[R] Michaelis-menten equation

[joerg van den hoff]

Chun-Ying Lee wrote:
> Dear R users:
>    I encountered difficulties in michaelis-menten equation. I found 
> that when I use right model definiens, I got wrong Km vlaue, 
> and I got right Km value when i use wrong model definiens. 
> The value of Vd and Vmax are correct in these two models. 
> 
> #-----right model definiens--------
> PKindex<-data.frame(time=c(0,1,2,4,6,8,10,12,16,20,24),
>        conc=c(8.57,8.30,8.01,7.44,6.88,6.32,5.76,5.20,4.08,2.98,1.89))
> mm.model <- function(time, y, parms) { 
>        dCpdt <- -(parms["Vm"]/parms["Vd"])*y[1]/(parms["Km"]+y[1]) 
>        list(dCpdt)}
> Dose<-300
> modfun <- function(time,Vm,Km,Vd) { 
>        out <- lsoda(Dose/Vd,time,mm.model,parms=c(Vm=Vm,Km=Km,Vd=Vd),
>               rtol=1e-8,atol=1e-8)
>           out[,2] } 
> objfun <- function(par) { 
>    out <- modfun(PKindex$time,par[1],par[2],par[3]) 
>    sum((PKindex$conc-out)^2) } 
> fit <- optim(c(10,1,80),objfun, method="Nelder-Mead)
> print(fit$par)
> [1] 10.0390733  0.1341544 34.9891829  #--Km=0.1341544,wrong value--
> 
> 
> #-----wrong model definiens--------
> #-----Km should not divided by Vd--
> PKindex<-data.frame(time=c(0,1,2,4,6,8,10,12,16,20,24),
>        conc=c(8.57,8.30,8.01,7.44,6.88,6.32,5.76,5.20,4.08,2.98,1.89))
> mm.model <- function(time, y, parms) { 
>    dCpdt <- -(parms["Vm"]/parms["Vd"])*y[1]/(parms["Km"]/parms["Vd"]+y[1]) 
>    list(dCpdt)}
> Dose<-300
> modfun <- function(time,Vm,Km,Vd) { 
> out <- lsoda(Dose/Vd,time,mm.model,parms=c(Vm=Vm,Km=Km,Vd=Vd),
>             rtol=1e-8,atol=1e-8)
>        out[,2] 
> } 
> objfun <- function(par) { 
>     out <- modfun(PKindex$time,par[1],par[2],par[3]) 
>     sum((PKindex$conc-out)^2)} 
> fit <- optim(c(10,1,80),objfun, method="Nelder-Mead)
> print(fit$par)
> [1] 10.038821  4.690267 34.989239  #--Km=4.690267,right value--
> 
> What did I do wrong, and how to fix it?
> Any suggestions would be greatly appreciated.
> Thanks in advance!!
> 
> 
> 

it is not clear to me what you are trying to do:
you seem to have a time-concentration-curve in PKindex and you seem to
set up a derivative of this time dependency according
to some model in dCpdt. AFAIKS this scenario is  not directly related to
the situation described by the Michaelis-Menten-Equation which relates
some "input" concentration with some "product" concentration. If Vm and
Km are meant to be the canonical symbols,
what is Vd, a volume of distribution? it is impossible to see (at least
for me) what exactly you want to achieve.

(and in any case, I would prefer "nls" for a least squares fit instead
of 'optim').

joerg
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