dna bending induced during molecular dynamics simulations
TRANSCRIPT
DNA bending induced during Molecular Dynamics
simulations: Basepair Kinks and Hinges
Jeremy Curuksu
Computational Biology Lab., Martin Zacharias
Jacobs University, Bremen, Germany
Thursday, October 23, 2008
Theoretical Approaches for the Genome
LAPTH-LAMA-LAPP-CNRS-University of Savoie
Annecy-le-Vieux, France
TALK OUTLINES
INTRODUCTION
1. Developpment: An all-atom DNA Bending Coordinate
2. Application: Molecular Dynamics of DNA kink motifs (example of a poly-Purine/Pyrimidine C/G DNA 15 bp sequence)
3. Further insights from enhanced sampling techniques
CONCLUSION
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Molecular Dynamics simulation
A Molecular Dynamics Trajectory
Time
qdtdMqV
amF
q 2
2
.)(
.
=∇−
= )/)(exp()( TkHP BΓ−=Γ
Constant Boltzmann :)()(n Hamiltonia the:),(
)( momenta and )( positions particle ofSet :
BkpKqVpqH
pq+=
Γ
Probability Density at constant N, V and T:
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Quasi-ergodicity of MD samples
Region of high energyOrder Parameter X
Ord
erP
aram
eter
Y
Region of low energy
A schematic representation of phase space
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’
ε: C4’–C3’–O3’–P
DNA conformational flexibility
Backbone dihedral angles Helical internal coordinates
{ } ),,()()()()',','( lkjXYZlkj ×Ω= τρ
SHIFT
SLIDE
RISE
TILT
ROLL
TWIST
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
BE
ND
ING
OF B
AS
EP
AIR
Curuksu J., Zakrzewska K., Zacharias M. (2008) Nucleic Acid Research 36(7): 2268-83.
Harmonic potential U(θ) = k * ( θ - θref ) 2
{ } ),,()',','( lkjAlkj ×=
(j’,k’,l’)
Rotation vector
triad (j, k, l)
DNA bend coordinate
Curuksu J., Zakrzewska K., Zacharias M. (2008) Nucleic Acid Research 36(7): 2268-83.
Adiabatic Mapping on DNA ds 5’(GCAAAAAACG)3’
Amplitude and Direction of bending
EnergyMinimisation
Free Energy (PMF) of DNA bending
Ben
ding
Free
Ene
rgy
(kca
l/mol
)
Bend angle θ (degrees)
d(CGCGCGCGCAAAAAC)d(CGCGCAAAAACGCGC)
d(CGCGCGCGCGCGCGC) d(CATATATATATATATC)
DNA bending energy probed by AtomicForce microscopy (Wiggins et al., 2006)
Umbrella Sampling Molecular Dynamics
parmbsc0 (Perez et al.,2007)
Truncated octahedral box
(~7600 water molecules)
Neutralising K+ counterions
PME electrostatics
2 fs timestep (SHAKE)
NVT (0K→300K)→NPT
Time frame every 2 ps
31*3ns fw trj (0°→150°)
using U(θ) = k * ( θ - θref)2
fw.3 ns fw.2 ns bk.1 ns
Curuksu J., Zacharias M., Lavery R., Zakrzewska K., Manuscript in preparation
Protocol
f
f
Kinking Occurs during Molecular Dynamics Simulations of Small DNA Minicircles (2006)
Lankas F., Lavery R, Maddocks J.H. (2006) Structure 14: 1527-34.
starting structurestarting structure
kink
kink
kink
stable conformations
TALK OUTLINES
INTRODUCTION
1. Developpment: an all-atom DNA Bending Coordinate
2. Application: Molecular Dynamics of DNA kink motifs (example of a poly-Purine/Pyrimidine C/G DNA 15 bp sequence)
3. Further insights from enhanced sampling techniques
CONCLUSION
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
The poly-Purine/Pyrimidine C/G DNA sequence (15 bp)
α = 6.9
Ben
ding
Free
Ene
rgy
(kca
l/mol
)
Bend angle (degrees)f
f
α =6.8 (Linear Sub-Elastic Chain model) from AFM [ Wiggins et al. (2006) ]
E(θ) = 1/2 * kBT * l/ξ * θ2
based on ξ ~ 144 bp
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Amber parm-94 force field Amber parm-bsc0 force field
√ ( roll2 + tilt2 ) in degrees √ ( roll2 + tilt2 ) in degrees
150°
Row 1: C1G2 C3G4 C5G6 C7G8 C9G10 C11G12 C13G14Row 2: G2C3 G4C5 G6C7 G8C9 G10C11 G12C13 G14C15
Probability Distribution of basepair bend angles
f
f15°
f
f15°
f
f150°
f
f
Legend
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
The poly-C/G DNA sequence (15 bp)
√( r
oll2
+ ti
lt2 ) i
n de
gree
s
Junction G6C7
Junction C7G8
Global Bend in degrees
Basepair Kink (type II)Pr
opel
leri
n de
gree
s
base pair at C7
The poly-C/G DNA sequence (15 bp, parmbsc0)
K(k
cal/m
ol/d
egre
e2)
Force Constantes of basepair bend
G6C7C7G8cubic polynomial fit
De Santis,2002, thermal stability data
Olson,1998, Crystallo.
