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.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/bip.1968.360061213

Single-chain triple helical structure.

Empirical energy calculations on cyclo-Gly-X with X- Phe, Tyr, Val, and Leu as a function of the side-chain torsion angles X indicate that the conformation of minimum energy are characterized by $X^1$ = 60 °, $X^2$ = 90 ° for Phe and Try, $X^1$ = -60 ° for Val and $X^1$ = -60 °, $X^2$ = 180 ° and $X^1$ = 60 ° and $X^2$ = 150 ° for Leu. The minimum energy conformation of cyclo-Gly-Phe and cyclo-Gly-Val have the side chains of Phe and Val stacked over the poperazinedione ring as suggested by NMR and found for cyclo-Gly-Tyr crystal structure. In contrast, the Leu side chain is expected to exist in an extended or a quasi-folded form.

Conformation of cyclic dipeptides from empirical energy calculations

The paper contains a classical description of the first order terms in the polarisability theory of optical activity. Optical activity essentially arises because the dipoles induced by the light wave in the medium are not all in the same phase. As a result of their mutual influences, the resultant induced moment will not be in phase with the electric field of the light wave and would lead to a rotation (ρ). By comparing the results calculated from the structure with the phenomenological theory of light propagation in the crystal, the magnitude ofρ is obtained. This method has been applied to a hypothetical tetragonal crystal having a spiral structure. It leads to the interesting result that the rotation at right angles to the optic axis is opposite in sign to that along the axis, as in quartz. The theory also predicts that, in general, the rotation will vary faster than 1/λ2, as is found to be the case with many substances.

Theory of optical activity of crystals. I. General ideas

https://science.sciencemag.org/content/sci/141/3577/288.full.pdf

Protein Structure and Crystallography.

All the photoelastic constants of diamond have been determined for the first time. The three stress-optic coefficients areq11=4·2×10−11,q12=−3·6×10−11,q44=2·6×10−11, from which the elasto-optic coefficients have been deduced to bep11=0·125,p12=−0·325,p44=0·11. It is found thatq11−q12 andq44 are both positive and also that the refractive index of the crystal should decrease when subjected to a hydrostatic pressure, both of which are unique for diamond among the cubic crystals studied so far. In the course of the investigation, a new technique has been developed for determining the absolute path retardation, based on the production of localised interference fringes by the light coming from the two surfaces of the crystal.

G. N. Ramachandran

Papers

Single-chain triple helical structure.

Conformation of cyclic dipeptides from empirical energy calculations

Theory of optical activity of crystals. I. General ideas

Protein Structure and Crystallography.

Photoelastic constants of diamond