Mathematics
Gene Expression Profiles of HCT116-p53-/- cells Treated with Paclitaxel or Stathmin-siRNA
Among the most difficult cancers to treat are those having mutated or non-functional p53, with concurrent overexpression of stathmin (stmn1), amicrotubule (MT) destabilizer (e.g. Yuan et al. 2006. J. Pathol. 209: 549-8). Alli et al. (2007. Oncogene. 26:1003-12) demonstrated that this type of cancer cell undergoes apoptosis in response to stmn1 knock down by siRNA. The mechanism by which stmn1 siRNA promotes apoptosis in cancerous cell lines is not understood, while efficient delivery of targeted siRNA therapies remains an elusive challenge. In this work, we aim to understand the apoptotic processes activated by stmn1 siRNA in a p53-null human colon cancer cell line, HCT116-p53-null, and specifically what is unique about stmn1 siRNA induced apoptosis compared to that induced by paclitaxel treatment, a MT stabilizing drug. We find that both stmn1 depletion and paclitaxel addition slowed cell growth and caused ~25% cell death beginning ~48 h after initial treatment. Microarray analyses of gene expression profiles were then examined to provide an unbiased screen for genes up or down regulated by either treatment. Time courses (~55-72 h) were analyzed for annotated genes showing expression fold changes of greater than or equal to 2. In stmn1 siRNA treated cells, we found 215 down-regulated and 157 up-regulated genes. Paclitaxel treatment resulted in 162 down-regulated and 642 up-regulated genes. Of the differentially regulated genes from each treatment, the number of shared genes included 27 of 350 (8%) down-regulated genes and 89 of 710 (13%) up-regulated genes. These data indicate that most expression changes were unique to each treatment. Comparing those genes whose expression is oppositely changed between the two treatments also demonstrated a low level of overlap (95 of 1081 genes, or ~9%) between treatments. To date our results indicate that stmn1 siRNA and paclitaxel induce apoptosis through unique upstream signals, although each treatment acts to stabilize MTs. Continued analysis and microarray verification are ongoing to confirm our conclusions. Understanding how stmn1 siRNA induces apoptosis could lead to identification of novel chemotherapy targets.
Partially funded by an HHMI grant to Lehigh and NIH (LC).
An Introduction to Galois Groups of CM Fields
A CM field is an imaginary quadratic extension of a totally real number field. In this talk we will explore the properties of the Galois groups of CM fields and consider some research problems related to the classification of all Galois groups of CM fields of a given degree.
The Lambert W Function
The Lambert W function is the inverse of the complex-valued function f(x) = xex. It has been studied since the 1700s by the likes of Johann Lambert, Leonhard Euler, and E.M. Wright, and it has applications to problems in calculus, differential equations, graph theory, and computer science. This talk will present a survey of the most important properties of W and describe some of its applications in detail.
Computing Multiple Dirichlet Series in a Rational Function Field
Friedberg, Hoffstein and Lieman showed how to construct two related multiple Dirichlet series from quadratic and higher-order twisted L-functions and Gauss sums. We compute these multiple Dirichlet series explicitly in the case of the rational function field. This is done by utilizing the functional equation of the L-functions and the functional equation relating the two multiple Dirichlet series. We also point out a very simple correspondence between the p-parts of these series and their sums.