Enzymes and proteins: study guide

Key ideas

Enzymes speed reactions by lowering the activation energy, and the Michaelis–Menten equation describes how the rate depends on substrate concentration. Inhibitors change the picture in a predictable way.

• Michaelis–Menten: v = Vmax[S] ÷ (Km + [S]). When [S] = Km the rate is exactly half of Vmax, so Km is a measure of how tightly the substrate binds (lower Km, tighter binding).
• At very high [S] the enzyme is saturated and v approaches Vmax. The turnover number is kcat = Vmax ÷ [E], the number of substrate molecules one enzyme converts per second.
• A competitive inhibitor competes with the substrate: Vmax is unchanged and Km appears larger. A non-competitive inhibitor lowers Vmax and leaves Km unchanged.
• Temperature and pH change rates, and extremes denature the enzyme. A protein’s concentration can be measured by its absorbance at 280 nm.

Key equations

• v = Vmax[S] ÷ (Km + [S])
• kcat = Vmax ÷ [E]
• A = εcl
• at [S] = Km, v = Vmax ÷ 2

Worked example

An enzyme has Vmax = 100 µmol/min and Km = 2 mM. At [S] = 6 mM, v = 100 × 6 ÷ (2 + 6) = 75 µmol/min, and at [S] = 2 mM it is 50 µmol/min. If 0.010 µmol of enzyme gave that Vmax, kcat = 100 ÷ 0.010 = 10 000 min⁻¹, or about 167 s⁻¹.

Common mistakes

• Thinking that Km is the substrate concentration that gives Vmax. It gives half of Vmax.
• Saying a competitive inhibitor lowers Vmax. It can be overcome by more substrate, so Vmax is unchanged.
• Treating a rate that has leveled off as a sign that the enzyme is destroyed. It is saturated, not denatured.

Practice

Test yourself with practice questions on this topic: Enzymes and proteins