Exploring the Sequence
Dependent Structure and
Dynamics of DNA with
Molecular Dynamics Simulation
Sarah Harris
School of Physics and Astronomy
University of Leeds
Introduction
Calculations of the charge transport properties of complex
biomolecules such as DNA are extremely difficult in general due to
both the size and flexibility of these systems.
Describe some relevant results from classical MD simulations:
i) Insight into sequence and environment dependent DNA
structure
ii) A description of the dynamic properties of DNA and the
methods developed to quantify them.
iii) A preliminary series of MD simulations to show the effect of
charged bases on DNA dynamics.
The Structure of Duplex DNA
CH3
HN H O
N
N
N H N
N
N
O
2 H-bonds
Adenine
Thymine
O H NH
N
N
N H N
N
N
HN H O
3 H-bonds
Guanine
Cytosine
Higher Order DNA Structures
i ) A triplex DNA structure
iii ) Certain quadruplexes
are associated with a
continuous channel of
counterions
ii ) Guanine-rich DNA
can form folded
quadruplex structures
The Flow of Genetic Information
Promoter of
Transcription Start Codon
Coding Region
Stop Codon
Terminator of
Transcription
DNA
Transcription
RNA Polymerase
Nascent mRNA
Splicing
Intron
Exon
(non-coding)
(coding)
Nucleus
Mature mRNA
tRNA
Translation
Ribosome
Protein
Importance of Charge Transport in DNA
Damage
The genome is under continuous chemical attack (generally oxidative)
which can result in dangerous mutations.
GG and GGG sequences are preferentially oxidised, despite the event
occuring remotely in the sequence. Such damage propagation has
been observed in intact cell nuclei1.
GGG rich motifs occur disproportionately at the termini of intron
regions, ideally positioned to sacrificially protect the coding regions
of genes2.
1. Nunez M. E., Holmquist G. P & Barton J. K. (2001) Biochemistry, 40, 12465-12471.
2. Friedman K. A. & Heller A. (2001) J. Phys. Chem. B, 105, 11859-11865.
Charge Transport in Solution
Excite tethered photoxidant
Rh(phi)2bpy3+
Vary DNA sequence, add
binding proteins etc
GGG
motif
Photoxidant
A hole is injected into the
DNA, which oxidises a
distant GG or GGG
Oxidative damage can occur up to
200Å (~60 base pairs) from the
site of hole injection
The relative charge transport efficiency can be measured by
detecting the amount of damage using biochemical methods
Williams T. T., Odom D. T & Barton J. K. (2000) J. Am Chem. Soc. 122, 9048-9049
DNA Dynamics and Charge Transport
The sequence dependence of charge transport efficiency remains
poorly understood.
Suggested mechanisms for electron/hole transport include:
i) Superexchange (~ 3-4 base pairs)
ii) Thermally activated hopping
iii) Polaron hopping
iv) Conformationally gated hopping through “charge
transport active domains1,2”
What role is played by the thermal fluctuations of the DNA, and
which dynamic timescales are associated with the most important
motions?
1.
2.
O’ Neill M. & Barton J. K. (2004) J. Am Chem. Soc. 126, 11471-11483
Shao F., O’ Neil M. & Barton J. K. (2004) Proc. Natl. Acad. Sci. USA 101, 17914-17919
The Importance of Sequence Dependent
Structure and Dynamics
The structure and flexibility of DNA must be highly sequence
dependent since DNA binding proteins must recognise specific
binding sites to exert cellular control.
Although much work has been done on quantifying sequence
dependent structure by X-ray and NMR the sequence dependent
dynamics of DNA remains poorly understood.
Much of the dynamic behaviour is not accessible theoretically,
therefore computer simulation is required.
Sequence Specific Recognition by Proteins
The TATA box protein-DNA
complex
Repair of a G-U mismatch
Barratt T. E. et al (1999) EMBO 18, 6599
Sequence Dependant Structure
Different DNA sequences have subtly
different structures.
For example ~ a run of AT bases will
give the DNA a particularly narrow
minor groove ~ this is responsible for
the “Spine of Hydration”
The precise position of chemical
groups (ie H-bonds) also depends on
the DNA sequence.
The spine of hydration in A-tract DNA
Changes in Structure Due to DNA
Environment
Canonical B-form
DNA
A-form DNA,
present in water/
methanol mixtures
Left-handed Z-form
DNA, present at
very high salt
The Hierarchy of Dynamic Timescales
Timescale
Picosecond
Nanosecond
Microsecond
Type of
internal
motion.
Local oscillations
of groups of
atoms with
amplitudes 0.1 A.
Bending and twisting
motions of the double
chain with amplitudes
A=5-7 A.
Bending, winding and
unwinding of the double
helix; opening of base
pairs of the DNA.
Energy of
activation.
E=0.6 Kcal/Mol; E=2-5Kcal/Mol:
Source: External Source: Collisions
thermal reservoir. with hot solvent
molecules.
Experimental NMR, Raman
spectroscopy,
methods.
X-ray.
Theoretical
Methods.
NMR, Raman
spectroscopy
fluorescence.
Molecular
Molecular dynamics;
dynamics;
harmonic analysis.
harmonic analysis. rod-like model.
E=5-20Kcal/Mol
Source: Changing of pH;
increasing temperature;
action of denaturation
agents.
NMR, hydrogen
exchange.
Theory of helix-coil
transition; non-linear
mechanics.
The AMBER Forcefield
The molecule is considered as a collection of atoms interacting through
simple, classical potential energy functions.
Electrostatic
Repulsion
-
-
Van Der
Waals
forces
-
Covalent
Bonds
-
The simple potential energy function is
fitted empirically for each specific
interaction through as series of constants
~ the AMBER force field parameters.
