The folding of proteins with a complex knot is still an unresolved question. Based on representative members of Ubiquitin C-terminal Hydrolases (UCHs) that contain the 52 knot in the native state, we explain how UCHs are able to unfold and refold in vitro reversibly within the structure-based model. In particular, we identify two, topologically different folding/unfolding pathways and corroborate our results with experiment, recreating the chevron plot. We show that confinement effect of chaperonin or weak crowding greatly facilitates folding, simultaneously slowing down the unfolding process of UCHs, compared with bulk conditions. Finally, we analyze the existence of knots in the denaturated state of UCHs. The results of the work show that the crowded environment of the cell should have a positive effect on the kinetics of complex knotted proteins, especially when proteins with deeper knots are found in this family.
The role of knots in protein structures is still not fully understood. The topological complexity induces stability to the structure [1,2] and enforces local motifs favorable for active sites of enzymes [3]. The latter fact may explain, why over 80% of known knotted proteins are enzymes with the active site located at the entangled region [4]. Nevertheless, folding process of knotted proteins is a fundamental and still not solved problem. One of the families of knotted proteins is Ubiquitin C-terminal Hydrolase (UCH) of which the characteristic feature is the presence of a complex topological fingerprint 523131 [4] as shown in the Fig 1. This means that the entire protein forms a 52 knot as a whole, but some of its subchains form two trefoil knots (see Table 1). Each entry in the matrix indicates the knot type, formed by one continuous subchain, by one particular color; e. g. the unknot is denoted in white. Each such subchain starts with the N-terminal amino acid at position x and ends with the C-terminal amino acid at position y, and the corresponding colored entry in the matrix is shown in position (x, y) (along respectively horizontal and vertical axes). Specifically, one can trace what is the topology of the subchain with one end in N-terminus. Pictorially, this is represented as the traveling down of the left-most vertical line in the matrix in Fig 1). In the beginning, successive subchains are unknotted, however reaching at least Ile163 the subchain becomes trefoil knotted (first green patch in the matrix). The subchain Met1-Tyr173 is still knotted, however then the chain winds back forming a slipknot loop and when the end of the subchain is in-between Glu174 and Pro180 (parts of C-terminal β-strands), such subchain is unknotted (the break between the green patches). Next, the subchain starting in N-terminus and ending in-between residues Pro182 and Ala216 is again trefoil knotted (bottom green patch) and finally the whole chain is 52 knotted (blue patch). The 523131 fingerprint is unique and conserved in all UCH members, which are separated by billion years of evolution and exhibit a very low sequence similarity (below 30%) [5]. Notably, the formation of the larger trefoil results in the formation of the inner-most (dipper) trefoil knot. Therefore, in subsequent analysis by “formation of 31 knot”, we mean the formation of the larger (and hence both) trefoil knot. The UCH superfamily is a group of deubiquitinating enzymes (DUBs). Their exact substrates have not yet been determined, however it seems that the role of UCHs is to detach the ubiquitin from small nucleophiles. Four of the UCH family members exist in humans: UCH-L1, UCH-L3, human UCH-L5 (UCH37) and BAP-1. They share a high degree of homology in their catalytic domains [6], surrounded by the deepest 31 knot. Moreover, UCHs have a tissue-specific expression in complex organisms such as humans and their activity is crucial from the therapeutical point of view. For example, UCH-L3 has been shown to be upregulated in breast cancer tissues [7], and a high expression of UCH-L5 is significantly associated with poor prognosis in human epithelial ovarian cancer [8]. On the other hand, UCH-L1 is one of the most common proteins in human brain (composing up to 1-2% of the brain the total protein content [9]), and it is highly expressed in pancreatic [10], esophageal [11], prostate [12], medullary thyroid [13], colorectal carcinomas [14] and HPV16-transformed cells [15]. Its misfolded forms were connected with neuronal disorders such as Parkinson’s, Huntington’s and Alzheimer’s diseases [16], which justifies the importance of studying the UCH folding process. In general, it is expected that folding of knotted proteins is governed mainly by the depth of the knot and the complexity of the topological fingerprint [17,18]. Self-tying was observed theoretically for the smallest knotted proteins with DNA binding motif and a rather shallow 31 knot [19,20]. They mainly fold by a slipknot conformation [17,19]. Similarly, it was shown that proteins with a deep trefoil knot, such as YibK and YbeA, can