Dynamics of Confined Polymer in Flow 陳彥龍 Yeng-Long

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 manipulate the structure and dynamics of biopolymers with statistical physics Fish schooling Blood flow

Micro- and Nano-scale Building Blocks Diameter: 7 nm Persistence length : ~10 m Endothelial Cell F-Actin DNA Rg Nuclei are stained blue with DAPI Actin filaments are labeled red with phalloidin Microtubules are marked green by an antibody 3. 4 nm Persistence length : ~ 50 nm xp

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 Organ printing and cell assembly • Embryonic tissues are viscoelastic • Smallest features ~ O(mm)

From Pancake to Tiramisu 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!” Edible Paper Moto restaurant Chicago

Confining Macromolecules Fluid plug reactor from Cheng group, RCAS Advantages of microfluidic chips Channel dimension ~ 10 nm - 100 m • 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 Multi-component systems : multiple scales for different components Atomistic Coarse graining Nanochannels 1 nm 10 nm C-C bond length 100 nm Persistence length ≈ 50 nm Essential physics : 3. 4 nm Microchannels 1 m 10 m Radius of gyration l DNA flexibility Solvent-DNA interaction 2 nm F 1 Entropic confinement F 2

Our Methods Molecular Dynamics Monte Carlo Cellular Automata - Model atoms and molecules using Newton’s law of motion - Statistically samples energy and configuration space of systems - Complex pattern formation from simple computer instructions Polymer configuration sampling Sierpinksi gasket Large particle in a granular flow -If alive, dead in next step -If only 1 living neighbor, alive

Coarse-grained DNA Dynamics DNA is a worm-like chain 2 a f ev(t) l-DNA 48. 5 kbps f W(t) f S(t) DNA as Worm-like Chain L = 22 m Ns = 10 springs Nk, s = 19. 8 Kuhns/spring 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) Exp t

Brownian Dynamics v 1 v 2 v 3 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. Ladd, J. Fluid Mech (1994) Ahlrichs & Dünweg, J. Chem. Phys. (1999)

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 T 2 DNA after 100 s oscillatory Poiseuille flow detector 25 m l-DNA in microcapillary flow Sugarman & Prud’homme (1988) Chen et al. (2005) Detection points at 25 cm and 200 cm Parabolic Flow Longer DNA higher velocity 40 m

Dilute DNA in Microfluidic Fluid Flow l-DNA Nc=50, cp/cp*=0. 02 V(y, z) h We=( trelax) geff = vmax / (H/2) Chain migration to increase as We increases

Non-dilute DNA in Lattice Fluid Flow Lattice Size = 40 X 20 X 40, corresponding to 20 x 10 x 20 m 3 box Nc=50, 200, 400 We=100 Re=0. 14 As the DNA concentration increases, the chain migration effect decreases Ld 40 m H = 10 m

Thermal-induced DNA Migration o. Tcold y Migration of a species due to temperature gradient Particle Current o. Thot Mass Diffusion Thermal Diffusion Soret Coefficient 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 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 ~ N 0 (Schimpf & Giddings, 1989, Braun et al. 2005, Köhler et al. , 2002, …) DT ↓ as N ↑ (Braun et al. 2007) Solvent quality : Electrostatics ? DT changes sign with good/poor solvent (Wiegand et al. 2003) DT changes sign with solvent thermal expansion coef.

Thermally Driven Migration in LBE T(y)=temperature at height y TH Thot TC T=2 T=0 g(y) 0 Tcold T=10 2 4 y, m 6 8 10 Thermal migration is predicted with a simple model

Thermal Diffusion Coefficient D( m 2/s) DT (x 0. 1 m 2/s/K) Duhr et al. (2005) (27 bp & 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 T=7 T=4 Momentum is exchanged between monomer and fluid through friction T=2 T=0 Thot Dissipation of Y-dependent fluctuations leads to a hydrodynamic stress in Y Tcold

Particle Thermal Diffusion Coefficient Diameter ( m) D ( m 2/s) DT ( m 2/K/s) d. T/dy=0. 2 K/ m DT ( m 2/K/s) d. T/dy=0. 4 K/ 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 Thermal gradient can modify the shear-induced migration profile TH 1. 6 TC DT=4 Thermal diffusion occurs independent of shear-induced migration DT=4 2. 0 g(y) 1. 0 0. 2 0 0. 4 y/H 0. 8 0 0. 2 0. 4 y/H 0. 6 0. 8 As N ↑, D ↓, ST↑ 40 m stronger shift in g(y) for larger polymers 1. 0

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. ØHow “solid” should the polymer be when it starts acting as a particle ? ØAs we move to nano-scale channels, what is the valid model? Ø How close are we from modeling blood vessels ? σm f r(t) f bend(t) f vib(t) f ev(t) ~2 nm

The Lattice Boltzmann Method Replace continuum fluid with discrete fluid positions xi and discrete velocity ci ni(r, v, t) = fluid velocity distribution function 3 D, 19 -vector model Hydrodynamic fields are moments of the velocity distribution function Ladd, J. Fluid Mech (1994) Boltzmann eqn. Ahlrichs & Dünweg, J. Chem. Phys. (1999) Fluid particle collisions relaxes fluid to equilibrium Lij = local collision operator =1/t in the simplest approx.