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Graphical Interpretation (I): The Association between a Gene and Bioactivity Accounting for the Effect of a Fingerprint Feature

Several association patterns between gene expression and a phenotypic variable accounting for the effect of a fingerprint feature can be discovered by using the joint model. The different patterns of association are presented in Figure 16.3 using hypothetical data. Each point in the plot represents a compound and the solid ones are compounds having the fingerprint feature.

For this application, the interest lies only in the fingerprint feature that shows differential effects on the bioactivity, the response in this case; thus the four possible scenarios between the gene and response presented in the upper panels of Figure 16.3 (a)-(d). The lower panels (e)-(h) display the same data with their respective upper panels adjusted for fingerprint feature effect for both the response and the gene expression.

In panel (a) the gene is not differentially expressed and has a linear association with the response irrespective of the presence or absence of the fingerprint feature. Note that the linear pattern remains after adjusting for the fingerprint feature as shown in panel (e). Panel (b) shows an example in which the gene is differentially expressed, the clouds of points are clearly separated in both dimensions. Moreover, it can be observed that within the group, the association between the gene expression and the response does not have a linear pattern, which is evident in panel (f) after the adjustment.

Panel (c) shows a combination of the previous two patterns. Both the gene expression and the response are differentially expressed, that is, compounds having the fingerprint feature induce higher activity than those that do not have the fingerprint feature. In this setting, the association between the gene expression and the response can be summarized by a straight line; this can be clearly seen from panel (g), which shows the same example after adjusting for fingerprint feature.

Lastly, most genes are expected to be uncorrelated with the bioassay data as depicted by panel (d). Within each group of compounds (with and without the fingerprint feature), a linear pattern is not evident; thus, adjusting for this effect also provides a random scattering of points (panel (h)).

The joint modeling framework is useful for identifying genes that can predict compound activity, measured by pIC50, and can therefore serve as genetic biomarkers for a compound’s efficacy. On top of this, the effect of a particular chemical substructure on the expression level of each gene and/or its influence on the observed transcriptomic-phenotypic association can be estimated.

FIGURE 16.3

Hypothetical examples of the association between response variable and expression levels when the effect of the fingerprint feature (FF) upon the response is significant. Each point represents a compound. Black and white points represent the presence/absence of a fingerprint feature, respectively. Upper row: scatterplots for the response versus the gene expression. Lower row: scatter- plots for the residuals after adjusting for fingerprint effects.

 
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