CN111583990B - Gene regulation network inference method combining sparse regression and elimination rule - Google Patents
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Abstract
The invention provides a gene regulation network inference method combining sparse regression and elimination rules, which comprises the following steps: reading gene expression data; respectively establishing a sparse regression model of the gene expression data; acquiring the weight and external noise of each regulation gene according to the sparse regression model, and establishing a weight matrix of all the regulation genes; and implementing a weight elimination rule on the weight matrix, removing regulatory genes with smaller absolute values of weights according to the elimination rule, and constructing a gene regulatory network among genes for the rest genes in the gene expression data. The invention can not only rapidly infer a gene regulation network, but also determine the regulation relationship among specific genes. By combining advanced machine learning algorithms and optimization rules, a more accurate and efficient mathematical model is constructed to infer a gene regulation network from gene expression data.
Description
Technical Field
The invention relates to the field of gene regulation, in particular to a gene regulation network inference method combining sparse regression and elimination rules.
Background
With the development of high throughput sequencing technology, a large amount of gene expression data provides a reliable basis for research. The purpose of the deduced gene regulation network is to obtain a network structure formed by mutually regulating genes from gene expression data, so that the analysis of expression level and gene regulation relationship can be used for identifying pathogenic genes, thereby providing reference for the treatment of diseases. While many methods of inference already exist, it remains a significant challenge to infer gene regulatory networks using gene expression data due to complex regulatory relationships between genes.
Many researches are carried out on the research of gene regulation networks by scientific researchers, but most methods have two disadvantages. The method is mainly characterized in that whether a regulation relation exists between genes can only be deduced, whether the relation is activated or inhibited can not be determined, and in addition, the method is deduced in a large-scale gene regulation network, the calculation complexity is high, the operation speed is low, and an accurate gene regulation network can not be provided for identifying pathogenic genes.
Disclosure of Invention
The invention provides a gene regulation network inference method combining sparse regression and elimination rules, which aims to overcome the technical problems.
The invention provides a gene regulation network inference method combining sparse regression and elimination rules, which comprises the following steps:
s1: reading gene expression data, and determining target genes and corresponding control genes of each gene in the gene expression data;
s2: respectively establishing a sparse regression model of the gene expression data;
s3: acquiring the weight and external noise of each regulation gene according to the sparse regression model, and establishing a weight matrix of all the regulation genes;
s4: and eliminating part of the regulatory genes of the weight matrix and constructing a gene regulatory network among genes.
Further, the step S2 includes: establishing a sparse regression model according to the gene expression data types, wherein the types comprise a time sequence data set or a steady state data set;
further, constructing a sparse regression model on the time series dataset is:
wherein k is more than or equal to 1 and less than or equal to T-h,expressed as gene j at t k Gene expression value at time->At t for all genes excluding gene j k The gene expression value at the moment, the parameter h is the time step, the w is the weight, and the external noise;
the establishing of the sparse regression model for the steady state data set is as follows:
wherein M is more than or equal to 1 and less than or equal to M, x j m Expressed as the gene expression value, x, of the gene j under the mth environmental condition -j m For all genes excluding gene j, the gene expression value under the mth environmental condition, w is the weight and e is the external noise.
Further, the step S2 includes: dividing the gene expression data into a training data set and a test data set;
establishing a sparse regression model for the training data set; and bringing the weight and the external noise into a sparse regression model established for the test data set, and determining index evaluation data based on the weight and the external noise.
Further, the elimination rule includes: threshold rule (Threshold rule), bidirectional rule (Symmetric rule), and Chain rule (Chain rule); sequentially eliminating regulatory genes corresponding to weights in the weight matrix according to the sequence of a threshold rule, a bidirectional rule and a chain rule;
the invention can not only rapidly infer a gene regulation network, but also determine the regulation relationship among specific genes. By combining advanced machine learning algorithm and optimization rules, a more accurate and efficient gene regulation network is constructed.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a flowchart for establishing a sparse regression model for gene expression data and obtaining a weight matrix,
FIG. 3 is a process of applying the weight elimination rule of the present invention;
FIG. 4 is a graph of a gene regulation network plotted against a sparse weight matrix in an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a gene regulation network inference method combining sparse regression and elimination rules, as shown in fig. 1, which is an overall flow chart of the invention; the method comprises the following steps:
s1: reading gene expression data; according to the interaction relation among genes, each gene in the gene expression data can be used as a target gene, and genes except the target gene are regulatory genes with regulatory effects on the target gene;
s2: respectively establishing a sparse regression model of the gene expression data;
s3: acquiring the weight and external noise of each regulation gene according to the sparse regression model, and establishing a weight matrix of all the regulation genes;
s4: and implementing a weight elimination rule on the weight matrix, removing regulatory genes with smaller absolute values of weights according to the elimination rule, and constructing a gene regulatory network among genes for the rest genes in the gene expression data.
Further, in S2, a sparse regression model is established when the gene expression data is a time series data set or a steady state data set.
