Package 'EKMCMC'

Function for estimating the catalytic constant

Description

The function estimates catalytic constant using progress-curve data, enzyme concentrations, substrate concentrations, and the Michaelis-Meten constant.

Usage

catalytic_est(
  method,
  timespan,
  products,
  enz,
  subs,
  K_M,
  catal_m,
  catal_v,
  nrepeat,
  jump,
  burn,
  volume,
  t_unit,
  c_unit
)

Arguments

method	This determines which model, the sQSSA or tQSSA model, is used for the estimation. Specifically, the input for method is TRUE (FALSE); then the tQSSA (sQSSA) model is used.
timespan	time points when the concentrations of products were measured.
products	measured concentrations of products
enz	initial enzyme concentrations
subs	initial substrate concentrations
K_M	true value of the Michaelis-Menten constant.
catal_m	prior mean of gamma prior for the catalytic constant k_cat.
catal_v	prior variance of gamma prior for the catalytic constant k_cat.
nrepeat	number of effective iteration, i.e., posterior samples.
jump	length of distance between sampling, i.e., thinning rate.
burn	length of burn-in period.
volume	the volume of a system. It is used to scale the product concentration. FALSE input provides automatic scaling.
t_unit	the unit of time points. It can be an arbitrary string.
c_unit	the unit of concentrations. It can be an arbitrary string.

Details

The function catalytic_est generates a set of Monte Carlo simulation samples from posterior distribution of the catalytic constant of enzyme kinetics model. Because the function estimates only the catalytic constant, the true value of the Michaelis-Menten constant should be given. Authors' recommendation: "Do not use this function directly. Do use the function main_est() to estimate the parameter so that the main function calls this function"

Value

A vector containing posterior samples of the estimated parameter: the catalytic constant.

Examples

## Not run: 
data("timeseries_data_example")
timespan1=timeseries_data_example[,c(1,3,5,7)]
products1=timeseries_data_example[,c(2,4,6,8)]
catalytic_result <- catalytic_est(method=TRUE,timespan=timespan1,
products=products1,enz = c(4.4, 4.4, 440, 440), subs=c(4.4, 4.4, 4.4, 4.4), 
K_M=44, catal_m = 1, catal_v = 1000, jump = 10, burn = 1000, nrepeat = 1000, 
volume = FALSE, t_unit = "sec", c_unit = "mM")

## End(Not run)

---

Main function for estimating catalytic constant k_cat and Michaelis-Menten (MM) constant K_M

Description

The function estimates either the catalytic constant, the Michaelis-Menten constant, or both simultaneously using progress-curve data, initial enzyme concentrations, and initial substrate concentrations.

Usage

main_est(
  method = TRUE,
  timeseries,
  enz,
  subs,
  K_M = FALSE,
  catal = FALSE,
  K_M_init = FALSE,
  std = FALSE,
  tun = 2.4,
  nrepeat = 1000,
  jump = 10,
  burn = 1000,
  catal_m = 1,
  catal_v = 1e+06,
  K_M_m = FALSE,
  K_M_v = FALSE,
  volume = FALSE,
  t_unit,
  c_unit
)

Arguments

method	This determines which model, the sQSSA or tQSSA model, is used for the estimation. Specifically, the input for method is TRUE (FALSE); then the tQSSA (sQSSA) model is used. Its default value is TRUE.
timeseries	Data frame containing the time points and measured concentrations of products. Every two columns represent the time points when the concentrations of the products were measured and the corresponding measured concentrations.
enz	initial enzyme concentrations
subs	initial substrate concentrations
K_M	true value of the Michaelis-Menten constant. Specify this object if the true value is known. Its default value is FALSE.
catal	true value of the catalytic constant. Specify this object if the true value is known. Its default value is FALSE.
K_M_init	initial value of K_M constant for the Metropolis-Hastings algorithm. If the input is FALSE then it is determined by max(subs). Its default value is FALSE.
std	standard deviation of proposal distribution. If the input is FALSE then it is determined by using the hessian of log posterior distribution. Its default value is FALSE.
tun	tuning constant for the Metropolis-Hastings algorithm when std is FALSE (i.e., hessian of the log posterior distribution is used). Its default value is 2.4.
nrepeat	number of effective iteration, i.e., posterior samples. Its default value is 1,000.
jump	length of distance between sampling, i.e., thinning rate. Its default value is 10.
burn	length of burn-in period. Its default value is 1,000.
catal_m	prior mean of gamma prior for the catalytic constant k_cat. Its default value is 1.
catal_v	prior variance of gamma prior for the catalytic constant k_cat Its default value is 1e+06.
K_M_m	prior mean of gamma prior for the Michaelis-Menten constant K_M. If the input is FALSE then it is determined by max(subs). Its default value is FALSE.
K_M_v	prior variance of gamma prior for the Michaelis-Menten constant K_M. If the input is FALSE then it is determined by max(subs)^2*1000. Its default value is FALSE.
volume	the volume of a system. It is used to scale the product concentration. FALSE input provides automatic scaling. Its default value is FALSE.
t_unit	the unit of time points. It can be an arbitrary string.
c_unit	the unit of concentrations. It can be an arbitrary string.

