New method of gene regulatory network integrating multi-omics data

Abstract

The application discloses a new method for gene regulation network combining multi-omics data, the method obtains a first matrix and a second matrix from transcriptome data; the first matrix contains transcription factors; the second matrix contains target expression profiles; prior knowledge of epigenetic omics data is obtained; using the first matrix, the second matrix and the prior knowledge, a relationship matrix of gene regulation is calculated through a regularization model; and a gene regulation network is generated using the relationship matrix. The application can improve the accuracy and stability of traditional gene regulation network inference methods by combining epigenetic omics and transcriptome data.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics, and in particular to a novel method for gene regulatory networks that combines multi-omics data. Background Technology

[0002] Gene regulatory networks are the regulatory systems governing gene expression in organisms. They control gene activity and expression levels, thereby determining cellular function and characteristics. Gene regulatory networks are complex structures composed of multiple regulatory factors and their target genes interacting with each other. Studying gene regulatory networks is crucial for understanding processes such as development, physiology, and disease in organisms. It can reveal the interactions and regulatory mechanisms between genes, helping us understand cellular function and tissue characteristics. Gene regulatory networks can be studied using various experimental techniques and computational methods. Experimental techniques include high-throughput omics methods such as epigenetics, transcriptomics, and proteomics, which can be used to identify interactions between genes and regulatory factors. Computational methods utilize mathematical models and computer algorithms to simulate and predict the structure and regulatory effects of gene regulatory networks. These methods can extract the roles of regulatory factors, the topological structure of gene regulatory networks, and the dynamic changes of regulatory networks from large-scale data.

[0003] In the era of network inference, reconstructing biological networks using big data has become a research hotspot in the life sciences. For example, extracting interactions between biomolecules from large-scale biological omics datasets can help predict unknown biological response mechanisms. A typical network inference workflow first involves estimating the relationships between variables based on preprocessed data, forming a correlation matrix. Then, hypothesis testing is used to determine which correlations are significant. Finally, significant correlations are constructed into a network representation, where nodes represent variables in the dataset and edges represent correlations.

[0004] Traditional methods, such as Bayesian, Boolean network, and other classic machine learning methods, use only transcriptome data and require hypothesis testing to determine which correlation coefficients are statistically significant. This test generates a p-value associated with each correlation coefficient and compares it to a given significance level threshold. Only when a correlation coefficient is statistically significant is a corresponding edge considered to exist. While this network inference process is simple, it has significant drawbacks that reduce the robustness and reproducibility of network inference. First, increasing the sample size significantly affects the statistical results; for example, a larger sample size results in a denser network. Second, different testing methods have different underlying assumptions, which may lead to completely different networks. Although these networks may be statistically sound, they may not effectively represent the underlying biological mechanisms.

[0005] In recent years, chromatin immunoprecipitation (ChIP) combined with high-throughput technologies, such as sequencing or microarray (ChIP-seq / ChIP-array, hereinafter referred to as ChIP-X) data, has been widely used to construct gene regulatory networks. However, the TF binding sites detected by ChIP-X only show the genomic location of TF binding, but cannot determine which gene is its target, or whether and how TF binding affects the transcription of its target. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems existing in related technologies. One of the purposes of this invention is to provide a new method for gene regulatory networks that combines multi-omics data, which can improve the accuracy and stability of traditional gene regulatory network inference methods by combining epigenetic and transcriptomic data.

[0007] The technical solution adopted in this invention is:

[0008] On one hand, embodiments of the present invention provide a novel method for gene regulatory networks that combines multi-omics data, comprising the following steps:

[0009] A first matrix and a second matrix are obtained from transcriptome data; the first matrix contains transcription factors; the second matrix contains target expression profiles.

[0010] Prior knowledge for acquiring epigenetic omics data;

[0011] Using the first matrix, the second matrix, and the prior knowledge, the gene regulation relationship matrix is ​​calculated through a regularization model;

[0012] Gene regulatory networks are generated using the aforementioned relationship matrix.

[0013] Furthermore, the prior knowledge for acquiring epigenetic data includes:

[0014] The epigenetic data were acquired; the epigenetic data included chromatin immunoprecipitation combined experimental data.

[0015] The epigenetic omics data are used as prior knowledge for the gene regulatory network inference model;

[0016] The prior knowledge is used to obtain the initialization matrix;

[0017] The penalty term is obtained using the prior knowledge.

