A method for inferring gene regulatory network combining information theory and machine learning

Abstract

The application discloses a gene regulation network inference method combining information theory and machine learning, including obtaining time series of different gene expression processes, converting the time series into symbol sequences, calculating the symbol transition entropy between different gene symbol sequences, calculating the regulation gene set of each gene, constructing a model for the time series of a target gene and the time series set corresponding to the regulation gene set of the target gene and training the model, calculating the importance score of the regulation gene, screening the regulation gene with the importance score meeting a first threshold value and adding the regulation gene into a core regulation gene set; obtaining the symbol transition entropy of all core regulation genes to the target gene, combining the importance score and the symbol transition entropy of the core regulation gene into a regulation coefficient after normalization, screening the core regulation gene set meeting a second threshold value, and obtaining the core regulation gene set of all target genes. The method reduces the calculation complexity, solves the overfitting problem of the model based on machine learning, and improves the prediction accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of gene regulatory network, and particularly relates to a gene regulatory network inference method combining information theory and machine learning. BACKGROUND

[0002] Gene regulatory network refers to the mechanism for controlling gene expression at the cellular level in a living organism, and inferring the gene regulatory network and revealing its topological structure are helpful for understanding cell functions from the molecular level and have wide biological significance. However, due to the complexity and sparsity of biological networks, it is difficult to determine the regulatory effects between genes through experimental means, and the determination is also easily affected by various external uncertain factors. The rapid development of bioinformatics and the massive gene expression data provided by high-throughput sequencing technology provide researchers with new ideas, and in recent years, inferring gene regulatory networks by establishing computational models has become a research hotspot.

[0003] At present, the method for inferring gene regulatory network based on information theory is based on the correlation between genes, but cannot determine the directionality and dynamic characteristics of information transmission between genes, and the complexity of gene time series brings certain difficulty to calculation. Meanwhile, relying only on setting threshold to determine the reliability of regulatory effect is low.

[0004] The method based on machine learning often has problems such as overfitting of the trained model and poor generalization ability. When predicting a large-scale gene regulatory network without processing, the accuracy needs to be improved. SUMMARY

[0005] The present application provides a gene regulatory network inference method combining information theory and machine learning to overcome the above technical problems.

[0006] A gene regulatory network inference method combining information theory and machine learning, comprising

[0007] Step one, obtaining time series of different gene expression processes, respectively converting the time series of different genes into symbol sequences, obtaining a symbol sequence set of different genes, and respectively calculating the symbol transfer entropy between different gene symbol sequences;

[0008] Step two, calculating the regulatory gene set having regulatory effect on each gene, including taking each gene as a target gene in turn, taking the genes other than the target gene as a residual gene set, judging whether the genes in the residual gene set have regulatory effect on the target gene based on the symbol transfer entropy value of the genes in the residual gene set to the target gene and the symbol transfer entropy value of the target gene to the genes in the residual gene set, if the genes have regulatory effect, adding the genes having regulatory effect to the regulatory gene set of the target gene, and obtaining the regulatory gene set of each gene;

[0009] Step 3: For any target gene and its set of regulatory genes, construct the relationship between the time series of the target gene and the time series set corresponding to its set of regulatory genes. Construct a CatBoost model for the relationship and train it. Calculate the number of times each regulatory gene is used as a leaf node in the model during each training process. Use the number of times as the importance score of the regulatory gene. Sort the genes according to their importance scores and delete the regulatory genes whose importance scores do not meet the first threshold. Add the remaining regulatory genes to the core regulatory gene set. Normalize the importance scores of the core regulatory genes in the core regulatory gene set.

[0010] Step 4: Obtain the symbol transfer entropy of all core regulatory genes to the target gene and normalize it. Combine the normalized importance score and symbol transfer entropy of the core regulatory gene into the regulatory coefficient. When the regulatory coefficient of the core regulatory gene does not meet the second threshold, delete the core regulatory gene and obtain the set of core regulatory genes of the target gene.

[0011] Step 5: Repeat steps 3 and 4 until the core regulatory gene set of all target genes is obtained.

[0012] Preferably, the step of converting the time series of different genes into symbolic sequences includes converting the N-point time series X = {x} of the gene X expression process. i If , 1≤i≤N} are embedded in an L-dimensional phase space, then an L-dimensional vector X(i) = {x i ,x i+μ ,···,x i+(L-1)μ}, where μ is the time delay;

[0013] Calculate the root mean square of the difference between two adjacent points for each L-dimensional vector according to formula (1), and use it as the interval scale R(i).

