Three types of associations were considered for a pair of gene: GG, EG, and EE associations. Using pCastNet (partial Correlation analysis of splicing transcriptome Network), the Pearson correlation coefficient for GG associations was calculated between gene 1 (g₁) and gene 2 (g₂) and denoted as rg1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGNbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347F@. For EG associations, considering an exon (e₁) of gene 1 (g₁) and gene 2 (g₂), as well as the Pearson correlation coefficient re1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347D@, the partial correlation coefficient between e₁ and g₂ conditioning on g₁ was calculated as re1g2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DF@. The partial correlation can be interpreted as the association between e₁ and g₂ after removing the effect of g₁. If the partial correlation is high, the association between e₁ and g₂ is not due to the correlation between g₁ and g₂. Otherwise, e₁ can be a constitutive exon of g₁ and the association between e₁ and g₂ is due to the correlation between the two genes. For EE associations, the correlation between an exon (e₁) of gene 1 (g₁) and an exon (e₂) of gene 2 (g₂) was calculated as re1e2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347B@. We also calculated the partial correlations re1e2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DD@, re1e2•g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleqaaaaa@37DE@ and re1e2•g1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbeaaaaa@39BB@ to exclude the possibility that the EE correlation is due to the EG or GG correlation. In summary, if the p-value for rg1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGNbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347F@ is significant, we declared a GG link between gene 1 and gene 2. If the p-values for both re1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347D@ and re1g2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DF@ are significant, we declared an EG link between e₁ and g₂. This association is not due to GG association. If the p-values for re1e2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347B@, re1e2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DD@, re1e2•g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleqaaaaa@37DE@, and re1e2•g1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbeaaaaa@39BB@ are significant, we declared an EE link between the two exons e₁ and e₂. The association is not due to GG or EG associations.

We performed simulation studies to illustrate the relative performance of pCastNet. A total of five genes were considered. Each of them has five constitutive exons and one alternative exon. The five alternative exons have the same inclusion rate relative to their gene levels. Thus, the five alternative exons are co-spliced. Exon intensity data were simulated for ten tissues. Gene-level intensity was estimated as the average intensity of the five constitutive exons for each gene. In pCastNet, the correlation and partial correlations between each pair of exons belonging to different genes were calculated as re1e2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347B@, re1e2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DD@, re1e2•g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleqaaaaa@37DE@, and re1e2•g1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbeaaaaa@39BB@. In the NI-based approach, the correlation between the NI values of each pair of exons across ten tissues was calculated as r. Different p-value thresholds were used to declare whether there is a co-splicing relationship between two exons. Figure 1 shows the ROC (receiver operating characteristic) curves of pCastNet (red) and the NI-based approach (black). Three scenarios were considered: the standard deviation of the exon intensity is 1 (circles), 2 (triangles), or 4 (crosses). pCastNet consistently performed better than the NI-based approach. When the variance of the exon intensity is large (2² or 4²), the power (true positive rate) of pCastNet is almost 50-100% higher than that of the NI-based approach given the same false positive rate. The true positive rates and the false positive rates are the average values across 1,000 simulations for each scenario.

