GP.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 Gaussian process is utilized for the likelihood function.

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GP.combi(method = T, RAM = F, time1, dat1, time2, dat2, enz, subs, MM,
  catal, nrepeat = 11000, jump = 1, burning = 1000,
  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)
`time1`	total time of dataset1
`dat1`	observed dataset1 ( trajectory column )
`time2`	total time of dataset2
`dat2`	observed dataset2 ( trajectory column )
`enz`	enzyme concentrate
`subs`	substrate concentrate
`MM`	initial value of MM constant
`catal`	initial value of catalytic constant
`nrepeat`	total number of iteration (defuault=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))
`MM_m_v`	MM prior gamma mean, variance(default=c(1,10000))
`sig`	variance of bivariate Normal proposal distribution
`va`	variance of data

The function GP.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 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 Gaussian process 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')
data('Chymo_high')
time1 = max(Chymo_low[,1])*1.01
time2 = max(Chymo_high[,1])*1.01
comb_GPMH=GP.combi(method=TRUE,dat1=Chymo_low[,2],time1=time1,dat2=Chymo_high[,2],time2=time2
                  ,enz=c(4.4e+7,4.4e+9),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(0.005,4.4e+8)^2,va=c(var(Chymo_low[,2]),var(Chymo_high[,2])))

# use RAM algorithm #
comb_GPRAM=GP.combi(method=TRUE,RAM=TRUE,dat1=Chymo_low[,2],time1=time1,dat2=Chymo_high[,2]
                     ,time2=time2,enz=c(4.4e+7,4.4e+9),subs=4.4e+7,MM=4.4e+8,catal=0.05
                     ,nrepeat=10000,jump=1,burning=0,catal_m_v=c(1, 1e+6),MM_m_v=c(1,1e+10)
                     ,sig=c(1,1e+11),va=c(var(Chymo_low[,2]),var(Chymo_high[,2])))

## End(Not run)