[0014]

[0015] Using α×R(i) as the standard for sequence symbolization, where α is an adjustable parameter, each L-dimensional vector is transformed into an L-dimensional symbol sequence S according to formula (2). i (x i ),

[0016]

[0017] Where i = 1, 2, 3, ..., N-L+1, k = 0, 1, 2, ..., L-1, R(i) represents the mean and the interval scale of the i-th L-dimensional vector, respectively.

[0018] Preferably, the relationship between the time series of the constructed target gene and the time series set corresponding to its regulatory gene set is established according to formula (3).

[0019] p = w l q + ε l (3)

[0020] where p represents the time series of the target gene, q represents the time series set of the set of regulatory genes, w l is the weight vector of the regulatory genes, and ε l is random noise.

[0021] Preferably, the judging whether a gene in the remaining gene set has a regulatory effect on the target gene comprises if the gene in the remaining gene set is X, the target gene is Y, the signed transfer entropy value of the gene X in the remaining gene set to the target gene Y is STE X→Y , the signed transfer entropy value of the target gene Y to the gene X in the remaining gene set is STE Y→X , when STE X→Y < STE Y→X , the gene Y has a regulatory effect on the gene X.

[0022] Preferably, the judging whether a gene in the remaining gene set has a regulatory effect on the target gene further comprises if the genes in the remaining gene set are X and Y, the target gene is Z, the signed transfer entropy value between the genes X and Y in the remaining gene set is STE X→Y , the signed transfer entropy value of the gene X in the remaining gene set to the target gene Z is STE X→Z , the signed transfer entropy value of the gene Y in the remaining gene set to the target gene Z is STE Y→Z , when STE X→Z ≤ min[STE X→Y , STE Y→Z ], the regulatory effect of the gene X on the gene Z is excluded.

[0023] Preferably, the combining the normalized importance score of the core regulatory gene and the signed transfer entropy into a regulatory coefficient comprises representing the normalized importance score of the core regulatory gene as w j , representing the normalized signed transfer entropy of the core regulatory gene as w’ j , and combining according to formula (4) into a regulatory coefficient,

[0024]

[0025] where I j represents the regulatory coefficient.

[0026] The application provides a gene regulation network inference method combining information theory and machine learning, which symbolizes the expression process of genes, reduces the calculation complexity, uses a CatBoost model to construct the regulation between genes, obtains core regulation genes through twice screening, solves the overfitting problem of the model based on machine learning, and improves the prediction accuracy as a whole. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, below the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings described below are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0028] Figure 1 is a flow chart of the method of the present application. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0030] Figure 1 is a flow chart of the method of the present application, as shown in Figure 1 , the method of the present embodiment can include:

[0031] Step one, obtaining the time series of different gene expression processes, respectively converting the time series of different genes into symbol sequences, obtaining the symbol sequence set of different genes, and respectively calculating the symbol transfer entropy between different gene symbol sequences;

[0032] Respectively converting the time series of different genes into symbol sequences includes embedding the N-point time series X of the expression process of gene X into L-dimensional phase space, and then there is an L-dimensional vector X(i)={x i ,1≤i≤N}, i x i+μ ,···,x i+(L-1)μ}, and μ is the time delay;

[0033] According to formula (1), the root mean square of the difference between adjacent two points is calculated as the interval scale R(i),

[0034]

[0035] Using α×R(i) as the standard for sequence symbolization, where α is an adjustable parameter, each L-dimensional vector is transformed into an L-dimensional symbol sequence S according to formula (1). i (x i ),

[0036]

[0037] Where i = 1, 2, 3, ..., N-L+1, k = 0, 1, 2, ..., L-1, R(i) represents the mean and the interval scale of the i-th L-dimensional vector, respectively.

