29. How many different protein sequences of 100 residues can be generated using 20 standard amino acids?
(A) 10020
(B) 100 × 20
(C) 20100
(D) 100! × 20!
Core Concept
Proteins consist of chains where each of the 100 positions can independently select any of 20 amino acids (glycine, alanine, etc.). This follows the multiplication principle: for position 1, 20 choices; position 2, another 20; up to position 100. Total sequences equal 20×20×⋯×20 (100 times), or 20100.
Option Analysis
- (A) 10020: Incorrect, as this assumes 100 amino acid types with 20 positions, reversing the actual scenario of 20 types over 100 positions.
- (B) 100 × 20: Wrong, representing just two positions’ choices (100 for one, 20 for another), not a full chain.
- (C) 20100: Correct, capturing all combinations since each residue independently chooses from 20 amino acids.
- (D) 100! × 20!: Invalid, as factorials count permutations of distinct items without replacement; amino acids allow repetition.
Biological Relevance
There are 20 standard amino acids encoded by the genetic code, enabling vast sequence diversity despite nature using only a fraction. 20100 exceeds 10130, dwarfing atoms in the universe (~1080), explaining why random proteins rarely fold functionally. This underscores protein engineering challenges in biotechnology.
Exam Application
Common in GATE BT/XL for testing combinatorics in molecular biology. Practice by calculating smaller cases: for 2 residues, 202=400 sequences verifies the exponent rule. For n residues, always 20n.
