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.

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.

Free energy landscapes of peptides by enhanced conformational sampling.

The free energy landscapes of peptide conformations in water have been observed by the enhanced conformational sampling method, applying the selectively enhanced multicanonical molecular dynamics simulations. The conformations of the peptide dimers, -Gly-Gly-, -Gly-Ala-, -Gly-Ser-, -Ala-Gly-, -Asn-Gly-, -Pro-Gly-, -Pro-Ala-, and -Ala-Ala-, which were all blocked with N-terminal acetyl and C-terminal N-methyl groups, were individually sampled with the explicit TIP3P water molecules. From each simulation trajectory, we obtained the canonical ensemble at 300 K, from which the individual three-dimensional landscape was drawn by the potential of mean force using the three reaction coordinates: the backbone dihedral angle, psi, of the first amino acid, the backbone dihedral angle, phi, of the second amino acid, and the distance between the carbonyl oxygen of the N-terminal acetyl group and the C-terminal amide proton. The most stable state and several meta-stable states correspond to extended conformations and typical beta-turn conformations, and their free energy values were accounted for from the potentials of mean force at the states. In addition, the contributions from the intra-molecular energies of peptides and those from the hydration effects were analyzed. Consequently, the stable beta-turn conformations in the free energy landscape were consistent with the empirically preferred beta-turn types for each amino acid sequence. The thermodynamic values for the hydration effect were decomposed and they correlated well with the empirical values estimated from the solvent accessible surface area of each molecular conformation during the trajectories. The origin of the architecture of protein local fragments was analyzed from the viewpoint of the free energy and its decomposed factors.

Conformational sampling of CDR-H3 in antibodies by multicanonical molecular dynamics simulation.

The diversity in the lengths and the amino acid sequences of the third complementarity determining region of the antibody heavy chain (CDR-H3) has made it difficult to establish a relationship between the sequences and the tertiary structures, in contrast to the other CDRs, which are classified by their canonical structures. Enhanced conformational sampling of two different CDR-H3s was performed by multicanonical molecular dynamics (multicanonical MD) simulation while restricting the base structures, with and without the other surrounding CDR segments. The results showed that the multicanonical MD sampled a much larger conformational space than the conventional MD, independent of the initial conformations of the simulations. When the other CDRs surrounding the CDR-H3 segments were included in the calculations, the predominant conformations at 300 K corresponded to the X-ray crystal structures. When only the single CDR-H3 loops were considered with the restricted base structures, a greater number of different conformations were sampled as putative loops, but only a small number of stable conformations appeared at 300 K. Analyses of the resultant conformations revealed a structural role for the glycine, when it is located at position three residues before the last residue of CDR-H3 (Gly-X-X-last residue), coincident with the statistical tendencies of many antibody crystal structures. This reflects the general consistency between the energetically stable conformations and the empirically observed conformations. The current method is expected to be applicable to the structural modeling and the design of antibodies, especially for the inherently flexible loops.

Interaction of the basic protrusion of Escherichia coli ribonuclease HI with its substrate.

In order to determine the actual distance between the active site and the substrate binding site, termed the basic protrusion, of Escherichia coli ribonuclease HI, synthetic oligonucleotide duplexes with gradually extended overhangs were used, in which the enzymatic cleavage was restricted to a single site with 2'-O-methylnucleosides. The affinity of the enzyme for each substrate was determined by kinetic analysis. It was found that the affinity increased markedly when one nucleotide was attached to the 3' end of the DNA strand of the nine-base-pair hybrid duplex and then increased slightly as the DNA strand was extended further, whereas elongation of the strand in the other direction caused no change. When a mutant enzyme, in which three lysine residues in the basic protrusion were altered to alanine, was used, no increase in the kcat/K(m) value was observed. The results indicate that, for the productive binding, the axis from the 3' to the 5' end of the RNA strand of the substrate duplex must be oriented in agreement with the direction from the active site to the basic protrusion of the enzyme. The distance between the active site and the basic protrusion in the enzyme-substrate complex was shorter than that anticipated in modeling studies. A dynamic structure refinement, referred to as the normal mode analysis, was carried out in order to simulate the fluctuations of the basic protrusion.

