the elastic network model, produced mixed results in our calculations. We present data that suggest that the elastic network model, with the popular parameterization, is not best suited for systems that do not have a close packed structure; this observation also hints at why the elastic network model has been found to be valid for many globular protein systems. The different behaviors of block normal-mode analysis and the elastic network model, which invoke similar degrees of coarse-graining to the dynamics but use different potentials, suggest the importance of applying a heterogeneous potential function in a robust analysis of the dynamics of biomolecules, especially those that are not closely packed. In addition to these comparisons, we briefly discuss insights into the conformational space available to the hammerhead ribozyme.     

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.     

Counterbalance of ligand‐ and self‐coupled motions characterizes multispecificity of ubiquitin

Date hub proteins are a type of proteins that show multispecificity in a time‐dependent manner. To understand dynamic aspects of such multispecificity we studied Ubiquitin as a typical example of a date hub protein. Here we analyzed 9 biologically relevant Ubiquitin‐protein (ligand) heterodimer structures by using normal mode analysis based on an elastic network model. Our result showed that the self‐coupled motion of Ubiquitin in the complex, rather than its ligand‐coupled motion, is similar to the motion of Ubiquitin in the unbound condition. The ligand‐coupled motions are correlated to the conformational change between the unbound and bound conditions of Ubiquitin. Moreover, ligand‐coupled motions favor the formation of the bound states, due to its in‐phase movements of the contacting atoms at the interface. The self‐coupled motions at the interface indicated loss of conformational entropy due to binding. Therefore, such motions disfavor the formation of the bound state. We observed that the ligand‐coupled motions are embedded in the motions of unbound Ubiquitin. In conclusion, multispecificity of Ubiquitin can be characterized by an intricate balance of the ligand‐ and self‐coupled motions, both of which are embedded in the motions of the unbound form.     

In silico investigation of conformational motions in superfamily 2 helicase proteins

Helicases are motor proteins that play a central role in the metabolism of DNA and RNA in biological cells. Using the energy of ATP molecules, they are able to translocate along the nucleic acids and unwind their duplex structure. They have been extensively characterized in the past and grouped into superfamilies based on structural similarities and sequential motifs. However, their functional aspects and the mechanism of their operation are not yet well understood. Here, we consider three helicases from the major superfamily 2--Hef, Hel308 and XPD--and study their conformational dynamics by using coarse-grained relaxational elastic network models. Specifically, their responses to mechanical perturbations are analyzed. This enables us to identify robust and ordered conformational motions which may underlie the functional activity of these proteins. As we show, such motions are well-organized and have large amplitudes. Their possible roles in the processing of nucleic substrate are discussed.     

Conservation of Flexible Residue Clusters among Structural and Functional Enzyme Homologues

Conformational flexibility between structural ensembles is an essential component of enzyme function. Although the broad dynamical landscape of proteins is known to promote a number of functional events on multiple time scales, it is yet unknown whether structural and functional enzyme homologues rely on the same concerted residue motions to perform their catalytic function. It is hypothesized that networks of contiguous and flexible residue motions occurring on the biologically relevant millisecond time scale evolved to promote and/or preserve optimal enzyme catalysis. In this study, we use a combination of NMR relaxation dispersion, model-free analysis, and ligand titration experiments to successfully capture and compare the role of conformational flexibility between two structural homologues of the pancreatic ribonuclease family: RNase A and eosinophil cationic protein (or RNase 3). In addition to conserving the same catalytic residues and structural fold, both homologues show similar yet functionally distinct clusters of millisecond dynamics, suggesting that conformational flexibility can be conserved among analogous protein folds displaying low sequence identity. Our work shows that the reduced conformational flexibility of eosinophil cationic protein can be dynamically and functionally reproduced in the RNase A scaffold upon creation of a chimeric hybrid between the two proteins. These results support the hypothesis that conformational flexibility is partly required for catalytic function in homologous enzyme folds, further highlighting the importance of dynamic residue sectors in the structural organization of proteins.     

Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.     

Conformational changes and allosteric communications in human serum albumin due to ligand binding

It is well recognized that knowledge of structure alone is not sufficient to understand the fundamental mechanism of biomolecular recognition. Information of dynamics is necessary to describe motions involving relevant conformational states of functional importance. We carried out principal component analysis (PCA) of structural ensemble, derived from 84 crystal structures of human serum albumin (HSA) with different ligands and/or different conditions, to identify the functionally important collective motions, and compared with the motions along the low-frequency modes obtained from normal mode analysis of the elastic network model (ENM) of unliganded HSA. Significant overlap is observed in the collective motions derived from PCA and ENM. PCA and ENM analysis revealed that ligand selects the most favored conformation from accessible equilibrium structures of unliganded HSA. Further, we analyzed dynamic network obtained from molecular dynamics simulations of unliganded HSA and fatty acids- bound HSA. Our results show that fatty acids-bound HSA has more robust community network with several routes to communicate among different parts of the protein. Critical nodes (residues) identified from dynamic network analysis are in good agreement with allosteric residues obtained from sequence-based statistical coupling analysis method. This work underscores the importance of intrinsic structural dynamics of proteins in ligand recognition and can be utilized for the development of novel drugs with optimum activity.     

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.     

ProMode: a database of normal mode analyses on protein molecules with a full-atom model

MOTIVATION: Although information from protein dynamics simulation is important to understand principles of architecture of a protein structure and its function, simulations such as molecular dynamics and Monte Carlo are very CPU-intensive. Although the ability of normal mode analysis (NMA) is limited because of the need for a harmonic approximation on which NMA is based, NMA is adequate to carry out routine analyses on many proteins to compute aspects of the collective motions essential to protein dynamics and function. Furthermore, it is hoped that realistic animations of the protein dynamics can be observed easily without expensive software and hardware, and that the dynamic properties for various proteins can be compared with each other. RESULTS: ProMode, a database collecting NMA results on protein molecules, was constructed. The NMA calculations are performed with a full-atom model, by using dihedral angles as independent variables, faster and more efficiently than the calculations using Cartesian coordinates. In ProMode, an animation of the normal mode vibration is played with a free plug-in, Chime (MDL Information Systems, Inc.). With the full-atom model, the realistic three-dimensional motions at an atomic level are displayed with Chime. The dynamic domains and their mutual screw motions defined from the NMA results are also displayed. Properties for each normal mode vibration and their time averages, e.g. fluctuations of atom positions, fluctuations of dihedral angles and correlations between the atomic motions, are also presented graphically for characterizing the collective motions in more detail. AVAILABILITY: http://promode.socs.waseda.ac.jp     

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

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

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.