Mathematical Enitites

Mathematical Types

Entity Types

• Model: The model time.
• Analysis: This is used for entities added by analysis tasks.
• Global Quantity: A global quantity is a model value which is neither a compartment nor a species.
• Compartment: Compartments are container for species.
• Species: Species are contained in compartments and have quantity and density values.
• Local Reaction Parameter: Local reaction parameters
• Stoichiometic Coefficient: Stoichiometic Coefficients (for future use, to support changing stoichiometry)
• Reaction: Reactions contain information about transitions of the system.
• Moiety: Based on the system of reactions mass conservation relationships are created which can be used instead of reaction derive ODEs to determine the value of some species.
• Event: Numerical values associated with events
• Delay: Numerical values associated with delays, i.e., value and lag.

The reason for this typing scheme is to avoid any dynamic casting and to facilitate easy determination of mathematical operations and values available for each entity.

Simulation Types

• Fixed: Constant value throughout the simulation
• EventTarget: Value which is only changed during events
• Time: The simulation time
• ODE: Value determined by an ODE
• Independent: Independent species determined by a reaction
• Dependent: Dependent species determined by a reaction
• Assignment: Values is determined by a mathematical assignment
• Conversion: Special assignment for to account for species duality (intensive vs extensive values)

Each entity type may be of a specific simulation type. Which combinations are suitable can be seen below.

Entity Type Combinations

	Time	ODE	Independent/Dependent	Assignment	Conversion	Fixed	Event Target
Model	required	prohibited	prohibited	prohibited	prohibited	prohibited	prohibited
Analysis	prohibited	allowed	prohibited	allowed	prohibited	allowed	allowed
Compartment	prohibited	allowed	prohibited	allowed	prohibited	allowed	allowed
Species	prohibited	allowed	allowed	allowed	allowed	allowed	allowed
Local Reaction Parameter	prohibited	prohibited	prohibited	prohibited	prohibited	allowed	allowed
Stoichiometric Coefficients	prohibited	prohibited	prohibited	prohibited	prohibited	required	prohibited
Global Quantity	prohibited	allowed	prohibited	allowed	prohibited	allowed	allowed
Reaction	prohibited	prohibited	prohibited	prohibited	prohibited	prohibited	prohibited
Moiety	prohibited	prohibited	prohibited	prohibited	prohibited	prohibited	prohibited

Entities with calculation type Time, ODE, Reaction, or Fixed may be used as targets of events.

Value Types

• Value: The value of an entity.
• Rate: The rate of an entity.
• Particle Flux: The particle flux of a reaction.
• Flux: The flux of a reaction.
• Propensity: The propensity of a reaction.
• Noise: The noise of an entity of type ODE or of a reaction.
• ParticleNoise: The particle noise of a reaction.
• Total Mass: The total mass of a moiety.
• Dependent Mass: The dependent mass of a moiety.
• Discontinuous: A object to track discontinuities in expression.
• Event Delay: The delay of an event.
• Event Priority: The priority of an event.
• Event Assignment: An assignment of an event.
• Event Trigger: The trigger of an event.
• Event Root: The root value derived from the trigger of an event.
• Event Root State: The state (true/false) of the root derived from the trigger of an event.
• Delay Value: The value of a delay.
• Delay Lag: The lag of a delay.
• Transition Time: Transition time is a species property.

Usage Declarations

This is not necessary for the mathematical computation but is a valuable feedback to the user. These settings are automatically determined by COPASI based on the model

• Event Target: This entity is target of an event assignment
• Relevant: This entity is used within the model, i.e., its value feeds back into ODEs or events.
• Observable: This entity is an observable of the model, it does not influence the model behavior.
• Unused: This entity is not used at all, i.e., its values is neither changed nor used.