DNA bending induced during Molecular Dynamics simulations: Basepair Kinks and Hinges

Transcription

1 DNA bending induced during Molecular Dynamics simulations: Basepair Kinks and Hinges Thursday, October 23, 2008 Theoretical Approaches or the Genome LAPTH-LAMA-LAPP-CNRS-University o Savoie Jeremy Curuksu Computational Biology Lab., Martin Zacharias Jacobs University, Bremen, Germany Annecy-le-Vieux, France

2 TALK OUTLINES INTRODUCTION 1. Developpment: An all-atom DNA Bending Coordinate 2. Application: Molecular Dynamics o DNA kink motis (example o a poly-purine/pyrimidine C/G DNA 15 bp sequence) 3. Further insights rom enhanced sampling techniques CONCLUSION

3 Molecular Dynamics simulation F = m. a V ( q) = M. d q 2 dt 2 q Probability Density at constant N, V and T: Γ : P( Γ) = exp( H ( Γ) / k T Set o particle positions ( q) and momenta ( p) H( q, p) : the Hamiltonian = V( q) + K( p) k B :Boltzmann Constant B ) Time A Molecular Dynamics Trajectory

4 Quasi-ergodicity o MD samples A schematic representation o phase space Order Parameter Y Order Parameter X Region o low energy Region o high energy

5 DNA conormational lexibility δ: C5 C4 C3 O3 γ: O5 C5 C4 C3 β: P O5 C5 C4 α: O3 P O5 C5 ζ: C3 O3 P O5 SHIFT SLIDE TILT ROLL BENDING OF BASEPAIR ε: C4 C3 O3 P RISE TWIST Backbone dihedral angles { Z( Ω) Y ( ρ) X ( )} ( j, k, ) ( j ', k', l') = τ l Helical internal coordinates

6 DNA bend coordinate { A} ( j, k, ) ( j ', k', l') = l (j,k,l ) Harmonic potential U(θ) = k * ( θ - θ re ) 2 triad (j, k, l) Rotation vector Curuksu J., Zakrzewska K., Zacharias M. (2008) Nucleic Acid Research 36(7):

7 Amplitude and Direction o bending Adiabatic Mapping on DNA ds 5 (GCAAAAAACG)3 Energy Minimisation Curuksu J., Zakrzewska K., Zacharias M. (2008) Nucleic Acid Research 36(7):

8 Free Energy (PMF) o DNA bending Umbrella Sampling Molecular Dynamics Protocol DNA bending energy probed by Atomic Force microscopy (Wiggins et al., 2006) w.3 ns w.2 ns bk.1 ns parmbsc0 (Perez et al.,2007) Truncated octahedral box (~7600 water molecules) Neutralising K + counterions PME electrostatics 2 s timestep (SHAKE) NVT (0K 300K) NPT Time rame every 2 ps 31*3ns w trj (0 150 ) using U(θ) = k * ( θ - θ re ) 2 Bending Free Energy (kcal/mol) d(cgcgcgcgcgcgcgc) d(cgcgcaaaaacgcgc) d(catatatatatatatc) d(cgcgcgcgcaaaaac) Bend angle θ (degrees) Curuksu J., Zacharias M., Lavery R., Zakrzewska K., Manuscript in preparation

9 Kinking Occurs during Molecular Dynamics Simulations o Small DNA Minicircles (2006) starting structure kink kink starting structure kink stable conormations Lankas F., Lavery R, Maddocks J.H. (2006) Structure 14:

10 TALK OUTLINES INTRODUCTION 1. Developpment: an all-atom DNA Bending Coordinate 2. Application: Molecular Dynamics o DNA kink motis (example o a poly-purine/pyrimidine C/G DNA 15 bp sequence) 3. Further insights rom enhanced sampling techniques CONCLUSION

11 The poly-purine/pyrimidine C/G DNA sequence (15 bp) Bending Free Energy (kcal/mol) α =6.8 (Linear Sub-Elastic Chain model) rom AFM [ Wiggins et al. (2006) ] E(θ) = 1/2 * k B T* l/ξ * θ 2 based on ξ ~ 144 bp α = 6.9 Bend angle (degrees)

12 The poly-c/g DNA sequence (15 bp) Probability Distribution o basepair bend angles Amber parm-94 orce ield Amber parm-bsc0 orce ield ( roll 2 + tilt 2 ) in degrees ( roll 2 + tilt 2 ) in degrees Legend Row 1: C1G2 C3G4 C5G6 C7G8 C9G10 C11G12 C13G14 Row 2: G2C3 G4C5 G6C7 G8C9 G10C11 G12C13 G14C15

