Predicts the Michaelis-Menten curve for a particular set of parameter values (M.C. Hannah).
||What to plot (
||Window in which to plot the graphs; default 1|
||Title for the graphs; default
||Title for the times axis; if this is unset, the identifier of the
||Title for the concentrations axis; if this is unset, the identifier of the
||Title for the rates axis; if this is unset, the identifier of the
||Variate with four values specifying the values of the parameters S0, Vmax, Km and K to use to form the predictions|
||Times at which to make predictions|
||Saves the predicted substrate concentrations|
||Saves the predicted reaction rates|
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
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
PLOT option controls the graphs that are plotted, with settings
||to plot the curve fitted to the concentrations, and|
||to plot the estimated reaction rates against the concentrations, and against time.|
WINDOW option specifies the window to use for the graphs (default 1). The
TITLE option can specify an overall title, and the
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
Golicnik, M. 2010. Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model. Analytical Biochemistry, 406, 94-96.
Commands for: Regression analysis.
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