Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data.

A dynamic structure refinement method for X-ray crystallography, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the low-frequency normal modes whose amplitudes and eigenvectors are experimentally optimized in the process of the crystallographic refinement. In this model, the atomic fluctuations are treated as anisotropic and concerted. The normal modes of the external motion (TLS model) are also introduced to cover the factors other than the internal fluctuations, such as the lattice disorder and diffusion. A program for the normal mode refinement (NM-REF) has been developed. The method has first been tested against simulated diffraction data for human lysozyme calculated by a Monte Carlo simulation. Applications of the method have demonstrated that the normal mode refinement has: (1) improved the fitting to the diffraction data, even with fewer adjustable parameters; (2) distinguished internal fluctuations from external ones; (3) determined anisotropic thermal factors; and (4) identified concerted fluctuations in the protein molecule.     

Calculation of rigid-body conformational changes using restraint-driven Cartesian transformations

We present an approach for calculating conformational changes in membrane proteins using limited distance information. The method, named restraint-driven Cartesian transformations, involves 1) the use of relative distance changes; 2) the systematic sampling of rigid body movements in Cartesian space; 3) a penalty evaluation; and 4) model refinement using energy minimization. As a test case, we have analyzed the structural basis of activation gating in the Streptomyces lividans potassium channel (KcsA). A total of 10 pairs of distance restraints derived from site-directed spin labeling and electron paramagnetic resonance (SDSL-EPR) spectra were used to calculate the open conformation of the second transmembrane domains of KcsA (TM2). The SDSL-EPR based structure reveals a gating mechanism consistent with a scissoring-type motion of the TM2 segments that includes a pivot point near middle of the helix. The present approach considerably reduces the amount of time and effort required to establish the overall nature of conformational changes in membrane proteins. It is expected that this approach can be implemented into restrained molecular dynamics protocol to calculate the structure and conformational changes in a variety of membrane protein systems.     

NMR study of the tetrameric KcsA potassium channel in detergent micelles

Nuclear magnetic resonance (NMR) studies of large membrane-associated proteins are limited by the difficulties in preparation of stable protein-detergent mixed micelles and by line broadening, which is typical of these macroassemblies. We have used the 68-kDa homotetrameric KcsA, a thermostable N-terminal deletion mutant of a bacterial potassium channel from Streptomyces lividans, as a model system for applying NMR methods to membrane proteins. Optimization of measurement conditions enabled us to perform the backbone assignment of KcsA in SDS micelles and establish its secondary structure, which was found to closely agree with the KcsA crystal structure. The C-terminal cytoplasmic domain, absent in the original structure, contains a 14-residue helix that could participate in tetramerization by forming an intersubunit four-helix bundle. A quantitative estimate of cross- relaxation between detergent and KcsA backbone amide protons, together with relaxation and light scattering data, suggests SDS-KcsA mixed micelles form an oblate spheroid with approximately 180 SDS molecules per channel. K(+) ions bind to the micelle-solubilized channel with a K(D) of 3 +/- 0.5 mM, resulting in chemical shift changes in the selectivity filter. Related pH-induced changes in chemical shift along the "outer" transmembrane helix and the cytoplasmic membrane interface hint at a possible structural explanation for the observed pH-gating of the potassium channel.     

Refinement of F-Actin Model against Fiber Diffraction Data by Long-Range Normal Modes

The atomic model of F-actin was refined against fiber diffraction data using long-range normal modes as adjustable parameters to account for the collective long-range filamentous deformations. To determine the effect of long-range deformations on the refinement, each of the four domains of G-actin was treated as a rigid body. It was found that among all modes, the bending modes make the most significant contributions to the improvement of the refinement. Inclusion of only 7–9 bending modes as adjustable parameters yielded a lowest R-factor of 6.3%. These results demonstrate that employing normal modes as refinement parameters has the advantage of using a small number of adjustable parameters to achieve a good fitting efficiency. Such a refinement procedure may therefore prevent the refinement from overfitting the structural model. More importantly, the results of this study demonstrate that, for any fiber diffraction data, a substantial amount of refinement error is due to long-range deformations, especially the bending, of the filaments. The effects of these intrinsic deformations cannot be easily compensated for by adjusting local structural parameters, and must be properly accounted for in the refinement to achieve improved fit of refined models with experimental diffraction data.     

