Single-particle tracking for DNA tether length monitoring
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《核酸研究医学期刊》
1 Institut de Pharmacologie et Biologie Structurale (UMR CNRS 5089), 205 route de Narbonne, 31077 Toulouse Cedex, France, 2 Laboratoire de Microbiologie et Génétique Moléculaire (UMR CNRS 5100), 118 route de Narbonne, 31062 Toulouse Cedex, France and 3 Laboratoire de Biologie Moléculaire Eucaryote (UMR CNRS 5099), 118 route de Narbonne, 31062 Toulouse Cedex, France
*To whom correspondence should be addressed. Tel: +33 5 61 17 59 39; Fax: +33 5 61 17 59 94; Email: laurence.salome@ipbs.fr
ABSTRACT
We describe a simple single-particle tracking approach for monitoring the length of DNA molecules in tethered particle motion experiments. In this method, the trajectory of a submicroscopic bead tethered by a DNA molecule to a glass surface is determined by videomicroscopy coupled to image analysis. The amplitude of motion of the bead is measured by the standard deviation of the distribution of successive positions of the bead in a given time interval. We were able to describe theoretically the variation of the equilibrium value of the amplitude of the bead motion with the DNA tether length for the entire applicable DNA length range (up to 3500 bp). The sensitivity of the approach was illustrated by the evidence obtained for conformational changes introduced into a Holliday junction by the binding of the Escherichia coli RuvA protein. An advantage of this method is that the trajectory of the tethered bead, rather than its averaged motion, is measured, allowing analysis of the conformational dynamics of DNA chains at the single-molecule level.
INTRODUCTION
The last decade has seen the opening of a new area in molecular and cellular biology with the development of techniques for manipulating and imaging single molecules in real time (1–3). In contrast with conventional biochemical techniques, which yield only information derived from population averages, these approaches give access to the dynamics of individual biomolecules, facilitating a clearer understanding of the molecular mechanisms involved in biological processes. Single-molecule approaches have been developed in many laboratories for investigation of a wide range of DNA machineries including chromatin fiber assembly (4), recombination (5) and transcription (6,7). Among the various experimental approaches available, the simplest is perhaps that known as tethered particle motion (TPM), first introduced by Schafer et al. in 1991 (8) to measure transcription elongation rate variations.
In the TPM approach, a microsphere is attached to the free end of a DNA molecule which has been immobilized by the other end to a glass surface. The Brownian motion of the microsphere is observed by video-enhanced optical microscopy. Changes in the DNA tether length are accompanied by changes in the amplitude of particle motion and can be measured by digital image analysis. This approach has been successfully applied to study transcript elongation by a single RNA polymerase molecule (8–11), and to analyze the kinetics of DNA looping by the lactose repressor protein (12) and DNA translocation by the RecBCD enzyme (13). In these TPM experiments, successive video frames from 0.5 to 4.8 s sequences were averaged, resulting in a blurred image of the bead whose diameter increases as the range of Brownian motion of the particle increases. The size of the blurred particle image was determined by fitting the intensity profile to an empirical shape function (8). The amplitude of Brownian motion was then calculated as the difference between the image size for a tethered particle and that for an immobile particle (9). Surprisingly, in spite of its conceptual simplicity and important informative potential, TPM has received very limited application to date.
We report here an alternative and more direct TPM approach in which, instead of averaging an image over time, the individual trajectories of the bead are measured. This single-particle tracking (SPT) method allows bead positions to be calculated with nanometer-scale precision on successive images obtained by differential interference contrast (DIC) videomicroscopy. The use of the standard deviation of the distribution of successive bead positions in a given time interval as a measure of the magnitude of the Brownian motion of the particle was validated by experiments carried out on double-stranded DNA molecules ranging from 276 to 3571 bp. The variation of the Brownian motion of the bead as a function of the DNA length was found to be linear up to a DNA length of 2400 bp consistently with the original time-averaged approach (9), and was interpreted by applying simple concepts of polymer theory.
One major advantage of the SPT method is that artifacts arising from particles linked to more than one tether or due to mechanical drift of the microscope stage can be eliminated simply by inspection of the bead trajectory. This method, coupled with algorithms pre-implemented in commonly available image analysis software, offers a simple and versatile approach for the TPM technique. As an illustration of the sensitivity of this approach, we have measured conformational changes introduced into a Holliday junction by binding of the Escherichia coli RuvA protein. Our results are consistent with previous demonstrations of RuvA- mediated unfolding of the Holliday junctions (14), detected here as an increase in the apparent length of the DNA tether.
MATERIALS AND METHODS
DNA templates and substrates
DNA substrates were obtained by PCR amplification from plasmid templates with a 5'-digoxigenin-modified forward primer and a 5'-biotin-labeled reversed primer (Eurogentec).
The fragment of 798 bp (positions 1064–1861) and both 2080 bp fragments (2080: 4625–1861, and 2080*: 1064–3146) were produced using pAPT72 (15) as a template. The fragments of 276, 991 and 1507 bp were produced using pBR322 (positions 1459–1735, 1381–2371 and 1381–2887, respectively). The fragments of 2264 and 3571 bp were produced using pFX288 (primers: biotin-5'-GAA ATG TTG AAT ACT CAT ACT CTT CC-3' and digoxigenin-5'-AGA GCG CAC GAG GGA GCT TC-3') and pFX293 (primers: biotin-5'-AAA GGC CGT AAT ATC CAG CTG AAC GGT CTG-3' and digoxigenin-5'-TAC CAC GAC GAT TTC CGG CAG TTT CTA CAC-3') respectively (kind gift from Dr F.-X. Barre and Dr C. Pérals, LMGM, Toulouse). The fragment of 2427 bp was produced using pFX346 (positions 3127–1648) (kind gift from Dr F.-X. Barre).
