COPASI

• run simulations of chemical networks based on differential equations
• run simulations of chemical networks based on stochastic processes
• easily switch between differential equations and stochastic processes within a single model
• calculate steady states and determine their stability
• estimate model parameter values using experimental data
• optimize arbitrary model variables using a menu of many optimization algorithms
• perform sensitivity analysis of model variables
• import/export models in the standard SBML format, or through OMEX files

COPASI is one of the the most widely used software for simulations of bio/chemical reaction networks. COPASI is widely used to model metabolic and signaling pathways, pharmacology, genetics, and many areas of chemistry, with special emphasis on microkinetic modeling.

Users define models in COPASI by focusing on the biochemistry components (species, reactions, kinetic rate laws, etc.) and the software automatically builds the corresponding mathematical equations. This feature makes it quickly accessible to biologists and chemists as model-building strongly relies on their domain knowledge, and minimizes the mathematical and programming skills required to a minimum.

COPASI allows many different types of time-dependent models (i.e. models where diffusion is not explicit), using several formalisms: ODEs, stochastic differential equations (SDEs), stochastic simulation with the Gillespie algorithm, and hybrid models where some variables are modeled with ODEs and others with the Gillespie approach. Additionally all the models can include discrete events, making such models hybrid continuous-discrete.

The most widely used functionality of COPASI is parameter estimation, where one fits parameter values of a model to experimental data. Users are able to associate an arbitrary number of experiments with the model variables and COPASI automatically builds a least-squares objective function for minimization which is carried out by nonlinear optimization algorithms (gradient-based, evolutionary algorithms, simulated annealing, particle swarm and several others). The user can additionally add any type of nonlinear constraints (for example, that a ratio of two concentrations must be above a certain value).

COPASI provides several methods to characterize models including algorithms for sensitivity analysis, stability analysis, cross-sections, Lyapunov exponents, and generic optimization. Additionally COPASI exposes its features to other programs through libraries and APIs available in several languages (Java, R, Python, etc.)