How knotted proteins fold has remained controversial since the identification of deeply knotted proteins nearly two decades ago. Both computational and experimental approaches have been used to investigate protein knot formation. Motivated by the computer simulations of Bölinger et al. [Bölinger D, et al. (2010) PLoS Comput Biol 6:e1000731] for the folding of the -knotted α-haloacid dehalogenase (DehI) protein, we introduce a topological description of knot folding that could describe pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. We analyze fingerprint data from crystal structures of protein knots as evidence that particular protein knots may fold according to specific pathways from our theory. Our results confirm Taylor’s twisted hairpin theory of knot folding for the -knotted proteins and the -knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the -knotted phytochromes and the - and -knotted proteins. Significance Knotting in proteins was once considered exceedingly rare. However, systematic analyses of solved protein structures over the last two decades have demonstrated the existence of many deeply knotted proteins. Conservation of knotting across some protein families strongly suggests that knotting can be important for protein structure and function, and hence, significant interest has arisen around how protein knots form. We build on results of previous computer simulations and prior theories of protein knot formation to obtain theoretical pathways for protein knotting that could apply to any knotted protein. By comparing our theoretical pathways with structural data on solved proteins, we determine which of our pathways may be feasible for each of the known protein knot types.
22 February 2006 in Journal of the London Mathematical Society