Unique features of EIGHT fold—Proteins with the most complex 8₃ knotted topology

Significance

We demonstrate the existence and unique structural properties of the Extraordinarily Intricate Globular Helical Tangled fold—proteins likely containing one of the most complex knots identified in nature to date, an $8_3$ knot. This previously uncharacterized topology was predicted de novo by AlphaFold without using template structures. The EIGHT fold structure occurs only in certain gut bacteria and exhibits unusual symmetry, likely from duplication of a simpler ancestor. In silico and in vitro analyses reveal unfolding through six distinct phases, spanning milliseconds to days. Native contacts allow the EIGHT fold to self-tie, but the observed folding pathway cannot be explained by any known protein-folding theory.

Abstract

Herein, we present three crystal structures of the most complex knotted protein to date, an $8_3$ knot with eight crossings, which belongs to a clasp knot family. The fold of this protein is also unique, and we call it the EIGHT fold (Extraordinarily Intricate Globular Helical Tangled fold). The $8_3$ knot is found only in a certain group of bacteria, where it is strictly conserved, despite sequence identities as low as 10%. The $8_3$ structure shows a high level of internal symmetry, with structurally analogous halves. It is possible that the EIGHT fold evolved from a single unknotted “half” that duplicated and formed a complex protein. Based on an in vitro study of three selected $8_3$ proteins, we estimated their thermal and thermodynamic stability, and showed that they follow a two-state unfolding model under equilibrium conditions and their refolding occurs to a compact, nonnative state. Unfolding kinetics of $8_3$ knotted proteins reveal a complex, multiphase process spanning milliseconds to days. Six kinetic phases were resolved using stopped-flow fluorescence and far-ultraviolet absorbance circular dichroism spectroscopy, highlighting both rapid early events and slower rearrangements in secondary and tertiary structures. Finally, with a structure-based model, we showed that proteins with an $8_3$ knot can self-tie through a $6_1$ knotted intermediate state. They can also self-untie, albeit via an additional intermediate knot such as $4_1$. Nevertheless, these proteins do not seem to fit with current folding theories known to date and require the development of a new approach.

Understanding the relationship between protein sequence and structure remains one of the most important challenges in structural biology (1). Despite differences in their sequences, proteins preserve certain structural features known as motifs. One of the least understood motifs is entanglement, e.g. a knot formed along the backbone (2–4), which is often located in the active site of a protein (5). There are only a few types of knots with confirmed experimental structure, based on the KnotProt Database (6): 3$1$ [natural and designed (7–10)], 4$1$, 5$2$, 6$1$ (11), 7$1$ (12), and double knotted 3$1$#3$1$ (13, 14).

The development of precise structure prediction methods [like the AlphaFold model (15)] allowed us to have insight into significantly more protein structures than before. With the help of AlphaKnot (16) and Topoly (17), it is possible to recognize new entangled motifs in these predicted protein models. The results show topologies more complex than expected (3) that go beyond the limit of random knotting or twisting mechanisms suggested for known proteins (3, 4, 18, 19). Herein, we present a family of proteins with a previously uncharacterized fold (Fig. 1) formed by a knot with as many as eight crossings, an $8_3$ type (20).

Fig. 1.

The EIGHT fold (Extraordinarily Intricate Globular Helical Tangled fold). Left panel: Crystal structure of protein with the EIGHT fold—protein $ϵ$ (PDB ID: 9TMH), with $C{l}^{-}$ (blue) and $M{n}^{2+}$ (purple) ions. Right panel: schematic representation of the protein architecture, in which the backbone forms an $8_3$ knot. A diagram of the $8_3$ knot is superimposed onto the structure.

The discovery of such a knot raises a number of questions, one of which is whether the fold formed by an $8_3$ knot is a completely unique structure or whether it is similar to any known motif in proteins. Similarity could help with understanding the evolution of knots in proteins, which is unknown for many families by filling a missing link (21–25). In some cases, a knot-promoting loop has been found to transform an unknotted protein into a knotted one (26). Knots in proteins are strictly conserved in any given family, even among proteins with very low sequence similarity (25, 27, 28). However, studying how knots evolve is challenging. This is largely because we often lack a known unknotted homolog [only two are known (26, 29)] and there is no unambiguous motif to indicate knotting (25, 30). Despite the lack of such a sequential signal, the AlphaFold models suggested a distinct twist-type knot (31, 32) as well as more complicated knots such as $5_1$, $6_3$, $8_3$, $3_1$#$4_1$ (20), for more see AlphaKnot Database (16). If the newly predicted knots form completely new protein folds, it will not only help us better understand the evolutionary process but also show that there are many different ways to arrive at a knotted topology.

Another question concerns the role of knots in proteins, which is still not known (33). The question is all the more interesting in the case of an $8_3$ knot, which is not usually observed even in polymers. It is known that in the case of the largest knotted family (SPOUT family of methyltransferases), the knot is forming part of the active site (22, 34) and it is required for enzymatic function (5, 34, 35). On the other hand, there are other knotted proteins where the knot occupies most of the structure, and it is difficult to directly link it to any function. Maybe the knot introduces thermal (36, 37) or mechanical stability (38–40), contributes to reactivity or other electronic structure properties (41), or impairs protein degradation by ATP-dependent proteases (24, 42–44). Learning about another knotted family is a step toward understanding potential correlation between knotted proteins and their role in the cell.

Finally, it is interesting how an $8_3$ knot folds to the native state. All previously identified proteins containing prime knots can fold according to one of the developed principles—Taylor’s loop-threading theory (3) via slipknot or plugging conformation (18, 45, 46) [successfully applied to many proteins (47–50)], the loop-flipping theory suggested based on proteins with a $6_1$ knot (51), extensions of the loop-flipping theory applied to proteins with a $6_3$ knot, folding with the help of ribosome (52–54) and other (55). An experimental study contributes a great deal to the understanding of the free energy landscape (8, 56–59), but there always remains the aspect of ambiguity in the interpretation of topology. Leaving that aside, it has been shown that chaperones can play an important role in knotting for one class of knotted proteins (60); however, not all knotted proteins need assistance for rapid folding; some of them can self-tie quickly (61). Interestingly, none of these theories can describe the folding of an $8_3$ knot.

Here, we report X-ray structures of proteins containing an $8_3$ knot and adopting a previously unrecognized fold. Using a combination of comprehensive in vitro and in silico analyzes, we establish the uniqueness of this fold and define the EIGHT fold protein family. Using various biophysical experimental techniques, we investigate the thermal and thermodynamic stability, in addition to the unfolding kinetics, of three selected members from this family and show that they follow a two-state unfolding model under equilibrium conditions; however, they refold to a compact and stable state that differs from the native state. Additionally, we show that the unfolding kinetics (determined based on far-UV CD and stopped-flow spectroscopy) are probably among the most complex of any protein described so far in the literature, consisting of six phases. We explain this data further based on numerical methods, where we found that the protein can self-tie and untie; however, the mechanism does not seem to fit the theories of folding known to date and requires the development of a new approach.

Results

Here, from a group of proteins that possess an $8_3$ knot (calcu lated by AlphaKnot), we selected six proteins based on their crystallizability potential—so-called protein $\alpha$ (UniProtKB ID: A0A352WGM4), $\beta$ (A0A7C6JW11), $\gamma$ (A0A7X4IB97), $\delta$ (A0A1I0QM73), $ϵ$ (A0A374JU36), $\zeta$ (A8SPL3); see the Methods section for details. They share no more than 53% of their amino acid sequence identity (SI Appendix, Figs. S1 and S2), thus, they are good representatives of the group of $8_3$ proteins.

