Somewhat Stochastic Matrices

The standard theorem for stochastic matrices with positive entries is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the positivity condition is replaced by a condition on the distances between columns

An Unexpected Limit of Expected Values

Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t\u3e1. We also consider four other solutions of this equation that are related to the above selection process

An Unexpected Limit of Expected Values

Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t\u3e1. We also consider four other solutions of this equation that are related to the above selection process

The Genome of Borrelia recurrentis, the Agent of Deadly Louse-Borne Relapsing Fever, Is a Degraded Subset of Tick-Borne Borrelia duttonii

In an effort to understand how a tick-borne pathogen adapts to the body louse, we sequenced and compared the genomes of the recurrent fever agents Borrelia recurrentis and B. duttonii. The 1,242,163–1,574,910-bp fragmented genomes of B. recurrentis and B. duttonii contain a unique 23-kb linear plasmid. This linear plasmid exhibits a large polyT track within the promoter region of an intact variable large protein gene and a telomere resolvase that is unique to Borrelia. The genome content is characterized by several repeat families, including antigenic lipoproteins. B. recurrentis exhibited a 20.4% genome size reduction and appeared to be a strain of B. duttonii, with a decaying genome, possibly due to the accumulation of genomic errors induced by the loss of recA and mutS. Accompanying this were increases in the number of impaired genes and a reduction in coding capacity, including surface-exposed lipoproteins and putative virulence factors. Analysis of the reconstructed ancestral sequence compared to B. duttonii and B. recurrentis was consistent with the accelerated evolution observed in B. recurrentis. Vector specialization of louse-borne pathogens responsible for major epidemics was associated with rapid genome reduction. The correlation between gene loss and increased virulence of B. recurrentis parallels that of Rickettsia prowazekii, with both species being genomic subsets of less-virulent strains

The genomic landscape of balanced cytogenetic abnormalities associated with human congenital anomalies

Despite the clinical significance of balanced chromosomal abnormalities (BCAs), their characterization has largely been restricted to cytogenetic resolution. We explored the landscape of BCAs at nucleotide resolution in 273 subjects with a spectrum of congenital anomalies. Whole-genome sequencing revised 93% of karyotypes and demonstrated complexity that was cryptic to karyotyping in 21% of BCAs, highlighting the limitations of conventional cytogenetic approaches. At least 33.9% of BCAs resulted in gene disruption that likely contributed to the developmental phenotype, 5.2% were associated with pathogenic genomic imbalances, and 7.3% disrupted topologically associated domains (TADs) encompassing known syndromic loci. Remarkably, BCA breakpoints in eight subjects altered a single TAD encompassing MEF2C, a known driver of 5q14.3 microdeletion syndrome, resulting in decreased MEF2C expression. We propose that sequence-level resolution dramatically improves prediction of clinical outcomes for balanced rearrangements and provides insight into new pathogenic mechanisms, such as altered regulation due to changes in chromosome topology

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Phylogenetic Analysis of Chlamydia trachomatis Tarp and Correlation with Clinical Phenotype▿ †

Chlamydia trachomatis is the leading cause of infectious blindness worldwide and is the most commonly reported pathogen causing sexually transmitted infections. Tarp (translocated actin recruiting phosphoprotein), a type III secreted effector that mediates actin nucleation, is central to C. trachomatis infection. The phylogenetic analysis of tarP from reference strains as well as ocular, genital, and lymphogranuloma venereum (LGV) clinical isolates demonstrated an evolutionary relationship with disease phenotype, with LGV and ocular isolates branched into clades that were separate from the urogenital isolates. The sequence analysis of Tarp indicated a high degree of variability and identified trends within clinical groupings. Tarps from LGV strains contained the highest number of tyrosine-rich repeat regions (up to nine) and the fewest (two) predicted actin binding domains. The converse was noted for Tarp proteins from ocular isolates that contained up to four actin binding domains and as few as one tyrosine-rich repeat region. The results suggest that Tarp is among the few known genes to play a role in C. trachomatis adaptations to specific niches within the host