| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
* Physics Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801; and Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, Missouri 63110
Correspondence: Address reprint requests to Taekjip Ha, E-mail: tjha{at}uiuc.edu.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
N 70 nucleotides), which provide systematic constraints for testing theoretical models. Unlike in mechanical studies where available ssDNA conformations are averaged out during the time it takes to perform measurements, fluorescence lifetimes may act here as an internal clock that influences fluorescence signals depending on how fast the ssDNA conformations fluctuate. A reasonably good agreement could be obtained between our data and the worm-like chain model provided that limited relaxations of the ssDNA conformations occur within the fluorescence lifetime of the donor. The persistence length thus estimated ranges from 1.5 nm in 2 M NaCl to 3 nm in 25 mM NaCl. |
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
; Eisenberg and Felsenfeld, 1967; Inners and Felsenfeld, 1970) were hampered by the inability to obtain monodisperse samples. More recent studies of ssDNA flexibility have used a variety of experimental approaches including mechanical stretching of natural ssDNA (Maier et al., 2000; Smith et al., 1996), transient electric birefringence (Mills et al., 1999), fluorescence resonance energy transfer (FRET) (Deniz et al., 2001), fluorescence recovery after photobleaching (Tinland et al., 1997), thermal melting profiles of DNA hairpins (Kuznetsov et al., 2001), and atomic force microscopy (Rivetti et al., 1998). The above-mentioned measurements were made on both long (>>100 nucleotides) polydisperse sequences (Maier et al., 2000; Smith et al., 1996) and short (<100 nucleotides) monodisperse sequences (Deniz et al., 2001; Kuznetsov et al., 2001; Mills et al., 1999; Rivetti et al., 1998). The data were interpreted using flexible polymer models such as freely jointed chain (Flory, 1969) or worm-like chain (Kratky and Porod, 1949) models, yielding estimates of the persistence length. Although such models and their modified forms have proven useful for characterizing long ssDNA (Dessinges et al., 2002; Koch et al., 2002; Montanari and Mezard, 2001; Smith et al., 1996; Storm and Nelson, 2003; Zhang et al., 2001), as well as very long duplex DNA (Bustamante et al., 1994; Hagerman, 1988), their validity for describing the conformational statistics of short ssDNA where the chain length, unit base length, and persistence length are similar, has not been well established. Oligodeoxythymidylates (oligo-dT) do not have basepairing capabilities under the conditions used in our experiment (Saenger, 1984), and thus should provide a better example of a flexible polymer, and are widely used for studying ssDNA-protein interactions. In this work, we have used single-molecule FRET measurements of fluorescently labeled oligo-dT to examine the conformational flexibility of ssDNA over a wide range of NaCl concentrations (from 25 mM to 2 M) and chain lengths (10–70 nucleotides) to obtain a comprehensive set of data against which the applicability of various statistical models can be tested.
FRET between donor and acceptor fluorophores is widely used to examine the conformational properties of biological molecules to which they are attached (Selvin, 2000). FRET applied at the single-molecule level (Ha et al., 1996) provides a powerful means of observing the dynamic structural changes of biomolecules as well as subpopulations in a heterogeneous mixture (Brasselet et al., 2000; Deniz et al., 2000; McKinney et al., 2003; Rothwell et al., 2003; Schuler et al., 2002; Zhuang et al., 2000). The energy transfer efficiency, E, defined experimentally as the fraction of the excitation of the donor that results in the excitation of the acceptor, is related to the characteristic Förster distance, R0, and the distance, R, between the two fluorophores by
 | (1) |
We measured R0 experimentally and this allowed us to relate FRET measurements directly to the distance. The direct benefits of performing a single-molecule measurement include the ability to discriminate against inactive acceptor molecules (Deniz et al., 1999).
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
). Cy3 and Cy5 were incorporated in phosphoramidite forms and biotin was added as BiotinTEG CPG (all three from Glen Research, Sterling, VA) during automated synthesis. The DNA was gel purified and annealed at 1:1.5 ratio of Cy3:Cy5 strands in 10 
30 µM concentrations in 20 mM Tris, pH8.0, and 500 mM NaCl.
