Table 1 Summary of results of better XAA sets as a function of set size.

From: Adaptive Properties of the Genetically Encoded Amino Acid Alphabet Are Inherited from Its Subsets

Set size (no. AAs)

# CAA Set Combinationsa

# CAA Maximal Setsb

% Better XAA Sets in 108 Trials

3

1,140

509

0.499

4

4,845

1,250

0.242

5

15,504

2,151

0.161

6

38,760

2,875

4.65 × 10−2

7

77,520

3,044

1.68 × 10−2

8

125,970

3,177

7.52 × 10−3

9

167,960

2,787

3.58 × 10−3

10

184,756

2,160

1.23 × 10−3

11

167,960

1,566

3.77 × 10−4

12

125,970

1,181

1.59 × 10−4

13

77,520

799

1.75 × 10−4

14

38,760

504

1.68 × 10−4

15

15,504

289

2.10 × 10−4

16

4,845

165

3.24 × 10−4

17

1,140

74

2.07 × 10−4

18

190

28

6.47 × 10−5

19

20

8

1.09 × 10−5

20c

1

1

6 × 10−6

  1. aThis number is derived from the formula for binomial coefficients, see SI Section 1. bThis is the number of maximal sets, see methods section. cThere is only one possible set, which is also maximal, of the 20 CAAs, and only 6 better XAA sets were found in a previous study, of which several contained CAAs3.