Further, constructing a sparse regression model on the time series dataset is:
wherein k is more than or equal to 1 and less than or equal to T-h,expressed as gene j at t k Gene expression value at time->At t for all genes excluding gene j k The gene expression value at the moment, the parameter h is the time step, w is the weight, and E is the external noise;
the establishing of the sparse regression model for the steady state data set is as follows:
wherein M is more than or equal to 1 and less than or equal to M, x j m Expressed as the gene expression value, x, of the gene j under the mth environmental condition -j m To exclude gene jThe gene expression value of the (c) is the weight, w is the external noise, and e is the gene expression value of the (c) under the mth environmental condition.
Further, in the step S2, the gene expression data is divided into a training data set and a test data set; and establishing a sparse regression model for the training data set, bringing the weight and the external noise into the sparse regression model established for the test data set, and performing index evaluation on the area under the curve of the precision rate and recall rate (AUPR score) or the area under the curve of the true case rate and false case rate (AUROC score) of the sparse regression model established for the test data set.
Specifically, first, a sparse regression-based feature is used to model gene expression data. Dividing the gene expression data into a training data set and a test data set; and establishing a sparse regression model for the training data set, and bringing the weight and the external noise into the sparse regression model established for the test data set.
As shown in fig. 2, there are two common data types for the gene expression data, namely a time series data set and a steady state data set, respectively, in order to perform a sparse regression model establishment on the gene expression data and obtain a weight matrix. Assume that the time series dataset is X TS ＝[x 1 ,...,x j ,...,x P ] T ∈R T×P T is the number of time points, P is the number of genes, x j ＝[x j 1 ,x j 2 ,...,x j T ] T The gene expression values of the gene j at T time points are included. Let the steady state dataset be X SS ＝[x 1 ,...,x j ,...,x P ] T ∈R M×P M is the number of environmental conditions, P is the number of genes, x j ＝[x j 1 ,x j 2 ,...,x j M ] T The gene expression values of the gene j under M environmental conditions are included. The sparse regression model is constructed for the time series dataset as follows:
wherein k is more than or equal to 1 and less than or equal to T-h,expressed as gene j at t k Gene expression value at time->At t for all genes excluding gene j k The gene expression value at the moment, the parameter h is the time step, w is the weight, and E is the external noise. The sparse regression model is constructed for the steady state dataset as follows:
wherein M is more than or equal to 1 and less than or equal to M, x j m Expressed as the gene expression value, x, of the gene j under the mth environmental condition -j m For all genes excluding gene j, the gene expression value under the mth environmental condition, w is the weight and e is the external noise. The linear regression based on sparse regression (Lasso) is adopted to calculate the functional relation g (, the Lasso regression enables the weight of genes to be reduced, even some weights with smaller absolute values to be directly changed into 0, so the method is particularly suitable for reducing the number of genes and selecting the genes, and is used for estimating a linear model of sparse parameters.
For a given gene j as a target gene, constructing a linear regression model using the formula (1) for time-series gene expression data, or constructing a linear regression model using the formula (2) for steady-state gene expression data, preliminarily obtaining weights w of all genes having a regulatory effect on the gene j j ＝[w 1,j ,...,w i,j ,...,w P,j ]∈R 1×P Wherein, the method comprises the steps of, wherein,if all genes are sequentially selected as target genes, we can obtain a weight matrix W= [ W ] 1 ,...,w j ,...,w P ] T ∈R P ×P . Weights w in the matrix i,j As the action intensity of the regulatory gene j on the target gene i thereof, the weight matrix W contains the action intensity of all regulatory genes on the target gene thereof. If matrix element w i,j > 0, representing gene i activating gene j; if w i,j < 0, representing that gene i has an inhibitory effect on gene j; if w i,j =0, representing that gene i has no effect on gene j.