Holliday junctions (2 kb) were formed by 997 bp branch migration substrates. These substrates were prepared as described (16) by ligation of synthetic partial duplexes containing 20-nt single-stranded tails to the unique AvaI site of PCR-amplified fragments derived from pBR322 using a non-modified 20 nt forward primer (position 1381 with respect to the EcoRI site) and a reverse primer containing either digoxygenin or biotin at the 5' end (position 2371). A 3 bp heterologous sequence was introduced in one long arm of the junction in the vicinity of the AvaI site to trap the junctions in a short (27 bp) and defined stretch of DNA between the origin and the sequence heterology (17). RuvA was expressed and purified as described (18).
Preparation of the microscope observation chambers
Two alternative buffers were used: 20 mM HEPES pH 7.5, 100 mM KCl, 10 mM MgCl2, 2% glycerol, 2 mM dithiothreitol (DTT), 10% dimethylsulfoxide (DMSO), 20 μg/ml bovine serum albumin (BSA) and 1 mg/ml dephosphorylated -casein (Sigma) for the 798, 2080, 2080* and 2427 bp substrates, and 2.5 mM Tris–acetate pH 8, 10 mM MgCl2, 0.2 mM DTT and 0.1 mg/ml dephosphorylated -casein for the 276, 991, 1507 and 3571 bp substrates. The 2264 bp DNA substrate was analysed in both buffers.
The chambers (50 μl volume) were built by mounting coverslips on microscope slides with double-faced adhesive tape. They were first treated with 20 μg/ml polyclonal anti-digoxigenin antibody (Roche) in PBS for 20 min at 4°C. To reduce non-specific DNA binding to the glass, the chambers were then incubated with the buffer containing dephosphorylated -casein for 1 h at 4°C.
A further incubation of 1 h at room temperature in buffer with DNA (3.4 x 10–11 M) modified at one end with digoxigenin and at the other with biotin was followed by extensive washing with buffer. Finally, the DNA molecules attached by their digoxigenin ends were coupled to 0.2 μm diameter neutravidin-labeled microspheres (Molecular Probes) at a final concentration of 0.003% (v/v) by incubation for 20 min at room temperature.
Single-particle tracking experiments
Imaging of the tethered beads was performed by video-enhanced differential interference contrast microscopy at room temperature (22 ± 2°C). The microscope (Axioplan II, Zeiss) was equipped with a 63x objective (NA = 1.4) (Plan-Neofluar) and an intermediate lens providing an additional 4x magnification. Images were recorded with a CCD camera (C2400-75i, Hamamatsu) at a video rate of 25 frames/s on a numerical videotape recorder (DSR30P, Sony) after real-time processing (Argus 20, Hamamatsu) for background subtraction and contrast enhancement. After digitization using a real-time acquisition board (IEC, France), the images were analyzed using in-house software written using Optimas (6.2 version, Media Cybernetics). The DIC bead image appears as a juxtaposition of white and dark half-circles. For each sequence of images, the position of the bead was automatically calculated for each image as the grey-value-weighted center of mass of the dark portion of the bead. The beads whose trajectories were <90% complete (i.e. with overall gaps in the trajectory of >10%) were rejected from further analysis. Since the gaps arise principally from a loss of focus, this limits the maximal length of DNA fragments to which the approach can be applied. We estimate that this upper limit is 3500 bp.
To estimate the accuracy of the bead position measurements, several sequences of images of beads non-specifically immobilized at the surface of untreated coverslips were analyzed. For 4 s periods (100 images), the standard deviations of the bead coordinates were found to be x = y = 8.7 ± 2.5 nm.
Results AND DISCUSSION
Experimental constraints
To ensure the validity of the measurements, particular attention must be paid to several potential sources of artifacts which deform the apparent movement of the bead. Attachment of one bead to more than one DNA molecule would result in underestimating DNA length. The occurrence of multiply attached beads is inherent to the mode of preparation of the chambers and cannot be entirely excluded experimentally. This is because a minimal concentration of DNA is necessary during the incubation to obtain a surface density of tethered beads compatible with an acceptable rate of data acquisition. If the bead is attached to a single DNA molecule, the trajectory is expected to be delineated by a circle as shown in Figure 1A. If more than one DNA molecule is linked to the bead, the envelope of its trajectory will be elliptical to a degree which will depend on the distance between the attachment points of the DNA molecules on the coverslip (Fig. 1B). A similar deformation of the trajectory would be generated by a mechanical drift of the microscope. These cases can simply be distinguished by computing the time-averaged particle positions over successive 4 s intervals. These should be stationary for multiply attached beads (Fig. 1B) or in the case of other constraints, but would be expected to move if caused by a microscope drift.
Figure 1. Coordinates (x,y) of beads tracked during 2 min undergoing a Brownian motion tethered to a glass support by DNA molecules as shown in the schemes: (a) a single attachment leading to a circular shape of the plot; (b) a multiple (double) attachment leading to a deformation of the plot. The green dots are the positions measured at 40 ms intervals and the black dots correspond to their time average over consecutive 4 s intervals.
In this study, after any necessary corrections for mechanical drift, beads exhibiting >10% difference between the equatorial and polar radius of the envelope of the trajectory were considered to be artifactual and were excluded from the final results. Such events represented 40% of the recordings. It should be stressed that if the bead is tethered to several closely grouped DNA molecules, little or no deformation of the trajectory would be detectable and such events would be recorded as trajectories of single DNA tethered beads. Nevertheless, owing to steric hindrance, the probability of such a configuration is expected to be low and should not have an important effect on the measurement of fixed DNA lengths.