[0018] Further, obtaining the initialization matrix using the prior knowledge includes:

[0019] In the absence of data from the combined chromatin immunoprecipitation experiment, the initialization matrix is ​​set to 0;

[0020] When the prior knowledge integrates the combined chromatin immunoprecipitation experimental data, if the transcription factor has a binding site around the promoter of a gene within 10 kilobase pairs, then the Pearson correlation coefficient between the expression profiles of the transcription factor and the gene is calculated, and the Pearson correlation coefficient is assigned to the initialization matrix.

[0021] Furthermore, obtaining the penalty term using the prior knowledge includes:

[0022] By incorporating the prior knowledge as an additional term into the loss function and mathematically adjusting the loss function, a sparse optimization model is obtained.

[0023] Penalty functions are used to control the regulatory relationship between transcription factors and genes.

[0024] Furthermore, the step of using the first matrix, the second matrix, and the prior knowledge to calculate the gene regulation relationship matrix through a regularization model includes:

[0025] Based on the first matrix, the second matrix, and the prior knowledge, obtain the optimized formula;

[0026] Based on the optimized formula, the gene regulation relationship matrix is ​​calculated using a regularization model.

[0027] Furthermore, the formula used to obtain the optimization formula based on the first matrix, the second matrix, and the prior knowledge includes:

[0028]

[0029] b=Ax+ε (1)

[0030]

[0031] Where 'a' is the first matrix, representing the expression profile matrix of n transcription factors in m samples, where 'a'... i Let i represent the expression level of the i-th transcription factor, where i ∈ [1, n];

[0032] b is the second matrix, representing the expression profile matrix of the target gene in m samples;

[0033] x in i This represents the adjustment relationship between the i-th element of the first matrix and the second matrix, where ε is the noise in the data;

[0034] Formula (2) is the optimization formula, where λ>0, and λ is the regularization parameter. It is a penalty function, and s is a parameter that controls the number of non-zero terms in x.

[0035] Furthermore, the formula used to calculate the gene regulation relationship matrix using a regularization model based on the optimized formula includes:

[0036]

[0037]

[0038]

[0039] The regularization model includes a first regularization model, a second regularization model, and a third regularization model;

[0040] Formula (3) is the optimization formula after using the first regularization model; Formula (3) is used to minimize the difference between Ax and b and maximize the sparsity of matrix x;

[0041] Formula (4) is the optimization formula after applying the second regularization model; where

[0042] Formula (5) is the optimized formula after applying the third regularization model; where

[0043] Furthermore, the formula used to calculate the gene regulation relationship matrix using a regularization model based on the optimized formula includes:

[0044]

[0045] Where, parameter η>0; x p This refers to the prior knowledge.

[0046] Furthermore, using the first matrix, the second matrix, and the prior knowledge, a gene regulation relationship matrix is ​​calculated through a regularization model. This relationship matrix includes:

[0047]

[0048] Furthermore, the novel method for gene regulatory networks combining multi-omics data also includes:

[0049] A gold standard network was constructed using high-throughput chromatin immunoprecipitation combined with transcriptome data.

[0050] On the other hand, embodiments of the present invention also provide an apparatus for implementing a novel gene regulatory network method combining multi-omics data, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the novel gene regulatory network method combining multi-omics data as described above.

[0051] On the other hand, embodiments of the present invention also provide a computer-readable storage medium storing a processor-executable program, which, when executed by a processor, is used to perform the novel gene regulatory network method combining multi-omics data as described above.

[0052] The beneficial effects of this invention are: it provides a novel method for gene regulatory networks combining multi-omics data. This method obtains a first matrix and a second matrix from transcriptome data; the first matrix contains transcription factors; the second matrix contains target expression profiles; prior knowledge of epigenetic data is acquired; using the first matrix, the second matrix, and the prior knowledge, a gene regulatory relationship matrix is ​​calculated through a regularization model; and a gene regulatory network is generated using the relationship matrix. This invention can improve the accuracy and stability of traditional gene regulatory network inference methods by combining epigenetic and transcriptomics data. Attached Figure Description

[0053] Figure 1 This is a flowchart of a novel gene regulatory network method combining multi-omics data provided in an embodiment of the present invention;

[0054] Figure 2 This is a flowchart of the new algorithm for inferring gene regulatory networks by combining prior knowledge, provided in this embodiment of the invention.

[0055] Figure 3 This is a framework diagram of the gene regulatory network inference algorithm that combines prior knowledge, provided in an embodiment of the present invention.

