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.     

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.     

Direct determination of crystallographic phases for diffraction data from lipid bilayers. I. Reliability and phase refinement.

Direct analysis of lipid lamellar packing based on the probabilistic estimate of sigma 1- and sigma 2-triplet phase invariants is evaluated here for a large variety of bilayer structures than examined in an original study of this problem (Dorset, D.L., 1990. Biophys. J. 58:1077-1087). Using x-ray crystal structures of five phospholipids, three glycerides and two cerebrosides, lamellar diffraction data were generated at the approximately 3 A resolution often found experimentally from oriented multilayers. For structures where no significant density occurs at the unit cell origin, the ab initio phase determination is successful for six of the ten structures. A seventh structure can be solved if a limited set of sigma 2-triples are used to determine the initial phase set based on the hierarchy of the A2 values. Bilayers, e.g., with solvent at the origin, can be analyzed if a modified criterion for accepting phase estimates for sigma 1-triples is used, as suggested by the distribution of normalized structure factors and the number of probable single-valued phase domains. In all cases, partial phase determinations can be refined effectively by density modification ("flattening") of the hydrocarbon region in real space. A figure of merit suggested by Luzzati et al. (Luzzati, V., A. Tardieu, and D. Taupin. 1972. J. Mol. Biol. 64:269-286) used to evaluate the success of such refinement can be supplemented by an evaluation of density smoothness, which can also detect the presence of near structure homomorphs not identified by the former test for density flatness.     

Effect of anisotropy and anharmonicity on protein crystallographic refinement. An evaluation by molecular dynamics

Molecular dynamics simulations are employed to determine the errors introduced by anharmonicity and anisotropy in the structure and temperature factors obtained for proteins by refinement of X-ray diffraction data. Simulations (25 ps and 300 ps) of metmyoglobin are used to generate time-averaged diffraction data at 1.5 A resolution. The crystallographic restrained-parameter least-squares refinement program PROLSQ is used to refine models against these simulated data. The resulting atomic positions and isotropic temperature factors are compared with the average structure and fluctuations calculated directly from the simulations. It is found that significant errors in the atomic positions and fluctuations are introduced by the refinement, and that the errors increase with the magnitude of the atomic fluctuations. Of particular interest is the fact that the refinement generally underestimates the atomic motions. Moreover, while the actual fluctuations go up to a mean-square value of about 5 A2, the X-ray results never go above approximately 2 A2. This systematic deviation in the motional parameters appears to be due to the use of a single-site isotropic model for the atomic fluctuations. Many atoms have multiple peaks in their probability distribution functions. For some atoms, the multiple peaks are seen in difference electron density maps and it is possible to include these in the refinement as disordered residues. However, for most atoms the refinement fits only one peak and neglects the rest, leading to the observed errors in position and temperature factor. The use of strict stereochemical restraints is inconsistent with the average dynamical structure; nevertheless, refinement with tight restraints results in structures that are comparable to those obtained with loose restraints and better than those obtained with no restraints. The results support the use of tight stereochemical restraints, but indicate that restraints on the variation of temperature factors are too restrictive.     

Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. III. Complete structure.

We present in this paper the complete structure of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) in the L alpha phase (66% RH, 23 degrees C) obtained by the joint refinement of neutron and x-ray lamellar diffraction data. The structural details obtained have previously required a large number of neutron diffraction experiments, using numerous specifically-deuterated phospholipid isomorphs (Büldt et al., 1978. Nature (Lond.). 271:182-184). The joint-refinement approach minimizes specific deuteration by utilizing independent neutron and x-ray data sets. The method yields a quasimolecular structure consisting of a series of multiatomic fragments that are each represented by one or several Gaussian distributions whose positions and widths can be determined to within 0.06 to 0.52 A exclusive of the methylene region. The image of DOPC at 66% RH (5.36 +/- 0.08 waters per lipid) is consistent with many aspects of bilayer structure previously determined by structural and spectroscopic studies. The most striking feature of the structure is the large amount of transbilayer thermal motion suggested by the widths and overlaps of the Gaussian envelopes of the quasimolecular fragments. We discuss the "dynamic bilayer thickness" which describes the minimum effective thickness of the hydrocarbon permeability barrier in terms of the thermal motion of the water. A gradient of thermal motion exists that increases in either direction away from the glycerol backbone which is the most constrained portion of the bilayer. The steric interactions between headgroups of apposed bilayers, expected at the hydration level of our experiments, are clearly revealed. A useful consequence of the quasimolecular structure is that average boundaries within bilayers calculated using composition and volumetric data and ad hoc assumptions can be related to the positions of the principal structural groups. Several measures of "bilayer thickness" in common use can be identified as the positions of the cholines for Luzzati's d1 (Luzzati and Husson. 1962. J. Cell Biol. 12:207-219) and the glycerols for Small's dL (Small. 1967. J. Lipid Res. 8:551-556). We do not know if these relations will be true at other hydrations or for other lipids. Of particular interest is the fact that the position of the carbonyl groups marks the average hydrocarbon/headgroup boundary. It must be emphasized, however, that this region of the bilayer must be generally characterized as one of tumultuous chemical heterogeneity because of the thermal motion of the bilayer.     