Measurement of the amplitude of the Brownian motion of the tethered beads
Once the trajectory of a tethered bead is established, the histograms of the positions x or y fluctuating with time can be determined. Ideally, the distribution of the tethered bead positions should reflect that of the end-to-end distance of the DNA molecule which is expected to be Gaussian for large DNA molecules of many persistence lengths lp . For linear DNA molecules of various lengths ranging from 2lp to 14lp (276, 798 and 2080 bp), the experimental distributions of the centered x positions (abcissa relative to the centre of mass) were found to deviate from Gaussian curves (Fig. 2) around the tails. The complete calculation of the function distribution is beyond the scope of the present study and would need to take into account the statistical mechanics of semiflexible polymers and excluded volume effects associated with the size of the bead.
Figure 2. Distribution of the centered x positions (abcissa relative to the center of mass) (nm) of the bead (average of 10 bead trajectories of 1 min duration) for different DNA tether lengths: 2080 bp (open diamonds), 798 bp (filled squares) and 276 bp (open circles). The lines give the Gaussian fit for the distributions. The error bars correspond to the standard deviation of the measurements. The distribution interval is 10 nm for the 276 bp DNA substrate and 20 nm otherwise.
The most straightforward manner of quantifying the bead motion is to calculate the standard deviation of its position distribution. The time interval chosen for these measurements is important. It is expected that the amplitude of motion A, calculated in this way, first increases with the number of successive images used for its calculation and then reaches a saturating value beyond the equilibriation time. This corresponds to the time required for the bead to explore the domain within which it is confined by the DNA tether (or for the DNA molecule to assume all its possible conformations) and increases as a function of DNA length. To unequivocally relate the amplitude of motion to the number of base pairs in a given DNA length range it must be measured over a time interval greater than or equal to the largest equilibriation time. In order to determine the time interval to be chosen for the applicable tether length range of the technique (i.e. the tether length range for which the bead remains within the depth of focus of the microscope objective), the calculation was performed for increasing successive numbers of images and DNA molecules of different lengths (276, 798, 2080 and 3571 bp). The amplitudes of motion averaged from the values calculated for consecutive time intervals along 1 min duration trajectories for 10 distinct beads are shown in Figure 3. For the DNA molecules considered here, the largest equilibriation time was found to be 4 s which corresponds to 100 images.
Figure 3. Amplitude of motion A of the bead (average of 10 bead trajectories of 1 min duration) as a function of the time interval for various DNA lengths: 3571 bp (filled triangles), 2080 bp (open diamonds), 798 bp (filled squares) and 276 bp (open circles). The error bars correspond to the averaged standard deviation of the measurements. The dotted lines connecting the points were fitted by eye. The horizontal lines give the asymptotic value Aeq reached at long term.
In the following, we systematically used the standard deviation of the bead positions over 4 s as a measurement of its equilibrium amplitude of motion Aeq.
Variation of the averaged equilibrium amplitude of bead motion with the DNA tether length
DNA molecules undergo conformational fluctuations. These result in fluctuations of the amplitude of tethered bead motion with time. An accurate measurement of the average of the bead motion for a DNA molecule of given length requires a large number of determinations to establish statistical significance. Ideally, if the system is ergodic, accumulating a long trajectory of a single DNA molecule should be equivalent to measuring shorter trajectories of multiple DNA molecules. However, because of a possible variability in the total length of the tether due to possible conformational differences at the attachment points of the DNA molecule, we accumulated 1- or 2-min trajectories of 20–40 different beads for DNA molecules of each length. The histograms of the distribution of the equilibrium amplitudes of bead motion Aeq measured for 276, 798, 2080 and 3571 bp DNA molecules are shown in Figure 4. As expected, the distributions are Gaussian and the fit by the corresponding equation allows determination of the mean value eq, the standard error of the mean and the standard deviation of the amplitude of motion. The values found for each DNA molecule are presented in Table 1. Note that in order to ascertain possible bias in the measurements due to non-specific adsorption of the DNA tether to the coated glass, we repeated the series of measurements for the 2080 bp DNA after having incubated the observation chamber with a non-specific competitor DNA fragment prior to the attachment of the DNA molecules. This operation had no effect on the final results (data not shown).
Figure 4. Relative frequency distribution of the equilibrium amplitude of motion Aeq (see text) for various DNA lengths: 3571 bp (filled triangles), 2080 bp (open diamonds), 798 bp (filled squares) and 276 bp (open circles). The lines give the Gaussian fits for the distributions.
Table 1. Mean values, standard errors (SE) and standard deviations of the equilibrium amplitudes of motion determined by a Gaussian fit of their distribution for various DNA molecules
We note that the measured motion amplitude of beads immobilized at the microscope slide surface in the absence of DNA is larger than that obtained for beads immobilized on an uncoated glass surface (see Materials and Methods). This can probably be attributed to the antibody coating which would lead to a cushioning effect and to a less efficient immobilization.
The plot of the observed averaged amplitude of motion eq as a function of the DNA length or number of base pairs l is presented in Figure 5. The extent of displacement of the bead is expected to be proportional to the gyration radius R of the DNA molecule:
Figure 5. Variation of the averaged equilibrium amplitude of motion eq (see text) of a tethered bead with the length of the DNA tether. The error bars correspond to the standard deviation associated to the mean value. The solid line is the fit by the theoretical relationships eq l in the rigid rod regime (gray shaded region) and eq l3/5 in the flexible polymer regime (see text). The slope of the dotted line is equal to 0.061 ± 0.003 nm/bp.
eq R
For short chain lengths, of the order of or less than the persistence length lp, the DNA chain behaves as a rigid rod and
R l
For larger chain lengths, the radius is given by the following relationship established by Flory (20) for a polymer in a good solvent:
R N3/5
where N = l/lp is the number of statistical segments.
As illustrated in Figure 5, the experimental data are robustly described by the expected theoretical equations with a cross-over between the two regimes at 300 bp, i.e. 2lp.
