Coarse-graining for self-assembly: - PowerPoint Presentation

Slide1

Coarse-graining for self-assembly:with applications to DNA

Ard Louis & Jonathan Doye

Alex Wilber, Iain Johnston

,

Tom

Ouldridge

,

Anna Lewis, Alex Williamson, Gabriel

Villar

,

Pavinder

Thiara

, Adam Levy

, Sebastian

Ahnert

, Emmanuel Levy, Mark Miller, Eva

Noya

, Pauline Wong, Rollo Hoare, Christian

Matek

,

Petr

Sulc

,

Flavio

Romano, Anton

Kan

, Tom Wyatt,

Debayan

Chakraborty

,Slide2

Outline

Transferability and RepresentabilityModelling DNA self-assemblySlide3

Coarse-graining is central to physics and chemistryIntuition: coarse-graining throws away information

representability problems:You can’t simultaneously represent all the properties of the underlying system with a coarse-grained potential. Slide4

(low

density

weak

w

(3)

limit)

O

riginal

system

C

oarse-grained

system

Representability

problems

:

one

potential

can’t simultaneously represent multiple properties of the system AAL, J. Phys.: Condens. Matter 14, 9187 (2002); Faraday Discuss. 144, 323 (2010)

veff(r) = w(2)(r) +δv(r)

Energy route:

Structure route:

g(r)

 veff(r)

Comparison

g(r) from full Hamiltonian

Same g(r)

– (use inversion method)

veff(r)=w(2)(r) +δvg(r)

pair potential only

2 and 3 body potentialsSlide5

g

OO

(r)





v

g

(r)

R.L. Henderson

Phys

.

Lett

.

49A

, 197 (1974)

J.T.

Chayes

and L. Chayes, J. Stat. Phys. 36, 471 (1984)

No free lunch for water pair potentials?Thermodynamics through compressibility route

Transferability problems alsoSlide6

virial

pressure

i

nternal

energy

Representability

problems

for

water

potentials

Representability

problems

can be surprisingly severe

Sophisticated coarse-graining methodologies do not substitute for physical insight.

It is better to fit to multiple properties

v

U

(r) to get g(r)? Slide7

virial

pressure

i

nternal

energy

Compromise

by

fitting

to

multiple

properties

?

CompromisesSlide8

Corrections to virial

equation from density dependence?

Wrong – only the veneer of stat

mech

!!!

HINT:

Coarse-grained potential does not generate a Hamiltonian systemSlide9

No free lunch but not all doom and

gloom either Representability problems mean that all potentials are at best compromisesTransferability is a different problem, but can be relatedState dependence in potentials is a signal of representability problemsThere is no substitute for physical insight & experience

E.g. hard-core

potentials and

crystallization

of

simple

particles

S

imple

geometric

rules

explain surfactant phases etc...SAW reproduces polymer scaling behaviour etc….Symmetriesproximity to phase lines

AAL, J. Phys.:

Condens. Matter 14, 9187 (2002); http://arxiv.org/abs/1001.1166 M. Johnson, T. Head-Gordon, AAL, J. Chem. Phys. 126, 144509 (2007)DYNAMICS? http://arxiv.org/abs/1001.1166 Slide10

Outline

Transferability and RepresentabilityModelling DNA self-assemblySlide11

R. Goodman et al (

Turberfield group)., Science 310, 1661 (Dec 2005)Self-assembly of DNA tetrahedraSlide12

Dynamic control of tetrahedraR.l

P. Goodman, et al., Nanotechnology 3, 93 (2008)Slide13

DNA origami

DNA OrigamiP.K.W. Rothebund, Nature 440, 297-302 (2006)Slide14

DNA origami in 3D

E.S. Andersen et al., Nature 459, 73 (2009)S.M. Douglas, et al., Nature 459, 414 (2009)Slide15

DNA origami in 3DC. Castro, et al, Nature Methods

, vol 8, p221 (2011) Slide16

How to model DNA self-assembly?Atomistic models orders of magnitude too

slowBottom-up coarse-grainingRepresentability problemsWe use top-down coarse-graining insteadSelf-assembly primarily determined by: chain-like molecule with specific bindingSlide17
Slide18
Slide19
Slide20

In DNA competition of 2 length-scales leads to double helix

0.34 nm

Two length-scales

T.

Ouldridge

, A.A. Louis and J.P.K.

Doye

,

Phys

.