Details

The function main_est generates a set of Markov Chain Monte Carlo (MCMC) simulation samples from the posterior distribution of the catalytic constant or (and) the Michaelis-Menten constant of enzyme kinetics model. Users should input initial enzyme concentrations, substrate concentrations, and progress-curve data. Prior information for both parameters can be given. The Gibbs sampling and Metropolis Hastings algorithms are used to sample the parameters. Parameters for the MCMC such as tuning parameter for proposal distribution, prior parameters, and the iteration number can be specified by users. This function use one of catalytic_est(), MM_est(), MM_catal_est() to generate the samples depending on parameter(s) to be estimated.

Value

A vector (or matrix) containing posterior samples of the estimated parameter(s).

Examples

## Not run: 
data("timeseries_data_example")
result <- main_est(method=TRUE, timeseries = timeseries_data_example, 
enz = c(4.4, 4.4, 440, 440), subs=c(4.4, 4.4, 4.4, 4.4), K_M_init = 1e+1, 
std=1e+1, tun = 3.5, jump=10, burn=1000, nrepeat=1000,
catal_m=1, catal_v=100, K_M_m=1, K_M_v=1e+4, volume = FALSE, 
t_unit = "sec", c_unit = "mM")

## End(Not run)

---

Function for estimating both of the Michaelis-Menten constant and catalytic constant simultaneously

Description

The function estimates both of the catalytic and the Michaelis-Meten constants simultaneously using progress-curve data, enzyme concentrations, and substrate concentrations.

Usage

MM_catal_est(
  method,
  timespan,
  products,
  enz,
  subs,
  K_M_init,
  std,
  tun,
  nrepeat,
  jump,
  burn,
  catal_m,
  catal_v,
  K_M_m,
  K_M_v,
  volume,
  t_unit,
  c_unit
)

Arguments

method	This determines which model, the sQSSA or tQSSA model, is used for the estimation. Specifically, the input for method is TRUE (FALSE); then the tQSSA (sQSSA) model is used.
timespan	time points when the concentrations of products were measured.
products	measured concentrations of products
enz	initial enzyme concentrations
subs	initial substrate concentrations
K_M_init	initial value of K_M constant for the Metropolis-Hastings algorithm. If the input is FALSE then it is determined by max(subs).
std	standard deviation of proposal distribution. If the input is FALSE then it is determined by using the hessian of log posterior distribution.
tun	tunning constant for the Metropolis-Hastings algorithm when std is FALSE (i.e., hessian of the log posterior distribution is used).
nrepeat	number of effective iteration, i.e., posterior samples.
jump	length of distance between sampling, i.e., thinning rate.
burn	length of burn-in period.
catal_m	prior mean of gamma prior for the catalytic constant k_cat.
catal_v	prior variance of gamma prior for the catalytic constant k_cat.
K_M_m	prior mean of gamma prior for the Michaelis-Menten constant K_M. If the input is FALSE then it is determined by max(subs).
K_M_v	prior variance of gamma prior for the Michaelis-Menten constant K_M. If the input is FALSE then it is determined by max(subs)^2*1000.
volume	the volume of a system. It is used to scale the product concentration. FALSE input provides automatic scaling.
t_unit	the unit of time points. It can be an arbitrary string.
c_unit	the unit of concentrations. It can be an arbitrary string.

Details

The function MM_catal_est generates a set of Markov Chain Monte Carlo simulation samples from the posterior distribution of K_M and catalytic constant of enzyme kinetics model. Authors' recommendation: "Do not use this function directly. Do use the function main_est() to estimate the parameters so that the main function calls this function"

Value

A matrix containing posterior samples of the estimated parameters: the catalytic constant and the Michaelis-Menten constant.

