1. Matrices
A set of elements organized in a table (along rows and columns)
Wikipedia image

2. Matrices
Python does not have direct support for matrix manipulation. For Bio/CS 251 matrices are provided through support.py
makeMatrix(rows, cols) # creates a matrix with the
# given rows and cols
randomMatrix(rows, cols) # creates a matrix with the # given rows and cols with all
# cells set to random values
getRows(M) # returns the number of rows
# of the given matrix
getCols(M) # returns the number of cols
M[r][c] = # puts 5 in cell (r, c)
score = M[r][c] # puts value of cell(r, c) in score

3. Matrices Indexing of rows and columns starts at 0 1 2 3 4 7 4 91 2 3 4 7 4 9
>>> M = makeMatrix(3, 5) # creates 3x5 matrix
>>> rows = getRows(M)
>>> print rows 3
>>> cols = getCols(M)
>>> print cols 5
>>> M[0][0] = 7
>>> M[2][4] = 9
>>> M[1][2] = 4
>>> total = M[0][0] + M[2][4] + M[1][2]
>>> print total

4. Matrix Processing Fill all cells of a matrix with the number 9
To FILL each cell of a given matrix with the value 9: 1. for each row index in the matrix:
2. for each column index in the matrix:
3. set cell of current row, col to 9
def fillMatrix(M):
for r in range(0, getRows(M)):
for c in range(0, getCols(M)):
M[r][c] = 9
>>> D = makeMatrix(3, 5)
>>> fillMatrix(D)
>>> print D
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5. Matrix Processing Add all the values in a matrix
To ADD all cells of a given matrix:
set current total to 0
1. for each row index in the matrix:
2. for each column index in the matrix:
3. update total with current cell value
4. return total
>>> D = randomMatrix(3, 5)
>>> print D
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>>> total = addElements(D)
>>> print total 32
def addElements(M):
total = 0
for r in range(0, getRows(M)):
for c in range(0, getCols(M)):
total = total + M[r][c]
return total

6. Sequence Similarity
Provides insight about the sequence under investigation – gene-coding regions (DNA), function (proteins)
Typically assessed via the process of “sequence alignment”
Standard sequence alignment algorithms
Dot Plots
Global Alignment
Semiglobal Alignment
Local Alignment
Standard software
BLAST, FASTA – find high scoring local alignments between query and a target database

7. Dot Plots
The simplest method for identifying similarities between two sequence
Uses a 2-dimensional table
one of the sequences labels the rows
the other sequence labels the columns
place a ● in each cell that has matching (row, column) labels
Example: Dot plot for “GATTACA” and “TACACATTG”

8. Dot Plots G A T C ? ? ● ? ? ● ? ? ? ? ● ? ? ? ? ● ? ? ● ?

9. Dot Plots G A T C ●
ACA
ACATT
TACA
TAC
ATT

10. Dot Plots
The simplest method for identifying similarities between two sequence
Diagonal lines indicate regions of similarity
SE slope – similarity along the direction of the sequences
SW slope – similarity along one sequence in reverse
Susceptible to noise – especially with DNA since only 4 possible symbols there will be a lot of “random hits”
Noise can be addressed using a sliding window
consider fragments of length W in the two sequences
place ● in each cell that is the “origin” of the sliding window

11. Dot Plots (W = 2) G A T C ? ? ? ? ● ? ? ? ? ? ? ? ● ?

12. Dot Plots (W = 2) Compare with next slide with W = 1G A T C ●
Compare with next slide with W = 1
noise has disappeared
one fewer dots per matching region
in general if N matches per region, #dots = N – (W-1)

13. Dot Plots (W = 1) G A T C ●
Compare with previous slide with W = 2

14. Self Alignment (W = 1) In self alignmentC ●
In self alignment
main diagonal is filled in completely
matrix is symmetric about main diagonal

15. Dot Plots Original paper
Maizel JV and Lenk RP: Enhanced graphic matrix analysis of nucleic acid and protein sequences. Proc Natl Acad Sci USA 78:7665, 1981.
Used a sliding window of odd length centered at the base
Our examples used a sliding window anchored at the base G G

16. Dot Plots in Python Compute the dot plot matrix given two sequences
To MAKE a DOT PLOT given two sequences:
1. Create a matrix with rows and columns equal to
length of first and second sequence respectively
2. for each row index in the matrix:
3. for each column index in the matrix:
4. if symbol in first sequence equals
symbol in second sequence
5. place a dot at current cell
6. return the matrix
>>> M = makeDotPlot("GATTACA", "TACACATTG")
>>> print M
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