An N⋅log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms. Timings and accuracies are presented for three large crystalline ionic systems.

Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems

A new statistical method for estimating divergence dates of species from DNA sequence data by a molecular clock approach is developed. This method takes into account effectively the information contained in a set of DNA sequence data. The molecular clock of mitochondrial DNA (mtDNA) was calibrated by setting the date of divergence between primates and ungulates at the Cretaceous-Tertiary boundary (65 million years ago), when the extinction of dinosaurs occurred. A generalized least-squares method was applied in fitting a model to mtDNA sequence data, and the clock gave dates of 92.3 +/- 11.7, 13.3 +/- 1.5, 10.9 +/- 1.2, 3.7 +/- 0.6, and 2.7 +/- 0.6 million years ago (where the second of each pair of numbers is the standard deviation) for the separation of mouse, gibbon, orangutan, gorilla, and chimpanzee, respectively, from the line leading to humans. Although there is some uncertainty in the clock, this dating may pose a problem for the widely believed hypothesis that the pipedal creature Australopithecus afarensis, which lived some 3.7 million years ago at Laetoli in Tanzania and at Hadar in Ethiopia, was ancestral to man and evolved after the human-ape splitting. Another likelier possibility is that mtDNA was transferred through hybridization between a proto-human and a proto-chimpanzee after the former had developed bipedalism.

Dating of the human-ape splitting by a molecular clock of mitochondrial DNA.

Solvent content of protein crystals.

https://zenodo.org/record/1258475/files/article.pdf

Electron transfers in chemistry and biology

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.

The crystal structure of the synthetic DNA dodecamer d(CpGpCpGpApApTpTpCpGpCpG) has been refined to a residual error of R = 17.8% at 1.9-A resolution (two-sigma data). The molecule forms slightly more than one complete turn of right-handed double-stranded B helix. The two ends of the helix overlap and interlock minor grooves with neighboring molecules up and down a 2(1) screw axis, producing a 19 degrees bend in helix axis over the 11-base-pair steps of the dodecamer. In the center of the molecule, where perturbation is least, the helix has a mean rotation of 36.9 degrees per step, or 9.8 base pairs per turn. The mean propeller twist (total dihedral angle between base planes) between A . T base pairs in the center of the molecule is 17.3 degrees, and that between C . G pairs on the two ends averages 11.5 degrees. Individual deoxyribose ring conformations as measured by the C5'-C4'-C3'-O3' torsion angle delta, exhibit an approximately Gaussian distribution centered around the C1'-exo position with delta avg = 123 degrees and a range of 79 degrees to 157 degrees. Purine sugars cluster at high delta values, and pyrimidine sugars cluster at lower delta. A tendency toward 2-fold symmetry in sugar conformation about the center of the molecule is detectable in spite of the destruction of ideal 2-fold symmetry by the molecular bending. More strikingly, sugar conformations of paired based appear to follow a "principle of anticorrelation," with delta values lying approximately the same distance to either side of the center value, delta = 123 degrees. This same anticorrelation is also observed in other DNA and DNA . RNA structures.

https://www.pnas.org/content/pnas/78/4/2179.full.pdf

Structure of a B-DNA dodecamer: conformation and dynamics.

Structure of a B-DNA dodecamer: III. Geometry of hydration

Ferricytochrome c: I. GENERAL FEATURES OF THE HORSE AND BONITO PROTEINS AT 2.8 A RESOLUTION

Structure of a B-DNA dodecamer: II. Influence of base sequence on helix structure☆

DNA is probably the most discussed and least observed of all biological macromolecules. Although its role in biology is a central one, with many examples such as operators and restriction sites where specific base sequences have control functions or interact with specific enzymes, the structures that DNA can adopt have been based until now only on sequence-averaged fibre diffraction patterns. Recent improvements in triester synthesis methods have made possible the preparation of sufficient homogeneous DNA of predetermined sequence for crystallization and X-ray structure analysis. We report here the first single-crystal structure analysis of more than a complete turn of right-handed B-DNA, with the self-complementary dodecamer sequence d(CpGpCpGPApApTpTpCpGpCpG) or CGCGAATTCGCG.

Richard E. Dickerson

Papers

Structure of a B-DNA dodecamer: conformation and dynamics.

Structure of a B-DNA dodecamer: III. Geometry of hydration

Ferricytochrome c: I. GENERAL FEATURES OF THE HORSE AND BONITO PROTEINS AT 2.8 A RESOLUTION

Structure of a B-DNA dodecamer: II. Influence of base sequence on helix structure☆

Crystal structure analysis of a complete turn of B-DNA