Topological descriptions of protein folding.

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 [Formula: see text]-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 [Formula: see text]-knotted proteins and the [Formula: see text]-knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the [Formula: see text]-knotted phytochromes and the [Formula: see text]- and [Formula: see text]-knotted proteins.