Epigenetic phenotypes distinguish microsatellite-stable and -unstable colorectal cancers

Aberrant DNA methylation is a common phenomenon in human cancer, but its patterns, causes, and consequences are poorly defined. Promoter methylation of the DNA mismatch repair gene MutL homologue (MLH1) has been implicated in the subset of colorectal cancers that shows microsatellite instability (MSI). The present analysis of four MspI/HpaII sites at the MLH1 promoter region in a series of 89 sporadic colorectal cancers revealed two main methylation patterns that closely correlated with the MSI status of the tumors. These sites were hypermethylated in tumor tissue relative to normal mucosa in most MSI(+) cases (31/51, 61%). By contrast, in the majority of MSI(−) cases (20/38, 53%) the same sites showed methylation in normal mucosa and hypomethylation in tumor tissue. Hypermethylation displayed a direct correlation with increasing age and proximal location in the bowel and was accompanied by immunohistochemically documented loss of MLH1 protein both in tumors and in normal tissue. Similar patterns of methylation were observed in the promoter region of the calcitonin gene that does not have a known functional role in tumorigenesis. We propose a model of carcinogenesis where different epigenetic phenotypes distinguish the colonic mucosa in individuals who develop MSI(+) and MSI(−) tumors. These phenotypes may underlie the different developmental pathways that are known to occur in these tumors.

Convex polytopes and quantization of symplectic manifolds

Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.