added an extra in caption figure 4b explaining the projection

content/06.a-gene-module-perspective-for-genetic-studies.md

@@ -5,7 +5,7 @@
 Each panel shows a component of the PhenoPLIER framework [@doi:10.1038/s41467-023-41057-4].
 *(a)* First, latent variables (LVs) or gene modules are learned from transcriptome data using the Pathway-Level Information Extractor (PLIER) matrix factorization method.
 PLIER generates matrix $\mathbf{Z}$, which has gene weights for each module, and matrix $\mathbf{B}$, which has the samples in the latent space.
-*(b)* Schematic of gene-trait associations from Transcriptome-wide association studies (TWAS) and gene-drug scores from LINCS L1000 being projected into the latent space for a joint analysis.
+*(b)* Schematic illustrating how gene-trait associations from Transcriptome-Wide Association Studies (TWAS) and gene-drug scores from LINCS L1000 are projected into the latent space for joint analysis. This involves a matrix multiplication that transforms a traits × genes matrix into a traits × LVs matrix, enabling integration and interpretation at the gene module level.
 *(c)* Schematic of a gene module-based drug reporposing framework, where the projection of TWAS and LINCS L1000 data is used to compute a drug-disease score.
 *(d)* Schematic of a regression model that tests whether genes that belong to a module (using a column of $\mathbf{Z}$) tend to be more strongly associated with a trait (using $p$-values from TWAS).
 *(e)* (top) Example of a gene module identified as LV246 analyzed in [@doi:10.1038/s41467-023-41057-4].