Anal. Chem. 2000, 72, 1649-1656
Investigation of the Hydrolysis of Single DNA Molecules Using Fluorescence Video Microscopy Yoshiaki Tachi-iri,† Mitsuru Ishikawa,* and Ken-ichi Hirano‡
Joint Research Center for Atom Technology, Angstrom Technology Partnership, 1-1-4 Higashi, Tsukuba, Ibaraki 305-0046, Japan
We developed a method of studying the hydrolysis of single DNA molecules by exonuclease (exo) III using fluorescence video microscopy. A single DNA molecule immobilized at one end on a coverslip and labeled with a fluorescent bead at the other end confined the motion of a bead to a two-dimensional projected circular area determined by the contour length of DNA. The radius of this area decreased with time after the addition of exo III, Mg2+, or a single-stranded DNA-binding protein (SSB), which caused the single-stranded (ss) DNA to twist around itself. However, the radius was relatively constant over time in the absence of Mg2+, which is a cofactor in exo III activity, even when exo III and SSB were both present. These observations indicated that the decrease in the radius was due to hydrolysis of DNA by exo III. We then evaluated the rate of exo III hydrolysis of single DNA molecules by monitoring the decrease in the radius. DNA sequencing based on single-molecule detection has generated our interest in single-molecule studies. In singlemolecule DNA sequencing, individual nucleotides are hydrolyzed by exonuclease and then detected and identified by fluorescence measurements.1 Basic technologies indispensable for establishing single-molecule DNA sequencing involve the evaluation of exonuclease activity. Evaluation of enzyme activity in the single-molecule regime has attracted the attention of many scientists in biochemistry and biophysics.2-12 An essential advantage of the single-molecule studies over ensemble-averaged studies is clarification of the * Corresponding author. E-mail:
[email protected]. † Present address: Hamamatsu Photonics K. K. Central Research Laboratory, 5000 Hirakuchi, Hamakita, Shizuoka 434-0041, Japan. ‡ Present address: Hamamatsu Photonics K. K. Tsukuba Research Laboratory, 5-9-2 Tokodai, Tsukuba, Ibaraki 300-2635, Japan. (1) Keller, R. A.; Ambrose, W. P.; Goodwin, P. M.; Jett, J. H.; Martin, J. C.; Wu, M. Appl. Spectrosc. 1996, 50, 12A-32A. (2) Schafer, D. A.; Gelles, J.: Sheetz, M. P.; Landick, R. Nature 1991, 352, 444-448. (3) Kabata, H.; Kurosawa, O.; Arai, I.; Washizu, M.; Margarson, S. A.; Glass, R. E.; Shimamoto, N. Science 1993, 262, 1561-1563. (4) Xue, Q.; Yeung, E. S. Nature 1995, 373, 681-683. (5) Funatsu, T.; Harada, Y.; Tokunaga, M.; Saito, K.; Yanagida, T. Nature 1995, 374, 555-559. (6) Vale, R. D.; Funatsu, T.; Pierce, D. W.; Romberg, L.; Harada, Y.; Yanagida, T. Nature 1996, 380, 451-453. (7) Craig, D. B.; Arriaga, E. A.; Wong, J. C. Y.; Lu, H.; Dovichi, N. J. J. Am. Chem. Soc. 1996, 118, 5245-5253. (8) Tan, W.; Yeung, E. S. Anal. Chem. 1997, 69, 4242-4248. (9) Lu, H. P.; Xun, L.; Xie, X. S. Science 1998, 282, 1877-1882. 10.1021/ac9911948 CCC: $19.00 Published on Web 02/25/2000
© 2000 American Chemical Society
characteristics of individual enzyme molecules. Except when enzymes producing fluorescent products4,7,8 or an enzyme containing an inherent fluorescent chromophore is used,9 enzymes or substrates with fluorescent dyes or light-scattering particles must be used to visualize single-molecule events with light microscopy. With the help of fluorescent dyes, several studies visualized the interaction between single enzyme molecules and substrates in real time.3,5,6,10,12 However, the use of fluorescent dyes poses two significant problems. First, the labeled dye molecules can prevent enzyme molecules from expressing their intrinsic activity and functions. Second, photobleaching of the labeled dye molecules usually makes experiments longer than a few minutes impossible. The use of light-scattering particles conjugated with target molecules enables researchers to avoid these two problems. Landick and co-workers2 analyzed kinetics of transcription by using single molecules of RNA polymerase (RNAP) and observing changes in Brownian motion of a nanometer-sized gold particle (40 nm in diameter) attached to the end of a single template DNA molecule. In this protocol, transcription by RNAP lengthens the DNA template linking a nanometer particle to a coverslip through a single RNAP molecule immobilized on a coverslip, thus resulting in an increased range of the particle Brownian motion. Landick and co-workers discovered that transcription lengths depend on the template sequences selected and found the longest length to be 3.75 kbp, which is equivalent to 1267 nm. Transcription lengths are associated with the processivity of RNAP. Thus, the method of Landick and co-workers, in which they used immobilized single RNAP molecules, would be restricted to enzymes whose processivity is higher than ∼200 bp (∼68 nm) because of the limited resolution of light microscopy: as reported in the Experimental Section, the size of a pixel was 106 × 106 nm2 in our current experiment, or 50 × 50 nm2 at best.12 We developed a method of evaluating enzyme activities, which correspond to hydrolysis reaction rates in our current study, without labeling enzymes and DNA with fluorescent dyes and without assuming high processivity of target enzymes. Our method resembles the previous method of Landick and co-workers in that Brownian motion of a particle conjugated to a single DNA molecule is measured. The major difference between our method and the method of Landick and co-workers is our use of free (10) Harada, Y.; Funatsu, T.; Murakami, K.; Nonoyama, Y.; Ishihama, A.; Yanagida, T. Biophys. J. 1999, 76, 709-715. (11) Ha, T.; Ting, A. Y.; Liang, J.; Caldwell, W. B.; Deniz, A. A.; Chemla, D. S.; Schultz, P. G.; Weiss, S. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 893-898. (12) Okada, Y.; Hirokawa, N. Science 1999, 283, 1152-1157.
Analytical Chemistry, Vol. 72, No. 7, April 1, 2000 1649
Figure 1. (A) Target 4.4-kbp DNA fragments prepared from λ-DNA/Hind III digests plus three primers. (B) The two kinds of DNA, pUC19 and M13mp18, used for calibration of the contour length LD of DNA with the radius rc of the circular trajectory area covered by the fluorescent bead.
enzyme molecules in a buffer solution; in the latter method, a single DNA molecule interacts with a single enzyme molecule immobilized on a glass surface. In our method, many enzyme molecules can interact with a single DNA molecule. Thus, our method is applicable to unlabeled enzymes with low or unknown processivity at the expense of being able to evaluate singlemolecule enzyme activities. We selected exo III as the exonuclease because it is readily available from commercial sources. EXPERIMENTAL SECTION Our experimental method comprises three parts: preparation of immobilized DNA molecules, observation of the trajectory of single molecules, and conversion of this observed trajectory into a change in the contour length of DNA. In the first part, single DNA molecules are immobilized at one end on a coverslip and labeled with fluorescent beads at the other end. The motion of the fluorescent bead is restricted within a space determined by the contour length of the DNA. In practice, a three-dimensional trajectory of the fluorescent bead is projected onto a twodimensional image because we use a conventional light microscope. We use fluorescent beads instead of gold nanoparticles to easily obtain a high contrast between a bead conjugated with a single DNA molecule and the background behind the bead. Photobleaching is not important when fluorescent beads are used. In the second part, the projected circular area formed by the trajectory of the fluorescent bead is observed by using video microscopy and then the change in the radius of this area with time is evaluated. The addition of exo III molecules, Mg2+, and SSB proteins changes the contour length of the DNA and the radius of a circular area. Exonuclease III is a 3′ f 5′ exonuclease catalyzing sequential hydrolysis of DNA, thus generating ss DNA.13 Following the hydrolysis, SSB proteins roll ss DNA molecules around themselves,14 thereby shortening the original (13) Richardson, C. C.; Kornberg, A. J. Biol. Chem. 1964, 239, 242-250. (14) Lohman, T. M.; Ferrari, M. E. Annu. Rev. Biochem. 1994, 63, 527-570.