[0056] Figure 4 This is an experimental result diagram provided in an embodiment of the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0058] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0059] On the one hand, embodiments of the present invention provide a novel method for gene regulatory networks that combines multi-omics data.

[0060] This embodiment discloses a novel method for gene regulatory networks that combines multi-omics data. Specifically, refer to... Figure 1 The method includes the following steps:

[0061] S100. Obtain the first matrix and the second matrix from the transcriptome data; the first matrix contains transcription factors; the second matrix contains target expression profiles.

[0062] S200, Prior knowledge for obtaining epigenetic omics data;

[0063] S300. Using the first matrix, the second matrix, and prior knowledge, calculate the gene regulation relationship matrix through a regularization model.

[0064] S400: Gene regulatory networks are generated using relational matrices.

[0065] As an optional implementation, prior knowledge is introduced to better determine the significance condition of the correlation coefficient, i.e., the threshold for generating connections, thereby improving the quality of network inference. This embodiment first utilizes prior knowledge to connect known nodes that are definitely related, constructing a reference network. Then, after comparing the overlap between the (inferred) network under different thresholds and the auxiliary (reference) network constructed using prior knowledge, the network inference result with the best overlap is selected. The overlap is calculated using Fisher's exact test method based on true positives (appearing in both the related and reference networks), false positives (appearing only in the related network), true negatives, and false negatives. From the related network, the network with the highest overlap with the reference network is searched, and this network is extracted; this is the optimal network.

[0066] Transcription factor binding sites (TFBSs) can serve as prior knowledge for predicting gene regulatory networks by identifying potential binding sites on target genes or in known gene-gene interactions. Incorporating ChIP-seq / ChIP-array data of TFBSs recorded in vivo into gene regulatory network inference algorithms can help identify biologically meaningful solutions.

[0067] This invention specifically discloses the prior knowledge for obtaining epigenetic data in step S200, including:

[0068] S210. Obtain epigenetic data; epigenetic data includes data from combined chromatin immunoprecipitation experiments.

[0069] S220. Use epigenetic omics data as prior knowledge for gene regulatory network inference models;

[0070] S230. Obtain the initialization matrix using prior knowledge;

[0071] S240. Obtain a penalty item using prior knowledge.

[0072] This invention specifically discloses that in step S230, an initialization matrix is ​​obtained using prior knowledge, including:

[0073] S231. In the absence of combined chromatin immunoprecipitation experimental data, set the initialization matrix to 0;

[0074] S232. When prior knowledge includes integrated chromatin immunoprecipitation combined experimental data, if the transcription factor has a binding site around the promoter of a gene within 10 kilobase pairs, calculate the Pearson correlation coefficient between the expression profile of the transcription factor and the gene, and assign the Pearson correlation coefficient to the initialization matrix.

[0075] As an optional implementation, embodiments of the present invention initialize matrix X by using epigenetic data as prior knowledge for a gene regulatory network inference model. 0 A reference network was constructed by connecting known, necessarily related nodes. Specifically, ChIP-X (Chromatin Immunoprecipitation Combined Assay) identifies the in vivo activity of specific TFs and cell-specific TF (transcription factor) binding sites. Genes with active TF binding sites around their promoters are considered potential TF targets. Therefore, ChIP-X data provides possible direct TF target connections and may contribute to solutions for regularized models approximating the biological significance of the entire genome. Since matrix X describes the connections between TFs and targets, the TF target connections defined by the ChIP-X data are converted into an initial matrix.

[0076] Assume that the expression data of gene b can be obtained from n... The expression data prediction can be achieved by reconstructing the regulatory network using a linear system:

[0077] b = Ax + ε

[0078] in, x in i Let ε represent the regulatory relationship between the i-th TF and gene b, and let ε represent noise in the data. In this step, this embodiment of the invention uses ChIP-X as prior knowledge as the initialization matrix to solve for the expression data of gene b.

[0079] b = AX 0 +ε

[0080] Initialize matrix X without prior ChIP-X data. 0 It was artificially set to 0. When integrating ChIP-X data, if the TFi is a gene within 10 kbp (kilobits), it is considered a TFi gene. j If there are binding sites around the promoter, calculate the Pearson correlation coefficient (PCC) between the expression profiles of TFi and genej, and assign it to... PCC can be positive or negative, indicating that TF can activate or inhibit the expression of target genes.

[0081] This invention specifically discloses a method for obtaining a penalty term using prior knowledge in step S240, including:

[0082] S241. By adding prior knowledge as an additional term to the loss function and mathematically adjusting the loss function, a sparse optimization model is obtained.

