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Inference of SNP-gene regulatory networks by integrating gene expressions and genetic perturbations.

Kim DC, Wang J, Liu C, Gao J - Biomed Res Int (2014)

Bottom Line: In the most of the network inferences named as SNP-gene regulatory network (SGRN) inference, pairs of SNP-gene are given by separately performing expression quantitative trait loci (eQTL) mappings.There are three main contributions.Second, the experimental results demonstrated that integration of multiple methods can produce competitive performances.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX 76019, USA.

ABSTRACT
In order to elucidate the overall relationships between gene expressions and genetic perturbations, we propose a network inference method to infer gene regulatory network where single nucleotide polymorphism (SNP) is involved as a regulator of genes. In the most of the network inferences named as SNP-gene regulatory network (SGRN) inference, pairs of SNP-gene are given by separately performing expression quantitative trait loci (eQTL) mappings. In this paper, we propose a SGRN inference method without predefined eQTL information assuming a gene is regulated by a single SNP at most. To evaluate the performance, the proposed method was applied to random data generated from synthetic networks and parameters. There are three main contributions. First, the proposed method provides both the gene regulatory inference and the eQTL identification. Second, the experimental results demonstrated that integration of multiple methods can produce competitive performances. Lastly, the proposed method was also applied to psychiatric disorder data in order to explore how the method works with real data.

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Related in: MedlinePlus

Optimization for adaptive lasso as a subroutine of Step 3.
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alg2: Optimization for adaptive lasso as a subroutine of Step 3.

Mentions: Adaptive lasso is defined as(15)arg min⁡bi,fi⁡//yi−biY−fiX//22+λ1//bi//1,wib+λ2//fi//1,wif,where(16)//bi//1,wib=∑jN/bij·wijb/,  //fi//1,wif=∑jN/fij·wijf/.In (16), penalty weights, vectors wib and wif, are defined as(17)wijb=/b^ij/−α, wijf=/f^ij/−β, ∀j={1,…,Mg},where and are estimated in Step 2 that yields a sparsity to fi but not bi. Zero coefficient of in Step 2 is not considered as an eQTL for gene i. So, zero yields zero wijf in (17), and then if wijf is zero, fij will never have nonzero value in adaptive lasso of Step 3 (16). The parameters α and β decide how much previous estimation such as or is reflected to next estimation of bij or fij. Therefore, fij that has smaller penalty weight wijf is more likely to have nonzero value. In addition, we consider a special case that α and β are set to zero supposing that (i) we do not give a penalty weight to bij or fij by setting wijb or wijf to 1 if or is nonzero and (ii) we do not estimate elements of bi or fi by setting wijb or wijf to infinity if or is zero. The solution is similar to Step 2 in which either bi or fi is optimized by coordinate descent algorithm but it is applied to solve both bi and fi in Step 3. Derivative of (15) with respect to bij yields(18)biYyjT−yiyjT+fiXyjT+λ1∂bij//bi//1,wib=bijyjyjT+(bi(−j)Y(−j)−yi+fiX)yjT+λ1∂bij//bi//1,wib,where bi(−j) indicates row vector bi whose jth element is removed and Y(−j) denotes matrix Y whose jth row is removed. After setting Cjb = (bi(−j)Y(−j) − yi + fiX)yjT and ajb = yjyjT, the update rule for bij is as follows:(19)bij={(−Cjb−wijb·λ1)ajbif  Cjb<−wijb·λ1,0if  /Cjb/≤wijb·λ1,(−Cjb+wijb·λ1)ajbif  Cjb>wijb·λ1.We can also estimate fij in similar way. After defining Cjf = (fi(−j)X(−j) − yi + biY)xjT and ajf = xjxjT, the update rule for fij is given as(20)fij={(−Cjf−wijf·λ2)ajfif  Cjf<−wijf·λ2,0if  /Cjf/≤wijf·λ2,(−Cjf+wijf·λ2)ajfif  Cjf>wijf·λ2.When bi and fi are updated, updated single element bij or fij immediately affects updating the next elements. In addition, updating order of elements can be changed since convex objective function is converged in any order of elements to update. Algorithm 2 shows the optimization procedure of adaptive lasso.


