pwAddA

 

 m = pwAddA(m, lhs, reactants, parameters, signature, type, timePoint, ...
               description, ID, name, designerProps, classname, targetType, ...
               compartment, valueType)
 or: m = pwAddA(m, lhs, rhs, [], [], type)

 Adds an algebraic equation to a model, equivalent to a rule in SBML.
 Currently, explicit equations (assignments) and start value assignments are supported.
 Implicit equations like a+b+c=0 are not yet supported.

Arguments for pwAddA

 lhs           string      Left hand side of the assigned quantity, usually an ID
 reactants     ID array    Used variables either from x or u (or y for start value assignments)
                           This field is named reactants because the placeholders
                           r1, r2, etc. are used within the signature in order to
                           refer to the first, second, etc. variable of the "reactants".
 parameters    ID array    Used parameters either from k or s
 signature     string      The right hand side expression using placeholders
                           r1, r2, ... and k1, k2, ... for the variables and parameters.
 type          string      'assignment' or 'startValueAssignment'
 timePoint     float       Time when the start value assignment should be applied.
                           If not specified, the integration start time is used.
 description   string
 ID            string      ID of the equation, usually the lhs.
 name          string
 designerProps cell array  Layout information internally used in the model designer.
 classname     string
 targetType    string      'species', 'parameter', or 'compartment'
 compartment   string
 valueType     string      'concentration','amount'. Default: 'concentration'

Description

 
 PottersWheel supports explicit algebraic equations, which are evaluated before
 every integration step. The assigned quantities can be used as modifiers or
 parameters in the reactions.

 Apart from assignments which are fulfilled throughout the integration,
 startValueAssignments are applied only once, usually before integration starts.

 The list of variables is interpreted similarly as in the reactions paragraph:
 r1 in the rule signature corresponds to the first reactant
 and k2 to the second parameter. Variables can be dynamic
 variables x, driving inputs u and already assigned
 quantities a. Parameters can be dynamic parameters k.

 The timePoint can be specified to define the exact time when the
 assignment should be executed. This is only possible for type 'startValueAssignment'.
 If no timePoint is given, the assignment if always executed at integration start
 (in most cases 0).

 Alternative syntax:
 As a shortcut, expressions like

  m = pwAddA(m, 'Stat_cyt', 'Stat + pStat + pStatDimer')

 are allowed, i.e., the right hand side is specified directly and
 not via a list of variables and parameters and a ruleSignature.
 However, it is recommended to use the normal syntax.
 Important: The shortcut can only be applied if all elements of
 the right hand side are already defined. Therefore please put
 pwAddA below pwAddU, pwAddK, pwAddK, etc.

Fitting

 
 Since the algebraic rule determines the value of the parameter or modifier,
 it is not possible to fit the same quantity.

Difference to SBML

 
 The notation used within PottersWheel is closer to the mathematical
 representation of the dynamical system. The SBML notation is closer
 to the biochemical representation.

 In PottersWheel, a dynamic variable 'x' is always part of the set of differential
 equations and a dynamic parameter 'k' is always independent from all other parameters
 and can potentially be fitted. Algebraic assignments 'a' are (algebraically)
 calculated based on x, k, and other algebraic assignments.

 In SBML, a species is either determined by the
 differential equations, a rate rule, or an algebraic equation. A parameter is
 either free or determined by an algebraic equation.

 Compatibility is ensured by specifying the 'targetType' of an algebraic equation
 in PottersWheel. If the target type is not specified, it is guessed by the following
 approach: If the lhs appears as a dynamic variable x or driving input u, the target
 type is set to 'species'. If it appears as a parameter in a reaction, it is a 'parameter'.
 It is not allowed to use an assigned quantity as a parameter and a modifier in
 the same model. The guessing can only be applied, if all reactions are known
 before the assignment is added.

Examples

 
 Example 1: Normal assignment

 m = pwAddA(m, 'Stat_cyt', {'Stat','pStat','pStatDimer'}, {}, 'r1+r2+r3');

 Example 2: Time dependent equation

 It is possible to use t in the signature, e.g. for time dependent compartment
 sizes like

 m = pwAddA(m, 'NucleusSize', {}, {'InitialNucleusSize', 'GrowthRate'}, 'k1 + k2*t');

 The parameters 'InitialNucleusSize' and 'GrowthRate' are
 normal parameters and can be fitted.

 Example 3: Start value assignment

 m = pwAddA(m, 'Stat', {'Stat_obs'}, {'scale_Stat_obs'}, 'r1/k1', 'startValueAssignment');

 This sets the value of Stat to Stat_obs/scale_Stat_obs at t=0 and
 forces the trajectory through the first measured data point.

See also

pwAddR