Reduced alphabet of prebiotic amino acids optimally encodes the conformational space of diverse extant protein folds

Table 3 Mutual information ranking for the prebiotic reduced alphabet

Interaction domain	Fold class [SCOP #]	Unweighted mutual information (I)		Normalized mutual information (I_norm)
Interaction domain	Fold class [SCOP #]	\( {\mathbf{\mathfrak{R}}}_{\mathrm{prebiotic}}^{\mathbf{10}} \) rank	\( {\mathfrak{R}}_{\mathrm{prebiotic}}^{10} \) percentile rank (%)	\( {\mathbf{\mathfrak{R}}}_{\mathrm{prebiotic}}^{\mathbf{10}} \) rank	\( {\mathfrak{R}}_{\mathrm{prebiotic}}^{10} \) percentile rank (%)
backbone (I_bb)	all data [1–4, 7]	48	99.97	859	99.54
	all-α [1]	3351	98.19	1688	99.09
	all-β [2]	2834	98.47	1899	98.97
	α/β [3]	13	99.99	124	99.93
	α + β [4]	52	99.97	396	99.79
	small [7]	270	99.85	878	99.52
backbone + contact (I_total)	all data [1–4, 7]	7389	96.00
	all-α [1]	18,289	90.10
	all-β [2]	18,333	90.08
	α/β [3]	4127	97.77
	α + β [4]	5325	97.12
	small [7]	104,252	43.57

The table shows the rank of the prebiotic reduced alphabet, in terms of mutual information (for both I_bb and I_total), among the spectrum of all 184,756 possible 10-amino-acid reduced alphabets. The unweighted mutual information is described in Eq. (7) for I_bb and in Eq. ((2) for I_total, while the normalized mutual information I_bb,norm is described in Eq. (8)

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