Amino acid alphabet size in protein evolution experiments:: better to search a small library thoroughly or a large library sparsely?

We compare the results obtained from searching a smaller library thoroughly versus searching a more diverse, larger library sparsely. We study protein evolution with reduced amino acid alphabets, by simulating directed evolution experiments at three different alphabet sizes: 20, 5 and 2. We employ a physical model for evolution, the generalized NK model, that has proved successful in modeling protein evolution, antibody evolution and T-cell selection. We find that antibodies with higher affinity are found by searching a library with a larger alphabet sparsely than by searching a smaller library thoroughly, even with well-designed reduced libraries. We also find ranked amino acid usage frequencies in agreement with observations of the CDR-H3 variable region of human antibodies.