The choice of significance threshold remains a major challenge for co-expression network studies. Previous studies have typically relied on a data-independent constant correlation threshold. Zhang and Horvath 23 proposed a weighted gene co-expression network approach. They used soft thresholding instead of hard thresholding to better identify GG links. This method needs a scale-free topology criterion to estimate the involved parameters. Other topology-based approaches include clustering coefficient-based threshold selection developed by Elo et al 24. Because there has been little study on the topology of alternative splicing regulatory networks, we avoided topology-based methods and instead propose a false discovery rate (FDR) approach. Specifically, we used the approach proposed by Efron 25 to control the expected FDR conditioning on a dependence effect parameter A. For GG, EG, and EE networks, hypotheses were performed to test the significance of pair-wise correlations. The dependence among hypotheses is largely ignored in traditional FDR control methods 2627, despite the fact that correlations among hypotheses may be high for genomics studies 28. In contrast, the conditional false discovery expectation takes the dependence of hypotheses into account and, therefore, achieves a more accurate estimate of FDR. For GG links, t-test statistics (rg1g2(n−2)/(1−rg1g22) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGNbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaGcdaGcaaqaaiaacIcacaqGUbGaeyOeI0IaaGOmaiaacMcacaGGVaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaSqaaiaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbaGaaGOmaaaakiaacMcaaSqabaaaaa@41EE@) were converted to z-values directly. For EG and EE links, t-test statistics (re1g2(n−2)/(1−re1g22) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaGcdaGcaaqaaiaacIcacaqGUbGaeyOeI0IaaGOmaiaacMcacaGGVaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaSqaaiaabwgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbaGaaGOmaaaakiaacMcaaSqabaaaaa@41EA@, re1g2•g1(n−3)/(1−re1g2•g12) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaOWaaOaaaeaacaGGOaGaaeOBaiabgkHiTiaaiodacaGGPaGaai4laiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleaacaaIYaaaaOGaaiykaaWcbeaaaaa@48AF@, re1e2(n−2)/(1−re1e22) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaaSqabaGcdaGcaaqaaiaacIcacaqGUbGaeyOeI0IaaGOmaiaacMcacaGGVaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaSqaaiaabwgadaWgaaadbaGaaGymaaqabaWccaqGLbWaaSbaaWqaaiaaikdaaeqaaaWcbaGaaGOmaaaakiaacMcaaSqabaaaaa@41E6@, re1e2•g1(n−3)/(1−re1e2•g12) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaOWaaOaaaeaacaGGOaGaaeOBaiabgkHiTiaaiodacaGGPaGaai4laiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleaacaaIYaaaaOGaaiykaaWcbeaaaaa@48AB@, re1e2•g2(n−3)/(1−re1e2•g22) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleqaaOWaaOaaaeaacaGGOaGaaeOBaiabgkHiTiaaiodacaGGPaGaai4laiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleaacaaIYaaaaOGaaiykaaWcbeaaaaa@48AD@, and re1e2•g1g2(n−4)/(1−re1e2•g1g22) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbeaakmaakaaabaGaaiikaiaab6gacqGHsislcaaI0aGaaiykaiaac+cacaGGOaGaaGymaiabgkHiTiaabkhadaqhaaWcbaGaaeyzamaaBaaameaacaaIXaaabeaaliaabwgadaWgaaadbaGaaGOmaaqabaWccqGHIaYTcaqGNbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqaaiaaikdaaaGccaGGPaaaleqaaaaa@4C68@) were first converted to z-values. The distribution of the minimum absolute z-value was estimated by a multivariate normal distribution; then, the minimum absolute z-value was further transformed to final z-values. Under the null hypotheses, the final z-values follow the standard normal distribution. By comparing the histogram of z-values and the standard normal distribution, we can estimate the dispersion parameter A that reflects the dependence among hypotheses. Then we can calculate the conditional FDR. However, the number of declared links is very sensitive to the conditional FDR threshold (Table 1). Therefore, instead of applying a threshold on the conditional FDR directly, we estimated the sparseness of a network according to the conditional FDR and then chose a threshold on the sparseness. The sparseness of a network is defined as the percentage of true links among all possible node pairs. The threshold selection has several advantages: first, the corresponding correlation thresholds are data dependent; second, we can derive an accurate estimate of the number of falsely declared links taking into consideration the dependence among hypotheses; and third, we can integrate prior information about the sparseness of networks if this information is available. Here we chose the sparseness threshold as 0.02%; this threshold corresponds to a reasonable conditional FDR and total number of declared GG, EG, and EE links. We also tried thresholds of 0.01% and 0.005%. The results discussed in the remaining of this paper are similar, although the number of links differs significantly (Table 1).

To study alternative splicing regulatory networks, we considered exon array data for human, mouse, and rat. For each organism, RNA samples from 11 tissues were profiled using Affymetrix exon arrays. The raw data were downloaded from the Affymetrix website 29 and the gene-level and the exon-level expressions were summarized using Affymetrix Power Tools.

GG association is the traditional GG co-expression association. EG association can be treated as the association between an alternatively spliced exon and its upstream regulators or its downstream target genes, which may not necessarily be direct regulators or direct target genes. Sophisticated models incorporating additional experiments (for example, CLIP experiments) are needed to infer the direct regulators or targets. EE association can be treated as the association between two alternatively spliced exons. The two exons could be regulated by the same direct or indirect splicing regulators. Another scenario could be that a specific transcript isoform of gene 1, which uniquely contains alternative exon 1 compared to other transcript isoforms of gene 1, regulates the exon of gene 2. The latter case is a special exon-transcript association and 'transcript' here represents a particular transcript isoform instead of a family of gene splice variants. The above possible regulation relationships for EG and EE links are diagrammed in Additional data file 2. Additional data file 3 shows the Venn diagram of gene pairs with GG, EG, or EE associations. If GG links mainly reflect the transcriptional regulatory network whereas EG and EE links mainly reflect the alternative splicing regulatory network, it shows that these two networks are largely independent of each other.

