Solvent accessibilities in glycyl, alanyl and seryl dipeptides.

Theoretical studies on glycyl-alanyl and seryl dipeptides were performed to determine the probable backbone and side-group conformations that are preferred for solvent interaction. By following the method of Lee & Richards [(1971) J. Mol. Biol. 55, 379-400], a solute molecule is represented by a set of interlocking spheres of appropriate van der Waals radii assigned to each atom, and a solvent (water) molecule is rolled along the envelope of the van der Waals surface, and the surface accessible to the solvent molecule, and hence the solvent accessibility for a particular conformation of the solute molecule, is computed. From the calculated solvent accessibilities for various conformations, solvation maps for dipeptides were constructed. These solvation maps suggest that the backbone polar atoms could interact with solvent molecules selectively, depending on the backbone conformation. A conformation in the right-handed bridge (zetaR) region is favoured for both solvent interaction and intrachain hydrogen-bonding. Also the backbone side-chain hydrogen-bonding within the same dipeptide fragment in proteins is less favoured than hydrogen-bonding between side chain and water and between side chain and atoms of other residues. Solvent accessibilities suggest that very short distorted alphaR-helical and extended-structural parts may be stabilized via solvent interaction, and this could easily be possible at the surface of the protein molecules, in agreement with protein-crystal data.     

Periodic conformations of deoxyribonucleic acids

The conformation of a deoxyribonucleotide unit in a deoxyribonucleic acid molecule can be defined by six angles, each of which specifies the relative orientations between two groups of atoms adjacent to a covalent bond. With the assumption that these atoms are hard spheres with fixed van der Waal radii, conformations are sought to minimize their overlapping. The additional requirement of the polymer having a periodic structure further reduces the allowable conformations.     

Layer-type complexes consisting of VOSO4 or VOPO4 and aliphatic alcohols

The intercalates of unhydrated VOSO₄ and VOPO₄ with alcohols (C₁ to C₈) have been prepared and characterized by their compositions, basal spacings and thermal stabilities. X-ray powder studies show that the layered structures of VOSO₄ and VOPO₄ lattices are maintained in these complexes. The alcohol molecules are penetrated into van der Waal's gaps of the host lattices and form bimolecular layers. The observed alternation of the basal spacing increments with the number of carbon atoms of the linear aliphatic chain is explained from the arrangement of these chains.     

Residue depth: a novel parameter for the analysis of protein structure and stability.

BACKGROUND: Accessible surface area is a parameter that is widely used in analyses of protein structure and stability. Accessible surface area does not, however, distinguish between atoms just below the protein surface and those in the core of the protein. In order to differentiate between such buried residues we describe a computational procedure for calculating the depth of a residue from the protein surface. RESULTS: Residue depth correlates significantly better than accessibility with effects of mutations on protein stability and on protein-protein interactions. The deepest residues in the native state invariably undergo hydrogen exchange by global unfolding of the protein and are often significantly protected in the corresponding molten-globule states. CONCLUSIONS: Depth is often a more useful gage of residue burial than accessibility. This is probably related to the fact that the protein interior and surrounding solvent differ significantly in polarity and packing density. Hence, the strengths of van der Waals and electrostatic interactions between residues in a protein might be expected to depend on the distance of the residue(s) from the protein surface.     

The packing density in proteins: standard radii and volumes.

The sizes of atomic groups are a fundamental aspect of protein structure. They are usually expressed in terms of standard sets of radii for atomic groups and of volumes for both these groups and whole residues. Atomic groups, which subsume a heavy-atom and its covalently attached hydrogen atoms into one moiety, are used because the positions of hydrogen atoms in protein structures are generally not known. We have calculated new values for the radii of atomic groups and for the volumes of atomic groups. These values should prove useful in the analysis of protein packing, protein recognition and ligand design. Our radii for atomic groups were derived from intermolecular distance calculations on a large number (approximately 30,000) of crystal structures of small organic compounds that contain the same atomic groups to those found in proteins. Our radii show significant differences to previously reported values. We also use this new radii set to determine the packing efficiency in different regions of the protein interior. This analysis shows that, if the surface water molecules are included in the calculations, the overall packing efficiency throughout the protein interior is high and fairly uniform. However, if the water structure is removed, the packing efficiency in peripheral regions of the protein interior is underestimated, by approximately 3.5 %.     

