The mechanism of type IA

N. H. Dekker*†, V. V. Rybenkov‡, M. Duguet§, N. J. Crisona¶, N. R. Cozzarelli¶, D. Bensimon*, and V. Croquette*

*Laboratoire de Physique Statistique et De´partement de Biologie, E´ cole Normale Supe´rieure, Unite´Mixte de Recherche 8550 Centre National de la Recherche Scientifique, 24 Rue Lhomond, 75231 Paris, France; ‡Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019; §Laboratoire d’Enzymologie des Acides Nucle´iques, Institut de Ge´ne´ tique et Microbiologie, Universite´Paris Sud, Unite´Mixte de Recherche 8621 Centre National de la Recherche Scientifique, 91405 Orsay, France; and ¶Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720

Contributed by N. R. Cozzarelli, June 25, 2002 The topology of cellular DNA is carefully controlled by where denaturation of duplex DNA by binding is called topoisomerases. By using single-molecule techniques, we thermodynamically favored and to the disentanglement of monitored the activity of two type IA topoisomerases in real time single-stranded regions of DNA. Indeed, the relaxation of (Ϫ) under conditions in which single relaxation events were detected. supercoils is the essential role of I (topo I) in The strict one-at-a-time removal of supercoils we observed estab- bacteria (1). Disentanglement is likely the critical function of lishes that these enzymes use an enzyme-bridged strand-passage topo III, which can act in complex with a helicase whose mechanism that is well suited to their physiological roles and malfunction is implicated in several human diseases (15–19). demonstrates a mechanistic unity with type II topoisomerases. In the present work, we followed the action of a mesophilic and a thermophilic bacterial type IA topoisomerase on single mol- opoisomerases are divided into two classes, depending on ecules of DNA in real time. We show that these enzymes do Twhether one strand (type I) or both strands (type II) of DNA indeed act by a strand-passage mechanism, as we observed a are transiently broken to permit a change in topology (reviewed ͉⌬Lk͉ ϭ 1 in individual steps of DNA relaxation. We also have in refs. 1 and 2). Type I enzymes, the subject of this report, are determined the kinetic parameters of both enzymes and found found in all three kingdoms of the living world: bacteria, archaea, that stretching DNA dramatically reduces their activity. and eukarya (2). These enzymes are divided further into IA and IB subclasses that share no structural similarity and differ in Materials and Methods reaction chemistry. Type I and II topoisomerases yield products Magnetic Tweezers. Single DNA molecules, attached at one end that differ in DNA linking number (Lk) by 1 and 2, respectively to a glass capillary and at the other to a magnetic bead, were (3–5). This result is often misinterpreted to indicate that the ⌬Lk maintained under tension by the field gradient of two small for each round of catalysis must be 1 for type I enzymes and 2 permanent magnets placed above the sample (Fig. 2A). The for type II enzymes. However, this assumption is true only if the NdFeB magnets (6 mm ϫ 6mmϫ 5 mm) were separated by 1.4 ⌬Lk per round is constant, as the experiments show only that the mm. Images of the bead grabbed by a charge-coupled device change per round is 1n and 2n, where n is an integer. This camera (model CV-M30, JAI, Copenhagen, Denmark) deter- distinction is important because biochemical (6), kinetic (7), and mine its distance l from the surface and the magnitude of its structural (8) data imply that n is not equal to 1 for type IB transverse fluctuations ͗␦x2͘. From these measurements, we cal- ϭ ͞ enzymes but, for example, about 5 for the vaccinia topoisomer- culate the force exerted on the DNA molecule F kBTl ͗␦ 2͘ ase. Such a nonunitary ⌬Lk is explained most simply by a x , where kB is the Boltzmann constant and T is the temper- strand-rotation model (Fig. 1 Lower) for type IB action in which ature (20). Translation of the magnets controls the magnitude of the enzyme breaks one strand of the DNA helix by addition this force (F Ͻ 50 pN), whereas rotation of the magnets controls across a , allowing limited rotation about the supercoiling density ␴, defined as ⌬Lk divided by the Lk of the intact strand to relax several supercoils before resealing relaxed DNA. occurs (8). A strand-rotation mechanism differs fundamentally from a sign inversion or an enzyme-bridged strand-passage DNA Constructs. We used three DNA substrates (Fig. 2C). To mechanism (Fig. 1 Upper) in which ⌬Lk must be uniquely 1 for observe topo I action on (Ϫ) supercoiled DNA, we used an type I enzymes (3, 9). In the latter model, both ends of the 11.5-kb double-stranded DNA multiply labeled with biotin or transient DNA are bound to the topoisomerase, preventing digoxygenin at its extremities. The DNA molecules were incu- DNA swiveling but allowing passage of a second DNA strand bated at room temperature for 5 min with 1.0-␮m diameter through the enzyme-bridged gate before resealing. streptavidin-coated paramagnetic beads (Merck). The DNA An enzyme-bridging mechanism for type II enzymes has been concentration was low enough that no more than one DNA verified by single-molecule experiments showing that in the molecule was bound, on average, to each magnetic bead. The elementary catalytic cycle, ⌬Lk is uniquely 2 (10, 11). No such digoxygenin end of the DNA was bound to a glass capillary experiments have been done with type I enzymes. Although surface coated with anti-digoxygenin. The capillary surface was biochemical (9, 12, 13) and structural (14) data suggest a also coated with polyglutamic acid (3 mg͞ml) to minimize strand-passage mechanism for the type IA subclass, the mech- nonspecific interactions. anism has not been established convincingly for either subclass To observe topoisomerase I (topo I) action on (ϩ) supercoiled of type I enzymes. It is important to know whether a strand DNA, we used an 8.7-kb duplex DNA that contained a small rotation or an enzyme-bridged mechanism operates for type I single-stranded region (13) consisting either of a mismatch of 12 topoisomerases, not only for the intrinsic enzymological interest unpaired or a bulge of 25 nucleotides midway but also because the mechanism is critical to understanding the through the DNA. To form the mismatched construct, two 60-nt complex roles of these enzymes in cells. Thus, the strand-rotation synthetic polynucleotides were annealed. The synthetic se- model has the advantage of allowing a rapid and efficient quences were complementary, except for 12 nucleotides at their relaxation of supercoils, for example, ahead of the replication fork (7). The enzyme-bridged strand-passage mechanism leads to much more controlled topological changes. Because type IA Abbreviation: topo I, topoisomerase I. enzymes bind preferentially to single-stranded DNA (1), they are See commentary on page 11998. limited to relaxation of (Ϫ) supercoils above a threshold value †To whom reprint requests should be addressed. E-mail: [email protected].

12126–12131 ͉ PNAS ͉ September 17, 2002 ͉ vol. 99 ͉ no. 19 www.pnas.org͞cgi͞doi͞10.1073͞pnas.132378799 Downloaded by guest on October 2, 2021 Fig. 2. The experimental configuration. (A) DNA molecules were tagged at their ends with biotin and digoxygenin, allowing attachment to a streptavi- Fig. 1. Proposed mechanisms for type I topoisomerases. Shown is a segment din-coated magnetic bead and an antidigoxygenin-coated glass surface. of DNA in a (Ϫ) supercoiled molecule that is acted on by a Translation and rotation of a pair of magnets above the DNA molecule (gray). (Upper) An enzyme-bridged mechanism for type IA topoisomerases. changed the extension of the DNA, which was recorded by tracking of the The free energy of (Ϫ) supercoiling promotes the melting of the DNA upon bead’s position with an inverted microscope. (B) The behavior of an 11.5-kb enzyme binding and the stabilization of a (Ϫ) crossing of single strands of duplex DNA molecule under superhelical stress at two applied forces. At F ϭ DNA. After cleavage of one strand of DNA, the enzyme bridges the break by 0.26 pN, (ϩ) and (Ϫ) superhelical turns equivalently reduced DNA extension covalent attachment to one end and noncovalent binding to the other. through the formation of plectonemic supercoils. Increase of the force to 1.9 Passage of the intact strand through the break inverts the sign of the crossing. pN resulted in an asymmetry of the supercoiling vs. extension curve because The result is a ⌬Lk of 1 per round of catalysis. (Lower) A strand-rotation denatured regions form at the expense of plectonemes in (Ϫ) but not (ϩ) mechanism, as proposed for type IB topoisomerases. After binding to duplex supercoiled DNA. For this DNA, 50 turns caused a ͉␴͉ of 0.045. (C) Three DNA, the enzyme nicks one strand by addition across the phosphodiester bond different were used in this study: fully duplex 11.5-kb DNA, 8.7-kb and thereby becomes covalently attached to one end of the nick. The other duplex DNA with a symmetric mismatch of 12 nucleotides, and 8.7-kb DNA end of the nick is not bound, resulting in rotation of the free end about the with an asymmetric bulge of 25 unpaired nucleotides. intact strand before rejoining of the DNA ends. The result is the relaxation of several supercoils and a nonunity ⌬Lk per round of catalysis.

