[R] Michaelis-menten equation

[Chun-Ying Lee]

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!!