1. Home
2. MMPREDICT procedure

# MMPREDICT procedure

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 in which to plot the graphs; default 1 Title for the graphs; default `'Michaelis-Menten process'` Title for the times axis; if this is unset, the identifier of the `TIMES` variate is used Title for the concentrations axis; if this is unset, the identifier of the `CONCENTRATIONS` variate is used if available, otherwise `'Concentration'` 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 at which to make predictions Saves the predicted substrate concentrations 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 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.

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
```
Updated on March 7, 2019