Introductory Biological Sequence Analysis Through Spreadsheets

1
Introductory Biological Sequence Analysis
Through Spreadsheets

• Stephen J. Merrill
• Sandra E. Merrill
• Marquette University
• Milwaukee, WI

2
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)

3
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

4
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

5
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

6
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

7
Spreadsheet 1 Simple Homology
8
Spreadsheet 1 (cont.)comparing random
sequences
9
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

10
Describing the Composition and Properties of a
String

• Counts of frequencies of particular letters due
  to their properties (e.g. regions rich in GC or
  AT in DNA)
• Properties of proteins (e.g. charge or
  hydrophobicity) which depend on the nature and
  frequencies of the particular amino acids

11
Spreadsheet 2 Hydropathy Plot
12
Spreadsheet 2 (Cont.)
13
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

14
Spreadsheet 3 Mutation Evolution
15
Spreadsheet 3 (cont.)
To study the evolution of a
sequence, we randomly pick a site for mutation,
then change its letter
16
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