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

Table 2 Optimal and prebiotic reduced alphabets and substitution rules for different SCOP fold classes

Interaction domain	Fold class [SCOP #]	\( {\mathbf{\mathcal{S}}}_{\mathrm{opt}}\left({\mathfrak{R}}_{\mathrm{best}}^{\mathbf{10}}\right) \) ACDEFGHIKLMNPQRSTVWY	\( {\mathbf{\mathcal{S}}}_{\mathrm{opt}}\left({\mathfrak{R}}_{\mathrm{prebiotic}}^{\mathbf{10}}\right) \) ACDEFGHIKLMNPQRSTVWY
backbone (I_bb)	all-α [1]	AADELGQLKLANPQASKLAL	AADEAGEIELEDPAASTVAA
	all-β [2]	TVDEVGHVKVVNPTTSTVVV	ATDEVGTITLIDPTTSTVVV
	α/β [3]	ALDELGSVKLLDPEKSTVAL	AVDELGDIELIDPEESTVLL
	α + β [4]	AVDEVGTVKLLDPEKSTVLV	AVDEIGTIELLDPETSTVIV
	small [7]	ACDECGSVKVKDPSTSTVVV	ASDETGSITLLDPTTSTVII
backbone + contact (I_total)	all-α [1]	ACDELGQLELADPQQEELWY	AADEIGSIELLDPEESTVLA
	all-β [2]	TCNSFGTVTVVNPTRSTVYY	AVDEVGTISLVSPTTSTVIV
	α/β [3]	AVDELGSVKLYDPKKSSVYY	AVDEIGSIELLDPESSTVIT
	α + β [4]	AVDELGTVRLVDPRRTTVYY	AVDEIGTITLIDPSTSTVIT
	small [7]	ACDDFGYVRFFSPSRSSVYY	AVDEVGSITLISPTTSTVTT

\( {\mathcal{S}}_{\mathrm{opt}}\left({\mathfrak{R}}_{\mathrm{best}}^{10}\right) \) refers to the optimal substitution rule for the reduced alphabet with the highest mutual information; \( {\mathcal{S}}_{\mathrm{opt}}\left({\mathfrak{R}}_{\mathrm{prebiotic}}^{10}\right) \) refers to the optimal substitution rule for the prebiotic reduced alphabet. The amino acids are indicated in alphabetical order by their single-letter code. The amino acids in bold are included in the reduced alphabet, and those not in bold are the amino acids that substitute for those not in the reduced alphabet. Two interaction domains are considered: I_bb refers to the mutual information between local trimer sequence and alpha-carbon virtual dihedral backbone; I_total refers to the total mutual information that includes I_bb plus the mutual information arising from contacting residues in tertiary structure

ISSN: 2730-7182