A study of deleterious gene structure in plants using Markov chain Monte Carlo

The characteristics of deleterious genes have been of great interest in both theory and practice in genetics. Because of the complex genetic mechanism of these deleterious genes, most current studies try to estimate the overall magnitude of mortality effects on a population, which is characterized classically by the number of lethal equivalents. This number is a combination of several parameters, each of which has a distinct biological effect on genetic mortality. In conservation and breeding programs, it is important to be able to distinguish among different combinations of these parameters that lead to the same number of lethal equivalents, such as a large number of mildly deleterious genes or a few lethal genes, The ability to distinguish such parameter combinations requires more than one generation of mating. We propose a model for survival data from a two-generation mating experiment on the plant species Brassica rapa, and we enable inference with Markov chain Monte Carlo. This computational strategy is effective because a vast amount of missing genotype information must be accounted for. In addition to the lethal equivalents, the two-generation data provide separate information on the average intensity of mortality and the average number of deleterious genes carried by an individual. In our Markov chain Monte Carlo algorithm, we use a vector proposal distribution to overcome inefficiency of a single-site Gibbs sampler. Information about environmental effects is obtained from an outcrossing experiment conducted in parallel with the two-generation mating experiments.     

Statistical inference for serial dilution assay data

Serial dilution assays are widely employed for estimating substance concentrations and minimum inhibitory concentrations. The Poisson-Bernoulli model for such assays is appropriate for count data but not for continuous measurements that are encountered in applications involving substance concentrations. This paper presents practical inference methods based on a log-normal model and illustrates these methods using a case application involving bacterial toxins.     

Approximate standard errors in semiparametric models

We consider semiparametric models with p regressor terms and q smooth terms. We obtain an explicit expression for the estimate of the regression coefficients given by the back-fitting algorithm. The calculation of the standard errors of these estimates based on this expression is a considerable computational exercise. We present an alternative, approximate method of calculation that is less demanding. With smoothing splines, the method is exact, while with loess, it gives good estimates of standard errors. We assess the adequacy of our approximation and of another approximation with the help of two examples.     

Isolation by distance and sharp discontinuities in gene frequencies: implications for the phylogeography of an alpine insect species, Carabus solieri

Analysis of genetic isolation by distance (IBD) is of prime importance for the study of processes responsible for spatial population genetic structure and is thus frequently used in case studies. However, the identification of a significant IBD pattern does not necessarily imply the absence of sharp discontinuities in gene frequencies. Therefore, identifying barriers to gene flow and/or secondary contact between differentiated entities remains a major challenge in population biology. Geographical genetic structure of 41 populations (1080 individuals) of an alpine insect species, Carabus solieri, was studied using 10 microsatellite loci. All populations were significantly differentiated and spatially structured according to IBD over the entire range. However, clustering analyses clearly identified three main clusters of populations, which correspond to geographical entities. Whereas IBD also occurs within each cluster, population structure was different according to which group of populations was considered. The southernmost cluster corresponds to the most fragmented part of the range. Consistently, it was characterized by relatively high levels of differentiation associated with low genetic diversity, and the slope of the regression of genetic differentiation against geographical distances was threefold those of the two other clusters. Comparisons of within-cluster and between-cluster IBD patterns revealed barriers to gene flow. A comparison of the two approaches, IBD and clustering analyses, provided us with valuable information with which to infer the phylogeography of the species, and in particular to propose postglacial colonization routes from two potential refugia located in Italy and in southeastern France. Our study highlights strongly the possible confounding contribution of barriers to gene flow to IBD pattern and emphasizes the utility of the model-based clustering analysis to identify such barriers.     

Protein fragment clustering and canonical local shapes

A novel clustering method is used to cluster protein fragments by shape. The centroids (mean fragments from each cluster) form a basis set of structural motifs. A database of 156,643 seven-residue fragments is used, and eight different basis sets with varying levels of resolution are generated. Coarse basis sets contain tens of centroids and provide meaningful local shapes, which are more detailed than the traditional secondary structure categories. High-resolution basis sets contain thousands of centroids and can be used to model tertiary structure of longer segments. The basis sets generated fit nontraining set proteins with the expected accuracy.     