The structure of bacteriorhodopsin at 3.0 A resolution based on electron crystallography: implication of the charge distribution.

Electron crystallography has the potential to visualise the charge status of atoms. This is due to the significantly different scattering factors of neutral and ionised atoms for electrons in the low-resolution range (typically less than 5 A). In previous work, we observed two different types of densities around acidic residues in the experimental (|Fo|) map of bacteriorhodopsin (bR), a light-driven proton pump. We suggested that these might reflect different states of the acidic residues; namely, the protonated (neutral) and the deprotonated (negatively charged) state. To evaluate the observed charge more quantitatively, we refined the atomic model for bR and eight surrounding lipids using our electron crystallographic data set between 8.0 and 3.0 A resolution, where the charge effect is small. The refined model yielded an R-factor of 23.7% and a free R-factor of 33.0%. To evaluate the effect of charges on the density map, we calculated a difference (|Fo|-|Fc|) map including data of a resolution lower than 8.0 A resolution, where the charge effect is significant. We found strong peaks in the difference map mainly in the backbone region of the transmembrane helices. We interpreted these peaks to come from the polarisation of the polar groups in the main chain of the alpha-helices and we examined this by assuming a partial charge of 0.5 for the peptide carbonyl groups. The resulting R and free R-factors dropped from 0.250 and 0.341 to 0.246 and 0.336, respectively. Furthermore, we also observed some strong peaks around some side-chains, which could be assigned to positively charged atoms. Thus, we could show that Asp36 and Asp102 are likely to interact with cations nearby. In addition, peaks found around the acidic residues Glu74, Glu194 and Glu212 have different features and might represent positive charges on polarised water molecules or hydroxonium ions.

Determinants of protein side-chain packing.

The problem of protein side-chain packing for a given backbone trace is investigated using 3 different prediction models. The first requires an exhaustive search of all possible combinations of side-chain conformers, using the dead-end elimination theorem. The second considers only side-chain-backbone interactions, whereas the third neglects side-chain-backbone interactions and instead keeps side-chain-side-chain interactions. Predictions of side-chain conformations for 11 proteins using all 3 models show that removal of side-chain-side-chain interactions does not cause a large decrease in the prediction accuracy, whereas the model having only side-chain-side-chain interactions still retains a significant level of accuracy. These results suggest that the 2 classes of interactions, side-chain-backbone and side-chain-side-chain, are consistent with each other and work concurrently to stabilize the native conformations. This is confirmed by analyses of energy spectra of the side-chain conformations derived from the fourth prediction model, the Independent model, which gives almost the same quality of the prediction as the dead-end elimination. The analyses indicate that the 2 classes of interactions simultaneously increase the energy difference between the native and nonnative conformations.

Diversity of functions of proteins with internal symmetry in spatial arrangement of secondary structural elements.

We carry out a systematic analysis of the correlation between similarity of protein three-dimensional structures and their evolutionary relationships. The structural similarity is quantitatively identified by an all-against-all comparison of the spatial arrangement of secondary structural elements in nonredundant 967 representative proteins, and the evolutionary relationship is judged according to the definition of superfamily in the SCOP database. We find the following symmetry rule: a protein pair that has similar folds but belong to different superfamilies has (with a very rare exception) certain internal symmetry in its common similar folds. Possible reasons behind the symmetry rule are discussed.

Response of dynamic structure to removal of a disulfide bond: normal mode refinement of C77A/C95A mutant of human lysozyme.