Fluorescence spectra
Fluorescence emission spectra were measured in Tris 12 20 mM (original 20 mM Tris buffer was diluted upon adding appropriate amount of 5 M NaCl solution, reaching 12 mM Tris for data obtained at 2 M NaCl). We independently confirmed that this range of Tris concentrations does not have detectable effects on the FRET data if [NaCl] > 100 mM), pH 8.0 at 24(±1)°C and the [NaCl] specified in the text using 532 nm excitation (Jobin Yvon, Edison, NJ). The donor quantum yield was measured relative to rhodamine 101 in ethanol. Absorption spectra were obtained using a Perkin-Elmer spectrophotometer (Shelton, CT) and fluorescence anisotropies were measured using an ISS fluorometer (Champaign, IL).
Single-molecule fluorescence
Single-molecule fluorescence data were taken at 24(±1)°C with a prism-type total internal reflection microscope (Funatsu et al., 1995) based on an inverted microscope (Olympus IX70) with 60x water objective (Olympus, Melville, NY) and an intensified CCD camera (Intensified Pentamax, Roper Scientific, Trenton, NJ). DNA was added at 10 pM to the sample cell coated by bovine serum albumin-biotin and streptavidin. Measurements were taken in a buffer of Tris 12 20 mM pH 8.0, containing an oxygen scavenging system (0.1 mg/ml glucose oxidase, 0.02 mg/ml catalase, 1% ß-mercaptoethanol, and 7% (w/w) ß-D-glucose), and [NaCl] between 25 mM and 2 M. The donor and acceptor emission were collected simultaneously using a 100-ms bin time by separating the two wavelengths with dichroic beam splitters (635DCLP, Chroma, Rockingham, VT) and redirecting the beams onto separate sides of the CCD face. 10 frames of data were averaged to yield single molecule donor and acceptor intensities, ID and IA. The experimental configuration results in three corrections that have been made to the raw data: a small background fluorescence signal, small contributions of the signal occur from direct excitation of the acceptor, and some donor fluorescence is detected in the acceptor channel (together typically accounting for 15% of the donor signal). These contributions were subtracted from the raw data to obtain a corrected value of E = IA/(IA + ID), where IA and ID are the corrected intensities of the sensitized emission of the acceptor and the donor emission, respectively (Ha et al., 1999). The correction process can yield negative values for IA or ID if FRET is very high or very low, respectively, which in turn can result in E values slightly >1 or <0.
Simulations
Metropolis Monte Carlo simulations (Metropolis et al., 1953) as described in the Results section were performed using MATLAB (Mathworks, Natick, MA) to compare the experimental data to the worm-like chain model. The probability distribution function of the end-to-end distance of a polymer as reported by Thirumalai and Ha (1998) was used to determine whether or not each randomly generated step in the simulation should be accepted.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
) only as a relative measure of FRET in bulk solution because of the presence of inactive acceptor species (see Fig. 3 A). Fig. 2 B shows that the values of increase steeply with [NaCl], saturating around 1 M NaCl. Also shown in Fig. 2 B are the total intensities, 
, which remain relatively constant (within 13%) for all [NaCl], reconfirming the anticorrelated nature of the fluorescence changes. These FRET changes are consistent with a reduction in the average end-to-end distance of the dT23 at higher [NaCl] as expected from additional Na+ binding to the dT23 and/or screening of electrostatic repulsion between the negative charges on the DNA backbone. However, if R0 were to vary with changes in the [NaCl], a change in FRET would be observed even without a conformational change in the molecule. R0 is defined as (Clegg, 1992),
 |
D is the quantum yield of the donor, J(
) is the spectral overlap between the donor's emission and the acceptor's absorption, n is the index of refraction of the medium, and 
is determined by the relative orientation of the two dipole moments.
|
|
), the effects of n were still taken into account when calculating D (Lakowicz, 1999). We assumed that 2 = 2/3 here to estimate the overall contribution of [NaCl] to R0. Because the value of R0 calculated using the measured values of D, n, and J at each [NaCl] ranged from 59 to 61 Å (only 3.4% change), we conclude that the uncertainties in these parameters are not significant enough to change R0, and the observed change in FRET is mostly due to a change in distance, R. The assumption of 2 = 2/3 is strictly valid only if the fluorophores freely rotate much more rapidly than the fluorescence lifetimes, hence, it is only an approximation in our studies. Although these control experiments were done for dT23 only, the conclusion is likely to hold for other ssDNA molecules because the local environment of each dye is expected to be similar regardless of the tail length.
