Classroom Pearls for Life Sciences and Mathematics Students J. de Varona, E. Demirci, S. Koksal

1. Classroom Pearls for Life Sciences and Mathematics StudentsJ. de Varona, E. Demirci, S. Koksal Activity 1: Precalculus , Library of Functions Activity 2: Linear Algebra, Eigenvalues of Matrices S2 Finding Similarities and Dissimilarities in DNA Sequences of HIV Patients Objective: Classify the types of Distances Matrices resulting from the alignment of DNA sequences of certain viruses and investigate the properties of symmetric Matrices. Learning Goals: Mathematics Majors can appreciate the beauty of mathematics and its application for solving real world problems arising from Biological data. Mathematical Keywords: • Symmetric Matrix • Eigenvalues Methodology: Give the students the summarized data of the HIV Study using DNA sequences and let them analyze the data, draw a graph and try to explain the situation. Then, introduce the concept of a function, different family of functions and their properties. Findings: Objectives: Introduce Library of Functions to Life Science Students using real biological data from real life cases. Learning Goals: Students can understand the different mathematical models that can be used to explain particular behavior and solve problems related to biological applications. Methodology: Give the students the summarized data of the HIV Study using DNA sequences and let them analyse the data, draw a graph and try to explain the situation. Then, introduce the concept of a function, different family of functions and their properties. Mathematical Keywords: • Domain, range and graph of a function • Linear Functions • Non Linear Functions • Continuous Functions • Piecewise functions Biological Keywords: • HIV • DNA sequence • CD4 Counts (counting t-helper lymphocytes)‏ • DNA Distance Matrices • Un rooted Trees Biological Keywords: • HIV • DNA sequence • CD4 Counts (counting t-helper lymphocytes)‏ • DNA Distance Matrices • Un rooted Trees Range of eigenvalues (range of variances): For crashed subjects λiε(0.1,1)‏ For uncrashed subjects λiε(0.01, 0.3))‏ Conclusion: Eigenvalues give us the variance of the DNA distance between the clones of the virus. Upper tail of the range for eigenvalues of uncrashed data overlaps with the lower end of the range for the crashed data. This is because CD4 counts of the uncrashed subjects in the upper end of the range are closer to 200 where the crash occurs. As the CD4 counts decrease, the eigenvalues increases within the given range. References 1. Biology Workbench-San Diego Super Computer Center http://workbench.sdsc.edu/ 2. John R. Jungck, Marion Field Fass, Ethel D. Stanley (2003) Microbes Count! BioQUEST Curriculum Consortium 3. Markham RB, Wang WC, Weisstein AE, Wang Z, Munoz A, Templeton A,Margolick J, Vlahov D, Quinn T, Farzadegan H, Yu HF (1998). Patterns of HIV-1 evolution in individuals with differing rates of CD4 T cell decline. Proc. Natl. Acad. Sci. 95(21):12568-73 4. Radnic M, Vracko M, Lers N, Plavsic D (2003).A nalysis of similarity/dissimilarity of DNA sequences based on novel 2-D graphical representation.Chem. Phiysics Letters.371: 202-207. 5. Jaklic G, Pisanski T, Randic M (2006). Characterization of Complex Biological Systems by Matrix Invariants. Journal of Comp. Bio. (13) No 9 :1558-1564. 6. Randic M, Vracko M, Lers N, Plavsic D (2003). Novel 2-D graphical representation of DNA sequences and their numerical characterization. Chemical Physics Letters (368): 1-6. Figure 1: Photo of corymbose Acropora coral colonies at 1 m, Kushibaru, southern Japan.