In order to investigate the response of dynamic structure to removal of a disulfide bond, the dynamic structure of human lysozyme has been compared to its C77A/C95A mutant. The dynamic structures of the wild type and mutant are determined by normal mode refinement of 1.5-A-resolution X-ray data. The C77A/C95A mutant shows an increase in apparent fluctuations at most residues. However, most of the change originates from an increase in the external fluctuations, reflecting the effect of the mutation on the quality of crystals. The effects of disulfide bond removal on the internal fluctuations are almost exclusively limited to the mutation site at residue 77. No significant change in the correlation of the internal fluctuations is found in either the overall or local dynamics. This indicates that the disulfide bond does not have any substantial role to play in the dynamic structure. A comparison of the wild-type and mutant coordinates suggests that the disulfide bond does not prevent the 2 domains from parting from each other. Instead, the structural changes are characteristic of a cavity-creating mutation, where atoms surrounding the mutation site move cooperatively toward the space created by the smaller alanine side chain. Although this produces tighter packing, more than half of the cavity volume remains unoccupied, thus destabilizing the native state.

Tailoring echistatin to possess higher affinity for integrin alpha(IIb)beta(3).

A mutant of echistatin, a disintegrin with a high affinity for the integrins, was constructed by substituting CRGDC for ARGDD in the Arg-Gly-Asp (RGD) region. The mutant was chemically synthesized, subjected to a folding process with air oxidation, and purified by reverse-phase HPLC. The peptide mapping and mass spectrometric analyses revealed that the two Cys residues introduced in the mutant are linked to each other, without any effect on the mode of the four disulfide bonds present in native echistatin, as expected. The mutant strongly inhibited the binding of human fibrinogen to its receptor, integrin alpha(IIb)beta(3) with an IC(50) value of 0.12 nM. This value shows that the mutant is twice as potent as the native form (IC(50) = 0.23 nM). These results indicate that the native disintegrin molecule, which has been considered to possess the optimum affinity for the integrins, can be tailored to exhibit even higher affinity by introducing the conformational constraint into the RGD region. Monte Carlo simulations of KRCRGDCMD, the RGD region in the mutant, suggested that the disulfide bond constrains the RGD region to assume a type II' beta-turn, with Gly and Asp in positions 2 and 3 of the turn.

Structural classification of CDR-H3 in antibodies.

Large varieties in the lengths and the amino acid sequences of the third complementarity determining region of the antibody heavy chain (CDR-H3) have made it difficult to establish a relationship between the sequences and the tertiary structures, in contrast to the other CDRs, which are classified by their canonical structures. A total of 55 CDR-H3 segments from well determined crystal structures were analyzed, and we have derived several remarkable rules, which could partly govern the CDR-H3 conformation dependence on the sequence. Since the rules are physically reasonable, they are expected to be applicable to structural modeling and design of antibodies.

H3-rules: identification of CDR-H3 structures in antibodies.

For the third complementarity determining region of the antibody heavy chain (CDR-H3), we propose the 'H3-rules', which should identify the tertiary structure from the amino acid sequence of the CDR-H3 segment. A total of 100 CDR-H3 segments from well-determined crystal structures were analyzed. Distinctive relationships between the structures and the sequences were revealed from 55 segments, and the rules were examined for the other 45 segments and were verified. In some antibodies, basic residues at specific positions were revealed to be notable signals, with their ability to form salt bridges and to assume conformations inconsistent with the rules.

Dynamic structure of human lysozyme derived from X-ray crystallography: normal mode refinement.

X-ray crystallography provides a wealth of information about the dynamic as well as static protein structure. A new method of dynamic structure refinement of protein X-ray crystallography, normal mode refinement, is proposed. In this method, the Debye-Waller factor is expanded in terms of the low-frequency internal normal modes and external normal modes, whose amplitudes and couplings are optimized in the process of crystallographic refinement. The internal and external contributions to the atomic fluctuations can be separated. Also, anisotropic atomic fluctuations and their inter-atomic correlations can be determined experimentally even with a relatively small number of adjustable parameters. The method is applied to the analyses of experimental data of human lysozyme and its mutant, C77A/C95A, to reveal its dynamic structure.

Environmental influence on electron scattering from a molecule.

