微米和納米尺度內的複雜物質和流體
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微米和納米尺度內的複雜物質和流體. 陳彥龍 Yeng-Long Chen ( [email protected] ) Institute of Physics and Research Center for Applied Science Academia Sinica. To understand and manipulate the structure and dynamics of biopolymers with statistical physics. Micro- and Nano-scale Building Blocks.

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微米和納米尺度內的複雜物質和流體

陳彥龍Yeng-Long Chen

([email protected])

Institute of Physics and Research Center for Applied Science

Academia Sinica

To understand and manipulate the structure and dynamics of biopolymers with statistical physics


Micro- and Nano-scale Building Blocks

Diameter: 7nm

Persistence length : ~10 mm

Endothelial Cell

F-Actin

DNA

Rg

3.4 nm

Nuclei are stained blue with DAPI

Actin filaments are labeled red with phalloidin Microtubules are marked green by an antibody

xp

Persistence length : ~ 50 nm


Organ Printing

Mironov et al. (2003)

Boland et al. (2003)

Forgacs et al. (2000)

  • Cells deposited into gel matrix fuse when they are in proximity of each other

  • Induce sufficient vascularization

  • Embryonic tissues are viscoelastic

  • Smallest features ~ O(mm)

Organ printing and cell assembly


Confining Macromolecules

Fluid plug reactor from Cheng group, RCAS

Advantages of microfluidic chips

Channel dimension ~ 10nm - 100 mm

  • High throughput

  • Low material cost

  • High degree of parallelization

Efficient device depends on controlled transport

Theory and simulations help us understand dynamics of macromolecules


Multi scale simulations of dna

Atomistic

Coarse graining

Microchannels

1 nm

1 mm

10 mm

C-C bond length

Radius of gyration

l

l

l

l

3.4 nm

F

F

F

F

1

1

1

1

F

F

F

F

2

2

2

2

2 nm

Multi-Scale Simulations of DNA

Multi-component systems : multiple scales for different components

Nanochannels

10 nm

100 nm

Persistence length ≈ 50nm

Essential physics :

DNA flexibility

Solvent-DNA interaction

Entropic confinement


Our Methods

Molecular Dynamics

- Model atoms and molecules using Newton’s law of motion

Monte Carlo

- Statistically samples energy and configuration space of systems

Cellular Automata

- Complex pattern formation from simple computer instructions

Large particle in a granular flow

Polymer configuration sampling

Sierpinksi gasket

  • If alive, dead in next step

  • If only 1 living neighbor, alive


100nm

l

F

1

T

4

F

2

5

m

m

R||

m

2

m

DNA Trapped in Nanoslit

Does the shape of the molecule change as it grows longer ?

R1

R2

Monte Carlo N=256 SAW H=2s slit

Po-keng Lin et al. PRE (2007)


Rg2 ~ Nn

Virtual & Real Experiments

Real Experiments

Rg ~ N0.68

trelax~N2.2

rod

slit(H=5s) 2D Slit(2D proj)

R12 n=1.21 1.51 1.33

R22n=1.20 1.51 1.33

Rg2n=1.19 1.53 1.35

sphere


Coarse grained dna dynamics

Expt

Coarse-grained DNA Dynamics

DNA is a worm-like chain

2a

f ev(t)

l-DNA 48.5 kbps

f W(t)

DNA as Worm-like Chain

L = 22 m

Ns = 10 springs

Nk,s = 19.8 Kuhns/spring

f S(t)

Marko and Siggia (1994)

Model parameters are matched to TOTO-1 stained l-DNA

Parameters matched in bulk are valid in confinement !

Chen et al., Macromolecules (2005)


Brownian dynamics

v1

v2

v3

Brownian Dynamics

How to treat solvent molecules ??

Explicit inclusion of solvent molecules on the micron scale is extremely computational expensive !!

solvent = lattice fluid (LBE)

Brownian motion through fluctuation-dissipation

z: particle friction coef.


The Lattice Boltzmann Method

Replace continuum fluid with discrete fluid positions xiand discrete velocity ci

3D, 19-vector model

Hydrodynamic fields are moments of the velocity distribution function

ni(r,v,t) = fluid velocity distribution function

Ladd, J. Fluid Mech (1994)

Ahlrichs & Dünweg, J. Chem. Phys. (1999)

Boltzmann eqn.