1650 Analytical Chemistry, Vol. 72, No. 7, April 1, 2000
contour length of the DNA. In the third part, changes in the radius of the circular area are converted into changes in the contour length of the DNA. We then evaluate hydrolysis reaction rates based on single DNA molecules. 1. Preparation of Immobilized DNA Molecules. Preparation of DNA Fragments for the Hydrolysis Reaction. We purified 4.4-kbp (1.5 µm, assuming a 3.4-Å axial rise per base pair) DNA fragments from λ-DNA/Hind III digests (Takara) by using 0.7% agarose gel electrophoresis and extracted the fragments from the gel with a Gene Clean II kit (Bio 101). The extracted fragments were labeled with biotin at the 5′-ends and with digoxigenin at the 3′-ends by using a modified preparation procedure. The original procedure was previously described.15 Three kinds of primers were used for linking a single DNA molecule at one end to a coverslip and for labeling it with a fluorescent bead at the other end: AGCTCGATACCGTCGACGTC (primer I), 3′-digoxigenin-modified GGGCGGCGACCTAAAT (primer II), and 5′biotinylated AAAACGAGGTCGACGGTATCG (primer III, Toyobo). A custom DNA synthesis service (BEX, Tokyo) supplied primers I and II. The 5′-ends of primers I and II were phosphorylated so that they could be joined covalently with the 3′-ends of 4.4-kbp λ-DNA/Hind III fragments. In the first step of this labeling procedure, primers I and II were hybridized with 5′-termini of the purified 4.4-kbp λ-DNA/ Hind III fragments. In the second step, primer III was hybridized with the single-stranded region of the hybridized primer I (Figure 1A). Then, T4 DNA ligase was used to repair three nicks on the 4.4-kbp fragments hybridized at 16 °C for 18 h. In the third step, excess primers were removed with a centrifuge (Pharmacia Biotech MicroSpin S-400HR). Preparation of DNA Fragments for Calibrating DNA Contour Lengths. Two kinds of DNA, pUC19 (2660 bp, when coupled with a primer) and M13mp18 (7223 bp, when coupled with a primer) (15) Perkins, T. T.; Smith, D. E.; Chu, S. Science 1994, 264, 819-822.
(Takara), were purified after digestion by Hind III and Eco RI, using the same procedure as that used in the purification of the 4.4-kbp λ-DNA/Hind III fragments (see preceding section). To immobilize each DNA at the Eco RI site on a coverslip, another 3′-digoxigenin-modified primer, AATTCCCA (primer IV) (BEX, Tokyo), was prepared. Thus, pUC19 and M13mp18 were modified at both ends by using the same procedure as that used in preparing the 4.4-kbp fragments but by using primer IV instead of primer II (Figure 1B). Linking of Single DNA Molecules on a Glass Surface. The procedures described here were used for all of the DNA fragments in a hydrolysis reaction and for all of the calibrations. All of the reactions linking the target DNA to a coverslip were carried out at 23 °C. First, we constructed a reaction vessel for attaching the ends of the single DNA molecules labeled with biotin and digoxigenin to a coverslip. A sheet of 0.5-mm-thick silicone rubber was attached to a slide glass. A 3 mm × 35 mm groove as a reaction vessel was cut in the silicone rubber. Then, the reaction vessel was filled with a protein and buffer mixture described in the next paragraph, after which it was covered with an 18-mmsquare siliconized coverslip, on which target DNA was to be immobilized. The coverslip was siliconized in advance with Sigma Coat (Sigma) to link protein G to its surface. The DNA labeled with biotin and digoxigenin was linked to the siliconized coverslip by using a modified procedure. The original procedure was previously described.2 A 200-µL portion of protein G (30 mg/mL) in TMNB (20 mM Tris-HCl (pH ) 7.6), 5 mM MgCl2, 100 mM NaCl, and 0.1% bovine serum albumin (BSA)) was poured into the reaction vessel to coat the coverslip with protein G. After a 20-min incubation, excess protein G was removed by washing the coverslip 10 times with TMNB. After the coverslip was coated with protein G, anti-digoxigenin polyclonal antibody (Boehringer, Mannheim, Germany) was added to the reaction vessel, and then the mixture was incubated for 20 min to bind the antibody with protein G on the coverslip. After the incubation, excess antibody was removed by washing the coverslip 10 times with TMNB. The DNA labeled with biotin and digoxigenin (20-100 ng) was added to the reaction vessel, and then the mixture was incubated for 20 min to bind the labeled DNA to the anti-digoxigenin antibody on the coverslip. After the reaction was completed, excess DNA was removed by washing the coverslip 10 times with TMNB. Finally, fluorescein-conjugated polystyrene beads (Polyscience) of 0.2-µm diameter were added to the reaction vessel. Maximum absorption and fluorescence of the beads were ∼490 and ∼520 nm, respectively. The surfaces of the fluorescent beads were coated with streptavidin, which would selectively bind to the biotin moiety of the labeled DNA. The reaction vessel was incubated for 10 min to bind fluorescent beads to the biotin moiety of the labeled DNA linked to the coverslip. Excess microbeads were removed by washing the coverslip 10 times with TMNB. 2. Observation of the Circular Trajectory Area of a Fluorescent Bead and of the Decrease in the Area Due to Exo III. Figure 2 shows a schematic view of the labeled DNA used for evaluating exo III reaction rates. We recorded trajectories of a fluorescent bead using a fluorescence microscope (Zeiss Axioplan) equipped with a 100× objective having a numerical aperture (NA) of 1.3, band-pass filters for excitation and fluores-
Figure 2. Schematic diagram of a target DNA molecule immobilized on a glass coverslip.