If an exon has association links with other exons or genes and such correlations are not due to the GG association, this exon is expected to be an alternatively spliced exon. Otherwise, if the exon is a constitutive exon that has a similar expression level to its gene, the EE or EG correlation is due to the GG correlation. We are interested to know whether EG or EE links can reflect the alternative splicing status of exons. Using the human data as an example, non-redundant transcript annotations were assembled from 14 sources (see details in Materials and methods). These transcripts may be experimentally verified or just computationally predicted. Two groups of exons were then assembled from the large pool of transcript annotations: exons that are present in ≥ 14 transcript isoforms and are not spliced out in any transcript isoform; exons that are present in ≥ 7 transcript isoforms and are spliced out in another ≥ 7 transcript isoforms. The first exon group can be treated as constitutive exons and the second exon group can be treated as alternative exons. Figure 2 shows boxplots of the EG and EE links that the two groups of exons have; exons in group 2 clearly have more EG and EE links than exons in group 1. Specifically, for exons in group 1, 12% have ≥ 5 EG links and 11% have ≥ 50 EE links. For exons in group 2, the percentages increase to 23% for EG links and 21% for EE links. One-sided Wilcoxon tests show that exons in group 2 tend to have more EG and EE links with p-values < 2.2 × 10^-16.

It has been reported that the conservation level of alternative exons is lower than that of constitutive exons 30. On the contrary, the intronic regions flanking alternative exons are more conserved than those flanking constitutive exons 3031. To assess whether exons with links to other exons (or genes) tend to be alternatively spliced, we plotted the conservation scores of exons and their flanking regions (Figure 3). Exons were divided into three groups: exons with node degree = 0 (black lines); exons with node degree > 0 and the node degree is in the top 10% of all non-zero node degrees (green lines); exons with node degree > 0 and the node degree is not in the top 10% list (red lines). Node degree is defined as the number of links that a node has to other nodes in the network. Here it represents the number of links that an exon has to other genes (EG) or exons (EE). The average PhastCons conservation score at each exon and flanking region position was calculated and plotted for the three exon groups. Exons with EG or EE links tend to be less conserved than exons without EG or EE links. The flanking intronic regions of exons with EG or EE links tend, however, to be more conserved than those of exons without EG or EE links, which is possibly related to the enriched cis-splicing regulatory elements in intronic regions. The more links an exon has, the less it is conserved and the more its flanking intronic regions are conserved. For Affymetrix exon arrays, an exon may represent a cluster of overlapping exons from transcript isoforms with different 5' or 3' splicing sites. The boundary of such an exon cluster may not be the real boundary of the exon in a cell. To eliminate this bias, we removed exons with more than one probe selection region (that is, exons with more than one pair of splicing sites). The results are similar (data not shown).

The relative position from 5' to 3' was calculated for each exon, ranging from 0 to 1. The relative positions were partitioned into 10 windows. The proportion of exons with relative positions falling in each window was counted for exons with or without EG (EE) links and denoted as p₁ or p₂, respectively. Figure 4 plots the ratio between p₁ and p₂ for each relative position window. It clearly shows that exons with EG or EE links tend to be enriched in the initial or terminal regions. Alternative promoters and alternative polyadenylation sites are two of the most prevalent mechanisms for generating transcript isoforms by including alternative first or last exons. Recent studies suggest that 30-50% of human and approximately 50% of mouse genes have multiple alternative promoters 3233343536. In addition, about 54% of human and 32% of mouse genes have alternative polyadenylation sites 37. Exons with links to other genes or other exons are very likely to be alternatively spliced. Many of them, therefore, are close to the initial or the terminal regions of genes.

We assembled exons with node degrees ranking in the top 1% in the EG network or the EE network. The DAVID functional annotation tool 38 was used with genes to which hub exons belong. The same was done for genes with node degrees ranking in the top 1% in the GG network. Table 2 lists the enriched annotation terms with at least five gene counts, with p-values after Bonferroni's correction ≤ 0.001, and that appear at least twice in the nine groups (EG, EE, and GG for human, mouse, and rat). Bonferroni's correction is a very stringent multiple comparison correction. Here it restricts the probability of having one or more falsely declared significant annotation terms to ≤ 0.001. The term 'alternative splicing' is a UniProt knowledgebase keyword meaning 'protein for which at least two isoforms exist due to distinct pre-mRNA splicing events'; it is enriched in genes with hub exons for all of the EG and EE networks. The Uniprot sequence feature 'splice variants' is also enriched in these hub exons. However, 'alternative splicing' and 'splice variants' are not enriched in the gene hubs of the GG networks.