Normal mode refinement: crystallographic refinement of protein dynamic structure applied to human lysozyme.

A new method of dynamic structure refinement of protein x-ray crystallography, normal mode refinement, is developed. In this method the Debye-Waller factor is expanded in terms of the low-frequency normal modes and external normal modes, whose amplitudes and couplings are optimized in the process of crystallographic refinement. By this method, internal and external contributions to the atomic fluctuations can be separated. Also, anisotropic atomic fluctuations and their interatomic correlations can be determined experimentally even with a relatively small number of adjustable parameters. The method is applied to the analysis of experimental data of human lysozyme to reveal its dynamic structure.     

Molecular Dynamics Simulation of WSK-3, a Computationally Designed, Water-Soluble Variant of the Integral Membrane Protein KcsA

Poor solubility and low expression levels often make membrane proteins difficult to study. An alternative to the use of detergents to solubilize these aggregation-prone proteins is the partial redesign of the sequence so as to confer water solubility. Recently, computationally assisted membrane protein solubilization (CAMPS) has been reported, where exposed hydrophobic residues on a protein's surface are computationally redesigned. Herein, the structure and fluctuations of a designed, water-soluble variant of KcsA (WSK-3) were studied using molecular dynamics simulations. The root mean square deviation of the protein from its starting structure, where the backbone coordinates are those of KcsA, was 1.8 angstroms. The structure of salt bridges involved in structural specificity and solubility were examined. The preferred configuration of ions and water in the selectivity filter of WSK-3 was consistent with the reported preferences for KcsA. The structure of the selectivity filter was maintained, which is consistent with WSK-3 having an affinity for agitoxin2 comparable to that of wild-type KcsA. In contrast to KcsA, the central cavity's side chains were observed to reorient, allowing water diffusion through the side of the cavity wall. These simulations provide an atomistic analysis of the CAMPS strategy and its implications for further investigations of membrane proteins.     

Nuclear magnetic resonance structural studies of a potassium channel-charybdotoxin complex

Ion channels play critical roles in signaling processes and are attractive targets for treating various diseases. Here we describe an NMR-based strategy for structural analyses of potassium channel-ligand complexes using KcsA (residues 1-132, with six mutations to impart toxin binding and to mimic the eukaryotic hERG channel). Using this approach, we determined the solution structure of KcsA in complex with the high-affinity peptide antagonist charybdotoxin. The structural data reveal how charybdotoxin binds to the closed form of KcsA and makes specific contacts with the extracellular surface of the ion channel, resulting in pore blockage. This represents the first direct structural information about an ion channel complexed to a peptide antagonist and provides an experimental framework for understanding and interpreting earlier mutational analyses. The strategy presented here overcomes many of the limitations of conventional NMR approaches to helical membrane protein structure determination and can be applied in the study of the binding of druglike molecules to this important class of proteins.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. II. Application to human lysozyme.

The dynamic structure of a protein, human lysozyme, is determined by the normal mode refinement of X-ray crystal structure. This method uses the normal modes of both internal and external motions to distinguish the real internal dynamics from the external terms such as lattice disorder, and gives an anisotropic and concerted picture of atomic fluctuations. The refinement is carried out with diffraction data of 5.0 to 1.8 A resolution, which are collected on an imaging plate. The results of the refinement show: (1) Debye-Waller factor consists of two parts, highly anisotropic internal fluctuations and almost isotropic external terms. The former is smaller than the latter by a factor of 0.72 in the scale of B-factor. Therefore, the internal dynamics cannot be recognized directly from the apparent electron density distribution. (2) The internal fluctuations show basically similar features as those predicted by the normal mode analysis, with almost the same amplitude and a similar level of anisotropy. (3) Correlations of fluctuations are detected between two lobes forming the active site cleft, which move simultaneously in opposite directions. This corresponds to the hinge-bending motion of lysozyme.     

Refinement of docked protein-ligand and protein-DNA structures using low frequency normal mode amplitude optimization

Prediction of structural changes resulting from complex formation, both in ligands and receptors, is an important and unsolved problem in structural biology. In this work, we use all-atom normal modes calculated with the Elastic Network Model as a basis set to model structural flexibility during formation of macromolecular complexes and refine the non-bonded intermolecular energy between the two partners (protein-ligand or protein-DNA) along 5-10 of the lowest frequency normal mode directions. The method handles motions unrelated to the docking transparently by first applying the modes that improve non-bonded energy most and optionally restraining amplitudes; in addition, the method can correct small errors in the ligand position when the first six rigid-body modes are switched on. For a test set of six protein receptors that show an open-to-close transition when binding small ligands, our refinement scheme reduces the protein coordinate cRMS by 0.3-3.2 A. For two test cases of DNA structures interacting with proteins, the program correctly refines the docked B-DNA starting form into the expected bent DNA, reducing the DNA cRMS from 8.4 to 4.8 A and from 8.7 to 5.4 A, respectively. A public web server implementation of the refinement method is available at http://lorentz.immstr.pasteur.fr.     

Mechanism of intracellular block of the KcsA K+ channel by tetrabutylammonium: insights from X-ray crystallography, electrophysiology and replica-exchange molecular dynamics simulations

The mechanism of intracellular blockade of the KcsA potassium channel by tetrabutylammonium (TBA) is investigated through functional, structural and computational studies. Using planar-membrane electrophysiological recordings, we characterize the binding kinetics as well as the dependence on the transmembrane voltage and the concentration of the blocker. It is found that the apparent affinity of the complex is significantly greater than that of any of the eukaryotic K(+) channels studied previously, and that the off-rate increases with the applied transmembrane voltage. In addition, we report a crystal structure of the KcsA-TBA complex at 2.9 A resolution, with TBA bound inside the large hydrophobic cavity located at the center of the channel, consistent with the results of previous functional and structural studies. Of particular interest is the observation that the presence of TBA has a negligible effect on the channel structure and on the position of the potassium ions occupying the selectivity filter. Inspection of the electron density corresponding to TBA suggests that the ligand may adopt more than one conformation in the complex, though the moderate resolution of the data precludes a definitive interpretation on the basis of the crystallographic refinement methods alone. To provide a rationale for these observations, we carry out an extensive conformational sampling of an atomic model of TBA bound in the central cavity of KcsA, using the Hamiltonian replica-exchange molecular dynamics simulation method. Comparison of the simulated and experimental density maps indicates that the latter does reflect at least two distinct binding orientations of TBA. The simulations show also that the relative population of these binding modes is dependent on the ion configuration occupying the selectivity filter, thus providing a clue to the nature of the voltage-dependence of the binding kinetics.     

Specific Xray diffraction patterns of membrane proteins caused by secondary structure collinearity

Diffraction anisotropy is a phenomenon that impacts more specifically membrane proteins, compared to soluble ones, but the reasons for this discrepancy remained unclear. Often, it is referred to a difference in resolution limits between highest and lowest diffraction limits as a signature for anisotropy. We show in this article that there is no single correlation between anisotropy and difference in resolution limits, with notably a substantial number of structures displaying various anisotropy with no difference in resolution limits. We further investigated diffraction intensity profiles, and observed a peak centred on 4.9 Å resolution more predominant in membrane proteins. Since this peak is in the region corresponding to secondary structures, we investigated the influence of secondary structure ratio. We showed that secondary structure content has little influence on this profile, while secondary structure collinearity in membrane proteins correlate with a stronger peak. Finally, we could further show that the presence of this peak is linked to higher diffraction anisotropy. These results bring to light a specific diffraction of membrane protein crystals, which calls for a specific handling by crystallographic software. It also brings an explanation for investigators struggling with their anisotropic data.     