Examples

## Not run: 
data("timeseries_data_example")
timespan1=timeseries_data_example[,c(1,3,5,7)]
products1=timeseries_data_example[,c(2,4,6,8)]
MM_catal_result <- MM_catal_est(method=TRUE,timespan=timespan1,
products=products1,enz = c(4.4, 4.4, 440, 440), subs=c(4.4, 4.4, 4.4, 4.4), 
K_M_init = 1, catal_m=1, catal_v = 1000, K_M_m = 1, K_M_v = 100000, 
std = 10, tun =3.5, nrepeat = 1000, jump = 10, burn = 1000, 
volume = FALSE, t_unit = "sec", c_unit = "mM")

## End(Not run)

---

Function for estimating the Michaelis-Menten constant

Description

The function estimates the Michaelis-Menten constant using progress-curve data, enzyme concentrations, substrate concentrations, and the catalytic constant.

Usage

MM_est(
  method,
  timespan,
  products,
  enz,
  subs,
  catal,
  K_M_init,
  std,
  tun,
  nrepeat,
  jump,
  burn,
  K_M_m,
  K_M_v,
  volume,
  t_unit,
  c_unit
)

Arguments

method	This determines which model, the sQSSA or tQSSA model, is used for the estimation. Specifically, the input for method is TRUE (FALSE); then the tQSSA (sQSSA) model is used.
timespan	time points when the concentrations of products were measured.
products	measured concentrations of products
enz	initial enzyme concentrations
subs	initial substrate concentrations
catal	true value of the catalytic constant.
K_M_init	initial value of K_M constant for the Metropolis-Hastings algorithm. If the input is FALSE then it is determined by max(subs).
std	standard deviation of proposal distribution. If the input is FALSE then it is determined by using the hessian of log posterior distribution.
tun	tuning constant for the Metropolis-Hastings algorithm when std is FALSE (i.e., hessian of the log posterior distribution is used).
nrepeat	number of effective iteration, i.e., posterior samples.
jump	length of distance between sampling, i.e., thinning rate.
burn	length of burn-in period.
K_M_m	prior mean of gamma prior for the Michaelis-Menten constant K_M. If the input is FALSE then it is determined by max(subs).
K_M_v	prior variance of gamma prior for the Michaelis-Menten constant K_M. If the input is FALSE then it is determined by max(subs)^2*1000.
volume	the volume of a system. It is used to scale the product concentration. FALSE input provides automatic scaling.
t_unit	the unit of time points. It can be an arbitrary string.
c_unit	the unit of concentrations. It can be an arbitrary string.

Details

The function MM_est generates a set of Markov Chain Monte Carlo simulation samples from posterior distribution of the Michaelis-Menten constant of enzyme kinetics model. Because the function estimates only the Michaelis-Menten constant the true value of the catalytic constant should be given. Authors' recommendation: "Do not use this function directly. Do use the function main_est() to estimate the parameter so that the main function calls this function"

Value

A vector containing posterior samples of the estimated parameter: the Michaelis-Menten constant.

Examples

## Not run: 
data("timeseries_data_example")
timespan1=timeseries_data_example[,c(1,3,5,7)]
products1=timeseries_data_example[,c(2,4,6,8)]
MM_result <- MM_est(method=TRUE,timespan=timespan1,products=products1,
enz = c(4.4, 4.4, 440, 440), subs=c(4.4, 4.4, 4.4, 4.4), catal = 0.051, 
K_M_init = 1, K_M_m = 1, K_M_v = 100000, std = 10, tun =3.5,
nrepeat = 1000, jump = 10, burn = 1000, volume = FALSE, 
t_unit = "sec", c_unit = "mM")

## End(Not run)

---

Product concentration of 101 observed time with different initial conditions

Description

An artificial data set containing the product concentration observed with the high and low enzyme concentrations. The 1st, 3rd, 5th, and 7th columns are observed times, and the 2nd, 4th, 6th, and 8th columns are product concentrations. The 2nd and 4th columns are observed with the initial enzyme concentrations of 4.4, and the 6th and 8th columns are observed with the initial enzyme concentrations of 440. The initial substrate concentrations are 4.4 for all data.

Usage

timeseries_data_example

Format

A data frame with 101 rows and 8 variables:

V1 V3 V5 V7

observed times, no unit

V2 V4 V6 V8

product concentrations, no unit

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