Dynamics of Confined Polymer in Flow 陳彥龍 Yeng-Long Chen 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 DAPI Actin 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 RgRg p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  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  m10  m Radius of gyration Coarse graining Microchannels 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 Chain L = 22  m N s = 10 springs N k,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 ! Exp t Chen et al., Macromolecules (2005)

Brownian Dynamics Explicit inclusion of solvent molecules on the micron scale is extremely computational expensive !! solvent = lattice fluid (LBE) How to treat solvent molecules ??  : particle friction coef. v1v1 v2v2 v3v3 Brownian motion through fluctuation-dissipation Ladd, J. Fluid Mech (1994) Ahlrichs & Dünweg, J. Chem. Phys. (1999)

Hydrodynamic Interactions (HI) Free spaceWall correction Particle motion perturbs and contributes to the overall velocity field Stokes Flow Solved w/ Finite Element Method For Different Channels Force z

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) 40  m T2 DNA after 100 s oscillatory Poiseuille flow

h V(y,z) Dilute DNA in Microfluidic Fluid Flow Chain migration to increase as We increases -DNA N c =50, c p /c p *=0.02 We=(  relax )  eff = v max / (H/2)

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

oT hot oT cold Particle Current Soret Coefficient y 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 D T ↑ as R ↑ (Braun et al. 2006) D T ↓ as R ↑ (Giddings et al. 2003, Schimpf et al., 1997) Factors that affect D T : Solvent quality : D T changes sign with good/poor solvent (Wiegand et al. 2003) D T changes sign with solvent thermal expansion coef. Polymer molecular weight D T ~ N 0 (Schimpf & Giddings, 1989, Braun et al. 2005, Köhler et al., 2002, …) D T ↓ as N ↑ (Braun et al. 2007) Electrostatics ?

Thermally Driven Migration in LBE y,  m g(y)  T=2 T hot T cold  T=0  T=10 T(y)=temperature at height y THTH TCTC Thermal migration is predicted with a simple model

Thermal Diffusion Coefficient D(  m 2 /s)D T (x 0.1  m 2 /s/K) Duhr et al. (2005) (27bp & 48.5 kbp) 1 (48.5 kbp) kbp DNA ± kbp DNA14.0± kbp DNA ±0.6 Simple model appears to quantitatively predict D T D T is independent of N – agrees with several expt’s What’s the origin of this ?

Fluid Stress Near Particles T hot T cold  T=4  T=0  T=2  T=7 Dissipation of Y-dependent fluctuations leads to a hydrodynamic stress in Y Momentum is exchanged between monomer and fluid through friction

Particle Thermal Diffusion Coefficient Diameter (  m) D (  m 2 /s) D T (  m 2 /K/s) dT/dy=0.2K/  m D T (  m 2 /K/s) dT/dy=0.4K/  m ±0.42.1± ± ± ± ±0.01 D T decreases with particle size  1/R – agrees with thermal fractionation device experiments D T independent of temperature gradient (Many) Other factors still to include …

Thermal and Shear-induced DNA Migration THTH TCTC Thermal gradient can modify the shear-induced migration profile Thermal diffusion occurs independent of shear-induced migration 40  m As N ↑, D ↓, S T ↑ 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 σmσm  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?  How close are we from modeling blood vessels ?

The Lattice Boltzmann Method Replace continuum fluid with discrete fluid positions x i and discrete velocity c i n i (r,v,t) = fluid velocity distribution function Hydrodynamic fields are moments of the velocity distribution function Boltzmann eqn. L ij = 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)