Structure of human lactoferrin: crystallographic structure analysis and refinement at 2.8 A resolution

The structure of human lactoferrin has been refined crystallographically at 2.8 A (1 A = 0.1 nm) resolution using restrained least squares methods. The starting model was derived from a 3.2 A map phased by multiple isomorphous replacement with solvent flattening. Rebuilding during refinement made extensive use of these experimental phases, in combination with phases calculated from the partial model. The present model, which includes 681 of the 691 amino acid residues, two Fe3+, and two CO3(2-), gives an R factor of 0.206 for 17,266 observed reflections between 10 and 2.8 A resolution, with a root-mean-square deviation from standard bond lengths of 0.03 A. As a result of the refinement, two single-residue insertions and one 13-residue deletion have been made in the amino acid sequence, and details of the secondary structure and tertiary interactions have been clarified. The two lobes of the molecule, representing the N-terminal and C-terminal halves, have very similar folding, with a root-mean-square deviation, after superposition, of 1.32 A for 285 out of 330 C alpha atoms; the only major differences being in surface loops. Each lobe is subdivided into two dissimilar alpha/beta domains, one based on a six-stranded mixed beta-sheet, the other on a five-stranded mixed beta-sheet, with the iron site in the interdomain cleft. The two iron sites appear identical at the present resolution. Each iron atom is coordinated to four protein ligands, 2 Tyr, 1 Asp, 1 His, and the specific Co3(2-), which appears to bind to iron in a bidentate mode. The anion occupies a pocket between the iron and two positively charged groups on the protein, an arginine side-chain and the N terminus of helix 5, and may serve to neutralize this positive charge prior to iron binding. A large internal cavity, beyond the Arg side-chain, may account for the binding of larger anions as substitutes for CO3(2-). Residues on the other side of the iron site, near the interdomain crossover strands could provide secondary anion binding sites, and may explain the greater acid-stability of iron binding by lactoferrin, compared with serum transferrin. Interdomain and interlobe interactions, the roles of charged side-chains, heavy-atom binding sites, and the construction of the metal site in relation to the binding of different metals are also discussed.     

Vibrational analysis of the structure of gramicidin A. I. Normal mode analysis.

Normal mode frequencies have been calculated for single-stranded beta 4.4 and beta 6.3 and for double-stranded increases decreases beta 5.6, increases decreases beta 7.2, increases increases beta 5.6, and increases increases beta 7.2 helices that are possible models for the structure of gramicidin A. The force field used in the calculations is one that reproduces the frequencies of model polypeptide chain structures to about +/- 5 cm-1, and is therefore expected to provide meaningful distinctions between these conformations. The calculations predict significant differences in the infrared and Raman spectra of these beta-helices, suggesting that they should be identifiable from their spectra (which is shown in the following paper to be the case). The most sensitive region is that of the amide I frequencies, where the predicted patterns of intense infrared mode, infrared splittings, and intense Raman mode provide a characteristic identification of each of the above structures.     

The structure of a repressor: crystallographic data for the Cro regulatory protein of bacteriophage lambda.

Crystals of the bacteriophage λ Cro repressor protein that are suitable for X-ray diffraction studies have been obtained. Preliminary crystallographic analysis reveals that the space group is R32, the cell dimensions in the hexagonal system are $\text{a = b = 91·9}\text{A}\text{?}\text{, c = 268·9}\text{A}\text{?}$, and there are three dimers per asymmetric unit.     

Direct determination of crystallographic phases for diffraction data from phospholipid multilamellar arrays.

Direct determination of crystallographic phases based on probabilistic of sigma 1 and sigma 2 "triplet" structure invariants has been found to be an effective technique for structure analysis with lamellar x-ray or electron diffraction intensity data from phospholipids. In many cases, nearly all phase values are determined, permitting a structure density (electron density for x-ray diffraction; electrostatic potential for electron diffraction) map to be calculated, which is directly interpretable in terms of known bilayer lipid structure. The major source of error is found to be due to the distortion of observed electron diffraction intensity data by incoherent multiple scattering, which can significantly affect the appearance of the electrostatic potential map, but not the success of the phase determination, as long as the observed Patterson function can be interpreted.     

Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. I. Scaling of neutron data and the distributions of double bonds and water.

