Synchronization of weakly perturbed Markov chain oscillators

Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained, symbolic dynamics. In contrast to limit cycle oscillators which are weakly perturbed by noise, the stochasticity in such systems may be strong and more complicated system topologies than the circle can be considered. Here we employ second order, time dependent perturbation theory to derive expressions for the mean frequency and phase diffusion constant of discrete state oscillators coupled or driven through weakly time dependent transition rates. We also describe a method of global control to optimize the response of the mean frequency in complex transition networks.Comment: 16 pages, 7 figure

Synchronization Transition in the Kuramoto Model with Colored Noise

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure

Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in form of dispersion, leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second order perturbation terms. We apply the theory to simple topologies, like a line or the sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter the synchronized state may become quasi degenerate. We demonstrate how perturbation theory fails at such a critical point.Comment: 22 pages, 5 figure

Quasi regular concentric waves in heterogeneous lattices of coupled oscillators

We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one-dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.Comment: 4 pages, 3 figures, submitted to PR

The role of rs2237781 within GRM8 in eating behavior

Introduction: The glutamate receptor, metabotropic 8 gene (GRM8) encodes a G-protein-coupled glutamate receptor and has been associated with smoking behavior and liability to alcoholism implying a role in addiction vulnerability. Data from animal studies suggest that GRM8 may be involved in the regulation of the neuropeptide Y and melanocortin pathways and might influence food intake and metabolism. This study aimed to investigate the effects of the genetic variant rs2237781 within GRM8 on human eating behavior. Methods: The initial analysis included 548 Sorbs from Germany who have been extensively phenotyped for metabolic traits and who completed the German version of the three-factor eating questionnaire. In addition, we analyzed two independent sample sets comprising 293 subjects from another German cohort and 430 Old Order Amish individuals. Genetic associations with restraint, disinhibition, and hunger were assessed in an additive linear regression model. Results: Among the Sorbs the major G allele of rs2237781 was significantly associated with increased restraint scores in eating behavior (P = 1.9 9 10?4; b =+1.936). The German cohort and the Old Order Amish population revealed a trend in the same direction for restraint (P = 0.242; b =+0.874; P = 0.908; b =+0.096; respectively). A meta-analysis resulted in a combined P = 3.1 9 10?3 (Z-score 2.948). Conclusion: Our data suggest that rs2237781 within GRM8 may influence human eating behavior factors probably via pathways involved in addictive behavior

Analyzing the link between anxiety and eating behavior as a potential pathway to eating-related health outcomes

Anxiety is a widespread phenomenon that affects various behaviors. We want to analyze in how far anxiety is connected to eating behaviors since this is one potential pathway to understanding eating-related health outcomes like obesity or eating disorders. We used data from the population-based LIFE-Adult-Study (n = 5019) to analyze the connection between anxiety (GAD-7) and the three dimensions of eating behaviors (FEV)-Cognitive Restraint, Disinhibition, and Hunger-while controlling for sociodemographic variables, smoking, physical activity, personality, and social support. Multivariate regression analyses showed significant positive associations between anxiety and Disinhibition as well as Hunger, but not between anxiety and Cognitive Restraint. Interventions that help individuals to better regulate and cope with anxiety, could be one potential pathway to reducing eating disorders and obesity in the population

Effects of Genetic Variants in ADCY5, GIPR, GCKR and VPS13C on Early Impairment of Glucose and Insulin Metabolism in Children

OBJECTIVE: Recent genome-wide association studies identified novel candidate genes for fasting and 2 h blood glucose and insulin levels in adults. We investigated the role of four of these loci (ADCY5, GIPR, GCKR and VPS13C) in early impairment of glucose and insulin metabolism in children. RESEARCH DESIGN AND METHODS: We genotyped four variants (rs2877716; rs1260326; rs10423928; rs17271305) in 638 Caucasian children with detailed metabolic testing including an oGTT and assessed associations with measures of glucose and insulin metabolism (including fasting blood glucose, insulin levels and insulin sensitivity/secretion indices) by linear regression analyses adjusted for age, sex, BMI-SDS and pubertal stage. RESULTS: The major allele (C) of rs2877716 (ADCY5) was nominally associated with decreased fasting plasma insulin (P = 0.008), peak insulin (P = 0.009) and increased QUICKI (P = 0.016) and Matsuda insulin sensitivity index (P = 0.013). rs17271305 (VPS13C) was nominally associated with 2 h blood glucose (P = 0.009), but not with any of the insulin or insulin sensitivity parameters. We found no association of the GIPR and GCKR variants with parameters of glucose and insulin metabolism. None of the variants correlated with anthropometric traits such as height, WHR or BMI-SDS, which excluded potential underlying associations with obesity. CONCLUSIONS: Our data on obese children indicate effects of genetic variation within ADCY5 in early impairment of insulin metabolism and VPS13C in early impairment of blood glucose homeostasis

Common Variants at 10 Genomic Loci Influence Hemoglobin A(1C) Levels via Glycemic and Nonglycemic Pathways

