As noted above, the design of the six-helix bundle is simple,10,11 but the design of the eighthelix
bundle is somewhat more complex. The theoretical diameter of the inner cavity is 3.2 nm
when the helices are placed on the edges of regular octagon. We gave higher priority to the
two-fold symmetric nature of the 8HB to achieve self-assembly from two 4HB molecules, and
correspondingly lower priority to distributing the inner angles evenly. Consequently, we used
rather different angles from those of a regular octagon (135°) for each dihedral angle. In helix
I, for example, four crossover points from the left in Figure 1a are placed 16 nucleotides (32/21
turn, assuming 10.5 nucleotide pairs/turn), 26 nucleotides (52/21 turn), and 16 nucleotides
apart, respectively. As a result, helix I is connected to helix II and another helix I, and the
theoretical dihedral angle between DX motifs of I/II and I/I is ca. 171°. Similarly, the theoretical
dihedral angles at helix II and III are ca. 154° (15 nucleotides = 10/7 turn) and 120° (14
nucleotides = 4/3 turn), respectively. These angles are calculated on the assumption that all the
crossovers are on the straight lines that connect adjacent helix axes. In the actual 8HB
molecules, however, some of these crossovers are expected to be off the lines as a consequence
of strain on the helices. Figure S3a shows proposed structures of the dimers of arched fourhelix
bundle capable of binding to itself only at Point A (8HB-A) or at Point B (8HB-B). There
is no collision in the theoretical structure of 8HB-A, thus each helix in this motif is expected
to be placed just according to the calculated dihedral angles to form a widely open eight-helix
bundle. On the other hand, there is an improbable overlapping of helices I due to dihedral angles
at helices III and IV that are too small. As a result, 8HB-B may be under strain to resolve this
overlap. The closed circular 8HB molecule has both of the above features, and the cross-section