A simple enzyme–substrate mechanism predicts saturating initial rates.
Key knowledge
For the simple mechanism E + S ⇌ ES → E + P, a quasi-steady-state approximation gives a saturating initial-rate relation. The Michaelis constant is the substrate concentration at half the model's maximum rate; it includes binding and turnover rate constants.
Values and equations
v₀ = Vmax [S] / (Km + [S])
v₀
initial product-formation rate mol L⁻¹ s⁻¹
Vmax
model maximum rate at the stated enzyme concentration mol L⁻¹ s⁻¹
[S]
free substrate concentration mol L⁻¹
Km
Michaelis constant for the stated mechanism and conditions mol L⁻¹
Conditions and scope
Use initial-rate conditions, substrate in sufficient excess, negligible reverse product reaction and approximately steady ES after its short transient.
Cooperativity, multiple substrates, inhibition or changing enzyme activity require other models. Km is not generally a pure binding dissociation constant.
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For the simple mechanism E + S ⇌ ES → E + P, a quasi-steady-state approximation gives a saturating initial-rate relation. The Michaelis constant is the substrate concentration at half the model's maximum rate; it includes binding and turnover rate constants.
The rate model is derived from a specific enzyme-binding and turnover mechanism.
In the stated reversible single-substrate Michaelis–Menten model, competitive inhibition increases apparent Km while leaving Vmax unchanged. Uncompetitive binding to the enzyme–substrate complex reduces both apparent Km and Vmax by the same factor. Observed patterns constrain a kinetic model without uniquely locating every molecular binding site.
The inhibition equations extend a bounded Michaelis–Menten model.
A low-concentration intermediate can have approximately equal formation and consumption rates after a short transient, allowing its rate equation to be eliminated from a mechanism. A pre-equilibrium approximation instead assumes a fast reversible step maintains its equilibrium ratio before slower conversion. These assumptions are distinct and require compatible timescales.
Michaelis–Menten uses a specifically bounded quasi-steady intermediate.
Enzymes are biological catalysts, most of which are proteins. A substrate is a reactant engaged by the enzyme; an active site provides the local binding and catalytic environment. Chemical groups, geometry and molecular motion influence substrate recognition and reaction pathways. Induced fit describes conformational changes associated with binding, rather than a perfectly rigid lock-and-key structure. Temperature, pH and regulatory interactions can alter catalytic activity without making one enzyme's optimum universal.
The E–S–ES kinetic model abstracts binding and turnover without representing every active-site conformation.