Enzymes & activation energy

Biological catalysts that lower the energy hill.

The idea

Enzymes are proteins (plus a few RNA ribozymes) that speed up reactions by lowering the activation energy — the energy barrier reactants must climb — without being used up and without changing the final equilibrium. A substrate binds a precisely shaped pocket called the active site; in the induced-fit model the site closes around the substrate and strains its bonds, which is why each enzyme works on only one substrate or family of substrates. Rate rises with substrate concentration until every active site is busy, giving the Michaelis–Menten curve: Vmax is the ceiling, and Km is the substrate concentration at half of Vmax, so a low Km signals tight binding. Every enzyme has an optimum temperature and pH; too much heat or the wrong pH breaks the hydrogen and ionic bonds holding the protein’s shape, the active site distorts, and the enzyme denatures.

Work through an example

An enzyme has Vmax = 100 µmol/min and Km = 2 mM. At [S] = 2 mM, v = 100 × 2 / (2 + 2) = 50 µmol/min, half of Vmax by definition. At 8 mM, v = 100 × 8 / 10 = 80 µmol/min; at 18 mM, v = 100 × 18 / 20 = 90 µmol/min. Quadrupling the substrate from 2 to 8 mM raised the rate from 50% to only 80% of Vmax. A competitive inhibitor would raise the apparent Km but leave Vmax alone; a non-competitive inhibitor would lower Vmax and leave Km alone.

What to watch for

Enzymes are not "killed" by heat — they were never alive. They are denatured: the tertiary structure unfolds so the active site no longer fits its substrate, and for most enzymes that is permanent. Cold does the opposite of denaturing; it just slows molecular collisions, which is why food keeps in a refrigerator and why the enzyme works again when warmed. Human enzymes generally peak near 37 °C, but pepsin prefers pH 2 in the stomach while trypsin prefers pH 8 in the small intestine.