Tying up the Loose Ends: A Mathematically Knotted Protein

Knots have attracted scientists in mathematics, physics, biology, and engineering. Long flexible thin strings easily knot and tangle as experienced in our daily life. Similarly, long polymer chains inevitably tend to get trapped into knots. Little is known about their formation or function in proteins despite >1,000 knotted proteins identified in nature. However, these protein knots are not mathematical knots with their backbone polypeptide chains because of their open termini, and the presence of a “knot” depends on the algorithm used to create path closure. Furthermore, it is generally not possible to control the topology of the unfolded states of proteins, therefore making it challenging to characterize functional and physicochemical properties of knotting in any polymer. Covalently linking the amino and carboxyl termini of the deeply trefoil-knotted YibK from Pseudomonas aeruginosa allowed us to create the truly backbone knotted protein by enzymatic peptide ligation. Moreover, we produced and investigated backbone cyclized YibK without any knotted structure. Thus, we could directly probe the effect of the backbone knot and the decrease in conformational entropy on protein folding. The backbone cyclization did not perturb the native structure and its cofactor binding affinity, but it substantially increased the thermal stability and reduced the aggregation propensity. The enhanced stability of a backbone knotted YibK could be mainly originated from an increased ruggedness of its free energy landscape and the destabilization of the denatured state by backbone cyclization with little contribution from a knot structure. Despite the heterogeneity in the side-chain compositions, the chemically unfolded cyclized YibK exhibited several macroscopic physico-chemical attributes that agree with theoretical predictions derived from polymer physics.

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.

Mechanically tightening, untying and retying a protein trefoil knot by single-molecule force spectroscopy

Optical tweezers are used to stretch a knotted protein along different directions to probe its unfolding–folding behaviors, and the conformational change of its knot structure.

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.