We expressed and purified all proteins successfully and obtained an X-ray structure of protein $ϵ$ (PDB ID: 9TMH) and $\alpha$ (PDB ID: 9RH0 and PDB ID: 32UY). Based on the X-ray structures, we confirm that the protein backbone forms an $8_3$ knot. Next, we conducted a comprehensive bioinformatic, numerical, and experimental investigation. In the case of $\beta$, $\delta$ and $\zeta$, due to aggregation, not all experiments could be carried out; these data are presented in SI Appendix. Note that protein $\zeta$ was removed from the UniProtKB.

Crystal Structures Confirm the $8_3$ Knot Type.

We determined the crystal structure of the protein $ϵ$ (Fig. 1) from Coprococcus bacterium at 2.2 Å resolution (see SI Appendix, Table S13; PDB ID: 9TMH; space group $\mathit{P}{2}_1{2}_1{2}_1$) and two crystal structures of the protein $\alpha$ from Lachnospiraceae bacterium from two different crystallization conditions, at 2.54 Å (Fig. 2) and 2.92 Å resolution (see SI Appendix, Table S13; PDB ID: 32UY and PDB ID: 9RH0; both in the space group $\mathit{P}{12}_{1}1$). Two protein molecules are present in the asymmetric unit with an estimated solvent content of 53.5%, and 65.7%/66.7% for one $ϵ$ and two $\alpha$ structures respectively. It is unlikely that they form a homodimer since they interact only via a small interface (buried surface area: 699 Ų for $ϵ$, 709 and 661 Ų for $\alpha$ structures with PDB ID’s 32UY and 9RH0 respectively). Moreover, none of the tested models (predicted with AlphaFold 3 or GalaxyGemini) yielded a dimer in which the interactions responsible for its formation are conserved. The monomer is a single-domain protein with a purely $\alpha$-helical structure (20 helices; Fig. 2).

Fig. 2.

Characteristics of an $8_3$ knotted protein based on its crystallographic structure. (A) Knotted $8_3$ protein $\alpha$ (PDB ID: 32UY) shown in a surface representation along with the $8_3$ knot schematics. The position of the $8_3$ knot core in the helical representation is colored green, and corresponds to the range shown on panel (B). (B) The knotting complexity of the protein is presented in the form of a matrix diagram that shows that the entire chain forms the $8_3$ knot and its subchains from $+6_1$, $-6_1$, and $3_1$ knot types. (C) Detailed presentation of the matrix diagram showing the location of internal knots: $-6_1$, $+6_1$, and $3_1$. The schematics of the knots show how the shortening of each terminus affects the topology.

For protein $ϵ$, no interpretable electron density is observed for two residues in chain A and four residues in chain B in the flexible loop regions (chain A: 389-390; chain B: residues 315 and 388-390). For protein $\alpha$, no interpretable electron density is observed for 10 residues in chain A and 24 residues in chain B in the flexible loop regions (chain A: 311-314, and 377-382; chain B: 283-284, 302-317, and 376-381) for PDB ID: 9RH0, and for 6 residues in chain A and 19 residues in chain B in the flexible loop regions (chain A: 376-381; chain B: 301-305 and 369-382) for PDB ID: 32UY. The missing subchains are small enough or located far away from the knot intersections that they cannot affect the interpretation of the knot. The protein $ϵ$ binds two Cl⁻ ions (one next to lysine 185 and one next to histidine 231) and four Mn²⁺ ions (next to: aspartic acid 190; aspartic acid 328; aspartic acid 397; asparagine 440).

The crystal structures of protein $\alpha$ were determined from crystals grown in two different crystallization conditions (0.16 M calcium acetate, 0.08 M MES pH 6.5, 14.4% w/v PEG 8000; 0.2 M lithium sulfate, 0.1 M sodium acetate, 0.1 M HEPES pH 7.5, 25% (w/v) PEG 4000). These crystal structures can be aligned with the RMSD of 0.84 Å based on pruned 417 C$\alpha$ atoms of chain A (SI Appendix, Fig. S22), and with the RMSD of 0.91 Å based on pruned 391 C$\alpha$ for chain B. Between protein $\alpha$ and $ϵ$ the values are 32UY – 1.7 (259 pairs) for chain A and 1.2 (221 pairs) for chain B (SI Appendix, Fig. S22); 9RH0 – 1.5 (302 pairs) for chain A and 1.2 (229 pairs) for chain B. Weak anomalous signal was obtained for the crystal structure of protein $\alpha$ that is shown on SI Appendix, Fig. S26, which is consistent with the refined data, confirming sequence register. Moreover, simulated-annealing omit maps over the chain-crossing region were calculated confirming the shape of the cross-sections of the knot (SI Appendix, Fig. S8).

Both proteins contain a high proportion of charged residues (mostly negative), constituting approximately 32% of the sequence. Consequently, the protein has a net negative charge ($-$31 at pH 7), creating an extensive negatively charged surface (SI Appendix, Fig. S23). Due to this charge, proteins with this fold may function in the cell in a bound form, e.g., in a heterodimeric complex with a positively charged protein.

Topology calculations confirm that both structures possess the $8_3$ knot. In protein $ϵ$, the knot spans residues 36 to 467, while in protein $\alpha$, it extends from residues 29 to 453, thus making the majority of these 475- and 465-amino acid-long proteins knotted. However, the knots have sufficiently long tails ($ϵ$ – 35 and 8 amino acids; $\alpha$ – 28 and 12 amino acids) to be a stable motif that is not prone to spontaneous unknotting (see more in the following section). We subjected these proteins to all-atom explicit-solvent MD simulations, and the knot remained stable in the same position.

Superposition of the AlphaFold2 model and the final structures of the $ϵ$ and $\alpha$ proteins (32UY and 9RH0) using C$\alpha$ atoms yields RMSD values of: 1.1, 1.6, and 1.5, respectively (based on 424, 381, and 397; outliers from flexible loops were excluded). The high level of agreement between the structures is remarkable, given that the AlphaFold-predicted model was generated in the absence of any available structural homologs; this phenomenon is explored further below.

Due to the type of knot (there are 21 types of knots with eight crossings), its topological properties, and the fact that protein (all members of this family) consists only of $\alpha$ helices connected by loops, we call this type of fold in a protein The EIGHT fold: Extraordinarily Intricate Globular Helical Tangled fold.

Unique Properties of 8₃ Knot from the Point of View of Protein Structure Complexity.

The $8_3$ knot is the most complex knot type found in proteins to date. From a mathematical standpoint, there are 21 types of knots with eight crossings. This knot belongs to the family of clasp knots, has an unknotting number 2, and is not a twist type. This knot type cannot be obtained with current protein knot folding models. Moreover, an $8_3$ is an amphichiral knot type, i.e., it can be continuously deformed into its own mirror image.

The protein with the $8_3$ knot has the most complex topological motif discovered to date in proteins. This motif is called K$8_3{6}_1{6}_1{4}_1$ (Fig. 2) and it consists of three internal knots: $-6_1$, $+6_1$, and $4_1$.

