Topological entropy and secondary folding

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically-computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with 'secondary folding': material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod-stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.Comment: 13 pages, 8 figures. pdfLaTeX with RevTeX4 macro

IBD risk loci are enriched in multigenic regulatory modules encompassing putative causative genes.

GWAS have identified >200 risk loci for Inflammatory Bowel Disease (IBD). The majority of disease associations are known to be driven by regulatory variants. To identify the putative causative genes that are perturbed by these variants, we generate a large transcriptome data set (nine disease-relevant cell types) and identify 23,650 cis-eQTL. We show that these are determined by ∼9720 regulatory modules, of which ∼3000 operate in multiple tissues and ∼970 on multiple genes. We identify regulatory modules that drive the disease association for 63 of the 200 risk loci, and show that these are enriched in multigenic modules. Based on these analyses, we resequence 45 of the corresponding 100 candidate genes in 6600 Crohn disease (CD) cases and 5500 controls, and show with burden tests that they include likely causative genes. Our analyses indicate that ≥10-fold larger sample sizes will be required to demonstrate the causality of individual genes using this approach

Prospective study of insulin-like growth factor-I, insulin-like growth factor-binding protein 3, genetic variants in the IGF1 and IGFBP3 genes and risk of coronary artery disease.

Although experimental studies have suggested that insulin-like growth factor I (IGF-I) and its binding protein IGFBP-3 might have a role in the aetiology of coronary artery disease (CAD), the relevance of circulating IGFs and their binding proteins in the development of CAD in human populations is unclear. We conducted a nested case-control study, with a mean follow-up of six years, within the EPIC-Norfolk cohort to assess the association between circulating levels of IGF-I and IGFBP-3 and risk of CAD in up to 1,013 cases and 2,055 controls matched for age, sex and study enrolment date. After adjustment for cardiovascular risk factors, we found no association between circulating levels of IGF-I or IGFBP-3 and risk of CAD (odds ratio: 0.98 (95% Cl 0.90-1.06) per 1 SD increase in circulating IGF-I; odds ratio: 1.02 (95% Cl 0.94-1.12) for IGFBP-3). We examined associations between tagging single nucleotide polymorphisms (tSNPs) at the IGF1 and IGFBP3 loci and circulating IGF-I and IGFBP-3 levels in up to 1,133 cases and 2,223 controls and identified three tSNPs (rs1520220, rs3730204, rs2132571) that showed independent association with either circulating IGF-I or IGFBP-3 levels. In an assessment of 31 SNPs spanning the IGF1 or IGFBP3 loci, none were associated with risk of CAD in a meta-analysis that included EPIC-Norfolk and eight additional studies comprising up to 9,319 cases and 19,964 controls. Our results indicate that IGF-I and IGFBP-3 are unlikely to be importantly involved in the aetiology of CAD in human populations

Genome-wide association identifies nine common variants associated with fasting proinsulin levels and provides new insights into the pathophysiology of type 2 diabetes

OBJECTIVE - Proinsulin is a precursor of mature insulin and C-peptide. Higher circulating proinsulin levels are associated with impaired b-cell function, raised glucose levels, insulin resistance, and type 2 diabetes (T2D). Studies of the insulin processing pathway could provide new insights about T2D pathophysiology. RESEARCH DESIGN AND METHODS - We have conducted a meta-analysis of genome-wide association tests of ;2.5 million genotyped or imputed single nucleotide polymorphisms (SNPs) and fasting proinsulin levels in 10,701 nondiabetic adults of European ancestry, with follow-up of 23 loci in up to 16,378 individuals, using additive genetic models adjusted for age, sex, fasting insulin, and study-specific covariates. RESULTS - Nine SNPs at eight loci were associated with proinsulin levels (P < 5 × 10-8). Two loci (LARP6 and SGSM2) have not been previously related to metabolic traits, one (MADD) has been associated with fasting glucose, one (PCSK1) has been implicated in obesity, and four (TCF7L2, SLC30A8, VPS13C/ C2CD4A/B, and ARAP1, formerly CENTD2) increase T2D risk. The proinsulin-raising allele of ARAP1 was associated with a lower fasting glucose (P = 1.7 3 10-4), improved b-cell function (P = 1.1 × 10-5), and lower risk of T2D (odds ratio 0.88; P = 7.8 × 10-6). Notably, PCSK1 encodes the protein prohormone convertase 1/3, the first enzyme in the insulin processing pathway. A genotype score composed of the nine proinsulin-raising alleles was not associated with coronary disease in two large case-control datasets. CONCLUSIONS - We have identified nine genetic variants associated with fasting proinsulin. Our findings illuminate the biology underlying glucose homeostasis and T2D development in humans and argue against a direct role of proinsulin in coronary artery disease pathogenesis