Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).Comment: 42 page

On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Network development in biological gels: role in lymphatic vessel development

In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model

Identifying low density lipoprotein cholesterol associated variants in the Annexin A2 (ANXA2) gene.

BACKGROUND AND AIMS: Annexin-A2 (AnxA2) is an endogenous inhibitor of proprotein convertase subtilisin/kexin type-9 (PCSK9). The repeat-one (R1) domain of AnxA2 binds to PCSK9, blocking its ability to promote degradation of low-density lipoprotein cholesterol-receptors (LDL-R) and thereby regulate low-density lipoprotein cholesterol (LDL-C) levels. Here we identify variants in ANXA2 influencing LDL-C levels and we determine the molecular mechanisms of their effects. RESULTS: The ANXA2 single nucleotide polymorphism (SNP) genotype-phenotype association was examined using the Second-Northwick-Park Heart Study (NPHSII) (n∼2700) and the UCL-LSHTM-Edinburgh-Bristol (UCLEB) consortium (n∼14,600). The ANXA2-R1 domain coding-SNP rs17845226 (V98L) associated with LDL-C, homozygotes for the minor allele having ≈18.8% higher levels of LDL-C (p = 0.004), and higher risk of coronary heart disease (CHD) (p = 0.04). The SNP is in modest linkage disequilibrium (r(2) > 0.5) with two intergenic SNPs, rs17191344 and rs11633032. Both SNPs showed allele-specific protein binding, and the minor alleles caused significant reduction in reporter gene expression (≈18%, p < 0.001). In the expression quantitative trait loci (eQTL) study, minor allele homozygotes have significantly lower levels of ANXA2-mRNA expression (p = 1.36 × 10(-05)). CONCLUSIONS: Both rs11633032 and rs17191344 SNPs are functional variants, where the minor alleles create repressor-binding protein sites for transcription factors that contribute to reduced ANXA2 gene expression. Lower AnxA2 levels could increase plasma levels of PCSK9 and thus increase LDL-C levels and risk of CHD. This supports, for the first time in humans, previous observations in mouse models that changes in the levels of AnxA2 directly influence plasma LDL-C levels, and thus implicate this protein as a potential therapeutic target for LDL-C lowering

The inner junction protein CFAP20 functions in motile and non-motile cilia and is critical for vision

Motile and non-motile cilia are associated with mutually-exclusive genetic disorders. Motile cilia propel sperm or extracellular fluids, and their dysfunction causes primary ciliary dyskinesia. Non-motile cilia serve as sensory/signalling antennae on most cell types, and their disruption causes single-organ ciliopathies such as retinopathies or multi-system syndromes. CFAP20 is a ciliopathy candidate known to modulate motile cilia in unicellular eukaryotes. We demonstrate that in zebrafish, cfap20 is required for motile cilia function, and in C. elegans, CFAP-20 maintains the structural integrity of non-motile cilia inner junctions, influencing sensory-dependent signalling and development. Human patients and zebrafish with CFAP20 mutations both exhibit retinal dystrophy. Hence, CFAP20 functions within a structural/functional hub centered on the inner junction that is shared between motile and non-motile cilia, and is distinct from other ciliopathy-associated domains or macromolecular complexes. Our findings suggest an uncharacterised pathomechanism for retinal dystrophy, and potentially for motile and non-motile ciliopathies in general.</p