Extensions to pedigree analysis. V. Optimal calculation of Mendelian likelihoods

Mendelian likelihoods are computed from human pedigree data for purposes of gene mapping, risk prediction in genetic counseling, and hypothesis testing in genetic epidemiology. The Mendelian likelihood of an extended pedigree can be written as a sum of products, the sum ranging over all possible genotypic combinations for the individuals in the pedigree. Exclusion of genotypes incompatible with the phenotypic information and pedigree structure reduces the ranges of summation and simplifies the likelihood calculation. To evaluate the likelihood with the fewest possible arithmetic operations requires carrying out the summations over one individual at a time and the intervening multiplications in some appropriate order. Each such removal of an individual reduces the likelihood evaluation to another evaluation of the same numerical form. Greedy-type algorithms are suggested for determining an order in which the summations and multiplications may be carried out. The greedy methods are fast and appear to generate good removal sequences. They are shown to work well when applied to a large, complex pedigree.     

Fine structure of influenza A virus observed by electron cryo-microscopy.

A rapidly frozen vitrified aqueous suspension of influenza A virus was observed by high resolution electron cryomicroscopy. The influenza particles were grouped into small (diameter < 150 nm) spherical particles with well organized interiors, large spherical ones with less internal organization, and filamentous ones. Envelopes of most of the large virus particles were phospholipid bilayers, and the chromatography fraction containing these large particles was largely devoid of viral activity. The envelopes of most of the filamentous and small spherical virus particles, on the other hand, gave a strange contrast which could be ascribed to a combination of a thin outer lipid monolayer and a 7.2 nm thick protein-containing inner layer. These latter particles represented most of the viral activity in the preparation. Densitometric traces of the near in-focus images confirmed these structural differences. Some viral envelope structures apparently intermediate between these two distinct types of membrane were also detected. A structural model of intact biologically active influenza virus particles was formulated from these results, together with computer simulations.     

Population structure and inbreeding from pedigree analysis of purebred dogs

Dogs are of increasing interest as models for human diseases, and many canine population-association studies are beginning to emerge. The choice of breeds for such studies should be informed by a knowledge of factors such as inbreeding, genetic diversity, and population structure, which are likely to depend on breed-specific selective breeding patterns. To address the lack of such studies we have exploited one of the world's most extensive resources for canine population-genetics studies: the United Kingdom (UK) Kennel Club registration database. We chose 10 representative breeds and analyzed their pedigrees since electronic records were established around 1970, corresponding to about eight generations before present. We find extremely inbred dogs in each breed except the greyhound and estimate an inbreeding effective population size between 40 and 80 for all but 2 breeds. For all but 3 breeds, >90% of unique genetic variants are lost over six generations, indicating a dramatic effect of breeding patterns on genetic diversity. We introduce a novel index Psi for measuring population structure directly from the pedigree and use it to identify subpopulations in several breeds. As well as informing the design of canine population genetics studies, our results have implications for breeding practices to enhance canine welfare.     

Subfibrillar structure of type I collagen observed by atomic force microscopy.

We have imaged native rat tail and reconstituted bovine dermal type I collagen by atomic force microscopy, obtaining a level of detail comparable to that obtained on the same samples by transmission electron microscopy. The characteristic 60-70 nm D periodicity consists of ridges exhibiting high tip-sample adhesion alternating with 5-15-nm-deep grooves having low adhesion. We also observe an intraperiod or "minor" band consisting of 1-nm-deep grooves, and "microfibrils" arranged parallel to or inclined approximately 5 degrees to the fibril axis. In air collagen fibrils exhibit negligible compression under the forces exerted by the tip. When immersed in water the subfibrillar features disappear and the fibrils become softer, compressing by 5% of their height under an 11-nN force. Material on the surface of the sample sometimes accumulates on the atomic force microscope tip; contrary to expectation such tip contamination can improve as well as reduce resolution.     

