Low frequency of HER2 amplification and overexpression in early onset gastric cancer

BACKGROUND: The recent ToGA trial results indicated that trastuzumab is a new, effective, and well-tolerated treatment for HER2-positive gastric cancer (GC). Although GC mainly affects older patients, fewer than 10% of GC patients are considered early-onset (EOGC) (presenting at the age of 45 years or younger). These EOGC show different clinicopathological and molecular profiles compared to late onset GC suggesting that they represent a separate entity within gastric carcinogenesis. In light of potential trastuzumab benefit, subpopulations of GC such as EOGC (versus late onset) should be evaluated for their frequency of amplification and overexpression using currently available techniques. METHODS: Tissue microarray (TMA) blocks of 108 early onset GC and 91 late onset GC were stained by immunohistochemistry (IHC, Hercep test, DAKO) and chromogenic in situ hybridization (CISH, SPoT-Light, Invitrogen). RESULTS: Overall, we found only 5% HER2 high level amplification and 3% HER2 3+ overexpression (6/199). In addition, 8 patients (4%) showed a low level CISH amplification and 9 patients (4.5%) showed a 2+ IHC score. IHC and CISH showed 92% concordance and CISH showed less heterogeneity than IHC. In 2/199 cases (1%), IHC showed clinically relevant heterogeneity between TMA cores, but all cases with focal IHC 3+ expression were uniformly CISH high level amplified. Early onset GCs showed a significantly lower frequency of HER2 amplification (2%) and overexpression (0%) than late onset GCs (8% and 7% respectively) (p = 0.085 and p = 0.008 respectively). Proximal GC had more HER2 amplification (9% versus 3%) and overexpression (7% versus 2%) than distal tumours although this difference was not significant (p = 0.181 and p = 0.182 respectively). HER2 CISH showed more high level amplification in the intestinal type (7%, 16% if low-level included) compared to the mixed (5%, 5% if low-level included) and diffuse type (3%, 4% if low-level included) GCs (p = 0.029). A similar association was seen for HER2 IHC and histologic type (p = 0.008). Logistic regression indicated a significant association between HER2 expression and age, which remained significant when adjusted for both location and histological type. CONCLUSIONS: Even focal HER2 overexpression in GC points to uniform HER2 amplification by CISH. We show for the first time that early onset GC has a lower frequency of HER2 amplification and overexpression than late onset GC, and confirm that intestinal type GC shows the highest rate of HER2 amplification and overexpression

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

Selfsimilarity and growth in Birkhoff sums for the golden rotation

We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with periodic continued fraction approximations p(n)/q(n), where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of S(q(n),a) with the existence of an experimentally established limit function f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity on the interval [0,1]. The function f satisfies a functional equation f(ax) + (1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n going to infinity can be expressed in terms of the function f.Comment: 14 pages, 8 figure

Differential Geometry of Group Lattices

In a series of publications we developed "differential geometry" on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of "bicovariant" Cayley graphs with the property that ad(S)S is contained in S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first order calculi extend to higher orders and then allow to introduce further differential geometric structures. Furthermore, we explore the properties of "discrete" vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analogue of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained.Comment: 51 pages, 11 figure

A new approach to deformation equations of noncommutative KP hierarchies

Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly nonassociative' (WNA) algebra structure, from which we can conclude, refering to previous work, that any solution of the Riccati system also solves the potential KP hierarchy (in the corresponding matrix algebra). We then turn to the case where the components of the matrices are multiplied using a (generalized) star product. Associated with the deformation parameters, there are additional symmetries (flow equations) which enlarge the respective KP hierarchy. They have a compact formulation in terms of the WNA structure. We also present a formulation of the KP hierarchy equations themselves as deformation flow equations.Comment: 25 page

Epistatic Interactions in Genetic Regulation of t-PA and PAI-1 Levels in a Ghanaian Population

The proteins, tissue plasminogen activator (t-PA) and plasminogen activator inhibitor 1 (PAI-1), act in concert to balance thrombus formation and degradation, thereby modulating the development of arterial thrombosis and excessive bleeding. PAI-1 is upregulated by the renin-angiotensin system (RAS), specifically by angiotensin II, the product of angiotensin converting enzyme (ACE) cleavage of angiotensin I, which is produced by the cleavage of angiotensinogen (AGT) by renin (REN). ACE indirectly stimulates the release of t-PA which, in turn, activates the corresponding fibrinolytic system. Single polymorphisms in these pathways have been shown to significantly impact plasma levels of t-PA and PAI-1 differently in Ghanaian males and females. Here we explore the involvement of epistatic interactions between the same polymorphisms in central genes of the RAS and fibrinolytic systems on plasma t-PA and PAI-1 levels within the same population (n = 992). Statistical modeling of pairwise interactions was done using two-way ANOVA between polymorphisms in the ETNK2, RENIN, ACE, PAI-1, t-PA, and AGT genes. The most significant interactions that associated with t-PA levels were between the ETNK2 A6135G and the REN T9435C polymorphisms in females (p = 0.006) and the REN T9435C and the TPA I/D polymorphisms (p = 0.005) in males. The most significant interactions for PAI-1 levels were with REN T9435C and the TPA I/D polymorphisms (p = 0.001) in females, and the association of REN G6567T with the TPA I/D polymorphisms (p = 0.032) in males. Our results provide evidence for multiple genetic effects that may not be detected using single SNP analysis. Because t-PA and PAI-1 have been implicated in cardiovascular disease these results support the idea that the genetic architecture of cardiovascular disease is complex. Therefore, it is necessary to consider the relationship between interacting polymorphisms of pathway specific genes that predict t-PA and PAI-1 levels

Explorations of the Extended ncKP Hierarchy

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.Comment: 34 pages, correction of typos in (7.2) and (7.5