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

Samuela Pasquali & Elisa Frezza

Laboratoire de Cristallographie et RMN Biologiques Faculté de Pharmacie, Université Paris Descartes

Development of coarse-grained models for nucleic acids (and aromatic systems)

Nucleic acids complex structural architectures

siRNA microRNA piRNA tRNA riboswitches ribosomal RNA ribozymes 20-25 nt ~30 40 100 80 snoRNA 300 60 mRNA > 1000

tRNA telomerase viral fragment ribozyme riboswitch triple helix

Physical description

Prediction of the dynamical and thermodynamical behavior in 3D

𝜈m nm Å 10 nm 100 nm

Folding Assembly Too large for an atomistic description Too small for a mesoscoptic description

Coarse-grained RNA modeling

Ab initio models: simplified models to represent the meaningful degrees of freedom of the system and the process of interest

P C4' B1 B2 C1' C5' O5' P O5' P

HiRE-RNA

High Resolution Energy Model for RNA and DNA

Flexible, unconstrained

MD, REMD, ST, MC model

... Why is RNA not a protein ...

At long-range is LJ-like potential appropriate/necessary?

At large distances the dominant effect should be the ELECTROSTATIC repulsion, with Van der Waals forces being subdominant

At short-range LJ-like potential between bases are inadequate

STACKING is the hydrophobic behavior of bases and it is short-ranged 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

model

E = Elocal + Eex vol + EBP + Eelectrostatics + Estacking HiRE-RNA, version 3 Eel = "el q2 4⇡✏0✏rre−r/` Eex vol = εex e−κ(r−rv)

genetic algorithm parameter optimization NDB - topology based harmonic statistical parameters

Planarity Non-canonical pairs Base orientation

bond stretching angle bending bond rotation

• T. Cragnolini,
• Y. Laurin, P

. Derreumaux, S. Pasquali, JCTC (2015)

• T. Cragnolini, P

. Derreumaux, S. Pasquali, J. Physics: Condensed Matter (2015)

model

Stacking

Est = "st e− (r−rst)2

σ

(~ ni · ~ nj)2 1 − |~ ni × ~ r |4 1 − | ~ nj × ~ r |4

θ

{

• 1.5
• 1.0
• 0.5

0.5 1.0 1.5 0.2 0.4 0.6 0.8 1.0

plane distance same plane

• rientation

vertical position

P C4' B1 B2 C1' C5' O5' P O5' P

model

Base pairing

canonical and non-canonical 288 theoretically possible pairs ⇢ 145 found experimentally (NDB)

Hoogsteen Watson-Crick Sugar

Base Pairing

EBP = EHB × Eplane

ν(α) = ⇢ cos6(α − Ω), for − 90 ≤ (α − Ω) ≤ 90; 0,

• therwise

α = ⇢ +α, if cos(τ) ≥ 0; −α,

• therwise

Ehb = εhbe−(r−ρ)2/ξ ν(α1)ν(α2)

Eplane = εpl

3

X

kj=1

✓ e−(d

kj Bi/δ)2

+ e

−(d

kj Bj /δ)2◆

P C4' B1 B2 C1' C5' O5' P O5' P

model

A A A A A A A C A C A G A G A G A G A U A U C C C U C U G C G C G G G G G U G U U U U U

trans HH trans HS trans WcWc cis WcWc cis WcWc cis WcS cis WcWc trans HS trans WcWc cis WcWc trans WcH trans WcWc cis WcWc trans WcH cis WcWc trans HH cis WcH cis WcH cis WcWc trans WcWc cis WcWc trans WcH

Wc: Watson-Crick H: Hoogsteen S: Sugar

3 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1

Non-canonical pairings

model

U H1 H2 F T1 T2

HiRE-RNA, version 3

Triple helix folding G-quadruplexes unfolding

CG

High-resolution techniques : biochemistry, NRM, X-ray

Constraints

Low-resolution techniques : SAXS, Cryo-EM

Biased simulations Interactive simulations

Single-molecule experiments : FRET, optical tweezers

External forces Constraints

3 contraintes d'appariement de bases ~7Å rmsd

Contraintes d'appariement de bases

Exp

Inclusion of experimental data

Interactive simulations: UnityMol + HiRE-RNA

Force appliquée par l'utilisateur en temps réel

• S. Doutreligne, P

. Derreumaux, S. Pasquali, M. Baaden (2015)

Energetic monitoring: total, electrostatic, stacking, base-pairing Simulation interface

• n-the-fly constraints
• n-the-fly SAXS curves
• n-the-fly 2D structure

Exp

• S. Doutreligne, L. Mazzanti, A. Taly, P

. Derreumaux, M. Baden, S. Pasquali (2017)

Behavior of biomolecules Behavior depends on environment

Temperature, ligands, ions, … pH

Coarse-grained models to study structural changes Titration scheme to account for pH and salt

pH

Tanford-Kirkwood model (1934, 1957)

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

pH

wT K ≈ e2 8⇡✏0✏r

Np

X

i>j

zizj rij − Z2

p

2(1 + b) ! ± (pH − pKa)

protonation (+) deprotonation (-)

Fast Monte Carlo titration scheme

Texeira, Lund, Barroso da Silva, JCTC, 2010 Barroso da Silva, MacKernan, JCTC 2017

Fast MC titration

individual effective pKa values pH

4.99 (4.3) 3.8 (4.73) 3.8 (4.73) 3.5 (4.9) 6.5 (5.6)

Bases pKa 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

exposed ⇢ protonable pKa ~ isolated N+ paired ⇢ protected higher pKa neutral paired ⇢ protected lower pKa

Base protonation is intertwined with base pairing!

pH

Idex Brazil project

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)

Future directions (to do list) Explicit IONS !!! 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)

Protein qi qj

All-atom or CG representation

RNA/DNA

HiRE-RNA representation

Energy minimisation

Internal normal mode analysis

∂E ∂qi

Technical caveat: Conversion from internal to cartesian coordinate space (non linear) immediate future

Internal coordinates

dihedral angles

• Faster and more harmonic exploration
• Better sampling for large

conformational changes

• Determination of torsions implied in

the global movements

• Conformational changes better

described by the lower frequency modes (<5)

• No deformation of the structure, but

large conformational changes

10% contribution <0.1% contribution

Target iNMA Starting RMSD = 20 Å RMSD = 3 Å

Frezza and Lavery JCTC 2015 Frezza and Lavery in preparation

immediate future

Internal Normal Mode Analysis

Advantages

• 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

immediate future

Internal Normal Mode Analysis

Applications

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

• J. Sponer’s group
• D. Wales’s group

Acknowledgements