model matrix design for multiple siRNAs targeting same gene

[Brandi]

Hi,
after lurking here for 2 years or so (and learning so much from this community!) I finally have a question I haven't been able to find an answer to and I am hoping someone could give me some insight into what I am doing wrong.

We performed RNAseq of cells treated with 3 different control siRNAs or 2 different siRNAs targeting the same gene. Each condition also has 2 biological replicates. The set up of the samples is shown below. So for example, samples 1 and 2 are biological replicates.

condition   siRNA
control   scr#1
control   scr#1
control   scr#2
control   scr#2
control   scr#3
control   scr#3
exp.   exp#1
exp.   exp#1
exp.   exp#2
exp.   exp#2

I have run a few analyses where i just combine all of the controls and all of the experimental (using cuffdiff or DESeq with the appropriate upstream pipelines). However, as individual targeting siRNAs have slightly different efficiency of knockdown and different controls could have different off-target effects I think I might be able to extract more information if I could build a model which incorporates the individual siRNAs.

To this end, I have been attempting to use either the GLM in DEseq or Voom/Limma, but can not seem to figure out how to appropriately construct a model matrix which can take into account these interactions.

My naive thought based on the vingettes I have read was that
(~ siRNA + condition) might work, but I get the following error:

the model matrix is not full rank, i.e. one or more variables in the design formula are linear combinations of the others

I've tried a number of other ways to construct the matrix using the functions in R but have so far completely failed. I also just can't wrap my head around the math of why this shouldn't be possible.

thank you in advance for your help.

[dpryan]

The "condition" factor can be determined by the "siRNA" factor, which is why you're getting that error. So there are a few ways to think about this experiment. The more conservative approach might be to consider the scrambled siRNAs together as a group rather than as different individual effects but consider the non-scrambled siRNAs individually (i.e., the model matrix would just be "~condition", where "condition" has 3 levels). I would actually argue that you might get a little more reliable of a result from this approach, since it's more likely to catch all of the scrambled siRNA variance, at least if the scrambled siRNAs were chosen wisely.

A few other possibilities are layed out in this relatively old thread on the bioconductor email list. That contains an example of a more nested design (in that example, "Phen" and "line" would be your "condition" and "siRNA", respectively). Gordon also mentions a route with duplicateCorrelation there. Some of that's limma-specific, but not all of it.

[Brandi]

dpryan,
thank you so much. Your explanation completely makes sense. Thanks for pointing me to the bioconductor thread. I had searched there, but had clearly not been using the correct key words as I didn't see this post.