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Knots, Lassos, and Links

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Knots, Lassos, and Links KNOTS, LASSOS, AND LINKS pawełdabrowski˛ -tumanski´ Topological manifolds in biological objects June 2019 – version 1.0 [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] PawełD ˛abrowski-Tuma´nski: Knots, lassos, and links, Topological man- ifolds in biological objects, © June 2019 Based on the ClassicThesis LATEXtemplate by André Miede. [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] To my wife, son, and parents. [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] STRESZCZENIE Ła´ncuchybiałkowe opisywane s ˛azazwyczaj w ramach czterorz ˛edowej organizacji struktury. Jednakze,˙ ten sposób opisu nie pozwala na uwzgl ˛ednienieniektórych aspektów geometrii białek. Jedn ˛az braku- j ˛acych cech jest obecno´s´cw˛ezła stworzonego przez ła´ncuchgłówny. Odkrycie białek posiadaj ˛acych taki w˛ezełbudzi pytania o zwijanie takich białek i funkcj ˛ew˛ezła. Pomimo poł˛aczonegopodej´sciateore- tycznego i eksperymentalnego, odpowied´zna te pytania nadal po- zostaje nieuchwytna. Z drugiej strony, prócz zaw˛e´zlonych białek, w ostatnich czasach zostały zidentyfikowane pojedyncze struktury zawie- raj ˛aceinne, topologicznie nietrywialne motywy. Funkcja tych moty- wów i ´sciezka˙ zwijania białek ich zawieraj ˛acych jest równiez˙ nieznana w wi ˛ekszo´sciprzypadków. Ta praca jest pierwszym holistycznym podej´sciemdo całego tematu nietrywialnej topologii w białkach. Prócz białek z zaw˛e´zlonymła´ncu- chem głównym, praca opisuje takze˙ inne motywy: białka-lassa, sploty, zaw˛e´zlonep ˛etlei ✓-krzywe. Niektóre spo´sród tych motywów zostały odkryte w ramach pracy. Wyniki skoncentrowano na klasyfikacji, wys- t ˛epowaniu, funkcji oraz zwijaniu białek z topologicznie nietrywial- nymi motywami. W cz ˛e´scipo´swi˛econejklasyfikacji, zaprezentowane zostały wszys- tkie topologicznie nietrywialne motywy wyst ˛epuj˛acew białkach. W szczególno´sci,zaproponowano i opisano nowe matematyczne narz ˛e- dzia umozliwiaj˙ ˛aceklasyfikacj ˛ebiałek-lass. W cz ˛e´scidotycz ˛acejwys- t ˛epowania struktur rozwazane˙ jest statystyczne prawdopodobie´nstwo wyst ˛epowania róznych˙ motywów. Ich mniejsza liczba w porównaniu z szacunkami wynikaj ˛acymiz modeli polimerowych stanowi wst ˛ep do rozwaza´nna˙ temat funkcji nietrywialnej topologii. W szczegól- no´scipokazano, ze˙ funkcj ˛asplotu jest wprowadzenie szczególnej sta- bilno´sciła´ncucha,a w przypadku niektórych białek topologia lassa jest najprawdopodobniej niezb ˛ednado pełnienia przez nie funkcji. W tej cz ˛e´scizaproponowana została równiez˙ funkcja w˛ezławła´ncuchu głównym, wspomagaj ˛acatworzenie i stabilizuj ˛acamiejsca aktywne enzymów. Nowy mechanizm zwijania zaw˛e´zlonych białek wykorzys- tuj ˛acyrybosom rozpoczyna cz ˛e´s´cczwart ˛a,w której analizowany jest równiez˙ wpływ topologii, ograniczonej obj ˛eto´scii długo´sciw˛ezła na zwijanie białek. Skrupulatna analiza wszystkich dost ˛epnych struktur przestrzen- nych białek mozliwa˙ była jedynie po stworzeniu odpowiednich narz ˛e- dzi programistycznych. Narz ˛edziate zostały przekazane naukowej wspólnocie pod postaci ˛abaz danych, serwerów, wtyczek do innych programów oraz paczki programistycznej. Narz ˛edziate opisane s ˛a w cz ˛e´scipi ˛atej.Praca ko´nczysi ˛ewskazaniem przyszłych kierunków rozwoju dziedziny oraz zbiorem literatury okalaj ˛acejzagadnienia za- warte w pracy. Zestaw ten skierowany jest do przyszłych adeptów, 5 [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] 6 stanowi ˛acprzewodnik po ´swieciebiałek o skomplikowanej topologii i zach ˛et˛edo dalszych prac. [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] ABSTRACT The organization of amino acids in the protein is usually described in terms of four levels of structure classification which, however, misses some important aspects of protein geometry. One of the protein fea- tures absent is the existence of the knot tied on the protein backbone. The discovery of such knotted proteins raises the questions of the folding of such proteins and the function of the backbone knot. De- spite theoretical and experimental investigation, the answers on both of these questions remain elusive. Moreover, apart from the knotted proteins, some singular cases of other topologically non-trivial pro- teins were recently identified, for which the folding and the function are also unknown. This work is the first holistic elaboration on the whole field of the proteins with complex topology. Apart from the backbone knots, the work describes also other motifs, some discovered as the result of the project: complex lassos, protein links, knotted loops, and ✓-curves. The work concentrates on the classification, occurrence, function, and folding of proteins with the topologically complex