and a reference bead stuck to the surface. For the analysis of SCIENCES

topoisomerase steps, these raw data l(t) were filtered at 2 Hz. AGRICULTURAL center, where cytidylic residues were opposite those of thymi- Steps of size S occurring at times tS were fit by using a sliding dylic residues. The annealed 60-mers were ligated onto one end Heaviside (step) function (24): l (t) ϭ S␪(t Ϫ t ) ϩ l defined of the 8.7-kb , which was then cyclized. The resulting step S 0 over a time window of typical size tav. That is, for every time point plasmid was digested with restriction endonucleases that cut 4.2 t0 of the data set, the parameters of the step function (S, tS, l0) kb upstream and 4.7 kb downstream from the insert to generate ␹2 ϭ Ϫ 2 were fit to minimize the error [l(t) lstep(t)] in the time a linear molecule with the insert near the center. The ends of the Ͻ Ͻ ϩ window t0 t t0 tav, where only one step was expected. The DNA were tagged with digoxygenin- and biotin-labeled DNA ␹2 Ϸ parameters that consistently scored for minima of were BIOPHYSICS fragments ( 400 bp long). An analogous protocol yielded the selected as steps. These were then binned to form histograms. DNA with a bulge. These constructs were attached to a capillary surface and a magnetic bead by using the procedure described Results and Discussion above. Our experiments are conducted on single DNA molecules maintained under tension by the field gradient of small magnets Enzymes. topo I was purified from an overpro- placed above a paramagnetic bead attached to the DNA (Fig. ducing strain obtained from R. DiGate (University of Maryland 2A). Translation of these magnets varies the magnitude of the School of Pharmacy, Baltimore) that contains a topB disruption applied force (20), whereas their rotation controls the degree of to ensure there is no contaminating topo III (21). Purification supercoiling, ␴, applied to the DNA. Specification of these two was as described (22) with the following modifications: (i) the parameters permits precise control of the topology of the DNA lysate was applied to a DE-52 cellulose column in buffer molecule (Fig. 2B). At a low force (0.26 pN), (ϩ) and (Ϫ) ␴ containing 50 mM KCl, and (ii) the unbound protein was equivalently reduced DNA extension by formation of plectone- collected and chromatographed on a single-stranded DNA mic supercoils. At a higher force (1.9 pN), (Ϫ) ␴ caused DNA cellulose column by using a 0.25–2 M KCl gradient. To prepare untwisting in place of supercoiling. Plectonemic supercoiling still the Thermotoga maritima topo I, the gene was amplified by using resulted at this force from a (ϩ) ␴. We used three DNA the PCR from genomic DNA and subcloned into the pET29b substrates (Fig. 2C). Besides an 11.5-kb double-stranded DNA, expression vector. The recombinant protein was expressed in E. we used an 8.7-kb duplex DNA that contained a small single- coli and purified as described (23). stranded region, consisting either of a mismatch of 12 unpaired Topo I reactions contained 50 mM Tris⅐HCl, pH 8.0, 120 mM nucleotides or a bulge of 25 nucleotides midway through the ␮ ͞ NaCl, 10 mM KCl, 3 mM MgCl2,1mMDTT,200 g ml BSA, DNA. Duplex DNA with a single-stranded region is a particu- and 0.1% Tween 20. The MgCl2 concentration was reduced to larly good substrate for type IA enzymes (13). We used two type 0.25 mM to observe step-wise activity of topo I. IA topoisomerases, from E. coli and T. maritima, that differ greatly in amino acid sequence (23). The enzyme from the Numerical Analysis. To cancel slow drifts of the optical micro- hyperthermophilic T. maritima has a temperature optimum of scope, we measured the distance l(t) between the tethered bead 80° C but retains high activity at room temperature. In this

Dekker et al. PNAS ͉ September 17, 2002 ͉ vol. 99 ͉ no. 19 ͉ 12127 Downloaded by guest on October 2, 2021 Fig. 4. Rate of (ϩ) supercoil removal by topo I as a function of the applied force. (A) Variation of the enzymatic rate with force on a DNA construct containing a symmetric mismatch of 12 nucleotides. The data shown are for E. coli topo I (similar results were obtained with T. maritima topo I) and were fit by using v ϳ exp(ϪF␦͞kBT), yielding ␦ (the distance DNA moves during the force-sensitive step) of about 10 nm. (B) Variation of the enzymatic rate with force on a DNA construct containing an asymmetric bulge of 25 nucleotides. The data shown are for T. maritima topo I, but similar results were obtained with the E. coli enzyme. The results were fit to a straight line that deviates from Fig. 3. Relaxation of (Ϫ) supercoiled DNA by E. coli topo I. The substrate was a flat line by less than 10%. fully duplex 11.5-kb DNA. Arrows (1) indicate the introduction of supercoil- ing by rotation of the magnets. (A) Topo I relaxes (Ϫ) supercoils, as shown by the increase in DNA extension, but cannot relax (ϩ) supercoils. (B) The effect of force on (Ϫ) supercoil relaxation. DNA supercoiling density equaled Ϫ0.03. activity as a function of force suggested to us that single The topo I concentration was 380 pM, which was above the Kd of Ϸ200 pM that relaxation events might be observable at a large enough force. we estimated with single-stranded DNA. Topo I is inactive at F ϭ 0.26 pN (gray) To quantify the elementary catalytic steps of a single molecule but active at F ϭ 0.53 pN (green), where more of the (Ϫ) superhelical stress is of topo I on supercoiled DNA, we needed [1] a single enzyme partitioned into DNA untwisting. To determine topo I activity at F Ͼ 1 pN, acting on DNA in reaction conditions within the physiological Ϫ where DNA extension is independent of ( ) superhelical density (Fig. 2B), we range, [2] a rate of supercoil removal slower than 1 per s, our periodically monitored DNA extension at F ϭ 0.26 pN. For example, to measure topo I activity at 2.8 pN (red), we measured the degree of (Ϫ) supercoiling of time-resolution limit, and [3] an increase in DNA extension per the DNA at 0.26 pN, increased the force to 2.8 pN on a time scale that was fast supercoil removal readily observable above the noise. The compared with that of topo I activity, added topo I, and reduced the force to properties of topo I relaxation of (Ϫ) supercoiled DNA pre- 0.26 pN to remeasure the degree of supercoiling. Thus, we found that topo I sented technical obstacles to fulfilling these criteria. remained active at 2.8 pN, but at a reduced rate. At F ϭ 5.4 pN (blue), no topo Therefore, we adopted a strategy based on the observation of I activity was detected. Kirkegaard and Wang (13) that a (ϩ) supercoiled DNA with an engineered short denatured region is an excellent substrate for topo I. Thus, we made a DNA construct with a central 12-bp report, we focus on the more extensively characterized topo I mismatch (Fig. 2C). We expected topo I would bind well to this from E. coli. region of single-stranded DNA, and that the short length of the We began by showing with our apparatus that E. coli topo I mismatch would allow only one topo I to bind each DNA removes (Ϫ), but not (ϩ), supercoils from DNA, its signature 1 activity. Supercoils were incorporated into a 11.5-kb duplex molecule, fulfilling criterion . As expected, topo I relaxed (ϩ) supercoiling of this substrate. DNA by rotation of the magnets, with resultant shortening of the ϩ molecule’s extension (Fig. 2B). With 380 pM E. coli topo I acting The rate of ( ) supercoil removal, independent of supercoiling density, decreased with applied force (Fig. 4A), just as we had on a DNA under 0.69 pN of tension, we observed brisk relaxation Ϫ of (Ϫ) supercoils but no activity with (ϩ) supercoils (Fig. 3A). observed with ( ) supercoiled DNA. This control of the relax- Next, we studied the effect of force on topo I relaxation of (Ϫ) ation rate of topo I by force helped us fulfill criterion 2. The supercoiled DNA (Fig. 3B). There was a force optimum for topo dependence could be fit to an Arrhenius law for the relaxation ϳ Ϫ ␦͞ ␦ Ϸ I activity. At a low force, 0.26 pN, no topo I activity was observed rate v: v exp( F kBT), yielding an effective length of 10 on DNA with ␴ ϭϪ0.03. When the force was increased to 0.53 nm associated with the work performed against the force F by an Ϸ pN, topo I relaxed (Ϫ) supercoils efficiently at an average rate enzyme of only 5 nm. This very large deformation of the DNA of Ϸ1 supercoil per s. The increased force caused more of the substrate is surprising. Perhaps it is associated with insertion of stress of the (Ϫ) ⌬Lk to be converted to untwisting rather than the enzyme between the two DNA strands upon binding. A writhe, which promotes enzyme binding (25). Interestingly, the parallel diminution of rate with applied force was observed with rate of relaxation was lower at 2.8 pN and was undetectable at the T. maritima enzyme (data not shown). In contrast, with a higher forces. This result was unexpected because denaturation DNA construct with a bulge of 25 nt instead of the mismatch, the bubbles become more prominent at higher forces. Thus, beyond relaxation rate was insensitive to applied force (Fig. 4B). We a minimal force required for the creation of a denaturation interpret this difference as due to whether the single-stranded bubble, the rate of topo I activity diminished with increasing region to which the enzyme binds is under tension. With the force, suggesting that the enzyme has to move DNA against the mismatch, the work performed by the enzyme against the tension force during DNA binding or strand transport. The decrease in increases with applied force, thus slowing it down.

