A structure-preserving parametric finite element method for area-conserved generalized mean curvature flow

We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) to simulate the motion of closed curves governed by area-conserved generalized mean curvature flow in two dimensions (2D). We first present a variational formulation and rigorously prove that it preserves two fundamental geometric structures of the flows, i.e., (a) the conservation of the area enclosed by the closed curve; (b) the decrease of the perimeter of the curve. Then the variational formulation is approximated by using piecewise linear parametric finite elements in space to develop the semi-discrete scheme. With the help of the discrete Cauchy's inequality and discrete power mean inequality, the area conservation and perimeter decrease properties of the semi-discrete scheme are shown. On this basis, by combining the backward Euler method in time and a proper approximation of the unit normal vector, a structure-preserving fully discrete scheme is constructed successfully, which can preserve the two essential geometric structures simultaneously at the discrete level. Finally, numerical experiments test the convergence rate, area conservation, perimeter decrease and mesh quality, and depict the evolution of curves. Numerical results indicate that the proposed SP-PFEM provides a reliable and powerful tool for the simulation of area-conserved generalized mean curvature flow in 2D.Comment: 24 pages, 8 figure

Averaging principle for McKean-Vlasov SDEs driven by multiplicative fractional noise with highly oscillatory drift coefficient

In this paper, we study averaging principle for a class of McKean-Vlasov stochastic differential equations (SDEs) that contain multiplicative fractional noise with Hurst parameter $H >$ 1/2 and highly oscillatory drift coefficient. Here the integral corresponding to fractional Brownian motion is the generalized Riemann-Stieltjes integral. Using Khasminskii's time discretization techniques, we prove that the solution of the original system strongly converges to the solution of averaging system as the times scale $\epsilon$ gose to zero in the supremum- and H\"older-topologies which are sharpen existing ones in the classical Mckean-Vlasov SDEs framework.Comment: 12 page

DNA methylation-based estimator of telomere length

Telomere length (TL) is associated with several aging-related diseases. Here, we present a DNA methylation estimator of TL (DNAmTL) based on 140 CpGs. Leukocyte DNAmTL is applicable across the entire age spectrum and is more strongly associated with age than measured leukocyte TL (LTL) (r ~-0.75 for DNAmTL versus r ~ -0.35 for LTL). Leukocyte DNAmTL outperforms LTL in predicting: i) time-to-death (p=2.5E-20), ii) time-to-coronary heart disease (p=6.6E-5), iii) time-to-congestive heart failure (p=3.5E-6), and iv) association with smoking history (p=1.21E-17). These associations are further validated in large scale methylation data (n=10k samples) from the Framingham Heart Study, Women's Health Initiative, Jackson Heart Study, InChianti, Lothian Birth Cohorts, Twins UK, and Bogalusa Heart Study. Leukocyte DNAmTL is also associated with measures of physical fitness/functioning (p=0.029), age-at-menopause (p=0.039), dietary variables (omega 3, fish, vegetable intake), educational attainment (p=3.3E-8) and income (p=3.1E-5). Experiments in cultured somatic cells show that DNAmTL dynamics reflect in part cell replication rather than TL per se. DNAmTL is not only an epigenetic biomarker of replicative history of cells, but a useful marker of age-related pathologies that are associated with it

GWAS of epigenetic aging rates in blood reveals a critical role for TERT.

DNA methylation age is an accurate biomarker of chronological age and predicts lifespan, but its underlying molecular mechanisms are unknown. In this genome-wide association study of 9907 individuals, we find gene variants mapping to five loci associated with intrinsic epigenetic age acceleration (IEAA) and gene variants in three loci associated with extrinsic epigenetic age acceleration (EEAA). Mendelian randomization analysis suggests causal influences of menarche and menopause on IEAA and lipoproteins on IEAA and EEAA. Variants associated with longer leukocyte telomere length (LTL) in the telomerase reverse transcriptase gene (TERT) paradoxically confer higher IEAA (P < 2.7 × 10-11). Causal modeling indicates TERT-specific and independent effects on LTL and IEAA. Experimental hTERT-expression in primary human fibroblasts engenders a linear increase in DNA methylation age with cell population doubling number. Together, these findings indicate a critical role for hTERT in regulating the epigenetic clock, in addition to its established role of compensating for cell replication-dependent telomere shortening

Blood DNA methylation sites predict death risk in a longitudinal study of 12,300 individuals

