Download Introductory Biological Sequence Analysis Through Spreadsheets

Introductory Biological Sequence
Analysis Through Spreadsheets
Stephen J. Merrill
Sandra E. Merrill
Marquette University
Milwaukee, WI
November 18, 2000
ICTCM 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, 2000
ICTCM 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, 2000
ICTCM 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, 2000
ICTCM 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, 2000
ICTCM 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, 2000
ICTCM 2000
Spreadsheet #1 Simple Homology
Part of 2 70 base sequences of yeast DNA
C
T
C
A
C
C
0
1
0
2
A
C
1
3
C
C
0
4
A
G
1
5
C
G
0
6
A
C
0
7
C
T
0
8
A
T
0
9
C
T
C
C
0
10
0
11
A
T
1
12
1 .2
1
0 .8
0 .6
S e rie s 1
0 .4
0 .2
0
0
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20
40
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60
80
0
13
Spreadsheet #1 (cont.)
comparing random sequences
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ICTCM 2000
0.
5
0.
4
0.
3
0.
2
0.
1
0
Frequency
Recording the results of many trials
Simresult
Trial #
alignment
0.271429 this is updated each time any cell is entered
1 0.314286
2 0.171429
3 0.271429
4 0.285714
Bin
Frequency
Histogram
5 0.228571
0
0
5 0.185714
0.05
0
5
6 0.242857
0.1
0
4
7 0.185714
0.15
0
3
8 0.271429
0.2
4
Frequency
2
9 0.357143
0.25
3
1
10 0.242857
0.3
3
11
0.2
0.35
1
0
0.4
1
0.45
0
0.5
0
Bin
More
0
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
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ICTCM 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, 2000
ICTCM 2000
Spreadsheet #2 Hydropathy Plot
Human IL-10 having 148 amino acids
Hydrophobic regions are yellow
Hydrophilic regions in blue
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ICTCM 2000
Spreadsheet #2 (Cont.)
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ICTCM 2000
Kyte-Doolittle Chart
144
133
122
100
111
amino acid sequence number
89
78
67
56
45
5
4
3
2
1
0
-1
-2
-3
-4
-5
1
12
23
34
Hydrophobicity Plot
S1
A
C
D
E
F
G
H
I
K
L
M
N
P
Q
R
S
T
V
W
Y
1.8
2.5
-3.5
-3.5
2.8
-0.4
-3.2
4.5
-3.9
3.8
1.9
-3.5
-1.6
-3.5
-4.5
-0.8
-0.7
4.2
-0.9
-1.3
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
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Spreadsheet #3 Mutation & Evolution
30
25
20
Series1
15
10
5
number of mutations
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31
28
25
22
19
16
13
10
7
4
0
1
total number of different
letters
Total Differences from original sequence
Spreadsheet #3 (cont.)
To study the evolution of a sequence,
we randomly pick a site for mutation, then change its letter
Site #
9
6
40
70
33
25
28
52
67
8
52
29
3
13
Letter
T
A
G
T
A
T
C
C
T
G
G
A
G
T
November 18, 2000
letter in the
different distance away
original sequence 1 for yes from original
orig.seq
T
0
0C
A
0
0T
T
1
1T
C
1
2C
C
1
3T
T
0
3A
A
1
4C
A
1
5A
T
0
5T
A
1
6A
A
1
7G
T
1
8C
T
1
9C
C
1
10 C
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postion #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
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
November 18, 2000
ICTCM 2000