Renewal theory and computable convergence rates for geometrically ergodic Markov chains

We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and Tweedie, and from estimates using coupling, although we start from essentially the same assumptions of a drift condition toward a ``small set.'' The estimates show a noticeable improvement on existing results if the Markov chain is reversible with respect to its stationary distribution, and especially so if the chain is also positive. The method of proof uses the first-entrance-last-exit decomposition, together with new quantitative versions of a result of Kendall from discrete renewal theory.Comment: Published at http://dx.doi.org/10.1214/105051604000000710 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lyapunov exponents and shear-induced chaos for a Hopf bifurcation with additive noise

This paper considers the effect of additive white noise on the normal form for the supercritical Hopf bifurcation in 2 dimensions. The main results involve the asymptotic behavior of the top Lyapunov exponent lambda associated with this random dynamical system as one or more of the parameters in the system tend to 0 or infinity. This enables the construction of a bifurcation diagram in parameter space showing stable regions where lambda is negative (implying synchronization) and unstable regions where lambda is positive (implying chaotic behavior). The value of lambda depends strongly on the shearing effect of the twist factor of the deterministic Hopf bifurcation. If the twist factor is sufficiently small then lambda is negative regardless of all the other parameters in the system. But when all the parameters except the shear coefficient are fixed then lambda tends to infinity as the shear coefficient tends to infinity.Comment: 47 pages, 3 figure

Uniform shrinking and expansion under isotropic Brownian flows

We study some finite time transport properties of isotropic Brownian flows. Under a certain nondegeneracy condition on the potential spectral measure, we prove that uniform shrinking or expansion of balls under the flow over some bounded time interval can happen with positive probability. We also provide a control theorem for isotropic Brownian flows with drift. Finally, we apply the above results to show that under the nondegeneracy condition the length of a rectifiable curve evolving in an isotropic Brownian flow with strictly negative top Lyapunov exponent converges to zero as $t\to \infty$ with positive probability

Comparison of Antibody Repertoires Produced by HIV-1 Infection, Other Chronic and Acute Infections, and Systemic Autoimmune Disease

Background Antibodies (Abs) produced during HIV-1 infection rarely neutralize a broad range of viral isolates; only eight broadly-neutralizing (bNt) monoclonal (M)Abs have been isolated. Yet, to be effective, an HIV-1 vaccine may have to elicit the essential features of these MAbs. The V genes of all of these bNt MAbs are highly somatically mutated, and the VH genes of five of them encode a long (≥20 aa) third complementarity-determining region (CDR-H3). This led us to question whether long CDR-H3s and high levels of somatic mutation (SM) are a preferred feature of anti-HIV bNt MAbs, or if other adaptive immune responses elicit them in general. Methodology and Principal Findings We assembled a VH-gene sequence database from over 700 human MAbs of known antigen specificity isolated from chronic (viral) infections (ChI), acute (bacterial and viral) infections (AcI), and systemic autoimmune diseases (SAD), and compared their CDR-H3 length, number of SMs and germline VH-gene usage. We found that anti-HIV Abs, regardless of their neutralization breadth, tended to have long CDR-H3s and high numbers of SMs. However, these features were also common among Abs associated with other chronic viral infections. In contrast, Abs from acute viral infections (but not bacterial infections) tended to have relatively short CDR-H3s and a low number of SMs, whereas SAD Abs were generally intermediate in CDR-H3 length and number of SMs. Analysis of VH gene usage showed that ChI Abs also tended to favor distal germline VH-genes (particularly VH1-69), especially in Abs bearing long CDR-H3s. Conclusions and Significance The striking difference between the Abs produced during chronic vs. acute viral infection suggests that Abs bearing long CDR-H3s, high levels of SM and VH1-69 gene usage may be preferentially selected during persistent infection

Disorders of sex development : insights from targeted gene sequencing of a large international patient cohort

Background: Disorders of sex development (DSD) are congenital conditions in which chromosomal, gonadal, or phenotypic sex is atypical. Clinical management of DSD is often difficult and currently only 13% of patients receive an accurate clinical genetic diagnosis. To address this we have developed a massively parallel sequencing targeted DSD gene panel which allows us to sequence all 64 known diagnostic DSD genes and candidate genes simultaneously. Results: We analyzed DNA from the largest reported international cohort of patients with DSD (278 patients with 46, XY DSD and 48 with 46, XX DSD). Our targeted gene panel compares favorably with other sequencing platforms. We found a total of 28 diagnostic genes that are implicated in DSD, highlighting the genetic spectrum of this disorder. Sequencing revealed 93 previously unreported DSD gene variants. Overall, we identified a likely genetic diagnosis in 43% of patients with 46, XY DSD. In patients with 46, XY disorders of androgen synthesis and action the genetic diagnosis rate reached 60%. Surprisingly, little difference in diagnostic rate was observed between singletons and trios. In many cases our findings are informative as to the likely cause of the DSD, which will facilitate clinical management. Conclusions: Our massively parallel sequencing targeted DSD gene panel represents an economical means of improving the genetic diagnostic capability for patients affected by DSD. Implementation of this panel in a large cohort of patients has expanded our understanding of the underlying genetic etiology of DSD. The inclusion of research candidate genes also provides an invaluable resource for future identification of novel genes

Phenotypic Characterization of EIF2AK4 Mutation Carriers in a Large Cohort of Patients Diagnosed Clinically With Pulmonary Arterial Hypertension.

