Michaelis-Menten model and derived equations to model competitive and non-competitive inhibition
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 = S/(S+Km)*Vmax
compet_mich is the Michaelis-Menten derived model with three parameters (Km, Vmax, Ki), describing
a competitive inhibition :
v = S/(S + Km*(1+I/Ki) ) * Vmax
non_compet_mich is the Michaelis-Menten derived model with three parameters (Km, Vmax, Ki), describing
a non-competitive inhibition :
v = S/( (S + Km)*(1+I/Ki) ) * Vmax
A formula
Florent Baty florent.baty@gmail.com
Marie-Laure Delignette-Muller ml.delignette@vetagro-sup.fr
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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.