You can always interpret data that you have - because even if you measure a value once you now have some information.

The difficult part is that most statistical techniques that you are likely to encounter will not be directly applicable, nor would be the predictive power or estimates be valid even if these tools ran (sometimes they will run). You will need to rethink and reformulate what you can and cannot state based on your data.

For example once you have a variability of the gene expression levels across all spots you can compute the likelihood that a systematic pattern of say all genes being at an given extreme occur by chance on a given time series.

And so on. You will need to substantially scale back of what you can state, validate intermediate results against other knowledge. As long as you only ask questions that the data can support you can use it.

Of course you can tell lots of stories about why it is not a good idea. But in reality it might not be so bad if you just want to get an impression about what happens.

The thing is you probably could get some idea about the biological variation for gene expression in the tissue you study and on the platform you use from the gene expression repositories GEO and Arrayexpress. Of course your own technical variation might be different from average (especially if this also was your first array), but it would still give you some impression.

Also part of your understanding from an array study comes from what genes are changed in groups that belong to the same pathway or biological process. You could still evaluate that even for just one array.

A biologist will tell you that all experiments contain useful information. A statistician will tell you that only experiments that are amenable to statistical testing contain useful information.

There are plenty of experiments in the GEO database which compare only 2 arrays - some of them have even been published in high-profile journals. Which is not to say that this is good practice.

I'm a "statistical bioinformatician", working in a division with professional statisticians and we would tell you that you can do very little (if any) useful analysis without replicates.

Simon Anders has some good posts on this on seqanswers, namely this one: http://seqanswers.com/forums/showpost.php?p=39704&postcount=2

Although it's targeted at RNA-Seq, I think his points about replicates extend to most studies. Since you don't know the natural variation, you can not attribute the variation you are seeing to the "condition" as it may be variation that is normal to the system. The variation be different for microarrays, but the problem is the same.

That said, DESeq has a method to find differentially expressed genes without replicates using the variation in the samples provided... You could look at that to see what to try.

Good question and good replies - so not much to add here. One thing I will offer is to consider looking at changes in gene sets, or gene set enrichment analysis. GSEA is an example. You do have issues, as mentioned by others, with regard to variation in signal and statistics. Just as a gene may have natural variation in expression, so too can a set of genes that share some function or mode of control. Nonetheless, it may be beneficial to look at something like GSEA.

Advice: Don't try to drill down to too much detail. Provide an overview - GO terms, pathways, gene sets - and stay within the realm where your confidence in the results is high.

In the end, the results do allow one to claim that testable hypotheses can be formulated and prioritized for later work.

In addition to what has been said here already, remember the folowing:

Nobody said that all biological replicates must be performed at the same time. In fact, you can add the biological replicates now. If your lab invests just little bit more in replication, repeating the experiment and adding two more biological replicates, your data will become so much more valuable.

The added value is so relevant in this case, from almost unusable and not publishable (anymore), to a analysis allowing for assessing significance!

Think about it: instead of helping the experimenter to salvage their crappy experimental design (and that's what I would seriously call it), resist the temptation and ask them to improve their experiment instead. You will avoid wasting a lot of time, yours and the experimenters (especially, unfortunately many don't understand the statistical implications).

Good luck!

Just to add, no one has mentioned a cutoff... How about 2-fold?

Of course, you might just rank your list of genes by log2(R/G) and take the top X genes where X is dependent upon how much follow up you plan to do.

Did you try to use RankProduct R Breitlinga - 2004 it has a good review by Jeffery 2006. It very good with experiment with few replica. Give it ago. Try to use it with R if that is hard then try the onechannelGUI (graphic interface in R) if that is too much then look at the RankProduct web interactive tool of RankProd URL . Also PCA of the experiment can tell you something about the data.