dynamics of confined polymer in flow 陳彥龍 yeng-long chen...
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Dynamics of Confined Polymer in Flow
陳彥龍 Yeng-Long Chen
(yenglong@phys.sinica.edu.tw)
Institute of Physics and Research Center for Applied Science
Academia Sinica
To understand and manipulate the structure and
dynamics of biopolymers with statistical physics
Fish schooling Blood flow
Micro- and Nano-scale Building Blocks
Nuclei are stained blue with DAPIActin filaments are labeled red with phalloidin Microtubules are marked green by an antibody
Endothelial Cell
F-Actin
DNA
Diameter: 7nm Persistence length : ~10 m
3.4 nm
Persistence length : ~ 50 nm
Rg
p
Organ Printing
Mironov et al. (2003)
Boland et al. (2003)
Forgacs et al. (2000)
Organ printing and cell assembly
• 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)
From Pancake to Tiramisu
Edible Paper
Moto restaurant
Chicago
Inkjet printer used as food processor
Food emulsions printed onto edible paper
Edible Menus
Not too far into the future :
“We had to go out for dinner because the printer ran out of ink!”
• High throughput
• Low material cost
• High degree of parallelization
Advantages of microfluidic chips
Efficient device depends on controlled transport
Channel dimension ~ 10nm - 100 m
Fluid plug reactor from Cheng group, RCAS
Confining Macromolecules
Theory and simulations help us understand dynamics of macromolecules
Multi-Scale Simulations of DNA
10 nm
2 nm
3.4 nm
1 nm
Atomistic
C-C bond length
100 nm
Persistence length ≈ 50nm
Nanochannels
Essential physics :
DNA flexibility
Solvent-DNA interaction
Entropic confinement
1F
2F
1F
2F
1F
2F
1F
2F
1 m 10 m
Radius of gyration
Coarse grainingMicrochannels
Multi-component systems : multiple scales for different components
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
Our Methods
Coarse-grained DNA Dynamics
DNA as Worm-like ChainL = 22 m
Ns = 10 springsNk,s = 19.8 Kuhns/spring
Marko and Siggia (1994)
2a
f S(t)
f ev(t) f W(t) -DNA 48.5 kbps
DNA is a worm-like chain
Model parameters are matched to TOTO-1 stained -DNA
Parameters matched in bulk are valid in confinement !
Expt
Chen et al., Macromolecules (2005)
Brownian Dynamics
))(( xUUf fpf
dtm
tUdttRd
)()(
Explicit inclusion of solvent molecules on the micron scale is extremely computational expensive !!
solvent = lattice fluid (LBE)
How to treat solvent molecules ??
dtm
dttfdttUd
)()(
: particle friction coef.
v1
v2
v3
Brownian motion through fluctuation-dissipation
flucfricwallWLCev ffffff
)'()'(2)','(),( rrttTktrftrf Bflucfluc
Ladd, J. Fluid Mech (1994)
Ahlrichs & Dünweg, J. Chem. Phys. (1999)
Hydrodynamic Interactions (HI)
Free space Wall correction
Particle motion perturbs and contributes to the overall velocity field
Stokes Flow
000W0s00 ),(),(v)(v),,(v frrrrrrfrr Ω
W
W2
v0
v0
ηp
Solved w/
Finite Element Method
For Different Channels
Force
z
velocityfluid.max
velocityDNAavg.fR
)2//(max Hv
Sugarman & Prud’homme (1988)
25 m
Detection points at 25 cm and 200 cm
detector
-DNA in microcapillary flow
Parabolic Flow
DNA Separation in Microcapillary
Longer DNA higher velocity
Chen et al.(2005)
40m
T2 DNA after 100 s oscillatory Poiseuille flow
relaxWe
v
h
V(y,z)
Dilute DNA in Microfluidic Fluid Flow
Chain migration to increase as We increases
-DNA Nc=50, cp/cp*=0.02
We=( relax)
eff = vmax / (H/2)
Non-dilute DNA in Lattice Fluid Flow
Lattice Size = 40 X 20 X 40, corresponding to 20 x 10 x 20 m3 box
As the DNA concentration increases, the chain
migration effect decreases
Nc=50, 200, 400
H = 10 m
We=100 Re=0.14
Ld
40m
oThot
oTcold
Particle Current
Soret Coefficient
y
TccD
y
cDJ Ty
)1(
y
yT
yc
ccD
DS T
T
/
/
)1(
1
Migration of a species due to temperature gradient
Mass Diffusion Thermal Diffusion
Thermal-induced DNA Migration
Thermal fractionation has been used to separate molecules
Many factors contribute to thermal diffusivity –
a “clean” measurement difficult
Wiegand, J. Phys. Condens. Matter (2004)
Hydrodynamic interactions
Experimental Observations
Colloid Particle size
DT ↑ as R ↑ (Braun et al. 2006)
DT ↓ as R ↑ (Giddings et al. 2003, Schimpf et al., 1997)
Factors that affect DT:
Solvent quality :
DT changes sign with good/poor solvent (Wiegand et al. 2003)
DT changes sign with solvent thermal expansion coef.