cence measurements, and an S-VHS videotape recorder (Victor BR-S605B). The microscope was coupled with a silicon intensified target (SIT) camera (Hamamatsu Photonics C2400-08). A target fluorescent bead was illuminated with a 100-W halogen lamp. Fluorescence from the bead was recorded on the video recorder at a frame rate of 1/30 s. The recorded trajectories were processed with an image processor (Hamamatsu Photonics ARGUS-50). Because the fluorescence intensity observed varied from frame to frame due to fluctuations associated with the optical measurements, such as excitation-light fluctuation, photon noise, detector-generated noise, and postdetector electronic noise, we normalized the recorded signal (Figure 3A(a)) to a unitary value prescribed by the image processor (Figure 3A(b)). This normalization procedure is called “binarization” because two values, zero and unity, are possible in a normalized fluorescence intensity. The fluorescence images thus obtained generally occupied several to 10 pixels on a frame memory and a video monitor. We determined the center of gravity of a binarized fluorescent image every 1/30 s, thereby correlating the position of a 0.2-µm diameter fluorescent bead with one pixel (Figure 3A(c)) on a frame memory and a video monitor. For our experimental setup, each pixel was 106 nm × 106 nm, and thus we were able to follow the trajectory of a target fluorescent bead as precisely as possible within the limits of resolution of the light microscope and the video frame rate. The trajectory of a fluorescent bead stored for 10 s covered a projected circular area, as shown in Figure 3B. We determined the decrease in the radius rc of this circular area every 20 s, in which a 10-s acquisition was followed by a 10-s interval. From this decrease in rc, we determined the hydrolysis rate of exo III by using eq 10 deduced in part 3. Both exo III (Toyobo, Tokyo) and SSB (Pharmacia Biotech, Tokyo) were used as supplied. To shorten the length of DNA, excess SSB (2 × 10-6 M; see the Discussion for an evaluation of the rate of association between SSB and ss DNA) was added to roll nascent ss DNA around SSB. We assumed that the rate of association between SSB and ss DNA is much faster than the rate of the hydrolysis of DNA by exo III. The meaning and validity Analytical Chemistry, Vol. 72, No. 7, April 1, 2000
1651
Figure 4. Our theoretical model used for converting rc into LD. A fluorescent bead F tethered by DNA, whose contour length is LD, at the origin O was in Brownian motion restricted by LD. Displacement was denoted as D(∆t) ) x(t) - x(0), involving two position vectors of the bead at time 0 and time t. For a lapse of time from t to t′, displacement was denoted as D(∆t′) ) x(t′) - x(0).
Figure 3. (A) Principles of binarization and finding the center of gravity of a fluorescence image of a fluorescent bead. Both of the procedures were carried out to enhance spatial resolution of the position of the fluorescent bead. (B) Schematic illustrations of signal acquisition with time. A signal that occupied one pixel with a normalized height, which was a result of binarization and finding the center of gravity, was stored one by one on a frame memory (512 × 483 pixels and 16 bits) and displayed on a video monitor every 1/ 30 s.