The K$8_3{6}_1{6}_1{4}_1$ motif stems from a matrix diagram that shows the knot type of the entire polypeptide chain and of each of its subchains (27). The elementary square in the lower left-hand corner of the matrix diagram with coordinates (1,465) (Fig. 2B), shows that the entire protein forms the $8_3$ knot. However, when smaller subchains are considered, for example by shortening it (from either side, N- or C-terminus), we can find two $6_1$ knots (colored blue) and one $4_1$ knot (colored red). This is due to the lack of the last threading of the terminus through a loop. The chirality of the $6_1$ knots depends on which terminus it is: shortening of the N-terminal results in a $-6_1$ knot and the C-terminal in a $+6_1$. If both termini are short enough to have one less threading, the resulting knot is a $4_1$ type. The positions of the internal knots are presented in Fig. 2D. Note that the boundaries of the knots fall in helical regions. Therefore, given that amino acids represent one of the possible options for the crossing points.

The EIGHT Fold Likely Defines a Previously Undescribed Protein Topology.

Using both the structure and sequence of the protein $\alpha$ as a guide, we found an additional 296 proteins of the same fold and topology in UniProtKB (using FoldSeek and HMMER, see Methods for details). During this search, we encountered no high-quality proteins of a different fold (1$e^{-3}$ e-value cutoff). In particular, there are no structurally or sequentially similar proteins outside of this group with either known (PDB) or predicted structures (AlphaFold Database).

Sequential similarity analysis using BLASTP identified an additional 423 candidate proteins in the NCBI Protein database. These candidates were supported by high alignment coverage and low e-values, indicating significant similarity. The structures of the least sequentially similar proteins were generated with AlphaFold, and their topology was confirmed to correspond to 8₃.

Another way of finding the nearest protein structure is to check for templates (experimental structures) utilized by the AlphaFold Model to create a predicted protein with an $8_3$ knot. We found that the most common structures used as templates belong to two CATH families (1.20.1250.10, and 1.20.1440.50). However, they represent different folds with no structural resemblance (SI Appendix, Fig. S3).

To further verify that the knotted motif represents a novel protein fold, we utilized the TED Database (The Encyclopedia of Domains) (62). TED enables the detection of folds in AlphaFold-predicted structures and, where possible, their classification within the CATH system. No known CATH domain was assigned to the $8_3$ knotted proteins. This finding was further validated through structural comparison with a dataset of novel folds, also provided by the TED authors, which identified a single match corresponding to one of the 296 $8_3$ knotted proteins analyzed in our study. Therefore, since no prior structural information was available, the $8_3$ knot prediction from the AlphaFold Database was correctly made de novo and the $8_3$ fold is new and unique. The accurate prediction of this unique topology by AlphaFold is attributed not to structural templates, but to its utilization of coevolutionary information derived from deep Multiple Sequence Alignments (MSAs). This capability allows AlphaFold to uncover entirely new folds, as demonstrated in recent studies (63), by decoding the residue covariation patterns across the sequence family and successfully determining the key spatial constraints necessary to form this complex, previously unseen $8_3$ fold.

The presence of the knot is experimentally confirmed by three X-ray structures, and robust bioinformatic characterization supports its conservation across the other 300 distinct proteins. To remain cautious, however, these AlphaFold models are treated as high-confidence predictions, as high per-residue pLDDT scores (see next section) do not automatically ensure correct global topology in highly entangled folds.

Proteins with EIGHT Fold Form a Deep Knot.

Characterizing knotted proteins involves determining the knot depth, which describes how deeply the knot is embedded in the protein’s structure. Deeper knots, which require more residues to be removed to untie them, increase the protein’s kinetic stability. This greater stability is seen as a higher energy barrier to unfolding and a slower unfolding rate.

The analysis of 296 proteins with the $8_3$ knotted motif reveals a highly consistent and deep knot topology. The structures are of high quality, with an average full-chain pLDDT of 89 (SI Appendix, Fig. S4). Moreover, the analysis of the per-residue pLDDT values distribution from 296 proteins reveal consistently high prediction confidence across the chain. Only a single short fragment exhibits a local decrease in pLDDT slightly below 70, corresponding to a flexible loop, with a position that does not affect the knot topology (SI Appendix,Fig. S19).

The knot core—the minimal knotted portion of the protein—is approximately 422 residues long on average, making up the majority of the average 474-amino acid protein (SI Appendix, Fig. S16 A and B). The remaining parts, called tails, determine the knot’s depth.

The analysis of the whole dataset shows that the N-tail knot (the N-terminus) is, on average, longer than its C-tail knot counterpart (36 and 15.9 residues long, respectively; SI Appendix, Fig. S16B). In several cases, the N-tail can be formed by as many as 49 amino acids. The distribution of the C-tail’s length has its lower bound cut off at 5 amino acids. A shorter tail would indicate a possibility of the protein changing the topology to $+6_1$ knot type (for details, see the section about the fingerprint).

In conclusion, most of the proteins with the EIGHT fold motif possess a deep knot, where a longer N-tail is probably unfavorable for the $8_3$ topology during folding. This suggests that the $8_3$ knot type is deliberately conserved and is important for protein function.

The EIGHT Fold Motif Is Conserved Among Specific Bacteria.

All the $8_3$ knotted proteins we found are in bacteria. In particular, in two orders of the Clostridia class—Eubacteriales, Lachnospirales, as well as from the Tissierellia class, Tissierellales order. Species from Clostridia class consist of strictly obligate anaerobes commonly found in human and animal gut microbiomes, where they ferment polysaccharides into short-chain fatty acids (e.g. butyrate) that support colonocyte energy and gut barrier integrity (64, 65). The bacteria from Tissierellia class comprise strictly anaerobic bacteria typically colonizing gut or mucosal environments, distinguished from spore-forming Clostridia and occurring as commensals or low-abundance opportunists (66). Even though the taxonomic relationship between the species is close, the proteins show sequence variability. There are 25 representative proteins with no more than 30% sequence identity, see SI Appendix, Fig. S16C. Moreover, the least similar pair among them has an identity lower than 10% and both proteins still maintain the same knotted fold (SI Appendix, Fig. S16D) based on the predicted structures. This shows that the $8_3$ knotted fold is conserved, even in proteins with significant sequence variation. Such low sequence conservation was not observed before for other knotted proteins (28, 67).

Highly Conserved Residues Inside the Knotted Elements.

Having established that the $8_3$ proteins are a distinct group in terms of sequence, we focused on finding the amino acids that are conserved. Using multiple sequence alignment and a cutoff for conservation at 85% for each residue, we found four conserved residues and two motifs (Fig. 3; logo showing the whole MSA is in SI Appendix, Fig. S5). Interestingly, the majority of the sequence has low conservation, which makes the conserved positions even more important (Fig. 3B).

Fig. 3.

Structurally and sequentially conserved regions. (A) Surface representation of protein with $\alpha$ structure PDB ID: 32UY colored by sequence conservation level. (B) $8_3$ knot schematic with highly conserved (in more than 85% of the proteins) residues/motifs. (C) Cartoon representation of the helix–loop–helix (HLH) regions with two conserved motifs (motif I—light green, motif II—dark green). (D) Fragment of a sequence alignment showing two HLH regions (of proteins with less than 20% identity and protein $\alpha$) with the conserved motifs marked with light and dark green. (E) Structurally similar elements in the EIGHT fold. The Inset shows a superposition of the three repeating segments. All the numbering is based on the protein $\alpha$ sequence.

All four single highly conserved amino acids (Arg95, Tyr108, Asn267, and Glu323—protein $\alpha$ numbering) are in close vicinity to the first three crossings (from the N-terminus) of the $8_3$ knot. In particular, there is a direct contact between Arg95 and Asn267 via a hydrogen bond (Fig. 3B).