[0038] Calculating the symbol transfer entropy between different gene symbol sequences involves setting the symbol sequences of genes X and Y to x' and y', respectively, and calculating the symbol transfer entropy STE from gene Y expression to gene X expression according to formula (3). Y→X ,

[0039]

[0040] Where p(x) i+,1 ,x' i ,y' i )express x' i ,y' i The joint probability, p(x) i+,1 │x' i ,y' i ) indicates that in x' i ,y' i under the condition x i+,1 The conditional probability, p(x) i+,1 │x' i ) indicates that in x' i under the condition x i+,1 Similarly, the conditional probability can be used to calculate the symbolic transfer entropy (STE) from gene X expression to gene Y expression. X→y ;

[0041] Step 2: Calculate the set of regulatory genes that have a regulatory effect on each gene. This includes taking turns using each gene as the target gene and using the genes other than the target gene as the remaining gene set. Based on the sign transfer entropy value of the genes in the remaining gene set to the target gene and the sign transfer entropy value of the target gene to the genes in the remaining gene set, determine whether the genes in the remaining gene set have a regulatory effect on the target gene. If they have a regulatory effect, add the genes with regulatory effect to the set of regulatory genes of the target gene to obtain the set of regulatory genes for each gene.

[0042] Similarly, the symbolic transfer entropy (STE) from gene X expression to gene Y expression can be calculated.X→Y .

[0043] To visualize the correlation between the time series of genes, all the computed values of signed transfer entropy between two genes in different directions are put into a table with the first row and the first column being the same arranged gene names. Then the gene regulatory relationships are filtered according to the values of signed transfer entropy.

[0044] Firstly, based on the directionality of signed transfer entropy, if STE X→Y >STE Y→X , it is considered that gene Y has no regulatory effect on gene X (initial assumption that all genes have mutual regulatory effects). At the same time, previous studies have shown that indirect regulation often causes false predictions in the process of inferring gene regulatory networks. Here, based on the chain screening rule, if STE X→Z ≤min[STE X→Y ,STE Y→Z ], the regulatory effect of gene X on gene Z is excluded. The important gene set Q = {q1, q2, ···, q j} that has regulatory effect on the target gene P is sorted out.

[0045] Step three, for any target gene and its regulatory gene set, the relationship between the time series of the target gene and the time series set of its regulatory gene set is established according to formula (4),

[0046] p = w l q + ε l (4)

[0047] where p represents the time series of the target gene, q represents the time series set of the regulatory gene set, w l is the weight vector of the regulatory gene, and ε l is random noise.

[0048] A CatBoost model is constructed for formula (4) and trained. In the training process, CatBoost fits the unbiased gradient estimate calculated by the current model on the training sample by constructing a new decision tree, effectively solving the problems of model overfitting and prediction deviation. Each time the model is trained, for a specific target gene P, the important regulatory gene set Q = {q1, q2, ···, q j} are regarded as features, the number of times that all regulatory genes in each training process are taken as leaf nodes in the model is calculated, the number of times is taken as the importance score of the regulatory gene, the importance score is sorted, the regulatory gene whose importance score does not satisfy the first threshold value is deleted, the remaining regulatory genes are added to the core regulatory gene set, the importance scores of the core regulatory genes in the core regulatory gene set are normalized, the number of genes in the core regulatory gene set is m, the normalization is performed according to formula (5),

[0049]

[0050] wherein h j is the importance score of the jth gene, w j is the normalized importance score;

[0051] Step four, the symbolic transfer entropy of all core regulatory genes to the target gene is obtained, and normalized and represented as w' j The normalized importance score w j and the symbolic transfer entropy w' of the core regulatory gene j are combined into the regulatory coefficient I according to formula (6) j ,

[0052]

[0053] When the regulatory coefficient of the core regulatory gene does not satisfy the second threshold value, the core regulatory gene is deleted, and the core regulatory gene set of the target gene is obtained, wherein the value of the second threshold value is determined according to the regulatory strength of the genes in the standard gene regulatory network.

[0054] Step five, steps three and four are repeatedly executed until the core regulatory gene set of all target genes is obtained.

[0055] The overall beneficial effect is that the method can reduce the computational complexity, solve the overfitting problem of the model based on machine learning, and improve the prediction accuracy as a whole.

