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Hill is an uninstantiated function used to indicate parameter values for a hill-function based reaction.
Hill[..] and hill[..] may be used interchangeably.
xCellerator has two types of Hill-function based reactions: catalytic and regulatory.
Catalytic Hill Reactions
The canonical form for a catalytic hill reaction is:
In a catalytic hill reaction both the reactant (A) and the product (B) change values. The catalyst (En) does not change. For the canonical form, the corresponding differential equation terms (produced by interpret) are:
![hill[v,K,n,r,m]](hill/eq1.gif)
All parameters are optional and may be omitted starting from the right. Default parameter values are: v=1, K=1, n=1, b=0, T=1, i.e.,
![(m*(r + v*A[t]^n*En[t]))/(K^n + A[t]^n)](hill/eq2.gif)
Alternate forms (and their corresponding ODE terms) that are allowed are:
If multiple catalytic reactions have the same product their corresponding ODE terms are added. Note that this is different from the way regulatory hill reactions are combined.
Regulatory Hill Reactions
The canonical form for a regulatory hill reaction is:
In a regulatory hill reaction, the value of the product (B) changes but the value of the regulator (A) does not:
![a |->B, hill[v,K,n,r.m]](hill/eq11.gif)
If there are multiple regulatory hill reactions with the same product, e,g.,
they are combined as in(1)
Note that all parameters except for the first (v) are ignored in all but the first reaction.
The following is an equivalent form of equation (1):
If an insufficient number of "T's" are provided, the last one (rightmost) in the list is repeated.
As with catalytic hill functions, all parameters are optional and may be omitted starting from the right. Default parameter values are the same for both types of hill arrow: T=1, K=1, n=1, b=0, v=1.
Cellerator Compatiblity
The form hill[options] may also be used. The following options are available:
| Option | Default | Corresponding Parameter |
| basalRate | 0 | b |
| khalf | 1 | K |
| nhill | 1 | n |
| Thill | 1 | T |
| vmax | 1 | v |
The Hill Function Palette
Reactions templates are provided on the Hill Function Palette