We also observe direct contact between the two conserved motifs. In this case, the residues constituting the motifs together form a crossing in the C-terminal part of the structure. The motifs are interlocked (Fig. 3C) and both are part of helix–loop–helix (HLH) regions—motif I has 5 residues conserved above 85% level that are mostly part of the loop. Motif II has six amino acids uniformly distributed in the HLH region (Fig. 3D).

Interestingly, both motifs have proline in the second position in the loop region (Pro165 and Pro425). Given the ability of the proline to bend the main chain of the protein, the positions, and the high conservation of these residues, they may be important for the topology.

Symmetry Within the EIGHT Fold.

The $8_3$ protein’s structure is composed of two structurally similar halves. Each half contains three analogous segments: a “zigzag” helical bundle, a long $\alpha$-helix, and a dual helix–loop–helix (HLH) region (Fig. 3E). The similarity between the two halves might be due to the duplication, similar to the case of transmembrane proteins that developed from two simpler, interacting proteins. The duplication and fusion events created a single, larger gene responsible for a more complex, multidomain protein (68, 69).

A “zigzag” domain contains three $\alpha$-helices in the N-terminal half and four in the C-terminal half. However, this difference is only because the C-terminal analog of the long helix present in the N-terminal domain is broken in the middle due to the glycine. These domains superimpose well, with the primary difference being the opposite orientation of their initial helices.

A long $\alpha$-helix of 40 amino acids shows a notable topological inversion between the two halves. It is positioned after the “zigzag” in the N-terminus but precedes it in the C-terminus.

Finally, the HLH motifs from both halves are intertwined, creating a significant interaction between them. Moreover, these two segments contain sequentially conserved motifs as shown in Fig. 3 C and D.

Functional Characteristic, Ion Binding Capability.

The $8_3$ knotted proteins possess a novel fold and topology whose function is unknown. To investigate, a machine-learning model [DeepFRI (70)] was used to predict functional annotations for 23 of 25 representative proteins. The majority (18) were predicted to have a high probability of binding ions, though the specific charge was unclear. These results appear to be reliable, as the solved structure contains ions (for more see SI Appendix, Fig. S21). Lower probability predictions suggested they might also bind to proteins or carbohydrates. No specific enzymatic or biological function was assigned to any protein. It is worth noting that the DeepFRI result should be interpreted as a testable hypothesis. This prediction, which is based on identifying local features like clustered coordinating residues, provides a structural basis for further investigation into whether a specific metal ion serves as a cofactor or structural element in the protein.

Further analysis using SignalP 6.0 (71) revealed that none of the proteins possess a signal sequence, indicating they do not have a specific cellular localization signal. Additionally, no organism from the dataset was found in the Database of Essential Genes (72), suggesting that the proteins are not essential for bacterial cell survival.

Thermal and Thermodynamic Stability.

Although one could expect that knotting introduces additional stability into the protein, based on the analysis of all known knotted proteins, it has not been shown that this type of protein is more common in thermophilic organisms (20). However, this does not mean that the knot cannot introduce stability, especially one as entangled as the $8_3$.

To assess the thermal and thermodynamic stability of proteins $\alpha$, $\gamma$ and $\zeta$, we conducted a range of experiments, including far-UV circular dichroism (far-UV CD) at varying temperatures (Fig. 4) and urea concentrations (Fig. 5), differential scanning fluorimetry (DSF), and differential scanning calorimetry (DSC) Fig. 4.

Fig. 4.

Characterization of the thermal stability of $8_3$ knotted $\alpha$,$\gamma$ and $\zeta$ proteins. (A) Differential scanning fluorimetry (DSF). Error bars represent SD values. Protein sample concentration: 1 to 11 $\mathrm{\mu }$M; (B) Differential scanning calorimetry (DSC), dashed lines indicate baseline correction around the peak. Protein sample concentration: 50 $\mathrm{\mu }$M; (C) Denaturation spectra for far-UV circular dichroism (CD) at increasing temperatures. Protein sample concentration: 15 $\mathrm{\mu }$M; All samples in 50 mM MOPS, 200 mM NaCl, 5% glycerol buffer, pH 6.5 at 4 ^°C. Full spectral data for DSF, DSC, and far-UV CD are available in the SI Appendix, Figs. S6, S9, and S10, respectively.

Fig. 5.

Thermodynamic stability of $8_3$ knotted $\alpha$, $\gamma$ and $\zeta$ proteins. Far-UV CD signal as a function of urea concentration for protein $\alpha$ (red circles), $\gamma$ (green squares), and $\zeta$ (blue triangles). Darker curves show denaturation, while lighter curves indicate renaturation after incubation in 7 M urea and dilution to the target conditions.Highlighted midpoint values were obtained from the fitting to a two-state model. Insets highlight spectra at the lowest and highest denaturant concentrations, the spectrum with the largest minimum is that of the native state, the spectrum with the smallest minimum is the 7 M urea-unfolded state, and the spectrum in between these two is that of the refolded protein from 7 M urea, which is at a concentration of 1.5 M urea. These spectra reveal that after renaturation, the signal is not fully restored. Full spectral data is available in SI Appendix, Fig. S11. Fitting parameters in SI Appendix, Table S1.

Thermal resistance analysis using DSF shows that protein $\alpha$ is more stable than both $\gamma$ (around 5 ^°C) and $\zeta$ (around 2 ^°C). As thermal unfolding is not reversible, measurements reveal the $T_{\mathit{ma}}$ (apparent melting temperature) are 55.2 $\pm$ 0.4 and 50.2 $\pm$ 1.6 and 52.8 $\pm$ 0.1 ^°C, respectively for 11 $\mathrm{\mu }$M samples. Additionally, DSF measurements performed at increasing protein concentrations (1 to 11$\mathrm{\mu }$M) showed that the $T_{\mathit{ma}}$ is increasing until reaching a plateau at around 5 $\mathrm{\mu }$M. However, this effect is not associated with oligomerization of the protein in the native state: SEC-MALS analysis performed at approximately threefold higher protein concentration, using material from the same production batch, confirmed a monomeric state. In the DSF experiment metastable oligomeric intermediates may form after partial unfolding under destabilizing conditions. The thermal unfolding is an irreversible process, so the observed plateau for the concentration higher than 5 $\mathrm{\mu }$M might be due to aggregation countering the expected effect of further increase in $T_{\mathit{ma}}$. A similar effect has been described previously (73). The $T_{\mathit{ma}}$ values (Table 1) for DSF are based on the peak position of the first derivative of the raw measurement curves.

Table 1.

Estimates of thermodynamic parameters obtained by analysis of the DSC curves (concentration 50 $\mathrm{\mu }$M) and DSF (concentration 11 $\mathrm{\mu }$M)

Protein	$\mathrm{\Delta }{H}_{\mathit{app}}$ [kJ/mol] DSC	$T_{\mathit{ma}}$ [°C] DSC	$T_{\mathit{ma}}$ [°C] DSF
$\alpha$	240 $\pm$ 80	53.2	55.2 $\pm$ 0.4
$\gamma$	475 $\pm$ 65	53.0	50.2 $\pm$ 1.6
$\zeta$	225 $\pm$ 25	55.5	52.8 $\pm$ 0.1

All samples in 50 mM MOPS, 200 mM NaCl, 5% glycerol buffer, pH 6.5 at 4 ^°C.

