Figure 1

(a) Trends in variability as the size of the cell population increases are shown for five different levels of λ, representing 'high', 'medium' and 'low' levels of gene expression. Variability is shown by the standardized standard deviation (a measure of variance) of simulated gene expression values calculated across 1,000-fold replicated populations of cells, and has been standardized by average gene expression. The standardized variance is another way of showing how the variance changes with respect to the number of cells in our virtual population. Higher values will always be associated with higher variance so we standardized by the mean value to see the true behavior of the system. As we expect the variance to follow the analytic solution $\frac{\lambda }{N}$, standardizing the variance by the mean (for a Poisson random variable, the mean is also λ) will give overall data that decays according to $\frac{1}{N}$. We chose to represent the standardized standard deviation (the square root transformation of the variance) because this quantity will follow the analytic solution $\sqrt{\frac{\lambda }{N}}/\lambda =\frac{1}{\sqrt{N\lambda }}$ and, therefore, we can represent different curves for different values of λ. (b) Trends in variability as the cell population size changes are highlighted for a simulated example with a lower (ten-fold) degree of replication. The standardized variance of simulated gene expression values is shown by dots, and the standardized variance given by our analytical model is shown by the bold line. This suggests that, even with a moderate number of replicates, we should be able to observe a distinct effect dependent on the gene expression level.