### Abstract

For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S] _{0}. In our formula the rate is already expressed through [S] _{0}, and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S] _{0}. Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S] _{0}.

Original language | English (US) |
---|---|

Pages (from-to) | 982-985 |

Number of pages | 4 |

Journal | Biochemical and Biophysical Research Communications |

Volume | 417 |

Issue number | 3 |

DOIs | |

State | Published - Jan 20 2012 |

### Fingerprint

### Keywords

- Enzyme excess
- Enzyme kinetics
- Michaelis-Menten rate equation
- Quasi-steady-state
- Substrate excess

### ASJC Scopus subject areas

- Biochemistry
- Biophysics
- Cell Biology
- Molecular Biology

### Cite this

*Biochemical and Biophysical Research Communications*,

*417*(3), 982-985. https://doi.org/10.1016/j.bbrc.2011.12.051

**About and beyond the henri-michaelis-menten rate equation for single-substrate enzyme kinetics.** / Bajzer, Željko; Strehler, Emanuel E.

Research output: Contribution to journal › Article

*Biochemical and Biophysical Research Communications*, vol. 417, no. 3, pp. 982-985. https://doi.org/10.1016/j.bbrc.2011.12.051

}

TY - JOUR

T1 - About and beyond the henri-michaelis-menten rate equation for single-substrate enzyme kinetics

AU - Bajzer, Željko

AU - Strehler, Emanuel E.

PY - 2012/1/20

Y1 - 2012/1/20

N2 - For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S] 0. In our formula the rate is already expressed through [S] 0, and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S] 0. Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S] 0.

AB - For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S] 0. In our formula the rate is already expressed through [S] 0, and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S] 0. Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S] 0.

KW - Enzyme excess

KW - Enzyme kinetics

KW - Michaelis-Menten rate equation

KW - Quasi-steady-state

KW - Substrate excess

UR - http://www.scopus.com/inward/record.url?scp=84855998054&partnerID=8YFLogxK

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U2 - 10.1016/j.bbrc.2011.12.051

DO - 10.1016/j.bbrc.2011.12.051

M3 - Article

VL - 417

SP - 982

EP - 985

JO - Biochemical and Biophysical Research Communications

JF - Biochemical and Biophysical Research Communications

SN - 0006-291X

IS - 3

ER -