Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

A detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new

Nuclear PtdIns(4,5)P-2 assembles in a mitotically regulated particle involved in pre-mRNA splicing

Phosphoinositide turnover regulates multiple cellular processes. Compared with their well-known cytosolic roles, limited information is available on the functions of nuclear phosphoinositides. Here, we show that phosphatidylinositol(4,5)-bisphosphate (PtdIns(4,5)P-2) stably associates with electron-dense particles within the nucleus that resemble interchromatin granule clusters. These PtdIns(4,5)P-2-containing structures have a distribution which is cell-cycle dependent and contain components of both the transcriptional and pre-mRNA processing machinery, including RNA polymerase It and the splicing factor SC-35. Immunodepletion and add-back experiments demonstrate that PtdIns(4,5)P-2 and associated factors are necessary but not sufficient for pre-mRNA splicing in vitro, indicating a crucial role for PtdIns(4,5)P-2-containing complexes in nuclear pre-mRNA processing

Mycobacteria in nerve trunks of long-term treated leprosy patients

Mycobacteria were present in 4 out of 8 mixed peripheral nerve trunks from patients (3 BT and 1 BL) treated with DDS and/or MDT for periods ranging from 21 months to 8 years. Most of the bacilli appeared to be 'whole'. Nerve destruction with areas of granulomatous infiltration appeared more active than expected. Possible reasons for a continued presence of bacilli in treated nerves and its implications in 'relapse' are discussed

An immunoelectronmicroscopical study of the expression of major histocompatibility complex (MHC) class II antigens in guinea pig sciatic nerves following induction of intraneural mycobacterial granulomas.

A guinea pig model of nerve damage in leprosy has been used to investigate the expression of major histocompatibility complex (MHC) class II antigens in granulomatous lesions in nerves. Using an immunoelectronmicroscopical technique, infiltrating mononuclear cells and endoneural fibroblast-like cells are shown to be class II-positive in the experimental neural lesions. Schwann cells are not class II-positive under these conditions, although at the light microscope level Schwann cell-like cells appear to be positively stained. This illustrates the value of immunoelectronmicroscopy in the investigation of cell surface proteins in situ as compared with conventional light immunohistochemistry

Major histocompatibility complex class II antigen expression in nerves in leprosy; an immunoelectronmicroscopical study.

A technique for immunoelectronmicroscopy has been used to investigate major histocompatibility class II expression in leprosy nerves. In normal nerves, endothelial cells and occasional endoneural cells (not Schwann cells) were constitutively class II positive. In both paucibacillary and multibacillary leprosy nerve biopsies, infiltrating leukocytes were positive but class II-positive Schwann cells were not seen. These observations indicate that Schwann cells may not be involved in presenting Mycobacterium leprae antigens to T cells in leprosy. This conflicts with evidence from in vitro studies, but may be explained by the fact that in vivo Schwann cells are surrounded by basement membranes and are closely associated with axons