SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION doi: /nphys00 Peter Gross, Niels Laurens, Lene B. Oddershede, Ulrich Bockelmann 3, Erwin J. G. Peterman*, and Gijs J. L. Wuite* LaserLaB and Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands Niels Bohr Institute, Blegdamsvej 17, 100 Copenhagen, Denmark 3 Laboratoire Nanobiophysique, ESPCI, CNRS UMR Gulliver 7083, 10 rue Vauquelin 75005, Paris, France * Authors contributed equally nature physics 1

2 Supplemental Figures Supplementary Figure 1: Experimental variability of the force-dependent twiststretch-coupling. A: Black line: Twist-stretch coupling determined from the measurements of Gore et al. (1) of the change in DNA twist as a function of force, calculated with eq. S3. Colored dots: Force-dependence of the twist-stretch coupling determined for different pkyb1 DNA constructs with a length of.85 µm (N=7), determined with eq. S5. The elastic parameters L c, L p and S, were determined by fitting each individual force-extension curve to the twistable worm-like chain model (equation S4). The twist rigidity C was taken from (). Using equation S6 as a functional form for g(f), we obtained the following ensemble average and standard error of the mean: g 0= ± 50 pn nm, g 1=18 ± 0.5 nm, F t= 30 ± 4 pn. B: Force-dependence of the twiststretch coupling determined for different lambda DNA constructs with a length of 16.4 µm (N=7), similar to panel A. Black line: Twist-stretch coupling determined from the measurements of Gore et al. (1) of the change in DNA twist as a function of force,

3 calculated with equation S3. We obtained the following ensemble average and standard error of the mean: g 0= ± 0 pn nm, g 1=18± 1 nm, F t= 30 ± 1 pn. Note that both ensembles yield identical values for the twist-stretch coupling (upon utilizing eq. S6). The experimental variability, however, is increased for the significantly shorter pkyb1 DNA construct (panel A). This is expected since the DNA extension in eq. S5 is normalized to the contour length, which will reduce the experimental variability in determining g(f) from eq. S5 for longer DNA molecules. Supplementary Figure : Stick-slip wise DNA unpeeling of phage lambda DNA with two non-confined strands; one on each end, such that two unpeeling fronts can progress, like in (3). A: The onset of DNA overstretching for 3 different lambda DNA molecules. The curves are vertically shifted for visibility. Pronounced stick-slip wise denaturation can be observed. In contrast to measurements with only one unpeeling front (figure 3A) no reproducible patterns emerge. B: Extension-rate dependence of the stick-slip DNA unpeeling pattern. Four measurements of the onset of DNA unpeeling at three different 3

4 extension-speeds, acquired at 3 Hz. Curves for different speeds are vertically shifted for visibility. The stick-slip pattern vanishes for high extension rates. Supplementary Figure 3: The molecular stick-slip dynamics occurring in the overstretching transition are deterministic. Four successive force-extension measurements on one individual pkyb1-dna molecule, with variable extension rates, acquisition rate 3 Hz. Curves are vertically shifted for visibility. 4

5 Supplementary Figure 4: Bistability close to the critical force of individual DNA unpeeling events. 5

6 A: Bistability observed in a force-extension measurement. Grey triangles depict the stick-slip melting behavior during unpeeling. In black, red, and blue, force and distance are plotted for three fixed separations between the optical traps. B: Histogram of the force-levels for each fixed separation of the two optical traps. C: Temporal evolution of the force-level for each separation, sampled at 3 Hz. Supplementary Figure 5: Comparison of the elasticity of dsdna and ssdna. Black: elastic properties of the dsdna construct with 3 confined ends, allowing unpeeling occur only from one free end. Red: subsequent force-extension measurement of the same DNA construct. Apparently, the DNA did not reanneal, presumably due to failure of the biotin-streptavidin bond of the unpeeled strand. At the end of the unpeeling process (forces above ~ 60 pn) the elastic properties of the DNA construct can be fully described by that of ssdna. Notably, in our experiments we did not observe a second, kinetic transition prior to final strand separation, at forces between 65 pn and 130 pn, as reported in (4-6). This kinetic barrier was interpreted to be due to large-scale rearrangements in the DNA conformation prior to the final melting transition. We show here that under our experimental conditions, which involve controlled strand attachment and slow extension speeds, no such kinetic barrier is present. This is consistent with our interpretation of DNA overstretching as burst-wise progression of a single unpeeling front. 6

7 Supplementary Figure 6: Energetics of individual unpeeling burst. A: Comparison of the energy penalty for melting a dsdna patch (red) and the mechanical energy gain due to the increased contour length (black) displayed against the sequence location. The melting energy was calculated using the nearest neighbor model for base-pairing of SantaLucia (7). The mechanical energy gain was determined by calculating the mechanical energy difference between the initial and final dsdna/ssdna hybrid up to the critical melting force, all extracted from the force-extension measurement seen in figure 1C. For comparison the absolute value of the energies is displayed. B: The energy penalty for a DNA unpeeling event and the mechanical energy gain due to extending the DNA contour length displayed against the number of base pairs in a single melting burst. The graph shows that both energies match over almost the whole range of burst lengths observed ( bp). This supports our interpretation that burst-wise, force-induced DNA unpeeling is a close to equilibrium process. 7

8 Supplementary Figure 7: Hysteresis during DNA reannealing. A: Two force-extension measurements of the pkyb1 DNA construct with three confined DNA ends. Black: force-induced DNA unpeeling; red: subsequent strand reannealing. B: Average energy per base pair stored in the secondary structure of the unpeeled strand (see equation S10). Red line: average base pairing energy of correctly paired nucleotides (.1 k BT). Grey lines highlight regions of delayed reannealing, as experimentally observed (panel C). C: Dwell-time histogram of the position of the double-stranded/single-stranded junction during strand reannealing (N=5). Locations of prolonged stalls in the reannealing process clearly show up and seem to occur prior to relatively stable secondary structures (grey vertical lines). 8

9 Supplemental Notes Incorporating the twist-stretch coupling in the extensible worm-like chain model for DNA Initially, we focus on the force regime where entropic bending fluctuations can be neglected (F> 15 pn, enthalpic regime). In a linear theory, the elastic energy stored in a DNA molecule (E DNA) stretched by a force (F) beyond its contour length (L c) can be written as (1, 8-10): E DNA = 1 C L c x 1 S θ + g( F) θ + ( x Lc ) x F. (S1) L L c c Here, the material parameters are represented by: L c the contour length, C the twist rigidity, g(f) the tension-dependent twist-stretch coupling, S the stretch modulus (, 11, 1). The end-to-end distance of the molecule is given by x, and θ denotes the winding angle relative to the Watson-Crick structure. Minimizing the enthalpic Hamiltonian (equation S1) with respect to x and θ yields: x enthalpic C Lc F, (S) g( F) + S C = g( F) Lc θ enthalpic = F. (S3) g( F) S C Since the worm-like chain model does not consider crosstalk between the enthalpic and entropic contributions, both can be addressed separately. Incorporation of equation S in the worm-like chain model (13) yields the following relation between the extension and the force acting on the DNA, the twistable worm-like chain (twlc) model: 9

10 1 kbt C x = L + F c 1. (S4) F Lp g( F) + SC This equation can be solved for g(f) : = x Lc 1 + k T F L B g ( F) S C C F 1. (S5) p 1 Note that this treatment yields the absolute value of g(f). From magnetic tweezer studies it is known that g(f) is negative at low forces and changes sign at ~35 pn (1) (figure S1). Determining the elastic parameter of DNA from force-extension measurements using the twistable worm-like chain model Our determination of the elastic parameters of DNA is based on three factors: the twlc chain model with a force-dependent twist-stretch coupling g(f), a priori knowledge of the functional form of g(f) and high quality force-extension measurements. Information on the twist-stretch coupling of DNA and its force dependence was obtained by either reparameterizing force-distance measurements with equation S5, or by extracting g(f) directly from unwinding vs. force measurements (1). Figure A shows that both approaches yield a negative, relatively constant value of g(f) for low forces, in agreement with (14). For forces higher than ~ 30 pn, the critical force F c, a forcedependence of the twist-stretch coupling appears to emerge. In a phenomenological approach we opted to describe this behaviour by the simple expression: g g g + g F F < F 0 1 c c ( F) = (S6) 0 + g F 1 F F c We tested two approaches to determine the elastic parameters of DNA. In one approach we determined the functional form of g(f) by fitting equation S6 to data from (1) (see figure S8), extracting g 0, g 1 and F c. Using these parameters fixed for g(f), we then fitted the twlc model (eq. 8) to force-distance measurements of DNA with the contour length L c, the stretch modulus S and the persistence length L p as only free fitting parameters. 10

11 Supplementary Figure 8: Phenomenological description of the force-dependence of the twist-stretch coupling of DNA. Data from figure A was fitted to equation S6, which yielded: g 0= -637 pn nm, g 1=17 nm, F c=30.6 pn. In the other approach we inserted the phenomenological functional form of g(f) into equation (1) and used g 0, g 1, the critical force F c as well as L c, S and L p as fitting parameters. These two approaches are compared in figure S9. Both procedures yielded the following ensemble average values (N=7, errors represent the standard error of the mean): Approach Lc (µm) Lp (nm) S (pn) g0(pnnm) g1 (nm) Fc (pn) g(f) fitted from.85± ± 1450± (*) 17 (*) 30.6 (*) unwinding vs force measurements g(f) fitted from F-d.85± ±3 1600±10-590±50 18±0.5 30±4 measurements (*) see figure S8 11

12 Supplementary Figure 9: Comparison of the fit-performance for two different approaches of determining the force-dependent twist-stretch coupling g(f). The blue trace shows a fit to a force-extension measurement of DNA with g(f) extracted from figure S8, (g 0= -637 pn nm, g 1=17 nm, F c=30.6 pn) while L c, S and L p were open fitting parameters (L c=.85 µm, S= 1430 pn and L p= 40 nm). For the red trace it was assumed that g(f) has the functional form of equation S6, such that the following parameters were fitted: g 0, g 1 and F c, L c, S and L p, (g 0=-558 pn nm, g 1=17. nm, F C= 3.5 pn, L c=.86 µm, S= 1545 pn and L p= 38.9 nm). As a last test, we evaluated the low-force approximation, the extensible WLC model. For forces lower than ~30 pn, the twist-stretch coupling does not reveal clear forcedependence. In such a situation, the twlc model and the extensible WLC model (13) have an identical functional form, possessing an effective spring constant that shows no force-dependence. Therefore the use of the extensible WLC model for forces below 30 pn is justifiable.we found the following ensemble average value (N=7, errors represent the standard error of the mean): L c=.85± µm, S= 1600 ± 10 pn and L p= 39±3 nm. It appears that the extensible worm-like chain model, restricted to forces below 30 pn, is able to provide realistic values for the persistence length and the stretch modulus. 1

13 Equilibrium model for DNA strand unpeeling during DNA overstretching Our theoretical description of DNA overstretching with a force measurement device is based on equilibrium statistical mechanics. It is related to the theoretical description of mechanical DNA unzipping described earlier (15, 16) and involves the interplay of different energy contributions. The first energy is called E DNA (j). It describes the work necessary to separate the two strands of the DNA double helix from the first base pair to the one of index j. This energy is derived from SantaLucia (7) that provides the binding energies of the different DNA base pairs while taking nearest neighbor interactions into account. The second energy, E dsdna, is associated with the elasticity of the double stranded DNA. The double stranded part shortens as the overstretching progresses, since it converts to single-stranded DNA, and its elasticity of dsdna is described by the twistable worm-like chain model proposed in the present work. The parameters are determined from our experimental data, as described in the supplementary information section entitled "Determining the elastic parameter of DNA from force-extension measurements using the twistable worm-like chain model". The third energy, called E ssdna, is associated with the elasticity of the single stranded parts of the molecular construction. The elasticity of the single stranded part under tension (the latter increases in length as the overstretching progresses) is described in a freely jointed chain model with entropic and enthalpic contributions, with elastic parameters taken from the literature (11). The forth energy, called E trap, is the potential energy, E trap=½k trapx of the beads in the traps. Here, the total stiffness k trap=(k 1+k ) -1 arises from the stiffness k 1 and k of the two traps that are obtained by experimental calibration. Finally, we have the thermal energy k BT that enters the calculation of the thermal averages in the canonical ensemble. In this work we do not consider temperature variations and use T=300 K. The state of our model system is characterized by three variables, the number of opened base pairs j and the lengths of the double stranded and the single stranded parts under tension, l ds and l ss respectively. The force induced shift of the beads is simply given by x=x 0-l ds-l ss, namely the difference between the displacement x 0 of the mobile trap and the total length of the DNA stretched between the beads. 13

