The brouwer fixed point theorem with equivalences, extensions, and applications

M.S.R. H. Kasrie

Some mixed boundary value problems in elastodynamics

Ph.D.Michael P. Stallybras

Experimentally validated quantitative linear model for the device physics of elastomeric microfluidic valves

A systematic experimental study and theoretical modeling of the device physics of polydimethylsiloxane “pushdown” microfluidic valves are presented. The phase space is charted by 1587 dimension combinations and encompasses 45–295 µm lateral dimensions, 16–39 µm membrane thickness, and 1–28 psi closing pressure. Three linear models are developed and tested against the empirical data, and then combined into a fourth-power-polynomial superposition. The experimentally validated final model offers a useful quantitative prediction for a valve's properties as a function of its dimensions. Typical valves (80–150 µm width) are shown to behave like thin springs

Identifying concerted evolution and gene conversion in mammalian gene pairs lasting over 100 million years

<p>Abstract</p> <p>Background</p> <p>Concerted evolution occurs in multigene families and is characterized by stretches of homogeneity and higher sequence similarity between paralogues than between orthologues. Here we identify human gene pairs that have undergone concerted evolution, caused by ongoing gene conversion, since at least the human-mouse divergence. Our strategy involved the identification of duplicated genes with greater similarity within a species than between species. These genes were required to be present in multiple mammalian genomes, suggesting duplication early in mammalian divergence. To eliminate genes that have been conserved due to strong purifying selection, our analysis also required at least one intron to have retained high sequence similarity between paralogues.</p> <p>Results</p> <p>We identified three human gene pairs undergoing concerted evolution (<it>BMP8A/B</it>, <it>DDX19A/B</it>, and <it>TUBG1/2</it>). Phylogenetic investigations reveal that in each case the duplication appears to have occurred prior to eutherian mammalian radiation, with exactly two paralogues present in all examined species. This indicates that all three gene duplication events were established over 100 million years ago.</p> <p>Conclusion</p> <p>The extended duration of concerted evolution in multiple distant lineages suggests that there has been prolonged homogenization of specific segments within these gene pairs. Although we speculate that selection for homogenization could have been utilized in order to maintain crucial homo- or hetero- binding domains, it remains unclear why gene conversion has persisted for such extended periods of time. Through these analyses, our results demonstrate additional examples of a process that plays a definite, although unspecified, role in molecular evolution.</p

On-chip absorption and fluorescence spectroscopy with polydimethylsiloxane (PDMS) microfluidic flow channels

We describe a system, which integrates PDMS microfluidic flow channels, a CMOS active pixel sensor (APS) imager, and commercial light sources for performing visible absorption and fluorescence spectroscopy. PDMS elastomer allows for spectroscopic measurements to be performed in the visible (350 to 750 nm) wavelength range. Along with a sensitive silicon photodetector such as an APS imager, measurements can be made on low concentrations of solutions by placing the microfluidic flow channels directly on the imager. Emission sources for absorption measurements are typically commercial LEDs with peak emission wavelengths that match the peak absorption wavelengths of the material under test. For calibration purposes, known dyes are tested and compared with the results obtained from the imager. Fluorescence measurements are performed in much the same way, but a band-blocking filter is placed between the microfluidic channels and the imager to greatly attenuate the pump wavelength. Typical emission sources for fluorescence are commercial Ar ion lasers and semiconductor lasers. We feel that the system has great advantages due to its miniaturized size and small fluid volumes required. Further system miniaturization is also possible due to the integration of emission sources and the expandability of CMOS imagers to integrate on board image processing