Generating tertiary structures with guided fragment assembly. (A) The midpoint in a hairpin loop preserves a 2:1 or 1:2 ratio between the 5′ and 3′ sides. (B) All possible pairing constraints can be mapped to the problem of identifying all paths (red, black, blue) between (0,0) and (3,3) on a 4 × 4 lattice, using only the moves (+1,+1), (+1,+2), and (+2,+1). (C) Illustration of secondary structure constraints (red, black, blue) identified from paths on 4 × 4 lattice. (D) Fragment assembly steps for the three constraint sets generated for the given midpoint in the hairpin loop. Positions being moved are shown as red circles, previously moved positions are shown as black circles, and positions not yet moved are shown as gray circles. The three possible constraint sets are shown as red, black, or blue lines.