14 The thermal average of an observable A is given by A = j, l ds, l ss where the total energy reads A( j, l j, l ds, l ss ds e, l E ss tot ) e ( j, l E ds, l tot ss ( j, l B ds )/ k T, l ss )/ k T B, (S7) E tot = E DNA ( j) + E ( j, l ) + E ( j, l ) + E ( x) dsdna ds ssdna ss trap (S8) For the results presented in Fig.4A and 4B we calculated averages of the force F=k trap x, while for Fig. 4C we calculated averages of the first and second momentum of the number of opened base pairs: 1 ( j j ) var( j ) + =. (S9) Experimental requirements to observe stick-slip dynamics in DNA unpeeling To observe the pronounced stick-slip pattern in DNA unpeeling, the number of unpeeling fronts needs to be small. For nick-free lambda DNA, two unconstrained ends are present and still show stick-slip dynamics. The stick-slip dynamics of lambda DNA are however not deterministic, due to the competition of two unpeeling fronts (figure SA). For nicked DNA, even more unpeeling fronts are present (3). The impact of multiple unpeeling fronts has been addressed using a qualitatively similar assay in studies of force-induced RNA hairpin opening (17). There it was shown that the parallel resolving of hairpins, opening individually in a bistable manner, results in an averaged, smoothed force extension curve. This emphasizes the importance of a constrained DNA molecule with only a single unpeeling front when quantitatively studying the sequence specific unpeeling process of DNA. In addition, the Nyquist theorem needs to be obeyed in order to observe the full dynamic range of the sharp unpeeling transitions. The Nyquist theorem sets an upper limit for the extension rate for a given sampling rate. Under our experimental conditions (sampling rate 3 Hz; DNA length.87 um; ~ 40 transitions) DNA needs to be stretched at a 14

15 velocity lower than ~ 50 nm/sec, in agreement with experimental observations (figure S3). At higher extension velocities, the transitions are smeared out due to under sampling and/or out-of-equilibrium dynamics. The same extension-rate dependence is observed for lambda DNA (figure SB). Energy stored in the secondary structure of the unpeeled DNA strand In order to obtain a quantitative idea about the way the secondary structure formed in the unpeeled strand contributes to the observed hysteresis during strand reannealing, we calculated the energy of this secondary structure using MFOLD (18). This program calculates the energetically most favorable hybridization state of a single DNA strand. We used the following parameters: temperature 0 C, ionic buffer strength 50 mm NaCl. We followed the increase in the energy of the secondary structure during unpeeling (G tot(j)) in the 5 to 3 direction by increasing the length of the unpeeled strand in steps of 100 base pairs from j=0 to j final. Reannealing the segment between j 1 and j needs to overcome the energy barrier posed by the secondary structure in the unpeeled strand (figure B), which can be determined by: g j j ) = G ( j ) G ( ). (S10) ( 1 tot tot j1 1. J. Gore et al., DNA overwinds when stretched. Nature 44, (006).. Z. Bryant et al., Structural transitions and elasticity from torque measurements on DNA. Nature 44, (003). 3. J. van Mameren et al., Unraveling the structure of DNA during overstretching by using multicolor, single-molecule fluorescence imaging. Proc Natl Acad Sci U S A 106, (009). 4. C. H. Albrecht, G. Neuert, R. A. Lugmaier, H. E. Gaub, Molecular force balance measurements reveal that double-stranded DNA unbinds under force in rate-dependent pathways. Biophys. J.94, (008). 5. H. Clausen-Schaumann, M. Rief, C. Tolksdorf, H. E. Gaub, Mechanical stability of single DNA molecules. Biophys. J.78, (000). 6. C. P. Calderon, W. H. Chen, K. J. Lin, N. C. Harris, C. H. Kiang, Quantifying DNA melting transitions using single-molecule force spectroscopy. J. Phys. Condens. Matter 1 (009). 15

16 7. J. SantaLucia, A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proc Natl Acad Sci U S A 95, (1998). 8. J. F. Marko, Stretching must twist DNA. Europhys. Lett. 38, (1997). 9. R. D. Kamien, T. C. Lubensky, P. Nelson, C. S. Ohern, Direct determination of DNA twist-stretch coupling. Europhys. Lett. 38, 37-4 (1997). 10. J. F. Marko, DNA under high tension: Overstretching, undertwisting, and relaxation dynamics. Phys. Rev. E 57, (1998). 11. S. B. Smith, Y. Cui, C. Bustamante, Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules. Science 71, (1996). 1. M. D. Wang, H. Yin, R. Landick, J. Gelles, S. M. Block, Stretching DNA with optical tweezers. Biophys. J 7, (1997). 13. T. Odijk, Stiff Chains and Filaments under Tension. Macromolecules 8, (1995). 14. M. Y. Sheinin, M. D. Wang, Twist-stretch coupling and phase transition during DNA supercoiling. Phys. Chem. Chem. Phys. 11, (009). 15. U. Bockelmann, B. EssevazRoulet, F. Heslot, Molecular stick-slip motion revealed by opening DNA with piconewton forces. Phys. Rev. Lett. 79, (1997). 16. U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, F. Heslot, Unzipping DNA with optical tweezers: high sequence sensitivity and force flips. Biophys. J 8, (00). 17. U. Gerland, R. Bundschuh, T. Hwa, Force-induced denaturation of RNA. Biophys. J 81, (001). 18. M. Zuker, Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Res. 31, (003). 16