We present a global attractivity result for maps generated by systems of autonomous difference equations. It is assumed that the map of the system leaves invariant a box, is monotone in a coordinate-wise sense (but not necessarily monotone with respect to a standard cone), and satisfies certain algebraic condition. It is shown that there exists a unique equilibrium, and that it is a global attractor. As an application, it is shown that a discretized version of the Lotka-Volterra system of differential equations of order $k$ has a global attractor in the positive orthant for certain range of parameters.

We have studied the consequences of two homoplasmic, pathogenic point mutations (T7512C and G7497A) in the tRNASer(UCN) gene of mitochondrial (mt) DNA using osteosarcoma cybrids. We identified a severe reduction of tRNASer(UCN) to levels below 10% of controls for both mutations, resulting in a 40% reduction in mitochondrial protein synthesis rate and in a respiratory chain deficiency resembling that in the patients muscle. Aminoacylation was apparently unaffected. On non-denaturating northern blots we detected an altered electrophoretic mobility for G7497A containing tRNA molecules suggesting a structural impact of this mutation, which was confirmed by structural probing. By comparing in vitro transcribed molecules with native RNA in such gels, we also identified tRNASer(UCN) being present in two isoforms in vivo, probably corresponding to the nascent, unmodified transcripts co-migrating with the in vitro transcripts and a second, faster moving isoform corresponding to the mature tRNA. In cybrids containing either mutations the unmodified isoforms were severely reduced. We hypothesize that both mutations lead to an impairment of post-transcriptional modification processes, ultimately leading to a preponderance of degradation by nucleases over maturation by modifying enzymes, resulting in severely reduced tRNASer(UCN) steady state levels. We infer that an increased degradation rate, caused by disturbance of tRNA maturation and, in the case of the G7497A mutant, alteration of tRNA structure, is a new pathogenic mechanism of mt tRNA point mutations.

In vivo Raman spectroscopy, using fiber-optic probes is hindered by the intense background signal, which is generated in the fused-silica fibers, in the fingerprint region of the Raman spectrum (approximately 0-2000 cm(-1)). Optical filtering is necessary to obtain tissue spectra of sufficient quality. The complexity of fiber-optic probes for fingerprint Raman spectroscopy, in combination with size constraints and flexibility requirements for in vivo use have been a major obstacle in the development of in vivo diagnostic tools based on Raman spectroscopy. A setup for remote Raman spectroscopic tissue characterization in the high-wavenumber region ( approximately 2400-3800 cm(-1)) is presented. It makes use of a single, unfiltered, optical fiber for guiding laser light to the sample and for collecting scattered light and guiding it back to a spectrometer. Such a simple configuration is possible because the fused-silica core and cladding of the fiber present almost no Raman background signal at these wavenumbers. Several commercially available optical fibers were tested with respect to Raman signal background, to determine their suitability for in vivo Raman spectroscopy measurements in the high-wavenumber region. Different fiber core, cladding, and coating materials were tested. Silica core-silica clad fibers, with an acrylate coating and a black nylon jacket, proved to be one of the best candidates. In vitro measurements on brain tissue of a 6-month-old pig were obtained with a remote high-wavenumber Raman setup. They illustrate the low background signal generated in the setup and the signal quality obtained with a collection time of 1 s.