Analyzing diffuse scattering with supercomputers

Two new approaches to quantitatively analyze diffuse diffraction intensities from faulted layer stacking are reported. The parameters of a probability-based growth model are determined with two iterative global optimization methods: a genetic algorithm (GA) and particle swarm optimization (PSO). The results are compared with those from a third global optimization method, a differential evolution (DE) algorithm [Storn & Price (1997). J. Global Optim. 11, 341–359]. The algorithm efficiencies in the early and late stages of iteration are compared. The accuracy of the optimized parameters improves with increasing size of the simulated crystal volume. The wall clock time for computing quite large crystal volumes can be kept within reasonable limits by the parallel calculation of many crystals (clones) generated for each model parameter set on a super- or grid computer. The faulted layer stacking in single crystals of trigonal three-pointedstar- shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example for the numerical computations. Based on numerical values of seven model parameters (reference parameters), nearly noise-free reference intensities of 14 diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers (reference crystal). The parameters derived from the reference intensities with GA, PSO and DE were compared with the original reference parameters as a function of the simulated total crystal volume. The statistical distribution of structural motifs in the simulated crystals is in good agreement with that in the reference crystal. The results found with the growth model for layer stacking disorder are applicable to other disorder types and modeling techniques, Monte Carlo in particular.

Adaptive Molecular Evolution in the Opsin Genes of Rapidly Speciating Cichlid Species

Cichlid fish inhabit a diverse range of environments that vary in the spectral content of light available for vision. These differences should result in adaptive selective pressure on the genes involved in visual sensitivity, the opsin genes. This study examines the evidence for differential adaptive molecular evolution in East African cichlid opsin genes due to gross differences in environmental light conditions. First, we characterize the selective regime experienced by cichlid opsin genes using a likelihood ratio test format, comparing likelihood models with different constraints on the relative rates of amino acid substitution, across sites. Second, we compare turbid and clear lineages to determine if there is evidence of differences in relative rates of substitution. Third, we present evidence of functional diversification and its relationship to the photic environment among cichlid opsin genes. We report statistical evidence of positive selection in all cichlid opsin genes, except short wavelength–sensitive 1 and short wavelength–sensitive 2b. In all genes predicted to be under positive selection, except short wavelength–sensitive 2a, we find differences in selective pressure between turbid and clear lineages. Potential spectral tuning sites are variable among all cichlid opsin genes; however, patterns of substitution consistent with photic environment–driven evolution of opsin genes are observed only for short wavelength–sensitive 1 opsin genes. This study identifies a number of promising candidate-tuning sites for future study by site-directed mutagenesis. This work also begins to demonstrate the molecular evolutionary dynamics of cichlid visual sensitivity and its relationship to the photic environment.