GP.cat: Estimation of single catalytic constant using Gaussian...
In SIfEK: Statistical Inference for Enzyme Kinetics

Description Usage Arguments Details Value Examples

The function estimates single catalytic constant using single data set with an initial enzyme concentrations and substrate concentration. The Gaussian processes is utilized for the likelihood function.

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GP.cat(method = T, RAM = F, time, dat, enz, subs, MM, catal,
  nrepeat = 10000, jump = 1, burning = 0, catal_m_v = c(1, 10000),
  sig, va)

`method`	method selection: T=TQ model, F=SQ model(default = T)
`RAM`	Robust Adaptive MCMC options (default = F)
`time`	total time of data
`dat`	observed dataset (trajectory column)
`enz`	enzyme concentrate
`subs`	substrate concentrate
`MM`	true value of MM constant
`catal`	initial value of catalytic constant
`nrepeat`	total number of iteration (default=10000)
`jump`	length of distance (default =1)
`burning`	length of burning period ( default =0)
`catal_m_v`	Catalytic prior gamma mean, variance(default=c(1,10000))
`sig`	standard deviation of univariate Normal proposal distribution
`va`	variance of dataset

The function GP.cat generates a set of MCMC simulation samples from the conditional posterior distribution of catalytic constant of enzyme kinetics model. As the catalytic constant is only parameter to be estimated in the function the user should assign MM constant as well as initial enzyme concentration and substrate concentration. The prior information for the parameter can be given. The GP.cat function can select Robust Adaptive Metropolis (RAM) algorithm as well as Metropolis-Hastings algorithm with random walk chain for MCMC procedure. When “RAM” is assigned T then the function use RAM method and the “sig” is used as initial standard deviation of normal proposal distribution. When “RAM” is F, the function use Metropolis-Hastings algorithm with random walk chain and the “sig” can be set to controlled proper mixing and acceptance ratio of the parameter from the conditional posterior distribution. The “va” is the variance of the Gaussian process. 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 Gaussian process method is used for construction of the likelihood.

A vector of posterior samples of catalytic constant

## Not run: 
data('Chymo_low')
time1=max(Chymo_low[,1])*1.01
sk_GPMH=GP.cat(method=TRUE,time=time1,dat=Chymo_low[,2],enz=4.4e+7,subs=4.4e+7
                      ,MM=4.4e+8,catal=0.05,nrepeat=10000,jump=1,burning=0
                      ,catal_m_v=c(1,10000),sig=0.016,va=var(Chymo_low[,2]))
# use RAM algorithm #
sk_GPRAM=GP.cat(method=TRUE,RAM=TRUE,time=time1,dat=Chymo_low[,2],enz=4.4e+7,subs=4.4e+7
                      ,MM=4.4e+8,catal=0.05,nrepeat=10000,jump=1,burning=0
                      ,catal_m_v=c(1,10000),sig=0.1,va=var(Chymo_low[,2]))

## End(Not run)