New 63 knot and other knots in human proteome from AlphaFold predictions

AlphaFold is a new, highly accurate machine learning protein structure prediction method that outperforms other methods. Recently this method was used to predict the structure of 98.5% of human proteins. We analyze here the structure of these AlphaFold-predicted human proteins for the presence of knots. We found that the human proteome contains 65 robustly knotted proteins, including the most complex type of a knot yet reported in proteins. That knot type, denoted 63 in mathematical notation, would necessitate a more complex folding path than any knotted proteins characterized to date. In some cases AlphaFold structure predictions are not highly accurate, which either makes their topology hard to verify or results in topological artifacts. Other structures that we found, which are knotted, potentially knotted, and structures with artifacts (knots) we deposited in a database available at: https://knotprot.cent.uw.edu.pl/alphafold.

Circuit Topology for Bottom-Up Engineering of Molecular Knots

The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide them with thermal and kinetic stability. Yet, little is known about the design principles of naturally evolved molecular knots. Intra-chain contacts and chain entanglement contribute to the folding of knotted proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized to account for chain entanglement. This generalization is unique to circuit topology and not motivated by other theories. In this conceptual paper, we systematically analyze the circuit topology approach to a description of linear chain entanglement. We utilize a bottom-up approach, i.e., we express entanglement by a set of four fundamental structural units subjected to three (or five) binary topological operations. All knots found in proteins form a well-defined, distinct group which naturally appears if expressed in terms of these basic structural units. We believe that such a detailed, bottom-up understanding of the structure of molecular knots should be beneficial for molecular engineering.

A Topological Selection of Folding Pathways from Native States of Knotted Proteins

Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.

Unfolding and Translocation of Knotted Proteins by Clp Biological Nanomachines: Synergistic Contribution of Primary Sequence and Topology Revealed by Molecular Dynamics Simulations

We use Langevin dynamics simulations to model, at atomistic resolution, how various natively–knotted proteins are unfolded in repeated allosteric translocating cycles of the ClpY ATPase. We consider proteins representative of different topologies, from the simplest knot (trefoil 31), to the three–twist 52 knot, to the most complex stevedore, 61, knot. We harness the atomistic detail of the simulations to address aspects that have so far remained largely unexplored, such as sequence–dependent effects on the ruggedness of the landscape traversed during knot sliding. Our simulations reveal the combined effect on translocation of the knotted protein structure, i.e. backbone topology and geometry, and primary sequence, i.e. side chain size and interactions, and show that the latter can even dominate translocation hindrance. In addition, we observe that, due to the interplay between the knotted topology and intramolecular contacts, the transmission of tension along the peptide chain occurs very differently from homopolymers. Finally, by considering native and non–native interactions, we examine how the disruption or formation of such contacts can affect the translocation processivity and concomitantly create multiple unfolding pathways with very different activation barriers.

f -distance of knotoids and protein structure

Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here, we investigate the relation between knotoids differing only by small perturbations of the direction of projection. Since such knotoids are connected by at most a single forbidden move, we characterize forbidden moves in terms of equivariant band attachment between strongly invertible knots and of strand passages between θ -curves. This allows for the determination of the optimal sample size needed to produce a well-approximated knotoid distribution. Based on that and on topological properties of the distribution, we probe the depth of knotted proteins with the trefoil as the predominant knot type without using subchain analysis.

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 61-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 31-knotted proteins and the 41-knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the 41-knotted phytochromes and the 52- and 61-knotted proteins.

Computer simulation of knotted proteins unfold and translocation through nano-pores

We study the unfold and translocation of knotted protein, YibK and YbeA, through α-hemolysin nano-pore via a coarse grained computational model. We observe that knot of protein unfold in advance before the translocation take place. We also characterized the translocation mechanism by studying the thermodynamical and kinetic properties of the process. In particular, we study the average of translocation time, and the translocation probability as a function of pulling force F acting in the channel. In limit of low pulling inward constant force acting along the axis of the pore, the YibK knotted protein takes longer average translocation time as compare to YbeA knotted protein.