Solution

ID: past-exam-of-the-biochemistry-course-of-the-university-of-cambridge/2025/paper-5/section-2/2/e/solution

There are
possible sequences of length 300 over the standard twenty-amino-acid alphabet. Sampling sequences would cover only about of that space, even before allowing repeated sequences. We cannot conclude that all possible protein folds have been explored.
However, this sequence count is not a count of folds: many sequences can share a fold, and many arbitrary sequences may not form a stable folded protein. Evolution also samples sequences non-uniformly. The calculation establishes vastly incomplete sequence-space exploration; proving either exhaustive or non-exhaustive coverage of physically realizable folds needs an additional model relating sequences to structures. The observed structural-cluster count alone supplies no such proof.

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