Thesis reading (57):2-hydr_ Ensemble: lysine 2-hydroxyisobutyrylation identification with ensemble method (task)

1 introduce

1.1 subject

  2021： Identification of lysine by integrated method 2- Hydroxyisobutyrylation (Lysine 2-hydroxyisobutyrylation identification with ensemble method)

1.2 summary

   Lysine 2- Hydroxyisobutyrylation is a new type of post-translational modification detected in proteomics . This modification research may contribute to the research and drug development of a variety of diseases . In this work , A new 2-hydr_Ensemble Residue identification algorithm , This residue has sequence information at the protein level . This method is compared with typical classification models . Results show HeLa cells 、 Spirococcus 、 Rice seeds , And Saccharomyces cerevisiae AUC The values reach... Respectively 0.9197、0.8192、0.9307, as well as 0.8897. The statistical characteristics of Bayes with two profiles are further used , Find out the potential information from several eigenvectors .

1.3 Bib

@article{
    Bao:2021:104351,
author		=	{
    Wen Zheng Bao and Bin Yang and Bai Tong Chen},
title		=	{
    2-hydr\_ensemble: Lysine 2-hydroxyisobutyrylation identification with ensemble method},
journal		=	{
    Chemometrics and Intelligent Laboratory Systems},
volume		=	{
    215},
pages		=	{
    104351},
year		=	{
    2021},
doi			=	{
    10.1016/j.chemolab.2021.104351}
}

2 Method

2.1 Modified residues

2.1.1 The correlation coefficient (CC)

   Pearson correlation coefficient is a linear correlation coefficient , It is generally used to correct the correlation between two variables of residues . For two gene sequences $X$ and $Y$, Pearson correlation coefficient The calculation is as follows ：
$$R_{X,Y}=\frac{\sum (X-\overline{X})(Y-\overline{Y})}{\sqrt{\sum (X-\overline{X}{)}^2(Y-\overline{Y}{)}^2}},\text{\hspace{1em}(1)}$$ among $\overline{X}$ Express $X$ Average value .

2.1.2 Partial correlation coefficient (PCC)

   Partial correlation coefficient is the correlation coefficient of two variables without the influence of other variables . Because the relationship between the two variables is very complex , May be affected by multiple variables , So the partial correlation coefficient is greater than CC Better choice .PCC According to its corresponding CC To define . Make $R$ Express CC matrix , Its inverse matrix is $R^{-1}$, be PCC The calculation for the ：
$$R_{X,Y}^{\prime }=\frac{R_{X,Y}^{-1}}{\sqrt{R_{X,X}^{-1}{R}_{Y,Y}^{-1}}}\text{\hspace{1em}(2)}$$

2.1.3 Conditional mutual information (CMI)

   Mutual information (MI) It can measure the non-linear correlation between modified residues and unmodified residues ：
$$I(X,Y)=\sum _{x\in X}\sum _{y\in Y}p(x,y)\log \frac{p(x,y)}{p(x)p(y)},\text{\hspace{1em}(3)}$$ among $p(x)$ yes $x$ Probability 、$p(x,y)$ It's the joint probability , They can be obtained by Gaussian kernel probability density estimation ：
$$p\left(x_i\right)=\frac{1}{N}\sum _{j=1}^N\frac{1}{(2\pi {)}^{n/2}{\sigma }_x^{n/2}}\exp \left(-\frac{1}{2}{\left(X_j-X_i\right)}^T{C}^{-1}\left(X_j-X_i\right)\right),\text{\hspace{1em}(4)}$$ among $C$ Express $X$ The covariance matrix of 、${\sigma }_x$ Express $C$ Standard deviation , as well as $n$ and $N$ It represents the number of genes and the number of gene expression points respectively . therefore ,MI It can be calculated as ：
$$I(X,Y)=\frac{1}{2}\log \left(\frac{{\sigma }_X^2{\sigma }_Y^2}{|C(X,Y)|}\right),\text{\hspace{1em}(5)}$$ among $|C(X,Y)|$ It's a determinant .
   However ,MI There are high estimate problems . therefore , Conditional mutual information (CMI) Proposed ：
$$CMI(X,Y|Z)=\sum _{x\in X,y\in Y,z\in Z}p(x,y,z)\log \frac{p(x,y\mid z)}{p(x\mid z)p(y\mid z)}.\text{\hspace{1em}(6)}$$ If two genes $X$$Y$ It's irrelevant , $CMI(X,Y|Z)=0$.

2.1.4 Maximum information coefficient (MIC)

   Maximum information coefficient (MIC) It is used to measure the linear or nonlinear relationship between two variables , It does not need to make assumptions about the distribution of data . Given a binary set , Where the data elements are ordered tuples $(a,b)$.$G$ It's a grid .$a$ and $b$ The maximum information gain of all meshes of size is calculated as ：
$$I^{\ast }(D,a,b)=\max I(D{|}_G),\text{\hspace{1em}(7)}$$ among $I(D{|}_G)$ Express $D{|}_G$ Mutual information of ,$M(D)$ yes $D$ Characteristic matrix of , It is calculated as ：
$$M(D{)}_{a,b}=\frac{I^{\ast }(D,a,b)}{\log (\min (a,b))}.\text{\hspace{1em}(8)}$$  $\max (M(D))$ It's genes $a$ and $b$ Between MIC, If the two genes are not related , Their MIC Will be equal to the 0.

2.2 Integration method

   In order to improve the accuracy of detecting directly modified residues , A new dual integration method is proposed ：
  1） Given contains $m$ Genes and $n$ Gene data set of sample points $D$, Generate $K$ Data sets $(D^1,D^2,\dots ,D^k)$;
  2） For datasets $D^i$,CC、PCC、CMI, as well as MIC It is used to directly calculate the correlation between genes , And get a list of four ranks $(G_{CC}^i,G_{PCC}^i,G_{CMI}^i,G_{MIC}^i)$, And integrate into $G^i$;
  3） Generate $(G^1,G^2,\dots ,G^k)$;
  4） Integrated as $G$.