HSimulator: Hybrid Stochastic/Deterministic Simulation of Biochemical Reaction Networks

Algorithm 4

The Runge-Kutta Fehlberg (RK45) algorithm.

Input: a system of ODEs corresponding to a biochemical reaction

system, the initial state of the system with species concentrations at time , the last

time instant to be simulated, an initial value for the discretization stepsize and a

threshold for the maximum local truncation error .

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

terms of molar concentrations.

Pseudocode:

   initialize time , state and discretization stepsize ;

   while    do

     compute ;

     compute ;

     compute ;

     compute ;

     compute ;

     compute ;

     compute ;

     compute ;

     compute according to (16);

     if    then

       update ;

       update ;

     end if

     compute ;

     if    then

       update ;

     end if

     if    then

       update ;

     end if

     update ;

   end while