Three-dimensional structure of abnormal human haemoglobins Chesapeake and J Capetown

The replacement of the invariant residue, arginine FG4(92)α, by a leucine in the mutant human haemoglobin Chesapeake causes drastically abnormal functional properties. When the arginine is replaced by a glutamine in haemoglobin J Capetown the mutant protein is almost normal. Crystallographic studies at 5.5 Å resolution show that the deoxy form of these two mutants have no significant structural distortions. In contrast, the structure of oxyhaemoglobin Chesapeake is considerably distorted. It appears that in the oxy form, the leucine side chain introduces impermissibly close van der Waal's contacts which disrupt the structure. This disturbance of the oxy structure is probably responsible for the abnormal properties displayed by haemoglobin Chesapeake. The structural basis for the milder abnormalities of haemoglobin J Capetown is as yet unknown.     

Mechanism of surface peptide proton exchange in bovine pancreatic trypsin inhibitor. Salt effects and O-protonation

The acid-catalyzed hydrogen exchange rate constants kH, and the base-catalyzed rate constants kOH, have been determined (in the preceding paper) for the 25 most rapidly exchanging NH groups of bovine pancreatic trypsin inhibitor. Most of these NH groups are at the protein-solvent interface. The correlation of kH, but not kOH, with the static accessibility and hydrogen bonding of the peptide carbonyl O atom indicates that the mechanism of acid catalysis in proteins involves O-protonation. Agreement between the ionic strength dependence observed for kH and kOH and the ionic strength dependence calculated for an O-protonation mechanism supports this conclusion. N-protonation for acid catalysis, as well as N-deprotonation for base catalysis, have traditionally been assumed in the mechanism of the chemical step in peptide amide proton exchange. A preference for the alternative O-protonation mechanism has far-reaching implications in the interpretation of protein hydrogen exchange kinetics. With an O-protonation mechanism, acid-catalyzed rates of surface NH groups are primarily a function of the average solvent accessibility of the carbonyl O atoms in the dynamic solution structure, while base-catalyzed rates of surface NH groups measure solvent accessibility of the peptide N. The relative dynamic accessibilities of peptide O atoms, as measured by relative values of kH (corrected for electrostatic effects), correlate with O static accessibilities in the crystal structure. A lower correlation of static accessibility of N atoms with kOH is observed for surface NH groups in peptide groups in which the carbonyl O is not hydrogen bonded. For some surface NH groups, the observed pH of minimum rate, pHmin, deviates widely from the pHmin of model compounds. This is explained as the combined result of electrostatic effects and of the differences in accessibility of the carbonyl O and N atoms that result in a change in the relative values of kH and kOH as compared to those of model peptides. A mechanism whereby exchange of interior sites is catalyzed by interactions of catalysis ions with protein surface atoms via charge transfer is suggested.     

The response of T4 lysozyme to large-to-small substitutions within the core and its relation to the hydrophobic effect.

To further examine the structural and thermodynamic basis of hydrophobic stabilization in proteins, all of the bulky non-polar residues that are buried or largely buried within the core of T4 lysozyme were substituted with alanine. In 25 cases, including eight reported previously, it was possible to determine the crystal structures of the variants. The structures of four variants with double substitutions were also determined. In the majority of cases the "large-to-small" substitutions lead to internal cavities. In other cases declivities or channels open to the surface were formed. In some cases the structural changes were minimal (mainchain shifts < or = 0.3 A); in other cases mainchain atoms moved up to 2 A. In the case of Ile 29 --> Ala the structure collapsed to such a degree that the volume of the putative cavity was zero. Crystallographic analysis suggests that the occupancy of the engineered cavities by solvent is usually low. The mutants Val 149 --> Ala (V149A) and Met 6 --> Ala (M6A), however, are exceptions and have, respectively, one and two well-ordered water molecules within the cavity. The Val 149 --> Ala substitution allows the solvent molecule to hydrogen bond to polar atoms that are occluded in the wild-type molecule. Similarly, the replacement of Met 6 with alanine allows the two solvent molecules to hydrogen bond to each other and to polar atoms on the protein. Except for Val 149 --> Ala the loss of stability of all the cavity mutants can be rationalized as a combination of two terms. The first is a constant for a given class of substitution (e.g., -2.1 kcal/mol for all Leu --> Ala substitutions) and can be considered as the difference between the free energy of transfer of leucine and alanine from solvent to the core of the protein. The second term can be considered as the energy cost of forming the cavity and is consistent with a numerical value of 22 cal mol(-1) A(-3). Physically, this term is due to the loss of van der Waal''s interactions between the bulky sidechain that is removed and the atoms that form the wall of the cavity. The overall results are consistent with the prior rationalization of Leu --> Ala mutants in T4 lysozyme by Eriksson et al. (Eriksson et al., 1992, Science 255:178-183).     

