Table 1. List of intra-chain hydrogen bonds that must/must not be satisfied for the systems I–IX.

The HB1 bond is defined as the hydrogen bond between the donor of the most N-terminal residue of the S1 strand in the system III, VI, or IX and the acceptor of the first residue of the GB loop. The HB2 and the HB3 bonds are defined as the hydrogen bonds required for the system of $R_{1-2}^N\ge 0$ and $R_{2-2^{\prime }}^N\le 0$, respectively. The graphical explanations of HB1, HB2, and HB3 are given in S20 Fig. The symbol “b” means that it must be bonded, “-” means that its hydrogen bond is ignored because a given system does not include such a donor-acceptor pair, and “n” means that it must not be bonded. HB1 is “n” in the systems III, VI, and IX because if HB1 is formed, the N-terminus of S2 will be stretched by one residue; therefore, it will not be a required register shift for these systems.

hydrogen bond\system	I	II	III	IV	V	VI	VII	VIII	IX
HB1	-	-	n	-	-	n	-	-	n
HB2	-	b	b	-	b	b	-	b	b
HB3	b	b	b	b	b	b	-	-	-