an introduction to modeling and simulation with...
TRANSCRIPT
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Pedro Mendeshttp://www.comp-sys-bio.org
An introduction to modeling and simulation
with COPASI
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Reactions and kinetic functions
The rate of each reaction is a function of:• concentration of the substrates• concentration of the products • concentration of the modifiers• a set of constants
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Species concentrations are represented by ODEs
The rate of change of a species concentration is the algebraic sum of the rates producing it and the ones consuming it
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An example
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COPASI simulation methods
COPASI allows simulations based on:●ODEs
● Built directly from reaction kinetics ● Arbitrary ODEs● Compartment volumes can be variables (ODE)
●Stochastic kinetics based on Gillespie's SSA●Models can have:
● Algebraic assignments● Discrete events
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Modelling and Analysis with COPASI
Parameters and variables
● Parameters are items that are independent of the system, i.e. are set by outside agents (causes).
● Variables are items of the system whose values are determined exclusively by the parameters (effects).
● State of the system is the set of all variables.● One set of parameters determines
unambiguously the variables. ● One set of variables can be caused by many
parameter sets.
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Modelling and Analysis with COPASI
The central modelling question
● Given a model of a system: how do the parameters affect the state of the system?
● Answers explain:• which parameters have highest effect on desired
outcomes (eg drug design)• what properties of the model are more fragile or
robust• which parameters need accurate estimates
(experimental design)
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Modelling cycle
Model ¶meters
behaviour:simulation
data
behaviour:experimental
data
literature
Forward modelling
Inverse modelling
Text mining
Publication ofexperiments
Knowledgeformation
Knowledgeretrieval
knowledge
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Hoops et al. (2006) Bioinformatics 22, 30673074
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Frequent releases...
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Documentation and support
Several sources available at www.copasi.org:• User manual• FAQ• User forum• Issue tracker• Technical documentation:
• File format specification (including schema)• Documentation of API
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Mendes, P, Hoops, S, Sahle, S, Gauges, R, Dada, J, Kummer, U (2009) Computational Modeling of Biochemical Networks Using COPASI. Methods Mol. Biol. 500, 17-59.
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Systems Biology Markup Language
• Exchange medium for systems biology models, based on XML (used by >100 programs)
• Specifies models based on the biology, not on the maths
• Software interpret the models and translate them into mathematical/computational representations
• Allows ODEs, assignment rules, and events
http://www.sbml.org
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Model Definition
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Model Definition
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Stoichiometric analyses
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Stoichiometric analyses
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Deterministic time course simulations
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Deterministic time course simulations
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Hybrid ODE-discrete event
• System of ODEs is associated with events• An event (conditional state transition) consist
of: • a trigger (Boolean expression) • at least one assignment• a delay (optional)
• When trigger expression changes from FALSE to TRUE, the even triggers and causes the assignments. If there is a delay, the trigger will only be that time after the trigger
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Stochastic time course simulations
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Stochastic time course simulations
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Histograms
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Automatic conversion to irreversible reactions
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Hybrid ODE-stochastic
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Parameter scanning & sampling
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Parameter scanning & sampling
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Parameter scanning & sampling
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Sensitivity analysis (MCA)
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Sensitivity analysis (general)
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Sensitivity analysis (general)
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Global optimisation
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Parameter estimation
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Command line version• CopasiSE
• All model relevant information is contained in .cps file (COPASIML, an XML schema)
Usage: CopasiSE [options] [file] --configdir string The configuration directory for copasi. The default is .copasi in the home directory. --configfile string The configuration file for copasi. The default is copasi in the ConfigDir. --exportBerkeleyMadonna string The Berkeley Madonna file to export. --exportC string The C code file to export. --home string Your home directory. --license Display the license. --verbose Enable output of messages during runtime to std::error. -c, --copasidir string The COPASI installation directory. -e, --exportSBML string The SBML file to export. -i, --importSBML string A SBML file to import. -s, --save string The file the model is saved to after work. -t, --tmp string The temp directory used for autosave.
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Condor-COPASI high-throughput computing