12128 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.132378799 Dekker et al. Downloaded by guest on October 2, 2021 Fig. 5. Step-wise relaxation of (ϩ) supercoiled DNA. The DNA contained a symmetric mismatch of 12 nucleotides. (A and B) Single relaxation events observed in supercoil removal by (A) E. coli topo I (F ϭ 2.0 pN) and (B) T. maritima topo I (F ϭ 1.5 pN) in 0.25 mM MgCl2. The blue points are the raw data, and the red lines are the best-fitted steps. (C) Probability distribution of E. coli topo I step-sizes (n ϭ 610) in seven experiments with forces ranging between 1.0 pN and 2.0 pN. The data were fit to a Gaussian to yield an average value of ͉͗⌬Lk͉͘ϭ1.03 Ϯ 0.01. (Inset) Results from a single experiment at 2.0 pN (n ϭ 90); peak fitted to ͉͗⌬Lk͉͘ϭ0.97 Ϯ 0.03.

Slowing down enzymatic activity at high forces on a DNA with cycle. Furthermore, the exponential fit predicts that 15 Ϯ 3 plectonemic supercoils presented two major advantages in terms steps-of-one would occur on time scales faster than our temporal of signal-to-noise. First, it permitted direct monitoring of topo I resolution tav (see Materials and Methods). This result agrees well activity through the increase in DNA extension, an option with the 17 observed fast steps-of-one contained in events compromised by DNA denaturation in (Ϫ) supercoiled DNA contributing ͉⌬Lk͉ Ն 2atF ϭ 2.0 pN (Fig. 5C Inset). We conclude (Fig. 3B). Relaxation of one (ϩ) supercoil (⌬Lk ϭϪ1) resulted that all steps of ͉⌬Lk͉ Ն 2 can be interpreted as rapid successions

in a 35.0-nm increase in length at F ϭ 2.0 pN (Fig. 2B). Second, of single steps, supporting the strand-passage model. SCIENCES it enabled these measurements to be made with lower noise, The experiments described above were conducted at a limiting AGRICULTURAL because the amplitude of the bead’s fluctuations decreased with concentration of MgCl2. It is conceivable that the observed the applied force. The combination of these factors helped step-of-one behavior is an artifact of reducing the rate, as the satisfy criterion 3. The final adjustment we made was to slow the limiting value of n is, of course, 1. To analyze the topo I step sizes reaction rate by decreasing the magnesium concentration to 0.25 at much higher reaction rates we used a second, independent mM. This completed the satisfaction of criterion 2. method based on analysis of the power spectrum of the fluctu- We could now test whether type IA topoisomerases used an ations of the DNA extension, l(t) (26, 27). In this method, the

enzyme-bridged strand-passage mechanism or a strand-rotation square of the amplitude of the Fourier transform of this signal BIOPHYSICS mechanism. We found that the (ϩ) supercoiled construct with is analyzed as a function of frequency. An attractive feature of a 12-bp mismatch was relaxed by E. coli and T. maritima topo I the fluctuation analysis is that information about topo I behavior ϳ in a step-wise fashion at a force F 2 pN in 0.25 mM MgCl2 (Fig. can be extracted without averaging the data. In the absence of 5 A and B). To analyze the distribution of step-sizes, we fitted the topo I, the amplitude of the Brownian fluctuations of the raw data to a series of steps of amplitude S, occurring at times magnetic bead did not vary as a function of the frequency of the tS, constrained by averaging to a minimum time interval tav fluctuations (Fig. 6B, gray dots). However, in the presence of (shown in red in Fig. 5 A and B). For seven experiments with E. enzyme, the random nature of the time between steps of coli topo I over a force range of 1–2 pN, the best fitted steps were supercoil relaxation caused the fluctuations to increase at low binned (Fig. 5C), and the peak was fitted to a ͉͗⌬Lk͉͘ϭ1.03 Ϯ frequencies as A͞f 2, where f is the frequency and A is the 0.01 (n ϭ 610). The result of an analysis limited to a single force amplitude (Fig. 6B, red dots). If the distribution of times between (2.0 pN, shown in the insert) yielded ͉͗⌬Lk͉͘ϭ0.97 Ϯ 0.03 steps is Poissonian, the magnitude A of these fluctuations is (n ϭ 90). related to the enzymatic rate v and step-size S by A ϭ Sv͞2␲2. Therefore, the overwhelming majority of steps corresponded Thus, analysis of the fluctuations in the experimental signal to ