Conceived and designed the experiments: JIS PV. Performed the experiments: DB JIS. Analyzed the data: DB JIS HPH LAM MK JNO PV. Contributed reagents/materials/analysis tools: PV. Wrote the paper: JIS LAM MK JNO PV.
The authors have declared that no competing interests exist.
Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In checking the new protein structures submitted to the Protein Data Bank, we encountered the most complex and the smallest knots to date: A recently uncovered α-haloacid dehalogenase structure contains a knot with six crossings, a so-called Stevedore knot, in a projection onto a plane. The smallest protein knot is present in an as yet unclassified protein fragment that consists of only 92 amino acids. The topological complexity of the Stevedore knot presents a puzzle as to how it could possibly fold. To unravel this enigma, we performed folding simulations with a structure-based coarse-grained model and uncovered a possible mechanism by which the knot forms in a single loop flip.
Knots are ubiquitous in many aspects of our life, but remain elusive in proteins. The multitude of protein structures archived in the Protein Data Bank can be grouped into several hundred patterns, but only a handful are folded into knots. Combing through the recently added structures we found several novel knotted proteins. A microbial enzyme that catalyzes the breakdown of pollutants is the most complex protein knot encountered so far (similar to a knot used by stevedores for lifting cargo). The smallest knotted protein on the other hand consists of only 92 amino acids. The existence of these complex motifs demonstrates that the ability of self assembly goes far beyond normal expectations. Aided by computer simulations we present evidence which suggests that the Stevedore protein knot, despite its topological complexity, may actually form in a single flipping movement.
In the last decade, our knowledge about structure and characteristics of proteins has considerably expanded. The ability of proteins of small and medium size to fold into native structures is attributed to a minimally frustrated free energy landscape, which allows for fast and robust folding
Not withstanding our daily experiences with shoelaces and cables, knots are mathematically only properly defined in closed loops, and not on open strings. In proteins, however, this issue can be resolved by connecting the termini (which are usually located on the surface) by an external loop
protein family | pdb | chain start-stop | knot type | knotted core |
RNA methytransferase ( |
1ns5 | 1–153 | 31 | 69–121 |
Carbonic anhydrase | 1lug | 2–260 | 31 | 31–257 |
SAM synthetase | 1fug | 1–383 | 31 | 33–260 |
Transcarbamylase fold | 1js1 | 1–324 | 31 | 169–267 |
2k0a | −1–107 | 31 | 18–78 | |
2efv | 6–87 | 31 | 19–66 | |
CII Ketol-acid reductoisomerase | 1yve | 83–595 | 41 | 321–533 |
Chromophore binding domain |
1ztu | 5–325 | 41 |
41–298 |
Ubiquitin Hydrolase | 2etl | 1–223 | 52 | 10–216 |
3bjx | −14–296 | 61 | 71–268 |
For each fold an example pdb code is given. Chain start-stop refers to the first and the last amino acid, which are resolved in the structure. The knotted core is the minimum configuration which stays knotted after a series of deletions from either terminus as given by our web server
There are several missing (unresolved) amino acids in 1ztu – the complete structure will likely contain a figure-eight knot. Slipknots are not listed in this table, which (of course) also contain knots in their backbone.
Even though some pioneering experiments
In this paper we present the most complex and also the smallest, knotted proteins known to date. To shed some light on potential folding routes of the former, we undertook molecular dynamics simulations with a coarse-grained model which only includes native contacts. Even though it is intrinsically difficult to fold such a large protein with a simple structure-based model, a small fraction of our trajectories (6 out 1000) folded into the knotted native state. Based on these simulations we propose a new mechanism by which this complex protein knot may fold in a single flipping movement. The proposed mechanism differs from mechanisms suggested before as it involves the flipping of a large loop over a mostly folded structure rather than folding via mostly unstructured knotted intermediates
By systematically analyzing structures submitted to the PDB
a: Crystal structure of α-haloacid dehalogenase DehI (PDB code 3bjx). The chain is composed of two homologous regions that form a pseudodimer and are connected by a proline-rich arc. The insert shows a reduced schematic representation of the protein. b: Crystal structure of the smallest knot discovered in an uncharacterized protein (PDB code 2efv). Both pictures were prepared with VMD
While DehI constitutes the most complex knot found so far, another protein was detected by our algorithm as having the smallest known knot. The backbone of an uncharacterized protein MJ0366 from
We also discovered two additional knotted DNA binding proteins. VirC2 (virulence protein from a plasmid of
It is difficult to imagine how proteins can actually fold into topologically elaborate structures like the 61 knot displayed in
Two loops are crucial for the formation of the 61 knot in DehI: a smaller loop which we call S-loop containing amino acids 64 to 135 and a slightly bigger loop termed B-loop ranging from amino acid 135 to 234. Note that the latter includes the proline rich unstructured segment mentioned earlier. The analysis of the crystallographic B-factor (see
In an attempt to elucidate the folding route of DehI, we undertook molecular dynamics simulations with a coarse-grained structure based Go-model
The S-loop (amino acids 64 to 135) is colored red, the B-loop (amino acids 135 to 234) green and the C-terminus blue. a: B- and S-loop form in the beginning by twists of the partially unfolded protein. b: B- and S-loop align. c: the S-loop twists once again, the C-terminus threads through the S-loop (in slipknot conformation) and the B-loop flips over the S-loop. In the alternative folding scenario (0→41→61), the B-loop flips over the (twisted) S-loop before the C-terminus (indicated in light blue) threads through the S-loop (41), shortly after the C-terminus threads through the S-loop in slipknot conformation. d: Native state without slipknotted C-terminus.
Unfortunately, the size and complexity of the protein does not allow us to study the full thermodynamic process and reconstruct the free energy profile along a reaction coordinate. However, kinetic data allow us to distinguish some characteristic times from which we can deduce a likely folding mechanism.
In
a: tB time (in units of MD-time steps) of flipping the B-loop over the S-loop versus time of threading the C-terminal through the S-loop (tc). Solid symbols are trajectories associated with route I (0→61), open symbols are trajectories associated with route II (0→41→61). b: tf – folding time (at which 90% of native contacts have been established) versus maximum of tB or tc.
In order to study the unfolding pathway, we raised the temperature above the folding temperature. Even though some native contacts are lost at higher temperatures, the global mechanism is by and large reversed as compared to the folding routes (see
To check how topological complexity restricts the free energy landscape the protein topology was changed from 61 to 41 (by eliminating a crossing, as previously performed with a different protein in Ref.
Our analysis of the Protein Data Bank revealed the most complex protein knot in
We investigated the folding route of the most topologically complex protein knot with molecular dynamics simulations of a structure-based model. The analysis of successful folding trajectories suggests that the Stevedore (61) knot in DehI folds via a simple mechanism: a large twisted loop in the protein flips over another previously twisted loop, thus essentially creating the six-fold knot in a single movement. Thus, the topological complexity of the Stevedore knot in DehI can be overcome and explained in the context of classical theories of protein folding
The programs used to detect knots are identical to those used in our previous work
Note that this class of structure based models was not created with protein knots in mind and is very prone to fold into topologically frustrated states. Even though Go-models can be adapted to enhance the formation of knots
Structural elements of DehI and B-factors
(0.18 MB PDF)
Order of contact formation for the folding of DehI
(0.10 MB PDF)
Unfolding routes which lead to unknotted conformations
(0.06 MB PDF)
PV and JS would like to thank Tetsuo Deguchi for organizing the conference on “Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology” in Kyoto 2008 which enabled this collaboration. PV would also like to acknowledge the support of Dmitry Ivanizki in sorting some of the more recent data.