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Is there a significance between 2 correlations of H3K36me3/PolII in genebody

Hi all, I am sorry for the long post, but I am hopping i got all needed information and related questions and concerns. The main biological question is this, after a treatment is the ratio of H3K36me3 Vs polII changes and is the change significant? Which genes are the once mostly affected. I am providing a full That would be "easy" with a limma approach. Which I did, but the results either are random, so the treatment has random effect, (AND HOW CAN I TEST this ?) or due to the data are worthless.

But, I noticed that the distribution of OlII Vs H3K36me3 is not that linear and there are 2 different "clouds". Thinking of it I assume that is expected, between H3K36me3 Vs polII, since there are in principle genes with low transcription and higher. I am providing 2 graphs that I believe illustrate the story. The pvalue in the violin plot is from Wilcoxon test. This is my first question and concern. I am unsure with this kind of distribution if even that test is correct where number of events = around 40k. What do you all think, and what should I do for these kind of distribution? Should I separate the clouds and how to "properly" separate the 2 clouds?

I tried using kmeans with the following command, that seems to work. I am telling it to brake them in 3 groups, since there is a smaller one that is being identified as different.,:

km_clusters <- kmeans(log2(merged_df$Mean_H3_DMSO + epsilon), centers = 2)

I tested the hclust that also works, still not optimal. the DBSCAN method failed, OR I really do not know how to work with it properly.

I have normalised the counts using the EDASeq packaged by PolII and H3K36me3 separately, nothing really changed since the 2 clouds are a biology inherited thing.

  set <- EDASeq::withinLaneNormalization(set, "gc", which = "full")
  set <- EDASeq::withinLaneNormalization(set, "length", which = "full")

The final 3 plots are separation of the plots by quartile of Gene length or GC content and the also, the ratio of h3/polII of DMS by Cond1

correlation and scatterplot with correlation violin and box plot distribution facet by GC content, no bias dettected PolII_DMSO-Vs-H3_DMSO_by_GC_content facet by GC content, no bias dettected PolII_DMSO-Vs-H3_DMSO_by_Genelength correlation of ratio H3_DMSO/PolII_DMSO by ratio H3_Cond1/PolII_Cond1 Ratio corelation pearson_Correlation facet by genelegth, correlation of ratio H3_DMSO/PolII_DMSO by ratio H3_Cond1/PolII_Cond1 Mean_H3_DMSObyMean_PolII_DMSO vs Mean_H3_Cond1byMean_PolII_Cond1_genelegth_pearson_Correlation facet by GC content, correlation of ratio H3_DMSO/PolII_DMSO by ratio H3_Cond1/PolII_Cond1 enter image description here

cutandrun correlation statistics

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