November 18, 2000ICTCM 2000 Introductory Biological Sequence Analysis Through Spreadsheets Stephen J. Merrill Sandra E. Merrill Marquette University Milwaukee, WI

November 18, 2000ICTCM 2000 Teaching Mathematics to Students of Biology  Need to make the math in the courses correlate with math that needed in that discipline  The most important “math” needed is statistics  The molecular biology revolution in biology presents data in a form in which calculus has little impact (sequences of letters)

November 18, 2000ICTCM 2000 The Nature of Biological Sequence Data  Primary structure of DNA, RNA, and proteins are sequences of letters -- 4 letters in the case of DNA (ATGC) and RNA (AUGC) and 20 letters representing the sequence of amino acids which makes up a protein  Secondary and Tertiary structures (bending, folding and twisting) of structures determines function -- hints seen through primary structure

November 18, 2000ICTCM 2000 Use of Spreadsheets in this setting  Commonly found and used in biological labs for data acquisition, storage and organization, and data analysis  Commonly present on student computers and computer labs  Unlike calculators -- able to handle data sets typical of “real world” applications  R.F. Murphy at CMU has developed a set of worksheets for sequence analysis

November 18, 2000ICTCM 2000 Meaningful Questions & Problems 1. Measuring the similarity between two strings -- “alignment” or “homology” 2. Finding instances of a pattern in a string 3. Describing the composition and properties of a string 4. Graphing the evolutionary process and construction of phylogenetic trees

November 18, 2000ICTCM 2000 Measuring the Similarity between Strings  Given a gene -- suggest the function of the protein coded for by finding a similar sequence (possibly in another species)  Simple homology involves assigning a “1” for agreement and “0” for nonagreement at each site. Then sum over all sites  Homology is the fraction of the highest possible score, in %

November 18, 2000ICTCM 2000 Spreadsheet #1 Simple Homology

November 18, 2000ICTCM 2000 Spreadsheet #1 (cont.) comparing random sequences

November 18, 2000ICTCM 2000 Finding Instances of a Particular Pattern in a String  The process of locating genes involves locating regions of the DNA sequences that contain patterns which resemble those of known genes  Identifying sites on DNA where one of the restriction enzymes can cleave DNA -- Also of interest is size of the fragments that result  Identify regions of RNA which correspond to particular features (e.g. loops) which may be splice sites

November 18, 2000ICTCM 2000 Describing the Composition and Properties of a String  Counts of frequencies of particular letters due to their properties (e.g. regions rich in G&C or A&T in DNA)  Properties of proteins (e.g. charge or hydrophobicity) which depend on the nature and frequencies of the particular amino acids

November 18, 2000ICTCM 2000 Spreadsheet #2 Hydropathy Plot

November 18, 2000ICTCM 2000 Spreadsheet #2 (Cont.)

November 18, 2000ICTCM 2000 Graphing Evolution and Phylogenetic Trees  Evolutionary distance between two DNA sequences used to determine the process of the changes in the sequences over time (e.g. the evolution of HIV or the flu viruses)  Trees constructed to express the relationship between related sequences -- distance in the tree a monotone function of homology

November 18, 2000ICTCM 2000 Spreadsheet #3 Mutation & Evolution

November 18, 2000ICTCM 2000 Spreadsheet #3 (cont.) To study the evolution of a sequence, we randomly pick a site for mutation, then change its letter

November 18, 2000ICTCM 2000 Conclusion  Use of a spreadsheet makes possible an experimental approach to introducing the mathematics of sequence analysis  The use of spreadsheets makes possible the use of real-world data and presents the computational tool in a meaningful context  The importance of the topics to all educated individuals suggests that the topics be included in many liberal arts math courses