This analysis of the variation of the tethered bead motion contrasts with that discussed in a previous study (9) in which a linear relationship between the bead motion and the DNA tether length was found. This discrepancy may be due to the more restricted DNA length range explored in this study. For DNA lengths up to 2400 bp, the variation of the bead motion observed here can be approximated by a straight line of slope 0.061 ± 0.003 nm/bp (see Fig. 5). This value is close to that found by Gelles and colleagues (9), indicating that the technique is extremely robust over a range of experimental conditions.
As shown in Table 1 for the 798 and 2080 bp DNA molecules, for a constant number of observed beads, the error of the mean value of the equilibrium amplitude of motion eq is smaller for the largest recorded time interval while the value of the mean itself is unchanged. Thus increasing the duration of observation of the beads allows measurement of the amplitude of DNA tethered bead motion with a very high precision. It should be stressed that this implies that the method enables detection of very small effective tether length variations on a given DNA molecule. On the other hand, discrimination between DNA molecules differing slightly in number of base pairs might be complicated by the influence of DNA sequence and base-pair distribution on the conformation of the molecule. This type of effect may explain the difference between the averaged amplitudes of motion observed for two DNA molecules of 2080 bp (cf. Table 1). It will be necessary to analyze these possible effects in detail.
An illustration of the application of the approach: unfolding of Holliday junctions by RuvA
To determine whether the technique is sufficiently sensitive to detect small length differences induced by conformational changes of the DNA tether, we chose to investigate the unfolding of a Holliday junction by the E.coli protein RuvA. The Holliday junction, the major intermediate of recombination, marks the exchange point between two recombining DNA molecules (21). Under physiological conditions, it adopts a so-called stacked X-structure which is characterized by coaxial pairwise stacking of duplex arms of the junction (14). In this structure, two conformational isomers can be formed, on the basis of which DNA strands are exchanged across the junction. The stacked X-structure introduces a sharp angle between two recombining DNA duplexes as determined by biochemical, biophysical and crystallographic studies (21,22). During homologous recombination in E.coli, the Holliday junctions are processed by coordinate action of the RuvA and RuvB proteins that promote rapid and unidirectional branch migration. To initiate branch migration, RuvA binds the Holliday junctions as a tetramer or double tetramer with high affinity and unfolds the junctions from the stacked X-structure into a square-planar conformation with four helical arms pointing out the corners of a square. The conformational change of the structure induced by RuvA facilitates the process of branch migration and is essential for homologous recombination and recombinational repair (21,23).
The Holliday junctions were designed to contain two short arms and two long arms. A 3 bp heterologous sequence was introduced in one long arm of the junction in the vicinity of the AvaI site (see Materials and Methods) to block spontaneous branch migration (17). Each long arm of the junction was labeled with either biotin or digoxigenin, permitting measurement of the Brownian motion of a bead tethered to an immobilized Holliday junction. The distribution of the amplitudes of motion measured in the absence and in the presence of RuvA are shown in Figure 6. The averaged equilibrium amplitudes of Brownian motion in the absence of RuvA were found to be asymmetrical, with a major peak at 126 ± 14 nm. This value approaches that expected for a linear DNA fragment of equivalent length (i.e. 1954 bp), calculated from the calibration curve as 136 ± 12 nm. A second minor peak was also detected at 165 ± 11 nm, which might be attributed to an alternative conformational isomer of the Holliday junctions (22). In the presence of 90 nM RuvA, the amplitude of Brownian motion increased to 155 ± 28 nm. This increase in the apparent length of the junction above the value found in the absence of protein is consistent with RuvA-mediated unfolding of the junctions into an open-square conformation (23) and therefore underlines the sensitivity of our experimental approach.
Figure 6. Unfolding of Holliday junctions in the presence of RuvA. Histograms for the amplitudes of Brownian motion of the beads tethered by 2-kb (1954 bp) Holliday junctions in the absence (open squares) or presence (filled diamonds) of RuvA collected from the 1 min tracking of 21 and 22 beads, respectively. The lines correspond to best fits for a double Gaussian distribution with maxima values of 126.1 ± 14.4 nm and 164.6 ± 11.3 nm (mean ± SD) in the absence of RuvA and a single Gaussian distribution with 155.4 ± 28.0 nm in the presence of RuvA. The schemes show the various conformations of the Holliday junctions supposed to correspond to the different populations.
Concluding remarks
The SPT technique was applied to the study of DNA tethered particle motion in a length range up to 3500 bp. Based on the simplest model for polymer conformations, a theoretical relationship for the observed variation of the tethered bead motion as a function of the number of DNA base pairs was observed over the entire DNA length range.
Besides the highly accurate information that this method can provide about the effective length of the DNA, we would like to emphasize its informative potential for the conformational dynamics of the DNA molecules as already stressed by Qian and Elson (24). Indeed, we were able to verify that over the whole DNA length range studied here the movement of the bead was dominated by the tether and not its own Brownian motion. Thus the study of the conformational dynamics of single DNA molecules is only limited by the temporal resolution of the measuring device. In the present work, the time interval needed to perform a measurement of the bead motion was fixed at 4 s but, depending on the biochemical processes under investigation, it can be shortened while retaining a precision sufficient to follow a change in the DNA tether length (see Fig. 3).
This approach opens the possibility of fine-scale kinetic analysis of biological processes such as DNA looping, branch migration of Holliday junctions and other protein-induced DNA conformational changes. This method is being used to study a number of processes of this type in our laboratories.
ACKNOWLEDGEMENTS
We thank D. Dean and N. Destainville for helpful discussions. L. Finzi and J. Gelles kindly provided invaluable details concerning the TPM technique. We are indebted to C. Loot for providing DNA samples, A. Martinez and S. Huet for performing initial experiments, F. Daumas for writing the data sorting software and A. Lopez for critically reading the manuscript. N.P. and C.D. were supported by grants from the Ministère de l’Education Nationale, de la Recherche et des Nouvelles Technologies. This work was funded by grants from the Centre National de la Recherche Scientifique (programme NanoObjet Individuel) and the Association pour la Recherche contre le Cancer.
