Introducing knowledge into differential expression analysis

Abstract

Gene expression measurements allow determining sets of up- or down-regulated, or unchanged genes in a particular experimental condition. Additional biological knowledge can suggest examples of genes from one of these sets. For instance, known target genes of a transcriptional activator are expected, but are not certain to go down after this activator is knocked out. Available differential expression analysis tools do not take such imprecise examples into account. Here we put forward a novel partially supervised mixture modeling methodology for differential expression analysis. Our approach, guided by imprecise examples, clusters expression data into differentially expressed and unchanged genes. The partially supervised methodology is implemented by two methods: a newly introduced belief-based mixture modeling, and soft-label mixture modeling, a method proved efficient in other applications. We investigate on synthetic data the input example settings favorable for each method. In our tests, both belief-based and soft-label methods prove their advantage over semi-supervised mixture modeling in correcting for erroneous examples. We also compare them to alternative differential expression analysis approaches, showing that incorporation of knowledge yields better performance. We present a broad range of knowledge sources and data to which our partially supervised methodology can be applied. First, we determine targets of Ste12 based on yeast knockout data, guided by a Ste12 DNA-binding experiment. Second, we distinguish miR-1 from miR-124 targets in human by clustering expression data under transfection experiments of both microRNAs, using their computationally predicted targets as examples. Finally, we utilize literature knowledge to improve clustering of time-course expression profiles.

Fig. 1.

(A) Model 1 assumed in the first test, with two well-separated components (drawn in black and gray), Gaussian parameters as indicated on the plot, and separated sets of 14 examples per component (marked below). (B) y-axis: average accuracy of belief-based, soft-label and semi-supervised methods in putting data into the same clusters as the true model in A. x-axis: different accuracy bar plots for increasing number of examples that are mislabeled (out of the pool of 14 per component). Both partially supervised methods deal significantly better with mislabeled examples than the semi-supervised method. (C) Model 2 assumed in the second test, with overlapping components and small example sets (14 per component), plotted as in A. (D) The plot as in B, but the x-axis shows the numbers of examples, correctly labeled, used per component (from those indicated in C). The example numbers proportions (from left to right 1:1, 1:2, 1:3, and 1:4) are increasingly biased with respect to the model mixing proportions (1:1). Applied to cluster the data from the model in C, belief-based modeling is more resistant to such bias than both soft-label and semi-supervised modeling. (E) Model 2 with a large number of 450 examples per component assumed in the third test, ploted as in C. (F) The plot as in D, but here the increasing bias is introduced in the proportions of observations that are not used as examples (from left to right 1:1, 2:3, 1:2, and 2:5). Applied to cluster the data from the model in E and given large example numbers, belief-based modeling less acurately estimates the model and is less resistant to such bias than both soft-label and semi-supervised modeling.

Fig. 2.

Partially supervised differential expression analysis on synthetic data. Given 8 examples of differential and 72 examples of unchanged genes (a 0.04 fraction of all elements in each cluster), the partially supervised belief-based and soft-label methods, as well as semi-supervised modeling achieve superior accuracy (red boxplots) over the standard differential analysis approaches (light blue for the 0.01 p-value cut-off and dark blue for the 0.05 cut-off ). Increasing the number of examples used by the supervised methods to 50 and 450 (a 0.25 fraction; brown boxplots) yields similar results. Belief-based method maintains high performance also when the known examples are given in reversed proportion 9:1 (orange boxplots) or are mislabeled (25 examples switched between the 50 differential and 450 unchanged genes, respectively; violet boxplots).

Fig. 3.

Biological validation of identified Ste12 targets. Enrichment p-values (shades of gray) of the sets of Ste12 targets identified by the compared methods (matrix rows; 0.01 and 0.05 denote cut-offs applied to differential expression p-values provided by Roberts et al. [2000]; set sizes are given in brackets) in Gene Ontology (GO) biological process terms (columns). Each presented term is enriched in at least one Ste12 target gene set with a p-value of <0.01 and FDR of <0.01. Significant enrichment represents distinct behavior of the target genes compared with the rest of all genes. The belief mixture modeling identified a set of Ste12 target genes with the lowest product of all p-values. Un, unsupervised; CF, cellular fusion; M-ORG, multi-organism; Res., response; PH, pheromone; MG, morphogenesis; Reg., regulation; CRP, coupled receptor protein; Sig. trans., signal transduction; w., with; d., during.

Fig. 4.

Different impact of examples on the models estimated by different supervised methods. Model estimated by the partially supervised belief-based (A) and by the semi-supervised mixture modeling (B). The plots are as in Figure 1A.

Fig. 5.

Improved accuracy of distinguishing miR-1 from miR-124 targets. (A) The adjusted Rand index (x-axis) indicates whether the different mixture modeling methods (y-axis) clustered the data correctly into true groups of known miR-1 and miR-124 targets. Analyzed expression data comes from the miR-1 transfection experiment. The semi-supervised and partially supervised methods utilized 16 computationally predicted examples of miR-1, and 11 of miR-124 targets. (B) Plot as in A, but for the data obtained under the miR-124 transfection. (C) Box-plots show the adjusted Rand index distribution (x-axis), obtained by the methods (y-axis) in 1000 tests, where 16 examples were drawn from all miR-1 targets, and 11 drawn from all miR-124 targets at random, and the data came from miR-1 transfection. (D) Plot as in C, but for the data from miR-124 transfection.

Fig. 6.

Cell cycle gene clustering. The probability of up-regulation estimated for each cell cycle gene (rows; ordered by their true cluster labels), in each time-point (columns) by three methods: NorDi, as well as unsupervised and belief-based mixture modeling, applied to each time point data separately. Belief-based mixture modeling, which uses examples of up-regulated and of unchanged genes in each time-point (marked in pink and green), achieves most clearly visible distinct gene expression profiles, characteristic for the five cell cycle phase clusters.

Fig. 7.

The accuracy of cell cycle gene clustering. From all compared methods, the partially supervised have higher accuracy (measured by adjusted Rand index, y-axis) in grouping genes into five cell-cycle gene clusters than the semi-supervised and unsupervised methods. The partially supervised modeling methods were initialized in two ways: either quantile- or example-based (see Section 2.7).