Predicts the Michaelis-Menten curve for a particular set of parameter values (M.C. Hannah).
Options
PLOT = string tokens |
What to plot (concentration, rate); default conc |
|---|---|
WINDOW = scalar |
Window in which to plot the graphs; default 1 |
TITLE = text |
Title for the graphs; default 'Michaelis-Menten process' |
TTIMES = text |
Title for the times axis; if this is unset, the identifier of the TIMES variate is used |
TCONCENTRATIONS = text |
Title for the concentrations axis; if this is unset, the identifier of the CONCENTRATIONS variate is used if available, otherwise 'Concentration' |
TRATES = text |
Title for the rates axis; if this is unset, the identifier of the RATES variate is used if available, otherwise 'Rate' |
Parameters
PARAMETERS = variates |
Variate with four values specifying the values of the parameters S0, Vmax, Km and K to use to form the predictions |
|---|---|
TIMES = variates |
Times at which to make predictions |
CONCENTRATIONS = variates |
Saves the predicted substrate concentrations |
RATES = variates |
Saves the predicted reaction rates |
Description
A generalized Michaelis-Menten equation, for biochemical reaction rate v(t), versus substrate concentration S(t) at time t may be written as
v(t) = dS(t) / dt = Vmax ( S(t) – K1 ) / ( Km + S(t) – K1 )
This can be fitted to concentration and time data in Genstat using the MICHAELISMENTEN procedure.
If we have values for the parameters, including an initial concentration S0, we might like to predict S(t) and/or its derivative v(t) at various times. This seems simple until it is realized that there is no closed-form expression for S(t). Thus this procedure uses the method of Golicnik (2010) to calculate S(t) and v(t). The required times must be specified in a variate, by the TIMES parameter. Values for S0, Vmax, Km and K must be supplied in a variate (in that order), by the PARAMETERS parameter.
The PLOT option controls the graphs that are plotted, with settings
concentration |
to plot the curve fitted to the concentrations, and |
|---|---|
rate |
to plot the estimated reaction rates against the concentrations, and against time. |
By default, PLOT=concentration.
The WINDOW option specifies the window to use for the graphs (default 1). The TITLE option can specify an overall title, and the TCONCENTRATIONS, TRATES and TTIMES options can specify titles for the axes for concentration, rate and time, respectively.
The values predicted for S(t) and v(t) can be saved, in variates, by the CONCENTRATIONS and RATES parameters.
Options: PLOT, WINDOW, TITLE, TTIMES, TCONCENTRATIONS, TRATES.
Parameters: PARAMETERS, TIMES, CONCENTRATIONS, RATES.
Reference
Golicnik, M. 2010. Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model. Analytical Biochemistry, 406, 94-96.
See also
Procedure: MICHAELISMENTEN.
Commands for: Regression analysis.
Example
CAPTION 'MMPREDICT example'; STYLE=meta
" Specify values for Michaelis-Menten parameters."
VARIATE [NVALUES=!t(S0,Vmax,Km,K1)] MM_Pars; VALUES=!(26.4,0.52,3.36,1.74)
PRINT MM_Pars
" Specify time data at which predictions will be made."
VARIATE [VALUES=0...90] Times
" Predict concentrations and reaction rates."
MMPREDICT [PLOT=concentration,rate] PARAMETERS=MM_Pars; TIMES=Times;\
CONCENTRATIONS=Concentrations; RATES=Rates
PRINT Times,Concentrations,Rates; DECIMALS=0,4,4