mimics the observation of the average kinetics for a large number of cells (Figure \[dimer1\]b, n=100,000). The system reaches a stationary state after about $4$ seconds.

![\[\]Study of dimerization system, initial values $\mathbf{x}=[301,0]$, parameters $\mathbf{k}=[1.66\cdot10^{-3}, 0.2]$. a) Single SSA realisation. b) Average of 100,000 SSA simulations. c-d) Histogram of SSA runs (grey bars) and probability density of normal distribution (blue line) calculated from mean and variance of SSA runs corresponding to points c and d in figure (b). e) Mean for both variables, calculated using SSA, the moment approximation using 1 moment (deterministic) and two central moments (2m). f) Variance of $x_1$ calculated using SSA, two central moments (2m), three central moments with Gaussian closure (3m) and four central moments (4m). g) Third central moment calculated using SSA and moment approximation method, fourth central moment calculated using SSA and moment approximation method. []{data-label="dimer1"}](Figure1){width="47.00000%"}

In Fig. \[dimer1\]c-d we plotted histograms of the SSA at two time points that correspond to different regimes in the trajectory: transient state with decreasing molecule number (Fig. \[dimer1\]c) and stationary state (Fig. \[dimer1\]d). We calculated the normal probability density function from the mean and variance of the SSA distribution at those two time points (blue line), 