The transitivity of the Hardy-Weinberg law

The reduction of multi-allelic polymorphisms to variants with fewer alleles, two in the limit, is addressed. The Hardy-Weinberg law is shown to be transitive in the sense that a multi-allelic polymorphism that is in equilibrium will retain its equilibrium status if any allele together with its corresponding genotypes is deleted from the population. Similarly, the transitivity principle also applies if alleles are joined, which leads to the summation of allele frequencies and their corresponding genotype frequencies. These basic polymorphism properties are intuitive, but they have apparently not been formalized or investigated. This article provides a straightforward proof of the transitivity principle, and its usefulness in practical genetic data analysis with multi-allelic markers is explored. In general, results of statistical tests for Hardy-Weinberg equilibrium obtained with polymorphisms that are reduced by deletion or joining of alleles are seen to be consistent with the formulated transitivity principle. We also show how the transitivity principle allows one to identify equilibrium-offending alleles, and how it can provide clues to genotyping problems and evolutionary changes. For microsatellites, which are widely used in forensics, the transitivity principle implies one expects similar results for statistical tests that use length-based and sequence-based alleles. High-quality autosomal microsatellite databases of the US National Institute of Standards and Technology are used to illustrate the use of the transitivity principle in testing both length-based and sequence-based microsatellites for Hardy-Weinberg proportions. Test results for Hardy-Weinberg proportions for the two types of microsatellites are seen to be largely consistent and can detect allele imbalance.

CNAHap: a germline haplotyping method using tumor allele-specific copy number alteration

Haplotype phasing is indispensable to study human genetics. The pervasiveness of large copy number variant segments in solid tumors brings possibilities to resolve long germline phasing blocks utilizing allele imbalance in tumor data. Although there exist such studies, none of them provide easy-use software based on availability and usability. Herein, we present a novel tool, CNAHap, to determine the allele-specific copy number in tumor and then phase germline variants according to the imbalanced alleles in tumor genomes. We also provide interactive web interfaces to visualize the copy number and phase landscape from CNAHap. On in silico datasets, CNAHap demonstrates higher allele-specific copy number calling accuracy than the benchmark tool and generates long phasing blocks. As a case study on Hepatocellular carcinoma, CNAHap successfully generates huge phase blocks with the averages of N50 and N90 as 25M and 7M, respectively, and finds the Olfactory receptor family is recurrent amplified. Our results illustrate the efficacy of CNAHap in determining tumor allele-specific copy numbers and their long germline haplotypes. CNAHap is available at https://github.com/bowentan/CNAHap and the CNAHap visualization web interfaces are hosted at bio.oviz.org.

Mutant Allele Imbalance in Cancer

The search for somatic mutations that drive the initiation and progression of human tumors has dominated recent cancer research. While much emphasis has been placed on characterizing the prevalence and function of driver mutations, comparatively less is known about their serial genetic evolution. Indeed, study of this phenomenon has largely focused on tumor-suppressor genes recessive at the cellular level or mechanisms of resistance in tumors with mutant oncogenes targeted by therapy. There is, however, a growing appreciation that despite a decades-old presumption of heterozygosity, changes in mutant oncogene zygosity are common and drive dosage and stoichiometry changes that lead to selective growth advantages. Here, we review the recent progress in understanding mutant allele imbalance and its implications for tumor biology, cancer evolution, and response to anticancer therapy. Expected final online publication date for the Annual Review of Cancer Biology, Volume 5 is March 4, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Conflicting pathology reports: a diagnostic dilemma

The differential diagnosis of a brain lesion with two discordant pathology reports includes the presence of collision tumor, metaplastic changes, and labeling errors that occurred during the processing of the specimen. The authors present a case in which the first brain biopsy from a 47-year-old patient with a history of heavy smoking was compatible with metastatic small cell carcinoma, and the second biopsy taken during decompression craniotomy 3 weeks later was compatible with WHO Grade IV glioblastoma. Using short tandem repeat (STR) analysis of the two specimens and nontumor-derived patient DNA, the authors found that the two specimens did not belong to the same individual. The authors conclude that allele imbalance or loss of heterozygosity detected by STR analysis is a reliable and valuable diagnostic tool for clarifying discrepancies in discordant pathology reports.