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We study the perturbation of a shock wave in conservation laws with physical viscosity. We obtain the detailed pointwise estimates of the solutions. In particular, we show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to be small, but independent. Our assumptions on the viscosity matrix are general so that our results apply to the Navier-Stokes equations for the compressible fluid and the full system of magnetohydrodynamics, including the cases of multiple eigenvalues in the transversal fields, as long as the shock is classical. Our analysis depends on accurate construction of an approximate Green’s function. The form of the ansatz for the perturbation is carefully constructed and is sufficiently tight so that we can close the nonlinear term through the Duhamel’s principle.

Variation in DNA methylation (DNAm) is associated with lifestyle factors such as smoking and body mass index (BMI) but there has been little research exploring its ability to identify individuals with major depressive disorder (MDD). Using penalised regression on genome-wide CpG methylation, we tested whether DNAm risk scores (MRS), trained on 1223 MDD cases and 1824 controls, could discriminate between cases (n = 363) and controls (n = 1417) in an independent sample, comparing their predictive accuracy to polygenic risk scores (PRS). The MRS explained 1.75% of the variance in MDD (β = 0.338, p = 1.17 × 10−7) and remained associated after adjustment for lifestyle factors (β = 0.219, p = 0.001, R2 = 0.68%). When modelled alongside PRS (β = 0.384, p = 4.69 × 10−9) the MRS remained associated with MDD (β = 0.327, p = 5.66 × 10−7). The MRS was also associated with incident cases of MDD who were well at recruitment but went on to develop MDD at a later assessment (β = 0.193, p = 0.016, R2 = 0.52%). Heritability analyses found additive genetic effects explained 22% of variance in the MRS, with a further 19% explained by pedigree-associated genetic effects and 16% by the shared couple environment. Smoking status was also strongly associated with MRS (β = 0.440, p ≤ 2 × 10−16). After removing smokers from the training set, the MRS strongly associated with BMI (β = 0.053, p = 0.021). We tested the association of MRS with 61 behavioural phenotypes and found that whilst PRS were associated with psychosocial and mental health phenotypes, MRS were more strongly associated with lifestyle and sociodemographic factors. DNAm-based risk scores of MDD significantly discriminated MDD cases from controls in an independent dataset and may represent an archive of exposures to lifestyle factors that are relevant to the prediction of MDD.

Parent-of-origin effects (POE) exist when there is differential expression of alleles inherited from the two parents. A genome-wide scan for POE on DNA methylation at 639,238 CpGs in 5,101 individuals identifies 733 independent methylation CpGs potentially influenced by POE at a false discovery rate ≤ 0.05 of which 331 had not previously been identified. Cis and trans methylation quantitative trait loci (mQTL) regulate methylation variation through POE at 54% (399/733) of the identified POE-influenced CpGs. The combined results provide strong evidence for previously unidentified POE-influenced CpGs at 171 independent loci. Methylation variation at 14 of the POE-influenced CpGs is associated with multiple metabolic traits. A phenome-wide association analysis using the POE mQTL SNPs identifies a previously unidentified imprinted locus associated with waist circumference. These results provide a high resolution population-level map for POE on DNA methylation sites, their local and distant regulators and potential consequences for complex traits. Parent-of-origin effects (POE) are observed when there are different effects from alleles inherited from the two parents on phenotypic measures. Here, Zeng et al. study POE on DNA methylation in 5,101 individuals and identify genetic variants that associate with methylation variation via POE and their potential phenotypic consequences.

We study gas flows with any finite number of thermal nonequilibrium modes. The equations describing such flows are a hyperbolic system with several relaxation equations. An important feature is entropy increase dictated by physics for any irreversible process. Under physical assumptions we obtain properties of thermodynamic variables relevant to stability. By the energy method we prove global existence and uniqueness for the Cauchy problem when the initial data are small perturbations of constant equilibrium states. We give a precise formulation of the fundamental solution for the linearized system, and use it to obtain large time behavior of solutions to the nonlinear system. In particular, we show that the entropy increases but stays bounded. The resulting asymptotic picture of nonequilibrium flows is in a pointwise sense both in space and in time.

To efficiently transform genetic associations into drug targets requires evidence that a particular gene, and its encoded protein, contribute causally to a disease. To achieve this, we employ a three-step proteome-by-phenome Mendelian Randomization (MR) approach. In step one, 154 protein quantitative trait loci (pQTLs) were identified and independently replicated. From these pQTLs, 64 replicated locally-acting variants were used as instrumental variables for proteome-by-phenome MR across 846 traits (step two). When its assumptions are met, proteome-by-phenome MR, is equivalent to simultaneously running many randomized controlled trials. Step 2 yielded 38 proteins that significantly predicted variation in traits and diseases in 509 instances. Step 3 revealed that amongst the 271 instances from GeneAtlas (UK Biobank), 77 showed little evidence of pleiotropy (HEIDI), and 92 evidence of colocalization (eCAVIAR). Results were wide ranging: including, for example, new evidence for a causal role of tyrosine-protein phosphatase non-receptor type substrate 1 (SHPS1; SIRPA) in schizophrenia, and a new finding that intestinal fatty acid binding protein (FABP2) abundance contributes to the pathogenesis of cardiovascular disease. We also demonstrated confirmatory evidence for the causal role of four further proteins (FGF5, IL6R, LPL, LTA) in cardiovascular disease risk.

Background The variation in the rate at which humans age may be rooted in early events acting through the genomic regions that are influenced by such events and subsequently are related to health phenotypes in later life. The parent-of-origin-effect (POE)-regulated methylome includes regions enriched for genetically controlled imprinting effects (the typical type of POE) and regions influenced by environmental effects associated with parents (the atypical POE). This part of the methylome is heavily influenced by early events, making it a potential route connecting early exposures, the epigenome, and aging. We aim to test the association of POE-CpGs with early and later exposures and subsequently with health-related phenotypes and adult aging. Results We perform a phenome-wide association analysis for the POE-influenced methylome using GS:SFHS ( N discovery  = 5087, N replication  = 4450). We identify and replicate 92 POE-CpG-phenotype associations. Most of the associations are contributed by the POE-CpGs belonging to the atypical class where the most strongly enriched associations are with aging (DNAmTL acceleration), intelligence, and parental (maternal) smoking exposure phenotypes. A proportion of the atypical POE-CpGs form co-methylation networks (modules) which are associated with these phenotypes, with one of the aging-associated modules displaying increased within-module methylation connectivity with age. The atypical POE-CpGs also display high levels of methylation heterogeneity, fast information loss with age, and a strong correlation with CpGs contained within epigenetic clocks. Conclusions These results identify the association between the atypical POE-influenced methylome and aging and provide new evidence for the “early development of origin” hypothesis for aging in humans.

Background The apolipoprotein E ( APOE ) ε4 allele is the strongest genetic risk factor for late onset Alzheimer’s disease, whilst the ε2 allele confers protection. Previous studies report differential DNA methylation of APOE between ε4 and ε2 carriers, but associations with epigenome-wide methylation have not previously been characterised. Methods Using the EPIC array, we investigated epigenome-wide differences in whole blood DNA methylation patterns between Alzheimer’s disease-free APOE ε4 ( n  = 2469) and ε2 ( n  = 1118) carriers from the two largest single-cohort DNA methylation samples profiled to date. Using a discovery, replication and meta-analysis study design, methylation differences were identified using epigenome-wide association analysis and differentially methylated region (DMR) approaches. Results were explored using pathway and methylation quantitative trait loci (meQTL) analyses. Results We obtained replicated evidence for DNA methylation differences in a ~ 169 kb region, which encompasses part of APOE and several upstream genes. Meta-analytic approaches identified DNA methylation differences outside of APOE : differentially methylated positions were identified in DHCR24 , LDLR and ABCG1 (2.59 × 10 −100  ≤  P  ≤ 2.44 × 10 −8 ) and DMRs were identified in SREBF2 and LDLR (1.63 × 10 −4  ≤  P  ≤ 3.01 × 10 −2 ). Pathway and meQTL analyses implicated lipid-related processes and high-density lipoprotein cholesterol was identified as a partial mediator of the methylation differences in ABCG1 and DHCR24 . Conclusions APOE ε4 vs. ε2 carrier status is associated with epigenome-wide methylation differences in the blood. The loci identified are located in trans as well as cis to APOE and implicate genes involved in lipid homeostasis.

