I'll try to answer to the best of my knowledge:

When counts are high we approach a continuos signal, similar to a microarray experiment, and estimates will also be very precise. For abundantly expressed genes and with deep sequencing coverage, the biological variability will therefore dominate over sampling errors. In this case it should be perfectly fine to use standard microarray tools (which typically assume the data is normally distributed) on the normalized data.

For low-abundance genes or low coverage, the discreteness needs to be considered, since non-normally distributed samplings errors will be important. Packages like deseq handle both situations (and anything in between) by using the negative binomial distribution. These tools therefore need to be fed the raw counts rather than normalized data.

Rounding the normalized data will not be helpful in any situation.

I'll try to answer to the best of my knowledge:

When counts are high we approach a continuos signal, similar to a microarray experiment, and estimates will also be very precise. For abundantly expressed genes and with deep sequencing coverage, the biological variability will therefore dominate over sampling errors. In this case it should be perfectly fine to use standard microarray tools (which typically assume the data is normally distributed) on the normalized data.

For low-abundance genes or low coverage, the discreteness needs to be considered, since non-normally distributed samplings errors will be important. Packages like deseq handle both situations (and anything in between) by using the negative binomial distribution. These tools therefore need to be fed the raw counts rather than normalized data.

Rounding the normalized data will not be helpful in any situation.

Magdy, You seem to have a problem with units, and I am curious about why you are annoyed. Are you similarly annoyed when your car tells you that you are driving 35.7 miles per hour? Would you also ask how this is expressed "in reality"? Using a normalization like reads per something allows you to make comparisons, for example between two experiments that generated overall different numbers of reads.

As for whether you can use micro-array analysis tools: these analyses do not simply require data of integer or real nature, but they make assumptions about the underlying distributions that generate read counts/expression values. If these assumptions are not met, you might still get results, but they will potentially be misleading.

Referring to an RPKM value is no different then referring to a normalized signal intensity value from a microarray experiment. Both are just numbers, expressing the normalized expression level or signal intensity for a particular transcript. An RPKM is no different in principle than an RMA normalized intensity value.

It's important to differentiate the processes of data normalization versus post-normalization data analysis. Different data requires different measures to normalize it properly. Normalization is about adjusting the entire data probability distribution into alignment for valid statistical analyses. When data is drawn from very different probability distributions to begin with, then of course each will require different normalization schemes.

One cannot use microarray normalization algorithms on RNA-Seq data as the raw data is fundamentally different. One is a measure of a continuous signal of intensity, while the other is discrete count data, and both have very different data distributions and dynamic range. They simple are not comparable in terms of the manipulations necessary to properly normalize them.

Once normalized however, many of the same analytical tools can be used for statistical inference - a simple ANOVA is wholly appropriate for either type of post-normalized data. And final differential gene expression is still presented as log2 fold change for both data types.

The continuous nature of a RPKM value is the fact that it describes the number of Reads mapped Per Kilobase (of reference) per Million mapped. If you gene is anything other than in multiples of 1000bp long, it is going to result in a non-discrete number most of the time. It therefore allows comparison of different genes by provide some normalisation for their different lengths.

@Marc Rehmsmeier, there is a fundamental difference between the two cases: my question and your analogy. In the real world, fractions of miles do exist. We can measure 0.5 or 0.7 mile-all the way to infinity. So, the estimated speed has the same meaning as the actual speed. In the other hand, given that genes are expressed in forms of "transcript" unit, which can't be divided, fractions of gene expression is meaningless unless it is an estimation or approximation. So, the number of transcribed message per any gene will always be natural number.

I understand the necessity of normalization to allow comparisons and fitting into some distribution models to allow statistical analysis. I am not concerned about why or should we be doing it.

I was kinda concerned whether converting RNAseq data from discrete to non-descrete will change the meaning of the data. Now, I have analogy that removed my concern. One should think of normalized RNA-seq gene expression (RPM/RPKM/FPKM) as a "rate" or "estimated proportion" (p-hat)- relative values, so can be real numbers-compared to the real value of expression, which is the actual number of transcripts per gene-can be natural number only.

Thanks you all for the insights.

In either case, we never know the "real" number of transcripts per gene. With RNA-Seq, that would require that the entire process, from sample collection to library prep., to sequencing and instrument signal capture was 100% effective. It would also assume we can map those sequences exactly and with complete certainty to their respective positions in the genome and thus count the transcript they land on with complete certainty. Any estimate of relative transcript abundance, be it count data or fluorescence signal intensity is a sampling estimate of what is actually there in the cell/sample.

Even when we do summarize reads as counts, we make decisions about what is and is not a valid count. Mapped reads do not all land cleanly within a transcript boundary, so mapping algorithms have to apply cutoffs and decision rules to arrive at an actual discrete count for any given transcript. That inherently means there is uncertainty in the number arrived at, and hence fractional estimates are perfectly valid, as it is an estimate derived from a distribution of hits.

Ultimately, it all is estimation and we can never say we know what the actual transcript abundance is for any transcript or gene. All we can do is estimate them from a distribution of counts obtained by sequence sampling.

On the meaningness of RPKM, I strongly suggest the following material:

http://www.ncbi.nlm.nih.gov/pubmed/22872506

So, if someone uses no normalisation method, RNA-seq analysis could actually give a gene expression difference between two samples, correct?

Ioannis - that is totally correct.

@Ioannis, I would be very careful about using NO normalisation method. You cannot compare raw RNA-Seq values as there will be differences in read depth etc. It is just that RPKM and FPKM are designed for WITHIN sample comparisons and do not normalise BETWEEN samples. Other methods (TPM, DESeq etc.) do normalise between samples but always based on certain assumptions, such as constant total RNA, constant total transcript counts, or lack of change in most genes. It is best to try multiple methods and check the assumptions to be sure that you understand how your data seems to be behaving. 

How to combine the RPM and FPKM data, or have some R package for this?

best wishes@