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*To whom correspondence should be addressed. Tel: +33 5 61 17 59 39; Fax: +33 5 61 17 59 94; Email: laurence.salome@ipbs.fr
ABSTRACT
We describe a simple single-particle tracking approach for monitoring the length of DNA molecules in tethered particle motion experiments. In this method, the trajectory of a submicroscopic bead tethered by a DNA molecule to a glass surface is determined by videomicroscopy coupled to image analysis. The amplitude of motion of the bead is measured by the standard deviation of the distribution of successive positions of the bead in a given time interval. We were able to describe theoretically the variation of the equilibrium value of the amplitude of the bead motion with the DNA tether length for the entire applicable DNA length range (up to 3500 bp). The sensitivity of the approach was illustrated by the evidence obtained for conformational changes introduced into a Holliday junction by the binding of the Escherichia coli RuvA protein. An advantage of this method is that the trajectory of the tethered bead, rather than its averaged motion, is measured, allowing analysis of the conformational dynamics of DNA chains at the single-molecule level.
INTRODUCTION
The last decade has seen the opening of a new area in molecular and cellular biology with the development of techniques for manipulating and imaging single molecules in real time (1–3). In contrast with conventional biochemical techniques, which yield only information derived from population averages, these approaches give access to the dynamics of individual biomolecules, facilitating a clearer understanding of the molecular mechanisms involved in biological processes. Single-molecule approaches have been developed in many laboratories for investigation of a wide range of DNA machineries including chromatin fiber assembly (4), recombination (5) and transcription (6,7). Among the various experimental approaches available, the simplest is perhaps that known as tethered particle motion (TPM), first introduced by Schafer et al. in 1991 (8) to measure transcription elongation rate variations.
In the TPM approach, a microsphere is attached to the free end of a DNA molecule which has been immobilized by the other end to a glass surface. The Brownian motion of the microsphere is observed by video-enhanced optical microscopy. Changes in the DNA tether length are accompanied by changes in the amplitude of particle motion and can be measured by digital image analysis. This approach has been successfully applied to study transcript elongation by a single RNA polymerase molecule (8–11), and to analyze the kinetics of DNA looping by the lactose repressor protein (12) and DNA translocation by the RecBCD enzyme (13). In these TPM experiments, successive video frames from 0.5 to 4.8 s sequences were averaged, resulting in a blurred image of the bead whose diameter increases as the range of Brownian motion of the particle increases. The size of the blurred particle image was determined by fitting the intensity profile to an empirical shape function (8). The amplitude of Brownian motion was then calculated as the difference between the image size for a tethered particle and that for an immobile particle (9). Surprisingly, in spite of its conceptual simplicity and important informative potential, TPM has received very limited application to date.
We report here an alternative and more direct TPM approach in which, instead of averaging an image over time, the individual trajectories of the bead are measured. This single-particle tracking (SPT) method allows bead positions to be calculated with nanometer-scale precision on successive images obtained by differential interference contrast (DIC) videomicroscopy. The use of the standard deviation of the distribution of successive bead positions in a given time interval as a measure of the magnitude of the Brownian motion of the particle was validated by experiments carried out on double-stranded DNA molecules ranging from 276 to 3571 bp. The variation of the Brownian motion of the bead as a function of the DNA length was found to be linear up to a DNA length of 2400 bp consistently with the original time-averaged approach (9), and was interpreted by applying simple concepts of polymer theory.
One major advantage of the SPT method is that artifacts arising from particles linked to more than one tether or due to mechanical drift of the microscope stage can be eliminated simply by inspection of the bead trajectory. This method, coupled with algorithms pre-implemented in commonly available image analysis software, offers a simple and versatile approach for the TPM technique. As an illustration of the sensitivity of this approach, we have measured conformational changes introduced into a Holliday junction by binding of the Escherichia coli RuvA protein. Our results are consistent with previous demonstrations of RuvA- mediated unfolding of the Holliday junctions (14), detected here as an increase in the apparent length of the DNA tether.
MATERIALS AND METHODS
DNA templates and substrates
DNA substrates were obtained by PCR amplification from plasmid templates with a 5'-digoxigenin-modified forward primer and a 5'-biotin-labeled reversed primer (Eurogentec).
The fragment of 798 bp (positions 1064–1861) and both 2080 bp fragments (2080: 4625–1861, and 2080*: 1064–3146) were produced using pAPT72 (15) as a template. The fragments of 276, 991 and 1507 bp were produced using pBR322 (positions 1459–1735, 1381–2371 and 1381–2887, respectively). The fragments of 2264 and 3571 bp were produced using pFX288 (primers: biotin-5'-GAA ATG TTG AAT ACT CAT ACT CTT CC-3' and digoxigenin-5'-AGA GCG CAC GAG GGA GCT TC-3') and pFX293 (primers: biotin-5'-AAA GGC CGT AAT ATC CAG CTG AAC GGT CTG-3' and digoxigenin-5'-TAC CAC GAC GAT TTC CGG CAG TTT CTA CAC-3') respectively (kind gift from Dr F.-X. Barre and Dr C. Pérals, LMGM, Toulouse). The fragment of 2427 bp was produced using pFX346 (positions 3127–1648) (kind gift from Dr F.-X. Barre).
