Mathematics and Computer Science in Modeling and Understanding

1. SimRNA: a coarse-grained method for RNA 3D structure modeling___ new ideas accounting for non-canonical base pairing ___ Mathematics and Computer Science in Modeling and Understanding of Structure and Dynamics of Biomolecules Michał Boniecki, 10.08.2019 International Institute of Molecular and Cell Biology (Janusz Bujnicki lab)

2. We want to fold biomolecues This is an example of simple 3D RNA structure 3D structure is a result of (base-base) interactions. What are non-canonicalbase pairings?

3. Just RNA ... Just make a polymer of this, with 4 different side groups ...You have an RNA

4. RNA Secondary Structure: Bracket Notation

5. sequence >>> structure secondary structure CGCAUUGCG(((...)))

6. Factors of RNA structure stabilization canonical base-base contacts: non–canonical base-base contacts: Leontis/Westhof base pairing classification

7. Leontis/Westhof base pairing classification

8. What really matters C – G G – C A – U U – A wobble: G – U U – G ?

9. How it looks like in SimRNA Representation of RNA chainpdb_id: 1zih – example of small RNA structure

10. REPRESENTATION simplified (coarse grained) • MODEL OF INTERACTIONS (energy function) statistical potential – derived from pdb • CONFORMATIONAL SAMPLING METHOD Monte Carlo methods: Metropolis algorithm, REMC Introduction of SimRNA (SimRNP) three major assumptions:

11. nucleic base representation

12. SimRNA all–atom representations of RNA chain

13. SimRNA Point of Interaction Level 1 Level 2 Level 3

14. We are deriving energy function(that allows to calculate energy for any 3D conformation) We are scanning data set of structures which are solved experimentally (crystal structures)We rely on what we see !We don’t have knowledge about physical interactions, how total energy is decomposed. ... and so on ...

15. SimRNA energy function componentsspecificity originates from contacts Energy function can be divided into short range (flat angles and distances) terms and long range (base-base pairing) terms. Allshort rangeterms are sequence independent, sequence specificity originates from long range interactions (base–base).

16. reference base --- contacting base

17. SimRNA specific energy terms 3D grid for AU middle point of U RNA: base – base

18. energy of base–base interaction +

19. 3D grids (lateral layers) (examples: AA, AC, AG, AU) ?

20. SimRNA specific energy terms

21. Non-canonical interactions?Where are they?

22. A reminder canonical base-base contacts: non–canonical base-base contacts: Leontis/Westhof base pairing classification

23. SimRNA representation of RNA chainpdb_id: 157d CGCGAAUUAGCG CGCGAAUUAGCG (((.((((.((( ))).)))).))) ...<....<.......>....>...

24. SimRNA representation of RNA chainpdb_id: 1a51 GGCCGAUGGUAGUGUGGGGUCUCCCCAUGCGAGAGUAGGCC ((((.......(((((((.....))))))).......)))) ....<<<<<<<...................>>>>>>>....

25. SimRNA representation of RNA chainpdb_id: 1cq5 GGCGUUUACCAGGUCAGGUCCGGAAGGAAGCAGCCAAGGCGCC ((((.......(((....(((....)))....)))....))))

26. SimRNA representation of RNA chainpdb_id: 1fqz GCCGAGUAGUGUUGGGUCGCGAAAGGC (((.....(((......)))....)))

27. SimRNA specific energy terms 3D grid for AU middle point of U RNA: base – base What we can do ... ?

28. edges ...

29. SimRNA specific energy terms: A-U 3D grid for AU middle point of U What we can do ... ?

31. SimRNA specific energy terms: A-G 3D grid for AG middle point of G What we can do ... ?

32. SimRNA4 main idea

33. Sampling ...

34. What SimRNA is doing? Monte Carlo simulation decision(Ebefore,Eafter) initial sample accepted sample decision(Ebefore,Eafter) decision(Ebefore,Eafter) sample accepted rejected decision(Ebefore,Eafter) sample accepted

35. conformer change (single nucleotide) • one atom position change(-P- or -C4’-) • two atoms position change(either -P-C4’- or -C4’-P-) • change direction of a bigger consecutive fragment SimRNA move set – geometry modifications atom changes involve recalculation of positions of conformers

36. Results ...

37. Folding of sircin-ricin motifpdb_id: 1fqz 1st cluster: 15.6 Å 2nd cluster: 5.66 Å 3rd cluster: 2.84 Å

38. A Some RNA-Puzzles examples Examples of Bujnicki-group expert predictions, supported by SimRNA, in RNA Puzzles (left: experimentally determined reference structure, right: our top model). (A) Puzzle 14: L-glutamine riboswitch (bound) (B) Puzzle 8: SAM I/IV riboswitch. model reference B reference model

39. Idea of RMSD vs. energy plots Energy RMSD (dissimilarity)

40. 1l2x folding pathway investigation Energy RMSD GGCGCGGCACCGUCCGCGGAACAAACGG ..(((((......))))).......... .........((((...........))))

41. 1l2x energy landscape Energy RMSD 1l2x shape of folding funnel (projection)

42. Folding pathwaysHow molecules fold? Energy function requirements? folding funnel pic. from the internet

43. “Let’s do that in non-canonical way”

44. ACKNOWLEDGEMNTS ICM help: Maciej Marchwiany, Witold Rudnicki Joanna Jędraszczyk other authors: Grzegorz Łach, Konrad Tomala, Wayne Dawson, Tomasz Sołtysiński, Paweł Łukasz, Kristian Rother Janusz Bujnicki my former boss: Andrzej Koliński help and valuable discussion: Grzegorz Chojnowski Staszek Dunin-Horkawicz Juliusz Stasiewicz Boguś Kluge Tomasz Waleń Dorota Matelska Marcin Pawłowski Wojciech Potrzebowski Łukasz Kozłowski Piotr PokarowskiKrzysztof Formanowicz Masoud Farsani ICM resources: (Okeanos) Topola 100 GB of diskspace C/C++ compiler This work was supported by the Polish National Science Center Poland (NCN) (grant 2016/23/B/ST6/03433 to Michal J. Boniecki). Previous developments were supported by the Polish Ministry of Science (HISZPANIA/152/2006 grant to Janusz M. Bujnicki and PBZ/MNiSW/07/2006 grant to Michał Boniecki) and by the EU (6FP grant “EURASNET” LSHG-CT-2005-518238) and DFG (SPP 1258), ERC (RNA+P=123D). We thank the current and former members of the Bujnicki group (in particular developers of methods and participants of the RNA-Puzzles experiment) for their intellectual contribution.