# Does the Michaelis-Menten equation take in account the non-enzyme formation of products?

I only recently learned about the Michaelis-Menten equation, since I am not studying biology or anything related. Let's write the equation as $$\frac{d[P]}{dt} = V_{max} \cdot \frac{[S]}{K + [S]}$$ If I'm not mistaken, this equation describes the rate at which products are formed ($\frac{d[P]}{dt}$) as a function of substrate concentration $[S]$ in steady-state. In a translation of Michaelis' paper I read that $V_{max}$ can be written as $k [E]$, where $k$ is a constant and $[E]$ is the total enzyme concentration.

Mathematically one would say that when the total enzyme concentration is zero ($[E] = 0$), the rate at which the product is formed should equal zero. If I recall correctly, in several reactions products are formed without enzymes (Enzymes only enhance the reaction rate?). Is the Michaelis-Menten equation specifically used for situations where $[E]>0$? If so, how does it account for very low enzyme concentrations where product formation from non-enzyme reactions cannot be neglected?

## 1 Answer

In any study of enzyme kinetics it is essential to subtract all 'blank' rates and to ensure that the measured rate is due only to enzyme catalysis.

That is, in kinetic 'parlance', the velocity vs [enzyme concentration] should be linear and go through the origin. Doubling the enzyme concentration should double the (enzymic) rate, and halving the enzyme concentration should halve the (enzymic) rate.

Failure to subtract blank rates may give rise to a variety of spurious kinetic effects such as downwardly-curving double-reciprocal plots (Lineweaver-Burk plots).

Downwardly-curving Lineweaver-Burk plots are diagnostic of negative co-operativity, but such a conclusion may be artefactual if blank rates are not subtracted.

A very good reference to this sort of this is Enzymes, (1979) by Dixon, M, Webb, E.C., Thorne, C. & Tipton, K.F. (3rd Edn), Longmans, in particular pp 461 - 462.

• Just for confirmation; the product formation rate would thus be $V_{0} + \frac{V_{max} \cdot [S]}{K+[S]}$ if blank rates were not subtracted? Is there a different notation/name for the rate of product formation when $V_{0}$ is not subtracted? – SMey1908 Mar 10 '16 at 15:52