Normal-modes-based prediction of protein conformational changes guided by distance constraints

Short-distance probes for protein backbone structure based on energy transfer between bimane and transition metal ions

The structure and dynamics of proteins underlies the workings of virtually every biological process. Existing biophysical methods are inadequate to measure protein structure at atomic resolution, on a rapid time scale, with limited amounts of protein, and in the context of a cell or membrane. FRET can measure distances between two probes, but depends on the orientation of the probes and typically works only over long distances comparable with the size of many proteins. Also, common probes used for FRET can be large and have long, flexible attachment linkers that position dyes far from the protein backbone. Here, we improve and extend a fluorescence method called transition metal ion FRET that uses energy transfer to transition metal ions as a reporter of short-range distances in proteins with little orientation dependence. This method uses a very small cysteine-reactive dye monobromobimane, with virtually no linker, and various transition metal ions bound close to the peptide backbone as the acceptor. We show that, unlike larger fluorophores and longer linkers, this donor-acceptor pair accurately reports short-range distances and changes in backbone distances. We further extend the method by using cysteine-reactive metal chelators, which allow the technique to be used in protein regions of unknown secondary structure or when native metal ion binding sites are present. This improved method overcomes several of the key limitations of classical FRET for intramolecular distance measurements.

Large-scale evaluation of dynamically important residues in proteins predicted by the perturbation analysis of a coarse-grained elastic model

Backgrounds

It is increasingly recognized that protein functions often require intricate conformational dynamics, which involves a network of key amino acid residues that couple spatially separated functional sites. Tremendous efforts have been made to identify these key residues by experimental and computational means.

Results

We have performed a large-scale evaluation of the predictions of dynamically important residues by a variety of computational protocols including three based on the perturbation and correlation analysis of a coarse-grained elastic model. This study is performed for two lists of test cases with >500 pairs of protein structures. The dynamically important residues predicted by the perturbation and correlation analysis are found to be strongly or moderately conserved in >67% of test cases. They form a sparse network of residues which are clustered both in 3D space and along protein sequence. Their overall conservation is attributed to their dynamic role rather than ligand binding or high network connectivity.

Conclusion

By modeling how the protein structural fluctuations respond to residue-position-specific perturbations, our highly efficient perturbation and correlation analysis can be used to dissect the functional conformational changes in various proteins with a residue level of detail. The predictions of dynamically important residues serve as promising targets for mutational and functional studies.

Large Protein Dynamics Described by Hierarchical-Component Mode Synthesis

Protein dynamics has played a pivotal role in understanding the biological function of protein. For investigation of such dynamics, normal-mode analysis (NMA) has been broadly employed with atomistic model and/or coarse-grained models such as elastic network model (ENM). For large protein complexes, NMA with even ENM encounters the expensive computational process such as diagonalization of Hessian (stiffness) matrix. Here, we suggest the hierarchical-component mode synthesis (hCMS), which allows the fast computation of low-frequency normal modes related to conformational change. Specifically, a large protein structure is regarded as a combination of several structural units, for which the eigen-value problem is utilized for obtaining the frequencies and their normal modes for each structural unit, and consequently, such frequencies and normal modes are assembled with geometrical constraint for interface between structural units in order to find the low-frequency normal modes of a large protein complex. It is shown that hCMS is able to provide the normal modes with accuracy, quantitatively comparable to those of original NMA. This implies that hCMS may enable the computationally efficient analysis of large protein dynamics.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

Vibrational subsystem analysis: A method for probing free energies and correlations in the harmonic limit

A new vibrational subsystem analysis (VSA) method is presented for coupling global motion to a local subsystem while including the inertial effects of the environment. The premise of the VSA method is a partitioning of a system into a smaller region of interest and a usually larger part referred to as environment. This method allows the investigation of local-global coupling, a more accurate estimation of vibrational free energy contribution for parts of a large system, and the elimination of the "tip effect" in elastic network model calculations. Additionally, the VSA method can be used as a probe of specific degrees of freedom that may contribute to free energy differences. The VSA approach can be employed in many ways, but it will likely be most useful for estimating activation free energies in QM/MM reaction path calculations. Four examples are presented to demonstrate the utility of this method.

Can morphing methods predict intermediate structures?