We described in two previous papers a method for the joint refinement of the structure of fluid bilayers using neutron and x-ray diffraction data (Wiener, M. C., and S. H. White 1991a, b. Biophys. J. 59: 162-173 and 174-185). An essential part of the method is the appropriate scaling of the diffraction data. Here we describe the scaling of the neutron data and the determination of the transbilayer distribution of double bonds in liquid-crystalline (L alpha phase) phospholipid bilayers of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). The distribution was determined by neutron diffraction of oriented multilayers (66% RH) of DOPC specifically deuterated at the 9- and 10-position of both acyl chains. The double-bond distribution is described accurately by a pair of Gaussian functions each located at a position Zcc = 7.88 +/- 0.09 A from the bilayer center with 1/e-halfwidths of Acc = 4.29 +/- 0.16 A. Previously, we determined the transbilayer distribution of bromine atoms in a specifically halogenated lipid, 1-oleoyl-2-9,10-dibromostearoyl-sn-glycero-3-phosphocholine (OBPC), and showed it to be an isomorphous replacement for DOPC (Wiener, M. C., and S. H. White, 1991c. Biochemistry. In press). A comparison of the double-bond and bromine profiles indicates that the positions of the centers of the deuterated double bond and the brominated methylene Gaussian distributions are equal within experimental error and that each label undergoes similar average thermal motions with respect to the bilayer normal.(ABSTRACT TRUNCATED AT 250 WORDS)     

A new Hybrid Monte Carlo algorithm for protein potential function test and structure refinement

A new Hybrid Monte Carlo (HMC) algorithm has been developed to test protein potential functions and, ultimately, refine protein structures. The main principle of this algorithm is, in each cycle, a new trial conformation is generated by carrying out a short period of molecular dynamics (MD) iterations with a set of random parameters (including the MD time step, the number of MD steps, the MD temperature, and the seed for initial MD velocity assignment); then to accept or reject the new conformation on the basis of the Metropolis criterion. The novelty in this paper is that the potential in MD iterations is different from that in the MC step. In the former, it is a molecular mechanics potential, in the latter it is a knowledge-based potential (KBP). Directed by the KBP, the MD iteration is used to search conformational space for realistic conformations with low KBP energy. It circumvents the difficulty in using KBP functions directly in MD simulation, as KBP functions are typically incomplete, and do not always have continuous derivatives required for the calculation of the forces. The new algorithm has been tested in explorations of conformational space. In these test calculations the KBP energy was found to drop below the value for the native conformation, and the correlation between the root mean square deviation (RMSD) and the KBP energy was shown to be different from the test results in other references. At the present time, the algorithm is useful for testing new KBP functions. Furthermore, if a KBP function can be found for which the native conformation has the lowest energy and the energy/RMSD correlation is good, then this new algorithm also will be a tool for refinement of the theory-based structural models.     

Crystallization and preliminary crystallographic data of bovine pancreatic deoxyribonuclease I

Bovine pancreatic deoxyribonuclease I has been crystallized using the method of precipitation by polyethylene glycol 6000. The crystals diffract to 1.8 Å and belong to space group C2 with cell dimensions: $\text{a = 131.6}\text{A}\text{?}\text{, b = 54.9}\text{A}\text{?}\text{, c = 38.4}\text{A}\text{?}\text{, β = 91.4 °}$ and one molecule per asymmetric unit.     

A productive NADP+ binding mode of ferredoxin-NADP + reductase revealed by protein engineering and crystallographic studies.

The flavoenzyme ferredoxin-NADP+ reductase (FNR) catalyzes the production of NADPH during photosynthesis. Whereas the structures of FNRs from spinach leaf and a cyanobacterium as well as many of their homologs have been solved, none of these studies has yielded a productive geometry of the flavin-nicotinamide interaction. Here, we show that this failure occurs because nicotinamide binding to wild type FNR involves the energetically unfavorable displacement of the C-terminal Tyr side chain. We used mutants of this residue (Tyr 308) of pea FNR to obtain the structures of productive NADP+ and NADPH complexes. These structures reveal a unique NADP+ binding mode in which the nicotinamide ring is not parallel to the flavin isoalloxazine ring, but lies against it at an angle of approximately 30 degrees, with the C4 atom 3 A from the flavin N5 atom.     

Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM

A new method for the flexible fitting of high-resolution structures into low-resolution maps of macromolecular complexes from electron microscopy has been recently described in applications to simulated electron density maps. This method uses a linear combination of low-frequency normal modes in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. Gradient-following techniques in the coordinate space of collective normal modes are used to optimize the overall correlation coefficient between computed and measured electron densities. With this approach, multi-scale flexible fitting can be performed using all-atoms or Calpha atoms. In this paper, illustrative studies of normal mode based flexible fitting to experimental cryo-EM maps are presented for three different systems. Large, functionally relevant conformational changes for elongation factor G bound to the ribosome, Escherichia coli RNA polymerase and cowpea chlorotic mottle virus are elucidated as the result of the application of NMFF from high-resolution structures to cryo-electron microscopy maps.     

