Development of coarse-grained models for nucleic acids (and - PowerPoint PPT Presentation

Development of coarse-grained models for nucleic acids (and aromatic systems) Samuela Pasquali & Elisa Frezza Laboratoire de Cristallographie et RMN Biologiques Faculté de Pharmacie, Université Paris Descartes

Nucleic acids complex structural architectures 20-25 ~30 40 60 80 100 300 > 1000 nt tRNA microRNA ribosomal RNA piRNA riboswitches siRNA ribozymes snoRNA mRNA tRNA telomerase viral fragment ribozyme triple helix riboswitch

Physical description Prediction of the dynamical and thermodynamical behavior in 3D 𝜈m Å nm 10 nm 100 nm Assembly Folding Too large for an atomistic description Too small for a mesoscoptic description

Coarse-grained RNA modeling model Ab initio models: simplified models to represent the meaningful degrees of freedom of the system and the process of interest HiRE-RNA High Resolution Energy Model for RNA and DNA B2 B1 O5' P C5' Flexible, unconstrained C4' C1' O5' P P MD, REMD, ST, MC

... Why is RNA not a protein ... model At large distances the dominant effect should be the ELECTROSTATIC repulsion, with Van der Waals forces being subdominant At long-range is LJ-like potential appropriate/necessary? STACKING is the hydrophobic behavior of bases and it is short-ranged At short-range LJ-like potential between bases are inadequate Hydrogen bonding occurs in the base PLANE Local geometries have to be taken into account Bases can form hydrogen bonds on 3 different SIDES Non-canonical base pairs and multiple pairings have to be included

HiRE-RNA, version 3 model E = E local + E ex vol + E BP + E electrostatics + E stacking Planarity Base orientation Non-canonical pairs bond stretching bond rotation angle bending harmonic statistical parameters E ex vol = ε ex e − κ ( r − r v ) q 2 4 ⇡✏ 0 ✏ r re − r/ ` E el = " el genetic algorithm parameter optimization NDB - topology based T. Cragnolini, Y. Laurin, P . Derreumaux, S. Pasquali, JCTC (2015) T. Cragnolini, P . Derreumaux, S. Pasquali, J. Physics: Condensed Matter (2015)

Stacking model B2 B1 P O5' C5' C4' C1' O5' P P E st = " st e − ( r − rst )2 n j ) 2 � r | 4 � � r | 4 � ( ~ n i · ~ 1 − | ~ 1 − | ~ n i × ~ n j × ~ σ { plane 1.0 distance same plane 0.8 vertical position orientation 0.6 0.4 0.2 θ - 1.5 - 1.0 - 0.5 0.5 1.0 1.5

Base pairing canonical and non-canonical Hoogsteen Watson-Crick Sugar 288 theoretically possible pairs ⇢ 145 found experimentally (NDB)

Base Pairing model E BP = E HB × E plane E hb = ε hb e − ( r − ρ ) 2 / ξ ν ( α 1 ) ν ( α 2 ) ⇢ cos 6 ( α − Ω ) , for − 90 � ≤ ( α − Ω ) ≤ 90 � ; ν ( α ) = 0 , otherwise ⇢ + α , if cos( τ ) ≥ 0; α = otherwise − α , 3 B2 ✓ Bj / δ ) 2 ◆ kj kj B1 Bi / δ ) 2 − ( d P O5' e − ( d X E plane = ε pl + e C5' C4' C1' k j =1 P O5' P

Non-canonical pairings model A A A A A A trans HH trans HS trans WcWc 2 1 2 A C A C A G cis WcWc cis WcWc cis WcS 1 1 1 A G A G A G cis WcWc trans HS trans WcWc 2 2 1 A U A U C C cis WcWc trans WcH trans WcWc 2 2 2 cis WcWc cis WcWc C U C U G C trans WcH 1 1 3 G C G G G G trans HH cis WcH cis WcH 1 1 2 G U G U U U cis WcWc trans WcWc cis WcWc 2 1 2 U U trans WcH Wc: Watson-Crick H: Hoogsteen S: Sugar 1

HiRE-RNA, version 3 CG U H1 Triple helix folding T2 F G-quadruplexes unfolding T1 H2