self-tie [21]. The theoretical results obtained for these proteins with a structure based model additionally revealed that a knotting event is a rate-limiting step [22] and the folding efficiency can be controlled by non-native contacts [23] or consideration of cotranslational on-ribosome folding [24]. For the protein with a 61 knot, DehI [25], there were only a few successful folding pathways observed theoretically. Surprisingly, this protein folds via a simple mechanism: a large twisted loop formed on the backbone flips over another protein fragment previously arranged in a twisted loop, and in consequence, the six-fold knot is created in a single movement. Even though this protein is prone to aggregate, the experimental data support this mechanism [26]. These results suggest that bulk structure-based models can be used to investigate knotted proteins. On the other hand, experimental data show that knotting process of trefoil-knotted YibK and YbeA bacterial proteins can be specifically and significantly accelerated by the GroEL-GroES chaperonin complex [21] encapsulating the folding protein. This agrees with the theoretical investigation showing that knotting probability of polymers increases in confinement [27]. Only due to the encapsulation (following [28]), successful reversible folding was observed for members of knotted proteins with DNA binding motif VirC and DndE [29]. It is then natural to expect, that chaperonins encapsulating proteins may also facilitate folding and self-knotting of eucaryotic UCHs, although no experimental result in this topic is available yet. Nevertheless, one has to bear in mind, that encapsulation is the simplest possible model of chaperonin, lacking many “biological features”—specific binding to the cage, chaperonin conformational changes, etc. However, any theoretical results have to be confronted with the experimental data concerning UCHs folding. It has been shown already that UCHs can fold and refold reversibly in two parallel pathways, each consisting of one slow and one fast phase, as determined from chevron plot [30,31]. Despite a common mechanism, folding processes of different UCHs is characterized by different kinetic parameters. Such differences can stem from a various depth of knots in UCH family [4], ranging from rather shallow (from the N-terminus) to the deep knot, which we just found, as shown in Table 1. The most attention-drawing are the S18Y and I93M mutations, which were found to modify (either decrease or increase) the risk of Parkinson’s disease [32], and the intermediates on folding pathway, as these are especially prone to oligomerization [33]. However, the results concerning these mutations are variable and differ in different studies. Despite the successful assignment of the majority of signals in NMR spectrum of the UCH-L1 [34], and in spite of studies of its tryptophan variants [33], the exact conformation of intermediates is still unclear. This may be due to a broad structural plasticity around the intermediate states [30]. The self-tying was postulated via the direct knotting event in accordance with the theoretical study of the on-lattice model of a designed by hand heteropolymer chain with 52 knot [35]. However, the optical tweezers stretching experiment showed that the threading significantly decelerates the folding [36]. Still, because the topology cannot be detected in the in vitro experiment, the mechanism of knot tying remains unresolved. In this study, we asked following questions: What is the difference between the two experimentally observed, parallel folding pathways? What is the influence of a chaperonin cage (confinement) on the folding and self-tying of UCHs? And more generally, what are the dynamical properties of UCH in a bulk and in a confinement? To answer these questions, we performed a comprehensive study of representative UCH members in a model of chaperonin cage (mimicked by repulsive cavity) and in the bulk, using structure-based model simulations. To ensure robustness of the results, we investigated proteins from different organisms, with low sequence similarity, and different depth of the knot. The results show that the structure-based model was sufficient to knot and unknot each of the studied proteins with and without the presence of confinement. However, only in the confinement, the simulations in transition temperature were accessible. We performed a comprehensive analysis of knot occurrence during simulations, resulting in the identification of two topologically distinct pathways. To relate our results to the experiment, we reproduce the chevron plot for a representative protein member of UCH family, revealing the existence of fast and slow phases. Next, we studied short-lived knots on the folding and the unfolding pathway and revealed for the first time the existence of random knots in the unfolded protein chain. To our knowledge, this is the first theoretical study with a direct investigation of the influence of the excluded volume on proteins containing complex knots.