Movement is crucial to the biological function of many proteins, yet crystallographic structures of proteins can give us only a static snapshot. The protein dynamics that are important to biological function often happen on a timescale that is unattainable through detailed simulation methods such as molecular dynamics as they often involve crossing high-energy barriers. To address this coarse-grained motion, several methods have been implemented as web servers in which a set of coordinates is usually linearly interpolated from an initial crystallographic structure to a final crystallographic structure. We present a new morphing method that does not extrapolate linearly and can therefore go around high-energy barriers and which can produce different trajectories between the same two starting points. In this work, we evaluate our method and other established coarse-grained methods according to an objective measure: how close a coarse-grained dynamics method comes to a crystallographically determined intermediate structure when calculating a trajectory between the initial and final crystal protein structure. We test this with a set of five proteins with at least three crystallographically determined on-pathway high-resolution intermediate structures from the Protein Data Bank. For simple hinging motions involving a small conformational change, segmentation of the protein into two rigid sections outperforms other more computationally involved methods. However, large-scale conformational change is best addressed using a nonlinear approach and we suggest that there is merit in further developing such methods.

Backbone relaxation coupled to the ionization of internal groups in proteins: a self-guided Langevin dynamics study

Pathways of structural relaxation triggered by ionization of internal groups in staphylococcal nuclease (SNase) were studied through multiple self-guided Langevin dynamics (SGLD) simulations. Circular dichroism, steady-state Trp fluorescence, and nuclear magnetic resonance spectroscopy have shown previously that variants of SNase with internal Glu, Asp, and Lys at positions 66 or 92, and Arg at position 66, exhibit local reorganization or global unfolding when the internal ionizable group is charged. Except for Arg-66, these internal ionizable groups have unusual pKa values and are neutral at physiological pH. The structural trends observed in the simulations are in general agreement with experimental observations. The I92D variant, which unfolds globally upon ionization of Asp-92, in simulations often exhibits extensive hydration of the protein core, and sometimes also significant perturbations of the beta-barrel. In the crystal structure of the V66R variant, the beta1 strand from the beta-barrel is domain-swapped; in the simulations, the beta1 strand is sometimes partially released. The V66K variant, which in solutions shows reorganization of six residues at the C-terminus of helix alpha1 and perturbations in the beta-barrel structure, exhibits fraying of three residues of helix alpha1 in one simulation, and perturbations and partial unfolding of three beta-strands in a few other simulations. In sharp contrast, very small structural changes were observed in simulations of the wild-type protein. The simulations indicate that charging of internal groups frequently triggers penetration of water into the protein interior. The pKa values of Asp-92 and Arg-66 calculated with continuum methods on SGLD-relaxed structures reached the normal values in most simulations. Detailed analysis of accuracy and performance of SGLD demonstrates that SGLD outperforms LD in sampling of alternative protein conformations without loss of the accuracy and level of detail characteristic of regular LD.

Conformational transition pathways explored by Monte Carlo simulation integrated with collective modes

Conformational transitions between open/closed or free/bound states in proteins possess functional importance. We propose a technique in which the collective modes obtained from an anisotropic network model (ANM) are used in conjunction with a Monte Carlo (MC) simulation approach, to investigate conformational transition pathways and pathway intermediates. The ANM-MC technique is applied to adenylate kinase (AK) and hemoglobin. The iterative method, in which normal modes are continuously updated during the simulation, proves successful in accomplishing the transition between open-closed conformations of AK and tense-relaxed forms of hemoglobin (C(alpha)-root mean square deviations between two end structures of 7.13 A and 3.55 A, respectively). Target conformations are reached by root mean-square deviations of 2.27 A and 1.90 A for AK and hemoglobin, respectively. The intermediate conformations overlap with crystal structures from the AK family within a 3.0-A root mean-square deviation. In the case of hemoglobin, the transition of tense-to-relaxed passes through the relaxed state. In both cases, the lowest-frequency modes are effective during transitions. The targeted Monte Carlo approach is used without the application of collective modes. Both the ANM-MC and targeted Monte Carlo techniques can explore sequences of events in transition pathways with an efficient yet realistic conformational search.

Evolutionary conservation of protein vibrational dynamics

The aim of the present work is to study the evolutionary divergence of vibrational protein dynamics. To this end, we used the Gaussian Network Model to perform a systematic analysis of normal mode conservation on a large dataset of proteins classified into homologous sets of family pairs and superfamily pairs. We found that the lowest most collective normal modes are the most conserved ones. More precisely, there is, on average, a linear correlation between normal mode conservation and mode collectivity. These results imply that the previously observed conservation of backbone flexibility (B-factor) profiles is due to the conservation of the most collective modes, which contribute the most to such profiles. We discuss the possible roles of normal mode robustness and natural selection in the determination of the observed behavior. Finally, we draw some practical implications for dynamics-based protein alignment and classification and discuss possible caveats of the present approach.

