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)










 


  
1


1,2,3 4

 

4,5

6

5

7


8

9

10

11




12

13,2

11

x, y , z
 14 11 




15 15

s n s y = {x1 , x2 , ..., xn } k ik n

f (y ) = k

i fi (y , i ) i i

=1

i µi

i i i µi
16

i i i i

k
16


x ln p(i|x) = (- 1 1 ln |i | - (x - µi ) 2 2
 -1 i

i (x - µi ) + ln i )

11

i i i l

i+1 i+1 l+1

8

Pij = fij i i j

nij / fij = fi Ni /

i n i ij Ni j fi

nij i


Ni i

12

11

   








2000

1 6

1500 1000

9 1 4

1000

500 0

6

0 0 PC 2 0 !11 !15
PC1

7

6

0 PC 2

0 !11 !15
PC1

7

-  P C4 < -0.70 +0.68 < P C3  + +0.72 < P C4  +

-  P C3 < -0.84

16

76% 


 i µ1 µ2 µ3 µ4 µ5 µ6 11 22 33 44 55 66 Pk
i

i = 1 i i

k = 11 µij ii

i i

j i

i 

i+3

di,i+3 di,i+3


di,i+3 Ar ea158  di,i+3 d18 voli,i+1,i+2,i+3 ar ea158 di,i+3 d18 voli,i+1,i+2,i+3 ar ea158 5.15 + / - 0.20 6.99 + / - 0.57

d18

V oli,i+1,i+2,i+3

10.64 + / - 0.33 10.40 + / - 1.49 i

11.38 + / - 0.74 18.53 + / - 4.16 i+3 5.56 + / - 2.61

5.51 + / - 0.45

5.64 + / - 0.57 5.31 + / - 3.00

8.64 + / - 1.59

11.38 + / - 5.93

i, i + 1, i + 2

i+3

di,i+3 di,i+3 d18  Area158 d18 Area158 d18 V oli,i+1,i+2,i+3
11

di,i+3

 Area158

d18



  


7000

6000

Number of Sequences

5000

4000

3000

2000

1000

0 0

10

20

30

40 50 60 Sequence Length

70

80

90



8  leng th  82

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1

Curved Helix Regular Helix Kinked Helix

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4

Curved Helix Regular Helix Kinked Helix

Propensity

Propensity
2 3 4 5 6 7 8

0.2 1

2

3

4

5

6

7

8

Sequence Position

Sequence Position



4







3 3.5

Length 10 Length 15 Length 25

2.5

3

Length 10 Length 15 Length 25

2 Propensity Propensity 5 10 15 20 25

2.5

2

1.5

1.5

1 1 0.5

0.5

0 0

0 0

5

10

15

20

25

Sequence Position

Sequence Position



  10


16

i 
5


5 8