[0083] S242. Use penalty functions to control the regulatory relationship between transcription factors and genes.

[0084] This invention specifically discloses that in step S300, a first matrix, a second matrix, and prior knowledge are used to calculate the gene regulation relationship matrix through a regularization model, including:

[0085] S310. Based on the first matrix, the second matrix, and prior knowledge, obtain the optimized formula;

[0086] S320. Based on the optimized formula, calculate the gene regulation relationship matrix using a regularization model.

[0087] This invention specifically discloses that in step S310, an optimization formula is obtained based on the first matrix, the second matrix, and prior knowledge. The formula used includes:

[0088]

[0089] b=Ax+ε (1)

[0090]

[0091] Where A is the first matrix, representing the expression profile matrix of n transcription factors in m samples, where a i Let i represent the expression level of the i-th transcription factor, where i ∈ [1, n].

[0092] b is the second matrix, representing the expression profile matrix of the target gene in m samples;

[0093] x in i This represents the adjustment relationship between the i-th element of the first matrix and the second matrix, where ε is the noise in the data;

[0094] Formula (2) is the optimization formula, where λ>0, and λ is the regularization parameter. It is a penalty function, and s is a parameter that controls the number of non-zero terms in x.

[0095] This invention specifically discloses that in step S320, a gene regulation relationship matrix is ​​calculated using a regularized model based on an optimized formula. The formula used includes:

[0096]

[0097]

[0098]

[0099] The regularization models include the first regularization model, the second regularization model, and the third regularization model;

[0100] Formula (3) is the optimization formula after using the first regularization model; Formula (3) is used to minimize the difference between Ax and b and maximize the sparsity of matrix x.

[0101] Formula (4) is the optimized formula after using the second regularization model; where

[0102] Formula (5) is the optimized formula after applying the third regularization model; where

[0103] This invention specifically discloses that in step S320, a gene regulation relationship matrix is ​​calculated using a regularized model based on an optimized formula. The formula used includes:

[0104]

[0105] Where, parameter η>0; x pIt is prior knowledge.

[0106] This invention specifically discloses that in step S300, a first matrix, a second matrix, and prior knowledge are used to calculate a gene regulation relationship matrix through a regularization model. The relationship matrix includes:

[0107]

[0108] This invention specifically discloses a novel method for gene regulatory networks that combines multi-omics data, and further includes:

[0109] S500, using high-throughput chromatin immunoprecipitation combined with transcriptome data to construct a gold standard network.

[0110] As an optional implementation, this embodiment of the invention uses eight machine learning algorithms, including five Lasso (minimum absolute shrinkage and selection operator) type algorithms and three Greedy algorithms. Prior information can be used as the initial matrix (Lasso+TFBS) or as a penalty term in the calculation process (prior Lasso / Greedy, pLasso / pGreedy), or both (pLasso+TFBS).

[0111] Table 1 provides a brief overview of eight machine learning algorithms, including five Lasso algorithms and three Greedy algorithms.

[0112]

[0113] As an optional implementation method, according to Figure 2 Workflow of a new algorithm for inferring gene regulatory networks by combining prior knowledge:

[0114] (A) Generate matrices A and B, containing TF and target expression profiles, respectively, from the transcriptome data; use the prior knowledge obtained from the ChIP-X data as the initialization matrix X. 0 Or the regularization penalty term x p .

[0115] (B) Using l0, l1 and l 1 / 2 Three regularization models are used to solve the gene regulation relationship matrix, Solution X, through the model's computational formula. * For each regularization model, a different algorithm can be used to solve it.

[0116] (C) Output sparse matrix Solution X * The interaction between TF-targets was described, gene regulatory networks were generated, and the results were evaluated using the gold standard.

[0117] As an optional implementation, embodiments of the present invention propose a sparse optimization model, called prior Lasso (pLasso), by incorporating prior knowledge as an additional term in the loss function and making mathematical adjustments to it, in order to include prior knowledge. Similarly, this optimization process can be applied to the Greedy algorithm, and using pLasso / pGreedy allows existing information to be considered during the computation process.