The DSC measurements provided complementary insights into thermal stability. Heating of $8_3$ knotted proteins is a nonreversible process (Fig. 4). The sudden drop of $C_P$ at high temperatures most probably indicates an aggregation process taking place under these conditions (SI Appendix, Fig. S9A). Moreover, lack of reversibility is observed in DSC experiment repeated for cooled and reheated sample (SI Appendix, Fig. S9B). There are some differences between $\mathrm{\Delta }{H}_{\mathit{app}}$ for the studied proteins.

Both aforementioned experiments have shown the irreversibility of the process. Consequently, the calculated values of melting temperature $T_{\mathit{ma}}$, and enthalpy of the unfolding reaction $\mathrm{\Delta }{H}_{\mathit{app}}$, should be regarded as apparent values only. They indicate the lower bound of $T_{\mathit{ma}}$, and the upper bound for $\mathrm{\Delta }H$. Despite this limitation the values of $T_{\mathit{ma}}$ remain relatively consistent across methods (Table 1).

Finally, temperature-dependent far-UV CD experiments for both proteins show similar thermal stability with $T_{\mathit{ma}}$ of approximately 59 and 53 ^°C, respectively for protein $\alpha$ and $\gamma$, with no reversibility observed (Fitting parameters in SI Appendix, Table S2). The melting temperatures we obtained are similar to those reported for other complex knotted proteins. For example, the DehI protein with the $6_1$ knot has $T_m$ at 66.3 $\pm$ 0.6 ^°C (not full unfolding reversibility) (74) and the protein with the $7_1$ knot at 59.0 ^°C (only unfolding data) (12).

Thermodynamic stability was evaluated through far-UV CD at varying urea concentrations, and the unfolding and refolding data signal values at 222 nm were fit to a two-state model (Fitting parameters in SI Appendix, Table S1). The unfolding experiment started with the native protein which was mixed with increasing concentrations of urea. Transition midpoints at 5.1 $\pm$ 0.02, 4.8 $\pm$ 0.04 and 4.9 $\pm$ 0.01 M urea for protein $\alpha$, $\gamma$ and $\zeta$, respectively, were obtained (Fig. 5). In contrast, for the refolding experiment, 7 M urea unfolded protein was used as the starting point, and the protein solution was diluted into target protein and urea concentrations facilitating the refolding process. The transition midpoints were 5.5 $\pm$ 0.02, 5.6 $\pm$ 0.02 and 5.6 $\pm$ 0.01 M, for protein with $\alpha$, $\gamma$ and $\zeta$, respectively. Both the fact that the far-UV CD spectra for the refolded proteins had a different shape to the native spectrum, and the fact that the transition midpoints for the refolded proteins were statistically higher than for the native protein, indicate that for all three 8₃ proteins, the protein refolded to a stable folded state which was not the same as the starting native state.

Unfolding Kinetics.

Studies of the unfolding kinetics of 8₃ proteins reveal at least six distinct unfolding phases, ranging from the fastest, phase A, with $t_{\frac{1}{2}}$ values typically between 100 and 300 ms, to the slowest phases, where $t_{\frac{1}{2}}$ exceeds 25 h. This broad temporal span highlights the complex, multistep nature of the unfolding process in these proteins. A comparison of the protein $\alpha$, $\gamma$, and $\zeta$ variants is presented in Fig. 6. All kinetic measurements were performed in 6 M urea at a final protein concentration of 5 $\mathrm{\mu }$M.

Fig. 6.

Kinetic measurements of $8_3$ knotted $\alpha$, $\gamma$ and $\zeta$ proteins in 6 M urea. (A) Fastest unfolding phase captured by stopped-flow measurements. (B) Slower kinetic phases B, C, and D resolved by stopped-flow. (C) Manual mixing experiment with far-UV CD at 222 nm shows phase C giving similar $t\frac{1}{2}$. (D–F) Time-resolved far-UV CD spectra of proteins $\alpha$, $\gamma$ and $\zeta$, respectively, reveal two additional slower unfolding phases E and F. Spectra were measured every 15 min. Complete spectral datasets and global fitting results are provided in SI Appendix, Figs. S12, S14, and S24 and Tables S3–S12 and S14.

Phases A–D were monitored using stopped-flow instrumentation, with data collected over durations up to 2,000 s. The fitted and averaged half-lives for all phases are summarized in Table 2 (see kinetics fitting results in SI Appendix, Figs. S12 and S14). Phase A posed the greatest experimental challenge due to its very short $t_{\frac{1}{2}}$ (100 to 300 ms) and overlap with the onset of phase B. As shown in Fig. 6A, the kinetics of phase A for $\alpha$, $\gamma$ and $\zeta$ proteins were measured over different timescales, some with higher temporal resolution, resulting in slightly different start times and higher signal to noise. Limited protein availability restricted repeat measurements and further optimization.

Table 2.

Half-lives ($t_{\frac{1}{2}}$) for the kinetic phases A–D of all three 8₃ proteins measured by stopped-flow, and phases E and F measured by far-UV CD in 6 M urea

Protein	$t_{\frac{1}{2}}$ phase A [s]	$t_{\frac{1}{2}}$ phase B [s]	$t_{\frac{1}{2}}$ phase C [s]	$t_{\frac{1}{2}}$ phase D [s]	$t_{\frac{1}{2}}$ phase E [h]	$t_{\frac{1}{2}}$ phase F [h]
$\alpha$	0.31*	8.8 $\pm$ 0.6	599 $\pm$ 33	1,617 $\pm$ 55	1.3*	27*
$\gamma$	0.38 $\pm$ 0.09	12 $\pm$ 3	334 $\pm$ 49	1,354 $\pm$ 32	2.4*	33*
$\zeta$	0.17 $\pm$ 0.01	11 $\pm$ 3	353 $\pm$ 43	1,646 $\pm$ 46	1.4*	25*

SD included. Asterisks (*) indicate values derived from a single reliable measurement. Fitting results are provided in SI Appendix, Figs. S12–S14 and Tables S3–S12.

Phase B, with half-lives around 9 to 12 s, partially overlaps with phase C (300 to 600 s). Phase C appears to constitute a lag phase observed before phase D starts, phase D showing sigmoidal kinetics with a $t_{\frac{1}{2}}$ value of 1,300 to 1,650 s. This result suggests that phases C and D are sequential. Representative stopped-flow kinetic traces for phases B–D are shown in Fig. 6B. Phase C was additionally monitored via far-UV CD kinetics at 222 nm after manual mixing of the samples (Fig. 6C), yielding consistent half-life estimates in the 300 to 600 s range (SI Appendix, Tables S10–S12). Notably, phase D was not detected in the far-UV CD kinetics, suggesting that this transition involves structural rearrangements primarily in regions enriched in tyrosine residues (these proteins lack tryptophan), with minimal secondary structure change. Phases A and B proceed too rapidly to be captured by manual-mixing experiments and fall within the instrument’s dead time (approximately 20 s at best).

The slowest transitions, phases E and F, were investigated by acquiring high-resolution far-UV CD spectra every 15 min over at least 36 h. A comparison with native-state spectra reveals a rapid initial loss of secondary structure within the dead time (estimated at 120 s). Subsequent spectral evolution follows a double-exponential decay pattern, indicative of continued loss of $\alpha$-helical content, as confirmed by SVD and SESCA deconvolution analyses (SI Appendix, Fig. S13). While further measurements were limited by protein availability, the high consistency across $\alpha$, $\gamma$, and $\zeta$ proteins underscores the reproducibility of these kinetic behaviors.

