 |
| Titel |
On the relationships between the Michaelis–Menten kinetics, reverse Michaelis–Menten kinetics, equilibrium chemistry approximation kinetics, and quadratic kinetics |
| VerfasserIn |
J. Y. Tang |
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| ISSN |
1991-959X
|
| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 8, no. 12 ; Nr. 8, no. 12 (2015-12-01), S.3823-3835 |
| Datensatznummer |
250116698
|
| Publikation (Nr.) |
 copernicus.org/gmd-8-3823-2015.pdf |
|
|
|
|
|
| Zusammenfassung |
| The Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics are
two popular mathematical formulations used in many land biogeochemical models
to describe how microbes and plants would respond to changes in substrate
abundance. However, the criteria of when to use either of the two are often
ambiguous. Here I show that these two kinetics are special approximations to
the equilibrium chemistry approximation (ECA) kinetics, which is the first-order
approximation to the quadratic kinetics that solves the equation of
an enzyme–substrate complex exactly for a single-enzyme and single-substrate
biogeochemical reaction with the law of mass action and the assumption of
a quasi-steady state for the enzyme–substrate complex and that the product
genesis from enzyme–substrate complex is much slower than the equilibration
between enzyme–substrate complexes, substrates, and enzymes. In particular, I
show that the derivation of the Michaelis–Menten kinetics does not consider
the mass balance constraint of the substrate, and the reverse
Michaelis–Menten kinetics does not consider the mass balance constraint of
the enzyme, whereas both of these constraints are taken into account in
deriving the equilibrium chemistry approximation kinetics. By benchmarking
against predictions from the quadratic kinetics for a wide range of substrate
and enzyme concentrations, the Michaelis–Menten kinetics was found to
persistently underpredict the normalized sensitivity ∂ ln v /
∂ ln k2+ of the reaction velocity v with respect to the
maximum product genesis rate k2+, persistently overpredict the
normalized sensitivity ∂ ln v / ∂ ln k1+ of v
with respect to the intrinsic substrate affinity k1+, persistently
overpredict the normalized sensitivity ∂ ln v / ∂ ln
[E]T of v with respect the total enzyme concentration
[E]T, and persistently underpredict the normalized
sensitivity ∂ ln v / ∂ ln [S]T of v
with respect to the total substrate concentration [S]T.
Meanwhile, the reverse Michaelis–Menten kinetics persistently underpredicts
∂ ln v / ∂ ln k2+ and ∂ ln v /
∂ ln [E]T, and persistently overpredicts
∂ ln v / ∂ ln k1+ and ∂ ln v /
∂ ln [S]T. In contrast, the equilibrium chemistry
approximation kinetics always gives consistent predictions of ∂ ln
v / ∂ ln k2+, ∂ ln v / ∂ ln k1+,
∂ ln v / ∂ ln [E]T, and ∂
ln v / ∂ ln [S]T, indicating that ECA-based
models will be more calibratable if the modeled processes do obey the law of
mass action. Since the equilibrium chemistry approximation kinetics includes
advantages from both the Michaelis–Menten kinetics and the reverse
Michaelis–Menten kinetics and it is applicable for almost the whole range of
substrate and enzyme abundances, land biogeochemical modelers therefore no
longer need to choose when to use the Michaelis–Menten kinetics or the
reverse Michaelis–Menten kinetics. I expect that removing this choice ambiguity
will make it easier to formulate more robust and consistent land
biogeochemical models. |
| |
|
| Teil von |
|
|
|
|
|
|
|
|