The standard network corresponding to the gene expression data set contains the correct regulation relation of all the regulation genes to the target genes, wherein the activation is represented by '1', and the inhibition is represented by '0'. A threshold is selected for the weight matrix, and when a single weight is greater than the threshold, the regulatory relationship may be considered active, and when the weight is less than the threshold, the regulatory relationship may be considered inhibited. Comparing the weight matrix subjected to threshold processing with a standard network, wherein the result is a two-classification problem, and an confusion matrix containing four indexes, which are True Positive (TP), can be obtained; false Positive (FP); false Negative (FN); true Negative (TN). For example, a standard network of gene regulatory networks comprising 4 genes is:
TABLE 1
| A | B | C | D | |
| A | 1 | 0 | 0 | |
| B | 0 | 1 | 1 | |
| C | 1 | 0 | 1 | |
| D | 1 | 0 | 1 |
The weight matrix deduced by sparse regression is:
TABLE 2
| A | B | C | D | |
| A | 0.8 | 0.2 | -0.3 | |
| B | -0.2 | 0.3 | 0.5 | |
| C | 0.1 | -0.3 | 0.6 | |
| D | -2 | 0.2 | 0.5 |
If the threshold value of the weight matrix is-0.1, the weight matrix after threshold value processing is:
TABLE 3 Table 3
| A | B | C | D | |
| A | 1 | 1 | 0 | |
| B | 0 | 1 | 1 | |
| C | 1 | 0 | 1 | |
| D | 0 | 1 | 1 |
Sequentially comparing the weight matrix subjected to threshold processing with the result in the standard network to obtain a confusion matrix which is:
TABLE 4 Table 4
| Predictive value=0 | Predictive value = 1 | |
| True value=1 | TP＝1 | FN＝6 |
| True value=0 | FP＝3 | TN＝2 |
According to the four indexes in the confusion matrix, four other indexes can be obtained, wherein the four indexes are respectively accuracy precision=tp/(tp+fp); recall = TP/(tp+fn); true case rate tpr=tp/(tp+fn); false positive rate fpr=fp/(fp+fn). If a series of thresholds are selected for the weight matrix, a corresponding series of values of accuracy, recall, true case rate, false case rate can be obtained. There are two commonly used areas Under the Curve (AUC) for inferring the index of gene regulatory networks. One is the area under the precision and recall curves, i.e., the AUPR score; the other is the area under the true case rate and false case rate curves, i.e., the AUROC score. And drawing two curves according to the four indexes, and finally calculating the areas under the two curves. The general evaluation criteria for the area under the two curves are: the area is 0.5-0.7, and the effect is low; 0.7-0.85, the effect is general; 0.85-0.95, and has good effect; 0.95-1, the effect is very good; in this embodiment, 0.85-1 is used as an evaluation criterion, and if the areas under the two curves are within the range, the weight and the external noise of the sparse regression model established by the training data set are proved to be effective, and finally the weight matrix of all genes is obtained.
Further, the elimination rule includes: threshold rule (Threshold rule), bidirectional rule (Symmetric rule), and Chain rule (Chain rule); and eliminating the regulatory genes corresponding to the weights in the weight matrix in sequence of a threshold rule, a bidirectional rule and a chain rule.
Specifically, the application process of the weight elimination rule is shown in fig. 3. Assuming that one weight matrix obtained by sparse regression is shown in fig. 3, in this embodiment, taking five genes A, B, C, D and E as examples, the weight matrix obtained by passing the five genes through the sparse regression model sequentially implements the following three elimination rules: (1) threshold rule: if |w i,j Let w be equal to or less than T, T being the threshold value i,j =0, the threshold rule eliminates the direct regulatory relationship with smaller absolute weight; in this example, when the threshold value is 0.1 and the threshold rule is performed, the weight in the table (a) in fig. 3, in which the absolute value of the weight is 0.09 or less, indicates that there is no relationship between genes, and the table (b) is obtained. (2) Bidirectional rule: if |w i,j |≤|w j,i Let w i,j =0, the bi-directional rule eliminates mutual regulation and control relation with smaller absolute value of weight; and (3) eliminating the weight matrix (table (b)) processed by the threshold rule through the bidirectional rule to obtain a table (c). (3) Chain rule: if |w i,j |≤min[|w i,k |,|w k,j |]Let w i,j =0, the chain rule eliminates the indirect regulation relation with smaller absolute weight in table (c) to obtain table (d). It can be seen that 7 weak or non-existing regulatory relationships are eliminated altogether, so that the inferred network is more sparse and accurate.
Finally, as shown in fig. 4, a directed graph is drawn on the finally obtained sparse weight matrix in the table (d), and a gene regulation network among five genes is obtained. Arrows at gene nodes represent activation regulation, and filled dots at gene nodes represent inhibition regulation.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (3)
1. A gene regulation network inference method combining sparse regression and elimination rules is characterized by comprising the following steps:
s1: reading gene expression data, and determining target genes and corresponding control genes of each gene in the gene expression data;
s2: respectively establishing a sparse regression model of the gene expression data;
s3: acquiring the weight and external noise of each regulation gene according to the sparse regression model, and establishing a weight matrix of all the regulation genes;
s4: eliminating part of the regulatory genes of the weight matrix and constructing a gene regulatory network among genes; establishing a sparse regression model according to the gene expression data types, wherein the types comprise a time sequence data set or a steady state data set;
the sparse regression model is constructed for the time sequence data set as follows:
wherein k is more than or equal to 1 and less than or equal to T-h,expressed as gene j at t k Gene expression value at time->At t for all genes excluding gene j k The gene expression value at the moment, the parameter h is the time step, w is the weight, and E is the external noise;
the establishing of the sparse regression model for the steady state data set is as follows:
wherein M is more than or equal to 1 and less than or equal to M, x j m Expressed as the gene expression value, x, of the gene j under the mth environmental condition -j m For all genes excluding gene j, the gene expression value under the mth environmental condition, w is the weight and e is the external noise.
2. The method according to claim 1, wherein S2 comprises: dividing the gene expression data into a training data set and a test data set;
establishing a sparse regression model for the training data set; and bringing the weight and the external noise into a sparse regression model established for the test data set, and determining index evaluation data based on the weight and the external noise.
3. The method of claim 2, wherein the elimination rule comprises: threshold rule (Threshold rule), bidirectional rule (Symmetric rule), and Chain rule (Chain rule); and eliminating the regulatory genes corresponding to the weights in the weight matrix in sequence of a threshold rule, a bidirectional rule and a chain rule.
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