Michaelis-Menten

Enzyme kinetics is the study of how fast enzymes work and how that speed changes when you vary conditions. The core equation is Michaelis-Menten, published by Leonor Michaelis and Maud Menten in 1913. Every MCAT kinetics question ultimately comes back to it.

The Scenario

Mix one substrate (S) with an enzyme (E). The enzyme grabs the substrate to form an enzyme-substrate complex (ES), does its chemistry, then releases the product (P) and returns free.

E + S ⇌ ES → E + P

If you keep adding substrate and measure how fast product appears, you get the classic Michaelis-Menten curve.

Three features jump out:

1. At low [S], the curve is nearly linear. Doubling substrate doubles the rate.
2. At high [S], the curve flattens. Enzyme is saturated - nearly every molecule is already working on a substrate. Adding more does not help.
3. The asymptote is called Vmax. The substrate concentration at half-Vmax is called Km.

The Equation

$V_0 = \frac{V_{max}[S]}{K_m + [S]}$

• V0 = initial velocity (rate of product formation at t near zero, before product builds up enough to matter)
• Vmax = maximum rate achievable, when enzyme is fully saturated
• Km = Michaelis constant, the [S] at which V0 = Vmax / 2
• [S] = substrate concentration

What Km Actually Means

Km has two equivalent interpretations:

1. The substrate concentration that gives half the maximum reaction rate.
2. A rough measure of the affinity of the enzyme for the substrate. A small Km means high affinity (the enzyme is satisfied at low [S]). A large Km means low affinity (the enzyme needs a lot of substrate before it hits half-Vmax).

Assumptions of Michaelis-Menten

The derivation relies on a few assumptions that matter for the MCAT:

• Steady state: the concentration of ES is approximately constant while you measure. Formation and breakdown of ES are balanced.
• [S] >> [E]: you add much more substrate than enzyme, so free [S] is not measurably depleted by forming ES.
• V0 is measured before the reverse reaction matters. Product concentration is near zero, so P → S is negligible.
• One substrate, one active site. Simple Michaelis-Menten kinetics do not apply directly to allosteric enzymes with multiple binding sites (those give sigmoidal curves - covered later).