The proposal "Mathematics for microscopy and cell biology," will allow the investigator to perform hands-on microscopy experiments on bacterial aggregation and growth and on epithelial cell migration. Analysis of images of these processes will help guide future mathematical modeling efforts into how bacteria accumulate near surfaces and how epithelial cells close wounds. Imaging and image analysis are critical steps needed for gaining mechanistic insight into how biofilm-mediated bacterial infections and wound healing occur. These are important problems in biomedicine and bioengineering which can be better addressed with the proposed quantitative and systematic experiments.
The investigator will also develop an applied mathematics course based on the different types of microscopy typically used in modern cell biology. The course will be intended for physicists and mathematicians and review the fundamental optics and chemical excitation occurring in modern microscopy. The investigator also plans to write a peer-reviewed journal review article on modern microscopy, emphasizing its theoretical aspects.
" (NSF-DMS-1032131) include both training for the PI as well as new mathematical tools developed by the PI. The PI spent two sabbatical quarters visiting the laboratory of Prof. Chin-Lin Guo in the Bioengineering Dept. at Caltech. The PI sought to learn a powerful tool used in modern science, especially in cell biology, that has made enormous advances over the last 20 years. A newly developed appreciation of the technology has allowed the PI to begin to learn and explore new algorithms for image analysis. During the grant period, the PI learned basic wet-lab techniques for culturing cells and performing video microscopy. Experiments were performed in which a grown layer of cells was scratched and the healing process observed. We tracked how cells moved to fill the scratch. The resealing of a circular punch experiment is shown in the attached figure. This experiment serves as a simple model system useful for studying epithelial wound-healing. Another outcome of the activities supported by this grant is the development of computational algorithms that we have begun to use to identify boundaries ("segmentation") in electron micrograph images of bacterial cells. The attached image shows the partial segmentation of of the outer bacterial membrane. The mathematical approach we have taken searches for connected short segemnts of high intensity regions and can be extended to the identification of internal structures inside cells.