Direct determination of crystallographic phases for diffraction data from lipid bilayers. II. Refinement of phospholipid structures.

Using a systematic approach for the acceptance of crystallographic phase assignment, based on the evaluation of triplet structure invariants, electron and x-ray diffraction data from phospholipid multilamellar arrays are analyzed by direct methods. After calculation of Fourier maps with a partial set of phased structure factor magnitudes, the structure is refined in real space by flattening of the hydrocarbon region of the bilayer and an optimal solution is sought either by the calculation of [delta rho 4] suggested by Luzzati, where rho is the structure density or by a test of density smoothness [magnitude of delta rho/ delta r magnitude of], where r positions are located along the normal to the lamellar surface. Reanalyses of previously determined structures sometimes lead to new conclusions (e.g., a possible similarity of the electron density profile for DL-DMPE and L-DMPE, and a clear indication of the fatty acid adduct in the mixed L-DPPC/palmitic acid bilayer). Because of presumed secondary scattering perturbations (primarily to the least intense reflections), the refinements of the electron diffraction intensities are less easily evaluated than those carried out with x-ray diffraction data.     

Crystallization and preliminary crystallographic data of chicken gizzard G-actin . DNase I complex and Physarum G-actin . DNase I complex.

Smooth muscle G-actin from chicken gizzard and Physarum plasmodium G-actin both interact with DNase I and form 1 : 1 complexes. These complexes were crystallized by using polyethylene glycol 6000 as a precipitant. Both crystals belong to the same orthorhombic space group P2(1)2(1)2(1). The cell dimensions of chicken gizzard G-actin.DNase I complex are a=42.00 +/- 0.07 A, b=225.3 +/- 0.4 A, and c=77.4 +/- 0.1 A, while those of Physarum G-actin.DNase I complex are a=42 A, b=221 A, and c=77 A.     

Study of the structure of immunoglobins by small-angle x-ray diffraction. I. The structure of IgMCep in solution

The data of small-angle X-ray scattering from monoclonal immunoglobulin MCep (IgM) enabled the shape and geometrical parameters of the molecule in solution at 23 degrees C to be established. The molecule is a flat, strongly anisometric particle with radius of gyration 115 A, volume 1,8 X 10(6) A3, maximum size 380 A, thickness 35-40 A. The most probable molecular model in the approximation of homogeneous electron density in the molecule was suggested, its geometry fitting the experimental parameters. The five IgM subunits are located in the equatorial plane, low-electronic-density regions are located in the centre and at the periphery of the macromolecule. In addition, the absence of fixed angle values between Fab-regions in each subunit is indicative of rather high structural mobility at the periphery of the IgM molecule.     

Schistosoma mansoni fatty acid binding protein: specificity and functional control as revealed by crystallographic structure

Schistosoma mansoni fatty acid binding protein (Sm14) was crystallized with bound oleic acid (OLA) and arachidonic acid (ACD), and their structures were solved at 1.85 and 2.4 A resolution, respectively. Sm14 is a vaccine target for schistosomiasis, the second most prevalent parasitic disease in humans. The parasite is unable to synthesize fatty acids depending on the host for these nutrients. Moreover, arachidonic acid (ACD) is required to synthesize prostaglandins employed by schistosomes to evade the host's immune defenses. In the complex, the hydrocarbon tail of bound OLA assumes two conformations, whereas ACD adopts a unique hairpin-looped structure. ACD establishes more specific interactions with the protein, among which the most important is a pi-cation bond between Arg78 and the double bond at C8. Comparison with homologous fatty acid binding proteins suggests that the binding site of Sm14 is optimized to fit ACD. To test the functional implications of our structural data, the affinity of Sm14 for 1,8-anilinonaphthalenesulfonic acid (ANS) has been measured; moreover the binding constants of six different fatty acids were determined from their ability to displace ANS. OLA and ACD exhibited the highest affinities. To determine the rates of fatty acid binding and dissociation we carried out stopped flow kinetic experiments monitoring displacement by (and of) ANS. The binding rate constant of ligands is controlled by a slow pH dependent conformational change, which we propose to have physiological relevance.     

Model studies of chromatin structure based on X-ray diffraction data.

Model calculations are presented in order to interpret the X-ray diffraction diagrams given by chromatin gels. It is shown that by taking into account the hydration of chromatin subunits, the problem of calculating the interference function in concentrated gels is greatly simplified. In this way it is spossible to fully interpret the influence of concentration on the position and intensity of the various rings present in the X-ray diffraction patterns. The possibilities and limitations of models based on spherical symmetry are also discussed. It is concluded that each chromatin subunit most likely contains three turns of DNA in each 200 base pairs segment surrounding a central protein core. With the method presented here it is possible to test if other models of chromatin based on different kinds of evidence are compatible with the X-ray diffraction data.