State Variables
Under state
variables we consider any numerical value which is required
to specify the current state of the model. This must include
all values needed to calculate the right hand site of all
ODEs and reaction fluxes.
COPASI supports 2 different mathematical views of the model.
These are the full model, where each species particle number
is viewed as an independent variable, and the reduced model,
where mass conservation relationships are used to reduce the
number of independent variables. In the below order we group
mathematical similar objects together, i.e., objects
determined by ODEs, reactions, assignments, events and
unchanged. It is not necessary to distinguish between
compartments and global quantities. In addition the particle
flux will be seen as an assignment which will in general be a
required object.
Initial Values
If the
mathematical simulation type is given as Fixed/Assignment the
choice depends on the fact whether we have an initial
assignment or not.
Order and Mapping of initial extensive Values
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Value |
Conversion |
Species |
| Compartment |
FIXED |
Value |
Fixed/Assignment |
Compartment |
| Global Quantity |
FIXED |
Value |
Fixed/Assignment |
GlobalQuantity |
|
FIXED |
Value |
Fixed/Assignment |
Analysis |
| Local Parameter |
FIXED |
Value |
Fixed |
LocalReactionParameter |
| Species |
FIXED (event target) |
Value |
Conversion |
Species |
| Compartment |
FIXED (event target) |
Value |
Fixed/Assignment |
Compartment |
| Global Quantity |
FIXED (event target) |
Value |
Fixed/Assignment |
Global Quantity |
|
FIXED (event target) |
Value |
Fixed/Assignment |
Analysis |
| Model |
TIME |
Value |
Fixed |
Model |
|
ODE |
Value |
Fixed/Assignment |
Analysis |
| Global Quantity |
ODE |
Value |
Fixed/Assignment |
GlobalQuantity |
| Compartment |
ODE |
Value |
Fixed/Assignment |
Compartment |
| Species |
ODE |
Value |
Conversion |
Species |
| Species |
REACTIONS |
Value |
Conversion |
Species |
| Species |
REACTIONS |
Value |
Conversion |
Species |
| Species |
ASSIGNMENT |
Value |
Conversion |
Species |
| Compartment |
ASSIGNMENT |
Value |
Assignment |
Compartment |
| Global Quantity |
ASSIGNMENT |
Value |
Assignment |
Global Quantity |
|
ASSIGNMENT |
Value |
Assignment |
Analysis |
Order and Mapping of initial intensive Values
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Value |
Conversion |
Species |
| Species |
FIXED (event target) |
Value |
Conversion |
Species |
| Species |
ODE |
Value |
Conversion |
Species |
| Species |
REACTIONS |
Value |
Conversion |
Species |
| Species |
REACTIONS |
Value |
Conversion |
Species |
| Species |
ASSIGNMENT |
Value |
Assignment |
Species |
Initial Rates
Order and Mapping of initial extensive Rates
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Rate |
Fixed (0) |
Species |
| Compartment |
FIXED |
Rate |
Fixed (0) |
Compartment |
| Global Quantity |
FIXED |
Rate |
Fixed (0) |
GlobalQuantity |
|
FIXED |
Rate |
Fixed (0) |
Analysis |
| Local Parameter |
FIXED |
Rate |
Fixed (0) |
LocalReactionParameter |
| Species |
FIXED (event target) |
Rate |
Fixed (0) |
Species |
| Compartment |
FIXED (event target) |
Rate |
Fixed (0) |
Compartment |
| Global Quantity |
FIXED (event target) |
Rate |
Fixed (0) |
Global Quantity |
|
FIXED (event target) |
Rate |
Fixed (0) |
Analysis |
| Model |
TIME |
Rate |
Time (1) |
Model |
|
ODE |
Rate |
ODE |
Analysis |
| Global Quantity |
ODE |
Rate |
ODE |
GlobalQuantity |
| Compartment |
ODE |
Rate |
ODE |
Compartment |
| Species |
ODE |
Rate |
ODE |
Species |
| Species |
REACTIONS |
Rate |
ReactionIndependent |
Species |
| Species |
REACTIONS |
Rate |
ReactionDependent |
Species |
| Species |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Species |
| Compartment |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Compartment |
| Global Quantity |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Global Quantity |
|
ASSIGNMENT |
Rate |
Assignment (NaN) |
Analysis |
| Reaction |
not applicable |
ParticleFlux |
SimulationTypeUndefined |
Reaction |
| Reaction |
not applicable |
Flux |
SimulationTypeUndefined |
Reaction |
Some rates (marked with NaN) will be only provided once we
have symbolic symbolic differentiation.