This is the final version. Available on open access from Impact Journals via the DOI in this recordDNA methylation has fundamental roles in gene programming and aging that may help predict mortality. However, no large-scale study has investigated whether site-specific DNA methylation predicts all-cause mortality. We used the Illumina-HumanMethylation450-BeadChip to identify blood DNA methylation sites associated with all-cause mortality for 12, 300 participants in 12 Cohorts of the Heart and Aging Research in Genetic Epidemiology (CHARGE) Consortium. Over an average 10-year follow-up, there were 2,561 deaths across the cohorts. Nine sites mapping to three intergenic and six gene-specific regions were associated with mortality (P < 9.3x10-7) independently of age and other mortality predictors. Six sites (cg14866069, cg23666362, cg20045320, cg07839457, cg07677157, cg09615688)-mapping respectively to BMPR1B, MIR1973, IFITM3, NLRC5, and two intergenic regions-were associated with reduced mortality risk. The remaining three sites (cg17086398, cg12619262, cg18424841)-mapping respectively to SERINC2, CHST12, and an intergenic region-were associated with increased mortality risk. DNA methylation at each site predicted 5%-15% of all deaths. We also assessed the causal association of those sites to age-related chronic diseases by using Mendelian randomization, identifying weak causal relationship between cg18424841 and cg09615688 with coronary heart disease. Of the nine sites, three (cg20045320, cg07839457, cg07677157) were associated with lower incidence of heart disease risk and two (cg20045320, cg07839457) with smoking and inflammation in prior CHARGE analyses. Methylation of cg20045320, cg07839457, and cg17086398 was associated with decreased expression of nearby genes (IFITM3, IRF, NLRC5, MT1, MT2, MARCKSL1) linked to immune responses and cardiometabolic diseases. These sites may serve as useful clinical tools for mortality risk assessment and preventative care

Genetic determinants of telomere length from 109,122 ancestrally diverse whole-genome sequences in TOPMed

Genetic studies on telomere length are important for understanding age-related diseases. Prior GWAS for leukocyte TL have been limited to European and Asian populations. Here, we report the first sequencing-based association study for TL across ancestrally-diverse individuals (European, African, Asian and Hispanic/Latino) from the NHLBI Trans-Omics for Precision Medicine (TOPMed) program. We used whole genome sequencing (WGS) of whole blood for variant genotype calling and the bioinformatic estimation of telomere length in n=109,122 individuals. We identified 59 sentinel variants (p-value OBFC1indicated the independent signals colocalized with cell-type specific eQTLs for OBFC1 (STN1). Using a multi-variant gene-based approach, we identified two genes newly implicated in telomere length, DCLRE1B (SNM1B) and PARN. In PheWAS, we demonstrated our TL polygenic trait scores (PTS) were associated with increased risk of cancer-related phenotypes

DNA methylation-based measures of biological age:meta-analysis predicting time to death

Estimates of biological age based on DNA methylation patterns, often referred to as "epigenetic age", "DNAm age", have been shown to be robust biomarkers of age in humans. We previously demonstrated that independent of chronological age, epigenetic age assessed in blood predicted all-cause mortality in four human cohorts. Here, we expanded our original observation to 13 different cohorts for a total sample size of 13,089 individuals, including three racial/ethnic groups. In addition, we examined whether incorporating information on blood cell composition into the epigenetic age metrics improves their predictive power for mortality. All considered measures of epigenetic age acceleration were predictive of mortality (p ≤ 8.2 x 10-9), independent of chronological age, even after adjusting for additional risk factors (p < 5.4 x 10-4), and within the racial/ethnic groups that we examined (non-Hispanic whites, Hispanics, African Americans). Epigenetic age estimates that incorporated information on blood cell composition led to the smallest p-values for time to death (p≤ 7.5 x 10-43). Overall, this study a) strengthens the evidence that epigenetic age predicts all-cause mortality above and beyond chronological age and traditional risk factors, and b) demonstrates that epigenetic age estimates that incorporate information on blood cell counts lead to highly significant associations with all-cause mortality

An integrative cross-omics analysis of DNA methylation sites of glucose and insulin homeostasis

Despite existing reports on differential DNA methylation in type 2 diabetes (T2D) and obesity, our understanding of its functional relevance remains limited. Here we show the effect of differential methylation in the early phases of T2D pathology by a blood-based epigenome-wide association study of 4808 non-diabetic Europeans in the discovery phase and 11,750 individuals in the replication. We identify CpGs in LETM1, RBM20, IRS2, MAN2A2 and the 1q25.3 region associated with fasting insulin, and in FCRL6, SLAMF1, APOBEC3H and the 15q26.1 region with fasting glucose. In silico cross-omics analyses highlight the role of differential methylation in the crosstalk between the adaptive immune system and glucose homeostasis. The differential methylation explains at least 16.9% of the association between obesity and insulin. Our study sheds light on the biological interactions between genetic variants driving differential methylation and gene expression in the early pathogenesis of T2D

Superconvergence of a New Nonconforming Mixed Finite Element Scheme for Elliptic Problem

A new nonconforming mixed finite element scheme for the second-order elliptic problem is proposed based on a new mixed variational form. It has the lowest degrees of freedom on rectangular meshes. The superclose property is proven by employing integral identity technique. Then global superconvergence result is derived through interpolation postprocessing operators. At last, some numerical experiments are carried out to verify the theoretical analysis