BACKGROUND: Pulmonary arterial hypertension (PAH) is a rare disease with an emerging genetic basis. Heterozygous mutations in the gene encoding the bone morphogenetic protein receptor type 2 (BMPR2) are the commonest genetic cause of PAH, whereas biallelic mutations in the eukaryotic translation initiation factor 2 alpha kinase 4 gene (EIF2AK4) are described in pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Here, we determine the frequency of these mutations and define the genotype-phenotype characteristics in a large cohort of patients diagnosed clinically with PAH. METHODS: Whole-genome sequencing was performed on DNA from patients with idiopathic and heritable PAH and with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis recruited to the National Institute of Health Research BioResource-Rare Diseases study. Heterozygous variants in BMPR2 and biallelic EIF2AK4 variants with a minor allele frequency of <1:10 000 in control data sets and predicted to be deleterious (by combined annotation-dependent depletion, PolyPhen-2, and sorting intolerant from tolerant predictions) were identified as potentially causal. Phenotype data from the time of diagnosis were also captured. RESULTS: Eight hundred sixty-four patients with idiopathic or heritable PAH and 16 with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis were recruited. Mutations in BMPR2 were identified in 130 patients (14.8%). Biallelic mutations in EIF2AK4 were identified in 5 patients with a clinical diagnosis of pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Furthermore, 9 patients with a clinical diagnosis of PAH carried biallelic EIF2AK4 mutations. These patients had a reduced transfer coefficient for carbon monoxide (Kco; 33% [interquartile range, 30%-35%] predicted) and younger age at diagnosis (29 years; interquartile range, 23-38 years) and more interlobular septal thickening and mediastinal lymphadenopathy on computed tomography of the chest compared with patients with PAH without EIF2AK4 mutations. However, radiological assessment alone could not accurately identify biallelic EIF2AK4 mutation carriers. Patients with PAH with biallelic EIF2AK4 mutations had a shorter survival. CONCLUSIONS: Biallelic EIF2AK4 mutations are found in patients classified clinically as having idiopathic and heritable PAH. These patients cannot be identified reliably by computed tomography, but a low Kco and a young age at diagnosis suggests the underlying molecular diagnosis. Genetic testing can identify these misclassified patients, allowing appropriate management and early referral for lung transplantation

A novel formulation of inhaled sodium cromoglicate (PA101) in idiopathic pulmonary fibrosis and chronic cough: a randomised, double-blind, proof-of-concept, phase 2 trial

Background Cough can be a debilitating symptom of idiopathic pulmonary fibrosis (IPF) and is difficult to treat. PA101 is a novel formulation of sodium cromoglicate delivered via a high-efficiency eFlow nebuliser that achieves significantly higher drug deposition in the lung compared with the existing formulations. We aimed to test the efficacy and safety of inhaled PA101 in patients with IPF and chronic cough and, to explore the antitussive mechanism of PA101, patients with chronic idiopathic cough (CIC) were also studied. Methods This pilot, proof-of-concept study consisted of a randomised, double-blind, placebo-controlled trial in patients with IPF and chronic cough and a parallel study of similar design in patients with CIC. Participants with IPF and chronic cough recruited from seven centres in the UK and the Netherlands were randomly assigned (1:1, using a computer-generated randomisation schedule) by site staff to receive PA101 (40 mg) or matching placebo three times a day via oral inhalation for 2 weeks, followed by a 2 week washout, and then crossed over to the other arm. Study participants, investigators, study staff, and the sponsor were masked to group assignment until all participants had completed the study. The primary efficacy endpoint was change from baseline in objective daytime cough frequency (from 24 h acoustic recording, Leicester Cough Monitor). The primary efficacy analysis included all participants who received at least one dose of study drug and had at least one post-baseline efficacy measurement. Safety analysis included all those who took at least one dose of study drug. In the second cohort, participants with CIC were randomly assigned in a study across four centres with similar design and endpoints. The study was registered with ClinicalTrials.gov (NCT02412020) and the EU Clinical Trials Register (EudraCT Number 2014-004025-40) and both cohorts are closed to new participants. Findings Between Feb 13, 2015, and Feb 2, 2016, 24 participants with IPF were randomly assigned to treatment groups. 28 participants with CIC were enrolled during the same period and 27 received study treatment. In patients with IPF, PA101 reduced daytime cough frequency by 31·1% at day 14 compared with placebo; daytime cough frequency decreased from a mean 55 (SD 55) coughs per h at baseline to 39 (29) coughs per h at day 14 following treatment with PA101, versus 51 (37) coughs per h at baseline to 52 (40) cough per h following placebo treatment (ratio of least-squares [LS] means 0·67, 95% CI 0·48–0·94, p=0·0241). By contrast, no treatment benefit for PA101 was observed in the CIC cohort; mean reduction of daytime cough frequency at day 14 for PA101 adjusted for placebo was 6·2% (ratio of LS means 1·27, 0·78–2·06, p=0·31). PA101 was well tolerated in both cohorts. The incidence of adverse events was similar between PA101 and placebo treatments, most adverse events were mild in severity, and no severe adverse events or serious adverse events were reported. Interpretation This study suggests that the mechanism of cough in IPF might be disease specific. Inhaled PA101 could be a treatment option for chronic cough in patients with IPF and warrants further investigation