We experimentally examined the pCastNet results by RT-PCR across various tissues. In particular, the EE link is a relatively new correlation subject (in biology) and a very interesting phenomenon. We randomly chose EE links at the lower bound of the correlation cut-off (about 0.75-0.80) but favored cassette exons because of the ease of RT-PCR design. Due to the nature of our data, we also favored genes that are expressed in multiple tissues in order for PCR to amplify with the same number of cycles across the tissues. pCastNet found significant EE links among Kinesin-associated protein 3 (Kifap3) exon 20 (exon id 24930 in Affymetrix exon array), Suppression of tumorigenicity 7 (St7) exon 7 (exon id 685163), and Mitogen-activated protein kinase kinase kinase 7 (Map3k7) exon 12 (exon id 572746). For convenience, we refer to these exons as Kifap3_20, St7_7, and Map3k7_12. Specifically, pCastNet predicted that Map3k7_12 has negative associations with both Kifap3_20 and St7_7 (correlations and partial correlations are about -0.75 for both), whereas Kifap3_20 has a positive association with St7_7 (correlation and partial correlations are about 0.80). NCBI EST database shows these exons are all alternative exons. Primers were designed in the flanking constitutive exons to amplify transcripts either containing or skipping these alternative exons. RT-PCR results and Pearson correlation analysis of exon inclusion levels (Figure 5b) show that Map3k7_12 is negatively correlated with both Kifap3_20 and St7_7 while Kifap3_20 is positively correlated with St7_7 in these tissues. Besides the tissues surveyed in the exon array study, we also performed RT-PCR experiments in seven other tissues (Figure 5d). Based on the RT-PCR experiments, the correlation between Kifap3_20 and St7_7 is 0.60 and the correlation between Map3k7_12 and St7_7 is -0.82 whereas the correlation between Map3k7_12 and Kifap3_20 dropped to -0.29. Another example is a positive correlation between Solute carrier family 35, member B3 (Slc35b3) exon4 (exon id 226950, or Slc35b3_4) and Retinoic acid induced 14 (Rail4) exon 11 (exon id 300782, or Rai14_11). pCastNet predicts a positive association between these two exons (correlation and partial correlations are about 0.80). RT-PCR and Pearson correlation analysis (Figure 5c) show a positive correlation of 0.75 among the tested tissues used by the Affymetrix exon array. In the second set of tissues, RT-PCR experiments show that their correlation is about 0.87 (Figure 5e). Note that Slc35b3 is not detectable in bladder, and thus has not been included in the correlation analysis.

All of the above results indicate that pCastNet can effectively identify EG and EE links. We then further explored the possible functional relationship between two genes with an EG link or an EE link. Using the human data and the Molecular Signatures Database 39, genes were grouped into gene sets according to: their chromosome positions; curated information from pathway databases; shared conserved cis-regulatory motifs; and shared Gene Ontology (GO) terms. We tested whether genes with EG or EE links tend to be in the same gene sets using hypergeometric tests. The results are summarized in Table 3. Genes in the same chromosomal cytogenetic band ('c1') are more likely to have GG and EG links than EE links. Gene pairs with GG, EG, or EE links tend to be in the same pathways (these pathways are collected by the BioCarta, GenMAPP, and KEGG databases). More interestingly, gene pairs with EG or EE links tend to be in the same motif gene sets ('c3'). Specifically, genes in those sets share a motif in the promoter regions ('c3_promoter_known' and 'c3_promoter_unknown') or a microRNA (miRNA) binding site in the 3' untranslated regions ('c3_miRNA'). On the contrary, the p-values of GG links in the promoter motif sets are less significant than those of EG and EE links. And gene pairs with GG links are not enriched in the 'miRNA binding' gene sets. In addition, exons with EE links and sharing miRNA binding motifs tend to be enriched at the 3' terminals of the genes (Additional data file 4). Finally, genes with GG, EG or EE links all tend to share GO terms.

We also examined p-values for the enrichment of links in each individual gene set. We counted the number of GG, EG, or EE links between members of a gene set for each gene set. To test the significance of the enrichment of links, we simulated gene sets by randomly selecting the same number of genes. The simulated gene sets have no functional similarity. We then calculated the empirical p-values of the number of observed GG, EG or EE links as Pr (the number of links in the simulated gene set ≥ the number of observed links) from 1,000 simulations. Figure 6 plots the histogram of the p-values of gene sets with at least one observed GG, EG, or EE link. For all gene set categories except category 1, there are more gene sets enriched with GG, EG or EE links compared with the random selections, where a uniform distribution of p-values is expected.