[0118] Assume that the expression data of gene b can be obtained from n... The expression data prediction can be achieved by reconstructing the regulatory network using a linear system:

[0119] b=Ax+ε (1)

[0120] in, x in i Let ε represent the regulatory relationship between the i-th TF and gene b, and ε represent noise in the data. Sparse optimization has been widely applied to various bioinformatics problems. This can be achieved by considering an appropriate penalty function. This is used to control the sparse structure in the solution x. It can be modeled as the following constrained optimization problem:

[0121]

[0122] Here, s is a parameter controlling the number of non-zero terms in x. Furthermore, through regularization techniques, the following optimization problem can be considered:

[0123]

[0124] Where λ>0 is the regularization parameter. Penalty function. Through regularization model l p Construction. Specifically, l p Including l0, l1 and l 1 / 2 Three models.

[0125] The l0 regularization model minimizes the difference between Ax and b, maximizing the sparsity of matrix x.

[0126]

[0127] Although the l0 regularization model is very close to the original problem that the embodiments of this invention aim to solve, achieving a globally optimal solution is difficult. Therefore, a popular relaxed l1 regularization model (LASSO) is introduced to address the following problem:

[0128]

[0129] in In many practical applications, the solutions obtained by the l1 regularization model are sparser than those obtained by the l0 regularization model.

[0130] Recently, l was proposed 1 / 2 A regularization model is proposed, and its performance is shown to be superior to that of the L1 regularization model:

[0131]

[0132] in Prior to this work, l0 and l 1 / 2 Regularized models were not used for inference in gene regulatory networks.

[0133] In the prior Lasso / Greedy method, in order to have prior knowledge x p To achieve a balance between the result and the outcome, an additional term is proposed, which can be expressed as follows:

[0134]

[0135] Where η>0 is a parameter used to balance the loss function and the distance between prior knowledge and the solution in the formula. Specifically, the embodiment of the present invention obtains the following through the objective function:

[0136]

[0137] Then (6) is equivalent to:

[0138]

[0139] As an optional implementation, embodiments of the present invention utilize prior knowledge x generated from ChIP-seq / chip data. p Combining this with b, we obtain the new response variable pLasso / pGreedy.

[0140] As an optional implementation method, according to Figure 3 This invention, incorporating a gene regulatory network inference algorithm framework based on prior knowledge, includes two frameworks: one using prior knowledge as the initial matrix and the other using prior knowledge as a penalty term. This invention utilizes five Lasso algorithms (ADMM, ADMM-Half, ADMM-Hard, SPG-L0, and SPG-L1) and three Greedy algorithms (OMP, CoSaMP, and Foba) for inference. Specifically, the Lasso algorithm can use prior knowledge as the initial matrix and as a penalty term to obtain three solution models: Lasso+TFBs, pLasso, and pLasso+TFBs; the Greedy algorithm can only use prior knowledge as a penalty term to obtain the pGreedy algorithm solution model.

[0141] The following section will introduce the five Lasso algorithms and three Greedy algorithms mentioned in the figure.

[0142] ADMM

[0143] The alternating direction method of multipliers is introduced to solve the l1 regularization problem, as an optimization problem (2). The penalty function. The idea behind ADMM is to apply Gaussian-Seidel decomposition to solve the joint minimization problem of the augmented Lagrangian function. By applying Gaussian-Seidel decomposition, the minimization of the augmented Lagrangian function can be calculated using an analytical formula consisting of the projected gradient descent step size, a soft threshold operator, and a multiplier update rule. The linear convergence rate of ADMM is established under the assumption of strong convexity or error constraints.

[0144] ADMM-Hard

[0145] Extended from ADMM, ADMM-Hard was introduced to solve the l0 regularization problem, as an optimization problem (2). The penalty function. The only difference from ADMM is the use of a hard thresholding operator instead of a soft thresholding operator. Global convergence and linear convergence of the sparse solution have been explored under the well-known RIP condition.

[0146] ADMM-Half

[0147] Similarly, ADMM-Half was developed, extending from ADMM, to solve the problem of... 1 / 2 The regularization problem, as an optimization problem (2) The penalty function replaces the soft thresholding operator in ADMM with a half-thresholding operator in each iteration. Within the framework of the splitting or descent method, global convergence of ADMM-Half to local minima can be guaranteed.

[0148] SPGL1

[0149] The Spectral Projection Gradient (SGPL1) method is proposed to solve the l1-constrained optimization problem (when the l1-constrained optimization problem (1.1) is in solution). SPGL1 is a projection gradient method for the Barzilai-Borwein step-size rule problem (1.1). It first performs a gradient descent step using a Barzilai-Borwein linear search scheme, and then projects onto the l1 norm sphere at each iteration. The effectiveness of the Barzilai and Borwein step-size rules in practice has been demonstrated by numerous studies, and the projection onto the l1 norm sphere is analytically expressed using a soft-thresholding operator, achieving efficient and simple computation. Furthermore, SPGL1 has a worst-case complexity of O(nlogn) and globally converges to the solution of problem (1.1).

