Download - APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,

APS March Meeting Dallas, March 22, 2011

FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS

Rastko Sknepnek, Cheuk-Yui Leung, Liam C. PalmerGraziano Vernizzi, Samuel I. Stupp, Michael J. Bedzyk, Monica Olvera de la Cruz


Motivation

Can electrostatic interactions lead to faceting?

100 nm

Greenfield, M., et al., JACS (2009)

Vernizzi & Olvera de la Cruz, PNAS (2007)

PCDA-OH

PCDA-KKK

-1

+3

Experiments find faceted structures in the 100nm size range.

Minimization of electrostatic energy on fixed geometry reveals that in certain cases faceted structures are energetically favorable.


Coarse-graining

Cooke, et al., PRE, 2005tail-tail interaction potential

wc

Cooke, et al., PRE, 2005

+1,+2,+3

-1

gel

liquid

unstable

e

exp

0

ij

i j DH c cDH ij ij

c

rq q V r for r r

V r r

for r r

Electrostatic effects treated within linearized Debye-Hueckel theory:


Molecular dynamics of a bilayer patch with 4000 lipids.

T=0.6

Focus on a small region of phase diagram T=0.6, 0.7wc=1.15

1:1 (liquid) 1:2 (ordered) 1:3 (ordered)T=0.7

1:1 (liquid) 1:2 (liquid) 1:3 (“almost” ordered)


224 2B

q

k TL h

q q

Use results of linearized Helfrich theory:

,,

, x y

x yx y

i q x q y

q qq qh x y h e

h(x,y) vertical position at (x,y)

s – lateral tension

T=0.7, wc=1.15

Electrostatic interactions significantly increase k.

Estimate of the bending rigidity k


Estimate of the Young’s modulus Y

Regular two-dimensional ionic crystals:

square triangular triangular triangular

1:1 1:2 1:3

12 6

'

,

14

2i j

cell celli j ij ij ij

q qE N E

r r r

Total energy:

(0) 31( )

2cell ijkl ij kl ijE c c u u O u extract Y

Estimate: Y3:1/Y2:1»1.8


In addition, different valence charges are expected to segregate.

MD simulation of a three component system (1:2 and 1:3) in liquid phase (T=0.9)

+3

+2

-1

Segregation leads to an onset of effective line tension between differently charged regions.

In continuum representation:

t CF dl


We find shaped using a discretized version of the continuum theory of elasticity.

Regions with different charge ratios have different elastic properties.

(Seung and Nelson, PRA 1988)

, , 1,

1 .discreteb i i t i t

i t

E n n

bending energy:

All effects of charge are encoded in the elastic properties.

stretching energy:

20,

1

2discretes ij

i j

E k l l

line tension: ,,

1 .2 i j

discretet t t

i j

F We used simulated annealing

Metropolis Monte Carlo simulations to find optimal shapes.


Optimal faceted structures khard/ksoft=10 Yhard/Ysoft=5

g=0.1

g=0.3

g=0.6

linetension

hard component

fraction 20% 40% 60% 80%


Optimal faceted structures khard/ksoft=30 Yhard/Ysoft=10

g=0.1

g=0.3

g=0.6

linetension

hard component

fraction 20% 40% 60% 80%

100 nm


Summary

Funding provided bythe U.S. Department of Energy

Experimental collaborators:

Dr. Megan GreenfieldCheuk LeungProf. Michael BedzykProf. Samuel Stupp

Northwestern High PerformanceComputing System - Quest

• We show that electrostatic interaction can lead to lipid crystallization• Charge significantly renormalizes elastic properties• Different regions segregate – effective line tension• Resulting shapes are faceted