Calculations of protein volumes: sensitivity analysis and parameter database

MOTIVATION: The precise sizes of protein atoms in terms of occupied packing volume are of great importance. We have previously presented standard volumes for protein residues based on calculations with Voronoi-like polyhedra. To understand the applicability and limitations of our set, we investigated, in detail, the sensitivity of the volume calculations to a number of factors: (i) the van der Waals radii set, (ii) the criteria for including buried atoms in the calculations or atom selection, (iii) the method of positioning the dividing plane in polyhedra construction, and (iv) the set of structures used in the averaging. RESULTS: We find that different radii sets have only moderate affects to the distribution and mean of volumes. Atom selection and dividing plane methods cause larger changes in protein atoms volumes. More significantly, we show how the variation in volumes appears to be clearly related to the quality of the structures analyzed, with higher quality structures giving consistently smaller average volumes with less variance.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Study on the mechanism of the interaction between acteoside and pepsin using spectroscopic techniques

The interaction of acteoside with pepsin has been investigated using fluorescence spectra, UV/vis absorption spectra, three‐dimensional (3D) fluorescence spectra and synchronous fluorescence spectra, along with a molecular docking method. The fluorescence experiments indicate that acteoside can quench the intrinsic fluorescence of pepsin through combined quenching at a low concentration of acteoside, and static quenching at high concentrations. Thermodynamic analysis suggests that hydrogen bonds and van der Waal's forces are the main forces between pepsin and acteoside. According to the theory of Förster's non‐radiation energy transfer, the binding distance between pepsin and acteoside was calculated to be 2.018 nm, which implies that energy transfer occurs between acteoside and pepsin. In addition, experimental results from UV/vis absorption spectra, 3D fluorescence spectra and synchronous fluorescence spectra imply that pepsin undergoes a conformation change when it interacts with acteoside. Copyright © 2015 John Wiley & Sons, Ltd.     

Atoms-in-molecules study of the genetically encoded amino acids. III. Bond and atomic properties and their correlations with experiment including mutation-induced changes in protein stability and genetic coding

This article presents a study of the molecular charge distributions of the genetically encoded amino acids (AA), one that builds on the previous determination of their equilibrium geometries and the demonstrated transferability of their common geometrical parameters. The properties of the charge distributions are characterized and given quantitative expression in terms of the bond and atomic properties determined within the quantum theory of atoms-in-molecules (QTAIM) that defines atoms and bonds in terms of the observable charge density. The properties so defined are demonstrated to be remarkably transferable, a reflection of the underlying transferability of the charge distributions of the main chain and other groups common to the AA. The use of the atomic properties in obtaining an understanding of the biological functions of the AA, whether free or bound in a polypeptide, is demonstrated by the excellent statistical correlations they yield with experimental physicochemical properties. A property of the AA side chains of particular importance is the charge separation index (CSI), a quantity previously defined as the sum of the magnitudes of the atomic charges and which measures the degree of separation of positive and negative charges in the side chain of interest. The CSI values provide a correlation with the measured free energies of transfer of capped side chain analogues, from the vapor phase to aqueous solution, yielding a linear regression equation with r2 = 0.94. The atomic volume is defined by the van der Waals isodensity surface and it, together with the CSI, which accounts for the electrostriction of the solvent, yield a linear regression (r2 = 0.98) with the measured partial molar volumes of the AAs. The changes in free energies of transfer from octanol to water upon interchanging 153 pairs of AAs and from cyclohexane to water upon interchanging 190 pairs of AAs, were modeled using only three calculated parameters (representing electrostatic and volume contributions) yielding linear regressions with r2 values of 0.78 and 0.89, respectively. These results are a prelude to the single-site mutation-induced changes in the stabilities of two typical proteins: ubiquitin and staphylococcal nuclease. Strong quadratic correlations (r2 approximately 0.9) were obtained between DeltaCSI upon mutation and each of the two terms DeltaDeltaH and TDeltaDeltaS taken from recent and accurate differential scanning calorimetry experiments on ubiquitin. When the two terms are summed to yield DeltaDeltaG, the quadratic terms nearly cancel, and the result is a simple linear fit between DeltaDeltaG and DeltaCSI with r2 = 0.88. As another example, the change in the stability of staphylococcal nuclease upon mutation has been fitted linearly (r2 = 0.83) to the sum of a DeltaCSI term and a term representing the change in the van der Waals volume of the side chains upon mutation. The suggested correlation of the polarity of the side chain with the second letter of the AA triplet genetic codon is given concrete expression in a classification of the side chains in terms of their CSI values and their group dipole moments. For example, all amino acids with a pyrimidine base as their second letter in mRNA possess side-chain CSI < or = 2.8 (with the exception of Cys), whereas all those with CSI > 2.8 possess an purine base. The article concludes with two proposals for measuring and predicting molecular complementarity: van der Waals complementarity expressed in terms of the van der Waals isodensity surface and Lewis complementarity expressed in terms of the local charge concentrations and depletions defined by the topology of the Laplacian of the electron density. A display of the experimentally accessible Laplacian distribution for a folded protein would offer a clear picture of the operation of the "stereochemical code" proposed as the determinant in the folding process.     