Single-molecule fluorescence
To estimate absolute values of the FRET efficiency, E, and to discriminate against any subpopulation of DNA molecules without active acceptors, we performed single-molecule FRET measurements. Fig. 3 A shows three representative histogram plots of data for dT17, dT27, and dT40 in 200 mM NaCl. The values of E that we report were calculated by fitting the second peak to a Gaussian distribution and finding the center. The first peak centered at zero FRET is due to a population of DNA molecules containing donors, but inactive acceptors (Deniz et al., 1999). The second peak shifts to higher E values for shorter tails. Interestingly, the presence of the donor-only subpopulation serves as a control from which we can calculate the leakage of the donor signal to the acceptor detector channel. It also provides an alternative method of measuring E via donor quenching (by using E = 1 - ID / IDo, where ID and IDo are average intensities of donor for each population with and without the active acceptor, respectively).
Fig. 3 B shows the average E vs. N obtained at several [NaCl]. The average E was determined for the two E values obtained using the two different methods described above. The two methods are in good agreement with each other with the largest difference being 10%. The average E values along with their relative errors are given in Table 1. Because the properties of the dyes do not change significantly with [NaCl], these FRET changes mainly reflect the average change in distance between the two ends of the (dT)N.
Estimating the contour length of ssDNA
Before making comparison to theoretical models, we need to estimate the unit length of each base b0 so that the entire length of a fully stretched ssDNA of N bases, or the contour length L, is given by L = b0N. To estimate b0, we used the average of distances between adjacent phosphorus atoms determined from five crystal structures of ssDNA-protein complexes and obtained b0 = 6.3 (±0.8) Å (Fig.4 A). The protein data bank identifications are 1A1V, 1UAA, 1EYG, 1J4W, and 1JMC corresponding to the structures of HCV NS3 helicase bound to oligo-dU (Kim et al., 1998), Escherichia coli Rep helicase bound to oligo-dT (Korolev et al., 1997), E. coli SSDNA binding protein bound to oligo-dT (Raghunathan et al., 2000), Fbp protein bound to mixed sequence ssDNA (Braddock et al., 2002), and human RPA bound to poly-dC (Bochkarev et al., 1997). Although it is possible that interactions with the proteins can significantly distort the dimension of each nucleotide, 6.3 Å is consistent with the interphosphate distances of ssDNA that can range between 5.9 Å and 7 Å depending on the sugar puckering (Olson, 1975; Saenger, 1984). The 6.3 Å we used is also close to 7 Å used to fit force versus extension curve by Smith et al. (1996) and is consistent with 5–7 Å estimated by Mills et al. (1999).
|
derived an analytical expression for the probability distribution p(r) of the end-to-end distance of a polymer that obeys the worm-like chain model.
 |
 |
Because no time-dependent FRET changes were observed with time resolutions down to 8 ms (data not shown), we can assume that the dynamic motion of the ssDNA is fully equilibrated within 1 s averaging time used for the single-molecule FRET histograms. If the ssDNA is rigid and immobile within the fluorescence lifetime of the donor, the time-averaged FRET efficiency can be obtained by
 |
The other extreme case entails conformational fluctuations rapid enough to be averaged within the fluorescence lifetime of the donor. The instantaneous energy transfer rate, kr(R0/R)6 where kr is the fluorescence decay rate of the donor in the absence of energy transfer, becomes much larger than kr if the two dyes are very close to each other (R << R0). Therefore, even if the probability of close approach is small, sufficiently fast conformational fluctuations will allow the energy transfer to occur before the donor decay and would yield FRET of 100% regardless of N or salt concentrations. This is clearly not the case in our studies. Nevertheless, there may be limited, but significant sampling of the phase space via intramolecular motions within the donor lifetime and this effect can influence FRET.
To compare our data to the worm-like chain model, we performed Metropolis Monte-Carlo simulations (Metropolis et al., 1953) of the end-to-end distance (R = rL) time trajectories. R is allowed to undergo a biased random walk between 0 and L taking steps of size 
(varied between 0 and 1.2 nm) every one-hundredth of the donor lifetime. Because the lifetime of Cy3 is 1 ns, this corresponds to a random walk in the radial coordinate R with diffusion coefficient ranging from 0 to 7 x 10-4 cm2/s. We use the probability function p(r) as the weighting function that determines whether or not each randomly generated step is accepted. For each step of the random walk, the energy transfer and donor fluorescence decay were allowed to occur with rates of kr(R0/R)6 and kr respectively, and the random walk continued until energy transfer or donor fluorescence decay occurred. Three-thousand such random walks were performed and energy transfer efficiency Esim was determined as the fraction of the random walks that ended with energy transfer.