Holliday junctions (2 kb) were formed by 997 bp branch migration substrates. These substrates were prepared as described (16) by ligation of synthetic partial duplexes containing 20-nt single-stranded tails to the unique AvaI site of PCR-amplified fragments derived from pBR322 using a non-modified 20 nt forward primer (position 1381 with respect to the EcoRI site) and a reverse primer containing either digoxygenin or biotin at the 5' end (position 2371). A 3 bp heterologous sequence was introduced in one long arm of the junction in the vicinity of the AvaI site to trap the junctions in a short (27 bp) and defined stretch of DNA between the origin and the sequence heterology (17). RuvA was expressed and purified as described (18).
Preparation of the microscope observation chambers
Two alternative buffers were used: 20 mM HEPES pH 7.5, 100 mM KCl, 10 mM MgCl2, 2% glycerol, 2 mM dithiothreitol (DTT), 10% dimethylsulfoxide (DMSO), 20 μg/ml bovine serum albumin (BSA) and 1 mg/ml dephosphorylated -casein (Sigma) for the 798, 2080, 2080* and 2427 bp substrates, and 2.5 mM Tris–acetate pH 8, 10 mM MgCl2, 0.2 mM DTT and 0.1 mg/ml dephosphorylated -casein for the 276, 991, 1507 and 3571 bp substrates. The 2264 bp DNA substrate was analysed in both buffers.
The chambers (50 μl volume) were built by mounting coverslips on microscope slides with double-faced adhesive tape. They were first treated with 20 μg/ml polyclonal anti-digoxigenin antibody (Roche) in PBS for 20 min at 4°C. To reduce non-specific DNA binding to the glass, the chambers were then incubated with the buffer containing dephosphorylated -casein for 1 h at 4°C.
A further incubation of 1 h at room temperature in buffer with DNA (3.4 x 10–11 M) modified at one end with digoxigenin and at the other with biotin was followed by extensive washing with buffer. Finally, the DNA molecules attached by their digoxigenin ends were coupled to 0.2 μm diameter neutravidin-labeled microspheres (Molecular Probes) at a final concentration of 0.003% (v/v) by incubation for 20 min at room temperature.
Single-particle tracking experiments
Imaging of the tethered beads was performed by video-enhanced differential interference contrast microscopy at room temperature (22 ± 2°C). The microscope (Axioplan II, Zeiss) was equipped with a 63x objective (NA = 1.4) (Plan-Neofluar) and an intermediate lens providing an additional 4x magnification. Images were recorded with a CCD camera (C2400-75i, Hamamatsu) at a video rate of 25 frames/s on a numerical videotape recorder (DSR30P, Sony) after real-time processing (Argus 20, Hamamatsu) for background subtraction and contrast enhancement. After digitization using a real-time acquisition board (IEC, France), the images were analyzed using in-house software written using Optimas (6.2 version, Media Cybernetics). The DIC bead image appears as a juxtaposition of white and dark half-circles. For each sequence of images, the position of the bead was automatically calculated for each image as the grey-value-weighted center of mass of the dark portion of the bead. The beads whose trajectories were <90% complete (i.e. with overall gaps in the trajectory of >10%) were rejected from further analysis. Since the gaps arise principally from a loss of focus, this limits the maximal length of DNA fragments to which the approach can be applied. We estimate that this upper limit is 3500 bp.
To estimate the accuracy of the bead position measurements, several sequences of images of beads non-specifically immobilized at the surface of untreated coverslips were analyzed. For 4 s periods (100 images), the standard deviations of the bead coordinates were found to be x = y = 8.7 ± 2.5 nm.
Results AND DISCUSSION
Experimental constraints
To ensure the validity of the measurements, particular attention must be paid to several potential sources of artifacts which deform the apparent movement of the bead. Attachment of one bead to more than one DNA molecule would result in underestimating DNA length. The occurrence of multiply attached beads is inherent to the mode of preparation of the chambers and cannot be entirely excluded experimentally. This is because a minimal concentration of DNA is necessary during the incubation to obtain a surface density of tethered beads compatible with an acceptable rate of data acquisition. If the bead is attached to a single DNA molecule, the trajectory is expected to be delineated by a circle as shown in Figure 1A. If more than one DNA molecule is linked to the bead, the envelope of its trajectory will be elliptical to a degree which will depend on the distance between the attachment points of the DNA molecules on the coverslip (Fig. 1B). A similar deformation of the trajectory would be generated by a mechanical drift of the microscope. These cases can simply be distinguished by computing the time-averaged particle positions over successive 4 s intervals. These should be stationary for multiply attached beads (Fig. 1B) or in the case of other constraints, but would be expected to move if caused by a microscope drift.
Figure 1. Coordinates (x,y) of beads tracked during 2 min undergoing a Brownian motion tethered to a glass support by DNA molecules as shown in the schemes: (a) a single attachment leading to a circular shape of the plot; (b) a multiple (double) attachment leading to a deformation of the plot. The green dots are the positions measured at 40 ms intervals and the black dots correspond to their time average over consecutive 4 s intervals.
In this study, after any necessary corrections for mechanical drift, beads exhibiting >10% difference between the equatorial and polar radius of the envelope of the trajectory were considered to be artifactual and were excluded from the final results. Such events represented 40% of the recordings. It should be stressed that if the bead is tethered to several closely grouped DNA molecules, little or no deformation of the trajectory would be detectable and such events would be recorded as trajectories of single DNA tethered beads. Nevertheless, owing to steric hindrance, the probability of such a configuration is expected to be low and should not have an important effect on the measurement of fixed DNA lengths.
Measurement of the amplitude of the Brownian motion of the tethered beads
Once the trajectory of a tethered bead is established, the histograms of the positions x or y fluctuating with time can be determined. Ideally, the distribution of the tethered bead positions should reflect that of the end-to-end distance of the DNA molecule which is expected to be Gaussian for large DNA molecules of many persistence lengths lp . For linear DNA molecules of various lengths ranging from 2lp to 14lp (276, 798 and 2080 bp), the experimental distributions of the centered x positions (abcissa relative to the centre of mass) were found to deviate from Gaussian curves (Fig. 2) around the tails. The complete calculation of the function distribution is beyond the scope of the present study and would need to take into account the statistical mechanics of semiflexible polymers and excluded volume effects associated with the size of the bead.
