How to interpret PCA output statistically and biologically? How can I interpret the PCA results statistically for biological data?

I have used FactoMineR and factoextra libraries for PCA

Scripts used:

library(FactoMineR)

res.PCA = PCA(df, scale.unit=TRUE, ncp=4, graph=F )
par(mfrow=c(1,2))
plot.PCA(res.PCA, axes=c(1, 2), choix="ind")
plot.PCA(res.PCA, axes=c(1, 2), choix="var")
dimdesc(res.PCA, axes=c(1,2))

library("factoextra")
fviz_pca_var(res.PCA, arrowsize = 1, labelsize = 3, repel = TRUE, col.var = "contrib", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))


Here is my PCA output of differnt KO genotypes); how can I explain/interpret the PCA output statistically and if possible biologically: esp, how this colors /contrib explain
All that plots like this are telling you is that there are some genes that contribute more to the variability seen between your various samples than others. In an ideal world these genes will also be differentially expressed between your groups, but since we don't live in an ideal world that might not be the case. In general, the longer the line and the closer it is to the X axis the more it contributes to the overall variation (since it's contributing more the PC1, which is 53.5% of the variation in your data).

Since you've asked in the comments for a brief "results and description" section style summary of such a PCA I'll include something brief below. Note that one should not over-interpret PCA plots. The axes are (mathematically) orthogonal and don't necessarily correspond to anything biologically relevant.


  We performed a PCA on the variance-stabilized counts to check for batch effects and overall clustering of the data. As can be seen, the "3T" and "5T" groups cluster together along the first principal component, while the "0T" and "1T" samples cluster on the opposite side. This suggests that these groups are more similar to each other, as further evidenced by ...


Assuming you had used the vst() function in DESeq2 (I note you've tagged your post with RNAseq, so perhaps you're using DESeq2) then something like that above would be a reasonable description.