To obtain robust results, three sequentially different members of UCH family denoted with their PDB codes 3IRT (UCH-L1), 2LEN (UCH-L1), and 4I6N (UCH-L5) were studied. Additionally, to check an influence of the length of knot tails, we constructed in silico mutant of 4I6N, denoted as 4I6N-m, obtained by removing 7 residues from the N-terminus. All investigated structures feature a left-handed 52 knot and complex topological fingerprint 523131. Alignment of the 3-dimensional structures of the studies proteins is shown in the Fig 1 and their most important topological and structural information is summarized in Table 1. Further structural and sequential comparison of chosen structures is presented in S1 Appendix, part 1. Not determined region (amino acids 142–152) in the structure of 4I6N was repaired using Modeller software [37], where the model with the lowest DOPE potential (Discrete Optimized Protein Energy) was chosen. The DOPE potential is one of the quantities assessing the structure correctness [38]. The dynamics of investigated structures was studied in structure based Cα model [39,40] with standard parameters as proposed by the SMOG server [41]. The model included bonded interactions (bonds, planar and dihedral angles), bead excluded volume (Lennard-Jones repelling part) and non-bonded interactions described with a 10-12 Lennard-Jones potential. The non-bonded attraction was applied between residues forming contacts in the native structure, as defined in [42]. The number of the native contacts for all considered proteins is presented in Table 1. The folding/unfolding transitions were studied through constant temperature molecular dynamics simulations with the Nose-Hoover thermostat (coupling constant eq. 0. 025) using Gromacs v4. 5. 4 package [43]. Temperature T ˜ in Gromacs is defined by the equation T ˜ = (k b T) / (ϵ k˜b), where k˜ b= 0. 00831451. Through the text, the temperature is denoted simply as T and the Boltzman constant k ˜b as kb. There were performed 200 simulations for each structure and temperature. The number of steps was in the range 107 − 1. 6⋅109 steps depending on the condition. The confinement is represented by a cylinder (Fig 1) with a diameter equal to its height equal 6. 0 nm [44], introduced into the system as in [29]. The interactions between the inner wall of the cylinder and protein are purely repulsive (only a confinement effect). Such model was previously used to study confinement or crowding effect on protein folding [44–46]. The data concerning the position of the knotted core and the length of the knot tails (Table 1) are taken from KnotProt server [4]. The knot type of each of the subchains of the protein is determined using the implementation of the HOMFLY-PT polynomial [47–49] and the chain closing method as in [5,50]. The same algorithm was used to detect the entanglement along the protein backbone during simulations. The knot was regarded as present in the simulation if it was detected for at least 5 consecutive frames. The similarity to the native state was measured by the fraction of native contacts, Q. At given conformation, each native contact was regarded as present, if the distance between a pair of Cα atoms was less than 1. 2 times their native distance. The untied structure was regarded as unfolded, if Q < 0. 2. By unfolding pathway, we mean the shortest part of trajectory connecting knotted structure with Q > 0. 9 and unfolded structure. By folding pathway, we mean the shortest part of the trajectory connecting unknotted structure with Q < 0. 4 and knotted structure with Q > 0. 9. Folding trajectories start from one of the previously generated 100 unknotted conformations with Q < 0. 2. All initial structures belong to separate clusters with 0. 1 nm cutoff, to remove any possible bias. The structures were visualized using UCSF Chimera [51].