Inference of SNP-gene regulatory networks by integrating gene expressions and genetic perturbations.

Kim DC, Wang J, Liu C, Gao J - Biomed Res Int (2014)

Optimization for adaptive lasso as a subroutine of Step 3.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4127230&req=5

alg2: Optimization for adaptive lasso as a subroutine of Step 3.
Mentions: Adaptive lasso is defined as(15)arg min⁡bi,fi⁡//yi−biY−fiX//22+λ1//bi//1,wib+λ2//fi//1,wif,where(16)//bi//1,wib=∑jN/bij·wijb/,  //fi//1,wif=∑jN/fij·wijf/.In (16), penalty weights, vectors wib and wif, are defined as(17)wijb=/b^ij/−α, wijf=/f^ij/−β, ∀j={1,…,Mg},where and are estimated in Step 2 that yields a sparsity to fi but not bi. Zero coefficient of in Step 2 is not considered as an eQTL for gene i. So, zero yields zero wijf in (17), and then if wijf is zero, fij will never have nonzero value in adaptive lasso of Step 3 (16). The parameters α and β decide how much previous estimation such as or is reflected to next estimation of bij or fij. Therefore, fij that has smaller penalty weight wijf is more likely to have nonzero value. In addition, we consider a special case that α and β are set to zero supposing that (i) we do not give a penalty weight to bij or fij by setting wijb or wijf to 1 if or is nonzero and (ii) we do not estimate elements of bi or fi by setting wijb or wijf to infinity if or is zero. The solution is similar to Step 2 in which either bi or fi is optimized by coordinate descent algorithm but it is applied to solve both bi and fi in Step 3. Derivative of (15) with respect to bij yields(18)biYyjT−yiyjT+fiXyjT+λ1∂bij//bi//1,wib=bijyjyjT+(bi(−j)Y(−j)−yi+fiX)yjT+λ1∂bij//bi//1,wib,where bi(−j) indicates row vector bi whose jth element is removed and Y(−j) denotes matrix Y whose jth row is removed. After setting Cjb = (bi(−j)Y(−j) − yi + fiX)yjT and ajb = yjyjT, the update rule for bij is as follows:(19)bij={(−Cjb−wijb·λ1)ajbif  Cjb<−wijb·λ1,0if  /Cjb/≤wijb·λ1,(−Cjb+wijb·λ1)ajbif  Cjb>wijb·λ1.We can also estimate fij in similar way. After defining Cjf = (fi(−j)X(−j) − yi + biY)xjT and ajf = xjxjT, the update rule for fij is given as(20)fij={(−Cjf−wijf·λ2)ajfif  Cjf<−wijf·λ2,0if  /Cjf/≤wijf·λ2,(−Cjf+wijf·λ2)ajfif  Cjf>wijf·λ2.When bi and fi are updated, updated single element bij or fij immediately affects updating the next elements. In addition, updating order of elements can be changed since convex objective function is converged in any order of elements to update. Algorithm 2 shows the optimization procedure of adaptive lasso.

Bottom Line: In the most of the network inferences named as SNP-gene regulatory network (SGRN) inference, pairs of SNP-gene are given by separately performing expression quantitative trait loci (eQTL) mappings.There are three main contributions.Second, the experimental results demonstrated that integration of multiple methods can produce competitive performances.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX 76019, USA.

ABSTRACT
In order to elucidate the overall relationships between gene expressions and genetic perturbations, we propose a network inference method to infer gene regulatory network where single nucleotide polymorphism (SNP) is involved as a regulator of genes. In the most of the network inferences named as SNP-gene regulatory network (SGRN) inference, pairs of SNP-gene are given by separately performing expression quantitative trait loci (eQTL) mappings. In this paper, we propose a SGRN inference method without predefined eQTL information assuming a gene is regulated by a single SNP at most. To evaluate the performance, the proposed method was applied to random data generated from synthetic networks and parameters. There are three main contributions. First, the proposed method provides both the gene regulatory inference and the eQTL identification. Second, the experimental results demonstrated that integration of multiple methods can produce competitive performances. Lastly, the proposed method was also applied to psychiatric disorder data in order to explore how the method works with real data.

Show MeSH
Related in: MedlinePlus