14. If a protein contains four cysteine residues, the number of different ways they can simultaneously
form two intra-molecular disulphide bonds is _________.
Disulfide Bond Basics
Disulfide bonds form when two cysteine residues oxidize, linking their sulfur atoms (-SH groups) covalently,
stabilizing protein tertiary structure. In a protein with four cysteines (label them 1, 2, 3, 4), two bonds
pair all four without crossing or leaving unpaired residues. This intramolecular process occurs during folding
in oxidizing environments like the endoplasmic reticulum.
Correct Answer: 3 Ways
The number of ways is 3, calculated by first choosing partners for bonds. Pair cysteine 1 with 2,
then 3 with 4; or 1 with 3, then 2 with 4; or 1 with 4, then 2 with 3.
Mathematically, total pairings for 4 items into 2 pairs is:
(1/2) × (4! / (22 × 2!)) = 3
This accounts for indistinguishable bond order.
Common Options Explained
Option 1 (1 way): Incorrect; assumes only adjacent cysteines pair (e.g., 1–2 and 3–4), ignoring non-adjacent possibilities like 1–3 or 1–4 bonds in folded proteins.
Option 2 (2 ways): Wrong; might count only linear pairings, excluding the third valid crossed pair (1–4 with 2–3).
Option 3 (3 ways): Correct, as detailed above; standard in biochemistry for distinct topological pairings.
Option 6 (too many): Overcounts by treating bonds as ordered or permutations without dividing by symmetries,
a common error in misapplications of:
( (4 choose 2) × (2 choose 2) ) / 2! = 3
Biological Relevance
These pairings affect protein function; wrong bonds cause misfolding diseases like cystic fibrosis.
Enzymes like protein disulfide isomerase rearrange non-native bonds to native ones. For biotech applications,
predicting pairings aids in engineering stable therapeutic proteins.