Models of Unfolding and Refolding.

To better understand the protein’s free energy landscape, we analyze the shape of far-UV CD spectra during unfolding and refolding at varying temperatures and urea concentrations. In addition, the size and shape of the proteins before and after refolding were analyzed based on size-exclusion chromatography (SEC) and size-exclusion chromatography linked to a multiangle light scattering device (SEC-MALS). Experiments to probe the aberrant formation of intermolecular disulfide bonds were probed by native PAGE.

In the case of varying temperatures, unfolding curves from far-UV CD can be fitted both to two- and three-state unfolding models (see SI Appendix for details, SI Appendix, Fig. S10, Left panel); however, due to protein aggregation, refolding cannot be investigated, see SI Appendix, Fig. S10.

The mechanism of unfolding and refolding, on the other hand, can be observed based on varying urea concentrations. Far-UV CD spectra show a two-state model of unfolding. The value of molar ellipticity suggests that at 7 M urea concentration, proteins are fully unfolded, and potentially unknotted. Refolding curves for both proteins were measured and suggest the ability to fold and possibly knot. However, the spectra after refolding possess different shapes (Inset in Fig. 5), suggesting that proteins refold to a structure different from N or only a fraction of the protein is actually refolding, while another fraction might be aggregating. This is further discussed in the section below.

Characterization of the Refolded State After Unfolding in Urea.

To assess protein conformations after refolding from a urea-denatured state, we compared them with the native state using SDS-PAGE, native-PAGE, SEC, and SEC-MALS. The rate of migration in SDS-PAGE is not determined by the protein’s pH-dependent electrical charge and protein conformation; e.g., SDS-PAGE separates proteins based on their molecular weight by denaturing them. However, the native-PAGE reveals the oligomeric state and subunit composition of proteins under nondenaturing conditions, preserving their native interactions, including any disulfide bonds that might have formed. SEC-MALS provides molecular weight and rms radius moments, enabling quantitative and qualitative characterization of protein conformations.

The SDS-PAGE, native-PAGE, and size-exclusion chromatography show the same overall size of all the native proteins, see SI Appendix, Fig. S17. To confirm the oligomeric state, the proteins (native and refolded) were further assessed using an analytical column. As shown in SI Appendix, Fig. S17A, the column calibration, the Inset plot in panel (A) allows an estimation of the molecular weight (MW) distribution of the eluted species. By comparing the $V_e$/$V_o$ values of the peaks with the calibration curve, we can estimate the MW of the proteins in each peak.

For the $8_3$ protein $\alpha$, the elution peaks for the native and refolded samples are $V_N$$\approx$ 14.1 ml and $V_R$$\approx$ 14.2 ml. For the $8_3$$\gamma$, the elution peaks for the native ($V_N$) and refolded ($V_R$) samples are approximately equal to 14.1 ml. The appearance of additional shoulder peaks or shifts in the main peak could point toward the formation of different oligomeric species or potentially some aggregation. The observed difference between proteins $\alpha$ and $\gamma$ likely reflects variations in their propensity to aggregation, possibly due to differences in their amino acid sequences.

The SEC-MALS profile, SI Appendix, Fig. S17B, of the native 8$3$ protein $\alpha$ shows a well-defined peak, indicating a homogeneous population. The calculated MW of 58.7 kDa is consistent with a monomer, while the refolded 8$3$ protein shows 54.3 kDa. The MW of the 8$3$ native protein, $\alpha$–based on the protein sequence, is 53.2 kDa. The native-PAGE displays a single band for all samples which corresponds to the same MW. This concordance between SEC-MALS and native-PAGE strongly suggests that the protein $\alpha$ exists primarily as a monomer under native and refolded conditions (SI Appendix, Fig. S17 A and B). To further evaluate if the oligomeric state is dependent on temperature, SEC-MALS at 50 ^°C was performed. Protein $\alpha$ continues to be a monomer as less than 10% of the sample forms oligomers and some aggregation was detected by light scattering (SI Appendix, Fig. S25). The experiment could not have been performed for proteins $\gamma$ and $\zeta$, because their $T_{\mathit{ma}}$ is too close to 50 ^°C and aggregation due to unfolding is the leading process.

SI Appendix, Fig. S17C compares the native and refolded 8$3$$\gamma$ protein. The native protein $\gamma$ shows a single peak in SEC-MALS with MW equal to 58.6 kDa, similar to the protein $\alpha$. The refolded protein $\gamma$ also shows a single peak, but with a slightly higher MW of 59.2 kDa. The MW based on the FASTA sequence is 54.3 kDa. Both native and refolded proteins $\gamma$ show single bands in native-PAGE, corroborating the SEC-MALS data and suggesting that refolding did not significantly alter the oligomeric state of the $\gamma$ protein. The observed MW values for native and refolded proteins $\gamma$ suggest that they exist predominantly as monomers, similar to the protein $\alpha$.

The $R_g$ values, determined by SEC-MALS, representing the rms radius moments (75), for 8$3$ protein $\alpha$ it was 11.0 nm in the native sample and 11.3 nm in the refolded samples. For 8$3$$\gamma$ protein, the $R_g$ values were 7.4 nm and 7.5 nm for the native and refolded samples, respectively, SI Appendix, Fig. S18.

Our findings conclude that the refolding protocol effectively recovers proteins to a state similar in compactness to the native state; however, it is impossible to determine whether the refolded state has the same fold as the native protein. Moreover, the refolded state is more stable than the native state. It may suggest that the described 8$3$ proteins need chaperones to be folded correctly.

Protein with $8_3$ Knot Can Self-Tie in a Coarse-Grained, Structure-Based Model.

The far-UV CD spectra, Fig. 5, suggest that both proteins unfold and then fold back to a compact state. However, the topologies (with or without a knot) of both the denatured state and the refolded state are not clear.

To test whether an $8_3$-knotted protein can self-tie and to establish a folding framework for this class of knotted proteins, we conducted molecular dynamics simulations, in which the topology is clearly visible. Owing to the large protein size, a coarse-grained structure-based model was used; such models are well validated and have been successfully applied to knotted proteins (18, 76).

We performed 300 folding simulations of the $\alpha$, A0A7X8EQ8 and R5TUW1 (UniProtKB ID) proteins. Each trajectory started from an unfolded, unknotted conformation generated at high temperature. The progress of folding and unfolding as a function of the number of native contacts ($Q$) and the topology corresponding to a given conformation, for representative trajectories are shown in Fig. 7.

Fig. 7.

Representative folding and unfolding pathways based on MD simulations. (A) Two folding pathways of the protein $\alpha$—folding through a $-6_1$ knot (Left panel) or through a $+6_1$ knot (Right panel). (B) Three unfolding pathways of the protein $\alpha$. The structures of protein snapshots were simplified using knot_pull package (77). Similar pathways were analyzed for two other $8_3$ proteins (UniProtKB ID: A0A7X8EQ82, R5TUW1, see SI Appendix, Fig. S20).

The $\alpha$ protein reached the native state in 75 of 260 trajectories and followed two folding pathways. The dominant pathway (83%) proceeds via a $+6_1$ knot. Initially, a native-like structure forms within the domain containing the N-terminal tail (residues 1–100 and 255–303), yielding an unknotted state with 40% native contacts ($Q=0.4$). Subsequent structuring of adjacent regions increases $Q$ to 0.65, leaving the C-terminal tail (60 residues) and residues 127–188 unstructured, the latter forming a loop. Threading of the C-terminal tail through this loop changes the topology from $0_1$ to $+6_1$. Then we observe an increase in $Q$ to 0.85. A second threading event, again involving the shortened C-terminal tail and a native-like loop (residues 123–165), produces the $8_3$ knot and completes folding to the native state.

