# Identifying mutually **exclusive** gene sets

I am interested in identifying gene pairs (or better: sets of genes) whose expression is mutually exclusive. Ideally, both genes (or gene sets) would be widely expressed but I am also interested in cases that are very cell type specific.

Familiar examples of the former would include some of the cyclin genes, in humans e.g. cyclin E and cyfclin B, which are expressed during S-phase and M-phase, respectively. Another example would be some of the clock-genes, where Per1 and Per2 are often highly expressed in the suprachiasmatic nucleus (SCN) before midday, and whereas Bmal1 is expressed after midday. However, such genes need not be cyclically expressed, they can simply be very specific markers for certain cell types. For example, GAD65 and GAD67 are very specific for interneurons, whereas CamKIIa is very specific for excitatory glutamatergic cells.

I have been able to find a single paper so far that systematically tries to find such genes from gene expression data, namely: Tzanis & Vlahavas (2010) Mining for Mutually Exclusive Gene Expressions. According to Google Scholar, this paper is cited by a single other paper that does not seem to be relevant. In Tzanis & Vlahavas (2010), they use a SAGE library (from 2002) of short expression sequence tags to find these strong negative associations. By today's standards, the data set is pretty small (basically, it contains 90 samples). The paper itself is hence anything but a canonical source for such negative interactions.

### Questions:

1. Is there a curated database of mutually exclusive gene pairs or gene sets?
2. If not, is there a curated database that would allow me to find such genes?

Otherwise, my current plan would be to use the human or mouse cell atlas single cell data to define a signed, weighted gene expression network. I would then search for pairs of clusters/modules, where genes have predominantly positive correlations within a cluster but predominantly negative correlations between clusters. So essentially, signed, weighted gene correlation network analysis (WGCNA) with extra steps.

1. Has somebody published such an analysis already (the WGCNA literature is pretty substantial)?

2. Is there other (recent) related work that I am unaware off?

I am fairly new to bioinformatics, so the lack of papers and resources that I am able to find is likely mostly a reflection of my lack of ability to find the correct search term.

• "I am interested in identifying gene pairs (or better: sets of genes) whose expression is mutually exclusive." To what biological end? Are you looking for marker genes/sets? There's extensive literature on that. – Devon Ryan Feb 28 at 14:07
• @DevonRyan The most basic, direct application that comes to mind would be to identify doublets in single cell RNA sequencing data. Most existing approaches are data set imminent and hence unreliable when the number of samples is small. More broadly speaking, I am thinking about ways to bake in biological priors into RNASeq analysis pipelines. From my own literature review, mutually exclusive interactions seemed to me an under-explored direction of research in this regard, and hence a good starting point. – Paul Brodersen Feb 28 at 14:21
• The only circumstance where doublets are an issue is when the technology is using microfluidics (or similar) and then you don't have issues with small sample sizes. It's unclear how mutual exclusivity (as much as that ever actually happens) would be relevant to generic RNA-seq analysis. As is this post needs much more focus on a single specific application so the solution can be appropriate, as there will exist no single generic solution. – Devon Ryan Feb 28 at 14:28
• @DevonRyan "The only circumstance where doublets are an issue is when the technology is using microfluidics (or similar) and then you don't have issues with small sample sizes. " -- Having access to (unpublished) data sets that are a) small, and b) may contain an appreciable number of doublets, I respectfully disagree. Irrespective of the sequencing method, not all tissues are easily dissociated such that you can get a single cell suspension that you could process further using conventional techniques. – Paul Brodersen Feb 28 at 14:49
• @DevonRyan "As is this post needs much more focus on a single specific application so the solution can be appropriate, as there will exist no single generic solution." -- Why in your opinion would my questions, in particular question 1 & 2, require more focus? If I were to ask a different but analogous question, e.g. if there exists a database that lists relationships between signalling molecules or metabolites, everybody would direct me towards KEGG. I am not trying to be combative -- I am new on this forum and trying to understand what extra-information you would find critical. – Paul Brodersen Feb 28 at 14:59

"Mutually exclusive" is not a precise statistical term because it could be seen as independence.

Anyway if truly mutually exclusive AND their behaviour follows periodicity, i.e. sine waves, which it might do in a cell cycle, i.e. the cells divide at periodic intervals, you can do this via asynchronicity.

If the gene expression can be described under periodicity analysis you simply sum the amplitude between two genes. When the amplitude is zero ... they are expression is antogonistic - when one is expressed the other is silent.

Amplitude simply means the height of the period.

Periodicity analysis is quite simple if you have uniform time measurements.

If you have 'missing data', i.e. you time intervals are not uniform, for example you skipped a reading then this is called missing data in periodicity analysis. Missing data periodicity analysis is complicated, but its doable.

So in this context its quite simple, you would identify the periodicity of all genes and construct a 2x2 matrix subtracting their respective amplitudes. It would be kinda juicy to do.

The above is cool if the genes are periodic, however covariance is a better solution in general terms.

What you want is negative co-variance. If two genes had a covariance of -1 ... that will mutually exclusive. As above 2x2 matrix and the co-variance across the grid. You do need to be careful that the program you are using doesn't remove negative values of the covariance.

Covariance = 1, meaning two genes are co-expressed
Covariance = 0, random distribution
Covariance = -1 mutually exclusive expression