Knoto-ID: a tool to study the entanglement of open protein chains using the concept of knotoids
Julien Dorier, Dimos Goundaroulis, Fabrizio Benedetti, Andrzej Stasiak
aa r X i v : . [ q - b i o . B M ] J un Knoto-ID: a tool to study the entanglement of open protein chains using the concept ofknotoids
Julien Dorier, Dimos Goundaroulis,
2, 3
Fabrizio Benedetti,
2, 1 and Andrzej Stasiak
2, 3 Vital-IT, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
The authors wish it to be known that, in their opinion, the first two authors should be regarded as joint FirstAuthors.
Abstract:
The backbone of most proteins forms an open curve. To study their entanglement, acommon strategy consists in searching for the presence of knots in their backbones using topologicalinvariants. However, this approach requires to close the curve into a loop, which alters the geometryof curve. Knoto-ID allows evaluating the entanglement of open curves without the need to close them,using the recent concept of knotoids which is a generalization of the classical knot theory to opencurves. Knoto-ID can analyse the global topology of the full chain as well as the local topology byexhaustively studying all subchains or only determining the knotted core.
Availability and Implementation:
Contact: [email protected]
I. INTRODUCTION
The observation that protein backbones can formknots([10]) initiated numerous studies of their nature andpotential advantages or disadvantages that they may pro-vide (e.g. [4, 17]). In this context, it was important toclassify protein knots in terms of their topology.A knot is a closed curve in 3-dimensional space thatdoesn’t intersect itself and it can be freely deformed aslong as it does not pass through itself ([1]). However, thebackbone of many biomolecules and specifically of manyproteins correspond to open spatial curves and so, in stricttopological sense, such curves are classified as unknotted.Until recently, the only way to study the topology of anopen protein chain was to first close them and then proceedwith the study of the entanglement. Of course, closing thechain alters its geometry. In 2012, V. Turaev introducedthe concept of knotoids as a generalization of the classicalknot theory to open knots ([16]). Knotoids were stud-ied further by N. G¨ug¨umc¨u and L. H. Kauffman ([7]). Asa consequence, a number of studies emerged that imple-mented this new mathematical tool in the analysis of aprotein backbone ([2, 5, 6]).In this note we introduce Knoto-ID, a command line toolthat is able to analyse and classify open spatial curves usingthis new mathematical concept. Moreover, we provide thepossibility of closing an open 3D curve, if a knot analysis isrequired, with either a direct closure (e.g. [15]) or using theuniform closure technique (e.g. [14]). This note focuseson individual open protein chains, however Knoto-ID can be used to analyse any open linear conformation in 3-spacesuch as chromosomes ([13]), synthetic polymers, randomwalks.
II. IMPLEMENTATION
To analyse a protein, the coordinates of the Cα III. CONCLUSION
Knoto-ID is the first tool that is able to handle, anal-yse as well as classify open linear conformations in 3-space such as proteins in terms of their topology without requir-ing them to be closed into a loop, using the concept ofknotoids.
ACKNOWLEDGEMENTS
This is the Author’s Original Version of the article hasbeen accepted for publication in Bioinformatics Publishedby Oxford University Press.We thank Louis H. Kauffman for fruitful discussions, Fr-dric Sch¨utz for his advice on Knoto-ID packaging. We alsothank Eric Rawdon, Elizabeth Annoni and Nicole Lopezfor kindly providing the list of projections distributed withKnoto-ID.
FUNDING
The work was funded in part by Leverhulme Trust(RP2013-K-017) and by the Swiss National ScienceFoundation (31003A-138267), both credited to AndrzejStasiak. [1] Adams, C. C. (1994)
The Knot Book
Freeman, New York.[2] Alexander, K., Taylor, A.J., Dennis, M. (2017) Proteinsanalysed as virtual knots.
Sci. Rep. , , 42300.[3] Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G.,and Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne,P.E. (2000) The Protein Data Bank. Nucleic Acids Res. , , 235-242.[4] Dabrowski-Tumanski, P., Stasiak, A., Sulkowska, J.I.(2016) In Search of Functional Advantages of Knots inProteins. PloS one , (11), e0165986.[5] Goundaroulis, D., Dorier, J., Benedetti, F., Stasiak, A.(2017) Studies of global and local entanglements of indi-vidual protein chains using the concept of knotoids. Sci.Rep. , , 6309.[6] Goundaroulis, D., Ggmc, N., Lambropoulou, S., Dorier, J.,Stasiak, A., Kauffman, L. (2017) Topological models for open-knotted protein chains using the concepts of knotoidsand bonded knotoids. Polymers , , 444.[7] G¨ug¨umc¨u, N. and Kauffman, L. H. (2017) New invariantsof knotoids, Eur. J. Combin. , , 186-229.[8] King, N. P., Yeates, E. O., Yeates, T. O. (2007) Identi-fication of rare slipknots in proteins and their implicationsfor stability and folding, J. Mol. Biol. , , 153-166.[9] Koniaris, K., Muthukumar, M. (1991) Self-entanglementin ring polymers. J. Chem. Phys. , (4), 2873-2881.[10] Mansfield, M.L. (1994) Are there knots in proteins? Nat.Struct. Biol. , , 213-214.[11] Rawdon, E. J., Millett, K. C., Stasiak, A. (2015) Subknotsin ideal knots, random knots, and knotted proteins. Sci.Rep. , , 8298.[12] Shi, Dashuang, Yu, Xiaolin, Roth, Lauren, Morizono, Hi-roki, Tuchman, Mendel, Allewell, Norma M. (2006) Struc- tures of N-acetylornithine transcarbamoylase from Xan-thomonas campestris complexed with substrates and sub-strate analogs imply mechanisms for substrate binding andcatalysis, Proteins: Struct., Funct., Bioinf. , , 1097-0134.[13] Siebert, J., Kivel, A., Atkinson, L., Stevens, T., Laue, E.,and Virnau, P. (2017) Are There Knots in Chromosomes? Polymers . , 317.[14] Sulkowska, J.I., Rawdon, E.J., Millett, K.C., Onuchic,J.N., Stasiak, A. (2012) Conservation of complex knotting and slipknotting patterns in proteins. Proc. Natl. Acad. Sci.U. S. A. , , E1715.[15] Taylor, W. R. (2000) A deeply knotted protein structureand how it might fold. Nature , (6798), 916.[16] Turaev, V. (2012) Knotoids. Osaka J. Math. , , 195-223.[17] Virnau, P., Mirny, L.A., Kardar, M. (2006) Intricate knotsin proteins: Function and evolution. PLoS Comput. Biol. ,2