Order and Mapping of initial intensive Rates
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Rate |
Assignment |
Species |
| Species |
FIXED (event target) |
Rate |
Assignment |
Species |
| Species |
ODE |
Rate |
Assignment |
Species |
| Species |
REACTIONS |
Rate |
Assignment |
Species |
| Species |
REACTIONS |
Rate |
Assignment |
Species |
| Species |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Species |
Initial Internal
Values
Order of internally calculated initial Values
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
|
|
TotalMass |
SimulationTypeUndefined |
Moiety |
|
|
EventTrigger |
SimulationTypeUndefined |
Event |
Transient Values
Order and Mapping of transient extensive Values
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Value |
Fixed |
Species |
| Compartment |
FIXED |
Value |
Fixed |
Compartment |
| Global Quantity |
FIXED |
Value |
Fixed |
GlobalQuantity |
|
FIXED |
Value |
Fixed |
Analysis |
| Local Parameter |
FIXED |
Value |
Fixed |
LocalReactionParameter |
| Species |
FIXED (event target) |
Value |
Conversion |
Species |
| Compartment |
FIXED (event target) |
Value |
EventTarget |
Compartment |
| Global Quantity |
FIXED (event target) |
Value |
EventTarget |
Global Quantity |
|
FIXED (event target) |
Value |
EventTarget |
Analysis |
| Model |
TIME |
Value |
Time |
Model |
|
ODE |
Value |
ODE |
Analysis |
| Global Quantity |
ODE |
Value |
ODE |
GlobalQuantity |
| Compartment |
ODE |
Value |
ODE |
Compartment |
| Species |
ODE |
Value |
ODE |
Species |
| Species |
REACTIONS |
Value |
ReactionIndependent |
Species |
| Species |
REACTIONS |
Value |
ReactionDependent |
Species |
| Species |
ASSIGNMENT |
Value |
Conversion |
Species |
| Compartment |
ASSIGNMENT |
Value |
Assignment |
Compartment |
| Global Quantity |
ASSIGNMENT |
Value |
Assignment |
Global Quantity |
|
ASSIGNMENT |
Value |
Assignment |
Analysis |
To allow switching during simulation between reduced and full
models all we need is to provide an moiety expression in
addition to the rate expression for the dependent species.
Technically the last 4 (5 for the reduced model) are not
state variables.
Order and Mapping of transient intensive Values
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Value |
Conversion |
Species |
| Species |
FIXED (event target) |
Value |
EventTarget |
Species |
| Species |
ODE |
Value |
Conversion |
Species |
| Species |
REACTIONS |
Value |
Conversion |
Species |
| Species |
REACTIONS |
Value |
Conversion |
Species |
| Species |
ASSIGNMENT |
Value |
Assignment |
Species |
Transient Rates
Order and Mapping of transient extensive Rates
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
| Species |
FIXED |
Rate |
Fixed (0) |
Species |
| Compartment |
FIXED |
Rate |
Fixed (0) |
Compartment |
| Global Quantity |
FIXED |
Rate |
Fixed (0) |
GlobalQuantity |
|
FIXED |
Rate |
Fixed (0) |
Analysis |
| Local Parameter |
FIXED |
Rate |
Fixed (0) |
LocalReactionParameter |
| Species |
FIXED (event target) |
Rate |
Fixed (0) |
Species |
| Compartment |
FIXED (event target) |
Rate |
Fixed (0) |
Compartment |
| Global Quantity |
FIXED (event target) |
Rate |
Fixed (0) |
Global Quantity |
|
FIXED (event target) |
Rate |
Fixed (0) |
Analysis |
| Model |
TIME |
Rate |
Time (1) |
Model |
|
ODE |
Rate |
ODE |
Analysis |
| Global Quantity |
ODE |
Rate |
ODE |
GlobalQuantity |
| Compartment |
ODE |
Rate |
ODE |
Compartment |
| Species |
ODE |
Rate |
ODE |
Species |
| Species |
REACTIONS |
Rate |
ReactionIndependent |
Species |
| Species |
REACTIONS |
Rate |
ReactionDependent |
Species |
| Species |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Species |
| Compartment |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Compartment |
| Global Quantity |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Global Quantity |
|
ASSIGNMENT |
Rate |
Assignment (NaN) |
Analysis |
| Reaction |
not applicable |
ParticleFlux |
SimulationTypeUndefined |
Reaction |
| Reaction |
not applicable |
Flux |
SimulationTypeUndefined |
Reaction |
Some rates (marked with NaN) will be only provided once we
have symbolic symbolic differentiation.