The motif (U)GCAUG has been reported as a binding motif for mammalian splicing factors FOX-1 (A2BP1) and FOX-2 (RBM9) 40414243. We studied the enrichment of motif GCAUG in exons with EG links to FOX-1 and FOX-2. For each exon, we counted the occurrence of the pentamer GCAUG in the exonic region and the flanking 200 bp intronic regions. Table 4 shows the enrichment of this motif for exons correlated with FOX-1 or FOX-2. The empirical p-values of the enrichment were based on 1,000 simulated exon groups. Among the 64 exons correlated with FOX-1 in human, GCAUG occurs 96 times. And none of the 1,000 simulated exon groups has more than 96 occurrences of GCAUG. The expression level of FOX-1 and the inclusion rates of its associated exons are plotted in Additional data file 5; this clearly shows the co-expression patterns between FOX-1 and exons with EG links to FOX-1. Although the p-values for FOX-2 in human (0.031) and Fox-1 and Fox-2 in mouse (0.172, 0.060) are less significant, the occurrences of GCAUG are about twice as many as the average occurrence among the 1,000 simulated groups. Note that after the filtering procedures for the raw data, FOX-1 and FOX-2 are not in the final gene list for rat.

The calcium signaling pathway has been shown to be intensively related to alternative splicing 44. In our gene set analysis, the KEGG calcium signaling pathway is enriched with EG and EE links with empirical p-values of 0.01 and 0.001, respectively. However, GG links are not enriched in the pathway, with a p-value of 0.354. Figure 7 plots the EG, EE, and GG links in the pathway. The gene layout is the same as the layout in the KEGG database. Most components of the calcium signaling pathway from the KEGG database have at least one link, as shown in Figure 7. Red lines represent GG links (the two gene pairs happen to have EE links also). Blue links represent EE links and green lines represent EG links. The above results indicate the important role of alternative splicing in signaling pathways and/or the important roles of calcium signaling pathways in alternative splicing regulation.

Exon array (Human Exon 1.0 ST, Mouse Exon 1.0 ST, Rat Exon 1.0 ST) data for 11 tissues were downloaded from the Affymetrix website 29. The profiled tissues for human include breast, cerebellum, heart, kidney, liver, muscle, pancreas, prostate, spleen, testis, and thyroid. The tissues for mouse and rat include brain, embryo, heart, kidney, liver, lung, muscle, ovary, spleen, testicle, and thymus. There are three replicates for each tissue. The probe intensities were quantile normalized and were adjusted based on the median intensity of probes with similar GC content. The PLIER method was used to summarize the probe-set-level intensity. The iter-PLIER method was used to summarize the gene-level intensity by iteratively calling PLIER with the core probe sets (that is, RefSeq supported) that correlate with signal estimates. In the design of Affymetrix exon arrays, gene annotations from databases were projected onto the genome to infer transcript clusters and exon clusters. A transcript cluster roughly corresponds to a gene. In many cases, an exon cluster represents a true biological exon and it acts as one probe selection region. In other cases, an exon cluster represents the union of multiple overlapping exons possibly due to alternative splice sites. Such exon clusters were further fragmented into multiple probe selection regions according to the hard edges (for example, splice sites). In exon array, hard edge was defined as the end of the sequence that defines the boundary of a probe selection region and cannot be extended beyond the border by other annotation evidence. The probe set annotation, the transcript cluster annotation, and the exon annotation were downloaded form the Affymetrix website (version hg18 for human, mm9 for mouse, and rn4 for rat) 29. To avoid knowledge bias, only core exons based on RefSeq transcripts or full-length mRNAs were considered. Note that 'core probe sets' in Affymetrix exon arrays only means that they are supported by RefSeq transcripts or full-length mRNAs; they do not contain any information about whether they are alternative exons or constitutive exons.

Presence or absence of probe sets was determined by a 'detection above background' p-value threshold of 0.05. Genes with more than 50% 'present' core probe sets were called 'present'. The following filtering procedures were performed for probe sets: remove probe sets that are not core probe sets; remove probe sets whose genes are present in < 11 arrays out of 33 arrays (11 tissues × 3 replicates) or whose genes are mapped to more than one Entrez gene ID; remove probe sets that are present in < 11 arrays out of 33 arrays; remove probe sets with (Maximum intensity)/(Minimum intensity) < 5. After the above procedures, a total of 97,293 probe sets corresponding to 76,038 exon clusters and 10,366 transcript clusters remain for human; a total of 102,729 probe sets corresponding to 82,145 exon clusters and 10,765 transcript clusters remain for mouse; and a total of 45,691 probe sets corresponding to 40,082 exon clusters and 5,077 transcript clusters remain for rat. The average intensity across the three replicates was log₂ transformed and used as the intensity level for each tissue.

