Nothing

```
#
# vim:set ff=unix expandtab ts=2 sw=2:
ThreepairMMmodel<- structure(
function # Implementation of a 6-pool Michaelis-Menten model
### This function implements a 6-pool Michaelis-Meneten model with pairs of microbial biomass and substrate pools.
(t, ##<< vector of times to calculate a solution.
ks, ##<< a vector of length 3 representing SOM decomposition rate (m3 d-1 (gCB)-1)
kb, ##<< a vector of length 3 representing microbial decay rate (d-1)
Km, ##<< a vector of length 3 representing the Michaelis constant (g m-3)
r, ##<< a vector of length 3 representing the respired carbon fraction (unitless)
Af=1, ##<< a scalar representing the Activity factor; i.e. a temperature and moisture modifier (unitless)
ADD, ##<< a vector of length 3 representing the annual C input to the soil (g m-3 d-1)
ival # a vector of length 6 with the initial values of the SOM pools and the microbial biomass pools (g m-3)
)
{
t_start=min(t)
t_end=max(t)
nr=6
if(length(ival)!=6) stop("The vector of initial values ival must be of length 6")
#function with system of equations
f=function(C,t){
S1=C[1] #SOM pool 1
B1=C[2] #Microbial biomass pool 1
S2=C[3] #SOM pool 2
B2=C[4] #Microbial biomass pool 2
S3=C[5] #SOM pool 3
B3=C[6] #Microbial biomass pool3
O=matrix(byrow=TRUE,nrow=6,ncol=1,c((Af*ks[1])*B1*(S1/(Km[1]+S1)),
kb[1]*B1,
(Af*ks[2])*B2*(S2/(Km[2]+S2)),
kb[2]*B2,
(Af*ks[3])*B3*(S3/(Km[3]+S3)),
kb[3]*B3))
return(O)
}
#List of transfer coefficients for T matrix
alpha=list()
alpha[["1_to_2"]]=function(C,t){
1-r[1]
}
alpha[["2_to_1"]]=function(C,t){
1
}
alpha[["3_to_4"]]=function(C,t){
1-r[2]
}
alpha[["4_to_3"]]=function(C,t){
1
}
alpha[["5_to_6"]]=function(C,t){
1-r[3]
}
alpha[["6_to_5"]]=function(C,t){
1
}
Anl=new("TransportDecompositionOperator",t_start,Inf,nr,alpha,f)
inputrates=BoundInFlux(
function(t){
matrix(
nrow=nr,
ncol=1,
c(ADD[1],0,ADD[2],0,ADD[3],0)
)
},
t_start,
t_end
)
modnl=GeneralNlModel( t, Anl, ival, inputrates, deSolve.lsoda.wrapper)
return(modnl)
### An object of class NlModel that can be further queried.
}
,
ex=function(){
days=seq(0,1000)
#Run the model with default parameter values
MMmodel=ThreepairMMmodel(t=days,ival=rep(c(100,10),3),ks=c(0.1,0.05,0.01),
kb=c(0.005,0.001,0.0005),Km=c(100,150,200),r=c(0.9,0.9,0.9),
ADD=c(3,1,0.5))
Cpools=getC(MMmodel)
#Time solution
matplot(days,Cpools,type="l",ylab="Concentrations",xlab="Days",lty=rep(1:2,3),
ylim=c(0,max(Cpools)*1.2),col=rep(1:3,each=2),main="Multi-substrate microbial model")
legend("topright",c("Substrate 1", "Microbial biomass 1",
"Substrate 2", "Microbial biomass 2",
"Substrate 3", "Microbial biomass 3"),lty=rep(1:2,3),col=rep(1:3,each=2),
bty="n")
#State-space diagram
plot(Cpools[,2],Cpools[,1],type="l",ylab="Substrate",xlab="Microbial biomass")
lines(Cpools[,4],Cpools[,3],col=2)
lines(Cpools[,6],Cpools[,5],col=3)
legend("topright",c("Substrate-Enzyme pair 1","Substrate-Enzyme pair 2",
"Substrate-Enzyme pair 3"),col=1:3,lty=1,bty="n")
#Microbial biomass over time
plot(days,Cpools[,2],type="l",col=2,xlab="Days",ylab="Microbial biomass")
}
)
```

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