Gaussian Mixture Modeling of Helix Subclasses: Structure and Sequence Variations. Ashish V. Tendulkar, Babatunde Ogunnaike, and Pramod P. Wangikar.
Gaussian Mixture Modeling of Helix Subclasses: Structure and Sequence Variations Ashish V. Tendulkar, Babatunde Ogunnaike, and Pramod P. Wangikar Pacific Symposium on Biocomputing 11:291-302(2006)
α
∗
†
α
∗ †
α α
1
α
α 1,2,3 4
4,5
α α
6
5
7
α 8
9
10
11
α
12
13,2
11
x, y, z α
α 14 11
α
α 15
15
s n s y = {"x1 , "x2 , ..., "xn } k
n
f (y) =
k !
φi fi (y, θi )
i=1
k
φi i
i
θi
i θi
µi φi µi 16
k 16
Σi Σi
i
"x ln p(i|"x) = (−
i
1 1 ln |Σi | − ("x − µ"i )" Σi −1 ("x − µ"i ) + ln φi ) 2 2
11
i+1
i
i+1
i i
l l+1
8
" nij / i nij fij " Pij = = fi Ni / i Ni
fij
i
i
j
j
nij fi
i
Ni i
12
11
α α α α
α
α
α
2000
1500
1
9 1
1000 1000
6
6
500
0 0 PC 2
4
0 !11 !15
7
PC1
6
0
PC0 2
!11 !15
7
PC1
−∞ ≤ P C3 < −0.84
−∞ ≤ P C4 < −0.70 +0.68 < P C3 ≤ +∞
0
+0.72 < P C4 ≤ +∞
16
76% α
α φi µ1 µ2 µ3 µ4 µ5 µ6 σ11 σ22 σ33 σ44 σ55 σ66 Pk i
k = 11
φi = 1 φi i
µij σii
i
j i
i α
i+3
i
di,i+3 di,i+3
di,i+3
d18
V oli,i+1,i+2,i+3
Area158 α 5.15 + / − 0.20
di,i+3 d18 voli,i+1,i+2,i+3 area158
5.51 + / − 0.45
5.64 + / − 0.57
5.56 + / − 2.61
5.31 + / − 3.00
10.64 + / − 0.33
11.38 + / − 0.74
10.40 + / − 1.49
18.53 + / − 4.16
6.99 + / − 0.57
di,i+3 d18 voli,i+1,i+2,i+3
i
8.64 + / − 1.59
11.38 + / − 5.93
i+3 i, i + 1, i + 2
i+3
area158
di,i+3
di,i+3
di,i+3 d18 α Area158 d18 Area158 d18
d18
α Area158
V oli,i+1,i+2,i+3 11
α
α α
α
7000
Number of Sequences
6000
5000
4000
3000
2000
1000
0 0
10
20
30
40 50 60 Sequence Length
70
80
90
8 ≤ length ≤ 82
α
4.5
1.8
Curved Helix Regular Helix Kinked Helix
4 3.5
1.4
3
Propensity
Propensity
Curved Helix Regular Helix Kinked Helix
1.6
2.5 2
1 0.8
1.5
0.6
1 0.5 0 1
1.2
0.4 2
3
4
5
Sequence Position
6
7
8
0.2 1
2
3
4
5
Sequence Position
α
4
6
7
8
α
α
α 3
3.5
Length 10 Length 15 Length 25
2.5 Propensity
2 Propensity
Length 10 Length 15 Length 25
3
2.5
1.5
2
1.5
1 1 0.5
0 0
0.5
5
10
15
20
25
Sequence Position
0 0
5
10
15
20
25
Sequence Position
α
α ≤ 10
16
φi α 5
5 8
α
