Enzyme Kinetics: Vmax, Km, and Inhibition

What are Enzymes?

Enzymes are biological catalysts — proteins that speed up reactions by lowering the activation energy ( $E_a$ ). They are highly specific (lock-and-key or induced-fit model).

Learning Goals:

Describe the Michaelis-Menten model of enzyme kinetics.

Define and interpret Vmax and Km.

Compare competitive and non-competitive inhibition.

Explain factors affecting enzyme activity (temperature, pH).

Michaelis-Menten Kinetics

E + S \rightleftharpoons ES \rightarrow E + P

The Michaelis-Menten equation:

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

Parameter	Meaning
$V_{max}$	Maximum reaction rate (all enzyme molecules saturated)
$K_m$	Substrate concentration at which $v = V_{max}/2$
$[S]$	Substrate concentration

Low $K_m$ = high affinity (enzyme binds substrate tightly). High $K_m$ = low affinity.

Inhibition

Feature	Competitive	Non-competitive
Binds to	Active site	Allosteric site
Effect on $V_{max}$	Unchanged	Decreased
Effect on $K_m$	Increased (apparent)	Unchanged
Overcome by	Increasing [S]	Cannot be overcome
Example	Methotrexate	Heavy metal ions

Factors Affecting Enzyme Activity

Factor	Effect
Temperature	Rate ↑ to optimum (usually 37°C for human enzymes), then drops sharply (denaturation)
pH	Each enzyme has an optimal pH; extremes denature
Substrate [S]	Rate ↑ until $V_{max}$ (enzyme saturation)
Enzyme [E]	More enzyme → higher $V_{max}$

Worked Examples

Example 1: Interpreting a rate curve

If the reaction rate plateaus at 5 mmol/min → $V_{max} = 5$ mmol/min. The [S] where rate = 2.5 mmol/min → $K_m$ for the enzyme.

Example 2: Drug design

Aspirin is a competitive inhibitor of cyclooxygenase (COX). It binds the active site, blocking the substrate (arachidonic acid) from entering → reduces prostaglandin synthesis → reduces inflammation.

Common Mistakes

"Competitive inhibitors reduce $V_{max}$ " — Wrong. With enough substrate, competitive inhibitors are outcompeted → $V_{max}$ is unchanged.
"Enzymes are used up in reactions" — Enzymes are catalysts — they're recycled and not consumed.
Confusing denaturation with reversible inhibition — Denaturation permanently destroys tertiary structure; inhibition is usually reversible.

Exam Tips

On graphs: competitive inhibition shifts the curve right (higher apparent $K_m$ ); non-competitive shifts it down (lower $V_{max}$ ).
If asked "how would you increase the rate?": increase [S], increase [E], increase temperature (up to optimum), or remove inhibitors.
The Lineweaver-Burk plot ( $1/v$ vs $1/[S]$ ) shows inhibition type more clearly: competitive changes x-intercept; non-competitive changes y-intercept.

Cellular Respiration — Every step is enzyme-catalyzed.
Photosynthesis — RuBisCO kinetics and saturation.
Membrane Transport — Carrier proteins share enzyme-like saturation kinetics.