22
Statistical Modeling
of DNA Sequences and Patterns
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Table 1
Conditional Nucleotide Probabilities for the 25-nt Example Sequence
↓ Si–1
Si →
A
C
T
G
A
C
T
G
25/144
50/168
25/168
25/120
25/144
25/168
100/168
25/120
75/144
75/168
0
25/120
25/144
25/168
50/168
25/120
Table 2
Patterns and Probabilities Deduced Using IID and Markov Models
Probability
Pattern
ATTTA
TGTTTTG
TTTTGGGG
CTTTTACCAAT
TCTTTATCTTTGCG
CTGAACATTGATGCA
IID Model
Markov Model
2.57 × 10– 3
1.06 × 10– 4
1.40 × 10– 5
5.181 × 10– 7
6.545 × 10– 9
1.238 × 10– 9
2.0 × 10– 3
1.64 × 10– 4
4.153 × 10– 5
7.596 × 10– 7
1.968 × 10– 9
3.19 × 10– 9
Table 3
Weight Matrix for TATAA Box
T
C
A
G
6
14
8
32
49
6
4
1
1
0
58
1
56
0
4
0
6
3
51
0
22
0
38
0
6
1
53
0
20
2
30
8
Fig. 1. The set of possibe transitions in a 2nd. Order Markov chain. Note that only 8 nonzero probabilities need to be estimated for this model, as not all of the 16 transitions are possible.
Fig. 2. A profile HMM utilizes the insert (diamond) and delete (circle) states. The delete states are
silent and are not associated with the emissions of any symbols. The parameters of a profile HMM are
learned from a multiple sequence alignment.
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