13 The poly-c/g DNA sequence (15 bp, parmbsc0) Basepair Kink (type II) Force Constantes o basepair bend Time Average o local bend and propeller with parmbsc0 ( roll 2 + tilt 2 ) in degrees Junction C7G8 Junction G6C7 K (kcal/mol/degree 2 ) k B T 2 2 σ ( roll + tilt cubic polynomial it 2 ) G6C7 C7G8 Global Bend in degrees Normal probability plots o basepair bend De Santis,2002, thermal stability data Olson,1998, Crystallo. Lankas,2003, MD Robinson,2002, EPR Propeller in degrees base pair at C7 Normalized Sample Junction G6C7 Junction C7G8 Global Bend in degrees Normal Distribution N(0,1)

14 DNA basepair hinge conormations Time Frames / Side View: three DNA kink substates K (kcal/mol/deg 2 ) GCG, type II kink AAC, type II kink CG, middle kink C7G8 A9A10 G6C7 A10C11 C7G8 Bend angle (degrees) Bend angle (degrees) Bend angle (degrees) Curuksu J., Zacharias M., Lavery R., Zakrzewska K., Manuscript in preparation

15 TALK OUTLINES INTRODUCTION 1. Developpment: an all-atom DNA Bending Coordinate 2. Application: Molecular Dynamics o DNA kink motis (example o a poly-purine/pyrimidine C/G DNA 15 bp sequence) 3. Further insights rom enhanced sampling techniques CONCLUSION

16 Molecular Dynamics simulation F = m. a V ( q) = M. d q 2 dt 2 q Probability Density at constant N, V and T: Γ : P( Γ) = exp( H ( Γ) / k T Set o particle positions ( q) and momenta ( p) H( q, p) : the Hamiltonian = V( q) + K( p) k B :Boltzmann Constant B ) Time A Molecular Dynamics Trajectory

17 Replica Exchange simulation??????? Time W ( C) ω( C C ') Detailed = W( C' Balance ac') ) P ( C = W ( C ') ω( C ' C) ) W ( C Replica 1 R2 R3 R4 R5 R6 Replica n

18 The poly-c/g DNA sequence (15 bp, parm94) ds DNA 5 (CGCGCGCGCGCGCGC)3 Replica Exchange Umbrella Sampling (Amber parm94 orce ield) Probability Distribution o base pair bend angles CG junctions original GC junctions 150 Bending Free Energy in kcal.mol -1, parm94 New: WITH REUS 1ns 2ns 1ns 2ns Original: WITHOUT REUS ( roll 2 + tilt 2 ) in degrees Global bend angle in degrees

19 The poly-c/g DNA sequence (15 bp, parmbsc0) ds DNA 5 (CGCGCGCGCGCGCGC)3 Replica Exchange Umbrella Sampling (Amber parmbsc0 orce ield) Probability Distribution o base pair bend angles CG junctions GC junctions 150 (degrees) ( roll 2 + tilt 2 ) at C7G8 bp junction Propeller at C7:G24 Watson-Crick bp 150 ( roll 2 + tilt 2 ) in degrees Time (nanoseconds)

20 Conclusion DNA bending ree energy not quadratic on short length scale [ 5 nm ] Amber parm-94 orce ield: - Type I kink at 5 CG3 requires longitudinal localization o DNA bending energy. (what could be used to code Breakpoints in the Genome) Amber parm-bsc0 orce ield: - No type I kink. - Type II kink at 5 GCG3 and 5 AAC3 ( For Global Bend [ 5 nm ] >> 100 ). - Type II kink is metastable and has reduced basepair bend orce constant. Valid inerence o DNA bend conormers rom MD orce-ield consensus

21 Acknowledgement Martin Zacharias Ragav, Sebastian, Shide and Ranjit Group o Computational Biology Jacobs University (Bremen, Germany) Krystyna Zakrzewska and Richard Lavery Laboratoire de Bioinormatique et RMN structurales Institut de Biologie et Chimie des Protéines (Lyon, France) Computational Laboratories or Analysis, Modelling and Visualization (CLAMV), Jacobs University, Germany. Universite Franco-Allemande (UFA) cotutelle agreement between Universite Paris 7 and Jacobs University. VolkswagenStitung PhD grant. and the Theoretical Approaches or the Genome 2008 organizers.

22