Identifying mutually **exclusive** gene sets
"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