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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.

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More than one thousand knotted protein structures have been identified so far, but the functional roles of these knots remain elusive. It has been postulated that backbone entanglement may provide additional mechanostability. Here, we employed a bacterial proteasome, ClpXP, to mechanically unfold 52-knotted human ubiquitin C-terminal hydrolase (UCH) paralogs from their C-termini, followed by processive translocation into the proteolytic chamber for degradation. Our results revealed unprecedentedly slow kinetics of ClpXP-mediated proteolysis for the proteasome-associated UCHL5: ten thousand times slower than that of a green fluorescence protein (GFP), which has a comparable size to the UCH domain but much higher chemical and thermal stabilities. The ClpXP-dependent mechanostability positively correlates with the intrinsic unfolding rates of the substrates, spanning over several orders of magnitude for the UCHs. The broad range of mechanostability within the same protein family may be associated with the functional requirements for their differential malleabilities.

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Oligomerization of misfolded protein species is implicated in many human disorders. Here we showed by size-exclusion chromatography-coupled multiangle light scattering (SEC-MALS) and small-angle X-ray scattering (SEC-SAXS) that urea-induced folding intermediate of human ubiquitin C-terminal hydrolase, UCH-L1, can form well-defined dimers and tetramers under denaturing conditions despite being highly disordered. Introduction of a Parkinson disease-associated mutation, I93M, resulted in increased aggregation propensity and formation of irreversible precipitants in the presence of a moderate amount of urea. Since UCH-L1 exhibits highly populated partially unfolded forms under native conditions that resemble urea-induced folding intermediates, it is likely that these metastable dimers and tetramers can form under physiological conditions. Our findings highlighted the unique strength of integrated SEC-MALS/SAXS in quantitative analyses of the structure and dynamics of oligomeric folding intermediates that enabled us to extract information that is inaccessible to conventional biophysical techniques.

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Human ubiquitin C-terminal hydrolyase UCH-L5 is a topologically knotted deubiquitinase that is activated upon binding to the proteasome subunit Rpn13. The length of its intrinsically disordered cross-over loop is essential for substrate recognition. Here, we showed that the catalytic domain of UCH-L5 exhibits higher equilibrium folding stability with an unfolding rate on the scale of 10-8 s-1, over four orders of magnitudes slower than its paralogs, namely UCH-L1 and -L3, which have shorter cross-over loops. NMR relaxation dynamics analysis confirmed the intrinsic disorder of the cross-over loop. Hydrogen deuterium exchange analysis further revealed a positive correlation between the length of the cross-over loop and the degree of local fluctuations, despite UCH-L5 being thermodynamically and kinetically more stable than the shorter UCHs. Considering the role of UCH-L5 in removing K48-linked ubiquitin to prevent proteasomal degradation of ubiquitinated substrates, our findings offered mechanistic insights into the evolution of UCH-L5. Compared to its paralogs, it is entropically stabilized to withstand mechanical unfolding by the proteasome while maintaining structural plasticity. It can therefore accommodate a broad range of substrate geometries at the cost of unfavourable entropic loss.

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Recent studies on the mechanisms by which topologically knotted proteins attain their natively knotted structures have intrigued theoretical and experimental biophysicists. Of particular interest is the finding that YibK and YbeA, two small trefoil knotted proteins, remain topologically knotted in their chemically denatured states. Using small-angle X-ray scattering (SAXS), we examine whether these chemically denatured knotted proteins are different from typical random coils. By revisiting the scaling law of radius of gyration (Rg) as a function of polypeptide chain length for chemically denatured proteins and natively folded proteins, we find that the chemically denatured knotted proteins in fact follow the same random coil-like behavior, suggesting that the formation of topological protein knots do not necessarily require global compaction while the loosely knotted polypeptide chains are capable of maintaining the correct chirality without defined secondary or tertiary structures.

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