Separatrix splitting at a Hamiltonian 02iω0^2 i\omega bifurcation

We discuss the splitting of a separatrix in a generic unfolding of a degenerate equilibrium in a Hamiltonian system with two degrees of freedom. We assume that the unperturbed fixed point has two purely imaginary eigenvalues and a double zero one. It is well known that an one-parametric unfolding of the corresponding Hamiltonian can be described by an integrable normal form. The normal form has a normally elliptic invariant manifold of dimension two. On this manifold, the truncated normal form has a separatrix loop. This loop shrinks to a point when the unfolding parameter vanishes. Unlike the normal form, in the original system the stable and unstable trajectories of the equilibrium do not coincide in general. The splitting of this loop is exponentially small compared to the small parameter. This phenomenon implies non-existence of single-round homoclinic orbits and divergence of series in the normal form theory. We derive an asymptotic expression for the separatrix splitting. We also discuss relations with behaviour of analytic continuation of the system in a complex neighbourhood of the equilibrium

Age-related difference in susceptibility of ApcMin/+ mice towards the chemopreventive efficacy of dietary aspirin and curcumin

The nonsteroidal anti-inflammatory drug aspirin and the spice curcumin retard adenoma formation when administered long-term to ApcMin/+ mice, a model of human familial adenomatous polyposis coli. Both agents interfere with cyclooxygenase activity. When aspirin is administered to ApcMin/+ mice only postweaning, but not before, it is inefficacious, while curcumin given postweaning is active. Here the hypothesis was tested that dietary aspirin (0.05%) or curcumin (0.2%) prevent or delay adenoma formation in offsprings when administered to ApcMin/+ mothers and up to the end of weaning, but not afterwards. Whereas curcumin was without effect when administered in this way, aspirin reduced numbers of intestinal adenomas by 21%. When aspirin given up to the end of weaning was combined with curcumin administered from the end of weaning for the rest of the animals' lifetime, intestinal adenoma numbers were reduced by 38%. The combination was not superior to intervention postweaning with curcumin alone. These results show that aspirin exerts chemopreventive activity in the ApcMin/+ mouse during tumour initiation/early promotion, while curcumin is efficacious when given at a later stage of carcinogenic progression. Thus, the results suggest that in this mouse model aspirin and curcumin act during different ‘windows’ of neoplastic development

Increased variability in ApcMin/+ intestinal tissue can be measured with microultrasound

Altered tissue structure is a feature of many disease states and is usually measured by microscopic methods, limiting analysis to small areas. Means to rapidly and quantitatively measure the structure and organisation of large tissue areas would represent a major advance not just for research but also in the clinic. Here, changes in tissue organisation that result from heterozygosity in Apc, a precancerous situation, are comprehensively measured using microultrasound and three-dimensional high-resolution microscopy. Despite its normal appearance in conventionally examined cross-sections, both approaches revealed a significant increase in the variability of tissue organisation in Apc heterozygous tissue. These changes preceded the formation of aberrant crypt foci or adenoma. Measuring these premalignant changes using microultrasound provides a potential means to detect microscopically abnormal regions in large tissue samples, independent of visual examination or biopsies. Not only does this provide a powerful tool for studying tissue structure in experimental settings, the ability to detect and monitor tissue changes by microultrasound could be developed into a powerful adjunct to screening endoscopy in the clinic

Identification of novel SNPs of ABCD1, ABCD2, ABCD3, and ABCD4 genes in patients with X-linked adrenoleukodystrophy (ALD) based on comprehensive resequencing and association studies with ALD phenotypes

Adrenoleukodystrophy (ALD) is an X-linked disorder affecting primarily the white matter of the central nervous system occasionally accompanied by adrenal insufficiency. Despite the discovery of the causative gene, ABCD1, no clear genotype–phenotype correlations have been established. Association studies based on single nucleotide polymorphisms (SNPs) identified by comprehensive resequencing of genes related to ABCD1 may reveal genes modifying ALD phenotypes. We analyzed 40 Japanese patients with ALD. ABCD1 and ABCD2 were analyzed using a newly developed microarray-based resequencing system. ABCD3 and ABCD4 were analyzed by direct nucleotide sequence analysis. Replication studies were conducted on an independent French ALD cohort with extreme phenotypes. All the mutations of ABCD1 were identified, and there was no correlation between the genotypes and phenotypes of ALD. SNPs identified by the comprehensive resequencing of ABCD2, ABCD3, and ABCD4 were used for association studies. There were no significant associations between these SNPs and ALD phenotypes, except for the five SNPs of ABCD4, which are in complete disequilibrium in the Japanese population. These five SNPs were significantly less frequently represented in patients with adrenomyeloneuropathy (AMN) than in controls in the Japanese population (p = 0.0468), whereas there were no significant differences in patients with childhood cerebral ALD (CCALD). The replication study employing these five SNPs on an independent French ALD cohort, however, showed no significant associations with CCALD or pure AMN. This study showed that ABCD2, ABCD3, and ABCD4 are less likely the disease-modifying genes, necessitating further studies to identify genes modifying ALD phenotypes