Beyond the rotamer library: genetic algorithm combined with the disturbing mutation process for upbuilding protein side-chains

The disturbing genetic algorithm, incorporating the disturbing mutation process into the genetic algorithm flow, has been developed to extend the searching space of side-chain conformations and to improve the quality of the rotamer library. Moreover, the growing generation amount idea, simulating the real situation of the natural evolution, is introduced to improve the searching speed. In the calculations using the pseudo energy scoring function of the root mean squared deviation, the disturbing genetic algorithm method has been shown to be highly efficient. With the real energy function based on AMBER force field, the program has been applied to rebuilding side-chain conformations of 25 high-quality crystallographic structures of single-protein and protein-protein complexes. The averaged root mean standard deviation of atom coordinates in side-chains and veracities of the torsion angles of chi(1) and chi(1) + chi(2) are 1.165 A, 88.2 and 72.9% for the buried residues, respectively, and 1.493 A, 79.2 and 64.7% for all residues, showing that the method has equal precision to the program SCWRL, whereas it performs better in the prediction of buried residues and protein-protein interfaces. This method has been successfully used in redesigning the interface of the Basnase-Barstar complex, indicating that it will have extensive application in protein design, protein sequence and structure relationship studies, and research on protein-protein interaction.     

Higher-order interhelical spatial interactions in membrane proteins

Higher-order interactions are important for protein folding and assembly. We introduce the concept of interhelical three-body interactions as derived from Delaunay triangulation and alpha shapes of protein structures. In addition to glycophorin A, where triplets are strongly correlated with protein stability, we found that tight interhelical triplet interactions exist extensively in other membrane proteins, where many types of triplets occur far more frequently than in soluble proteins. We developed a probabilistic model for estimating the value of membrane helical interaction triplet (MHIT) propensity. Because the number of known structures of membrane proteins is limited, we developed a bootstrap method for determining the 95% confidence intervals of estimated MHIT values. We identified triplets that have high propensity for interhelical interactions and are unique to membrane proteins, e.g. AGF, AGG, GLL, GFF and others. A significant fraction (32%) of triplet types contains triplets that may be involved in interhelical hydrogen bond interactions, suggesting the prevalent and important roles of H-bond in the assembly of TM helices. There are several well-defined spatial conformations for triplet interactions on helices with similar parallel or antiparallel orientations and with similar right-handed or left-handed crossing angles. Often, they contain small residues and correspond to the regions of the closest contact between helices. Sequence motifs such as GG4 and AG4 can be part of the three-body interactions that have similar conformations, which in turn can be part of a higher-order cooperative four residue spatial motif observed in helical pairs from different proteins. In many cases, spatial motifs such as serine zipper and polar clamp are part of triplet interactions. On the basis of the analysis of the archaeal rhodopsin family of proteins, tightly packed triplet interactions can be achieved with several different choices of amino acid residues.     

Modelling zinc-binding proteins with GADGET: genetic algorithm and distance geometry for exploring topology

A novel combination of optimization methods (Genetic Algorithm with Distance Geometry) has been developed and shown to find near-optimal solutions to a set of imposed structural constraints. With this modelling tool (GADGET), the fold-space of a variety of small zinc-binding proteins was investigated under the constraints required to form a zinc-binding site (or pair of sites). Analysis of the results concentrated on the ring-finger domain as the "classic" zinc-finger domains were too constrained to provide much topological variety, whilst the TFIIH domain (which has large unstructured loops) did not behave well. The intermediate ring-finger domain, however, was found to adopt a variety of different folds, many of which had near-optimal scores under the fitness function employed in GADGET (forming good secondary structures and zinc-coordination). Although the native fold was dominant amongst the solutions, the discovery of good alternate folds shows that even the eight residues constrained to form two zinc-binding sites was not sufficient to uniquely determine the native fold. Despite this, the fold-space of 48 theoretically possible folds was greatly reduced with just six topologies found in significant numbers.     

Parameterization and classification of the protein universe via geometric techniques

We present a scheme for the classification of 3487 non-redundant protein structures into 1207 non-hierarchical clusters by using recurring structural patterns of three to six amino acids as keys of classification. This results in several signature patterns, which seem to decide membership of a protein in a functional category. The patterns provide clues to the key residues involved in functional sites as well as in protein-protein interaction. The discovered patterns include a "glutamate double bridge" of superoxide dismutase, the functional interface of the serine protease and inhibitor, interface of homo/hetero dimers, and functional sites of several enzyme families. We use geometric invariants to decide superimposability of structural patterns. This allows the parameterization of patterns and discovery of recurring patterns via clustering. The geometric invariant-based approach eliminates the computationally explosive step of pair-wise comparison of structures. The results provide a vast resource for the biologists for experimental validation of the proposed functional sites, and for the design of synthetic enzymes, inhibitors and drugs.