The impact of pedigree structure on heritability estimates for pulse pressure in three studies

OBJECTIVES: Pulse pressure (PP) is a measure of large artery stiffness and has been shown to be an important predictor of cardiovascular morbidity and mortality. The aims of the present study were to investigate the heritability of PP in three studies, the Diabetes Heart Study (DHS), the Insulin Resistance Atherosclerosis Family Study (IRAS FS), and the NHLBI Family Heart Study (FHS), to estimate the residual heritability after inclusion of a common set of covariates, and to investigate the impact of pedigree structure on estimating heritability. METHODS AND RESULTS: DHS is primarily a sibling pair nuclear family study design, while both IRAS FS and FHS have large pedigrees. Heritability estimates of log-transformed PP were obtained using variance component models. After adjusting for age, gender, ethnicity/center, height, diabetes status, and mean arterial pressure (MAP), heritability estimates of PP were 0.40 +/- 0.08 , 0.22 +/- 0.05, and 0.19 +/- 0.03 in DHS, IRAS FS, and FHS, respectively. The heritability estimate from DHS was significantly different from both IRAS FS and FHS (both p values <0.05). A random re-sampling technique (modified bootstrap) was used to explore the heritability in the IRAS FS and FHS data when these pedigrees were trimmed to mimic the DHS pedigree structure. The re-sampling method (mimicking a sibling pair nuclear family design in all studies) yielded PP heritability estimates of 0.37, 0.34, and 0.27 in DHS, IRAS FS, and FHS, respectively. There was no significant difference among the heritability estimates from the three studies based on the re-sampling method. CONCLUSION: We have shown that PP has a moderately heritable component in three different studies. These data illustrate the influence of pedigree structure can have on estimating heritability. Thoughtful comparisons of heritability estimates must consider study design factors such as pedigree structure.     

Evaluating pedigree data. I. The estimation of pedigree error in the presence of marker mistyping

Pedigrees used in the analysis of genetic or medical data are usually ascertained from sources subject to a variety of errors including misidentification of individuals, faults in historical documents or record linkage, nonpaternity, and unidentified adoption. Genetic markers can be used to verify putative family and pedigree data through the search for inconsistencies, or genetic exclusions, between putative parents and offspring. The probability of observing an exclusion given the occurrence of an error depends upon the gene frequencies at the loci under study and the forms of error. In addition, inconsistencies can arise from laboratory errors in marker determination. Together, these problems make the proper statistical analysis of such data desirable. Here we give a model that specifies the combined effects of various kinds of pedigree error along with genetic marker error. This model allows the maximum-likelihood estimation of the rates of various forms of pedigree error and laboratory error from genetic marker data collected on putative families. The method is illustrated by applying it to data obtained from a South Pacific island population, Tokelau. From the observed distribution of genetic marker inconsistencies between the parents and offspring of putative families, derived from the extensive genealogy of this population, we are able to estimate that the error of a paternal link is 4%, the error of a maternal link is zero, and the overall system typing error is 1%.     

Shape and fine structure of nucleoids observed on sections of ultrarapidly frozen and cryosubstituted bacteria.

Very rapidly frozen cells of Escherichia coli and Bacillus subtilis were substituted at low temperature into acetone with 1% OsO4 and embedded in Epon. They showed ribosome-free spaces filled with globular and fibrillar material of up to 15 nm. The sizes of structures seen do not exclude DNA superstructures such as supercoils, aggregates, and nucleosomes. With the Feulgen analog osmium-ammines stain, DNA was localized within the ribosome-free space. The bulk of DNA, the nucleoid, is therefore a major part of, or identical to, the main ribosome-free space. The ribosome-free space would correspond directly to the light microscopy phase-contrast image of nucleoids in living bacteria. The shape of the ribosome-free space does not reflect intracellular salt concentrations, nor do the Feulgen-positive areas. The previously observed dependency on the salt concentration of the growth medium seems to be due to permeabilization induced by the chemical fixative at room temperature. The ribosome-free space is more cleft in appearance than the nucleoid obtained by fixation with OsO4 but more confined than its very dispersed form found after aldehyde fixation.     