A Targeted Constitutive Mutation in the Apc Tumor Suppressor Gene Underlies Mammary But Not Intestinal Tumorigenesis

Germline mutations in the adenomatous polyposis coli (APC) gene are responsible for familial adenomatous polyposis (FAP), an autosomal dominant hereditary predisposition to the development of multiple colorectal adenomas and of a broad spectrum of extra-intestinal tumors. Moreover, somatic APC mutations play a rate-limiting and initiating role in the majority of sporadic colorectal cancers. Notwithstanding its multifunctional nature, the main tumor suppressing activity of the APC gene resides in its ability to regulate Wnt/β-catenin signaling. Notably, genotype–phenotype correlations have been established at the APC gene between the length and stability of the truncated proteins encoded by different mutant alleles, the corresponding levels of Wnt/β-catenin signaling activity they encode for, and the incidence and distribution of intestinal and extra-intestinal tumors. Here, we report a novel mouse model, Apc1572T, obtained by targeting a truncated mutation at codon 1572 in the endogenous Apc gene. This hypomorphic mutant allele results in intermediate levels of Wnt/β-catenin signaling activation when compared with other Apc mutations associated with multifocal intestinal tumors. Notwithstanding the constitutive nature of the mutation, Apc+/1572T mice have no predisposition to intestinal cancer but develop multifocal mammary adenocarcinomas and subsequent pulmonary metastases in both genders. The histology of the Apc1572T primary mammary tumours is highly heterogeneous with luminal, myoepithelial, and squamous lineages and is reminiscent of metaplastic carcinoma of the breast in humans. The striking phenotype of Apc+/1572T mice suggests that specific dosages of Wnt/β-catenin signaling activity differentially affect tissue homeostasis and initiate tumorigenesis in an organ-specific fashion

Photosynthetic growth despite a broken Q-cycle

Central in respiration or photosynthesis, the cytochrome bc1 and b6f complexes are regarded as functionally similar quinol oxidoreductases. They both catalyse a redox loop, the Q-cycle, which couples electron and proton transfer. This loop involves a bifurcated electron transfer step considered as being mechanistically mandatory, making the Q-cycle indispensable for growth. Attempts to falsify this paradigm in the case of cytochrome bc1 have failed. The rapid proteolytic degradation of b6f complexes bearing mutations aimed at hindering the Q-cycle has precluded so far the experimental assessment of this model in the photosynthetic chain. Here we combine mutations in Chlamydomonas that inactivate the redox loop but preserve high accumulation levels of b6f complexes. The oxidoreductase activity of these crippled complexes is sufficient to sustain photosynthetic growth, which demonstrates that the Q-cycle is dispensable for oxygenic photosynthesis

Using molecular data for epidemiological inference: assessing the prevalence of Trypanosoma brucei rhodesiense in Tsetse in Serengeti, Tanzania

Background: Measuring the prevalence of transmissible Trypanosoma brucei rhodesiense in tsetse populations is essential for understanding transmission dynamics, assessing human disease risk and monitoring spatio-temporal trends and the impact of control interventions. Although an important epidemiological variable, identifying flies which carry transmissible infections is difficult, with challenges including low prevalence, presence of other trypanosome species in the same fly, and concurrent detection of immature non-transmissible infections. Diagnostic tests to measure the prevalence of T. b. rhodesiense in tsetse are applied and interpreted inconsistently, and discrepancies between studies suggest this value is not consistently estimated even to within an order of magnitude. Methodology/Principal Findings: Three approaches were used to estimate the prevalence of transmissible Trypanosoma brucei s.l. and T. b. rhodesiense in Glossina swynnertoni and G. pallidipes in Serengeti National Park, Tanzania: (i) dissection/microscopy; (ii) PCR on infected tsetse midguts; and (iii) inference from a mathematical model. Using dissection/microscopy the prevalence of transmissible T. brucei s.l. was 0% (95% CI 0–0.085) for G. swynnertoni and 0% (0–0.18) G. pallidipes; using PCR the prevalence of transmissible T. b. rhodesiense was 0.010% (0–0.054) and 0.0089% (0–0.059) respectively, and by model inference 0.0064% and 0.00085% respectively. Conclusions/Significance: The zero prevalence result by dissection/microscopy (likely really greater than zero given the results of other approaches) is not unusual by this technique, often ascribed to poor sensitivity. The application of additional techniques confirmed the very low prevalence of T. brucei suggesting the zero prevalence result was attributable to insufficient sample size (despite examination of 6000 tsetse). Given the prohibitively high sample sizes required to obtain meaningful results by dissection/microscopy, PCR-based approaches offer the current best option for assessing trypanosome prevalence in tsetse but inconsistencies in relating PCR results to transmissibility highlight the need for a consensus approach to generate meaningful and comparable data