[0150] SPGL0

[0151] The projected gradient method (called the M-sparse algorithm) is proposed to solve the l0-constrained optimization problem (when the l0-constrained optimization problem is in problem (1.1)). Inspired by the Barzilai and Borwein step-size rules, this invention proposes and applies SGPL0 (Spectral Projection Gradient Method) to solve it. The only difference from the M-sparse algorithm is the use of the Barzilai-Borwein step-size rule instead of a constant step size. SPGL0 can also be understood as an extension of SGPL1, where this invention uses a projection onto the M coefficients with the largest amplitude, instead of a projection onto the 10-norm sphere. Although the theory of SPGL0 has not yet been established, numerical results show that it can converge to local minima with high quality.

[0152] OMP

[0153] The Orthogonal Matching Pursuit (OMP) algorithm is introduced to recover high-dimensional sparse signals based on linear measurements with minimal noise. OMP is a forward greedy method for approximating solutions to l0-constrained optimization problems. The idea behind OMP is to iteratively select the 'a' columns most relevant to the current residual, thus achieving the most significant progress in each iteration to reduce the loss function and achieve sparsity. A major advantage of OMP is that it always explicitly uses sparse solutions, resulting in high computational efficiency. Furthermore, due to explicit sparsity, it does not significantly overfit the data. However, a major drawback is its inability to correct errors in early iterations.

[0154] CoSaMP

[0155] Compacted Sampling Matching Pursuit (CoSaMP) is an approximate algorithm proposed to solve the l0-constrained optimization problem. CoSaMP is ultimately based on OMP, but it incorporates sampling techniques to accelerate the algorithm and enjoys stronger theoretical guarantees than OMP. In each iteration of CoSaMP, some random samples are added to the set of selected features, and then an approximation is estimated from the selected feature set using a least-squares scheme. This process is repeated until a recoverable feature is found. CoSaMP has the advantage of fast implementation and overcomes the problem that OMP cannot correct. Under the assumption of RIP, CoSaMP converges to an approximate sparse solution to the l0-constrained optimization problem.

[0156] FoBa

[0157] Another method to compensate for the shortcomings of the forward greedy method in terms of correction capability is the so-called backward greedy method. The idea behind the backward greedy method is to train a complete model with all features and greedily remove one feature in each iteration (minimizing the increase in the loss function). The backward greedy method seems to solve the correction capability problem of the forward greedy method, but it is computationally expensive because it starts with a complete model with all features.

[0158] Combining the ideas of forward and backward greedy algorithms, Zhang designed an adaptive forward-backward greedy (FoBa) algorithm to solve the l0-constrained optimization problem. FoBa uses OMP (i.e., forward step) to select features and an adaptive backward step to eliminate any errors caused by the previous forward step. A backward step should be used when the increase in the loss function does not exceed half of the reduction in the loss function during the forward step. This backward step principle guarantees the elimination of any errors caused by the previous forward step and avoids eliminating the gains obtained in the forward step. FoBa can overcome the fundamental defects of forward and backward greedy methods and share their advantages of fast implementation.

[0159] FoBa converges to sparse solutions with high probability under RIP or SEC (sparse eigenvalue condition). Oracle inequalities are also provided to measure FoBa's feature selection accuracy and prediction accuracy. FoBa outperforms OMP and CoSaMP in sparse learning.

[0160] As an optional implementation, embodiments of the present invention apply an iterative threshold algorithm to solve the inference of gene regulatory networks based on omics data. p(p = 1, 1 / 2, 0) Regularization model. Iterative thresholding algorithms are one of the most widely studied first-order methods for solving sparse optimization problems. They are convergent and have very low computational complexity. This method has advantages such as simple formulas and small storage space, and can be well applied even to large-scale sparse optimization problems. For the l1 regularization problem, an iterative soft thresholding algorithm was proposed and developed; for the l0 regularization problem, an iterative hard thresholding algorithm was proposed; for the l... 1 / 2 For the regularization problem, an iterative half-threshold algorithm was designed. In short, in each iteration, all three algorithms initially have the same gradient step size:

[0161] Z k =X k -2vA T (Ax k -b) (8)

[0162] Then perform threshold calculations respectively:

[0163]

[0164]

[0165]

[0166] in

[0167] Here, Z represents a temporary variable in each iteration, serving as a temporary storage and update variable. In each iteration, it obtains the updated value of X by performing different types of threshold operations on the gradient step size. The superscripts of X and Z indicate the iteration number, and v represents the step size; in this study, v is set to 1 / 2. All three algorithms iteratively update the regularization parameter λ to maintain the sparsity of X. Since the number of TFs regulating a specific gene is usually unknown (the sparsity of X), biologists need to select a small number of TFs for experimental verification; therefore, this embodiment sets this parameter to be user-adjustable.

