SSA.combi: Simultaneous estimation of Michaelis-Menten constant and...
In SIfEK: Statistical Inference for Enzyme Kinetics

Description Usage Arguments Details Value Examples

The function estimates both catalytic constant and Michaelis-Menten constant simultaneously using combined data sets with different enzyme concentrations or substrate concentrations. The diffusion approximation is utilized for the likelihood function.

SSA.combi(method = T, time1, time2, species1, species2, enz1, enz2,
  subs1, subs2, MM, catal, tun = 2.4, std, nrepeat, jump = 1,
  burning = 0, catal_m = 1, catal_v = 1e+05, MM_m = 1,
  MM_v = 1e+05)

`method`	method selection: T=TQ model, F=SQ model(default = T)
`time1`	observed time interval for data1
`time2`	observed time interval for data2
`species1`	observed trajectory of product for data1
`species2`	observed trajectory of product for data2
`enz1`	enzyme concentration for data1
`enz2`	enzyme concentration for data2
`subs1`	substrate concentration for data1
`subs2`	substrate concentration for data2
`MM`	initial value of MM constant
`catal`	initial value of catalytic constant
`tun`	tunning constant of MH algorithm (default =2.4)
`std`	standard deviation of proposal distribution
`nrepeat`	total number of iteration
`jump`	length of distance (default =1)
`burning`	lenth of burning period (default =0)
`catal_m`	prior mean of gamma prior (default =1)
`catal_v`	prior variance of gamma prior (default =10000)
`MM_m`	prior mean of gamma prior (default =1)
`MM_v`	prior variance of gamma prior (default =10000)

The function DA.combi generates a set of MCMC simulation samples from the posterior distribution of catalytic constant and MM constant of enzyme kinetics model. As the function uses combined data set with different initial concentration of enzyme or substrate concentration the user should input two values of enzyme and substrate initial concentration. The prior information for both two parameters can be given. The function utilizes the Gibbs sampler to update two parameters iteratively from conditional posterior distribution. Updating catalytic constant is conducted using conditional gamma distribution. The posterior samples of MM constant are drawn vis Metropolis-Hasting algorithm with random walk chain. The turning constant (scale_tun) and standard deviation of proposal normal distribution (sig) can be set to controlled proper mixing and acceptance ratio of the parameter from the conditional posterior distribution. The posterior samples are only stored with fixed interval according to set "jump" to reduce serial correlation. The initial iterations are removed for convergence. The “burning” is set the length of initial iterations. The stochastic simulation approximation method is used for construction of the likelihood.

A n*2 matrix of postrior samples of catalytic constant and MM constant

## Not run: 
data("Chymo_low")
time1=Chymo_low[,1]
species1=Chymo_low[,2]
data("Chymo_high")
time2=Chymo_high[,1]
species2=Chymo_high[,2]
enz.Chymotrypsin<-SSA.combi(method=TRUE, time1=time1 ,time2=time2 ,species1=species1
                               ,species2=species2,enz1=4.4e+7,enz2=4.4e+9
                               ,subs1=4.4e+7,subs2=4.4e+7,MM=1e+9,catal=0.01,
                               tun=2.0,std=8e+7,nrepeat=10000,jump=1,burning=0
                               ,catal_m=1,catal_v=1e+6, MM_m=1,MM_v=1e+10)

## End(Not run)