Figure 2. Distribution of the centered x positions (abcissa relative to the center of mass) (nm) of the bead (average of 10 bead trajectories of 1 min duration) for different DNA tether lengths: 2080 bp (open diamonds), 798 bp (filled squares) and 276 bp (open circles). The lines give the Gaussian fit for the distributions. The error bars correspond to the standard deviation of the measurements. The distribution interval is 10 nm for the 276 bp DNA substrate and 20 nm otherwise.
The most straightforward manner of quantifying the bead motion is to calculate the standard deviation of its position distribution. The time interval chosen for these measurements is important. It is expected that the amplitude of motion A, calculated in this way, first increases with the number of successive images used for its calculation and then reaches a saturating value beyond the equilibriation time. This corresponds to the time required for the bead to explore the domain within which it is confined by the DNA tether (or for the DNA molecule to assume all its possible conformations) and increases as a function of DNA length. To unequivocally relate the amplitude of motion to the number of base pairs in a given DNA length range it must be measured over a time interval greater than or equal to the largest equilibriation time. In order to determine the time interval to be chosen for the applicable tether length range of the technique (i.e. the tether length range for which the bead remains within the depth of focus of the microscope objective), the calculation was performed for increasing successive numbers of images and DNA molecules of different lengths (276, 798, 2080 and 3571 bp). The amplitudes of motion averaged from the values calculated for consecutive time intervals along 1 min duration trajectories for 10 distinct beads are shown in Figure 3. For the DNA molecules considered here, the largest equilibriation time was found to be 4 s which corresponds to 100 images.
Figure 3. Amplitude of motion A of the bead (average of 10 bead trajectories of 1 min duration) as a function of the time interval for various DNA lengths: 3571 bp (filled triangles), 2080 bp (open diamonds), 798 bp (filled squares) and 276 bp (open circles). The error bars correspond to the averaged standard deviation of the measurements. The dotted lines connecting the points were fitted by eye. The horizontal lines give the asymptotic value Aeq reached at long term.
In the following, we systematically used the standard deviation of the bead positions over 4 s as a measurement of its equilibrium amplitude of motion Aeq.
Variation of the averaged equilibrium amplitude of bead motion with the DNA tether length
DNA molecules undergo conformational fluctuations. These result in fluctuations of the amplitude of tethered bead motion with time. An accurate measurement of the average of the bead motion for a DNA molecule of given length requires a large number of determinations to establish statistical significance. Ideally, if the system is ergodic, accumulating a long trajectory of a single DNA molecule should be equivalent to measuring shorter trajectories of multiple DNA molecules. However, because of a possible variability in the total length of the tether due to possible conformational differences at the attachment points of the DNA molecule, we accumulated 1- or 2-min trajectories of 20–40 different beads for DNA molecules of each length. The histograms of the distribution of the equilibrium amplitudes of bead motion Aeq measured for 276, 798, 2080 and 3571 bp DNA molecules are shown in Figure 4. As expected, the distributions are Gaussian and the fit by the corresponding equation allows determination of the mean value eq, the standard error of the mean and the standard deviation of the amplitude of motion. The values found for each DNA molecule are presented in Table 1. Note that in order to ascertain possible bias in the measurements due to non-specific adsorption of the DNA tether to the coated glass, we repeated the series of measurements for the 2080 bp DNA after having incubated the observation chamber with a non-specific competitor DNA fragment prior to the attachment of the DNA molecules. This operation had no effect on the final results (data not shown).
Figure 4. Relative frequency distribution of the equilibrium amplitude of motion Aeq (see text) for various DNA lengths: 3571 bp (filled triangles), 2080 bp (open diamonds), 798 bp (filled squares) and 276 bp (open circles). The lines give the Gaussian fits for the distributions.
Table 1. Mean values, standard errors (SE) and standard deviations of the equilibrium amplitudes of motion determined by a Gaussian fit of their distribution for various DNA molecules
We note that the measured motion amplitude of beads immobilized at the microscope slide surface in the absence of DNA is larger than that obtained for beads immobilized on an uncoated glass surface (see Materials and Methods). This can probably be attributed to the antibody coating which would lead to a cushioning effect and to a less efficient immobilization.
The plot of the observed averaged amplitude of motion eq as a function of the DNA length or number of base pairs l is presented in Figure 5. The extent of displacement of the bead is expected to be proportional to the gyration radius R of the DNA molecule:
Figure 5. Variation of the averaged equilibrium amplitude of motion eq (see text) of a tethered bead with the length of the DNA tether. The error bars correspond to the standard deviation associated to the mean value. The solid line is the fit by the theoretical relationships eq l in the rigid rod regime (gray shaded region) and eq l3/5 in the flexible polymer regime (see text). The slope of the dotted line is equal to 0.061 ± 0.003 nm/bp.
eq R
For short chain lengths, of the order of or less than the persistence length lp, the DNA chain behaves as a rigid rod and
R l
For larger chain lengths, the radius is given by the following relationship established by Flory (20) for a polymer in a good solvent:
R N3/5
where N = l/lp is the number of statistical segments.
As illustrated in Figure 5, the experimental data are robustly described by the expected theoretical equations with a cross-over between the two regimes at 300 bp, i.e. 2lp.
This analysis of the variation of the tethered bead motion contrasts with that discussed in a previous study (9) in which a linear relationship between the bead motion and the DNA tether length was found. This discrepancy may be due to the more restricted DNA length range explored in this study. For DNA lengths up to 2400 bp, the variation of the bead motion observed here can be approximated by a straight line of slope 0.061 ± 0.003 nm/bp (see Fig. 5). This value is close to that found by Gelles and colleagues (9), indicating that the technique is extremely robust over a range of experimental conditions.
As shown in Table 1 for the 798 and 2080 bp DNA molecules, for a constant number of observed beads, the error of the mean value of the equilibrium amplitude of motion eq is smaller for the largest recorded time interval while the value of the mean itself is unchanged. Thus increasing the duration of observation of the beads allows measurement of the amplitude of DNA tethered bead motion with a very high precision. It should be stressed that this implies that the method enables detection of very small effective tether length variations on a given DNA molecule. On the other hand, discrimination between DNA molecules differing slightly in number of base pairs might be complicated by the influence of DNA sequence and base-pair distribution on the conformation of the molecule. This type of effect may explain the difference between the averaged amplitudes of motion observed for two DNA molecules of 2080 bp (cf. Table 1). It will be necessary to analyze these possible effects in detail.
An illustration of the application of the approach: unfolding of Holliday junctions by RuvA
To determine whether the technique is sufficiently sensitive to detect small length differences induced by conformational changes of the DNA tether, we chose to investigate the unfolding of a Holliday junction by the E.coli protein RuvA. The Holliday junction, the major intermediate of recombination, marks the exchange point between two recombining DNA molecules (21). Under physiological conditions, it adopts a so-called stacked X-structure which is characterized by coaxial pairwise stacking of duplex arms of the junction (14). In this structure, two conformational isomers can be formed, on the basis of which DNA strands are exchanged across the junction. The stacked X-structure introduces a sharp angle between two recombining DNA duplexes as determined by biochemical, biophysical and crystallographic studies (21,22). During homologous recombination in E.coli, the Holliday junctions are processed by coordinate action of the RuvA and RuvB proteins that promote rapid and unidirectional branch migration. To initiate branch migration, RuvA binds the Holliday junctions as a tetramer or double tetramer with high affinity and unfolds the junctions from the stacked X-structure into a square-planar conformation with four helical arms pointing out the corners of a square. The conformational change of the structure induced by RuvA facilitates the process of branch migration and is essential for homologous recombination and recombinational repair (21,23).
The Holliday junctions were designed to contain two short arms and two long arms. A 3 bp heterologous sequence was introduced in one long arm of the junction in the vicinity of the AvaI site (see Materials and Methods) to block spontaneous branch migration (17). Each long arm of the junction was labeled with either biotin or digoxigenin, permitting measurement of the Brownian motion of a bead tethered to an immobilized Holliday junction. The distribution of the amplitudes of motion measured in the absence and in the presence of RuvA are shown in Figure 6. The averaged equilibrium amplitudes of Brownian motion in the absence of RuvA were found to be asymmetrical, with a major peak at 126 ± 14 nm. This value approaches that expected for a linear DNA fragment of equivalent length (i.e. 1954 bp), calculated from the calibration curve as 136 ± 12 nm. A second minor peak was also detected at 165 ± 11 nm, which might be attributed to an alternative conformational isomer of the Holliday junctions (22). In the presence of 90 nM RuvA, the amplitude of Brownian motion increased to 155 ± 28 nm. This increase in the apparent length of the junction above the value found in the absence of protein is consistent with RuvA-mediated unfolding of the junctions into an open-square conformation (23) and therefore underlines the sensitivity of our experimental approach.
Figure 6. Unfolding of Holliday junctions in the presence of RuvA. Histograms for the amplitudes of Brownian motion of the beads tethered by 2-kb (1954 bp) Holliday junctions in the absence (open squares) or presence (filled diamonds) of RuvA collected from the 1 min tracking of 21 and 22 beads, respectively. The lines correspond to best fits for a double Gaussian distribution with maxima values of 126.1 ± 14.4 nm and 164.6 ± 11.3 nm (mean ± SD) in the absence of RuvA and a single Gaussian distribution with 155.4 ± 28.0 nm in the presence of RuvA. The schemes show the various conformations of the Holliday junctions supposed to correspond to the different populations.
Concluding remarks
The SPT technique was applied to the study of DNA tethered particle motion in a length range up to 3500 bp. Based on the simplest model for polymer conformations, a theoretical relationship for the observed variation of the tethered bead motion as a function of the number of DNA base pairs was observed over the entire DNA length range.
Besides the highly accurate information that this method can provide about the effective length of the DNA, we would like to emphasize its informative potential for the conformational dynamics of the DNA molecules as already stressed by Qian and Elson (24). Indeed, we were able to verify that over the whole DNA length range studied here the movement of the bead was dominated by the tether and not its own Brownian motion. Thus the study of the conformational dynamics of single DNA molecules is only limited by the temporal resolution of the measuring device. In the present work, the time interval needed to perform a measurement of the bead motion was fixed at 4 s but, depending on the biochemical processes under investigation, it can be shortened while retaining a precision sufficient to follow a change in the DNA tether length (see Fig. 3).
This approach opens the possibility of fine-scale kinetic analysis of biological processes such as DNA looping, branch migration of Holliday junctions and other protein-induced DNA conformational changes. This method is being used to study a number of processes of this type in our laboratories.
ACKNOWLEDGEMENTS
We thank D. Dean and N. Destainville for helpful discussions. L. Finzi and J. Gelles kindly provided invaluable details concerning the TPM technique. We are indebted to C. Loot for providing DNA samples, A. Martinez and S. Huet for performing initial experiments, F. Daumas for writing the data sorting software and A. Lopez for critically reading the manuscript. N.P. and C.D. were supported by grants from the Ministère de l’Education Nationale, de la Recherche et des Nouvelles Technologies. This work was funded by grants from the Centre National de la Recherche Scientifique (programme NanoObjet Individuel) and the Association pour la Recherche contre le Cancer.
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