The $\alpha$ protein can also fold via a less populated pathway (17% of trajectories), which is effectively a mirror image of the dominant route. In this case, native-like structure first forms in the C-terminal region (residues 389–465) together with residues 107–206 ($Q=0.38$), followed by structuring of adjacent regions ($Q\approx 0.6$), while the N-terminal tail (residues 1–94) and a large loop (261–384) remain unstructured. Then, the N-terminal fragment pierces a loop which leads to the introduction of the $-6_1$ knot into the structure. The N-terminal tail then pierces a loop, introducing a $-6_1$ knot. Subsequent rearrangement increases $Q$ to 0.8, as unstructured elements include the N-terminal tail (60 amino acids long), and the loop, which has now decreased to the range of 279 to 340 amino acids. A second N-terminal threading event then forms the $8_3$ knot, completing folding to the native state. Because of the dynamic nature of the structure, the reported residue ranges are approximate and may vary by over ten residues between trajectories; in some cases, a loop unfolds and refolds before the next threading event.

Simulations of $\alpha$ protein unfolding reveal additional path ways, not observed in the case of the folding process. In the most populated route, followed in 65% of the cases, there are two unknotting events involving the C-terminal end, which lead $8_3\to +6_1$ and $+6_1\to 0_1$ topology transitions. First, we observe an unfolding of the domain containing the C-terminal end, and the first unknotting event, which take place simultaneously. The second unknotting can happen before or during the unfolding of the other domain, which finally leads to the total unfolding of the protein. The next most populated pathway, observed in 27% of the simulations, also starts with the topolology transition $8_3\to +6_1$ in the same way as in the previous one. However, then the polypeptide unknots by involving the N-terminal end with the topology transition $+6_1\to 4_1$. When the protein embeds a $4_1$ knot, it is already unfolded, and the complete unknotting may involve any one of the ends. Unfolding by involving the N-terminal end in the first unknotting event may also take place. These pathways follow $8_3\to -6_1\to 0_1$ and $8_3\to -6_1;\to -4_1\to 0_1$ topology transitions, however, they are scarcely populated, by 6% and 2%, respectively.

We summarize the observed unfolding schemes as follows. Unknotting via the C-terminus yields a $+6_1$ topology, whereas unknotting via the N-terminus produces a $-6_1$ topology. A second unknotting event at the same terminus leads to an unknotted ($0_1$) state, while involvement of the opposite terminus results in a $4_1$ knot. Subsequent unknotting at either terminus yields a fully unknotted polypeptide.

The SI reports folding and unfolding results for two additional $8_3$-knotted proteins showing similar two-pathway behavior. Whether these are the only folding/unfolding routs to an $8_3$ knot remains unresolved, particularly given that some family members have very long C-terminal tails (e.g., A0A0X8VD89 with an 86-residue C-tail).

Conclusions

We identified protein fold, EIGHT, characterized by an 8₃ knot topology not present in AlphaFold’s training data and unlike any previously known structure. We solved the crystal structures of two representatives using molecular replacement with AlphaFold models—one structure for protein $ϵ$ deposited under PDB ID: 9TMH, and two for protein $\alpha$ from two different crystallization conditions: PDB ID: 32UY and PDB ID: 9RH0. While molecular replacement with the AlphaFold model carries a risk of bias, the additional anomalous signal from sulfur atoms confirms the sequence register, as well as simulated-annealing omit map positions over the knot regions. Importantly, the negative control provides independent support for the conclusion that the data favor the knotted fold: the unknotted search model failed to yield a molecular-replacement solution, whereas the knotted model succeeded. Additionally, AlphaFold models show that the knot is a conserved structural feature within the entire protein family. The $8_3$ knot belongs to the nontwist family and possesses an unknotting number of 2. This implies that the folding/unfolding pathway of proteins from this family is unique and different from all other known knotted proteins, which we demonstrate using various biophysical experimental techniques and computer simulations.

We identified 296 proteins in the UniProtKB Database with the same $8_3$ knotted fold, all of which originated from bacteria. These include bacteria that play a role in human gut health, highlighting the critical need for further research to understand the functional implications of this specific protein fold. The $8_3$ structure shows a high level of internal symmetry, with structurally analogous halves. It is possible that the EIGHT fold evolved from a single unknotted “half” that duplicated and formed a complex protein (similarly to the case of transmembrane proteins). Even though the structure has a high level of evolutionary conservation, the sequence does not. We observe variability along most of the protein sequence, with only a few conserved spots. In particular, there are two motifs located near the important elements for knot formation (the crossings).

Analysis of all family members shows that the knot can be classified as deep, buried on average 36 and 16 residues from the N and C termini, respectively. The minimal tail length in these $8_3$-knotted proteins is 5 residues. A lower value would imply the possibility of the chain end slipping through the loop and changing the topology of the structure ($6_1$ knot instead of the $8_3$). This suggests that the specific $8_3$ entanglement is functionally important.

Stability measurements on three of the $8_3$-knotted proteins, $\alpha$, $\gamma$ and $\zeta$, show that they all have similar but rather moderate thermal stabilities with $T_{\mathit{ma}}$ values between 50 to 55 ^°C. In addition, thermal unfolding probed by far-UV CD showed that although the proteins had undergone a major unfolding transition, they were not fully unfolded at 60 ^°C. Despite this, the partial unfolding observed was not reversible. Urea denaturation was also used in an attempt to reversibly unfold the proteins. In this case, a single major unfolding transition was observed between 4 and 6 M urea for all the proteins studied; however, again there was evidence from far-UV CD spectra that the structure had not fully unfolded due to the residual signal. In contrast to the thermal denaturation experiments, the urea-induced unfolding was partially reversible, with some secondary structure reforming upon refolding. However, both far-UV CD and refolding stability measurements establish that this is unlikely to be the native state as it differs in both secondary structure and stability. Of interest is the fact that the refolded, compact but nonnative state is more stable than the original native proteins. These results lead us to speculate that these $8_3$-knotted proteins may need cellular factors such as chaperones and/or the ribosome to refold to the correct knotted native state.

The unfolding kinetics of 8₃ knotted proteins are complex and span at least six distinct phases, with half-lives ranging from milliseconds to over 25 h. Rapid early transitions (phases A and B) and sequential intermediate steps (phases C and D) reflect a multistep unfolding pathway, while slower phases (E and F) involve the progressive loss of remaining secondary structure. Overall, the data highlight reproducible and similar unfolding behavior across different protein variants under denaturing conditions.

Materials and Methods

Finding the Homologs.

Using the structure and the sequence of the $8_3$ knotted protein (UniProtKB ID: A0A352WGM4), we searched for similar proteins. FoldSeek (78) on the AlphaFold Database representative sets (afdb50, afdb-proteome, afdb-swissprot) and PDB found 113 hits with e-value cutoff of ${10}^{-3}$ (none from PDB). Next, we prepared an MSA with MAFFT (79) and used it to sequentially search the whole AlphaFold Database with HMMER (e-value cutoff of ${10}^{-3}$); 305 sequences were found in UniProtKB. Finally, using the Topoly package and AlphaKnot, we obtained their topologies and kept only those with the $8_3$ knot (9 had a different topology). The final dataset contains 296 AlphaFold models sharing the $8_3$ knotted fold (see Dataset S1). Twenty-five representatives were obtained by MMseqs2 clustering (0.3 sequence identity, 0.8 coverage). Structures with the new knotted fold were collected from the AlphaKnot 2.0 Database (16, 80). Knot detection was performed using polynomial invariants [e.g., Alexander polynomial (81)] based on the Topoly package (17).