The UCHs are known to fold and refold along two parallel pathways, each featuring one slow and one fast phase [30,31,52]. Therefore, to correlate our model with experimental results we recreated the chevron plot for UCH-L1, with the temperature as a denaturant. In conventional chevron plots, the folding constants are calculated based on the time dependence of e. g. fluorescence. The fluorescence of a protein’s tryptophan depends on its neighborhood. Hence, the fluorescence trace can be understood as a measure of similarity of the tryptophan neighborhood to the native structure. In our simulations, such a measure is given by the fraction of the native contacts—Q. Therefore, we calculated the average Q as a function of time (representative trace in Fig 5A). The average was taken over all simulations in a given T and in each condition (bulk/confinement). Next, we fitted the smoothed Qaver (t) with the sum of exponential functions. In particular, we fitted the trace with the sum of the highest number of exponents, for which the fitting errors were lower than 5% of the value. The details of the plot along with the values of obtained constants and errors are presented in S1 Appendix, part 6. Although Qaver (t) is only a rough equivalent for the fluorescence, in almost all cases we were able to decompose the trace as a sum of 2-4 exponentials, i. e. to find up to 2 fast and 2 slow phases. These data are shown in Fig 5B (bulk) and 5C (confinement) in the form of chevron plot with the inverse of temperature (precisely −ϵ/kbT) mimicking the denaturant concentration [53]. For the consistency with conventional chevron plot, we plot the logarithm of k = 1/τ where τ is a characteristic time of a given phase. The obtained values create the trends characteristic for chevron plots, therefore they were connected by dashed lines. Note that in some cases the connection of values is arbitrary. For most cases, the fitting error was an order of magnitude smaller than the value obtained (Fig 5), and those, for which the error was higher (e. g. the point for confinement, −ϵ/kbT = −1. 10), still corresponds to reasonable values. The presence of the fast and slow phase during folding/unfolding process shows that our results are clearly consistent with previous experimental observations [30,52]. However, in most cases, we were not able to determine four individual phases (as in the experiment). This may be due to similar characteristic times of separate phases, the model imperfection, or because of a much more complicated folding pathway. Indeed, the curvature of the limbs of the chevron plot indicates more complicated mechanism in each phase, again consistently with the experiment [33]. The detailed analysis of folding/unfolding pathway should be the next step in investigating of these proteins. To determine the influence of the confinement, we compared the “most complete” kinetic trace for the slow and the fast phases for bulk and confinement (Fig 5D). The slowest phases can be fitted to an equation describing chevron plot, which yields an approximate Tf equal 114 (−ϵ/kbT = −1. 05) for bulk and 120 (−ϵ/kbT = −0. 99) for the confinement (for details see S1 Appendix, part 6). This indicates that confinement stabilizes UCH as it was observed for proteins with trivial topology [44,54]. Moreover, the chevron plot indicates that the confinement significantly accelerates the folding process, especially the slow phase. In particular, the simulations in the Tf for bulk were not accessible computationally due to very slow rates, while they were accessible in Tf for the confinement. This enables us to calculate near-equilibrium F (Q) dependence for confinement, which in principle could give additional information on UCHs folding. However in this case, due to the complexity of the folding landscape, the standard ways of its representation do not reveal any new information (S1 Appendix, part 7). Regardless of the conditions, a collapse of the protein (the first phase of folding) occurs relatively fast, which stays in accordance with the experimental results, that the knotting (occurring in our model for Q > 0. 7) should be the rate-limiting step [36]. Therefore in our case, the fast phase corresponds to arriving at collapsed, non-knotted form (first part of folding) and the slow phase should correspond to knotting and subsequential reaching of the native structure. The impact of the confinement on the slow phase indicates that the confinement facilitates knotting by restricting the conformational space of the termini. On the other hand, the confinement slows down the unfolding process by slowing down the unknotting—note the change of order in the curves in Fig 5D. The lower unfolding rates in the confinement may be also a result of the retying during unfolding (discussed in the next section). As it turns out that the once unfolded knot has a higher probability to retie in the confinement which results in higher knot stability and slower unfolding. Slow unfolding is again in agreement with intuition and experimental observation made for proteins with trivial topology [55]. To additionally investigate the influence of the confinement on both unfolded and folded state, we determined the average asphericity [56] parameter for bulk and confinement in both states. Again, the asphericity of folded state was comparable in both conditions, indicating, that the confinement does not influence the near-folded structures significantly. On the other hand, the asphericity of unfolded state was different in the confinement than in bulk, showing the influence of confinement on the unfolded basin (S1 Appendix, part 8). The probability of knot presence in a polymer chain increases rapidly with its length. As a result, it is highly probable that the sufficiently long polymer will spontaneously form a knot. However, the fraction of knotted proteins is far lower than in the case of equally long polymers [57]. Moreover, the spontaneous self-tying of protein chains in the denaturated state was not reported so far even in the natively deeply-knotted structures [22,58,59] or in the case of small knotted proteins in confinement [29]. However, in the case of UCHs we observe a significant fraction of (in most cases short-lived) knots, appearing during folding/unfolding pathway, or in the denaturated state (with Q < 0. 