The Pearson correlation coefficient is denoted as r_ab between variable a and variable b. The first-order partial correlation coefficient between a and b conditioning on c is 57:

r ab • c = r ab − r ac r bc ( 1 − r ac 2 ) ( 1 − r bc 2 ) . MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqGYbWaaSbaaSqaaiaabggacaqGIbGaeyOiGCRaae4yaaqabaGccqGH9aqpjuaGdaWcaaqaaiaabkhadaWgaaqaaiaabggacaqGIbaabeaacqGHsislcaqGYbWaaSbaaeaacaqGHbGaae4yaaqabaGaaeOCamaaBaaabaGaaeOyaiaabogaaeqaaaqaamaakaaabaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaeaacaqGHbGaae4yaaqaaiaaikdaaaGaaiykaiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaabaGaaeOyaiaabogaaeaacaaIYaaaaiaacMcaaeqaaaaacaGGUaaaaa@4ED4@

The second-order partial correlation coefficient between a and b conditioning on c and d is:

r ab • cd = r ab • c − r ad • c r bd • c ( 1 − r ad • c 2 ) ( 1 − r bd • c 2 ) . MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@5BD6@

Note that r_ab·cd = r_ab·dc theoretically (see proof in Additional data file 6). In pCastNet, for GG associations, the Pearson correlation coefficient between gene 1 (g₁) and gene 2 (g₂) was calculated as rg1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGNbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347F@. For EG associations, the partial correlation coefficient between an exon (e₁) of gene 1 and gene 2 (g₂) conditioning on gene1 (g₁) was calculated as re1g2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DF@. The Pearson correlation was calculated as re1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347D@. For EE associations, the Pearson correlation re1e2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaaSqabaaaaa@347B@ and the partial correlations re1e2•g1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaaaa@37DD@, re1e2•g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleqaaaaa@37DE@, and re1e2•g1g2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbeaaaaa@39BB@ were calculated according to the above equations.

In simulation studies, five genes were considered. Each of them has five constitutive exons and one alternative exon. The intensity data of the five constitutive exons of gene g (g = 1,..., 5) in tissue t (t = 1,..., 10) were simulated according to the normal distribution N(μ_gt, σ²), where μ_gt is a value sampled from the range 4 to 9 and it is different for different genes g and different tissues t. All of the five alternative exons have the same inclusion rate relative to their genes: (τ₁, τ₂,..., τ₁₀) = (0.1, 0.2,..., 1.0) for the 10 tissues. Thus, the intensity data of the alternative exon of gene g was simulated according to the normal distribution N(μ_gtτ_t, σ²). The gene-level intensity was estimated as the average value of the constitutive exons. pCastNet and the NI-based approach were conducted to calculate the correlations and partial correlations between exons belonging to different genes. Three scenarios were considered (σ = 1, 2, or 4). For each scenario, 1,000 simulations were performed and the average true positive rate and the average false positive rate were calculated according to different correlation thresholds.

For GG associations, the test statistic:

t = r g 1 g 2 ( n − 2 ) / ( 1 − r g 1 g 2 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqG0bGaeyypa0JaaeOCamaaBaaaleaacaqGNbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaGcdaGcaaqaaiaacIcacaqGUbGaeyOeI0IaaGOmaiaacMcacaGGVaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaSqaaiaabEgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbaGaaGOmaaaakiaacMcaaSqabaaaaa@448D@

is converted to z-value:

z = Φ^-1(G₀(t))

G₀(t) is the null cumulative distribution function for the t-values, Φ^-1 is the inverse function of the cumulative distribution function of standard normal, and n is the number of tissues being surveyed. Under the null hypothesis that there is no correlation between gene g₁ and gene g₂, t follows a Student t distribution with degrees of freedom n - 2 and z follows the standard normal distribution.

For EG association, the t values are:

t 1 = r e 1 g 2 ( n − 2 ) / ( 1 − r e 1 g 2 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqG0bWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0JaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaaSqabaGcdaGcaaqaaiaacIcacaqGUbGaeyOeI0IaaGOmaiaacMcacaGGVaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaSqaaiaabwgadaWgaaadbaGaaGymaaqabaWccaqGNbWaaSbaaWqaaiaaikdaaeqaaaWcbaGaaGOmaaaakiaacMcaaSqabaaaaa@457A@

and

t 2 = r e 1 g 2 • g 1 ( n − 3 ) / ( 1 − r e 1 g 2 • g 1 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqG0bWaaSbaaSqaaiaaikdaaeqaaOGaeyypa0JaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaOWaaOaaaeaacaGGOaGaaeOBaiabgkHiTiaaiodacaGGPaGaai4laiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaae4zamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleaacaaIYaaaaOGaaiykaaWcbeaaaaa@4C40@

They are converted to z-values:

z₁ = Φ^-1(G₀₁(t₁))

and

z₂ = Φ^-1(G₀₂(t₂))

Under the null hypothesis, t₁ follows a Student t distribution with degrees of freedom n - 2 and t₂ follows a Student t distribution with degrees of freedom n - 3. The test statistic is:

z₀ = min(|z₁|, |z₂|)

p = pr(Z₀ ≥ z₀) = pr(|Z₁| ≥ z₀, |Z₂| ≥ z₀)