[0168] As an optional implementation, this embodiment of the invention uses transcriptome data downloaded from the Gene Expression Omnibus (GEO) for the research. This embodiment of the invention collects transcriptome data from 245 mESC perturbation experiments to infer gene regulatory networks.

[0169] As mentioned above, suppose the expression data of gene b can be obtained from n... The expression data prediction can be achieved by reconstructing the regulatory network using a linear system:

[0170] b = Ax + ε,

[0171] in, x ini Let ε represent the regulatory relationship between the i-th TF and gene b, and let ε represent noise in the data. In this step, this embodiment of the invention uses ChIP-X as prior knowledge as the initialization matrix to solve for the expression data of gene b.

[0172] b = AX 0 +ε,

[0173] From the above, the embodiments of the present invention yield the calculation formula for using prior knowledge as a penalty term:

[0174]

[0175] For the 19,978 genes in the transcriptome data, the embodiments of the present invention perform log2 transformation, which is used as gene expression data matrix b.

[0176] Regulatory factors (including TFs, mediators, co-factors, chromatin modifiers, and repressors) were collected from the TRANSFAC, JASPAR, UniPROBE, and TFCat databases and literature, resulting in 939 regulatory factors. The expression profiles of these regulatory factors were then used as matrix A.

[0177] Another gold-standard mESC network was constructed using high-throughput ChIP-X and transcriptome data. Specifically, for each TF (transfer agent), the binding sites of the TFs were retrieved using the Cisgenome tool. The distance truncation between the TF binding sites and potential target genes was set to 10 kbp. Differentially expressed genes under TF perturbation were defined as the top 5% of upregulated and downregulated genes, with significant expression changes (p < 0.05). Using this method, a TF-centric network was constructed for each TF and integrated into a gold-standard mESC network containing 13,092 nodes and 40,006 links. This embodiment of the invention collected 28 TFs with evidence from both high-throughput ChIP-X and perturbed transcriptome data, and constructed a gold-standard regulatory network containing these 28 TFs.

[0178] ChIP-X data provides potential TF-target connections, which can be used for prior knowledge of gene regulatory networks. Specifically, in this embodiment of the invention, the Pearson's correlation coefficient (PCC) values ​​between connected TF and target expression profiles in the ChIP-X data are calculated and assigned to matrix X. 0 In the matrix X 0 It is used as the initial matrix for the gene regulatory network inference model.

[0179] In the Prior Lasso / Greedy method, the TF and target expression profile PCC values ​​of the ChIP-X connected data can be assigned to matrix x. p In this context, the penalty term in the gene regulatory network inference model makes the generated results sparser.

[0180] This invention employs eight Lasso / Greedy-based algorithms to study gene regulatory network inference algorithms incorporating prior knowledge. These algorithms are ADMM, ADMM-Hard, ADMM-Half, SPG-L1, SPG-L0, OMP, CoSaMP, and FoBa, all of which have been described above. In practical application, this invention integrates these algorithms into the unpublished work GRNITools, using input matrix A and prior knowledge matrix X. 0 (x p By selecting the appropriate algorithm and using the default parameters (or by modifying the parameters), the corresponding calculation can be performed.

[0181] according to Figure 4 The experimental results in Tables 2 and 3 are presented below, and the experimental effects of this invention are as follows:

[0182] Table 2 Experimental Results

[0183]

[0184] Table 3 Experimental Results

[0185]

[0186] This invention uses mESC epigenetics data as prior knowledge to predict GRNs from the mESC bulk transcriptome. It was found that incorporating ChIP-seq / chip data as the initial matrix improved the performance of all Lasso-type inference methods, significantly increasing the AUROC from approximately 0.534 to 0.719–0.796, an increase of 34.6–49.1%. Furthermore, in addition to improving AUROC, prior information was also found to enhance the stability of ADMMHal and ADMMHard.