Inclusion of experimental data Exp Biased simulations Low-resolution techniques : SAXS, Cryo-EM Interactive simulations High-resolution techniques : biochemistry, NRM, X-ray Constraints External forces Single-molecule experiments : FRET, optical tweezers Constraints Contraintes d'appariement de bases 3 contraintes d'appariement de bases ~7Å rmsd

Interactive simulations: UnityMol + HiRE-RNA Exp Energetic monitoring: Simulation interface total, electrostatic, stacking, base-pairing Force appliquée par l'utilisateur en temps réel on-the-fly constraints on-the-fly SAXS curves on-the-fly 2D structure S. Doutreligne, P . Derreumaux, S. Pasquali, M. Baaden (2015) S. Doutreligne, L. Mazzanti, A. Taly, P . Derreumaux, M. Baden, S. Pasquali (2017)

Behavior of biomolecules pH Behavior depends on environment Temperature, ligands, ions, … pH Coarse-grained models to study Titration scheme to account for structural changes pH and salt

Tanford-Kirkwood model (1934, 1957) pH Molecule represented as a sphere impenetrable to solvent. Titratable group are independent (interact only through electrostatics) ⇢ molecule’s titration curve as superposition of titration curves of individual types of groups N p ! Z 2 e 2 z i z j p  X ± ( pH − pK a ) w T K ≈ − 8 ⇡✏ 0 ✏ r 2(1 +  b ) r ij protonation (+) i>j deprotonation (-) Fast Monte Carlo titration scheme Texeira, Lund, Barroso da Silva, JCTC, 2010 Barroso da Silva, MacKernan, JCTC 2017

Fast MC titration pH Bases pKa values 3.5 (4.9) 3.8 (4.73) 3.8 (4.73) 4.99 (4.3) 6.5 (5.6) individual effective pK a values Barroso da Silva, Pasquali, Derreumaux, Dias, Soft Matter 2016 Barroso da Silva, Derreumaux, Pasquali, BBRC 2017 Barroso da Silva, Derreumaux, Pasquali, J Chem Phys 2017

Base protonation is intertwined with base pairing! pH exposed ⇢ protonable pK a ~ isolated neutral paired ⇢ protected lower pKa N + paired ⇢ protected higher pKa Idex Brazil project

HiRE-RNA v3 achievements Correctly fold molecules of complex architectures, including triplets and quadruplets, giving access to folding pathways and metastable states. Investigate the importance of non-canonical paris in RNA folding Give access to the plurality of states of G-quadruplexes and study the possible interconversions between different conformations. Development of interactive simulation software for teaching and experimentalists (software presentation on Friday) Future directions (to do list) HiRE-RNA v4, including ions and base-phosphate interactions Enhance sampling for rare events (collaboration D. Wales) Proteins/Nucleic acids systems (collaboration LBT) Strenghten coupling with experiments (collaborations LCRB, LBT) Couple Titration and HiRE-RNA (collaboration F. Barroso da Silva) Generalization to other aromatic systems (collaboration B. Baumeier) Explicit IONS !!!

Internal coordinates immediate future Protein RNA/DNA dihedral angles q j q i All-atom or CG representation HiRE-RNA representation Energy minimisation Internal normal mode analysis ∂ E ∂ q i Technical caveat: Conversion from internal to cartesian coordinate space (non linear)

Internal Normal Mode Analysis immediate future Advantages • Faster and more harmonic exploration • Better sampling for large conformational changes 10% contribution • Determination of torsions implied in the global movements <0.1% contribution • Conformational changes better described by the lower frequency modes (<5) iNMA • No deformation of the structure, but large conformational changes Target Starting RMSD = 3 Å RMSD = 20 Å Frezza and Lavery JCTC 2015 Frezza and Lavery in preparation

Internal Normal Mode Analysis immediate future Applications • Sampling methods • Prediction of candidate structures for docking experiments • Prediction of RNA structure by combining SAXS data and MD • Parametrization and optimisation of a coarse-grained force-field

Acknowledgements Elisa Frezza Philippe Derreumaux Fernando LB Da Silva Marc Baaden LCRB LBT, Paris 7 University of Sao Paolo LBT, CNRS HiRE-RNA UnityMol Titration Internal coordinates Tristan Cragnolini Liuba Mazzanti Sébastien Doutreligne Post-doc Cambridge Post-doc Cambridge grad student J. Sponer’s group D. Wales’s group HiRE-RNA + SAXS HiRE-RNA, v2 & v3 UnityMol