|
• Compute all reaction rates
|
|
• Loop:
|
|
* Set μ = sum of rates for the discrete reactions
|
|
* if (p
t
= μΔt > ε), use Gillespie algorithm:
|
|
* R = a uniform random number in (0,1)
|
|
* Set timeStep = -log(R)/μ
|
|
* Find which reaction occurred, update the species involved
|
|
* else, use small Δt approximation:
|
|
* R = a uniform random number in [0,1]
|
|
* timeStep = continuousTimeStep
|
|
* if (R <p
t
= μ × timeStep), discrete transition has occurred:
|
|
• Determine which discrete transition occurred:
|
• Find the first value of k for which 
|
• If  , the forward reaction occurred, otherwise the backward reaction occurred
|
|
* else, no discrete transition:
|
|
• No discrete reaction occurs, update is entirely due to continuous reactions (below)
|
|
* end if (small Δt method, determination if discrete transition occurred)
|
|
* end if (selection of Gillespie or small Δt method for discrete reactions)
|
|
* Update the continuous species using the Langevin equation, with step size timeStep (where timeStep is either equal to continuousTimeStep or to the step size found by the Gillespie algorithm), using a semi-implicit numerical method
|
|
* Update any rates that have been changed by the continuous reactions and the single discrete reaction
|
|
* Break when user-defined total simulation time is reached
|
|
• end loop
|
, the forward reaction occurred, otherwise the backward reaction occurred