ANTIGEN RECOGNITION AND THE IMMUNE RESPONSE : STRUCTURAL REQUIREMENTS IN THE SIDE CHAIN OF TYROSINE FOR IMMUNOGENICITY OF L-TYROSINE-AZOBENZENEARSONATE

The low molecular weight compound L-tyrosine-azobenzenearsonate (RAT) induces a cellular immune response in guinea pigs. The contribution of the side chain of tyrosine to the immunogenicity of RAT and the structural requirements at that position for immunogenicity were assessed by synthesizing a series of analogs of RAT containing modifications in the side chain of tyrosine and employing them as immunogens. Removal of either the carboxyl or amino group did not markedly affect immunogenicity, measured by the induction of delayed cutaneous sensitivity, whereas deletion of both completely abolished it. However, a charged group was not required since side chains containing a polar hydroxyl group could substitute for chains bearing an amino or carboxyl group. The size of the side chain exerted a pronounced influence; the charged or polar substituent had to be extended from the phenolic ring by at least two carbon atoms in order to confer immunogenicity

The Stratified Structure of Spaces of Smooth Orbifold Mappings

We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) manifold. For the notion of complete reduced orbifold map, the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifold. The remaining two notions carry a stratified structure: The C^r orbifold maps between O and P is locally a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) manifolds while the set of C^r reduced orbifold maps between O and P locally has the structure of a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifolds. Furthermore, we give the explicit relationship between these notions of orbifold map. Applying our results to the special case of orbifold diffeomorphism groups, we show they inherit the structure of C^\infty Banach (r finite)/Frechet (r=infty) manifolds. In fact, for r finite they are topological groups, and for r=infty they are convenient Frechet Lie groups.Comment: 31 pages, 2 figures; corrected and expande

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Impact of Tumor Grade on Prognosis in Pancreatic Cancer: Should We Include Grade in AJCC Staging?

AJCC staging of pancreatic cancer (PAC) is used to determine prognosis, yet survival within each stage shows wide variation and remains unpredictable. We hypothesized that tumor grade might be responsible for some of this variation and that the addition of grade to current AJCC staging would provide improved prognostication. The Surveillance, Epidemiology, and End Results (SEER) database (1991–2005) was used to identify 8082 patients with resected PAC. The impact of grade on overall and stage-specific survival was assessed using Cox regression analysis. Variables in the model were age, sex, tumor size, lymph node status, and tumor grade. For each AJCC stage, survival was significantly worse for high-grade versus low-grade tumors. On multivariate analysis, high tumor grade was an independent predictor of survival for the entire cohort (hazard ratio [HR] 1.40, 95% confidence interval [95% CI] 1.31–1.48) as well as for stage I (HR 1.28, 95% CI 1.07–1.54), stage IIA (HR 1.43, 95% CI 1.26–1.61), stage IIB (HR 1.38, 95% CI 1.27–1.50), stage III (HR 1.28, 95% CI 1.02–1.59), and stage IV (HR 1.58, 95% CI 1.21–2.05) patients. The addition of grade to staging results in a statistically significant survival discrimination between all stages. Tumor grade is an important prognostic variable of survival in PAC. We propose a novel staging system incorporating grade into current AJCC staging for pancreas cancer. The improved prognostication is more reflective of tumor biology and may impact therapy decisions and stratification of future clinical trials