HSimulator: Hybrid Stochastic/Deterministic Simulation of Biochemical Reaction Networks

Algorithm 6

The hybrid rejection-based stochastic simulation algorithm (HRSSA, please refer to [21] for details). In HSimulator, step is implemented by a deterministic Runge-Kutta numerical method.

Input: The same as RSSA (Algorithm 2) together with the time granularity used for the

(approximate) simulation of fast reactions; the minimum amount of molecules that

has to be available for fast reactions; the minimum number of times that a fast

reaction has to be applied, in average, within the time range of size .

Output: a time series of states , providing the dynamics of the system.

Pseudocode:

   ;

   while    do

     Define the fluctuation interval according to (8);

     For each reaction , compute propensity bounds and ;

     Update reaction partitioning (sets and ) by applying the algorithm

     in Algorithm 5 according to input parameters , and ;

     Compute according to (20);

     ;

     while    do

       , where is a random number in ;

       Compute by simulating fast reactions (), at time steps of

       maximum length , according to an approximate algorithm (either

       stochastic or deterministic), where is a value such that ;

       if    then

         Select a candidate slow reaction by applying RSSA steps

         in Algorithm 2;

         if   is accepted by RSSA  then  update computed at step by

         applying ;

         if    then  ;

       else

         ;

       end if

       ;

     end while

   end while