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Computer Simulationsof DNA Topology at the
atomic level
Sarah HarrisPolymer IRC
School of Physics and AstronomyLeeds University
Introduction
1) An introduction to biological thermodynamics
2) A description of Molecular Dynamics using DNAas a working example
3) DNA supercoiling
4) Peptide aggregation into amyloid-like fibrils
The Structure of Duplex DNA
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Guanine Cytosine
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Adenine Thymine
CH3
2 H-bonds
3 H-bonds
Majorgroove
Minorgroove
Helix diameter 20Å
Hel
ical
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10 b
ase
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s / 3
4Å
Classical (MD) with AMBER
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H-Bonds
CovalentBonds
ElectrostaticRepulsion
Van DerWaalsforces
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Bonds
Angles
Dihedrals
Van derWaals
Electrostatics
MD represents all of the atoms as classical “balls” possessing atomtypes which mimic the chemistry of the biomolecule.
Contents of the Simulation Cell
iii) Enough water molecules tosurround the macromolecule.
The simulation cell contains:
Implicit solvent models cannot reproduce structural waterand also neglect friction and solvent damping
i) The DNA
ii) Sufficient counterions(Na+/K+) to neutralise the
system.
The Spine of Hydration
Different DNA sequences have subtlydifferent structures.
For example ~ a run of AT bases willgive the DNA a particularly narrowminor groove ~ this is responsible forthe “Spine of Hydration”
The precise position of chemicalgroups (ie H-bonds) also depends onthe DNA sequence.
The spine of hydration in A-tract DNA
DNA Dynamics
Global, large amplitude quasi-harmonicoscillations over ns timescales.
High frequency, low amplitude localmodes over ps timescales
DNA is a highly flexible molecule with hybrid solid/liquid likecharacteristics
Topoisomerase
DNA gyrase
Supercoiled DNA
RelaxedDNA
DNA Supercoiling and Packing
In chromosomes, 1-20cm of DNA is densely packaged into only~1-10μm
Bacterial DNA is compacted by supercoiling the circular plasmidsinto higher order helical structures.
Cellular DNA is generally under-wound ~ only thermophiles containenzymes which can over-wind DNA
Topoisomerases
Topoisomerases controlsupercoiling by changingthe number of times thetwo strands wrap around
each other
Energy (ATP) isrequired to increase
levels of torsional stressand induce supercoiling
Topoisomerase I (single strand breaks)
Looped and Circular DNA Structures
The ability of DNA to form eitherlooped or circular DNA structuresdepends on the bending rigidity of
the duplex.
DNA circles as small as 89base pairs have been reported
experimentally.
The CAP/DNA complex1. Cloutier T. E. & Widom J. (2005)
PNAS 102, 3645-3650.2. Du at al (2005) PNAS 102, 5397-
5402.
Simulations of 90bp DNA Circles
8 helical turnsAlternating AT
A circle containing ~ 90bp + solvent consists of ~150,000 atoms1ns takes ~ 48hrs on 32 processors of the Oxford NGS node.
90bp of DNA possesses 8.5 helical turns when torsionally relaxed
~ 100Å
Undertwisted DNA Circles
When the DNA is under-wound by 2.5 turns the DNA locallymelts to relieve torsional stress
6 helical turns: Alternating AT
Overtwisted DNA Circles
DNA overtwisted by 1.5 turns undergoes a buckle instability toform a supercoiled structure which relaxes when one strand is
nicked.
10 helical turns: Alternating GC
Supercoiling occurs spontaneously as it is thermodynamically favourable
Twisting, Supercoiling and Transcription
Under-winding is thought topromote cellular processes which
require strand separation (egtranscription, translation,
replication) by destablising theduplex.
Bacteria placed under environmental stress respond using dramaticchanges in the levels of supercoiling to alter gene expression.
Melting
Untwisting
Untwisting critically weakensthe van der Waals interactionsbetween stacked bases and lead
to strand separation
Destabilisation and the Helical Repeat
Under-wound DNA structures denaturewhenever the minor groove is on theinside of the circle.
Overwound circles preferentiallydenature at the apices of the supercoil
Bending the DNA into a circular or supercoiled structure breaks thehelical symmetry of the linear molecule.
90 base pairs-1.5 helical
turns
+1.5 turnsCould this be used to in vivo tofine tune genetic control?
The Importance of the Environment 1
Under-winding lead to negative supercoiling only for larger circles(>118 base pairs) in high salt conditions (1M)
Reducing the salt to0.01M leads to
rapid unwindingdue to electrostaticrepulsion between
crossed DNAstrands
178 base pairs at -2 turns in 1M salt
Simulations use an implicit solvent model
~170Å
The Importance of the Environment 2
The 178 base paircircles at 1M saltforms a supercoilwith two crossing
points.
When the salt isreduced to 0.01M
the circle refolds toform a structure
containing only onecrossing point.
