Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in \mathbb R2R2 to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves.

Association of vitamin D status with arterial blood pressure and hypertension risk: a mendelian randomisation study

BACKGROUND: Low plasma 25-hydroxyvitamin D (25[OH]D) concentration is associated with high arterial blood pressure and hypertension risk, but whether this association is causal is unknown. We used a mendelian randomisation approach to test whether 25(OH)D concentration is causally associated with blood pressure and hypertension risk. METHODS: In this mendelian randomisation study, we generated an allele score (25[OH]D synthesis score) based on variants of genes that affect 25(OH)D synthesis or substrate availability (CYP2R1 and DHCR7), which we used as a proxy for 25(OH)D concentration. We meta-analysed data for up to 108 173 individuals from 35 studies in the D-CarDia collaboration to investigate associations between the allele score and blood pressure measurements. We complemented these analyses with previously published summary statistics from the International Consortium on Blood Pressure (ICBP), the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) consortium, and the Global Blood Pressure Genetics (Global BPGen) consortium. FINDINGS: In phenotypic analyses (up to n=49 363), increased 25(OH)D concentration was associated with decreased systolic blood pressure (β per 10% increase, -0·12 mm Hg, 95% CI -0·20 to -0·04; p=0·003) and reduced odds of hypertension (odds ratio [OR] 0·98, 95% CI 0·97-0·99; p=0·0003), but not with decreased diastolic blood pressure (β per 10% increase, -0·02 mm Hg, -0·08 to 0·03; p=0·37). In meta-analyses in which we combined data from D-CarDia and the ICBP (n=146 581, after exclusion of overlapping studies), each 25(OH)D-increasing allele of the synthesis score was associated with a change of -0·10 mm Hg in systolic blood pressure (-0·21 to -0·0001; p=0·0498) and a change of -0·08 mm Hg in diastolic blood pressure (-0·15 to -0·02; p=0·01). When D-CarDia and consortia data for hypertension were meta-analysed together (n=142 255), the synthesis score was associated with a reduced odds of hypertension (OR per allele, 0·98, 0·96-0·99; p=0·001). In instrumental variable analysis, each 10% increase in genetically instrumented 25(OH)D concentration was associated with a change of -0·29 mm Hg in diastolic blood pressure (-0·52 to -0·07; p=0·01), a change of -0·37 mm Hg in systolic blood pressure (-0·73 to 0·003; p=0·052), and an 8·1% decreased odds of hypertension (OR 0·92, 0·87-0·97; p=0·002). INTERPRETATION: Increased plasma concentrations of 25(OH)D might reduce the risk of hypertension. This finding warrants further investigation in an independent, similarly powered study.

Potential role of NF-kappaB in adult neural stem cells: the underrated steersman?

Neural stem cells are precursors of neurons and glial cells. During brain development, these cells proliferate, migrate and differentiate into specific lineages. Recently neural stem cells within the adult central nervous system were identified. Informations are now emerging about regulation of stem cell proliferation, migration and differentiation by numerous soluble factors such as chemokines and cytokines. However, the signal transduction mechanisms downstream of these factors are less clear. Here, we review potential evidences for a novel central role of the transcription factor nuclear factor kappa B (NF-kappaB) in these crucial signal transduction processes. NF-kappaB is an inducible transcription factor detected in neurons, glia and neural stem cells. NF-kappaB was discovered by David Baltimore's laboratory as a transcription factor in lymphocytes. NF-kappaB is involved in many biological processes such as inflammation and innate immunity, development, apoptosis and anti-apoptosis. It has been recently shown that members of the NF-kappaB family are widely expressed by neurons, glia and neural stem cells. In the nervous system, NF-kappaB plays a crucial role in neuronal plasticity, learning, memory consolidation, neuroprotection and neurodegeneration. Recent data suggest an important role of NF-kappaB on proliferation, migration and differentiation of neural stem cells. NF-kappaB is composed of three subunits: two DNA-binding and one inhibitory subunit. Activation of NF-kappaB takes place in the cytoplasm and results in degradation of the inhibitory subunit, thus enabling the nuclear import of the DNA-binding subunits. Within the nucleus, several target genes could be activated. In this review, we suggest a model explaining the multiple action of NF-kappaB on neural stem cells. Furthermore, we discuss the potential role of NF-kappaB within the so-called brain cancer stem cells.

