微米和纳米尺度内的复杂物质和流体

1、微米和納米尺度內的複雜物質和流體微米和納米尺度內的複雜物質和流體 陳彥龍陳彥龍Yeng-Long Chen (.tw)Institute of Physics and Research Center for Applied ScienceAcademia SinicaTo understand and manipulate the structure and dynamics of biopolymers with statistical physicsMicro- and Nano-scale Building BlocksNuclei are

2、stained blue with DAPIActin filaments are labeled red with phalloidin Microtubules are marked green by an antibodyEndothelial CellF-ActinDNADiameter: 7nm Persistence length : 10 mm3.4 nmPersistence length : 50 nmRgxpOrgan PrintingMironov et al. (2003)Boland et al. (2003)Forgacs et al. (2000)Organ pr

3、inting 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)High throughputLow material costHigh degree of parallelizationAdvantages of microfluidic chipsEfficient d

4、evice depends on controlled transportChannel dimension 10nm - 100 mmFluid plug reactor from Cheng group, RCASConfining MacromoleculesTheory and simulations help us understand dynamics of macromoleculesMulti-Scale Simulations of DNA10 nm2 nm3.4 nm1 nmAtomisticC-C bond length100 nmPersistence length 5

5、0nmNanochannelsEssential physics : DNA flexibilitySolvent-DNA interactionEntropic confinement1Fl2F1Fl2F1Fl2F1Fl2F1 mm10 mmRadius of gyrationCoarse grainingMicrochannelsMulti-component systems : multiple scales for different componentsMolecular Dynamics- Model atoms and molecules using Newtons law of

6、 motionMonte Carlo- Statistically samples energy and configuration space of systemsCellular Automata- Complex pattern formation from simple computer instructionsLarge particle in a granular flowPolymer configuration samplingSierpinksi gasket -If alive, dead in next step-If only 1 living neighbor, al

7、iveOur MethodsDNA Trapped in Nanoslitl1F4T2F5m mR|m m2Po-keng Lin et al. PRE (2007)Does the shape of the molecule change as it grows longer ?100nm222122212RRRRA22212RRRgR1R2Monte Carlo N=256 SAW H=2s slitVirtual & Real ExperimentsRg N0.68trelaxN2.2Real Experiments slit(H=5s) 2D Slit(2D proj)R12n

8、=1.21 1.51 1.33R22n=1.20 1.51 1.33Rg2n=1.19 1.53 1.35222122212RRRRA22212RRRgRg2 NnrodsphereCoarse-grained DNA DynamicsDNA as Worm-like ChainL = 22 mm Ns = 10 springsNk,s = 19.8 Kuhns/springMarko and Siggia (1994) 2af S(t)f ev(t)f W(t)l l-DNA 48.5 kbpsDNA is a worm-like chainModel parameters are matc

9、hed to TOTO-1 stained l-DNAParameters matched in bulk are valid in confinement ! ExptChen et al., Macromolecules (2005)Brownian Dynamics)(xUUffpfdtmtUdttRd)()(Explicit inclusion of solvent molecules on the micron scale is extremely computational expensive ! solvent = lattice fluid (LBE)How to treat

10、solvent molecules ?dtmdttfdttUd)()(: particle friction coef. v1v2v3Brownian motion through fluctuation-dissipationflucfricwallWLCevffffff0flucf) () (2) , (),(rrttTktrftrfBflucflucThe Lattice Boltzmann MethodReplace continuum fluid with discrete fluid positions xi and discrete velocity cicolltdtdnnvn

11、ni(r,v,t) = fluid velocity distribution functionHydrodynamic fields are moments of the velocity distribution functionBoltzmann eqn. ),(),(),(trtrntttcrniiiin)(),(eqjjjijinnLtr nLij = local collision operator =1/t in the simplest approx.3D, 19-vector modelFluid particle collisions relaxes fluid to eq

12、uilibrium Ladd, J. Fluid Mech (1994)Ahlrichs & Dnweg, J. Chem. Phys. (1999)Hydrodynamic Interactions (HI)Free spaceWall correctionParticle motion perturbs and contributes to the overall velocity field Stokes Flow000W0s00),(),(v)(v),(vfrrrrrrfrrWW2v0v0pSolved w/ Finite Element MethodFor Different

13、 Channels Forcezvelocityfluid.maxvelocityDNAavg.fR)2/(maxHvSugarman & Prudhomme (1988)25 mmDetection points at 25 cm and 200 cmdetectorl-DNA in microcapillary flowParabolic FlowDNA Separation in Microcapillary Longer DNA higher velocityChen et al.(2005)40mmT2 DNA after 100 s oscillatory Poiseuil

14、le flowrelaxWetvzyhV(y,z)Dilute DNA in Microfluidic Fluid FlowChain migration to increase as We increasesl-DNA Nc=50, cp/cp*=0.02We=( trelax)eff = vmax / (H/2)Non-dilute DNA in Lattice Fluid FlowLattice Size = 40 X 20 X 40, corresponding to 20 x 10 x 20 mm3 boxAs the DNA concentration increases, the

15、 chain migration effect decreasesNc=50, 200, 400H = 10 mmWe=100 Re=0.14Ld40mmoThotoTcoldParticle CurrentSoret CoefficientyTccDycDJTy)1 ( yyTycccDDSTT/)1 (1Migration of a species due to temperature gradientMass DiffusionThermal DiffusionThermal-induced DNA Migration Thermal fractionation has been use

16、d to separate molecules Many factors contribute to thermal diffusivity a “clean” measurement difficultWiegand, J. Phys. Condens. Matter (2004)Hydrodynamic interactionsExperimental Observations Colloid Particle sizeDT as R (Braun et al. 2006)DT as R (Giddings et al. 2003, Schimpf et al., 1997)Factors

17、 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 weightDT N0 (Schimpf & Giddings, 1989, Braun et al. 2005, Khler et al., 2002, )DT as N (Braun et al. 2007)Electrostatics ?Thermally

18、 Driven Migration in LBE2468100y, mmg(y)T=2ThotTcoldT=0T=10T(y)=temperature at height y ) () ()(2) , (),(rrttyTktrftrfBflucflucTHTCThermal migration is predicted with a simple model)()/ln(00TTccDDTThermal Diffusion CoefficientD(mm2/s)DT (x 0.1 mm2/s/K)Duhr et al. (2005)(27bp & 48.5 kbp)1 (48.5 k

19、bp)467.9 kbp DNA0.824.10.6 48.5 kbp DNA14.00.6 19.4 kbp DNA1.74.6 0.6 Simple model appears to quantitatively predict DTDT is independent of N agrees with several exptsWhats the origin of this ? Fluid Stress Near ParticlesThotTcoldT=4T=0T=2T=7Dissipation of Y-dependent fluctuations leads to a hydrody

20、namic stress in Y)(xUUffpfMomentum is exchanged between monomer and fluid through friction Particle Thermal Diffusion CoefficientDiameter(mm)D(mm2/s)DT (mm2/K/s)dT/dy=0.2K/mmDT (mm2/K/s)dT/dy=0.4K/mm0.038770 1.120.050.15401.40.600.040.590.01DT decreases with particle size

21、 1/R agrees with thermal fractionation device experimentsDT independent of temperature gradient (Many) Other factors still to include Thermal and Shear-induced DNA Migrationy/H00.40.8g(y)1.01.60.2T=4y/H00.61.01.02.0),(),(ygTygTHTCThermal gradient can modify the shear-induced migration profileThermal diffusion