For each NaCl concentration, the persistence length was assigned so that the root mean square deviation between the experimental E and Esim, 
, was minimized. Here the summation is over all seven values of ssDNA length N. This process was performed for various values of the random walk step size , and the values of 
averaged over all NaCl concentrations is shown in Fig. 4 B as a function of . The deviation is minimized at = 0.55 nm and grows if is increased or decreased. Therefore, we fixed at 0.55 nm and obtained the persistent length for each NaCl concentration by minimizing . The persistence length thus obtained decreased from 3 nm at low salt (25 mM NaCl) to 1.5 nm at high salt (2 M NaCl) (Fig. 5). Corresponding Esim vs. N curves are shown in Fig. 3 B overlaid with the experimental E values.
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
; Montanari and Mezard, 2001; Zhang et al., 2001). These mechanical measurements were performed on the timescales of milliseconds and seconds during which the available conformational space of the DNA is likely to be fully sampled. In contrast, fluorescence measurements have an additional internal clock, the radiative lifetime of the donor, and fluorescence signals can be influenced depending on how quickly the relative distance and orientation between the fluorophores fluctuate compared to the donor lifetime. Therefore we incorporated limited relaxations of the ssDNA conformation into the worm-like chain model to compare with the experimental data.
The best agreement could be obtained with the random walk step size of 0.55 nm with the stepping time of 0.01 ns. This corresponds to a diffusion coefficient of 3 x 10-4 cm2/s (= [0.55 nm]2/2/[0.01 ns]), and simulations assuming no diffusional motion during the donor lifetime or much faster diffusional motion yielded worse agreements. This diffusion coefficient could be an overestimate, however; additional relaxation processes may exist. For instance, it is likely that some relative rotations occur between the donor and acceptor during the fluorescence lifetime because the measured fluorescence anisotropy values are <0.3. If relative angles that yield large 2 values are reached frequently, this could have an analogous effect as having very small distances, providing an additional source for fluorescence signal averaging.
Overall, the worm-like chain model can adequately describe our fluorescence data if it is assumed that some relaxation mechanisms are operating during the donor lifetime, be it diffusional motion of the ssDNA itself or fluorophores' rotational motion. The persistence length thus estimated changed by a factor of two from 3 nm to 1.5 nm when NaCl concentration was varied from 2 M to 25 mM. It is probable that the screening of the electrostatic repulsion between the negatively charged phosphate groups is responsible for the increased flexibility at higher salt concentrations.
There have been three previous studies that estimated the persistence length of oligo-dT. Rivettie et al. (1998) performed atomic force microscope imaging of DNA molecules with oligo-dT gaps up to (dT)20. They estimated the persistence length of 1.3 nm for gaps up to five nucleotides and the persistence length between 2 and 4 nm for larger gaps. Mills et al. (1999) estimated the persistence length in the range of 2 3 nm from transient electric birefringence studies of two DNA duplexes connected by an oligo-dT gap (12 or 24 mer) in 3 8 mM Mg2+ at 4°C. Kuznetsov et al. (2001) used equilibrium DNA hairpin melting profiles to obtain the persistence length of 1.4 nm in 100 mM NaCl. Therefore, our results (1.5 3 nm) reasonably agree with previous estimates that utilized different techniques.
In a previous single-molecule FRET study by Deniz et al. (2001) it was suggested that oligo-dT in [NaCl] 
100 mM is more compact than an ideal polymer. This was based on the observation that R2/N was a decreasing function of N. In an ideal polymer, 
R2
scales linearly with N hence R2/N should be a constant. Indeed, if we calculate R using Eq. 1 and experimentally determined E values, our data also show that R2/N is a decreasing function of N (data not shown). However, this procedure is unlikely to be valid because what is being averaged in FRET measurements is not R2 and the apparent deviation from the ideal polymer behavior in their analysis may have originated from the way the data were compared to the theoretical model.
|
CONCLUSION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
ACKNOWLEDGEMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
This work was funded by the National Institutes of Health (T.M.L.), the NIH, National Science Foundation, Research Corporation, and Searle Scholars Award (T.H.), and NIH Institutional NRSA in Molecular Biophysics (5T32GM08276, M.C.M).
