Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two-well potential, with a forcing term depending on the ``memory'' of the particle past motion. The dynamics of the original Lorenz system in the new particle phase space can then be rewritten in terms of an one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system which preserves all the essential properties of the original model.Comment: 48 pages, 25 figure

Effects of pH and low density lipoprotein (LDL) on PCSK9-dependent LDL receptor regulation

Mutations within PCSK9 (proprotein convertase subtilisin/kexin type 9) are associated with dominant forms of familial hyper- and hypocholesterolemia. Although PCSK9 controls low density lipoprotein (LDL) receptor (LDLR) levels post-transcriptionally, several questions concerning its mode of action remain unanswered. We show that purified PCSK9 protein added to the medium of human endothelial kidney 293, HepG2, and Chinese hamster ovary cell lines decreases cellular LDL uptake in a dose-dependent manner. Using this cell-based assay of PCSK9 activity, we found that the relative potencies of several PCSK9 missense mutants (S127R and D374Y, associated with hypercholesterolemia, and R46L, associated with hypocholesterolemia) correlate with LDL cholesterol levels in humans carrying such mutations. Notably, we found that in vitro wild-type PCSK9 binds LDLR with an 3c150-fold higher affinity at an acidic endosomal pH (KD = 4.19 nM) compared with a neutral pH (KD = 628 nM). We also demonstrate that wild-type PCSK9 and mutants S127R and R46L are internalized by cells to similar levels, whereas D374Y is more efficiently internalized, consistent with their affinities for LDLR at neutral pH. Finally, we show that LDL diminishes PCSK9 binding to LDLR in vitro and partially inhibits the effects of secreted PCSK9 on LDLR degradation in cell culture. Together, the results of our biochemical and cell-based experiments suggest a model in which secreted PCSK9 binds to LDLR and directs the trafficking of LDLR to the lysosomes for degradation

Structural and biochemical characterization of the wild type PCSK9-EGF(AB) complex and natural familial hypercholesterolemia mutants

PCSK9 regulates low density lipoprotein receptor (LDLR) levels and consequently is a target for the prevention of atherosclerosis and coronary heart disease. Here we studied the interaction, of LDLR EGF(A/AB) repeats with PCSK9. We show that PCSK9 binds the EGF(AB) repeats in a pH-dependent manner. Although the PCSK9 C-terminal domain is not involved in LDLR binding, PCSK9 autocleavage is required. Moreover, we report the x-ray structure of the PCSK9 Delta C-EGF(AB) complex at neutral pH. Compared with the low pH PCSK9-EGF(A) structure, the new structure revealed rearrangement of the EGF( A) His-306 side chain and disruption of the salt bridge with PCSK9 Asp-374, thus suggesting the basis for enhanced interaction at low pH. In addition, the structure of PCSK9 Delta C bound to EGF(AB)(H306Y), a mutant associated with familial hypercholesterolemia (FH), reveals that the Tyr-306 side chain forms a hydrogen bond with PCSK9 Asp-374, thus mimicking His-306 in the low pH conformation. Consistently, Tyr-306 confers increased affinity for PCSK9. Importantly, we found that although the EGF(AB)(H306Y)-PCSK9 interaction is pH-independent, LDLRH306Y binds PCSK9 50-fold better at low pH, suggesting that factors other than His-306 contribute to the pH dependence of PCSK9-LDLR binding. Further, we determined the structures of EGF(AB) bound to PCSK9 Delta C containing the FH-associated D374Y and D374H mutations, revealing additional interactions with EGF(A) mediated by Tyr-374/His-374 and providing a rationale for their disease phenotypes. Finally, we report the inhibitory properties of EGF repeats in a cellular assay measuring LDL uptake