Fluid particle collisions relaxes fluid to equilibrium

Lij = local collision operator

=1/t in the simplest approx.


Hydrodynamic Interactions (HI)

Particle motion perturbs and contributes to the overall velocity field

Free space

Wall correction

Force

Stokes Flow

Solved w/

Finite Element Method

For Different Channels

z


DNA Separation in Microcapillary

T2 DNA after 100 s oscillatory Poiseuille flow

detector

25 mm

l-DNA in microcapillary flow

40mm

Sugarman & Prud’homme (1988)

Chen et al.(2005)

Detection points at 25 cm and 200 cm

Parabolic Flow

Longer DNA  higher velocity


V(y,z)

h

Dilute DNA in Microfluidic Fluid Flow

l-DNA Nc=50, cp/cp*=0.02

We=( trelax)

geff = vmax / (H/2)

Chain migration to increase as We increases


Ld

Non-dilute DNA in Lattice Fluid Flow

Lattice Size = 40 X 20 X 40, corresponding to 20 x 10 x 20 mm3 box

Nc=50, 200, 400

We=100 Re=0.14

As the DNA concentration increases, the chain migration effect decreases

40mm

H = 10 mm


  • Tcold

  • Thot

Thermal-induced DNA Migration

y

Migration of a species due to temperature gradient

Thermal Diffusion

Mass Diffusion

Particle Current

Soret Coefficient

Thermal fractionation has been used to separate molecules


Many factors contribute to thermal diffusivity –

a “clean” measurement difficult

Hydrodynamic interactions

Wiegand, J. Phys. Condens. Matter (2004)


Experimental Observations

Factors that affect DT:

Colloid Particle size

DT ↑ as R ↑ (Braun et al. 2006)

DT↓ as R ↑ (Giddings et al. 2003, Schimpf et al., 1997)

Polymer molecular weight

DT ~ N0(Schimpf & Giddings, 1989, Braun et al. 2005, Köhler et al., 2002, …)

DT ↓ as N ↑ (Braun et al. 2007)

Electrostatics ?

Solvent quality :

DT changes sign with good/poor solvent (Wiegand et al. 2003)

DT changes sign with solvent thermal expansion coef.


Thermally driven migration in lbe

Tcold

Thot

T=10

T=2

T=0

TH

TC

g(y)

0

2

4

6

8

10

y,m

T(y)=temperature at height y

Thermally Driven Migration in LBE

Thermal migration is predicted with a simple model


Thermal diffusion coefficient

Thermal Diffusion Coefficient

Simple model appears to quantitatively predict DT

DT is independent of N – agrees with several expt’s

What’s the origin of this ?


Fluid stress near particles

T=7

T=4

T=2

T=0

Thot

Tcold

Fluid Stress Near Particles

Momentum is exchanged between monomer and fluid through friction

Dissipation of Y-dependent fluctuations leads to a hydrodynamic stress in Y


Particle thermal diffusion coefficient

Particle Thermal Diffusion Coefficient

DT decreases with particle size 1/R

– agrees with thermal fractionation device experiments

DT independent of temperature gradient

(Many) Other factors still to include …


1.6

DT=4

g(y)

1.0

2.0

0.2

0

0.4

0.8

y/H

1.0

0

0.2

0.4

0.6

0.8

1.0

y/H

Thermal and Shear-induced DNA Migration

Thermal gradient can modify the shear-induced migration profile

Thermal diffusion occurs independent of shear-induced migration

TH

TC

DT=4

As N ↑, D ↓, ST↑

stronger shift in g(y) for larger polymers

40mm


σm

f r(t)

f bend(t)

~2nm

f ev(t)

f vib(t)

Summary and Future Directions

  • Shear and thermal gradient can be used to control the position of DNA in the microchannel and their average velocity

  • Shear and thermal driving forces for manipulating DNA appear to have weak or no coupling => two independent control methods.

  • Inclusion of counterions and electrostatics will make things more complicated and interesting.

  • How “solid” should the polymer be when it starts acting as a particle ?

  • As we move to nano-scale channels, what is the valid model?

    --can we choose the coarse-graining dynamically ?


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