Lankas,2003, MD
Robinson,2002, EPR
Global Bend in degrees
Junction G6C7
Normal Distribution N(0,1)
JunctionC7G8
Nor
mal
ized
Sam
ple
Normal probability plots of basepair bend
Time Average of local bendand propeller with parmbsc0
20° 120° 140° 150°
20° 120° 140° 150°
)tiltroll(
Tk B
222σ +
Curuksu J., Zacharias M., Lavery R., Zakrzewska K., Manuscript in preparation
DNA basepair hinge conformations
Bend angle (degrees)
K(k
cal/m
ol/d
eg2 )
Time Frames / Side View: three DNA kink substates
91.3° 88.6°66.3°
G6C7
C7G8A9A10
A10C11 C7G8
GCG, type II kink AAC, type II kink CG, middle kink
Bend angle (degrees) Bend angle (degrees)
TALK OUTLINES
INTRODUCTION
1. Developpment: an all-atom DNA Bending Coordinate
2. Application: Molecular Dynamics of DNA kink motifs (example of a poly-Purine/Pyrimidine C/G DNA 15 bp sequence)
3. Further insights from enhanced sampling techniques
CONCLUSION
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Molecular Dynamics simulation
A Molecular Dynamics Trajectory
Time
qdtdMqV
amF
q 2
2
.)(
.
=∇−
= )/)(exp()( TkHP BΓ−=Γ
Constant Boltzmann :)()(n Hamiltonia the:),(
)( momenta and )( positions particle ofSet :
BkpKqVpqH
pq+=
Γ
Probability Density at constant N, V and T:
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Replica Exchange simulation
Replica 1 R2 Replica n…
…
Time)'()'(
)'()(
CCCW
CCCW
→
→=ω
ω
R3 R4 R5 R6
? ? ? ?? ? ? ?? ? ?? ? ? ?? ? ?
DetailedBalance )(
)'()'(CWCWCCP =a
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
New: WITH REUS
√ ( roll2 + tilt2 ) in degrees
Pro
babi
lity
Dis
tribu
tion
of b
ase
pair
bend
angl
es
ds DNA 5’(CGCGCGCGCGCGCGC)3’
Global bend angle in degrees
Bending Free Energy in kcal.mol-1, parm94
Original: WITHOUT REUS
Replica Exchange Umbrella Sampling (Amber parm94 force field)
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
f
f
CG junctions
150° f
f
GC junctions
1ns
2ns
2ns
1ns
original
The poly-C/G DNA sequence (15 bp, parm94)
√ ( roll2 + tilt2 ) in degrees
Pro
babi
lity
Dis
tribu
tion
of b
ase
pair
bend
angl
es
ds DNA 5’(CGCGCGCGCGCGCGC)3’
Time (nanoseconds)
√ ( roll2 + tilt2 ) at C7G8 bp junctionPropeller at C7:G24 Watson-Crick bp
(deg
rees
)
150°f
f
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Replica Exchange Umbrella Sampling (Amber parmbsc0 force field)
CG junctions
GC junctions
150° f
f
The poly-C/G DNA sequence (15 bp, parmbsc0)
Conclusion
DNA bending free energy not quadratic on short length scale [ 5 nm ]
• Amber parm-94 force field:
- Type I kink at 5’CG3’ requires longitudinal localization of DNA bending energy. (what could be used to code Breakpoints in the Genome)
• Amber parm-bsc0 force field:
- 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 force constant.
Valid inference of DNA bend conformers from MD ⇒ force-field consensus
Jeremy Curuksu - TAG’08, Annecy-le-Vieux - October 23, 2008
Acknowledgement
Martin Zacharias
Ragav, Sebastian, Shide and Ranjit
Group of Computational Biology
Jacobs University (Bremen, Germany)
Krystyna Zakrzewska and Richard Lavery
Laboratoire de Bioinformatique et RMN structurales
Institut de Biologie et Chimie des Protéines (Lyon, France)
Computational Laboratories for Analysis, Modelling and Visualization (CLAMV), Jacobs University, Germany.
Universite Franco-Allemande (UFA) cotutelle agreement between Universite Paris 7 and Jacobs University.
VolkswagenStiftung PhD grant.
and the Theoretical Approaches for the Genome 2008 organizers.