Algorithm 3 RDME simulation algorithm using DFSP for diffusion and SSA for reactions

1: initialize system state: X, t=0

2: Calculate the propensity functions ajk(X) and $a_0\leftarrow {\sum }_{k=1}^K{\sum }_{j=1}^M{a}_{jk}\left(X\right)$ {where M is the number of reactions and K is the number of voxels}

3: Generate two random numbers r1,r2∊U(0,1)

4: $t_{next\text{\_}rxn}\leftarrow t+\frac{1}{a_0}\text{ln}\left(\frac{1}{r_1}\right)$

5: tnext_diff←t+τD

6: whilet<tfinaldo

7:  iftnext_rxn<tnext_diffthen

8:   Find μr, μx smallest integers to satisfy ${\sum }_{k=1}^{{\mu }_x}{\sum }_{j=1}^{{\mu }_r}{a}_{jk}>r_2{a}_0$

9:   Update Xμx(tnext_rxn)=Xμx(t)+νμr

10:   Generate two random numbers r1,r2∊U(0,1)

11:   t←tnext_rxn

12:  else

13:   Xnext←∅

14:   fork∊(1…K) do

15:    fori∊(1…N) do

16:     Xnext←Xnext+DFSP_Diffusion(Xk,i) {diffusion of species i in voxel k}

17:    end for

18:   end for

19:   X←Xnext

20:   t←tnext_diff

21:   tnext_diff←t+τD

22:  end if

23:  Update propensity functions ajk(X) and $a_0\leftarrow {\sum }_{k=1}^K{\sum }_{j=1}^M{a}_{jk}\left(X\right)$

24:  $t_{next\text{\_}rxn}\leftarrow t+\frac{1}{a_0}\text{ln}\left(\frac{1}{r_1}\right)$

25: end while