SIfEK (version 0.1.0)

GP.combi: Simultaneous estimation of Michaelis-Menten constant and catalytic constant using combined data and the likelihood function with the Gaussian process method

Description

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.

Usage

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)

Arguments

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

Value

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

Details

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 <U+201C>RAM<U+201D> is assigned T then the function use RAM method and the <U+201C>sig<U+201D> is used as initial variances of normal proposal distribution for catalytic and MM constant. When <U+201C>RAM<U+201D> is F, the function use Metropolis-Hastings algorithm with random walk chain and the <U+201C>sig<U+201D> can be set to controlled proper mixing and acceptance ratio of the parameter for updating two parameters simultaneously. The <U+201C>va<U+201D> 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 <U+201C>burning<U+201D> is set the length of initial iterations. The Gaussian process method is used for construction of the likelihood

Examples

# 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])))
# }
# NOT RUN {
# }