Figure 1. Lattice proteins used in this study that have a trefoil knot.

Lattice protein k0 is the reference system that was used to construct the other lattice proteins. The first bead is colored in black and the last bead in grey. The knotted core is located between bead three and bead 22 in k0, which classifies as a shallow knot. In systems k1 and k2 (a) we added one and two beads, respectively, to the first bead to extend the size of the first terminus thus increasing knot depth. The addition of three beads was done in two manners (b). In k3l they form a linear segment and in k3h they are arranged into a hairpin like conformation. In protein kd (c) the size of the first terminus was extended with seven beads and that of the last terminus with eight beads. We have also considered three knotted trefoils where the extended terminus does not establish any native contacts (d). These are used as control systems. Throughout this work we use the color code adopted in these figures to identify each considered lattice system.