Fig. 5.

a The mean number of morphogens in $C_2$ at time $t=50\mathrm{s}$. Different simulation methods are compared with $\alpha =10$, 20, 30, 40, 50: the Gillespie SSA with multigrid discretization ($\alpha$ grid points with size $\Delta x$ and one grid point with size h), Scheme 1, Scheme 2 and “Scheme 2 with no noise” due to diffusion in ${\Omega }_s$. b The probability distribution of the normalized morphogen number in $C_1$ with Scheme 2. The probability distributions are computed for $X^{\ell }(t)/\Delta x$, $\ell =1,2,\dots ,\alpha$ and compared among the cases with $\alpha =10$, 50 at time $t=0.01$, $50\mathrm{s}$. Initially, 50 molecules are located in ${\Omega }_s$ in panels (a, b) (Color figure online)