Computational Systems Biology Methods and Protocols.7z

2.2.4 Adapted Normal
Distribution Bi-profile
Bayes

The bi-profile Bayes feature extraction approach was first proposed

by Xu et al. [31], in which each peptide in a training dataset can be

encoded as (p 1 ,p 2 ,...,pn,pn+1,...,p 2 n), where (p 1 ,p 2 ,...,pn)

represents the posterior probability of each amino acid at each

position in the positive dataset and (pn+1,...,p 2 n) represents the

posterior probability of each amino acid at each position in the

negative dataset. The posterior probability is calculated as the

occurrence of each amino acid at each position in the training

dataset. This feature extraction approach was improved by encod-

ing the frequency of each amino acid at each position as random

variablesXij, wherei(i¼1,2,...,20) represents theith amino acid.

{A,C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W,Y} and

j(j¼1,2,...,L) represents thejth position. The random variables

Xij(i¼1,2,...,20;j¼1,2,...,L) are independent and obey the

same binomial distributionb(n,p), wheren¼339 is the number of

peptide sequences in the positive/negative dataset andp¼1/20 is

the probability of each amino acid occurring in each position.

According to the De Moivre-Laplace theorem [42], the normal

form variable

Xffiffiffiffiffiffiffiffiffiffiffiffiffiijnp

npðÞ 1 p

p has a limiting cumulative distribution func-

tion which approximates a normal distribution N(0,1). In

O-GlcNAcPRED [8], the standard variable normalization method

was modified to highlight and emphasize the distinct distribution

of each amino acid at the same position. IfVjdenotes the standard

variance ofXij(i¼1,2,...,20), i.e., the deviation of frequencies of

each amino acid at the samejth position, thenX^0 ij¼

Xijffiffiffiffiffinp

Vj

p denotes

the new normalization ofXijand ensures it obeys the standard

normal distribution. Thus, the posterior probability pj

(j¼1,2,...,2n) is coded by the adapted normal distribution as

follows:

pj¼P(XXij)¼φ(X^0 ij), whereφ(x) is the standard normal

distribution function given byφðÞ¼x p^1 ffiffiffiffi 2 π

Rx

1

e

t 22

dt.

2.2.5 Position-Specific
Scoring Matrix

Evolutionary information is an important characteristic of proteins,

because the conserved residues at specific sequence sites are under

strong selective pressure and therefore are always functionally rele-

vant [32–35]. In [9, 10], a position-specific scoring matrix (PSSM)

was used to encode the evolutionary information of a protein

sequence. The PSSM profiles were obtained by PSIBLAST searches

[36] against nonredundant sequences at O-GlcNAcylated sites.

The matrix of (2n+1)20 elements had rows centered on the

substrate sites (serine/threonine) extracted from the PSSM profile,

where 2n+ 1 represents the window size and 20 represents the

position-specific scores for each type of amino acid. Then, the

(2n+1)20 matrix was transformed into a 2020 matrix by

summing up the rows that were associated with the same type of

amino acid. Finally, every element in the 2020 matrix was

divided by the window length 2n+ 1 and then normalized using

240 Cangzhi Jia and Yun Zuo