TNF-alpha mediated transport of NF-kappaB to the nucleus is independent of the cytoskeleton-based transport system in non-neuronal cells

In unstimulated cells, proteins of the nuclear factor kappaB (NF-kappaB) transcription factor family are sequestered in the cytoplasm through interactions with IkappaB inhibitor proteins. Tumor necrosis factor alpha (TNF-alpha) activates the degradation of IkappaB-alpha and the nuclear import of cytoplasmic NF-kappaB. Nuclear localization of numerous cellular proteins is mediated by the ability of the cytoskeleton, usually microtubules, to direct their perinuclear accumulation. In a former study we have shown that activated NF-kappaB rapidly moves from distal processes in neurons towards the nucleus. The fast transport rate suggests the involvement of motor proteins in the transport of NF-kappaB. Here we address the question how NF-kappaB arrives at the nuclear membrane before import in non-neuronal cells, i.e., by diffusion alone or with the help of active transport mechanisms. Using confocal microscopy imaging and analysis of nuclear protein extracts, we show that NF-kappaB movement through the cytoplasm to the nucleus is independent of the cytoskeleton, in the three cell lines investigated here. Additionally we demonstrate that NF-kappaB p65 is not associated with the dynein/dynactin molecular motor complex. We propose that cells utilize two distinct mechanisms of NF-kappaB transport: (1) signaling via diffusion over short distances in non-neuronal cells and (2) transport via motor proteins that move along the cytoskeleton in neuronal processes where the distances between sites of NF-kappaB activation and nucleus can be vast.

Tumor necrosis factor alpha triggers proliferation of adult neural stem cells via IKK/NF-kappaB signaling

BACKGROUND: Brain inflammation has been recognized as a complex phenomenon with numerous related aspects. In addition to the very well-described neurodegenerative effect of inflammation, several studies suggest that inflammatory signals exert a potentially positive influence on neural stem cell proliferation, migration and differentiation. Tumor necrosis factor alpha (TNF-alpha) is one of the best-characterized mediators of inflammation. To date, conclusions about the action of TNF on neural stem or progenitor cells (NSCs, NPCs) have been conflicting. TNF seems to activate NSC proliferation and to inhibit their differentiation into NPCs. The purpose of the present study was to analyze the molecular signal transduction mechanisms induced by TNF and resulting in NSC proliferation. RESULTS: Here we describe for the first time the TNF-mediated signal transduction cascade in neural stem cells (NSCs) that results in increased proliferation. Moreover, we demonstrate IKK-alpha/beta-dependent proliferation and markedly up-regulated cyclin D1 expression after TNF treatment. The significant increase in proliferation in TNF-treated cells was indicated by increased neurosphere volume, increased bromodeoxyuridin (BrdU) incorporation and a higher total cell number. Furthermore, TNF strongly activated nuclear factor-kappa B (NF-kappaB) as measured by reporter gene assays and by an activity-specific antibody. Proliferation of control and TNF-treated NSCs was strongly inhibited by expression of the NF-kappaB super-repressor IkappaB-AA1. Pharmacological blockade of IkappaB ubiquitin ligase activity led to comparable decreases in NF-kappaB activity and proliferation. In addition, IKK-beta gene product knock-down via siRNA led to diminished NF-kappaB activity, attenuated cyclin D1 expression and finally decreased proliferation. In contrast, TGFbeta-activated kinase 1 (TAK-1) is partially dispensable for TNF-mediated and endogenous proliferation. Understanding stem cell proliferation is crucial for future regenerative and anti-tumor medicine. CONCLUSION: TNF-mediated activation of IKK-beta resulted in activation of NF-kappaB and was followed by up-regulation of the bona-fide target gene cyclin D1. Activation of the canonical NF-kappaB pathway resulted in strongly increased proliferation of NSCs.