[0187] pLasso / pGreedy significantly improves the performance of all methods, increasing AUROC from approximately 0.5 to >0.7, and even to 0.88 for FoBa. Using prior data, the performance of the Lasso-type and Greedy algorithms ranks among the top of all traditional gene regulation network algorithms. When using the initial matrix, pLasso brings significant improvements to 8 methods with AUROC greater than 0.8.

[0188] On the other hand, embodiments of the present invention also provide an apparatus for implementing a novel gene regulatory network method that combines multi-omics data, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the novel gene regulatory network method that combines multi-omics data as described above.

[0189] The processor and memory can be connected via a bus or other means. Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0190] The non-transitory software program and instructions required to implement the novel gene regulatory network method combining multi-omics data in the above embodiments are stored in memory. When executed by the processor, the novel gene regulatory network method combining multi-omics data in the above embodiments is executed.

[0191] On the other hand, embodiments of the present invention also provide a computer-readable storage medium storing a processor-executable program, which, when executed by a processor, is used to perform the novel gene regulatory network method combining multi-omics data as described above.

[0192] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0193] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A novel method for gene regulatory networks combining multi-omics data, characterized in that, Includes the following steps: A first matrix and a second matrix are obtained from transcriptome data; the first matrix contains transcription factors; the second matrix contains target expression profiles. Prior knowledge for acquiring epigenetic omics data; Using the first matrix, the second matrix, and the prior knowledge, a gene regulation relationship matrix is ​​calculated through a regularization model, including: Based on the first matrix, the second matrix, and the prior knowledge, an optimization formula is obtained, including the following formulas: in, It is the first matrix, representing In each sample, The expression profile matrix of each of the transcription factors, wherein Indicates the first The expression levels of the aforementioned transcription factors, among which ; It is the second matrix, representing Expression profile matrix of target genes in each sample; In Indicates the first The adjustment relationship between the elements of the first matrix and the second matrix. It's noise in the data; Formula (2) is the optimization formula, where, >0, It is a regularization parameter. It is a penalty function. It is control The parameter for the number of non-zero terms; Based on the optimized formula, the gene regulation relationship matrix is ​​calculated using a regularized model. The formulas used include: The regularization model includes a first regularization model, a second regularization model, and a third regularization model; Formula (3) is the optimization formula after applying the first regularization model; Formula (3) is used to minimize The difference between them, maximize the matrix sparsity; Formula (4) is the optimization formula after applying the second regularization model; where ; Formula (5) is the optimized formula after applying the third regularization model; where ; Gene regulatory networks are generated using the aforementioned relationship matrix.

2. The novel method for gene regulatory networks combining multi-omics data according to claim 1, characterized in that, The prior knowledge for acquiring epigenetic data includes: The epigenetic data were acquired; the epigenetic data included chromatin immunoprecipitation combined experimental data. The epigenetic omics data are used as prior knowledge for the gene regulatory network inference model; The prior knowledge is used to obtain the initialization matrix; The penalty term is obtained using the prior knowledge.

3. The novel method for gene regulatory networks combining multi-omics data according to claim 2, characterized in that, The process of obtaining the initialization matrix using the prior knowledge includes: In the absence of data from the combined chromatin immunoprecipitation experiment, the initialization matrix is ​​set to 0; When the prior knowledge integrates the combined chromatin immunoprecipitation experimental data, if the transcription factor has a binding site around the promoter of a gene within 10 kilobase pairs, then the Pearson correlation coefficient between the expression profiles of the transcription factor and the gene is calculated, and the Pearson correlation coefficient is assigned to the initialization matrix.

4. The novel method for gene regulatory networks combining multi-omics data according to claim 2, characterized in that, The process of obtaining the penalty term using the prior knowledge includes: By incorporating the prior knowledge as an additional term into the loss function and mathematically adjusting the loss function, a sparse optimization model is obtained. Penalty functions are used to control the regulatory relationship between transcription factors and genes.

5. The novel method for gene regulatory networks combining multi-omics data according to claim 1, characterized in that, The formula used to calculate the gene regulation relationship matrix using a regularization model based on the optimized formula includes: Among them, parameters ; This refers to the prior knowledge.

6. The novel method for gene regulatory networks combining multi-omics data according to claim 5, characterized in that, The first matrix, the second matrix, and the prior knowledge are used to calculate the gene regulation relationship matrix through a regularization model. The relationship matrix includes:

7. The novel method for gene regulatory networks combining multi-omics data according to claim 1, characterized in that, The novel method for gene regulatory networks that combines multi-omics data also includes: A gold standard network was constructed using high-throughput chromatin immunoprecipitation combined with transcriptome data.

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