dna bending induced during molecular dynamics simulations

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:



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


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



CONCLUSION


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


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


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



CONCLUSION


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:


Replica Exchange simulation

Replica 1 R2 Replica n…

…

Time)'()'(

)'()(

CCCW

CCCW

→

→=ω

ω

R3 R4 R5 R6

? ? ? ?? ? ? ?? ? ?? ? ? ?? ? ?

DetailedBalance )(

)'()'(CWCWCCP =a


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)


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


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


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.

dna bending induced during molecular dynamics simulations

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