Bonds
∑ Kθ (θ − θ eq ) +
Angles
2
Bonds
+
H-Bonds
∑ K r (r − req )
U Total =
2
Angles
V
[1 + cos(ηφ − γ ] + Dihedrals
∑
Dihedrals 2
⎡⎛ R
ij
⎜
⎢
ε
∑
ij ⎜
⎢⎝ rij
Atoms
⎣
∑
12
6
⎛ Rij ⎞ ⎤ Van der
⎞
⎟ −⎜ ⎟ ⎥ +
⎜r ⎟ ⎥
⎟
Waals
⎝ ij ⎠ ⎦
⎠
qi q j
Partial
Charges
εrij
Electrostatics
Contents of the Simulation Cell
The simulation cell
contains:
i) The DNA.
ii) Sufficient Na+
counterions to
neutralise the system.
iii) Enough water
molecules to surround
the DNA.
A Molecular Dynamics Simulation of DNA
Obtain the positions of all
atoms in the system over
timescales ~2fs to 50ns
The most accurate
simulations include water
and counterions explicitly
(~700 solute and ~3000
solvent atoms) and use
PME to calculate long
range electrostatics
The Structure of DNA in a Vacuum
MD simulations of DNA in the gas phase based on electrospray data
show that the DNA does not remain in its B-form configuration.
In vacuo DNA structures after
100ns of MD
Rueda M. et al (2003) J. Am Chem. Soc. 125,
8007-8014
Principal Component Analysis (PCA)
Calculate the ‘3Nš3N’ covariance matrix from the trajectory. Indicates
how individual atomic motions were correlated during the simulation.
C p ,q
1
=
M
∑ (X
M
m =1
m, p
− Xp
)(X
m ,q
− Xq
)
Diagonalise the covariance matrix to find the set of ‘3N’ eigenvectors
and their corresponding eigenvalues. Find the types of overall structural
deformation that were independent during the trajectory - called components
or modes.
C = u −1λ u
Order the components in terms of their eigenvalues. The component
with the highest eigenvalue has contributed the most to the system’s
dynamics.
Principal Component 1
The components with
large eigenvalues are
large, scale, quasiharmonic oscillations of
the entire helix
Tyically, the 1st,2nd
and 3rd components
contribution ~ 60% of
the dynamics of the
system
The Dynamics of d(GGTAATTACC)2
The DNA helix has very simple mechanical properties which are
sequence dependant.
Bend at TA step 1
Bend at TA Step 2
Helix Twisting
However, it can be difficult to obtain a quantitative comparison of
flexibility between simulations using PCA due to anharmonic
effects.
MD Simulations of Charged Bases
Caution: Preliminary Results!!
Perform 5ns classical MD on d(GAAAAAAAAC) including i) neutral,
ii) positive and iii) negatively charged thymine base.
(placed at position 15 based, partial charges calculated using HF and RESP fitting).
Neutral thymine nucleotide
Positive thymine nucleotide Negative thymine nucleotide
Does the presence of a charged base affect the dynamics of the DNA
relative to the neutral system?
The Configurational Entropy
The entropy of a classical harmonic oscillator:
1 3 N −6
2
S = k ∑ ln xi
2 i =1
A formula is required which gives identical results for large
eigenvalues, but which also gives:
S → 0 as x i
2
→0
This is true for a function of the form:
1 3 N −6 ⎡ ⎛ kTe 2 ⎞
2 ⎤
S = k ∑ ln ⎢1 + ⎜⎜ 2 ⎟⎟ mxi ⎥
2 i =1 ⎣ ⎝ = ⎠
⎦
The Schlitter Formula.
Schlitter J. (1993) Chem. Phys. Lett. 217, No. 6, 617.
Entropy Convergence
An quantitative comparison of the flexibility of each sequence
can be obtained by calculating the entropy from MD/PCA.
TšS (kcal/Mol)
The entropy contains a hidden dependence on time due to the
finite length of the trajectory.
The presence of a singly
650
charged base slightly increases
the overall flexibility of the
600
Neutral
helix
550
Positive
Negative
500
450
0
1000
2000
3000
Length of Sampling Window (ps)
4000
No simple dependence on key
structural parameters (such as
H-bond distances) has yet been
detected
Future Work
Use these simple MD simulations to investigate whether the
local or global dynamic modes are influenced by the presence
of the charged base.
Correctly optimise the geometry of these charged bases using
DFT and perform equivalent simulations for comparison1.
Construct semi-empirical QM/MM models of DNA including
a charged base using results from these classical calculations
to optimise the system.
1. Smith D. M. A. & Adamowicz L. (2001) J. Phys. Chem. 105, 9345-9354
Concluding Remarks
DNA structure and dynamics is exquisitely dependent on both
the sequence and the environment.
DNA dynamics consists of high frequency, low amplitude
local modes over ps timescales combined with global quasiharmonic oscillations over ns timescales.
The flexibility of DNA is slightly increased in the presence of
a charged base, which may be important in constructing
models of transport processes.
Other Useful References
A general discussion of nucleic acid structure:
Nucleic Acid Structure and Recogition, Steve Neidle, OUP.
www.oup.co.uk/molbiol2/na-structure/
References which discuss the counterion distribution
around DNA:
Exploring the Counterion Atmosphere around DNA: What can be
learned from Molecular Dynamics simulations? Rueda et al
(2004) Biophys. J. 87, 800-811.
DNA and its Counterions: A Molecular Dynamics Study. Varnai
P. & Zakrzewska K. (2004) Nucl. Acid Res. 32 4269-4280