Energetics of protein folding

The energetics of protein folding determine the 3D structure of a folded protein. Knowledge of the energetics is needed to predict the 3D structure from the amino acid sequence or to modify the structure by protein engineering. Recent developments are discussed: major factors are reviewed and auxiliary factors are discussed briefly. Major factors include the hydrophobic factor (burial of non-polar surface area) and van der Waals interactions together with peptide hydrogen bonds and peptide solvation. The long-standing model for the hydrophobic factor (free energy change proportional to buried non-polar surface area) is contrasted with the packing-desolvation model and the approximate nature of the proportionality between free energy and apolar surface area is discussed. Recent energetic studies of forming peptide hydrogen bonds (gas phase) are reviewed together with studies of peptide solvation in solution. Closer agreement is achieved between the 1995 values for protein unfolding enthalpies in vacuum given by Lazaridis-Archontis-Karplus and Makhatadze-Privalov when the solvation enthalpy of the peptide group is taken from electrostatic calculations. Auxiliary factors in folding energetics include salt bridges and side-chain hydrogen bonds, disulfide bridges, and propensities to form alpha-helices and beta-structure. Backbone conformational entropy is a major energetic factor which is discussed only briefly for lack of knowledge.     

Mechanical response and deformation mechanics of Type IV pili investigated using steered coarse-grained molecular dynamics simulation

Type IV pili are long filamentous structures on the surface of bacteria, which can be rapidly assembled or disassembled with pilin subunits by molecular motors. They can generate force during retraction and are involved in many bacterial functions. Steered molecular dynamics simulations with coarse-grained MARTINI models are carried out to investigate the mechanical behaviors of pili under tension. Our study is the first to report a Young's modulus of 0.80 ± 0.07 GPa and a spring constant of 1294.6 ± 116.5 kJ mol⁻¹ nm⁻² for pilus. Our results show the mechanical responses of pili are different from those described by the worm-like chain model and the van der Waal's interactions play a critical role in the mechanical responses. Moreover, the effects of pulling rates and virtual spring constants of pilus on Young's modulus are studied and two distinct morphological stages with the conformational changes appear during the extension of pilus are observed. This work provide insight into the mechanics and the deformation mechanism of pilus assembly.     

Investigation on the interaction of nanoAg with Cu–Zn SOD

Silver nanoparticles (nanoAg) are used more and more widely, particularly because of their antimicrobial properties. The effect of exposure to nanoAg on the structure of superoxide dismutase (SOD) was thoroughly investigated using fluorescence measurements, synchronous fluorescence spectroscopy, steady‐state and time‐resolved fluorescence quenching measurements, UV/Vis absorption spectroscopy, resonance light scattering (RLS), circular dichroism (CD), isothermal titration calorimetry (ITC) and high‐resolution transmission electron microscopy (HRTEM). Through van der Waal's force, nanoAg interacted with Cu–Zn SOD and influenced the active site by inducing structural changes, which influenced the function of SOD. The fluorescence studies show that both static and dynamic quenching processes occur. This paper provides reference data for toxicological studies of nanoAg, which are important in the future development of nanotechnology. Copyright © 2015 John Wiley & Sons, Ltd.     