OBJECTIVE Glycated hemoglobin (HbA1c), used to monitor and diagnose diabetes, is influenced by average glycemia over a 2- to 3-month period. Genetic factors affecting expression, turnover, and abnormal glycation of hemoglobin could also be associated with increased levels of HbA1c. We aimed to identify such genetic factors and investigate the extent to which they influence diabetes classification based on HbA1c levels. RESEARCH DESIGN AND METHODS We studied associations with HbA1c in up to 46,368 nondiabetic adults of European descent from 23 genome-wide association studies (GWAS) and 8 cohorts with de novo genotyped single nucleotide polymorphisms (SNPs). We combined studies using inverse-variance meta-analysis and tested mediation by glycemia using conditional analyses. We estimated the global effect of HbA1c loci using a multilocus risk score, and used net reclassification to estimate genetic effects on diabetes screening. RESULTS Ten loci reached genome-wide significant association with HbA1c, including six new loci near FN3K (lead SNP/P value, rs1046896/P = 1.6 × 10−26), HFE (rs1800562/P = 2.6 × 10−20), TMPRSS6 (rs855791/P = 2.7 × 10−14), ANK1 (rs4737009/P = 6.1 × 10−12), SPTA1 (rs2779116/P = 2.8 × 10−9) and ATP11A/TUBGCP3 (rs7998202/P = 5.2 × 10−9), and four known HbA1c loci: HK1 (rs16926246/P = 3.1 × 10−54), MTNR1B (rs1387153/P = 4.0 × 10−11), GCK (rs1799884/P = 1.5 × 10−20) and G6PC2/ABCB11 (rs552976/P = 8.2 × 10−18). We show that associations with HbA1c are partly a function of hyperglycemia associated with 3 of the 10 loci (GCK, G6PC2 and MTNR1B). The seven nonglycemic loci accounted for a 0.19 (% HbA1c) difference between the extreme 10% tails of the risk score, and would reclassify ∼2% of a general white population screened for diabetes with HbA1c. CONCLUSIONS GWAS identified 10 genetic loci reproducibly associated with HbA1c. Six are novel and seven map to loci where rarer variants cause hereditary anemias and iron storage disorders. Common variants at these loci likely influence HbA1c levels via erythrocyte biology, and confer a small but detectable reclassification of diabetes diagnosis by HbA1c

Genome Wide Meta-analysis Highlights the Role of Genetic Variation in RARRES2 in the Regulation of Circulating Serum Chemerin.

Chemerin is an adipokine proposed to link obesity and chronic inflammation of adipose tissue. Genetic factors determining chemerin release from adipose tissue are yet unknown. We conducted a meta-analysis of genome-wide association studies (GWAS) for serum chemerin in three independent cohorts from Europe: Sorbs and KORA from Germany and PPP-Botnia from Finland (total N = 2,791). In addition, we measured mRNA expression of genes within the associated loci in peripheral mononuclear cells by micro-arrays, and within adipose tissue by quantitative RT-PCR and performed mRNA expression quantitative trait and expression-chemerin association studies to functionally substantiate our loci. Heritability estimate of circulating chemerin levels was 16.2% in the Sorbs cohort. Thirty single nucleotide polymorphisms (SNPs) at chromosome 7 within the retinoic acid receptor responder 2 (RARRES2)/Leucine Rich Repeat Containing (LRRC61) locus reached genome-wide significance (p<5.0×10?8) in the meta-analysis (the strongest evidence for association at rs7806429 with p = 7.8×10?14, beta = ?0.067, explained variance 2.0%). All other SNPs within the cluster were in linkage disequilibrium with rs7806429 (minimum r2 = 0.43 in the Sorbs cohort). The results of the subgroup analyses of males and females were consistent with the results found in the total cohort. No significant SNP-sex interaction was observed. rs7806429 was associated with mRNA expression of RARRES2 in visceral adipose tissue in women (p<0.05 after adjusting for age and body mass index). In conclusion, the present meta-GWAS combined with mRNA expression studies highlights the role of genetic variation in the RARRES2 locus in the regulation of circulating chemerin concentrations

The Effect of ACACB cis-Variants on Gene Expression and Metabolic Traits

Acetyl Coenzyme A carboxylase β (ACACB) is the rate-limiting enzyme in fatty acid oxidation, and continuous fatty acid oxidation in Acacb knock-out mice increases insulin sensitivity. Systematic human studies have not been performed to evaluate whether ACACB variants regulate gene expression and insulin sensitivity in skeletal muscle and adipose tissues. We sought to determine whether ACACB transcribed variants were associated with ACACB gene expression and insulin sensitivity in non-diabetic African American (AA) and European American (EA) adults.ACACB transcribed single nucleotide polymorphisms (SNPs) were genotyped in 105 EAs and 46 AAs whose body mass index (BMI), lipid profiles and ACACB gene expression in subcutaneous adipose and skeletal muscle had been measured. Allelic expression imbalance (AEI) was assessed in lymphoblast cell lines from heterozygous subjects in an additional EA sample (n = 95). Selected SNPs were further examined for association with insulin sensitivity in a cohort of 417 EAs and 153 AAs.ACACB transcribed SNP rs2075260 (A/G) was associated with adipose ACACB messenger RNA expression in EAs and AAs (p = 3.8×10(-5), dominant model in meta-analysis, Stouffer method), with the (A) allele representing lower gene expression in adipose and higher insulin sensitivity in EAs (p = 0.04). In EAs, adipose ACACB expression was negatively associated with age and sex-adjusted BMI (r = -0.35, p = 0.0002).Common variants within the ACACB locus appear to regulate adipose gene expression in humans. Body fat (represented by BMI) may further regulate adipose ACACB gene expression in the EA population