Rev

.

Lett

.

104

178101 (2010

);

J.

Chem

Phys. 134, 085101 (2011) Slide21

In DNA single strands are flexible and can stack

disordered single strand

stacked single strand

Hybridized double strand

T.

Ouldridge

, A.A. Louis and J.P.K.

Doye

,

Phys

.

Rev

.

Lett

.

104

178101 (2010); J. Chem Phys. 134, 085101 (2011)

Two length-scalesSlide22

2nd

generation unified base DNA model InteractionsH-bond between complementary basesStacking between basesBackbone: FENE springHelicity emerges naturallyPropellor twist emerges naturallyBut no minor/major groove

disordered single strand

stacked single strand

Hybridized double strand

Base

Repulsion site

Base

normal

Base stacking

site

Hydrogen-bonding / cross-stacking siteSlide23

Single stranded stacking

Simulations of a 15mer at 300 KAgree well with aResults

from a Poland-Scheraga

type model with

weak

cooperativity

with ΔH = -5.6 kcal and ΔS= -16.4 kcal K

-1

per mole of stack

(

good

agreement

with

Holbrook et al., Biochemistry, 38, 8409 (1999)Slide24

Duplex formation & length dependence

Good agreement of Tm with L is a measure of the cooperativity of the transition – influenced by the single strand cooperativitySlide25

Duplex formation & transition widths

The width of the transition is related to how well you can predict the concentration dependence of the melting temperaturesSlide26

Free-energy profile for duplex formation

frayingformation of a 15mer duplexSlide27

mismatches

(left) Tm of 15 bp helix with 1 mismatch against position(right) Free energy at 339 K

for 15 bp with

one mismatch place 2 (red) and 6 (blue) positions

from

end.Slide28

Hairpins – varying stem lengthSlide29

Hairpins: varying loop length

18 bp loop6 bp loopSlide30

Mechanical properties

Duplex ~ 125 bpUnstacked single strand ~ 2-4 basesFully stacked single strand ~ 64 basesTwist persistence length of duplex ~ 3.74°/bpSlide31

Mechanical properties – many subtleties we can’t get

dsDNA undertwists upon initial stretchingSequence dependent elastic properties are very very subtle – need a much better representation of excluded volume etc…..Slide32

Model is good for DNA processes with hybridization

Model does well for single strands, double strands, duplex formation, hairpin formation, peristence lengths ….. Should be suitable for studying generic behaviour of DNA nanostructures ?Slide33

DNA Tweezers

Yurke, B.,et al., A DNA-fuelled molecular machine made of DNA. Nature 406, 605 (2000)Slide34

DNA tweezers and displacementSlide35
Slide36
Slide37
Slide38
Slide39
Slide40
Slide41
Slide42
Slide43

Initial displacement of fuel arm:Free energy rises even though the number of base pairs is constant.

Causes: entropy metastable hairpin formation.Slide44

Initial displacement of fuel arm:

Free energy rises even though the number of base pairs is constant. Causes: entropy metastable hairpin formation.Slide45

Coarse-grained DNA : Cruciform

Cruciform arises from a combination of supercoiling and palindromesSlide46

Coarse grained DNA: tetrahedron

Preliminary results …Slide47

ConclusionsSelf-assembly of patchy particles and crystallization?:Positive

, negative, and evolutionary designDynamics can be complexA new coarse-grained model for DNA self-assemblyRefinement of model:sequence dependence minor/major grooving

T. Ouldridge, A.A. Louis and J.P.K. Doye

, Phys. Rev

.

Lett

.

104

178101 (2010) Slide48

Biological self-assemblyBiology is soft-matter come aliveSelf-assembly of multi-component structures

can we understand?can we emulate? What hope for the modeller?http://www.npn.jst.go.jp/ Keiichi Namba, Osaka ERATO project

assembly is regulated by a gene network which sets FIFO timing... see

Kalir et al, (Alon

group) Science (2001)Slide49

Coarse-grained DNA : Cruciform

Cruciform arises from a combination of supercoiling and palindromesSlide50

Coarse-grained DNA : Cruciform

Cruciform arises from a combination of supercoiling and palindromesSlide51

Coarse-grained DNA : Cruciform

Cruciform arises from a combination of supercoiling and palindromesSlide52

326 KSlide53

326 KSlide54

302 KSlide55

302 KSlide56

302 KSlide57
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