motifs. In the classification part, all the topologically non-trivial motifs present in proteins are described. In particular, novel mathematical tools to classify the complex lasso structures are proposed. In the part devoted to occurence of the motifs, their statistical probability is presented. Observed underrepresentation of the motifs in comparison with polymer models becomes a prelude to the function of the com- plex topology. In particular, the links are shown to stabilize the struc- ture, and the lasso topology is strongly suggested to be crucial for the function of some proteins. In this part also the enzyme-favoring func- tion of the backbone knot is proposed. The novel, ribosome-based mechanism of folding of the proteins with backbone knots begins the fourth part, in which also the influence of the topology, confinement, and knot tails on folding process is analyzed. The scrupulous analysis of the whole database of the protein struc- tures was possible only with the creation of the special tools. These were given to the broad scientific community in the form of databases, servers, plugins, and a Python package, to which the fifth part of the work is devoted. The work is finalized with the future directions and further reading sections which, hopefully, will inspire younger adepts to immerse into the field of complex topology proteins. 7 [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] PUBLICATIONS The thesis covers the following publications: Dabrowski-Tumanski P, Gren B, Sulkowska JI (2019). Statistical Prop- D1 erties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function. Polymers, 11(4), 707. Gierut AM, Dabrowski-Tumanski P, Niemyska W, Millett KC, D2 Sulkowska JI (2019). PyLink: a PyMOL plugin to identify links. Bioin- formatics, bty1038 Dabrowski-Tumanski P, Rubach P, Goundaroulis D, Dorier J, Sułkowski P, Millett KC, Rawdon E, Stasiak A, Sulkowska JI (2018). D3 KnotProt 2.0: a database of proteins with knots and other entangled structures. Nucleic acids research, 47(D1), D367–D375. Zaj ˛acS, Geary C, Andersen ES, Dabrowski-Tumanski P, Sulkowska JI, D4 Sułkowski P. (2018). Genus trace reveals the topological complexity and domain structure of biomolecules. Scientific Reports, 8(1), 17537. Dabrowski-Tumanski P, Piejko M, Niewieczerzal S, Stasiak A, Sulkowska JI (2018) Protein Knotting by Active Threading of Nascent D5 Polypeptide Chain Exiting from the Ribosome Exit Channel. The Jour- nal of Physical Chemistry B, 122(49), 11616–11625. Dabrowski-Tumanski P, Sulkowska JI (2018). The APS-bracket–A D6 topological tool to classify lasso proteins, RNAs and other tadpole- like structures. Reactive and Functional Polymers, 132, 19–25. Jarmolinska AI, Kadlof M, Dabrowski-Tumanski P, Sulkowska JI D7 (2018). GapRepairer: a server to model a structural gap and validate it using topological analysis. Bioinformatics, 34(19), 3300–3307. Zhao Y, Dabrowski-Tumanski P, Niewieczerzal S, Sulkowska JI (2018). D8 The exclusive effects of chaperonin on the behavior of proteins with 52 knot. PLoS computational biology, 14(3), e1005970. Dabrowski-Tumanski P, Sulkowska J. (2017). To tie or not to tie? That D9 is the question. Polymers, 9(9), 454. Gierut AM, Niemyska W, Dabrowski-Tumanski P, Sułkowski P, D10 Sulkowska JI (2017). PyLasso: a PyMOL plugin to identify lassos. Bioinformatics, 33(23), 3819–3821. Dabrowski-Tumanski P, Sulkowska JI (2017). Topological knots and D11 links in proteins. Proceedings of the National Academy of Sciences, 114(13), 3415–3420. 9 [ June 25, 2019 at 18:23 – classicthesis version 1.0 ] 10 Dabrowski-Tumanski P, Sklodowski M, Sulkowska JI (2016). Current D12 approaches to disentangle the mystery of knotted protein folding. TASK Quarterly, 20(4), 361–371. Niemyska W, Dabrowski-Tumanski P, Kadlof M, Haglund E, D13 Sułkowski P, Sulkowska JI (2016). Complex lasso: new entangled mo- tifs in proteins. Scientific reports, 6, 36895. Dabrowski-Tumanski P, Stasiak A, Sulkowska JI (2016). In search of D14 functional advantages of knots in proteins. PloS one, 11(11), e0165986. Dabrowski-Tumanski P, Jarmolinska AI, Niemyska W, Rawdon EJ, Millett KC, Sulkowska JI (2016). LinkProt: A database collecting in- D15 formation about biological links. Nucleic acids research, 45(D1), D243— D249. Dabrowski-Tumanski P, Niemyska W, Pasznik P, Sulkowska JI (2016) D16 Lassoprot: server to analyze biopolymers with lassos. Nucleic acids research, 44(W1), W383–W389. Dabrowski-Tumanski P, Jarmolinska AI, Sulkowska JI (2015). Predic- D17 tion of the optimal set of contacts to fold the smallest knotted protein. Journal of Physics: Condensed Matter, 27(35), 354109. Dabrowski-Tumanski P, Niewieczeral S, Sulkowska JI (2014). Deter- D18 mining critical amino acid contacts for knotted protein folding. TASK Quarterly,
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