Structural characterization and pH-induced conformational transition of full-length KcsA

The bacterial K+ channel KcsA from Streptomyces lividans was analyzed by neutron and x-ray small-angle solution scattering. The C-terminally truncated version of KcsA, amenable to crystallographic studies, was compared with the full-length channel. Analyzing the scattering data in terms of radius of gyration reveals differences between both KcsA species of up to 13.2 A. Equally, the real-space distance distribution identifies a 40 to 50 A extension of full-length KcsA compared to its C-terminally truncated counterpart. We show that the x-ray and neutron scattering data are amenable for molecular shape reconstruction of full-length KcsA. The molecular envelopes calculated display an hourglass-shaped structure within the C-terminal intracellular domain. The C-terminus extends the membrane spanning region of KcsA by 54-70 A, with a central constriction 10-30 A wide. Solution scattering techniques were further employed to characterize the KcsA channel under acidic conditions favoring its open conformation. The full-length KcsA at pH 5.0 shows the characteristics of a dumbbell-shaped macromolecular structure, originating from dimerization of the tetrameric K+ channel. Since C-terminally truncated KcsA measured under the same low pH conditions remains tetrameric, oligomerization of full-length KcsA seems to proceed via structurally changed C-terminal domains. The determined maximum dimensions of the newly formed complex increase by 50-60%. Shape reconstruction of the pseudooctameric complex indicates the pH-induced conformational reorganization of the intracellular C-terminal domain.     

High-resolution membrane protein structure by joint calculations with solid-state NMR and X-ray experimental data

X-ray diffraction and nuclear magnetic resonance spectroscopy (NMR) are the staple methods for revealing atomic structures of proteins. Since crystals of biomolecular assemblies and membrane proteins often diffract weakly and such large systems encroach upon the molecular tumbling limit of solution NMR, new methods are essential to extend structures of such systems to high resolution. Here we present a method that incorporates solid-state NMR restraints alongside of X-ray reflections to the conventional model building and refinement steps of structure calculations. Using the 3.7 Å crystal structure of the integral membrane protein complex DsbB-DsbA as a test case yielded a significantly improved backbone precision of 0.92 Å in the transmembrane region, a 58% enhancement from using X-ray reflections alone. Furthermore, addition of solid-state NMR restraints greatly improved the overall quality of the structure by promoting 22% of DsbB transmembrane residues into the most favored regions of Ramachandran space in comparison to the crystal structure. This method is widely applicable to any protein system where X-ray data are available, and is particularly useful for the study of weakly diffracting crystals.     

Fluid bilayer structure determination by the combined use of x-ray and neutron diffraction. II. "Composition-space" refinement method.

This is the second of two papers describing a method for the joint refinement of the structure of fluid bilayers using x-ray and neutron diffraction data. We showed in the first paper (Wiener, M. C., and S. H. White. 1990. Biophys. J. 59:162-173) that fluid bilayers generally consist of a nearly perfect lattice of thermally disordered unit cells and that the canonical resolution d/hmax is a measure of the widths of quasimolecular components represented by simple Gaussian functions. The thermal disorder makes possible a "composition space" representation in which the quasimolecular Gaussian distributions describe the number or probability of occupancy per unit length across the width of the bilayer of each component. This representation permits the joint refinement of neutron and x-ray lamellar diffraction data by means of a single quasimolecular structure that is fit simultaneously to both diffraction data sets. Scaling of each component by the appropriate neutron or x-ray scattering length maps the composition space profile to the appropriate scattering length space for comparison to experimental data. Other extensive properties, such as mass, can also be obtained by an appropriate scaling of the refined composition space structure. Based upon simple bilayer models involving crystal and liquid crystal structural information, we estimate that a fluid bilayer with hmax observed diffraction orders will be accurately represented by a structure with approximately hmax quasimolecular components. Strategies for assignment of quasimolecular components are demonstrated through detailed parsing of a phospholipid molecule based upon the one-dimensional projection of the crystal structure of dimyristoylphosphatidylcholine. Finally, we discuss in detail the number of experimental variables required for the composition space joint refinement. We find fluid bilayer structures to be marginally determined by the experimental data. The analysis of errors, which takes on particular importance under these circumstances, is also discussed.     

Normal modes as refinement parameters for the F-actin model.

The slow normal modes of G-actin were used as structural parameters to refine the F-actin model against 8-A resolution x-ray fiber diffraction data. The slowest frequency normal modes of G-actin pertain to collective rearrangements of domains, motions that are characterized by correlation lengths on the order of the resolution of the fiber diffraction data. Using a small number of normal mode degrees of freedom (< or = 12) improved the fit to the data significantly. The refined model of F-actin shows that the nucleotide binding cleft has narrowed and that the DNase I binding loop has twisted to a lower radius, consistent with other refinement techniques and electron microscopy data. The methodology of a normal mode refinement is described, and the results, as applied to actin, are detailed.     