Polymer molecular weight
DT ~ N0 (Schimpf & Giddings, 1989, Braun et al. 2005, Köhler et al., 2002, …)
DT ↓ as N ↑ (Braun et al. 2007)
Electrostatics ?
Thermally Driven Migration in LBE
2 4 6 8 100y, m
g(y)
T=2
ThotTcold
T=0
T=10
T(y)=temperature at height y )'()'()(2)','(),( rrttyTktrftrf Bflucfluc
TH TC
Thermal migration is predicted with a simple model)(
)/ln(
0
0
TT
cc
D
DT
Thermal Diffusion Coefficient
D(m2/s) DT (x 0.1 m2/s/K)
Duhr et al. (2005)
(27bp & 48.5 kbp)1 (48.5 kbp) 4
67.9 kbp DNA 0.82 4.1±0.6
48.5 kbp DNA 1 4.0±0.6
19.4 kbp DNA 1.7 4.6 ±0.6
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
Thot Tcold
T=4
T=0
T=2
T=7
Dissipation of Y-dependent fluctuations leads to a hydrodynamic stress in Y
))(( xUUf fpf
Momentum is exchanged between monomer and fluid
through friction
Particle Thermal Diffusion Coefficient
Diameter
(m)
D
(m2/s)
DT (m2/K/s)
dT/dy=0.2K/m
DT (m2/K/s)
dT/dy=0.4K/m
0.0385 5.6 2.3±0.4 2.1±0.3
0.0770 2.8 1.1±0.2 1.12±0.05
0.1540 1.4 0.60±0.04 0.59±0.01
DT decreases with particle size 1/R
– agrees with thermal fractionation device experiments
DT independent of temperature gradient
(Many) Other factors still to include …
Thermal and Shear-induced DNA Migration
y/H0 0.4 0.8
g(y)
1.0
1.6
0.2
T=4
y/H0 0.4 0.80.2 0.6 1.0
1.0
2.0),(
),,(
yg
TygTH TC
Thermal gradient can modify the shear-induced migration profile
Thermal diffusion occurs independent of shear-induced migration
40m
)(
)/ln(
CH
CHT
TTD
D
As N ↑, D ↓, ST↑
stronger shift in g(y) for larger polymers
T=4
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.
f ev(t)
f r(t)
f vib(t)
f bend(t) ~2nm
σmHow “solid” should the polymer be when it starts acting as a particle ?
As we move to nano-scale channels, what is the valid model?
How close are we from modeling blood vessels ?
The Lattice Boltzmann Method
Replace continuum fluid with discrete fluid positions xi and discrete velocity ci
collt dt
dnnvn
ni(r,v,t) = fluid velocity distribution function
Hydrodynamic fields are moments of the velocity distribution function
Boltzmann eqn.
)],([),(),( trtrntttcrn iiii n
)()],([ eqj
jjiji nnLtr n
Lij = local collision operator
=1/ in the simplest approx.
3D, 19-vector model
Fluid particle collisions relaxes fluid to equilibrium
Ladd, J. Fluid Mech (1994)
Ahlrichs & Dünweg, J. Chem. Phys. (1999)
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