| User-defined arrows | Reference Home |
Regulatory Stoichiometric Palette
Two types of reactions can be defined "on the fly:" regulatory and stoichiometric. They have the following differences:
- Rate laws from stoichiometric reactions combine additively; rate laws from regulatory reactions combined vectorally.
- Rate laws for stoichiometric reactions affect all species in the reaction; rate laws for regulatory reactions only affect the species on the right side of the arrow.
User Defined Regulatory Reactions
In a regulatory reaction, the concentrations of the reactants (the species on the left side of the arrow) do not change, only those of the products (the species on the right hand side of the arrow).
The canonical form for a user-defined regulatory reaction is
where
mytype is any uninstantiated identifier chosen by the user, giving the name of the arrow, in analogy with pre-defined names such as GRN, Hill, NHCA, etc.
r, T, n, h are scalar identifiers or numbers.
f is any function of one variable that defines the rate law (as described below).
Note that mytype and f are redundant but both are required. Any specified mytype may only be used with a single f and vice-versa (see below).
and which is interpreted as 
The forms:
are equivalent and are interpreted as
Note that only one function (parameter f can be applied to any given arrow name. If the same arrow name is repeated for the same productthe same function must be used. Thus the following is permitted:
while the following is not permitted:
Furthermore, different regulatory arrows may not be combined with the same product. The following is not permitted:
Examples
The first example shows how a predefined function can be used; in this case, the function is the sqrt function, but it can be replaced with any defined function (including functions previously defined by the user):
The next example illustrates the use of pure functions to define a regulatory function f(x)=1+Tanh(x) (the hyperbolic tangent):
User Defined Stoichiometric Reactions
In a stoichiometric reaction, the concentrations of all reactants as well as all products change, according to their stoichiometry. The canonical form is: .
where f[...] is any function where all species are expressly stated as a function of time. The variables in the canonical form are interpreted as,
where:
Xi is any species on either side of the reaction;
pi is the stoichiometry of Xi on the left side of the arrow;
qi is the stoichiometry of Xi on the right side of the arrow;
The rate laws for stoichiometric reactions are combined additively, i.e., the rate law for any given species is the sum of the rate laws for each reaction involving that species.
Example
The User Palette
User-defined reactions can be entered from the User Palette:
