Physics of Nano-Bio Systems Pik-Yin Lai 黎璧賢 Department of Physics & Center for Complex Systems, National Central University, Chung-Li, Taiwan 320 Email: firstname.lastname@example.org • Introduction: DNA, proteins, molecular biology • Biopolymers/DNA • Single molecule Force experiments. • Elastic models of DNA & DNA mechanics • Charge Transport in DNA • DNA microarray • Nano-technology & DNA bio-sensor • DNA as nano-materials 2005
Cell Nucleus Chromosome Chromatin Double-stranded biopolymer, 2 sugar-phosphate chains (backbones) twisted around each other forming a RH (B-form) double helix.
Brief Molecular biology • Molecular Biology of the Cell Central Dogma Proteins
Bonding & • Forces in bio-systems • Van der Waals: ~2.5kT • Ionic: ~250kT • Covalent: ~100-300kT • H-bonds: ~5-10kT • Hydrophobic: ~few kT Room Temp: 1kT~ 4x10^-21 J
Some common Biomolecular chains Spectrin Globular actin Intermediate filament Microtubule F-actin
Linear mass persistence density length Actin filaments, microtubules are stiff in cellular scales --- thermal fluctuations not important
Watson-Crick Base Pairs • Hydrogen bonded base pairs: A-T & C-G • A-T: 2 H-bonds; C-G: 3 H-bonds • 10.5bps/turn, helix pitch ~3.4nm. • helical structure is further stabilized by vertical stacking interactions (induced-dipole--induced-dipole) between the aromatic bases • ~10 to 10 bps in a human DNA 11 12 Nature review: 50 years of DNA
Mechanics/Elasticity of Single Bio-molecules • To investigate the conformational changes in single bio-molecules, may provide significant insight into how the molecule functions. • How forces at the molecular level of the order of pN underlie the varied chemistries and molecular biology of genetic materials?
Force scales • Size of bead/cell, d~2 micron • thermal agitation sets the lower limit to force measurements; • Langevin force~10fN/Hz • Weight of a cell ~ 10fN • Entropic forces ~kT/nm ~ 4 pN • Non-covalent bond~eV; elastic forces~eV/nm=160pN • Force to break covalent bond~ eV/A~1600pN 1/2
Experimental Tools in Force expts. • Micro-mechanical springs (fibers,micro-pipette,cantilevers), • Hydrodynamic drag • Optical or magnetic tweezers • Scanning force/Atomic force microscopy • Imaging techniques and Fluorescence microscopy Strick et al., Science 271, 1835 (96); Ann. Rev. Biophys. 29, 523 (00)
Scanning force microscopy • Commercial SFM tips can have stiffness low as ~10mN/m; • can measure forces as low as 10pN. • Etched optical fibre/glass microneedles are ultra-soft, ~1.7 mN/m; • force precision of ~1 pN
Optical Traps Polarizability of bead, c F=grad (p.E)=2c(grad E)E net force acts radially towards the more intense beam & vertically towards the focus. Calibrate by Brownian motion & fluid flow near infrared lasers for biomolecules single beam gradient trap dual counter propagating beam trap optical tweezers
Optical tweezers Bustamante et al., Science 258, 1122 (92); Biophys. J. 79, 1155 (00)
Micropipette aspiration Pipette diameter~1~10mm Suction P~1 Pa to 50kPa; f~1 pN to 1mN Biointerface force probe
Force-Induced Transition of an overwound DNA to P-DNA • positively supercoiled DNA reveals the existence of a sharp transition at f~ 3 pN • P-DNA corresponds to an overwound structure with 2.62 base pairs per turn. • The bases are exposed tothe solvent with the phosphate backbone allowed to wind at the center,
Biological implications of torque-induced transitions • Many proteins interacting with DNA modify its twist (e.g. histones). • DNA overwinds/underwinds during transcription as the RNA polymerase progresses on its substrate. • during replication, helicases unwind the molecule to make way for the replication complex. • torsional stress in the molecule thus depends on the balance between the generation • of torsional stress (for example, during transcription or replication) and its relaxation by topoisomerases. • conceivable that the cell uses the torsional • stress signal might control the expression of nearby genes. Some experiments suggest that the wave of unwinding left behind the transcription complex may turn on other genes
Unzipping DNA • Measure force to unpair two bases • Stick-slip response • Prototype for DNA sequencing, need higherresoultion • Complexed with protein can make filament stifferhigher sensitivity
Stretching Proteins • undergo independent folding/unfolding transitions as the polypeptide is stretched. • display a typical sawtooth pattern, due to the coexistence in the stretched protein of folded and unfolded domains. • Pulling rate dependent: ~20pN to unfolding titin at 60nm/s (optical tweezers); ~150pN at 1000nm/s (AFM) • Two-level model.
Unfolding pathway of spectrin • a-helical domain • Little common between force and temp. • induced unfolding pathways Paci & Karplus PNAS 97, 6521 (2000)
Unfolding pathway of Immunoglobulin • b-sandwich domain • Important differences between force and temp. • induced unfolding pathways, but common • features of folding cores Paci & Karplus PNAS 97, 6521 (2000)
Interactions among different Bio-molecules • To investigate the formation of DNA/protein complex • How stresses affect biological process? (e.g. transcription, replication, unwrapping DNA from nucleosome, RNA/RecA polymerase, gene expression…..)
Physicist’s view of the DNA chain Double helix stabilized by H-bonds (bp interactions) Polymer of persistence length ~50nm under low force (<10pN):Entropic elasticity. Complicated at high forces: cooperative behavior Elasticity of dsDNA affect its structure and can influence the biological functions
Worm-like chain model(stiff chain) |t|=1 inextensible single strand Rod-like chain model(twisted stiff chain) Marko et al., Science 256, 506, 1599 (94); Bouchiat et al., PRL 80, 1556 (98) Fitting from expts: A=53nm; Can account for some supercoiling properties of DNA Phenomenological model, no description of underlying mechanism.
Stretching a single dsDNA lo =B-form contour length Low force regime described well by worm-like chain (WLC) model. Abrupt increase in length at ~65pN from B-form DNA to S-form DNA
dsDNA model with bending and bp stacking interactions Zhou, Zhang & Ou-Yang. PRL (99); PRE (00)
ZZO model Bending: • ro =backbone arclength between adjacent bps • Asymmetric potential: a free DNA is RH • ro cosjo=0.34nm, eqm. distance between 2 stacks • e=14kT, averaged value take to be sequence indep. Base-pair stacking:
Stretching force: Twisting:
Low force: WLC is accurate High force: ZZO model: Good agreement with force experiment data.
dsDNA w/ bp stacking wormlike-rod chain (at low force) Zhou & Lai, Chem .Phys. Lett. 346, 449 (01) Since WLRC is a generic phenomenological model which describe the low force elastic behavior well, any good microscopic model must reduce to it at low force/torque. cosj measures the extend the backbones are folded w.r.t. central axis Comparing Tw in both models: In force-free state: jm minimizes V(j) and for low force/torque: j is not far away from jm
B-form to S-form Transition under a Stretching force Lai & Zhou, J. Chem. Physics 118, 11189 (2003) • Force Experiments • Stretching a single end-grafted DNA • S-form • B-form • Abrupt increase of 1.7 times in contour length of dsDNA near 65pN. • Thermal fluctuations unimportant near onset of transition.
ZZO model for double-stranded DNA H. Zhou, Z. Yang, Z-.c. Ou-Yang, PRL 82, 4560 (99) j=folding angle
Classical mechanics approach • (thermal effects can be neglected since the DNA is quite straight near the onset of BS) • All lengths in units of R, energy in units of k/R f=fz, dimensionless forceb=fR /2k, t=(sinqcosf,sinq,sinf,cosq) • Minimizing Ebs: Euler Lagrange eqns. • B.C.s: 2
to // f, jo non-zero • q(s)=0 • Effective potential • Behavior governed by the minima of U(j) in the long L limit.
First order phase transition at bt 2 b=fR /2k
Detail configurations of the strands can be explicitly calculated. First-order elongation:Stretch by untwisting b=0.073 b=0.075
Untwisting upon stretching • Untwist per contour length from BS, DTw/Lo~-100 deg. /nm; • Almost completely unwound ~ 34deg./bp • Torque ~ 60 pN nm
Direct observation of DNA rotationduring transcription by Escherichia coli RNA polymeraseHarada et al., Nature 409 , 113 (2001) • DNA motor: untwisting gives rise to a torque • BS transition provides a switch for such a motor. G > 5 pN nm from hydrodynamic drag estimate
Relative Extension • qo=10 deg.jo=53 deg. L=10 Transition to S-form occurs at f~45pN (c.f. expt.: ~65pN) • Relatvie extension Z/Lo increases by 1.7 times from BS. (c.f. expt. ~1.65 times)
Including external Torque Torque couple with Linking number Left-handed Z-form DNA obtained for large negative external torque Z-form S-form B-form Left to right: Torque increasing from –ve to +ve values
Z-DNA is left-handed, its bases seem to zigzag. One turn spans 4.6 nm, comprising 12 base pairs. The DNA molecule with alternating G-C sequences in alcohol or high salt solution tends to have such structure. In a solution with higher salt concentrations or with alcohol added, the DNA structure may change to an A form, which is still right-handed, but every 2.3 nm makes a turn and there are 11 base pairs per turn.
Electrical properties of Single Bio-molecules • Electronic excitations and motion of electric charges are well known to play a significant role in a wide range of bio-macromolecules • DNA is negatively charged • Electron transfer involving the DNA double helix is thought to be important in radiation damage and repair and in biosynthesis • the double helix may mediate charge transfer between different metal complexes • DNA can be viewed as a one dimensional well conducting molecular wire • Molecular electronics /devices
Direct measurement of electricaltransport through DNA molecules Porath et al. Nature 403, 635 (2000) • Electrical transport measurements on micrometer-long DNA `ropes', and also on large numbers of DNA molecules in films, have indicated that DNA behaves as a good linear conductor. • 10.4nm-long, (30bps) double-stranded poly(G)-poly(C) DNA molecules connected to two metal nano-electrodes • After a DNA molecule was trapped from the solution, the device was dried in a flow of nitrogen and electrical transport was measured. No current was measured between the bare electrodes before trapping
Semiconducting behavior in poly-A & poly-C Porath et al. Nature 403, 635 (2000) • By contrast, for poly-A or poly-C DNA, large-bandgap semiconducting behavior. Nonlinear current-voltage curves that exhibit a voltage gap at low applied bias. This is observed in air as well as in vacuum down to cryogenic temperatures. • Electronic interactions between the bases in the DNA molecule lead to a molecular band where the electronic states are delocalized over the entire length of the molecule. • Electron transport in the hopping and band models is facilitated when the Fermi level of the electrode is aligned with the band edge by applying the bias voltage. Once electrons are injected, transport occurs through hopping or band conduction. • charge carrier transport being mediated by the molecular energy bands of DNA.
Electron transport is indeed due to DNA trapped between the electrodes • Dashed curve: after incubation of the same sample for 1 h in a solution with 10 mg ml-1 DNAse I enzyme (5mM Tris-HCl, 5mM MgCl2, 10 mg ml-1 DNAse I (pH 7.5)). Double-stranded DNA was cut by the enzyme. • Inset: two curves measured in a complementary experiment where the procedure was repeated but in the absence of the Mg2+ ions that activate the enzyme and in the presence of 10mM EDTA (ethylenediamine tetraacetic acid) that complexes any residual Mg ions. The curve did not change. • DNA was indeed cut by the enzyme in the original experiment. Porath et al. Nature 403, 635 (2000)
Voltage gap widens with increasing temperature Porath et al. Nature 403, 635 (2000)
3 plausible transport models Porath et al. Nature 403, 635 (2000) • Black and red lines : with and without an applied bias voltage. • Tunneling barriers : the contact between the DNA and the metal electrodes. • Model 1 : common uni-step tunneling, as in electron-transfer studies (ruled out since tunneling distance is too large: 8nm) • Model 2 : sequential hopping between localized states associated with basepairs—1d diffusion (unlikely due to the high field used & the large e-transfer rate observed) • Model 3 : molecular band conduction due to electronic interaction that leads to de-localization over the entire DNA (facilitated when the Fermi level of the electrode is aligned with the band edge by applying the bias voltage. Once electrons are injected, transport occurs through hopping or band conduction.)
Direct measurement of hole transport dynamics in DNA Lewis et al. Nature 406, 51 (2000) • oxidative damage to double helical DNA and the design of DNA-based devices for molecular electronics depend upon the mechanism of electron and hole transport in DNA. • Electrons and holes can migrate from the locus of formation to trap sites and such migration can occur through either a single-step ‘‘super-exchange’’ mechanism or a multi-step charge transport ‘‘hopping’’ • The rates of single-step charge separation and charge recombination processes are found to decrease rapidly with increasing transfer distances, whereas multi-step hole transport processes are only weakly distance dependent. • spectroscopic measurements of photo-induced electron transfer in synthetic DNA
to investigate the distance-dependent electron transfer in DNA utilizing hairpin-formation bis(oligonucleotide) • stilbene(St) serves as a linker between two complementary oligonucleotides, • The singlet St selectively photo-oxidizes G, but not A,C,T, resulting in the formation of the St- & G+ radicals. • By monitoring the formation and decay of St- , the dynamics of charge separation and charge recombination can be determined by transient spectroscopy over a large dynamic range (sub-ps) to ms). • The hairpins that contain three G:C base pairs were designed to probe the dynamics of hole transport from G+1, formed upon photoinduced charge separation, to a GG step separated from G+1 by one T:A base pair.