Physical Sciences and Mathematics Commons^™

An Examination Of Mathematical Models For Infectious Disease, David M. Jenkins

Williams Honors College, Honors Research Projects

Starting with the original 1926 formulation of the SIR (Susceptible-Infected-Removed) model for infectious diseases, mathematical epidemiology continued to grow. Many extensions such as the SEIR, MSIR, and MSEIR models were developed using SIR as a basis to model diseases in a variety of circumstances. By taking the original SIR model, and reducing the system of three first-order equations to a single first-order equation, analysis shows that the model predicts two possible situations. This analysis is followed by discussion of an alternative use of the SIR model which allows for one to track the amount of sustainable genetic variation in a …

Application Of Lipid Styryl Dye For Staining Intracytoplasmic Membranes In Gram-Negative Bacteria, Theodore J. Hammer

Williams Honors College, Honors Research Projects

Intracytoplasmic membranes are structures that form within cells which help facilitate a variety of different metabolic processes. This feature of intracellular membranes makes them particularly valuable for studying compartmentalization and cell dynamics in bacteria. In the past, transmission electron microscopy has been the primary method for imaging bacteria with intracytoplasmic membranes. Because transmission electron microscopy takes images of a cell in fixed slices, it’s impossible to follow a cell’s growth and development over time. Fluorescence microscopy is a particularly effective method of measurement that can combat these issues when evaluating live bacterial cells. Here, standard biochemical laboratory procedures were used …

The Effects Of Substrate Roughness In Air And Water On The Gecko Adhesive System, Amanda Palecek

Williams Honors College, Honors Research Projects

In an effort to better understand the fascinating gecko adhesive system, scientists have long tested the abilities of the gecko in controlled conditions that mimic the gecko’s native environment. The effects of humidity, environmental temperature, and exposure to water have all been tested. Roughness, however has not been studied in great detail. Surfaces of varying roughnesses are all over the gecko’s natural environment. We tested geckos on hydrophilic silicon carbide sandpapers of varying roughnesses in both air and water to attempt to better study the effects of roughness on gecko adhesion. When tested on the rougher (1 µm) surface, the …

Evaluation Of The Signature Molecular Descriptor With Blosum62 And An All-Atom Description For Use In Sequence Alignment Of Proteins, Lindsay M. Aichinger

Williams Honors College, Honors Research Projects

This Honors Project focused on a few aspects of this topic. The second is comparing the molecular signature kernels to three of the BLOSUM matrices (30, 62, and 90) to test the accuracy of the mathematical model. The kernel matrix was manipulated in order to improve the relationship by focusing on side groups and also by changing how the structure was represented in the matrix by increasing the initial height distance from the central atom (Height 1 and Height 2 included).

There were multiple design constraints for this project. The first was the comparison with the BLOSUM matrices (30, 62, …

Sharp Rna Recognition Motif Optimizations, Extensions, And Mutations For Use In 2d And 3d Nmr Experiments, Shaun M. Christie

Williams Honors College, Honors Research Projects

SMRT/HDAC Associated Repressor Protein interacts with the long noncoding RNA, produced by SRA, by binding at the RRMs. Three projects were done to prepare the truncated proteins for use in 2D and 3D NMR experiments. The first focuses on RRM 3 and its optimization during the purification process. The second focuses on RRM 2-4, which was found to be missing two alpha helices that may be important for protein stability. These helices can also interact with RRM 3 as well due to the tight association of RRMs 3 and 4. The two step PCR extension of RRM 2-4 was assumed …