GP.multi: 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 single data set with an initial enzyme concentrations and substrate concentration. the Gaussian process is utilized for the likelihood function.

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GP.multi(method = T, RAM = F, time, dat, enz, subs, MM, catal,
  nrepeat = 10000, jump = 1, burning = 0, catal_m_v = c(1, 10000),
  MM_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`	initial value of MM constant
`catal`	initial value of cataldattic constant
`nrepeat`	total number of iteration (default=10000)
`jump`	length of distance (default =1)
`burning`	length of burning period (default =0)
`catal_m_v`	MM prior gamma mean, variance(default=c(1,10000))
`MM_m_v`	MM prior gamma mean, variance(default=c(1,10000))
`sig`	variance of bivariate Normal proposal distribution
`va`	variance of dataset

The function GP.multi generates a set of MCMC simulation samples from the posterior distribution of catalytic constant and MM constant of enzyme kinetics model. As the function estimates both two constants the user should input the enzyme and substrate initial concentration. The prior information for both two parameters can be given. The 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 variances of normal proposal distribution for catalytic and MM constant. 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 for updating two parameters simultaneously. 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 diffusion approximation 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
dou_GPMH=GP.multi(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(1,1e+10)
                    ,MM_m_v=c(1e+9,1e+18),sig=c(0.05,4.4e+8)^2,va=var(Chymo_low[,2]))
# use RAM algorithm #
dou_GPRAM=GP.multi(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(1,1e+10)
                      ,MM_m_v=c(1e+9,1e+18),sig=c(1,1),va=var(Chymo_low[,2]))

## End(Not run)