of this assumption will be presented in the Discussion. Lohman and Ferrari reported that an SSB tetramer rolls 56 bases of ss DNA digested by exo III.14 Two research groups reported that the length of a complex of an SSB and an ss M13 DNA is 2024%16 or 30%17 of the original contour length of undigested M13 DNA. In our current study, we prepared exo III and SSB in a mixture of 50 mM Tris-HCl (pH ) 8.0), 5 mM MgCl2, 10 mM DTT, 100 mM NaCl, 0.1% BSA, 0.08% heparin, and 4% glycerol at 25 °C. The viscosity of the mixture was ∼1.3 cP. Pouring the mixture containing exo III, SSB, and Mg2+ into the reaction vessel initiated the hydrolysis reaction. The molar ratio of DNA to exo III was ∼1:20. 3. Conversion of rc to the Contour Length of DNA. Because the motion of the bead was projected onto a surface, we used a two-dimensional bead-spring model (Figure 4) to find the relationship between rc and the contour length of DNA LD. In this model, a bead is tethered on a surface through an imaginary harmonic spring whose length is denoted by x(t). The validity of using the harmonic spring model will be presented in the Discussion. The potential energy of the oscillator is written as
U(x) ) 1/2kx2
Analytical Chemistry, Vol. 72, No. 7, April 1, 2000
〈[D(∆t)]2〉 ≡ 〈[x(t) - x(0)]2) ) 〈[x(t)]2〉 + 〈[x(0)]2〉 + 2〈x(t) x(0)〉 (2)
where the pointed brackets indicate ensemble averaging. We assume that a stochastic process involving x(t) is in steady state; that is, 〈[x(t)]2〉 ) 〈[x(0)]2〉 ≡ 〈x2〉. Thus eq 2 is written as
〈[D(∆t)]2〉 ) 2〈x2〉 + 2〈x(t) x(0)〉
(3)
Equation 3 implies that the ensemble of D(∆t) is equivalent to that of x(t) except for a factor of 2 if x(t) and x(0) are not correlated; that is, 〈x(t) x(0)〉 ) 0. The time correlation function of x(t) is written as18
〈x(t) x(0)〉 )
kBT ∆t exp k τ
( )
(4)
where kB is the Boltzmann constant, T is the absolute temperature, and τ is the relaxation constant of the oscillator. Substituting eq 4 into eq 3 gives
(1)
where x(t) is simplified to x and k is the force constant of the oscillator. The ensemble of x(t) is assumed to follow a Gaussian distribution. Thus, the center of the distribution should be 1652
considered as the natural length of an imaginary spring. Because we can set the center of the distribution to zero, the imaginary oscillator is a two-dimensional harmonic oscillator whose natural length is zero. The displacement of a bead is given by D(∆t) ) x(t) - x(0), where x(0) is the position vector of the bead at time zero and x(t) is the position vector of the bead at time t. The mean square of D(∆t) during ∆t is written as
(16) Griffith, J. D.; Harris, L. D.; Register, J., III. Cold Spring Harbor Symp. Quant. Biol. 1984, 49, 553-559. (17) Chrysogelos, S.; Griffith, J. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 58035807. (18) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon: Oxford, U.K., 1986; Chapter 3, eq 3.80.
2kBT ∆t 1 - exp k τ
[
〈[D(∆t)]2〉 )
( )]
(5)
The force constant k can be written as
k)
3kBT LDb
(6)
where b is the segment length of DNA (see eq 13 in the Discussion). Substituting eq 6 into eq 5 gives
〈[D(∆t)]2) )
2LDb ∆t 1 - exp 3 τ
[
( )]
(7)
If ∆t . τ, then eq 7 is simplified to
〈[D(∆t)]2〉 ) 2〈x2〉 )
2LDb 3
(8)
The validity of the assumption ∆t . τ will be examined in the Disccusion. We then define a parameter jx from eq 8
jx ≡ x〈x2〉 ) C0xLD
(9)
where C0 ) (b/3)1/2. Assuming that jx is equivalent to rc,19 we obtain
rc ) C0xLD
(10)
We then used this equation to convert the observed rc to LD. RESULTS Screening Single DNA Molecules Labeled with Single Fluorescent Beads. On a video monitor, we observed from a few to several tens of fluorescent spots, depending on the selected concentration of the DNA labeled with fluorescent beads. Whether or not a single fluorescent bead was really bound to a single DNA molecule is a critical point in our study. We used two criteria for screening a single fluorescent bead bound to a single DNA molecule. The first criterion was that the concentration of DNA used be low enough to prevent DNA from aggregating. Thus, it is highly probable that a single fluorescent bead coupled with a single DNA molecule. The second criterion was that the fluorescence intensity of aggregated beads be stronger than that of a single bead. Some fluorescent beads were aggregated owing to possible hydrophobic interactions among the streptoavidin molecules on the surface of the fluorescent beads. However, we could (19) In this assumption, rc ) jx is equivalent to the standard deviation of the Gaussian distribution of a position of the bead. We can alternatively select rc ) 2xj, rc ) 3xj, rc ) 4xj, and so forth. However, such selection is not critical to our purpose because it is always possible to renormalize the numerical factors (2, 3, 4, and so forth) in C0, which is only a fitting parameter. The important conclusion is that rc is proprotional to LD1/2. We estimated rc as illustrated in Figure 3B(c) because data acquisition time was insufficient for obtaining a smooth Gaussian profile and determining rc ) jx from the Gaussian profile. In practice, the estimated rc would be closer to 2xj or more, rather than to jx. Considering the data quality obtained, one finds that the selection of the numerical factors in the theory is not essential to our data analysis.
