ignoring higher order moments. The normal probability density functions fit the histograms very well, which indicates that the distribution of molecule numbers is approximately normal over the time course, and higher order moments would have limited influence on describing the kinetics of the mean for this system.

Figure \[dimer1\]d shows the mean molecule numbers calculated with the moment approximation method compared to the SSA results. The results for the deterministic (including only the mean) as well as the two moment approximation are approximately equal to the means calculated with the SSA. We compare the higher order central moments calculated with the general moment approximation method described above with the results from the SSA simulations in Figures \[dimer1\]f-h. In the 3–moment approximation we closed the equations using the Gaussian probability distribution (setting the fourth cumulant equal to zero [@Grima2012]), while in the other approximations we truncated higher order moments. The approximated moments are close to the exact moments calculated from the SSA, which is also clear from the errors displayed in Table \[table1\], calculated as $\epsilon=(1/N)\sum_{n} \sqrt{((M_{SSA}-M_{ma})/M_{SSA})^2}$ with $M_{SSA}$ the moment or central moment calculated based on the SSA, $M_{ma}$ the corresponding value calculated with the moment approximation, and $N$ the 