Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

<p>The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsionp><p>and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.p>

Associations between smoking behavior-related alleles and the risk of melanoma.

Several studies have reported that cigarette smoking is inversely associated with the risk of melanoma. This study further tested whether incorporating genetic factors will provide another level of evaluation of mechanisms underlying the association between smoking and risk of melanoma. We investigated the association between SNPs selected from genome-wide association studies (GWAS) on smoking behaviors and risk of melanoma using 2,298 melanoma cases and 6,654 controls. Among 16 SNPs, three (rs16969968 [A], rs1051730 [A] and rs2036534 [C] in the 15q25.1 region) reached significance for association with melanoma risk in men (0.01 < = P values < = 0.02; 0.85 < = Odds Ratios (ORs) <= 1.20). There was association between the genetic scores based on the number of smoking behavior-risk alleles and melanoma risk with P-trend = 0.005 among HPFS. Further association with smoking behaviors indicating those three SNPs (rs16969968 [A], rs1051730 [A] and rs2036534 [C]) significantly associated with number of cigarettes smoked per day, CPD, with P = 0.009, 0.011 and 0.001 respectively. The SNPs rs215605 in the PDE1C gene and rs6265 in the BDNF gene significantly interacted with smoking status on melanoma risk (interaction P = 0.005 and P = 0.003 respectively). Our study suggests that smoking behavior-related SNPs are likely to play a role in melanoma development and the potential public health importance of polymorphisms in the CHRNA5-A3-B4 gene cluster. Further larger studies are warranted to validate the findings.

TRPV4 is necessary for trigeminal irritant pain and functions as a cellular formalin receptor.

Detection of external irritants by head nociceptor neurons has deep evolutionary roots. Irritant-induced aversive behavior is a popular pain model in laboratory animals. It is used widely in the formalin model, where formaldehyde is injected into the rodent paw, eliciting quantifiable nocifensive behavior that has a direct, tissue-injury-evoked phase, and a subsequent tonic phase caused by neural maladaptation. The formalin model has elucidated many antipain compounds and pain-modulating signaling pathways. We have adopted this model to trigeminally innervated territories in mice. In addition, we examined the involvement of TRPV4 channels in formalin-evoked trigeminal pain behavior because TRPV4 is abundantly expressed in trigeminal ganglion (TG) sensory neurons, and because we have recently defined TRPV4's role in response to airborne irritants and in a model for temporomandibular joint pain. We found TRPV4 to be important for trigeminal nocifensive behavior evoked by formalin whisker pad injections. This conclusion is supported by studies with Trpv4(-/-) mice and TRPV4-specific antagonists. Our results imply TRPV4 in MEK-ERK activation in TG sensory neurons. Furthermore, cellular studies in primary TG neurons and in heterologous TRPV4-expressing cells suggest that TRPV4 can be activated directly by formalin to gate Ca(2+). Using TRPA1-blocker and Trpa1(-/-) mice, we found that both TRP channels co-contribute to the formalin trigeminal pain response. These results imply TRPV4 as an important signaling molecule in irritation-evoked trigeminal pain. TRPV4-antagonistic therapies can therefore be envisioned as novel analgesics, possibly for specific targeting of trigeminal pain disorders, such as migraine, headaches, temporomandibular joint, facial, and dental pain, and irritation of trigeminally innervated surface epithelia.