A class of Bayesian methods to combine large numbers of genotyped and non-genotyped animals for whole-genome analyses

Background

To obtain predictions that are not biased by selection, the conditional mean of the breeding values must be computed given the data that were used for selection. When single nucleotide polymorphism (SNP) effects have a normal distribution, it can be argued that single-step best linear unbiased prediction (SS-BLUP) yields a conditional mean of the breeding values. Obtaining SS-BLUP, however, requires computing the inverse of the dense matrix G of genomic relationships, which will become infeasible as the number of genotyped animals increases. Also, computing G requires the frequencies of SNP alleles in the founders, which are not available in most situations. Furthermore, SS-BLUP is expected to perform poorly relative to variable selection models such as BayesB and BayesC as marker densities increase.

Methods

A strategy is presented for Bayesian regression models (SSBR) that combines all available data from genotyped and non-genotyped animals, as in SS-BLUP, but accommodates a wider class of models. Our strategy uses imputed marker covariates for animals that are not genotyped, together with an appropriate residual genetic effect to accommodate deviations between true and imputed genotypes. Under normality, one formulation of SSBR yields results identical to SS-BLUP, but does not require computing G or its inverse and provides richer inferences. At present, Bayesian regression analyses are used with a few thousand genotyped individuals. However, when SSBR is applied to all animals in a breeding program, there will be a 100 to 200-fold increase in the number of animals and an associated 100 to 200-fold increase in computing time. Parallel computing strategies can be used to reduce computing time. In one such strategy, a 58-fold speedup was achieved using 120 cores.

Discussion

In SSBR and SS-BLUP, phenotype, genotype and pedigree information are combined in a single-step. Unlike SS-BLUP, SSBR is not limited to normally distributed marker effects; it can be used when marker effects have a t distribution, as in BayesA, or mixture distributions, as in BayesB or BayesC π. Furthermore, it has the advantage that matrix inversion is not required. We have investigated parallel computing to speedup SSBR analyses so they can be used for routine applications.

Electronic supplementary material

The online version of this article (doi:10.1186/1297-9686-46-50) contains supplementary material, which is available to authorized users.     

Copy number alterations and allelic ratio in relation to recurrence of rectal cancer

Background

In rectal cancer, total mesorectal excision surgery combined with preoperative (chemo)radiotherapy reduces local recurrence rates but does not improve overall patient survival, a result that may be due to the harmful side effects and/or co-morbidity of preoperative treatment. New biomarkers are needed to facilitate identification of rectal cancer patients at high risk for local recurrent disease. This would allow for preoperative (chemo)radiotherapy to be restricted to high-risk patients, thereby reducing overtreatment and allowing personalized treatment protocols. We analyzed genome-wide DNA copy number (CN) and allelic alterations in 112 tumors from preoperatively untreated rectal cancer patients. Sixty-six patients with local and/or distant recurrent disease were compared to matched controls without recurrence. Results were validated in a second cohort of tumors from 95 matched rectal cancer patients. Additionally, we performed a meta-analysis that included 42 studies reporting on CN alterations in colorectal cancer and compared results to our own data.

Results

The genomic profiles in our study were comparable to other rectal cancer studies. Results of the meta-analysis supported the hypothesis that colon cancer and rectal cancer may be distinct disease entities. In our discovery patient study cohort, allelic retention of chromosome 7 was significantly associated with local recurrent disease. Data from the validation cohort were supportive, albeit not statistically significant, of this finding.

Conclusions

We showed that retention of heterozygosity on chromosome 7 may be associated with local recurrence in rectal cancer. Further research is warranted to elucidate the mechanisms and effect of retention of chromosome 7 on the development of local recurrent disease in rectal cancer.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1550-0) contains supplementary material, which is available to authorized users.     

The mutation rates of di-, tri- and tetranucleotide repeats in Drosophila melanogaster

In a recent study, we reported that the combined average mutation rate of 10 di-, 6 tri-, and 8 tetranucleotide repeats in Drosophila melanogaster was 6.3 x 10(-6) mutations per locus per generation, a rate substantially below that of microsatellite repeat units in mammals studied to date (range = 10(-2)-10(-5) per locus per generation). To obtain a more precise estimate of mutation rate for dinucleotide repeat motifs alone, we assayed 39 new dinucleotide repeat microsatellite loci in the mutation accumulation lines from our earlier study. Our estimate of mutation rate for a total of 49 dinucleotide repeats is 9.3 x 10(-6) per locus per generation, only slightly higher than the estimate from our earlier study. We also estimated the relative difference in microsatellite mutation rate among di-, tri-, and tetranucleotide repeats in the genome of D. melanogaster using a method based on population variation, and we found that tri- and tetranucleotide repeats mutate at rates 6.4 and 8.4 times slower than that of dinucleotide repeats, respectively. The slower mutation rates of tri- and tetranucleotide repeats appear to be associated with a relatively short repeat unit length of these repeat motifs in the genome of D. melanogaster. A positive correlation between repeat unit length and allelic variation suggests that mutation rate increases as the repeat unit lengths of microsatellites increase.      

Ultrastructural localization of amiloride-sensitive sodium channels and Na+,K(+)-ATPase in the rat's olfactory epithelial surface

Several studies have indicated that olfactory responses are impeded by amiloride. Therefore, it was of interest to see whether, and if so which, olfactory epithelial cellular compartments have amiloride- sensitive structures. Using ultrastructural methods that involved rapid freezing, freeze-substitution and low temperature embedding of olfactory epithelia, this study shows that, in the rat, this tissue is immunoreactive to antibodies against amiloride sensitive Na(+)- channels. However, microvilli of olfactory supporting cells, as opposed to receptor cilia, contained most of the immunoreactive sites. Apices from which the microvilli sprout and receptor cell dendritic knobs had much less if any of the amiloride-antibody binding sites. Using a direct ligand-binding cytochemical method, this study also confirms earlier ones that showed that olfactory receptor cell cilia have Na+, K(+)-ATPase. It is proposed that supporting cell microvilli and the receptor cilia themselves have mechanisms, different but likely complementary, that participate in regulating the salt concentration around the receptor cell cilia. In this way, both structures help to provide the ambient mucous environment for receptor cells to function properly. This regulation of the salt concentration of an ambient fluid environment is a function that the olfactory epithelium shares with cells of transporting epithelia, such as those of kidney.