Figure 5. Calibration of rc with LD obtained from three types of DNA with known LD values: pUC19 (2660 bp), λ-DNA/Hind III (4400 bp), and M13mp18 (7223 bp). The solid line is the fitted curve represented by eq 11. Note that the data acquisition time was set for 10 s, which was identical to that for the hydrolysis reactions.
clearly distinguish aggregated beads from a single bead on the basis of a difference in the fluorescence intensities. After screening isolated single fluorescent beads, we classified the mobility of the beads into three groups for further screening. The first group remained stationary due to possible adsorption on a glass surface. The second group freely migrated within a field of view as if it were not tethered on a glass surface. We discarded these two groups of beads as unsuitable for further experiments. The third group exhibited Brownian motion within a restricted area, and thus the beads in this group were most likely tethered to the coverslip via DNA. We used this group of fluorescent beads in the following experiment, in which hydrolysis reactions of exo III were observed. Despite the careful screening, the selected bead sometimes jumped drastically out of its restricted area of motion. We inferred that this was due to release of the bead from DNA or of the labeled DNA from the coverslip. In another event, a bead stopped moving possibly because of adhesion to a coverslip surface. Because unusual behaviors such as these two events occurred abruptly, we easily discriminated them from the desired hydrolysis reaction of exo III. Calibration of the Contour Length of DNA with the Radius of a Circular Trajectory Area. To calibrate the contour length LD of DNA with the radius of a circular area rc, we measured rc by using three different DNA molecules with known LD values. Figure 5 shows the calibration plot between the LD values of the selected DNA molecules and the measured rc values. In practice, a finitely sized (1 pixel ) 106 × 106 nm2) fluorescent spot coming from a fluorescent bead appeared even when the bead was at rest. For this reason, a constant C1 was added to eq 10:
rc ) C0xLD + C1
(11)
By using eq 11, we determined the fitting constants C0 and C1 with an iterative least-squares curve-fitting method as 45 nm/ (bp)1/2 and 63 nm, respectively. The fitting curve is shown as a solid line in the calibration plot of Figure 5. Hydrolysis of Single DNA Molecules by Exo III. Figure 6 shows representative images demonstrating a decrease in the Analytical Chemistry, Vol. 72, No. 7, April 1, 2000
1653
Table 1. Hydrolysis Reaction Rates (nt/min) Obtained with and without the Requirements for Hydrolysis Reactions of DNAa exo III + SSB + MgCl2
exo III + SSB
only SSB
-20 -25 -29 -36 -46 -73 -75 -123 -235 -348 -410
+10.3 -0.7 -27.8
+23 +0.1 -7.6 -9.6 -23.5
a The plus and minus signs indicate that the radius r increased c and decreased with time, respectively.
Figure 6. Changes in the area covered by the fluorescent bead tethered on a glass coverslip through DNA after the addition exo III, Mg2+, and SSB. The data-sampling time was 10 s.
Figure 7. Representative time lapse of rc after the addition of exo III, Mg2+, and SSB. The data-sampling time was 10 s.
circular trajectory area covered by a fluorescent bead. The image at 0 min was obtained immediately after exo III, Mg2+, and SSB, Mg2+, were poured into a reaction vessel. After the addition of exo III and SSB, the circular area remained relatively constant for ∼5 min and then successively decreased.20 Figure 7 shows changes in rc with time. After the circular area stopped decreasing (∼12 min), i.e., after the hydrolysis reaction was complete, we estimated the residual rc at 275 ( 25 nm. On the basis of the (20) Time lags between 0 min and the beginning of a decrease in the radius were not always observed. The presented time lag (∼5 min) was the longest one among our observations. In other experiments, a decrease in the radius began immediately after injection of exo III and SSB. The reason for the time lag is not clear; however, a possibility is that exo III molecules spend time in encountering the site on DNA for initiation of the hydrolysis reaction.
