Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems

Algorithm 1

The pseudocode of the 𝑆𝜏-DPP algorithm.

(1)  load the description of the 𝑆𝜏-DPP system;

(2) for each membrane 𝑖∈[1,…,𝑛] calculate 𝐹_𝑖(𝑡₀);

(3) for each membrane 𝑖∈[1,…,𝑛]

  (a) ∀ rule 𝑟_𝑘, (𝑘∈{1,…,𝑙}): compute 𝑎_𝑘;

  (b) evaluate the sum of all the propensity functions 𝑎₀ in the compartment;

  (c) IF 𝑎₀≠0: 𝜏_𝑖=∞;

    ELSE generate the step size 𝜏_𝑖 according to the internal state, and select the way to proceed in the current

    iteration (i.e. 𝜏 leaping evolution with or without critical reactions);

(4) select 𝜏_min=𝜏_𝑖=min𝜏_𝑖,…𝜏_𝑛;

(5) for each membrane 𝑖∈[1,…,𝑛]

  (a) IF 𝜏_𝑖=∞ goto (6);

  (b) switch the evolution strategy type:

   (I) case “𝜏 leaping with one critical reaction”:

      if 𝜏_𝑖>𝜏_𝑖: goto (d) else: goto (c);

   (II) else goto (d);

  (c) extract the critical and the non-critical rules that will be applied in the current iteration;

  (d) IF the execution of the selected rules in all the compartments leads to an unfeasible state 𝜏_min=𝜏_𝑖/2;

(6) IF a new value of 𝜏_min was computed: 𝜏_𝑖=𝜏_min and goto (4);

(7) for each membrane 𝑖∈[1,…,𝑛]

  (a) update the internal state by applying the internal rules

  (b) update the state of other membranes by applying the communication rules;

(8) for each membrane 𝑖∈[1,…,𝑛] update the value of the free space 𝐹_𝑖;

(9) IF the termination criteria is satisfied, namely (i) the current time exceeds the end time OR (ii) there is not enough

   free space in any membrane: finish;

   ELSE: goto (3).