+ COPASI is a software application for simulation and analysis of biochemical + networks and their dynamics. +
++ COPASI is a stand-alone program that supports models in the SBML standard + and can simulate their behavior using ODEs or Gillespie's stochastic + simulation algorithm; arbitrary discrete events can be included in such + simulations. +
++ COPASI carries out several analyses of the network and its dynamics and + has extensive support for parameter estimation and optimization. + COPASI provides means to visualize data in customizable plots, histograms and + animations of network diagrams. +
++ MODELS + + Models in COPASI are based on reactions that convert a set of species into another set of species. Each species is located in a compartment, + which is a physical location with a size (volume, area, etc). This maps directly to biochemical reaction networks, + but can also represent other types of processes (for example, the species could be cell types). + COPASI automatically converts the reaction network to a set of differential equations or to a system of stochastic reaction events + — the user does not have to write down the math explicitly, the software does that. + + Models can also have: + * Unlimited number of species, reactions, and compartments. + * Arbitrary discrete events; these can be used to change the model, or just to monitor the progress of simulations. + * Arbitrary differential equations; these have to be added explicitly by the user and can be mapped to species, compartments, or generic variables. + * Compartments can have variable sizes (ie they can be variables of the model). + * The rates of reaction can be picked from a set of predefined kinetic functions (the most common in biochemistry), or arbitrary functions defined by the user. + + Models can be visualized through + * the GUI interface, with tables for reactions, species, compartments, etc.; + * an arbitrary number of network diagrams (including an SBGN-compliant option); + * the full set of differential equations; these can be exported in Latex or MathML formats. + + COPASI can import and export models in the SBML format (levels 1 to 3). Models can also be exported in XPP format, + Berkeley Madonna format, and as C code (in addition to MathML and Latex). + + SIMULATION + + Simulation can be performed either with stochastic kinetics or with differential equations, and the software easily allows + switching between them. The software provides an interface to create parameter scans (sweeps), + parameter sampling and repeated simulations — including complex simulation scenarios mixing parameter samples + with scans and repeats of simulations (or other analyses). + + Algorithms available for simulation: + + * LSODAR for ordinary differential equation modeling. + * Gillespie's direct method for exact stochastic kinetics. + * Gibson-Brooke's version of Gillespie's algorithm for exact stochastic kinetics. + * τ-leap algorithm for faster (approximate) stochastic kinetics. + * Adaptive SSA/τ-leap algorithm for faster (approximate) stochastic kinetics. + * Hybrid Runge-Kutta/SSA for hybrid simulations with stochastic kinetics and differential equations. + * Hybrid LSODA/SSA for hybrid simulations with stochastic kinetics and differential equations. + + Simulations can be of time courses or steady states. + + ANALISYS + + Models can be analyzed and modified with a large set of methods: + * Stoichiometric analysis of the reaction network, including mass conservation analysis and elementary flux modes. + * Optimization of arbitrary components of the model using a range of diverse algorithms. + * Parameter estimation using a range of diverse optimization algorithms. This can be done over several different experiments simultaneously, + including mixtures of steady-state and time course experiments. + * Local sensitivity analysis. + * Metabolic control analysis (a special form of sensitivity analysis). + * Time scale separation analysis; this allows definition of fast and slow components of the model, in a time-dependent way. + * Analysis of stochasticity using the linear noise approximation (allows estimating variances and co-variances even in the presence + of large numbers of particles). + * Cross sections, which allow to characterize non-linear dynamics properties, such as oscillations and chaos. + * Lyapunov exponents, which allows to establish if the system dynamics are chaotic. + + + DATA VISUALIZATION + + COPASI allows users to visualize data in various ways: + * Network diagrams can be used to visualize time course simulations as movies; + * Network diagrams can also be used to visualize mass conservation moieties, and elementary flux modes; + * Arbitrary 2D plots of any model variables and parameters (including trajectories in phase space); + * A series of plots that are most commonly used are already pre-defined; + * Color-coded matrices, for easily identifying large and small values; + * 3D bar chart representation of matrices + + + DATA OUTPUT + + COPASI allows users to define report files where data is written to during simulations and analyses. + These report files are useful for importing data onto other applications for further analysis and visualization. +
+- COPASI is a software application for simulation and analysis of biochemical - networks and their dynamics. -
-- COPASI is a stand-alone program that supports models in the SBML standard - and can simulate their behavior using ODEs or Gillespie's stochastic - simulation algorithm; arbitrary discrete events can be included in such - simulations. -
-- COPASI carries out several analyses of the network and its dynamics and - has extensive support for parameter estimation and optimization. - COPASI provides means to visualize data in customizable plots, histograms and - animations of network diagrams. -
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