Submitted on April 18, 2003; accepted for publication November 24, 2003.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Bochkarev, A., R. A. Pfuetzner, A. M. Edwards, and L. Frappier. 1997. Structure of the single-stranded-DNA-binding domain of replication protein A bound to DNA. Nature. 385:176–181.[Medline]
Braddock, D. T., J. M. Louis, J. L. Baber, D. Levens, and G. M. Clore. 2002. Structure and dynamics of KH domains from FBP bound to single-stranded DNA. Nature. 415:1051–1056.[Medline]
Brasselet, S., E. J. G. Peterman, A. Miyawaki, and W. E. Moerner. 2000. Single-molecule fluorescence resonant energy transfer in calcium concentration dependent cameleon. J. Phys. Chem. B. 104:3676–3682.
Bustamante, C., J. F. Marko, E. D. Siggia, and S. Smith. 1994. Entropic elasticity of lambda-phage DNA. Science. 265:1599–1600.
Cheng, W., J. Hsieh, K. M. Brendza, and T. M. Lohman. 2001. E. Coli Rep oligomers are required to initiate DNA unwinding in vitro. J. Mol. Biol. 310:327–350.[Medline]
Clegg, R. M. 1992. Fluorescence resonance energy transfer and nucleic acids. Methods Enzymol. 211:353–388.[Medline]
Deniz, A. A., M. Dahan, J. R. Grunwell, T. J. Ha, A. E. Faulhaber, D. S. Chemla, S. Weiss, and P. G. Schultz. 1999. Single-pair fluorescence resonance energy transfer on freely diffusing molecules: observation of Förster distance dependence and subpopulations. Proc. Natl. Acad. Sci. USA. 96:3670–3675.
Deniz, A. A., T. A. Laurence, G. S. Beligere, M. Dahan, A. B. Martin, D. S. Chemla, P. E. Dawson, P. G. Schultz, and S. Weiss. 2000. Single-molecule protein folding: diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2. Proc. Natl. Acad. Sci. USA. 97:5179–5184.
Deniz, A. A., T. A. Laurence, M. Dahan, D. S. Chemla, P. G. Schultz, and S. Weiss. 2001. Ratiometric single-molecule studies of freely diffusing biomolecules. Annu. Rev. Phys. Chem. 52:233–253 [Review].[Medline]
Dessinges, M. N., B. Maier, Y. Zhang, M. Peliti, D. Bensimon, and V. Croquette. 2002. Stretching single stranded DNA, a model polyelectrolyte. Phys. Rev. Lett. 89:248102.[Medline]
Eisenberg, H., and G. Felsenfeld. 1967. Studies of the temperature-dependent conformation and phase separation of polyriboadenylic acid solutions at neutral pH. J. Mol. Biol. 30:17–37.[Medline]
Flory, P. J. 1969. Statistical Mechanics of Chain Molecules. Interscience Publishers, New York, NY.
Funatsu, T., Y. Harada, M. Tokunaga, K. Saito, and T. Yanagida. 1995. Imaging of single fluorescent molecules and individual ATP turnovers by single myosin molecules in aqueous solution. Nature. 374:555–559.[Medline]
Ha, T., T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss. 1996. Probing the interaction between two single molecules: fluorescence resonance energy transfer between a single donor and a single acceptor. Proc. Natl. Acad. Sci. USA. 93:6264–6268.
Ha, T. J., A. Y. Ting, J. Liang, W. B. Caldwell, A. A. Deniz, D. S. Chemla, P. G. Schultz, and S. Weiss. 1999. Single-molecule fluorescence spectroscopy of enzyme conformational dynamics and cleavage mechanism. Proc. Natl. Acad. Sci. USA. 96:893–898.
Hagerman, P. J. 1988. Flexibility of DNA. Annu. Rev. Biophys. Biophys. Chem. 17:265–286.[Medline]
Inners, L. D., and G. Felsenfeld. 1970. Conformation of polyribouridylic acid in solution. J. Mol. Biol. 50:373–389.[Medline]
Kim, J. L., K. A. Morgenstern, J. P. Griffith, M. D. Dwyer, J. A. Thomson, M. A. Murcko, C. Lin, and P. R. Caron. 1998. Hepatitis C virus Ns3 RNA helicase domain with a bound oligonucleotide: the crystal structure provides insights into the mode of unwinding. Structure. 6:89–100.[Medline]
Koch, S. J., A. Shundrovsky, B. C. Jantzen, and M. D. Wang. 2002. Probing protein-DNA interactions by unzipping a single DNA double helix. Biophys. J. 83:1098–1105.
