微米和納米尺度內的複雜物質和流體

1. 微米和納米尺度內的複雜物質和流體 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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)

8. 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

9. 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)

10. 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.

11. 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.

12. 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

13. 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

14. 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

15. 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

16. 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

17. Many factors contribute to thermal diffusivity – a “clean” measurement difficult Hydrodynamic interactions Wiegand, J. Phys. Condens. Matter (2004)

18. 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.

19. 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

20. 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 ?

21. 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

22. 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 …

23. 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

24. 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 ?