Hi all experts, 
I’m very new in this field and it’s my first experience, so please correct me when I’m wrong during the conversation.I have 5 libraries (unfortunately without replicate) as below, 

Control-Sensitive cell line (CS)

Treatment-Sensitive cell line after 12 hours (TS12)

Control-Tolerant cell line (CT)

Treatment-Tolerant cell line after 12 hours (TT12)

Treatment-Tolerant cell line after 24 hours (TT24)

I’m aware of the replication importance, however, at this moment, there is no way to have replication in this experiment. As far as I read, I can use just the exact test from edgeR package, which the interaction effects could not be controlled by it. Given this experiment, please kindly clear me about the below questions.

1) As you know better me, in order to use exact test, we set dispersion parameter manually. For dispersion estimation, I ignored the cell line type and time; in fact, I considered the experiment as control with two replicates (CS and CT) and treatment with three replicate (TS12, TT12, and TT24), and it is the related MDS plot. 

As this plot shows, the difference between control and treatment is more than between cell lines (CS and CT, ST12 and TT12), it returned to me this consideration (control and treatment) sounds right, do you agree? Please share me your opinion. Then I calculated dispersion using "y <- estimateDisp(y, design, robust=TRUE)", the related plotBCV is here. Please let me know if I can use the calculated dispersion for the exact test? 

Regarding the interaction effect, when we use the exact test for comparing two cell line types say, CS and CT as well as TS12 and TT12, and comparing control and treatment within each cell line, please kindly tell me if we can say those DE genes that are common when comparing was done within each cell line and when two cell line types were compared with each other might be due to the cell line effect not treatment?

As the last question, please tell me how is important the control for interaction effects? Please advise and introduce me if there is any software that can handle the interaction effect without replication?

Sorry for several questions and many thanks for your help and time in advance.

You already know that not having replicates isn't ideal, and Aaron and Ryan have already discussed that, so I won't go over it again. This is how I would do the best with what you have.

Following item 3 on page 22 of the edgeR User's Guide, I would create an artificial factor that ignores the difference between sensitive and tolerant cell lines. This is similar to what you have done, but with 3 groups instead of just 2.

Here is the real design matrix:

Group <- factor(c("CS","TS12","CT","TT12","TT24"))
design <- model.matrix(~0+Group)
colnames(design) <- levels(Group)

Here is the reduced design matrix:

Group2 <- factor(c(1,2,1,2,3))
design2 <- model.matrix(~Group2)

Estimate a trended dispersion with the reduced design matrix:

y <- estimateGLMTrendedDisp(y, design2)

Again, this is similar to what you have done but with trended dispersion.

Then fit a glm with the real design matrix:

fit <- glmFit(y,design)

Now you can test any hypothesis you want:

cm <- makeContrasts(
   TS12 = TS12-CS,
   TT12 = TT12-CT,
   TT24 = TT24-CT,
   TT12.TS12 = (TT12-CT) - (TS12-CS),
   levels=design
)

To get 12 hr treatment effect in sensitive line:

lrt <- glmLRT(fit, contrast=cm[,"TS12"])
topTags(lrt)

To get 12 hr treatment effect in tolerant line:

lrt <- glmLRT(fit, contrast=cm[,"TT12"])
topTags(lrt)

To get 24 hr treatment effect in tolerant line:

lrt <- glmLRT(fit, contrast=cm[,"TT24"])
topTags(lrt)

To test for different effects (interaction) in tolerant vs sensitive lines:

lrt <- glmLRT(fit, contrast=cm[,"TT12.TS12"])
topTags(lrt)

This analysis is generally conservative, but it may also be liberal for some genes, so the p-values should be taken with a grain of salt. However it's the best that can be done, and the ranking of genes may be informative.

Your MDS plot suggests a huge treatment effect, but little systematic difference between sensitive and tolerant lines. The huge size of the treatment effect may complicate your conclusions just as much as the lack of replicates.

Please let me know if I can use the calculated dispersion for the exact test? 

Can you? Yes. Should you? That's harder to answer. If your treatment effects are very different from each other, than the dispersion will be inflated if you pretend that the different samples are replicates. This will make your analysis more conservative (possibly a lot more so) than it should be.

The only way to know is to get replicates to estimate the dispersion. Besides, cell lines are about the easiest system to get replicates from; substantially simpler than live animal models, and orders of magnitude easier than patient samples. So there's no practical argument for not having replicates in your experimental design.

Regarding the interaction effect... ?

From what I understand, you're looking for genes that are DE between cell lines and also DE upon treatment. These genes have both a cell line effect and a treatment effect, so I don't know why you want to ignore the latter.

... how is important the control for interaction effects?

If you don't have the control sample for each cell line, you won't be able to calculate the treatment effect for that cell line. That means you won't be able to calculate the interaction effect, as this describes the differential response to treatment between cell lines.

Please advise and introduce me if there is any software that can handle the interaction effect without replication?

Any interaction model will contain one coefficient for each combination of treatment and cell line. If you only have one sample per combination, then you don't have any replication. Without replication, you can't model variability in the counts, which is critical to a sensible analysis as overdispersion is definitely present in RNA-seq data. This is a fundamental statistical issue that cannot be waved away with some magic software. Get some replicates instead. I mean, statistics aside, it's just good science.

Thank you, Aaron Lun for the explanation. You're right about replication, however, as I mentioned in the post, we cannot generate replication at the moment and we have to go ahead with the available data. As you correctly understood, I'm looking for DE genes between cell lines and also DE after treatment. Please kindly let me know if edgeR (exact test) and simple pairwise comparisons can correctly answer these questions? the false positive rate could be high due to the lack of replication, though.