1654 Analytical Chemistry, Vol. 72, No. 7, April 1, 2000
calibration curve in Figure 5, this rc corresponds to an LD of 1000 ( 100 bp. Here, the use of the calibration assumes that the complex between ss DNA and SSB is flexible, such as that seen in double-stranded (ds) DNA. Note again that the initial LD of DNA that we used was 4400 bp and that the shrinking ratio of ss DNA to SSB is 20-24%16 or 30%.17 Thus, the expected residual length corresponds to an LD of 880-1056 or 1320 bp after the completion of the hydrolysis reaction. This expected LD value is consistent with our calibration-based LD value of 1000 ( 100 bp. Thus, our assumption that the complex between ss DNA and SSB is flexible such as that seen in double-stranded (ds) DNA is correct within the limits of our observations.21 We determined the rate of hydrolysis by calculating the slope of the line fitted to the measured changes in rc with time (Figure 7). On the basis of the calibration curve, rc ≈ 430 nm at 5 min (Figure 7) corresponds to an LD of 3000 bp and rc ≈ 270 nm at 10 min corresponds to an LD of 950 bp. On the basis of these two values, the estimated rate of hydrolysis was 410 nt/min. Table 1 shows representative estimated reaction rates in the absence and presence exo III, SSB, and Mg2+. DISCUSSION In this section, we investigate three assumptions from which some conclusions were deduced in this work and then discuss the hydrolysis reaction rates of exo III. First, we assumed in the Experimental Section that the rate of association between SSB and ss DNA is much faster than the rate of hydrolysis of DNA by exo III. If this assumption is not valid, then a decrease in the radius rc cannot directly be related to the hydrolysis reaction rate. Urbanke and co-workers estimated the rate constant ka′ for the association between SSB and ss DNA to be 2.5 × 108 M-1 s-1 by using a fluorescence stopped-flow technique.22 The rate constant for association ka is related to ka′ and the concentration of SSB, CSSB, by the expression ka ) ka′CSSB. In our experiments, we used CSSB ) 2 × 10-6 M, which was an excess of SSB compared to possible binding sites on ss DNA, and thus, from this expression for ka, we obtained ka ) 500/s. (21) To our knowledge, there is no reported direct evidence that an SSB-ss DNA complex is as flexible as ds DNA itself. The flexibility should be confirmed by future experiments similar to those described in refs 24 and 28. (22) Urbanke, C.; Schaper, A. Biochemistry 1990, 29, 1744-1749.
Rogers and Weiss reported an exo III hydrolysis rate of 150 nt/ min by using an electrophoresis analysis.23 The association rate of SSB was much faster than the hydrolysis rate of exo III; thus, the assumption was valid. Second, we assumed (see part 3 of the Experimental Section) that the harmonic spring model is valid in our data analysis. Here we briefly review a widely known theoretical model that supports this assumption. The validity of the assumption, however, should finally be judged by the conclusions based on the assumption. The freely joined chain (FJC) model is a simple statisticalmechanical model used in the theoretical treatment of singlepolymer dynamics.24 The FJC model treats the polymer as a chain of statistically independent segments of length b whose orientations are uncorrelated in the absence of external forces. From the FJC model, when a single polymer molecule with a contour length LD is stretched by force f and equilibrated in a thermal bath at temperature T, an averaged end-to-end distance x(t) is described by
[ ( ) ]
〈x(t)〉 ) LD coth
kBT fb kBT fb
(12)
In the absence of external force, the segment length b is twice the persistence length a of the polymer involved. When 〈x(t)〉 is small (or f is small), eq 12 is reduced to
f)
3kBT 〈x(t)〉 LDb
(13)
In eq 13, Hook’s law holds between f and x(t); and thus, we obtain the force constant k in eq 6. To continue the validation of our second assumption, we need to examine if the condition that 〈x(t)〉 is small (i.e., f is small) is satisfied. Consider that an external force comes from the bead. Then the averaged instantaneous force squared is expressed as25
〈f(t) f(t′)〉 ) 2ζkBTδ(t - t′)
(14)
The friction constant ζ is related to the radius of the bead r and solvent viscosity η by
ζ ) 6πηr
(15)
Substituting η ) 1.3 cP ) 1.3 × 10-3 N s/m2 and r ) 0.1 × 10-6 m into eq 15, and the resultant ζ ) 2.45 × 10-9 N s/m and T ) 298 K into eq 14 after setting t ) t′, we obtain f ≡ 〈[f(t)]2〉1/2 ) 4.5 × 10-15 N. If the energy needed for extension of the polymer by b is smaller than the thermal energy kBT, that is
fb/kBT e 1
(16)
then the harmonic spring model is valid in our data analysis. In fact, eq 16 is the criterion for determining the suitability of using (23) Rogers, S. G.; Weiss, B. Methods Enzymol. 1980, 65, 201-211. (24) Smith, S. B.; Finzi, L.; Bustamante, C. Science 1992, 258, 1122-1126. (25) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon: Oxford, U.K., 1986; Chapter 3, eq 3.28.
