nlstools (version 2.1-0)

michaelismodels: Michaelis-Menten model and derived equations to model competitive and non-competitive inhibition

Description

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

Usage

michaelis
  compet_mich
  non_compet_mich

Value

A formula

Author

Florent Baty, Marie-Laure Delignette-Muller

Details

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 : $$v = \frac{S}{(S+K_m)(1+\frac{I}{Ki})} V_{max}$$

References

Dixon M and Webb EC (1979) Enzymes, Academic Press, New York.

Examples

# 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)