Fast computation of genetic likelihoods on human pedigree data.

Gene mapping and genetic epidemiology require large-scale computation of likelihoods based on human pedigree data. Although computation of such likelihoods has become increasingly sophisticated, fast calculations are still impeded by complex pedigree structures, by models with many underlying loci and by missing observations on key family members. The current paper 'introduces' a new method of array factorization that substantially accelerates linkage calculations with large numbers of markers. This method is not limited to nuclear families or to families with complete phenotyping. Vectorization and parallelization are two general-purpose hardware techniques for accelerating computations. These techniques can assist in the rapid calculation of genetic likelihoods. We describe our experience using both of these methods with the existing program MENDEL. A vectorized version of MENDEL was run on an IBM 3090 supercomputer. A parallelized version of MENDEL was run on parallel machines of different architectures and on a network of workstations. Applying these revised versions of MENDEL to two challenging linkage problems yields substantial improvements in computational speed.     

Protein 8-class secondary structure prediction using conditional neural fields

Compared with the protein 3-class secondary structure (SS) prediction, the 8-class prediction gains less attention and is also much more challenging, especially for proteins with few sequence homologs. This paper presents a new probabilistic method for 8-class SS prediction using conditional neural fields (CNFs), a recently invented probabilistic graphical model. This CNF method not only models the complex relationship between sequence features and SS, but also exploits the interdependency among SS types of adjacent residues. In addition to sequence profiles, our method also makes use of non-evolutionary information for SS prediction. Tested on the CB513 and RS126 data sets, our method achieves Q8 accuracy of 64.9 and 64.7%, respectively, which are much better than the SSpro8 web server (51.0 and 48.0%, respectively). Our method can also be used to predict other structure properties (e.g. solvent accessibility) of a protein or the SS of RNA.     

Comparison of the predicted and observed secondary structure of T4 phage lysozyme.

Predictions of the secondary structure of T4 phage lysozyme, made by a number of investigators on the basis of the amino acid sequence, are compared with the structure of the protein determined experimentally by X-ray crystallography. Within the amino terminal half of the molecule the locations of helices predicted by a number of methods agree moderately well with the observed structure, however within the carboxyl half of the molecule the overall agreement is poor. For eleven different helix predictions, the coefficients giving the correlation between prediction and observation range from 0.14 to 0.42. The accuracy of the predictions for both beta-sheet regions and for turns are generally lower than for the helices, and in a number of instances the agreement between prediction and observation is no better than would be expected for a random selection of residues. The structural predictions for T4 phage lysozyme are much less successful than was the case for adenylate kinase (Schulz et al. (1974) Nature 250, 140-142). No one method of prediction is clearly superior to all others, and although empirical predictions based on larger numbers of known protein structure tend to be more accurate than those based on a limited sample, the improvement in accuracy is not dramatic, suggesting that the accuracy of current empirical predictive methods will not be substantially increased simply by the inclusion of more data from additional protein structure determinations.     

Dynamic DNA contacts observed in the NMR structure of winged helix protein-DNA complex.

Genesis is an HNF-3/fkh homologous protein. By using multi-dimensional NMR techniques, we have obtained the solution structure and backbone dynamics of Genesis complexed with a 17 base-pair DNA. Our results indicate that both the local folding and dynamic properties of Genesis are perturbed when it binds to the DNA site. Our data show that a conserved flexible amino acid sequence (wing 1) makes dynamic contacts to DNA in the complex and a short helix is induced by Genesis-DNA interactions. Our data indicate that, unlike the HNF-3gamma/DNA complex, a magnesium ion is not required in forming the stable Genesis-DNA complex.     

Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure.

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.