Influence of oligomerization on the dynamics of G-protein coupled receptors as assessed by normal mode analysis

The recently discovered impact of oligomerization on G-protein coupled receptor (GPCR) function further complicates the already challenging goal of unraveling the molecular and dynamic mechanisms of these receptors. To help understand the effect of oligomerization on the dynamics of GPCRs, we have compared the motion of monomeric, dimeric, and tetrameric arrangements of the prototypic GPCR rhodopsin, using an approximate-yet powerful-normal mode analysis (NMA) technique termed elastic network model (ENM). Moreover, we have used ENM to discriminate between putative dynamic mechanisms likely to account for the recently observed conformational rearrangement of the TM4,5-TM4,5 dimerization interface of GPCRs that occurs upon activation. Our results indicate: (1) significant perturbation of the normal modes (NMs) of the rhodopsin monomer upon oligomerization, which is mainly manifested at interfacial regions; (2) increased positive correlation among the transmembrane domains (TMs) and between the extracellular loop (EL) and TM regions of the rhodopsin protomer; (3) highest interresidue positive correlation at the interfaces between protomers; and (4) experimentally testable hypotheses of differential motional changes within different putative oligomeric arrangements.

Mechanism of signal propagation upon retinal isomerization: insights from molecular dynamics simulations of rhodopsin restrained by normal modes

As one of the best studied members of the pharmaceutically relevant family of G-protein-coupled receptors, rhodopsin serves as a prototype for understanding the mechanism of G-protein-coupled receptor activation. Here, we aim at exploring functionally relevant conformational changes and signal transmission mechanisms involved in its photoactivation brought about through a cis-trans photoisomerization of retinal. For this exploration, we propose a molecular dynamics simulation protocol that utilizes normal modes derived from the anisotropic network model for proteins. Deformations along multiple low-frequency modes of motion are used to efficiently sample collective conformational changes in the presence of explicit membrane and water environment, consistent with interresidue interactions. We identify two highly stable regions in rhodopsin, one clustered near the chromophore, the other near the cytoplasmic ends of transmembrane helices H1, H2, and H7. Due to redistribution of interactions in the neighborhood of retinal upon stabilization of the trans form, local structural rearrangements in the adjoining H3-H6 residues are efficiently propagated to the cytoplasmic end of these particular helices. In the structures obtained by our simulations, all-trans retinal interacts with Cys(167) on H4 and Phe(203) on H5, which were not accessible in the dark state, and exhibits stronger interactions with H5, while some of the contacts made (in the cis form) with H6 are lost.

A unification of the elastic network model and the Gaussian network model for optimal description of protein conformational motions and fluctuations

Coarse-grained elastic models with a C(alpha)-only representation and harmonic interactions have been increasingly used to describe the conformational motions and flexibility of various proteins. In this work, we will unify two complementary elastic models--the elastic network model (ENM) and the Gaussian network model (GNM), in the framework of a generalized anisotropic network model (G-ANM) with a new anisotropy parameter, f(anm). The G-ANM is reduced to GNM at f(anm) = 1, and ENM at f(anm) = 0. By analyzing a list of protein crystal structure pairs using G-ANM, we have attained optimal descriptions of both the isotropic thermal fluctuations and the crystallographically observed conformational changes with a small f(anm) (f(anm) < or = 0.1) and a physically realistic cutoff distance, R(c) approximately 8 A. Thus, the G-ANM improves the performance of GNM and ENM while preserving their simplicity. The properly parameterized G-ANM will enable more accurate and realistic modeling of protein conformational motions and flexibility.

Coarse-grained free energy functions for studying protein conformational changes: a double-well network model

In this work, a double-well network model (DWNM) is presented for generating a coarse-grained free energy function that can be used to study the transition between reference conformational states of a protein molecule. Compared to earlier work that uses a single, multidimensional double-well potential to connect two conformational states, the DWNM uses a set of interconnected double-well potentials for this purpose. The DWNM free energy function has multiple intermediate states and saddle points, and is hence a "rough" free energy landscape. In this implementation of the DWNM, the free energy function is reduced to an elastic-network model representation near the two reference states. The effects of free energy function roughness on the reaction pathways of protein conformational change is demonstrated by applying the DWNM to the conformational changes of two protein systems: the coil-to-helix transition of the DB-loop in G-actin and the open-to-closed transition of adenylate kinase. In both systems, the rough free energy function of the DWNM leads to the identification of distinct minimum free energy paths connecting two conformational states. These results indicate that while the elastic-network model captures the low-frequency vibrational motions of a protein, the roughness in the free energy function introduced by the DWNM can be used to characterize the transition mechanism between protein conformations.

