Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Droplet digital PCR assay as an innovative and promising highly sensitive assay to unveil residual and cryptic HBV replication in peripheral compartment

: Droplet digital PCR is an innovative and promising approach for highly sensitive quantification of nucleic acids that is being increasingly used in the field of clinical virology, including the setting of hepatitis B virus (HBV). Here, we comprehensively report a robust and reproducible ddPCR assay for the highly sensitive quantification of serum HBV-DNA. The assay showed a limit of detection of 4 copies/ml (<1IU/ml) by Probit analysis, showed a good linearity (R2 = 0.94) and a high intra- and inter-run reproducibility with differences between the values obtained in the same run or in two independent runs never exceeding 0.14logcopies/mL and 0.21logcopies/mL, respectively. By analysing serum samples from chronically HBV infected patients (mostly under antiviral treatment), ddPCR successfully quantified serum HBV-DNA in 89.8% of patients with detectable serum HBV-DNA < 20 IU/mL [equivalent to <112copies/ml] by classical Real-Time PCR assay, with a median (IQR) of 8(5-14)IU/mL [45(28-78)copies/ml], and in 66.7% of patients with undetectable serum HBV-DNA, with a median (IQR) of 5(4-9)IU/mL [28(20-50)copies/ml]. Similarly, by analysing serum samples from patients with a serological profile compatible with occult HBV infection (anti-HBc+/HBsAg-), ddPCR successfully quantified serum HBV-DNA in 40% of patients with a median (IQR) value of 1(1-2)IU/mL [5(5-11)copies/ml], in line with the extremely limited viral replication typically observed in occult HBV infection. Overall, the availability of assays for the highly sensitive quantification of serum HBV-DNA can provide an added value in optimizing the diagnosis of occult hepatitis B infection, improving the therapeutic management of chronically HBV infected patients, also in the light of innovative drugs (upcoming in clinical practise) aimed at achieving HBV functional cure

Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

Persistent B cell memory after SARS-CoV-2 vaccination is functional during breakthrough infections

Breakthrough SARS-CoV-2 infections in fully vaccinated individuals are considered a consequence of waning immunity. Serum antibodies represent the most measurable outcome of vaccine-induced B cell memory. When antibodies decline, memory B cells are expected to persist and perform their function, preventing clinical disease. We investigated whether BNT162b2 mRNA vaccine induces durable and functional B cell memory in vivo against SARS-CoV-2 3, 6, and 9 months after the second dose in a cohort of health care workers (HCWs). While we observed physiological decline of SARS-CoV-2-specific antibodies, memory B cells persist and increase until 9 months after immunization. HCWs with breakthrough infections had no signs of waning immunity. In 3–4 days, memory B cells responded to SARS-CoV-2 infection by producing high levels of specific antibodies in the serum and anti-Spike IgA in the saliva. Antibodies to the viral nucleoprotein were produced with the slow kinetics typical of the response to a novel antigen