michaelismodels | R Documentation |
Formula of Michaelis-Menten model commonly used to describe enzyme kinetics, and derived formulas taking into account the effect of a competitive or a non-competitive inhibitor
michaelis
compet_mich
non_compet_mich
These models describe the evolution of the reaction rate (v) as a function
of the concentration of substrate (S) and the concentration of inhibitor (I) for compet_mich
and non_compet_mich
.
michaelis
is the classical Michaelis-Menten model (Dixon, 1979) with two parameters (Km, Vmax) :
v = \frac{S}{S+K_m} V_{max}
compet_mich
is the Michaelis-Menten derived model with three parameters (Km, Vmax, Ki), describing
a competitive inhibition :
v = \frac{S}{S + K_m (1+\frac{I}{K_i})} V_{max}
non_compet_mich
is the Michaelis-Menten derived model with three parameters (Km, Vmax, Ki), describing
a non-competitive inhibition :
v = \frac{S}{(S+K_m)(1+\frac{I}{Ki})} V_{max}
A formula
Florent Baty, Marie-Laure Delignette-Muller
Dixon M and Webb EC (1979) Enzymes, Academic Press, New York.
# Example 1
data(vmkm)
nls1 <- nls(michaelis,vmkm,list(Km=1,Vmax=1))
plotfit(nls1, smooth = TRUE)
# Example 2
data(vmkmki)
def.par <- par(no.readonly = TRUE)
par(mfrow = c(2,2))
nls2_c <- nls(compet_mich, vmkmki, list(Km=1,Vmax=20,Ki=0.5))
plotfit(nls2_c, variable=1)
overview(nls2_c)
res2_c <- nlsResiduals(nls2_c)
plot(res2_c, which=1)
nls2_nc <- nls(non_compet_mich, vmkmki, list(Km=1, Vmax=20, Ki=0.5))
plotfit(nls2_nc, variable=1)
overview(nls2_nc)
res2_nc <- nlsResiduals(nls2_nc)
plot(res2_nc, which=1)
par(def.par)
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