Under the null, Z₁ and Z₂ follow a bivariate normal distribution with the correlation approximated as the sample correlation between Z₁ and Z₂ across different node pairs. The final z-value is:

z = sign (t₁)Φ^-1(1 - p/2)

For EE associations, the t values are:

t 1 = r e 1 e 2 ( n − 2 ) / ( 1 − r e 1 e 2 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqG0bWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0JaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaaSqabaGcdaGcaaqaaiaacIcacaqGUbGaeyOeI0IaaGOmaiaacMcacaGGVaGaaiikaiaaigdacqGHsislcaqGYbWaa0baaSqaaiaabwgadaWgaaadbaGaaGymaaqabaWccaqGLbWaaSbaaWqaaiaaikdaaeqaaaWcbaGaaGOmaaaakiaacMcaaSqabaaaaa@4576@

t 2 = r e 1 e 2 • g 1 ( n − 3 ) / ( 1 − r e 1 e 2 • g 1 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqG0bWaaSbaaSqaaiaaikdaaeqaaOGaeyypa0JaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleqaaOWaaOaaaeaacaGGOaGaaeOBaiabgkHiTiaaiodacaGGPaGaai4laiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGymaaqabaaaleaacaaIYaaaaOGaaiykaaWcbeaaaaa@4C3C@

t 3 = r e 1 e 2 • g 2 ( n − 3 ) / ( 1 − r e 1 e 2 • g 2 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqG0bWaaSbaaSqaaiaaiodaaeqaaOGaeyypa0JaaeOCamaaBaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleqaaOWaaOaaaeaacaGGOaGaaeOBaiabgkHiTiaaiodacaGGPaGaai4laiaacIcacaaIXaGaeyOeI0IaaeOCamaaDaaaleaacaqGLbWaaSbaaWqaaiaaigdaaeqaaSGaaeyzamaaBaaameaacaaIYaaabeaaliabgkci3kaabEgadaWgaaadbaGaaGOmaaqabaaaleaacaaIYaaaaOGaaiykaaWcbeaaaaa@4C3F@

t 4 = r e 1 e 2 • g 2 g 1 ( n − 4 ) / ( 1 − r e 1 e 2 • g 2 g 1 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@4FFB@

They are converted to z-values:

z₁ = Φ^-1(G₀₁(t₁))

z₂ = Φ^-1(G₀₂(t₂))

z₃ = Φ^-1(G₀₃(t₃))

z₄ = Φ^-1(G₀₄(t₄))

Under the null hypothesis, t₁ follows a Student t distribution with degrees of freedom n - 2; t₂ and t₃ follow a Student t distribution with degrees of freedom n - 3; t₄ follows a Student t distribution with degrees of freedom n - 4. The test statistic is:

z₀ = min(|z₁|, |z₂|, |z₃|, |z₄|)

p = pr(Z₀ ≥ z₀) = pr(|Z₁| ≥ z₀, |Z₂| ≥ z₀, |Z₃| ≥ z₀, |Z₄| ≥ z₀,)

Under the null, Z₁, Z₂, Z₃, Z₄ follow a multivariate normal distribution with the correlations approximated as the sample correlations between Z₁, Z₂, Z₃, Z₄ across different node pairs. The final z-value is:

z = sign (t₁)Φ^-1(1 - p/2)

For a threshold x, the conditional FDR is estimated as 25:

FDR ( x | A ) = 2 N Φ ( − x ) # { | z i | ≥ x } [ 1 + A x ϕ ( x ) 2 Φ ( − x ) ] MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaacaqGgbGaaeiraiaabkfacaGGOaGaaeiEaiaacYhacaqGbbGaaiykaiabg2da9KqbaoaalaaabaGaaGOmaiaab6eacqqHMoGrcaGGOaGaeyOeI0IaaeiEaiaacMcaaeaacaGGJaGaai4EaiaacYhacaqG6bWaaSbaaeaacaqGPbaabeaacaGG8bGaeyyzImRaaeiEaiaac2haaaGcdaWadaqaaiaaigdacqGHRaWkcaqGbbqcfa4aaSaaaeaacaqG4bGaeqy1dyMaaiikaiaabIhacaGGPaaabaWaaOaaaeaacaaIYaaabeaacqqHMoGrcaGGOaGaeyOeI0IaaeiEaiaacMcaaaaakiaawUfacaGLDbaaaaa@57C3@

where Φ is the standard normal cumulative distribution function, N is the total number of node pairs, φ is the standard normal density function, and A=2Φ(1)−1−#{zi∈[−1,1]}/N2ϕ(1) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaaeyqaiabg2da9KqbaoaalaaabaGaaGOmaiabfA6agjaacIcacaaIXaGaaiykaiabgkHiTiaaigdacqGHsislcaGGJaGaai4EaiaabQhadaWgaaqaaiaabMgaaeqaaiabgIGiolaacUfacqGHsislcaaIXaGaaiilaiaaigdacaGGDbGaaiyFaiaac+cacaqGobaabaWaaOaaaeaacaaIYaaabeaacqaHvpGzcaGGOaGaaGymaiaacMcaaaaaaa@4A1E@. For a FDR(x|A), the percentage of true links among all possible node pairs is estimated as #{|z_i| ≥ x}(1 - FDR(x|A))/N.

