Why are there 20 amino acids and 4 nucleotides?

Abstract

Evolution of folded biopolymers requires effective and fast search of both the conformational space for folding and the sequence space for evolution. Molecular information theory and energy landscape theory show that the alphabet size of extant proteins and RNA is just enough to fulfill these requirements, given the constraints posed by the chemical physics of these polymers. Empirical estimations of the size of the effective sequence and conformational spaces of natural biopolymers support the theoretical predictions.