Sat Reactions

From BioNetWiki

July 3, 2006

Modified RateLaw.pm and network.c to handle Sat reactions with a single rate constant. The syntax for the Sat reaction is now as follows:

A0(Y~pY) -> A0(Y~Y)   Sat(k1)

specifies a zeroth order reaction with rate k1.

A1(Y~pY) -> A1(Y~Y) Sat(k1,K1m)

specifies a first order saturation reaction with rate

k1*S1/(K1m+S1)

where S1 is the concentration of the first reactant in the reaction. For Sat reactions with two rate parameters, additional reactants add a multiplicative factor in the numerator.

A1(Y~pY) + E() -> A1(Y~Y) + E() Sat(k1,K1m)

goes at the rate

k1*S1*S2/(K1m+S1)

Each additional parameter to Sat adds a saturation term in the denominator of the rate. Thus,

A2(Y~pY) + B() -> A2(Y~Y) + B() Sat(k1,K1m,K2m)

has the rate

k1*S1*S2/((K1m+S1)*(K2m+S2))

The number of parameters to Sat may not exceed the number of reactants plus 1.

Here is an example BNGL file that illustrates the use of these types.

begin parameters
k1	1
K1m     1
K2m     1
end parameters

begin species
A0(Y~pY) 10
A1(Y~pY) 10
A2(Y~pY) 10
B()       1
end species

begin reaction rules
A0(Y~pY) -> A0(Y~Y) Sat(k1)
A1(Y~pY) -> A1(Y~Y) Sat(k1,K1m)
A2(Y~pY) + B() -> A2(Y~Y) + B() Sat(k1,K1m,K2m)
end reaction rules

begin observables
A0p A0(Y~pY)
A1p A1(Y~pY)
A2p A2(Y~pY)
end observables

generate_network({overwrite=>1});
toSBMLfile({});
simulate_ode({t_end=>20,n_steps=>20});

and the resulting plot of the output variables.