In prokaryotes, the error rate in protein synthesis may be as high as 5 × 10−4 per codon. What fraction of polypeptides containing (a) 500 residues or (b) 2000 residues would you expect to contain at least one amino acid substitution?

(a) 2.5 residues

(b) 10 residues

Explanation:

The amino acid substitution rate is a measure of evolutionary change for a given taxonomic group, species, etc. In general, this value is accompanied by a unit of time (often, the number of generations in prokaryotic organisms).

1 codon = 1 amino acid

Error rate >> 5 × 10−4 per codon = 50/ 10,000 (i.e. 50 amino acid substitutions per 10,000 residues)

500 residues >>  (500 x 50)/ 10,000 = 2.5 residues

2000 residues >>  (2,000 x 50)/ 10,000 =  10 residues