Various tissues from adult C57BL mice and embryonic cortex from E16 embryos were dissected and quickly submerged in Trizol (Invitrogen, Carlsbad, CA, USA) followed by immediate tissue homogenization. Total RNA samples were prepared according to manufacturer's protocol. RT-PCR was done as previously described 30. Primer design was done with the Primer3 online software 58. Primer sequences were. Kifap3, CCTCCAGAATGGAGATGTGG (forward), ACATGGGAGGGGTGATTTTA (reverse); St7, GCAGATGCAATAATGCAAAAAG (forward), GTAACAACCATCTCCAGCCTTC (reverse); Map3k7, TCTGAAATAGAAGCCAGGATCG (forward), CTTCTCTGAGGTTGGTCCTGAG (reverse); Slc35b3, AGCCTTACGGCTGGTACCTT (forward), AGTTTGGTGCAATTGTGCTG (reverse); Rai14, TCTCATGCTGGCTTGTGAAA (forward), GTTATTGATCGTGGGGAGGA (reverse). Identities of each RT-PCR product were confirmed by direct sequencing. PCR bands were quantified using ImageQuant TL software (GE Healthcare Bio-Sciences, Piscataway, NJ, USA). The correlation value of the each exon pair was calculated as the Pearson correlation coefficient between the inclusion levels of the two tested exons. Inclusion levels based on the PCR results were calculated as Inclusion form/(Inclusion form + Exclusion form).

Non-redundant human transcript annotations were assembled based on AceView gene 59, AUGUSTUS gene 60, CCDS gene 6162, Ensembl gene 61, Geneid gene, Genescan gene 63, MGC gene, N-SCAN gene 64, ORFeome gene, RefSeq gene 62, SGP gene, SIB gene 65, UCSC genes 66, and ASTD gene 67. The first 13 data sources were downloaded from the UCSC Genome Browser website (hg18) 68 and the last was downloaded from the ASTD database (release 1.0) 69. A gene may have multiple transcript isoforms. For each exon cluster defined by the Affymetrix exon array, if one exon of a transcript isoform locates in the exon cluster region, the exon cluster is called 'present' in this transcript isoform. If the exon cluster locates in an intron region of a transcript isoform, the exon cluster is called 'spliced out' in this transcript isoform. Exon clusters (or exons for simplicity) were divided into two groups: exons that are present in ≥ 14 transcript isoforms and are not spliced out in any transcript isoform; exons that are present in ≥ 7 transcript isoforms and are spliced out in another ≥ 7 transcript isoforms.

The PhastCons conservation score 70 was downloaded from the UCSC Genome Browser (hg18) 68. The score of each site is the posterior probability that the site is in the conserved state of the phylogenetic hidden Markov model for 17 vertebrates.

For each gene with multiple exons, all of the core exons were sorted according to their genomic coordinates (from 5' to 3'). The relative position of the i-th exon is calculated as (i - 1)/(n - 1), where n is the total number of exons. The relative position ranges from 0 to 1.

Gene sets downloaded from the Molecular Signatures Database 39 belong to four categories: 'c1', positional gene sets for each chromosomal cytogenetic band; 'c2', curated gene sets from pathway databases; 'c3', motif gene sets sharing conserved cis-regulatory motifs 71; 'c4', GO gene sets sharing the same GO term. We removed gene sets without any gene in our final gene list for exon arrays. Category 2 was further divided into 'c2_BioCarta', 'c2_GenMAPP', and 'c2_KEGG'; genes in the same pathways and the pathways were collected from the BioCarta database, the GenMAPP database, or the KEGG database. Category 3 was further divided into: 'c3_promoter_known' and 'c3_promoter_unknown' - genes sharing a motif in the promoter regions (covering -2 kb to 2 kb around transcription start sites) and the motif matches a known transcription factor binding site or the motif does not match any known transcription factor binding site; 'c3_miRNA' - genes sharing a miRNA binding site. Category 4 was divided into: 'c4_bp' - genes sharing biological process ontology terms; 'c4_cc' - genes sharing cellular component ontology terms; 'c4_mf' - genes sharing molecular function ontology terms.