The environmental influence on the electron scattering amplitudes of a molecule was evaluated by ab initio molecular-orbital calculations. The model system is formic acid in various states, i.e. the monomer, hydrogen-bonded dimer and ionized formate form. The model electrostatic potentials were calculated either in vacuo or with the polarizable continuum model as a simple model of an aqueous environment. It was found that charge compensation due to the environment affects the scattering amplitudes significantly. The resultant molecular electrostatic potential was fitted by six nucleus-centered Gaussians of site/environment-dependent atomic electrostatic potentials with small residual errors. Therefore, the site/environment-dependent atomic electrostatic potentials will give a good model for electron crystallography.

Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide.

A Monte Carlo simulation method for globular proteins, called extended-scaled-collective-variable (ESCV) Monte Carlo, is proposed. This method combines two Monte Carlo algorithms known as entropy-sampling and scaled-collective-variable algorithms. Entropy-sampling Monte Carlo is able to sample a large configurational space even in a disordered system that has a large number of potential barriers. In contrast, scaled-collective-variable Monte Carlo provides an efficient sampling for a system whose dynamics is highly cooperative. Because a globular protein is a disordered system whose dynamics is characterized by collective motions, a combination of these two algorithms could provide an optimal Monte Carlo simulation for a globular protein. As a test case, we have carried out an ESCV Monte Carlo simulation for a cell adhesive Arg-Gly-Asp-containing peptide, Lys-Arg-Cys-Arg-Gly-Asp-Cys-Met-Asp, and determined the conformational distribution at 300 K. The peptide contains a disulfide bridge between the two cysteine residues. This bond mimics the strong geometrical constraints that result from a protein's globular nature and give rise to highly cooperative dynamics. Computation results show that the ESCV Monte Carlo was not trapped at any local minimum and that the canonical distribution was correctly determined.

Refinement of protein dynamic structure: normal mode refinement.

An x-ray crystallographic refinement method, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the effective normal modes whose amplitudes and eigenvectors are experimentally determined by the crystallographic refinement. In contrast to the conventional method, the atomic motions are treated generally as anisotropic and concerted. This method is assessed by using the simulated x-ray data given by a Monte Carlo simulation of human lysozyme. In this article, we refine the dynamic structure by fixing the average static structure to exact coordinates. It is found that the normal mode refinement, using a smaller number of variables, gives a better R factor and more information on the dynamics (anisotropy and collectivity in the motion).

Vibrational energy transfer in a protein molecule.

Mode coupling in a protein molecule was studied by a molecular dynamics simulation of the intramolecular vibrational energy transfer in myoglobin at near zero temperature. It was found that the vibrational energy is transferred from a given normal mode to a very few number of selective normal modes. These modes are selected by the relation between their frequencies, like Fermi resonance, governed by the third order mode coupling term. It was also confirmed that the coupling coefficients had high correlation with how much the coupled modes geometrically overlapped with each other.

Intrinsic nature of the three-dimensional structure of proteins as determined by distance geometry with good sampling properties.

A protocol for distance geometry calculation is shown to have excellent sampling properties in the determination of three-dimensional structures of proteins from nuclear magnetic resonance (NMR) data. This protocol uses a simulated annealing optimization employing mass-weighted molecular dynamics in four-dimensional space (Havel, T.F. (1991) Prog. Biophys. Mol. Biol., 56, 43-78). It attains an extremely large radius of convergence, allowing a random coil conformation to be used as the initial estimate for the succeeding optimization process. Computations are performed with four systems of simulated distance data as tests of the protocol, using an unconstrained L-alanine 30mer and three different types of proteins, bovine pancreatic trypsin inhibitor, the alpha-amylase inhibitor Tendamistat, and the N-terminal domain of the 434-repressor. The test of the unconstrained polypeptide confirms that the sampled conformational space is that of the statistical random coil. In the larger and more complicated systems of the three proteins, the protocol gives complete convergence of the optimization without any trace of initial structure dependence. As a result of an exhaustive conformational sampling by the protocol, the intrinsic nature of the structures generated with distance restraints derived from NMR data has been revealed. When the sampled structures are compared with the corresponding X-ray structures, we find that the averages of the sampled structures always show a certain pattern of discrepancy from the X-ray structure. This discrepancy is due to the short distance nature of the distance restraints, and correlates with the characteristic shape of the protein molecule.