the harmonic spring model.26 For b ) 2a and a ) 50 nm, we obtain fb/kBT ≈ 0.1, thus satisfying eq 16.27 Therefore, our second assumption was valid. Third, we assumed (see part 3 in the Experimental Section) that 〈x(t) x(0)〉 ) (kBT/k) exp(-∆t/τ) ≈ 0. The observations by Perkins and co-workers28 support our assumption. Perkins and co-workers concluded that τ is denoted by
τ≈
η L 1.66(0.10 kBT D
(17)
They found τ ) 0.56 s when LD ) 4 µm and η ) 15 cP. Assuming that T in our experiments was the same as that reported by Perkins and co-workers, we estimated τ ) 9.5 × 10-3 s on the basis of eq 17 using LD ) 1.5 µm and η ) 1.3 cP. This estimated value of τ means that 〈x(t) x(0)〉 ≈ 0 when we used a data acquisition time of 10 s. Therefore, the third assumption was valid. An apparent increase or decrease in rc occurred (Table 1) even under conditions where hydrolysis reactions should not occur, such as the lack of Mg2+ or the lack of exo III and Mg2+, and thus these variations may reflect the accuracy of our experiments. Therefore, the values of -20 to -36 nt/min in the left column in Table 1 may be considered artifacts, although all requirements (exo III, SSB, and MgCl2) for the hydrolysis reactions of DNA were satisfied. The average for all observations is 129 nt/min, or 187 nt/min when the observations of -20 to -36 nt/min are excluded. Both of these averaged values are similar to the ensemble-averaged value, 150 nt/min.23 The number of exo III molecules contributing to a decrease in rc is unknown; however, the conclusion that only a single exo III molecule contributes to the decrease is unacceptable. We estimated a possible number to be 44, on the basis of the length of the target DNA (4.4 kbp) and the reported processivity (100 nt) of exo III.29 This estimated value makes it highly probable that we observed averaged results over several tens of exo III molecules from a decrease in rc. Thus, we expected a relatively constant decrease in rc with time from experiment to experiment even though individual hydrolysis reaction rates of exo III vary by a factor of 10.30 However, this was not the case; the decrease in rc with time varied from experiment to experiment by a factor of 20. This large variation cannot be explained only by variation in activity of individual exo III molecules. Details of this large variation remain unknown and thus require further study. Despite the limited number of our observations, our results revealed heterogeneous exo III activities based on single DNA molecules. CONCLUSION We evaluated the hydrolysis reaction rate of exo III by measuring the decrease in the circular trajectory area covered (26) Tanaka, F. Introduction to Physical Polymer Science; Shokabo: Tokyo, 1994; Chapter 2. (27) The higher [Na+] becomes, the shorter the persistence length a is. When [Na+] is 10 mM, a ) 50 nm.24 Although [Na+] was 100 mM in our experiment, we assume a ) 50 nm. (28) Perkins, T. T.; Quake, S. R.; Smith, D. E.; Chu, S. Science 1994, 264, 822826. (29) Wu, R.; Ruben, G.; Siegel, B.; Jay, E.; Spielman, P.; Tu, C. P. D. Biochemistry 1976, 15, 734-740. (30) In refs 4, 7, and 8, the authors reported single-molecule enzyme activities that varied by a factor of 10.
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by a fluorescent bead bound to a single DNA molecule linked to a coverslip. Although our experimental setup is not suitable for evaluating activities of single enzyme molecules, it could be applicable to a possible scheme of single-molecule DNA sequencing without labeling each nucleotide with fluorescent dyes. In this scheme the use of single DNA molecules, not single exonuclease molecules, is one requisite; and the chemical conversion of inherently less fluorescent nucleotides detached from DNA into fluorescent derivatives is another requisite. To meet the requirements for single-molecule DNA sequencing without dye labeling, (31) Ye, J. Y.; Ishikawa, M.; Yamane, Y.; Tsurumachi, N.; Nakatsuka, H. Appl. Phys. Lett. 1999, 75, 3605-3607.
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we implemented several experiments and recently demonstrated a method for enhancing two-photon-excitation fluorescence of an adenine derivative with the help of dielectric multilayers.31 ACKNOWLEDGMENT This study was performed with support from the New Energy and Industrial Technology Development Organization at the Joint Research Center for Atom Technology. Received for review October 18, 1999. Accepted January 3, 2000. AC9911948