Vascular Remodeling in Health and Disease

The term vascular remodeling is commonly used to define the structural changes in blood vessel geometry that occur in response to long-term physiologic alterations in blood flow or in response to vessel wall injury brought about by trauma or underlying cardiovascular diseases.1, 2, 3, 4 The process of remodeling, which begins as an adaptive response to long-term hemodynamic alterations such as elevated shear stress or increased intravascular pressure, may eventually become maladaptive, leading to impaired vascular function. The vascular endothelium, owing to its location lining the lumen of blood vessels, plays a pivotal role in regulation of all aspects of vascular function and homeostasis.5 Thus, not surprisingly, endothelial dysfunction has been recognized as the harbinger of all major cardiovascular diseases such as hypertension, atherosclerosis, and diabetes.6, 7, 8 The endothelium elaborates a variety of substances that influence vascular tone and protect the vessel wall against inflammatory cell adhesion, thrombus formation, and vascular cell proliferation.8, 9, 10 Among the primary biologic mediators emanating from the endothelium is nitric oxide (NO) and the arachidonic acid metabolite prostacyclin [prostaglandin I2 (PGI2)], which exert powerful vasodilatory, antiadhesive, and antiproliferative effects in the vessel wall

The essential roles of cytidine diphosphate-diacylglycerol synthase in bloodstream form Trypanosoma brucei

Funded by Wellcome Trust: Senior Research Fellowship, Grant Number: 067441 and Wellcome Trust, Grant Numbers: 082596, 093228.Lipid metabolism in Trypanosoma brucei, the causative agent of African sleeping sickness, differs from its human host in several fundamental ways. This has lead to the validation of a plethora of novel drug targets, giving hope of novel chemical intervention against this neglected disease. Cytidine diphosphate diacylglycerol (CDP-DAG) is a central lipid intermediate for several pathways in both prokaryotes and eukaryotes, being produced by CDP-DAG synthase (CDS). However, nothing is known about the single T. brucei CDS gene (Tb927.7.220/ EC 2.7.7.41) or its activity. In this study we show TbCDS is functional by complementation of a non-viable yeast CDS null strain and that it is essential in the bloodstream form of the parasite via a conditional knockout. The TbCDS conditional knockout showed morphological changes including a cell-cycle arrest due in part to kinetoplast segregation defects.Biochemical phenotyping of TbCDS conditional knockout showed drastically altered lipid metabolism where reducing levels of phosphatidylinositol detrimentally impacted on glycoylphosphatidylinositol biosynthesis. These studies also suggest that phosphatidylglycerol synthesised via the phosphatidylglycerol-phosphate synthase is not synthesised from CDP-DAG, as was previously thought. TbCDS was shown to localised the ER and Golgi, probably to provide CDP-DAG for the phosphatidylinositol synthases.Publisher PDFPeer reviewe

Polymorphisms in the superoxide dismutase-3 gene are associated with emphysema in COPD

Superoxide dismutase-3 (SOD3) is a major extracellular antioxidant enzyme, and previous studies have indicated a possible role of this gene in chronic obstructive pulmonary disease (COPD). We hypothesized that polymorphisms in the SOD3 gene would be associated with COPD and COPD-related phenotypes. We genotyped three SOD3 polymorphisms (rs8192287 (E1), rs8192288 (I1), and rs1799895 (R213G)) in a case-control cohort, with severe COPD cases from the National Emphysema Treatment Trial (NETT, n = 389) and smoking controls from the Normative Aging Study (NAS, n = 472). We examined whether the single nucleotide polymorphisms (SNPs) were associated with COPD status, lung function variables, and quantitative computed tomography (CT) measurements of emphysema and airway wall thickness. Furthermore, we tried to replicate our initial findings in two family-based studies, the International COPD Genetics Network (ICGN, n = 3061) and the Boston Early-Onset COPD Study (EOCOPD, n = 949). In NETT COPD cases, the minor alleles of SNPs E1 and I1 were associated with a higher percentage of emphysema (%LAA950) on chest CT scan (p = .029 and p = .0058). The association with E1 was replicated in the ICGN family study, where the minor allele was associated with more emphysema (p = .048). Airway wall thickness was positively associated with the E1 SNP in ICGN; however, this finding was not confirmed in NETT. Quantitative CT data were not available in EOCOPD. The SNPs were not associated with lung function variables or COPD status in any of the populations. In conclusion, polymorphisms in the SOD3 gene were associated with CT emphysema but not COPD susceptibility, highlighting the importance of phenotype definition in COPD genetics studies