Time Course Calculation

Time course simulation allows you to calculate the trajectories of species in your model over a specified time interval. There are several approaches for computing such trajectories, and depending on your model, one or more of these methods may be suitable.

COPASI supports three main methodologies for calculating trajectories:

1. Deterministic simulation: This method uses the LSODA algorithm (or LSODAR if events are present) Petzold83. It is generally appropriate for models with large numbers of molecules, where random fluctuations are negligible. Additionally, Radau5 is available to be used.

2. Stochastic simulation: When systems have small particle numbers, stochastic effects can become significant. COPASI offers several stochastic simulation methods:
   • Next reaction method Gibson00
   • Direct method Gillespie76 Only this method supports discrete events.
   • Tau leaping Gillespie01
   • Adaptive SSA Cao07

3. Hybrid methods: In situations where deterministic simulation is not appropriate, but full stochastic simulation is too computationally expensive, hybrid methods can be used. These approaches combine the strengths of both deterministic and stochastic simulations. COPASI includes several hybrid methods that can produce accurate time series where pure deterministic approaches would fail, yet remain less demanding than purely stochastic simulations. Only the RK-45 method supports discrete events.

4. Stochastic Differential Equations: The [stochastic Runge–Kutta (RI5)] integrator represents an integration for solving SDEs. This method supports discrete events.