Theoretical studies of the electrostatic potential of some enzyme inhibitors using computer graphics techniques

A molecular graphics program is described for the depiction of electrostatic potentials on the van der Waals surface of molecules, using colored polygons. An example is given on the application of this method to the study of coumarins and flavones that inhibit the enzyme Glyoxalase I.     

Molecular dynamics simulation of solvated azurin: correlation between surface solvent accessibility and water residence times

A system containing the globular protein azurin and 3,658 water molecules has been simulated to investigate the influence on water dynamics exerted by a protein surface. Evaluation of water mean residence time for elements having different secondary structure did not show any correlation. Identically, comparison of solvent residence time for atoms having different charge and polarity did not show any clear trend. The main factor influencing water residence time in proximity to a specific site was found to be its solvent accessibility. In detail for atoms belonging to lateral chains and having solvent-accessible surface lower than approximately 16 A(2)a relation is found for which charged and polar atoms are surrounded by water molecules characterized by residence times longer than the non polar ones. The involvement of the low accessible protein atom in an intraprotein hydrogen bond further modulates the length of the water residence time. On the other hand for surfaces having high solvent accessibility, all atoms, independently of their character, are surrounded by water molecules which rapidly exchange with the bulk solvent. Proteins 2000;39:56-67.     

Reduced surface: An efficient way to compute molecular surfaces

Because of their wide use in molecular modeling, methods to compute molecular surfaces have received a lot of interest in recent years. However, most of the proposed algorithms compute the analytical representation of only the solvent-accessible surface. There are a few programs that compute the analytical representation of the solvent-excluded surface, but they often have problems handling singular cases of self-intersecting surfaces and tend to fail on large molecules (more than 10,000 atoms). We describe here a program called MSMS, which is shown to be fast and reliable in computing molecular surfaces. It relies on the use of the reduced surface that is briefly defined here and from which the solvent-accessible and solvent-excluded surfaces are computed. The four algorithms composing MSMS are described and their complexity is analyzed. Special attention is given to the handling of self-intersecting parts of the solvent-excluded surface called singularities. The program has been compared with Connolly's program PQMS [M. L. Connolly (1993) Journal of Molecular Graphics, Vol. 11, pp. 139–141] on a set of 709 molecules taken from the Brookhaven Data Base. MSMS was able to compute topologically correct surfaces for each molecule in the set. Moreover, the actual time spent to compute surfaces is in agreement with the theoretical complexity of the program, which is shown to be O[n log(n)] for n atoms. On a Hewlett-Packard 9000/735 workstation, MSMS takes 0.73 s to produce a triangulated solvent-excluded surface for crambin (1crn, 46 residues, 327 atoms, 4772 triangles), 4.6 s for thermolysin (3tln, 316 residues, 2437 atoms, 26462 triangles), and 104.53 s for glutamine synthetase (2gls, 5676 residues, 43632 atoms, 476665 triangles). © 1996 John Wiley & Sons, Inc.     

Determination of three-dimensional structures of proteins from interproton distance data by dynamical simulated annealing from a random array of atoms. Circumventing problems associated with folding

A new real space method, based on the principles of simulated annealing, is presented for determining protein structures on the basis of interproton distance restraints derived from NMR data. The method circumvents the folding problem associated with all real space methods described to date, by starting from a completely random array of atoms and introducing the force constants for the covalent, interproton distance and repulsive van der Waals terms in the target function appropriately. The system is simulated at high temperature by solving Newton's equations of motion. As the values of all force constants are very low during the early stages of the simulation, energy barriers between different folds of the protein can be overcome, and the global minimum of the target function is reliably located. Further, because the atoms are initially only weakly coupled, they can move essentially independently to satisfy the restraints. The method is illustrated using two examples of small proteins, namely crambin (46 residues) and potato carboxypeptidase inhibitor (39 residues).