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MMPREDICT procedure

Predicts the Michaelis-Menten curve for a particular set of parameter values (M.C. Hannah).


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 = 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


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.




Golicnik, M. 2010. Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model. Analytical Biochemistry, 406, 94-96.

See also


Commands for: Regression analysis.


" 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
Updated on March 7, 2019

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