Phenotypic Characterization of <i>EIF2AK4</i> Mutation Carriers in a Large Cohort of Patients Diagnosed Clinically With Pulmonary Arterial Hypertension

Background: Pulmonary arterial hypertension (PAH) is a rare disease with an emerging genetic basis. Heterozygous mutations in the gene encoding the bone morphogenetic protein receptor type 2 ( BMPR2 ) are the commonest genetic cause of PAH, whereas biallelic mutations in the eukaryotic translation initiation factor 2 alpha kinase 4 gene ( EIF2AK4 ) are described in pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Here, we determine the frequency of these mutations and define the genotype-phenotype characteristics in a large cohort of patients diagnosed clinically with PAH. Methods: Whole-genome sequencing was performed on DNA from patients with idiopathic and heritable PAH and with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis recruited to the National Institute of Health Research BioResource–Rare Diseases study. Heterozygous variants in BMPR2 and biallelic EIF2AK4 variants with a minor allele frequency of &lt;1:10 000 in control data sets and predicted to be deleterious (by combined annotation-dependent depletion, PolyPhen-2, and sorting intolerant from tolerant predictions) were identified as potentially causal. Phenotype data from the time of diagnosis were also captured. Results: Eight hundred sixty-four patients with idiopathic or heritable PAH and 16 with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis were recruited. Mutations in BMPR2 were identified in 130 patients (14.8%). Biallelic mutations in EIF2AK4 were identified in 5 patients with a clinical diagnosis of pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Furthermore, 9 patients with a clinical diagnosis of PAH carried biallelic EIF2AK4 mutations. These patients had a reduced transfer coefficient for carbon monoxide (K co ; 33% [interquartile range, 30%–35%] predicted) and younger age at diagnosis (29 years; interquartile range, 23–38 years) and more interlobular septal thickening and mediastinal lymphadenopathy on computed tomography of the chest compared with patients with PAH without EIF2AK4 mutations. However, radiological assessment alone could not accurately identify biallelic EIF2AK4 mutation carriers. Patients with PAH with biallelic EIF2AK4 mutations had a shorter survival. Conclusions: Biallelic EIF2AK4 mutations are found in patients classified clinically as having idiopathic and heritable PAH. These patients cannot be identified reliably by computed tomography, but a low K co and a young age at diagnosis suggests the underlying molecular diagnosis. Genetic testing can identify these misclassified patients, allowing appropriate management and early referral for lung transplantation. </jats:sec

Telomerecat: A ploidy-agnostic method for estimating telomere length from whole genome sequencing data.

Telomere length is a risk factor in disease and the dynamics of telomere length are crucial to our understanding of cell replication and vitality. The proliferation of whole genome sequencing represents an unprecedented opportunity to glean new insights into telomere biology on a previously unimaginable scale. To this end, a number of approaches for estimating telomere length from whole-genome sequencing data have been proposed. Here we present Telomerecat, a novel approach to the estimation of telomere length. Previous methods have been dependent on the number of telomeres present in a cell being known, which may be problematic when analysing aneuploid cancer data and non-human samples. Telomerecat is designed to be agnostic to the number of telomeres present, making it suited for the purpose of estimating telomere length in cancer studies. Telomerecat also accounts for interstitial telomeric reads and presents a novel approach to dealing with sequencing errors. We show that Telomerecat performs well at telomere length estimation when compared to leading experimental and computational methods. Furthermore, we show that it detects expected patterns in longitudinal data, repeated measurements, and cross-species comparisons. We also apply the method to a cancer cell data, uncovering an interesting relationship with the underlying telomerase genotype