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 S_{0}, V, _{max}K and _{m}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* = *V _{max}* (

*S*(

*t*) –

*K*

_{1}) / (

*K*+

_{m}*S*(

*t*) –

*K*

_{1})

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 *S*_{0}, 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 *S*_{0}, *V _{max}*,

*K*and

_{m}*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