[0056] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for inferring gene regulatory networks combining information theory and machine learning, characterized in that, include Step 1: Obtain the time series of different gene expression processes, convert the time series of different genes into symbol sequences, obtain the symbol sequence sets of different genes, and calculate the symbol transfer entropy between the symbol sequences of different genes. Step 2: Calculate the set of regulatory genes that have a regulatory effect on each gene. This includes taking turns using each gene as the target gene and using the genes other than the target gene as the remaining gene set. Based on the sign transfer entropy value of the genes in the remaining gene set to the target gene and the sign transfer entropy value of the target gene to the genes in the remaining gene set, determine whether the genes in the remaining gene set have a regulatory effect on the target gene. If they have a regulatory effect, add the genes with regulatory effect to the set of regulatory genes of the target gene to obtain the set of regulatory genes for each gene. Step 3: For any target gene and its set of regulatory genes, construct the relationship between the time series of the target gene and the time series set corresponding to its set of regulatory genes. Construct a CatBoost model for the relationship and train it. Calculate the number of times each regulatory gene is used as a leaf node in the model during each training process. Use the number of times as the importance score of the regulatory gene. Sort the genes according to their importance scores and delete the regulatory genes whose importance scores do not meet the first threshold. Add the remaining regulatory genes to the core regulatory gene set. Normalize the importance scores of the core regulatory genes in the core regulatory gene set. Step 4: Obtain the symbol transfer entropy of all core regulatory genes to the target gene and normalize it. Combine the normalized importance score and symbol transfer entropy of the core regulatory gene into the regulatory coefficient. When the regulatory coefficient of the core regulatory gene does not meet the second threshold, delete the core regulatory gene and obtain the set of core regulatory genes of the target gene. Step 5: Repeat steps 3 and 4 until the core regulatory gene set of all target genes is obtained.

2. The gene regulatory network inference method combining information theory and machine learning according to claim 1, characterized in that, The step of converting the time series of different genes into symbolic sequences includes converting the N-point time series X = {x} of the gene X expression process. i If the vectors 1 ≤ i ≤ N are embedded in an L-dimensional phase space, then the L-dimensional vector X(i) = {x i ,x i+μ ,···,x i+(L-1)μ }, where μ is the time delay; The root mean square of the difference between two adjacent points of the i-th L-dimensional vector is calculated according to formula (1) and used as the interval scale R(i). Using α×R(i) as the standard for sequence symbolization, where α is an adjustable parameter, each L-dimensional vector is transformed into an L-dimensional symbol sequence S according to formula (2). i (x i ), Where i = 1, 2, 3, ..., N-L+1, k = 0, 1, 2, ..., L-1, R(i) represents the mean and the interval scale of the i-th L-dimensional vector, respectively.

3. The gene regulatory network inference method combining information theory and machine learning according to claim 1, characterized in that, The relationship between the time series of the constructed target gene and the time series set corresponding to its regulatory gene set is established according to formula (3). p=w l q+ε l (3) Where p represents the time series of the target gene, q represents the time series set of the regulatory gene set, and w l ε is the weight vector for regulating genes. l It is random noise.

4. The gene regulatory network inference method combining information theory and machine learning according to claim 1, characterized in that, The determination of whether genes in the remaining gene set have a regulatory effect on the target gene includes, if the gene in the remaining gene set is X and the target gene is Y, the symbol transfer entropy value of gene X to target gene Y is STE. X→Y The symbol transfer entropy of target gene Y to gene X in the remaining gene set is STE. Y→X When STE X→Y <STE Y→X Gene Y has a regulatory effect on gene X.

5. The gene regulatory network inference method combining information theory and machine learning according to claim 4, characterized in that, The determination of whether the genes in the remaining gene set have a regulatory effect on the target gene also includes, if the genes in the remaining gene set are X and Y, and the target gene is Z, the symbol transfer entropy value between genes X and Y in the remaining gene set is STE. X→Y The symbol transfer entropy value of gene X in the remaining gene set to target gene Z is STE. X→Z The symbol transfer entropy value of gene Y in the remaining gene set to target gene Z is STE. Y→Z When STE X→Z ≤min[STE X→Y STE Y→Z If the result is negative, then the regulatory effect of gene X on gene Z is excluded.

6. The gene regulatory network inference method combining information theory and machine learning according to claim 1, characterized in that, The process of combining the normalized importance score and symbol transfer entropy of the core regulatory gene into a regulatory coefficient includes expressing the normalized importance score of the core regulatory gene as w. j The normalized symbolic transfer entropy of the core regulatory genes is represented as w' j According to formula (4), they are combined into a control coefficient. Among them, I j This represents the control coefficient.

Images