Coarse-graining of protein structures for the normal mode studies

The coarse-grained structural model such as Gaussian network has played a vital role in the normal mode studies for understanding protein dynamics related to biological functions. However, for the large proteins, the Gaussian network model is computationally unfavorable for diagonalization of Hessian (stiffness) matrix for the normal mode studies. In this article, we provide the coarse-graining method, referred to as "dynamic model condensation," which enables the further coarse-graining of protein structures consisting of small number of residues. It is shown that the coarser-grained structures reconstructed by dynamic model condensation exhibit the dynamic characteristics, such as low-frequency normal modes, qualitatively comparable to original structures. This sheds light on that dynamic model condensation and may enable one to study the large protein dynamics for gaining insight into biological functions of proteins.

Improved sampling methods for molecular simulation

Molecular simulation has broad application in the biological sciences. One of the greatest challenges in molecular simulation is the limited conformational sampling due to slow barrier crossing on the rugged energy landscape of complex biomolecules and to the relatively short simulation time. Many enhanced sampling techniques have been developed over the years to alleviate this problem. Significant progress has been made in the past couple of years, with emerging methods targeting specific aspects of the potential energy surface and new variants of the replica exchange method.

Simulation of the coupling between nucleotide binding and transmembrane domains in the ATP binding cassette transporter BtuCD

The nucleotide-induced structural rearrangements in ATP binding cassette (ABC) transporters, leading to substrate translocation, are largely unknown. We have modeled nucleotide binding and release in the vitamin B(12) importer BtuCD using perturbed elastic network calculations and biased molecular dynamics simulations. Both models predict that nucleotide release decreases the tilt between the two transmembrane domains and opens the cytoplasmic gate. Nucleotide binding has the opposite effect. The observed coupling may be relevant for all ABC transporters because of the conservation of nucleotide binding domains and the shared role of ATP in ABC transporters. The rearrangements in the cytoplasmic gate region do not provide enough space for B(12) to diffuse from the transporter pore into the cytoplasm, which could suggest that peristaltic forces are needed to exclude B(12) from the transporter pore.

SYMMETRY, FORM, AND SHAPE: Guiding Principles for Robustness in Macromolecular Machines

Computational studies of large macromolecular assemblages have come a long way during the past 10 years. With the explosion of computer power and parallel computing, timescales of molecular dynamics simulations have been extended far beyond the hundreds of picoseconds timescale. However, limitations remain for studies of large-scale conformational changes occurring on timescales beyond nanoseconds, especially for large macromolecules. In this review, we describe recent methods based on normal mode analysis that have enabled us to study dynamics on the microsecond timescale for large macromolecules using different levels of coarse graining, from atomically detailed models to those employing only low-resolution structural information. Emerging from such studies is a control principle for robustness in Nature's machines. We discuss this idea in the context of large-scale functional reorganization of the ribosome, virus particles, and the muscle protein myosin.

Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes

Recently we have developed a normal-modes-based algorithm that predicts the direction of protein conformational changes given the initial state crystal structure together with a small number of pairwise distance constraints for the end state. Here we significantly extend this method to accurately model both the direction and amplitude of protein conformational changes. The new protocol implements a multisteps search in the conformational space that is driven by iteratively minimizing the error of fitting the given distance constraints and simultaneously enforcing the restraint of low elastic energy. At each step, an incremental structural displacement is computed as a linear combination of the lowest 10 normal modes derived from an elastic network model, whose eigenvectors are reorientated to correct for the distortions caused by the structural displacements in the previous steps. We test this method on a list of 16 pairs of protein structures for which relatively large conformational changes are observed (root mean square deviation >3 angstroms), using up to 10 pairwise distance constraints selected by a fluctuation analysis of the initial state structures. This method has achieved a near-optimal performance in almost all cases, and in many cases the final structural models lie within root mean square deviation of 1 approximately 2 angstroms from the native end state structures.

Functional modes of proteins are among the most robust

It is shown that a small subset of modes which are likely to be involved in protein functional motions of large amplitude can be determined by retaining the most robust normal modes obtained using different protein models. This result should prove helpful in the context of several applications proposed recently, like for solving difficult molecular replacement problems or for fitting atomic structures into low-resolution electron density maps. It may also pave the way for the development of methods allowing us to predict such motions accurately.

Coarse-grained normal mode analysis in structural biology

The realization that experimentally observed functional motions of proteins can be predicted by coarse-grained normal mode analysis has renewed interest in applications to structural biology. Notable applications include the prediction of biologically relevant motions of proteins and supramolecular structures driven by their structure-encoded collective dynamics; the refinement of low-resolution structures, including those determined by cryo-electron microscopy; and the identification of conserved dynamic patterns and mechanically key regions within protein families. Additionally, hybrid methods that couple atomic simulations with deformations derived from coarse-grained normal mode analysis are able to sample collective motions beyond the range of conventional molecular dynamics simulations. Such applications have provided great insight into the underlying principles linking protein structures to their dynamics and their dynamics to their functions.