2). We found that confinement leads to faster and more efficient folding of UCH proteins for two reasons. First, encapsulation provides the possibility to fold via an alternative pathway. More precisely, the confinement facilitates folding via the trefoil knot (the FC pathway) for entropic reasons, while it does not affect folding via the FN pathway (direct tying, the N-terminus folds the last). This surprising behavior is supported by the experimental observation of uneven influence of chaperonin [63] on the substrate protein rhodanese, which decelerates the folding of the C-terminal domain, but leaves the folding rate of the N-terminal domain unaffected [64]. Second, at the same confinement stabilizes native interactions and destabilizes non-native ones in comparison to bulk, and thus it reduces the height of the free energy barrier and accelerates the folding rate as it was observed for a protein with trivial topology [55,65,66]. The two pathways clearly distinguishable in our analysis are in accordance with two pathways identified in experiment [30]. However, there is still no technique, which could determine the topology of the protein during folding in vitro, which prevents from direct validation of our results. Some insights can however be given by the study of the tryptophan variants of UCH [33]. In particular, it was shown that the pathways differ in the structure of intermediates for which highly stable central β-sheet core and flanking α-helices and loop regions are formed differently. This is in accordance with our results, however detailed analysis of folding pathway, with special emphasis put on the location of tryptophan mutations, is required to precisely compare the experimental and theoretical results. On the other hand, our results show that the confinement introduced by the chaperone-like cage decelerates the unfolding of UCH proteins. Firstly due to a decrease in the effective mobility of the protein backbone upon encapsulation and under topological constrains, which reduce the rate at which new configuration can be explored (especially in twisted loops). This argument without topological contribution is used to explain lower folding rate for a protein with the trivial topology [64]. Secondly, the decelerated unfolding in the confinement is caused by the retying phenomena. It is worth pointing out that the retying phenomena can be used by other knotted proteins with a rather shallow knot, e. g. carbonic anhydrase, to stabilize the structure in a crowded environment (moreover carbonic anhydrase structures with deeper knots also start to be crystallized). Under the confinement, a significant number of short living knots is observed in the denatured state and in folding and unfolding routes of UCH proteins, what has not been reported for other knotted proteins. More and more complicated knots are more common to occur upon encapsulation, which is in the agreement with the polymer theory [61,62]. These knots seem to have only positive effect, i. e. their formation accelerates folding. In principle, deeply knotted structures could lead to misfolding, but contrary to the situation in the bulk, they are not formed due to the constrained configurational space. In summary, we took advantages of structure based model and knot theory, and made the step forward in characterizing folding/unfolding routes for UCH proteins identified experimentally in [30]. We identified possible oligomerization-prone forms of UCHs, which may cause neurodegenerative diseases. We found that weak confinement smooths the rough and not continuous free energy landscape of UCH proteins in a subtle way, e. g. enhancing an indirect tying route. However, at low temperature or strong confinement slower folding should be again observed due to restriction on indirect tying. The deceleration under strong confinement was suggested for a protein with the trivial topology in [63].
Self-tying of knotted proteins remains a challenge both for theoreticians and experimentalist. In this work, we study the proteins with complex, the 52 knot, in a bulk and confined within a chaperonin box. We show that in our model we recreate the experimental results, identify two topologically distinct folding pathways and explain the beneficial role of confinement for complex knotted proteins. Encapsulation provides a possibility to fold via alternative pathway—folding via trefoil intermediate knot (N-terminal pathway) from entropic reason while folding via the C-terminal (direct tying) appears with the same probability. The results of this work show, how crowded environment in the real cell may enhance self-tying of proteins. The results are also the first step to the identification of possible oligomerization-prone forms of UCHs, which may cause neurodegenerative diseases.
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The exclusive effects of chaperonin on the behavior of proteins with 52 knot