Order and Mapping of transient intensive Rates
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation
Type |
Mathematical Entity Type |
| Species |
FIXED |
Rate |
Assignment |
Species |
| Species |
FIXED (event target) |
Rate |
Assignment |
Species |
| Species |
ODE |
Rate |
Assignment |
Species |
| Species |
REACTIONS |
Rate |
Assignment |
Species |
| Species |
REACTIONS |
Rate |
Assignment |
Species |
| Species |
ASSIGNMENT |
Rate |
Assignment (NaN) |
Species |
Internal Values
Order of internally calculated transient Values
| Entity |
Status |
Mathematical Value Type |
Mathematical Simulation Type |
Mathematical Entity Type |
|
|
TotalMass |
SimulationTypeUndefined |
Moiety |
|
|
EventTrigger |
SimulationTypeUndefined |
Event |
|
ODE |
Noise |
ODE |
Analysis |
| Global Quantity |
ODE |
Noise |
ODE |
GlobalQuantity |
| Compartment |
ODE |
Noise |
ODE |
Compartment |
| Species |
ODE |
Noise |
Assignment |
Species (extensive) |
| Species |
REACTIONS |
Assignment |
ReactionIndependent |
Species (extensive) |
| Species |
REACTIONS |
Assignment |
ReactionDependent |
Species (extensive) |
| Species |
ODE |
Noise |
ODE |
Species (intensive) |
| Species |
REACTIONS |
Noise |
ReactionIndependent |
Species (intensive) |
| Species |
REACTIONS |
Noise |
ReactionDependent |
Species (intensive) |
| Reaction |
|
Noise |
SimulationTypeUndefined |
Reaction |
| Reaction |
|
ParticleNoise |
SimulationTypeUndefined |
Reaction |
|
|
EventDelay |
SimulationTypeUndefined |
Event |
|
|
EventPriority |
SimulationTypeUndefined |
Event |
|
|
EventAssignment |
SimulationTypeUndefined |
Event |
|
|
EventRoot |
SimulationTypeUndefined |
Event |
|
|
EventRootState |
SimulationTypeUndefined |
Event |
|
|
Propensity |
SimulationTypeUndefined |
Reaction |
|
|
DependentMass |
SimulationTypeUndefined |
Moiety |
|
|
Discontinuous |
SimulationTypeUndefined |
Event |
|
|
DelayValue |
SimulationTypeUndefined |
Delay |
|
|
DelayLag |
SimulationTypeUndefined |
Delay |
|
|
TransitionTime |
Assignment (NaN) |
Species |
It is important to realize that for the reduced model we need
to recalculate the total number of a moiety in case an event
changes any species involved in it. We do not add this value
to the list of required objects determined by assignments as
this must not be recalculated in any other
circumstances.
We add all constant values to the state to allow parallel
calculation of different parameter sets in optimization,
parameter estimation and scan. This means that all local
reaction constants will be added as global quantities.
For the initial state and the rates we will use the same
order since we do not have any special order
requirement.
