Enterolactone restricts the proliferation of the LNCaP human prostate cancer cell line in vitro

Ecological data suggest a long-term diet high in plant material rich in biologically active compounds, such as the lignans, can significantly influence the development of prostate cancer over the lifetime of an individual. The capacity of a pure mammalian lignan, enterolactone (ENL), to influence the proliferation of the LNCaP human prostate cancer cell line was investigated as a function of cell density, metabolic activity, expression and secretion of prostate specific antigen (PSA), cell cycle profile, and the expression of genes involved in development and progression of prostate cancer. Treatment with a subcytotoxic concentration of ENL (60 mu M for 72 h) was found to reduce: cell density (57.5%, SD 7.23, p < 0.001), metabolic activity (55%, SD 0.03, p < 0.001), secretion of PSA (48.50% SD 4.74, p = 0.05) and induce apoptosis (8.33-fold SD 0.04, p = 0.001) compared to untreated cells. Cotreatment with 10 mu M etoposide was found to increase apoptosis by 50.17% (SD 0.02, p < 0.001). Additionally, several key genes (e.g. MCMs, survivin and CDKs) were beneficially regulated by ENL treatment (p < 0.05). The data suggest that the antiproliferative activity of ENL is a consequence of altered expression of cell cycle associated genes and provides novel molecular evidence for the antiproliferative properties of a pure lignan in prostate cancer.

Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.