Korolev, S., J. Hsieh, G. H. Gauss, T. M. Lohman, and G. Waksman. 1997. Major domain swiveling revealed by the crystal structures of complexes of E-Coli Rep helicase bound to single-stranded DNA and ATP. Cell. 90:635–647.[Medline]
Kratky, O., and G. Porod. 1949. Recl. Trav. Chim. 68:1106–1122.
Kuznetsov, S. V., Y. Q. Shen, A. S. Benight, and A. Ansari. 2001. A semiflexible polymer model applied to loop formation in DNA hairpins. Biophys. J. 81:2864–2875.
Lakowicz, J. R. 1999. Principles of Fluorescence Spectroscopy. Kluwer Academic/Plenum, New York, NY.
Maier, B., D. Bensimon, and V. Croquette. 2000. Replication by a single DNA polymerase of a stretched single-stranded DNA. Proc. Natl. Acad. Sci. USA. 97:12002–12007.
McKinney, S. A., A. C. Declais, D. M. J. Lilley, and T. Ha. 2003. Structural dynamics of individual Holliday junctions. Nat. Struct. Biol. 10:93–97.[Medline]
Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Tell. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21:1087–1092.
Mills, J. B., E. Vacano, and P. J. Hagerman. 1999. Flexibility of single-stranded DNA: use of gapped duplex helices to determine the persistence lengths of poly(dT) and poly(dA). J. Mol. Biol. 285:245–257.[Medline]
Montanari, A., and M. Mezard. 2001. Hairpin formation and elongation of biomolecules. Phys. Rev. Lett. 86:2178–2181.[Medline]
Olson, W. K. 1975. Configurational statistics of polynucleotide chains. A single virtual bond treatment. Macromolecules. 8:272–275.[Medline]
Raghunathan, S., A. G. Kozlov, T. M. Lohman, and G. Waksman. 2000. Structure of the DNA binding domain of E. coli SSB bound to ssDNA. Nat. Struct. Biol. 7:648–652.[Medline]
Rivetti, C., C. Walker, and C. Bustamante. 1998. Polymer chain statistics and conformational analysis of DNA molecules with bends or sections of different flexibility. J. Mol. Biol. 280:41–59.[Medline]
Rothwell, P. J., S. Berger, O. Kensch, S. Felekyan, M. Antonik, B. M. Wohrl, T. Restle, R. S. Goody, and C. A. Seidel. 2003. Multiparameter single-molecule fluorescence spectroscopy reveals heterogeneity of HIV-1 reverse transcriptase:primer/template complexes. Proc. Natl. Acad. Sci. USA. 100:1655–1660.
Saenger, W. 1984. Principles of Nucleic Acid Structure. Springer-Verlag, New York, NY.
Schuler, B., E. A. Lipman, and W. A. Eaton. 2002. Probing the free-energy surface for protein folding with single-molecule fluorescence spectroscopy. Nature. 419:743–747.[Medline]
Selvin, P. R. 2000. The renaissance of fluorescence resonance energy transfer. Nat. Struct. Biol. 7:730–734 [Review].[Medline]
Smith, S. B., Y. J. Cui, and C. Bustamante. 1996. Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules. Science. 271:795–799.[Abstract]
Storm, C., and P. C. Nelson. 2003. Theory of high-force DNA stretching and overstretching. Phys Rev E Stat Nonlin Soft Matter Phys. 67:051906.[Medline]
Thirumalai, D., and B. Y. Ha. 1998. Statistical mechanics of semiflexible chains. In Theoretical and Mathematical Models in Polymer Research. A. Grosberg, editor. Academic Press, San Diego, CA. 1–35.
Tinland, B., A. Pluen, J. Sturm, and G. Weill. 1997. Persistence length of single-stranded DNA. Macromolecules. 30:5763–5765.
Weast, R. C. 1972. CRC Handbook of Chemistry and Physics. R. C. Weast, editor. Chemical Rubber Co., Cleveland, Ohio.
Zhang, Y., H. Zhou, and Z. C. Ou-Yang. 2001. Stretching single-stranded DNA: interplay of electrostatic, basepairing, and basepair stacking interactions. Biophys. J. 81:1133–1143.
