Linear Algebra Course Activity 2: Finding Similarities and Dissimilarities in DNA Sequences of HIV Patients Objective: Classify the types of Distances.

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Presentation transcript:

Linear Algebra Course Activity 2: 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 Biological Keywords: HIV DNA sequence CD4 Counts (counting t-helper lymphocytes) DNA Distance Matrices Un rooted Trees Methodology: Present the students a Case Study related to HIV virus. Ask the students to formulate questions about what they know and what they need to know about the case in order to find similarities and dissimilarities in the DNA sequences of the virus in diagnosed HIV subjects. Provide the students a table with the summarized data of the HIV Study using DNA sequences and let them analyze the data using a particular software that can be obtained free on the web. Show the student how to obtain the DNA sequences of the virus using this software and ask them to find the DNA Distance Matrices using the same tool. This can be done in small groups assigning two or three subjects to each group and then collecting the information for all the subjects. Once the Distance Matrices are gathered, explain the concept of symmetric matrices and their properties. Define and compute the eigenvalues of the symmetric matrices and ask the students, that applying this concepts to the DNA distances matrices that they already have analyzed the data an draw conclusions about the similarities or dissimilarities of the DNA sequences of the HIV-1 virus found on infected subjects. Technological Tools: Biology Workbench Mathematica Online tool for computation of eigenvalues and eigenvectors

10 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1) S3V (2) S3V (3) S3V (4) S3V (5) S3V (6) S3V (7) S3V (8) S3V (9) S3V (10) S3V DNA DISTANCE Matrix for Subject 3 Visit 5