SIfEK (version 0.1.0)

SSA.multi: Simultaneous estimation of Michaelis-Menten constant and catalytic constant using the likelihood function with the stochastic simulation approximation method

Description

The function estimates both catalytic constant and Michaelis-Menten constant simultaneously using single data set with an initial enzyme concentrations and substrate concentration. The stochastic simulation approximation is utilized for the likelihood function

Usage

SSA.multi(method = T, time, species, enz, subs, MM, catal, tun = 2.4,
  std, nrepeat, jump = 1, burning = 0, catal_m = 1,
  catal_v = 10000, MM_m = 1, MM_v = 10000)

Arguments

method

method selection: T=TQ model, F=SQ model(default = T)

time

observed time interval

species

observed trajectory of product

enz

enzyme concentration

subs

substrate concentration

MM

true 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 (if =0, caclulated by Opt. function)

nrepeat

total number of iteration (default=10000)

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)

Value

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

Details

The function DA.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 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 <U+201C>burning<U+201D> is set the length of initial iterations. The stochastic simulation approximation method is used for construction of the likelihood.

Examples

# NOT RUN {
data("Chymo_low")
time1=Chymo_low[,1]
species1=Chymo_low[,2]
Chymotrypsin.low<-SSA.multi(method=TRUE, time=time1,species=species1,enz=4.4e+7
,subs=4.4e+7,MM=1e+9,catal=0.01,tun=2.4,std=8e+7,nrepeat=10000,jump=1,
burning=0,catal_m=1,catal_v=1e+10, MM_m=1e+9,MM_v=1e+18)
# }