Proteins containing 6-crossing knot types andtheir folding pathways

Studying complex protein knots can provide new insights into potential knot folding mechanisms and other fundamental aspects of why and how proteins knot. This paper presents results of a systematic analysis of the 3D structure of proteins with 6-crossings knots predicted by the artificial intelligence program AlphaFold 2. Furthermore, using a coarse-grained native based model, we found that three representative proteins can self tie to a 63 knot, the most complex knot found in a protein thus far. Because it is not a twist knot, the 63 knot cannot be folded via a simple mechanism involving the threading of a single loop. Based on successful trajectories for each protein, we determined that the 63 knot is formed after folding a significant part of the protein backbone to the native conformation. Moreover, we found that there are two distinct knotting mechanisms, which are described here. Also, building on a loop flipping theory developed earlier, we present two new theories of protein folding involving the creation and threading of two loops, and explain how our theories can describe the successful folding trajectories for each of the three representative 63-knotted proteins.