MOLMOL: a program for display and analysis of macromolecular structures.

The interpretation of protein structures: estimation of static accessibility.

Geometrical validation around the Calpha is described, with a new Cbeta measure and updated Ramachandran plot. Deviation of the observed Cbeta atom from ideal position provides a single measure encapsulating the major structure-validation information contained in bond angle distortions. Cbeta deviation is sensitive to incompatibilities between sidechain and backbone caused by misfit conformations or inappropriate refinement restraints. A new phi,psi plot using density-dependent smoothing for 81,234 non-Gly, non-Pro, and non-prePro residues with B < 30 from 500 high-resolution proteins shows sharp boundaries at critical edges and clear delineation between large empty areas and regions that are allowed but disfavored. One such region is the gamma-turn conformation near +75 degrees,-60 degrees, counted as forbidden by common structure-validation programs; however, it occurs in well-ordered parts of good structures, it is overrepresented near functional sites, and strain is partly compensated by the gamma-turn H-bond. Favored and allowed phi,psi regions are also defined for Pro, pre-Pro, and Gly (important because Gly phi,psi angles are more permissive but less accurately determined). Details of these accurate empirical distributions are poorly predicted by previous theoretical calculations, including a region left of alpha-helix, which rates as favorable in energy yet rarely occurs. A proposed factor explaining this discrepancy is that crowding of the two-peptide NHs permits donating only a single H-bond. New calculations by Hu et al. [Proteins 2002 (this issue)] for Ala and Gly dipeptides, using mixed quantum mechanics and molecular mechanics, fit our nonrepetitive data in excellent detail. To run our geometrical evaluations on a user-uploaded file, see MOLPROBITY (http://kinemage.biochem.duke.edu) or RAMPAGE (http://www-cryst.bioc.cam.ac.uk/rampage).

Structure validation by Calpha geometry: phi,psi and Cbeta deviation.

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure-function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc-pVxZ//MP2/6-31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc-pVQZ//MP2/6-31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone phi, psi dihedral crossterms or a phi, psi grid-based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the phi, psi dihedral parameters along with the grid-based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of phi and psi in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid-based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.

Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations.

Publisher Summary This chapter investigates the anatomy and taxonomy of protein structures. A protein is a polypeptide chain made up of amino acid residues linked together in a definite sequence. Amino acids are “handed,” and naturally occurring proteins contain only L-amino acids. A simple mnemonic for that purpose is the “corncrib.” The sequence of side chains determines all that is unique about a particular protein, including its biological function and its specific three-dimensional structure. The major possible routes to knowledge of three-dimensional protein structure are prediction from the amino acid sequence and analysis of spectroscopic measurements such as circular dichroism, laser Raman spectroscopy, and nuclear magnetic resonance. The analysis and discussion of protein structure is based on the results of three-dimensional X-ray crystallography of globular proteins. The basic elements of protein structures are discussed. The most useful level at which protein structures are to be categorized is the domain, as there are many cases of multiple-domain proteins in which each separate domain resembles other entire smaller proteins. The simplest type of stable protein structure consists of polypeptide backbone wrapped more or less uniformly around the outside of a single hydrophobic core. The outline of the taxonomy is also provided in the chapter.

The anatomy and taxonomy of protein structure.

The phenomenon of the transmission of light through a cloud of particles distributed at random in a transparent medium is theoretically investigated on the basis of wave-optics. The cases of both transparent and of opaque particles are considered, and it is found that the transmitted beam is progressively attenuated, the intensity diminishing exponentially with the increase in the thickness of the medium. The actual values of the attenuation coefficient are calculated in both cases. It is found that for an opaque particle, the diminution of intensity in the forward direction is actually double what would be expected from simple geometric considerations. For transparent particles, the transmitted intensity shows spectral variations, and this explains some of the phenomena hitherto not well understood, such as the colours shown by the transmitted light, and the complementary nature of this colour and the colour of the light scattered by the cloud in the forward direction.

On the transmission of light through a cloud of randomly distributed particles

SummaryThe theory outlined in Part I of these series has been applied to calculate the thermal variation of refractive index of fused silica. It is found that the theory can account quantitatively for the experimental values ofdn/dt over the range of wavelengths from 1850 Å.U. to 6000 Å.U. Using the fact that the frequencies of vitreous silica are practically the same as those of crystalline quartz, the variation of the refractive index with temperature from −130°C. to 500°C. has been calculated and found to fit well with the experimental data.

http://link.springer.com/content/pdf/10.1007/BF03171410.pdf

Thermo-optic behaviour of solids: II. Fused quartz

The phases of x-ray reflection of a crystal can be measured, except for an ambiguity, if the crystal contains heavy atoms which scatter x-rays anomalously. Theoretical studies show that the method of resolving this ambiguity by choosing the phases closer to those of the heavy atoms has a good potentiality for solving complicated structures, in which the average heavy atom contribution to the intensity is as low as 10 percent.

http://science.sciencemag.org/content/sci/150/3693/212.full.pdf

Anomalous Dispersion Method: Its Power for Protein Structure Analysis

The paper deals with the theory of an interesting phenomenon (which has been designated as “anti-reflection”) that the intensity of the transmitted beam may exhibit a peak larger than the background when a Bragg reflection occurs in an absorbing crystal. The theory is based on the dynamical theory of Ewald and Laue. It comes out that the effect is due to a decrease in the effective absorption coefficient of the crystal near the Bragg reflection, and to the consequent increase in the transmitted intensity predominating over the loss of energy by reflection. The anti-reflection peak becomes more prominent, the greater the thickness of the crystal. The results of the theory are found to be in accord with the previous observations of Borrmann and Campbell. The theory further predicts that the peaks in the reflected and transmitted beams would not be coincident and this requires further verification.

G. N. Ramachandran

Papers

On the transmission of light through a cloud of randomly distributed particles

Thermo-optic behaviour of solids: II. Fused quartz

Anomalous Dispersion Method: Its Power for Protein Structure Analysis

X-ray anti-reflections in crystals

X-ray topographs of diamond—Part II