Zhuang, X. W., L. E. Bartley, H. P. Babcock, R. Russell, T. J. Ha, D. Herschlag, and S. Chu. 2000. A single-molecule study of RNA catalysis and folding. Science. 288:2048–2051.
This article has been cited by other articles:
 |
|
 |
|
  S. V. Kuznetsov, C.-C. Ren, S. A. Woodson, and A. Ansari Loop dependence of the stability and dynamics of nucleic acid hairpins Nucleic Acids Res., March 27, 2008; 36(4): 1098 - 1112. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 P. L. Biancaniello, A. J. Kim, and J. C. Crocker Long-Time Stretched Exponential Kinetics in Single DNA Duplex Dissociation Biophys. J., February 1, 2008; 94(3): 891 - 896. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Doose, H. Barsch, and M. Sauer Polymer Properties of Polythymine as Revealed by Translational Diffusion Biophys. J., August 15, 2007; 93(4): 1224 - 1234. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
C. Yuan, E. Rhoades, X. W. Lou, and L. A. Archer Spontaneous sharp bending of DNA: role of melting bubbles Nucleic Acids Res., September 11, 2006; 34(16): 4554 - 4560. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. N. Nedelcheva-Veleva, D. B. Krastev, and S. S. Stoynov Coordination of DNA synthesis and replicative unwinding by the S-phase checkpoint pathways Nucleic Acids Res., September 10, 2006; 34(15): 4138 - 4146. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Newby Lambert, E. Vocker, S. Blumberg, S. Redemann, A. Gajraj, J.-C. Meiners, and N. G. Walter Mg2+-Induced Compaction of Single RNA Molecules Monitored by Tethered Particle Microscopy Biophys. J., May 15, 2006; 90(10): 3672 - 3685. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. T. Woodside, W. M. Behnke-Parks, K. Larizadeh, K. Travers, D. Herschlag, and S. M. Block Nanomechanical measurements of the sequence-dependent folding landscapes of single nucleic acid hairpins PNAS, April 18, 2006; 103(16): 6190 - 6195. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
X. Liang, H. Kuhn, and M. D. Frank-Kamenetskii Monitoring Single-Stranded DNA Secondary Structure Formation by Determining the Topological State of DNA Catenanes Biophys. J., April 15, 2006; 90(8): 2877 - 2889. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
L. Moiseev, M. S. Unlu, A. K. Swan, B. B. Goldberg, and C. R. Cantor DNA conformation on surfaces measured by fluorescence self-interference PNAS, February 21, 2006; 103(8): 2623 - 2628. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Kim, S. Doose, H. Neuweiler, and M. Sauer The initial step of DNA hairpin folding: a kinetic analysis using fluorescence correlation spectroscopy. Nucleic Acids Res., January 1, 2006; 34(9): 2516 - 2527. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Y. Lee, B. Okumus, D. S. Kim, and T. Ha Extreme conformational diversity in human telomeric DNA PNAS, December 27, 2005; 102(52): 18938 - 18943. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. A. Laurence, X. Kong, M. Jager, and S. Weiss Probing structural heterogeneities and fluctuations of nucleic acids and denatured proteins PNAS, November 29, 2005; 102(48): 17348 - 17353. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Magee and J. Warwicker Simulation of non-specific protein-mRNA interactions Nucleic Acids Res., November 27, 2005; 33(21): 6694 - 6699. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Q. Du, M. Vologodskaia, H. Kuhn, M. Frank-Kamenetskii, and A. Vologodskii Gapped DNA and Cyclization of Short DNA Fragments Biophys. J., June 1, 2005; 88(6): 4137 - 4145. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 J. B. Robbins, M. C. McKinney, C. E. Guzman, B. Sriratana, S. Fitz-Gibbon, T. Ha, and I. K. O. Cann The Euryarchaeota, Nature's Medium for Engineering of Single-stranded DNA-binding Proteins J. Biol. Chem., April 15, 2005; 280(15): 15325 - 15339. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
B. Okumus, T. J. Wilson, D. M. J. Lilley, and T. Ha Vesicle Encapsulation Studies Reveal that Single Molecule Ribozyme Heterogeneities Are Intrinsic Biophys. J., October 1, 2004; 87(4): 2798 - 2806. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Hohng, C. Joo, and T. Ha Single-Molecule Three-Color FRET Biophys. J., August 1, 2004; 87(2): 1328 - 1337. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||