Highly efficient neural differentiation of human somatic stem cells, isolated by minimally invasive periodontal surgery

Neural stem cells (NSCs) are potential sources for cell therapy of neurodegenerative diseases and for drug screening. Despite their potential benefits, ethical and practical considerations limit the application of NSCs derived from human embryonic stem cells (ES) or adult brain tissue. Thus, alternative sources are required to satisfy the criteria of ready accessibility, rapid expansion in chemically defined media and reliable induction to a neuronal fate. We isolated somatic stem cells from the human periodontium that were collected during minimally invasive periodontal access flap surgery as part of guided tissue regeneration therapy. These cells could be propagated as neurospheres in serum-free medium, which underscores their cranial neural crest cell origin. Culture in the presence of epidermal growth factor (EGF) and fibroblast growth factor-2 (FGF-2) under serum-free conditions resulted in large numbers of nestin-positive/Sox-2-positive NSCs. These periodontium-derived (pd) NSCs are highly proliferative and migrate in response to chemokines that have been described as inducing NSC migration. We used immunocytochemical techniques and RT-PCR analysis to assess neural differentiation after treatment of the expanded cells with a novel induction medium. Adherence to substrate, growth factor deprivation, and retinoic acid treatment led to the acquisition of neuronal morphology and stable expression of markers of neuronal differentiation by more than 90% of the cells. Thus, our novel method might provide nearly limitless numbers of neuronal precursors from a readily accessible autologous adult human source, which could be used as a platform for further experimental studies and has potential therapeutic implications.

Transcription factor NF-kappaB is transported to the nucleus via cytoplasmic dynein/dynactin motor complex in hippocampal neurons

Background Long-term changes in synaptic plasticity require gene transcription, indicating that signals generated at the synapse must be transported to the nucleus. Synaptic activation of hippocampal neurons is known to trigger retrograde transport of transcription factor NF-κB. Transcription factors of the NF-κB family are widely expressed in the nervous system and regulate expression of several genes involved in neuroplasticity, cell survival, learning and memory. Principal Findings In this study, we examine the role of the dynein/dynactin motor complex in the cellular mechanism targeting and transporting activated NF-κB to the nucleus in response to synaptic stimulation. We demonstrate that overexpression of dynamitin, which is known to dissociate dynein from microtubules, and treatment with microtubule-disrupting drugs inhibits nuclear accumulation of NF-κB p65 and reduces NF-κB-dependent transcription activity. In this line, we show that p65 is associated with components of the dynein/dynactin complex in vivo and in vitro and that the nuclear localization sequence (NLS) within NF-κB p65 is essential for this binding. Conclusion This study shows the molecular mechanism for the retrograde transport of activated NF-κB from distant synaptic sites towards the nucleus.

Interactions between uncoupling protein 2 gene polymorphisms, obesity and alcohol intake on liver function: a large meta-analysed population-based study

BACKGROUND AND OBJECTIVE: Given the role of uncoupling protein 2 (UCP2) in the accumulation of fat in the hepatocytes and in the enhancement of protective mechanisms in acute ethanol intake, we hypothesised that UCP2 polymorphisms are likely to cause liver disease through their interactions with obesity and alcohol intake. To test this hypothesis, we investigated the interaction between tagging polymorphisms in the UCP2 gene (rs2306819, rs599277 and rs659366), alcohol intake and obesity traits such as BMI and waist circumference (WC) on alanine aminotransferase (ALT) and gamma glutamyl transferase (GGT) in a large meta-analysis of data sets from three populations (n=20 242). DESIGN AND METHODS: The study populations included the Northern Finland Birth Cohort 1966 (n=4996), Netherlands Study of Depression and Anxiety (n=1883) and LifeLines Cohort Study (n=13 363). Interactions between the polymorphisms and obesity and alcohol intake on dichotomised ALT and GGT levels were assessed using logistic regression and the likelihood ratio test. RESULTS: In the meta-analysis of the three cohorts, none of the three UCP2 polymorphisms were associated with GGT or ALT levels. There was no evidence for interaction between the polymorphisms and alcohol intake on GGT and ALT levels. In contrast, the association of WC and BMI with GGT levels varied by rs659366 genotype (Pinteraction=0.03 and 0.007, respectively; adjusted for age, gender, high alcohol intake, diabetes, hypertension and serum lipid concentrations). CONCLUSION: In conclusion, our findings in 20 242 individuals suggest that UCP2 gene polymorphisms may cause liver dysfunction through the interaction with body fat rather than alcohol intake.