Molecular Dynamics Simulations.

Protein stability near the native state was examined using all-atom MD simulations in explicit solvent (Gromacs 2023, CHARMM27). Protein folding and unfolding were simulated with a C$\alpha$ coarse-grained structure-based model generated using the SMOG server, employing the shadow native contact map with a Gaussian potential (82–84). All coarse-grained simulations were performed in Gromacs v4.5.4. Long thermal unfolding simulations at T $=$ 190 generated unfolded, unknotted conformations that were used to initiate folding trajectories at T $=$ 125.

Production and Purification.

Protein $\alpha$ (UniProtKB ID: A0A352WGM4), $\beta$ (A0A7C6JW11), $\gamma$ (A0A7X4IB97), $\delta$ (A0A1I0QM73, $ϵ$ (A0A374JU36), and $\zeta$ (A8SPL3) were produced and purified according to the procedure described in SI Appendix.

Crystallization, X-Ray Data Collection, and Structure Determination.

Protein crystallization details are provided in SI Appendix. All of the structures were determined with molecular replacement based on Alpha Fold 2 models. Attempts to produce, purify, and crystallize the proteins with Met substituted to Se-Met were undertaken. However, none of the crystals that were obtained diffracted beyond 6 Å. Additionally, molecular replacement trials for data collected on protein $\alpha$ crystals were conducted with other search models based on unknotted topology and other than $8_3$ topologies but it ended in failure, see SI Appendix.

Far-UV Circular Dichroism (CD).

CD measurements for chemical stability were performed on a BioLogic MOS-450/AF-CD spectrometer with a 0.1 mm quartz cuvette. Protein samples (15 $\mathrm{\mu }$M) were prepared in SEC buffer (Production and Purification) without glycerol. Measurements at 10 ^°C (samples on ice prior) covered 200 to 250 nm. Each sample was measured twice (5 s acquisition), blanks under identical conditions. Data were averaged and smoothed using the Savitzky–Golay algorithm.

Urea solutions were freshly prepared. Denaturation curves were equilibrated for 3 h (native) and up to 5 h in 7 M urea (unfolded). Refolding curves used samples unfolded in 7 M urea for 5 h, then diluted to 15 $\mathrm{\mu }$M and target concentrations; refolded samples were equilibrated 2 to 5 h in 1.5 M urea. Optimal concentrations and equilibration times were determined by additional testing (SI Appendix). Far-UV CD thermal stability experiments used a Chirascan spectrometer (Applied Photophysics) with a 1 mm quartz cuvette. Protein samples (10 $\mathrm{\mu }$M) in SEC buffer were measured across 20 to 64 ^°C ($\alpha$) and 20 to 60 ^°C ($\gamma$), 5 repetitions and 0.5 s acquisition (one protein sample for the full heating range). Data were recorded from 200 to 250 nm, as signal below 200 nm was unreliable due to optical density. Far-UV CD kinetics were measured with a Chirascan spectrometer and 1 mm cuvette. Protein samples (5 $\mathrm{\mu }$M in SEC buffer) mixed with 6 M urea were measured at 25 ^°C. Short-term kinetics (up to 2,000 s) used 10 s integration per time point. Long-term kinetics (36 to 60 h) recorded spectra every 15 min with a 5 s acquisition per wavelength, 0.5 nm step size, 190 to 250 nm range.

Stopped-Flow Fluorescence Spectroscopy.

Stopped-flow single-jump measurements were performed using an Applied Photophysics stopped-flow spectrophotometer. The mixing ratio was 1:10 (protein: buffer), resulting in a final concentration of 5 $\mathrm{\mu }$M for protein and 6 M for urea. Experiments used fluorimetry mode with an excitation wavelength of 275 nm. Total emission was collected above 295 nm.

Analytical Size-Exclusion Chromatography (SEC).

Analytical SEC was used to investigate the oligomeric state of proteins in their native and refolded states. Experiments were performed on a Superdex 200 Increase 10/300 GL column (Cytiva), and calibration was carried out with standard protein markers (see SI Appendix for details).

SDS- and Native-PAGE Gels.

SDS-PAGE was used to evaluate protein purity and molecular weight under denaturation conditions. To confirm that 83 α and $\gamma$ proteins after denaturation will refold into their native oligomeric states, native-PAGE was performed following the same refolding protocol as in CD experiments (see SI Appendix for details).

SEC-Multiangle Light Scattering (SEC-MALS).

SEC-MALS was performed to determine with high accuracy the molecular weight and oligomeric states of proteins in both native and refolded states. Measurements for native proteins were performed at 25 ^°C and 50 ^°C. Samples with 2 mg/ml were loaded and the light scattering (LS), ultraviolet absorbance (UV), and differential refractive index (dRI) signals were recorded and analyzed to determine the molecular weight and assess the oligomeric state of the protein (see SI Appendix for details).

Differential Scanning Calorimetry (DSC).

DSC measurements were performed using a MicroCal VP-DSC calorimeter (Malvern, UK). The temperature range for the experiments was set between 25 and 90 ^°C, with a scan rate of 90 ^°C per hour. Protein samples had a concentration of 50 $\mathrm{\mu }$M in a DSC buffer comprising 50 mM MOPS, 200 mM NaCl, and 5% glycerol (v/v) (pH 6.5). Three measurements were taken. To assess the reversibility of the process, a heat-cool-reheat cycle was conducted (SI Appendix, Fig. S9B). The initial heating was performed from 25 ^°C to an upper limit chosen to capture the full transition while attempting to minimize thermal aggregation: 65 ^°C for $\gamma$. This endpoint selection was informed by the preceding DSC data (SI Appendix, Fig. S9). The samples were immediately cooled and then subjected to a second heating scan over the identical temperature range.

For the analysis of DSC data, we used a modified version of the pyDSC program (85), which matches our input parameters. The program calculates baseline correction following an iterative procedure presented in refs. 86 and 87.

Differential Scanning Fluorimetry.

DSF samples were prepared at increasing protein concentrations from 1 to 11 $\mathrm{\mu }$M, using a blank as a benchmark and Sypro Orange as the signal dye (Sigma-Aldrich). Measurements were performed on the CFX96 Real-Time PCR machine (Bio-Rad). The experiment began with 2 min of temperature equilibration at 22 ^°C, followed by a temperature increase to 95 ^°C at a rate of 0.5 ^°C per 30 seconds, and fluorescence intensity (FRET channel) was measured at each step. All experiments were repeated at least 3 times to ensure reliability. Data analysis was conducted using custom scripts.

Supplementary Material

Appendix 01 (PDF)

Dataset S01 (XLSX)

Dataset S02 (TXT)

Dataset S03 (TXT)

Data, Materials, and Software Availability

Crystal structures can be obtained at https://www.rcsb.org/ under accession codes: 9TMH, 9RH0, and 32UY (88–90)—will be accessible upon publication. All bioinformatics data are listed in the SI Appendix or accessible in the public database AlphaKnot. All other experimental data are available in Dane Badawcze UW (91).