Diffracted X-ray tracking method for recording single-molecule protein motions

BackgroundProteins change their conformation depending on function. Although a vast number of static pictures of proteins have been accumulated, information regarding their dynamics in function is limited. Diffracted X-ray tracking (DXT) is a good candidate to obtain the missing data.Scope of reviewA gold nanocrystal was attached to the target protein as a probe and the motion of the X-ray diffraction spots from the crystal corresponded to the motion of the target. Although it has advantages of high temporal (sub-millisecond) and spatial (approximately 0.1°) resolutions, it is not extensively utilized. This review focused on its effective application from a user's perspective. We also present an example with the KcsA channel and the status of recent developments to show the future possibilities of the method.Major conclusionsDXT is a powerful method to investigate intramolecular structural changes. For instance, in the KcsA channel, the method revealed a wave of conformational changes transmitted from the gate region to the end of the molecule. The method is continuously being developed, and users can choose an appropriate measurement system depending on the condition of their sample.General significanceRevealing the protein structural changes with respect to function is an important frontier. The most distinctive feature of the DXT method is that both high temporal and spatial resolutions are achievable, and it is possible to track the motions of multiple molecules at the same time. This feature is an advantage for screening molecules associated with the target proteins (e.g., ligands and medicines).     

Setting up and optimization of membrane protein simulations

In this paper we describe a method for setting up an atomistic simulation of a membrane protein in a hydrated lipid bilayer and report the effect of differing electrostatic parameters on the drift in the protein structure during the subsequent simulation. The method aims to generate a suitable cavity in the interior of a lipid bilayer, using the solvent-accessible surface of the protein as a template, during the course of a short steered molecular dynamics simulation of a solvated lipid membrane. This is achieved by a two-stage process: firstly, lipid molecules whose headgroups are inside a cylindrical volume equivalent to that defined by the protein surface are removed; then the protein-lipid interface is optimized by applying repulsive forces perpendicular to the protein surface, and of gradually increased magnitude, to the remaining lipid atoms inside the volume occupied by the protein surface until it is emptied. The protein itself may then be inserted. Using the bacterial membrane proteins KcsA and FhuA as test cases, we show how the method achieves the formation of a suitable cavity in the interior of a dimyristoylphosphatidylcholine lipid bilayer without perturbing the configuration of the non-interfacial regions of the previously equilibrated lipid bilayer, even in cases of membrane proteins with irregular geometrical shapes. In addition, we compare subsequent simulations in which the long-range electrostatic interactions are treated via either a cut-off or a particle-mesh Ewald method. The results show that the drift from the initial structure is less in the latter case, especially for KcsA and for the non-core secondary structural elements (i.e. surface loops) of both proteins.     

Mapping of unfolding states of integral helical membrane proteins by GPS-NMR and scattering techniques: TFE-induced unfolding of KcsA in DDM surfactant

Membrane proteins are vital for biological function, and their action is governed by structural properties critically depending on their interactions with the membranes. This has motivated considerable interest in studies of membrane protein folding and unfolding. Here the structural changes induced by unfolding of an integral membrane protein, namely TFE-induced unfolding of KcsA solubilized by the n-dodecyl β-d-maltoside (DDM) surfactant is investigated by the recently introduced GPS-NMR (Global Protein folding State mapping by multivariate NMR) (Malmendal et al., PlosONE 5, e10262 (2010)) along with dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS). GPS-NMR is used as a tool for fast analysis of the protein unfolding processes upon external perturbation, and DLS and SAXS are used for further structural characterization of the unfolding states. The combination allows addressing detergent properties and protein conformations at the same time. The mapping of the states reveals that KcsA undergoes a series of rearrangements which include expansion of the tetramer in several steps followed by dissociation into monomers at 29% TFE. Supplementary studies of DDM and TFE in the absence of KcsA suggest that the disintegration of the tetramer at 29% TFE is caused by TFE dissolving the surrounding DDM rim. Above 34% TFE, KcsA collapses to a new structure that is fully formed at 44% TFE.