178 base pairs over-wound by 2 helical
turns in 1M salt
“Frustrated” DNA Circles
Supercoiling relievestorsional stress but
requires sharp bendsat the apices
This bending stressis larger for smaller
circles
118 base pairs at -2 helical turns in
1M salt
These terms almostbalance for circles of
118 base pairs.
This system undergoes large thermal fluctuations between circular andsupercoiled structures
~ 130Å
A Phase Diagram for Nanocircle Topology 1
C
S+D
C
D
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0.0
0.1
0.2
0.3
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-0.2
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SuperhelicalDensity
Circle Size (bp)
C/D
Low Salt
A Phase Diagram for Nanocircle Topology 2
S+S++
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0.1
0.2
0.3
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-0.2
-0.3
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SuperhelicalDensity
Circle Size(bp)
C S-
DNot investigated
C/D
C
DNot investigated
C
High Salt
Thermodynamics and Supercoiling
Supercoiling is easier when:
i) The circles are larger ~ bending energy at theapices is reduced (end loops can be larger)
ii) The salt concentration is high ~ better electrostaticscreening
iii) Circles are over-wound rather than under-wound
Can we use our theoretical methods to quantify thechanges in enthalpy and entropy when supercoils form?
Harris, Laughton, Liverpool Nucleic Acids Res. 36, 21-29, 2008
Liverpool, Harris, Laughton Phys. Rev. Lett. 100, 238103, 2008
Thermodynamics from Experiment
Experimental measurements show that 178 base pairsnegatively supercoils in high salt, but that topoisomerase can
only supercoil sequences larger than 148 base pairs1
Larger DNA sequences supercoil more easily experimentally2,as we also observe in the simulations
Future calculations aim to make a quantitative comparison
1. Bates, A.D. and Maxwell, A. (1989) DNA Gyrase Can Supercoil DNA Circles as Small as 174Base-Pairs. EMBO, 8, 1861-1866.
2. Fogg, J.M., Kolmakova, N., Rees, I., Magonov, S., Hansma, H., Perona, J.J. and Zechiedrich, E.L.(2006) Exploring writhe in supercoiled minicircle DNA. J. Phys. Cond. Mat., 18, S145-S159
Calculating the Enthaply Change
The enthalpy change should be straightforward toestimate from the molecular dynamics forcefield.
Can we estimate the relative contributions frombending/crossing electrostatics?
Usually, we use GB/SA – but may have to use moreexpensive PB methods due to the high salt
concentration.
But ~ what happens when there is ordered water?
Quasiharmonic analysis calculates a covariance matrix of atomicpositions and then diagonalises it to find the eigenvectors andeigenvalues.
The entropy is given by:
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Can these methods be extended to systems as large asnanocircles?
The Entropy from Quasiharmonic Analysis
Current Work ~ “Programmable” Sequences
GCGC…
GGGG…
As might be expected, the alternating GCGC…sequences (which are less rigid than GGGG…)
lie at the apices of the writhed circle
Current Work ~ Mixed Sequences
AT rich regions have atendency to denature
during writhing ~ is thecorrect for these
superhelical densities ~or an artefact of our
equilibration protocols?
Trial run in explicit solvent ~ 1million atoms ~128 processors
on Hector supercomputer
Some Concluding remarks…
Entropy/dynamics/physics is important in determining thethermodynamic and biomechanical properties of
biomolecules as well as internal energy/structure/chemistry
Thermal fluctuations can produce interesting effects (egentropic allostery, frustration) at the nanoscale that have no
macroscopic analogue.
The lowest free energy state is often determined by a delicatebalance of large but compensating terms.
This enables biomolecules to be highly responsive to changesin the environment ~ as is necessary for living systems
Acknowledgements
DNA StretchingZara Sands (AstraZenica)Pavel Hobza (Chemistry, Prague)Jan Rezac (Chemistry, Prague)BBSRC
DNA CirclesJon MitchellTannie Liverpool (Maths, Bristol)Ramin Golestanian (Physics, Sheffield)Agnes Noy (Scientific Park, Barcelona)Tony Maxwell (Biological Chemistry, Norwich)Andy Bates (Biological Sciences, Liverpool)EPSRC
GeneralAlan Real
(Supercomputing,Leeds)
The National GridService
Entropic AllosteryCharlie Laughton (Pharmacy, Nottingham)Mark Searle (Chemistry, Nottingham)Modesto Orozco (Scientific Park, Barcelona)Tom McLeish (Physics, Leeds)Hedvika Toncrova (Physics, Leeds)BBSRC
Computational BiophysicsCurrent Projects
i) MD Simulations of Amyloid-like aggregates Josh Berryman Sheena Radford
Binbin Liu Amalia Aggeli/Tom McLeish
ii) DNA mechanics, topology and packagingJon Mitchell Charlie Laughton/Tannie Liverpool
iii) Multi-scale models of charge transfer through DNADavid Reha William Barford
iv) Melting kinetics of RNA aptamers Jonathan Westwood Peter Stockley
v) Calculation of protein dielectric constantsGeorge Patargias John Harding
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