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Mathematics

Calculating a Critical Distance for Metastasis

Sam Antill ('13); Mentor: Ami Radunskaya

Abstract: In this work we seek conditions under which a tumor’s growth will be contained and metastasis will not occur. We hypothesize that there exists a critical distance from the blood vessel for which there will be insufficient nutrients for metastasis. In this model, we focus on the qualities of tumor gluttony and adhesion rather than tumor immune interactions as a means of potentially impeding tumor growth. We develop a hybrid cellular automata model to simulate tumor growth and using this model we find that a critical distance from the initial tumor to the nearest blood vessel does exist. Our results show that tumors that begin further than this distance from a vessel will not metastasize. The results indicate a critical distance for the model that agrees with experimentally determined data. We conclude that distance between a tumor and the nearest blood vessel can be an important factor in tumor prognosis.
Funding Provided by: The Norris Foundation

Microarray Data Analysis: Finding Life’s Music through Statistical Noise

Joseph Replogle ('13); Mentors: Johanna Hardin, Laura Hoopes

Abstract: Microarray technology measures thousands of genes’ transcription levels simultaneously. Analyzed properly, microarray data allows biologists to identify differential expression in cells from scientifically interesting experimental conditions. Due to the heterogeneity of microarray experimental designs, scientists choose from numerous analysis techniques to obtain proper results. Therefore, in my SURP I sought to integrate normalization, differential expression identification, and gene ontology (GO) techniques to analyze yeast microarray data produced in summer 2010 by Hoopes’ lab. Using limma and GOstats R packages, I built off the methods of Yui et al. including loess scaling for normalization and an empirical Bayes method to identify differential expression. Additionally, I included GO terms described in Falcon et. al. I analyzed data from 10 Saccharomyces cerevisiae microarrays to identify differential expression and GO terms. The methodology used this summer could be applied to future experiments in identifying differential ex-pression and GO terms in yeast or other organisms.
Funding Provided by: The Fletcher Jones Foundation

Research at Pomona