Variation in obesity-related traits has a genetic basis with heritabilities between 40 and 70%. While the global obesity pandemic is usually associated with environmental changes related to lifestyle and socioeconomic changes, most genetic studies do not include all relevant environmental covariates, so the genetic contribution to variation in obesity-related traits cannot be accurately assessed. Some studies have described interactions between a few individual genes linked to obesity and environmental variables but there is no agreement on their total contribution to differences between individuals. Here we compared self-reported smoking data and a methylation-based proxy to explore the effect of smoking and genome-by-smoking interactions on obesity related traits from a genome-wide perspective to estimate the amount of variance they explain. Our results indicate that exploiting omic measures can improve models for complex traits such as obesity and can be used as a substitute for, or jointly with, environmental records to better understand causes of disease.

Chronic pain is highly prevalent and a significant source of disability, yet its genetic and environmental risk factors are poorly understood. Its relationship with major depressive disorder (MDD) is of particular importance. We sought to test the contribution of genetic factors and shared and unique environment to risk of chronic pain and its correlation with MDD in Generation Scotland: Scottish Family Health Study (GS:SFHS). We then sought to replicate any significant findings in the United Kingdom Biobank study. Using family-based mixed-model analyses, we examined the contribution of genetics and shared family environment to chronic pain by spouse, sibling, and household relationships. These analyses were conducted in GS:SFHS (n = 23,960), a family- and population-based study of individuals recruited from the Scottish population through their general practitioners. We then examined and partitioned the correlation between chronic pain and MDD and estimated the contribution of genetic factors and shared environment in GS:SFHS. Finally, we used data from two independent genome-wide association studies to test whether chronic pain has a polygenic architecture and examine whether genomic risk of psychiatric disorder predicted chronic pain and whether genomic risk of chronic pain predicted MDD. These analyses were conducted in GS:SFHS and repeated in UK Biobank, a study of 500,000 from the UK population, of whom 112,151 had genotyping and phenotypic data. Chronic pain is a moderately heritable trait (heritability = 38.4%, 95% CI 33.6% to 43.9%) that is significantly concordant in spouses (variance explained 18.7%, 95% CI 9.5% to 25.1%). Chronic pain is positively correlated with depression (ρ = 0.13, 95% CI 0.11 to 0.15, p = 2.72x10-68) and shows a tendency to cluster within families for genetic reasons (genetic correlation = 0.51, 95%CI 0.40 to 0.62, p = 8.24x10-19). Polygenic risk profiles for pain, generated using independent GWAS data, were associated with chronic pain in both GS:SFHS (maximum β = 6.18x10-2, 95% CI 2.84 x10-2 to 9.35 x10-2, p = 4.3x10-4) and UK Biobank (maximum β = 5.68 x 10-2, 95% CI 4.70x10-2 to 6.65x10-2, p < 3x10-4). Genomic risk of MDD is also significantly associated with chronic pain in both GS:SFHS (maximum β = 6.62x10-2, 95% CI 2.82 x10-2 to 9.76 x10-2, p = 4.3x10-4) and UK Biobank (maximum β = 2.56x10-2, 95% CI 1.62x10-2 to 3.63x10-2, p < 3x10-4). Limitations of the current study include the possibility that spouse effects may be due to assortative mating and the relatively small polygenic risk score effect sizes. Genetic factors, as well as chronic pain in a partner or spouse, contribute substantially to the risk of chronic pain for an individual. Chronic pain is genetically correlated with MDD, has a polygenic architecture, and is associated with polygenic risk of MDD.

In the original version of this Article, the legend in the upper panel of Figure 2 incorrectly read ‘paternal imprinting’ and should have read ‘maternal imprinting’. This has been corrected in both the PDF and HTML versions of the Article.