use ODE model and noise to study epistasis using simulated yeast cell populations

No evidence that protein noise-induced epigenetic epistasis constrains gene expression evolution
Gábor Boross, Balázs Papp, 2016 MBE


Boros use analytic yeast glycolysis pathway model to study epigenetic interactions. Positive and negative epistasis were found by analyzing fitness of simulated large population of yeast cells with random levels of protein activities whose fitness is calculated with  a deterministic fitness function. 

Molecular number and noises using coefficient of variation -> diploid cells are more robust than haploid cells

Diploid cells are more robust than haploid cells.

Diploid cells are generally considered more robust than haploid cells. If we use binomial distribution to model the stochastic variation in the n number of molecules as a source gene expression noises, the coefficient of variation (CV) can be calculated from standard deviation divided by mean: 
                sqrt(np(1-p)) / np  = 1/ sqrt(np/(1-p) ~ 1/sqrt(n)
Hence, doubling the numbers of molecules in diploid cells will reduce CV by sqrt(2). Because small CV indicate less noisy and more robustness, diploid cells are sqrt(2) more robust than haploid cells. Similar argument was put by Schroedinger in 1944.

For binomial distribution, mean = np. Variance = np(1-p). Standard deviation = sqrt(np(1-p)). So, 
  CV = stddev / mean 

CV is basically the inverse of the signal-to-noise ration. 



References:
http://www.mathsisfun.com/data/standard-deviation.html
http://en.wikipedia.org/wiki/Standard_deviation
http://en.wikipedia.org/wiki/Coefficient_of_variation