Table 3
| • Initialize all species and rate constants |
| • Compute all reaction rates |
| • Loop: |
| * Set μ = sum of rates for the discrete reactions |
| * if (pt = 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 <pt = 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 |
Adalsteinsson et al. BMC Bioinformatics 2004 5:24 doi:10.1186/1471-2105-5-24 |