parallel lines (cluster) in PCA plots (PC1 vs PC2) There are about 20 subjects, 3 treatment groups, and 1000+ genes in my data; the 1000+ genes were processed in two batches. Could anyone comment on why I am seeing parallel lines/clusters in the PCA plots? The plots strike me as funny because

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*The way the analyte was processed shouldn't differ by batch. But why am I seeing two clusters that are perfectly aligned with batch?




*PCA doesn't create lines, so I think the lines represent some hidden, non-random pattern in the original data that are revealed by PCA after transformation. What kind of raw data would become lines after running PCA?

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*Also, "lines" in the PCA plot suggest PC1 and PC2 are linearly correlated...but isn't PC1 supposed to orthogonal to PC2?

 A: 
The way the analyte was processed shouldn't differ by batch.

That's always the hope, but it's seldom the case in practice. Correction for batch effects has been a critical part of gene-expression analysis going back to ancient times with spotted microarrays.

why am I seeing two clusters that are perfectly aligned with batch?

Although you don't say what software you used to produce these plots, I infer that PCA was done separately for each sample. Then the PC2 magnitudes were plotted against the PC1 magnitudes sample-by-sample. The two clusters very strongly suggest a batch difference, however much you might have hoped not to have one.

What kind of raw data would become lines after running PCA?

Your coloring by treatment helps to explain that. In each batch, samples with treatment 1 tend to have points toward the top right while those with treatment 2 tend to have points toward the bottom left. That suggests that treatments and their associated differences in gene expression account for what you see. Versus treatment 0, both PC1 and PC2 increase under treatment 1; they both decrease versus treatment 0 under treatment 2.

isn't PC1 supposed to orthogonal to PC2?

The orthogonality is with respect to the principal component vectors, linear combinations of the gene-expression values in this case. Within any PCA, the gene-expression vector for PC1 is orthogonal to that of PC2.
What you plot, however, are magnitudes of PC2 versus PC1 among different samples. That's an important part of quality control in this type of study, but such plots need not have any particular shape.
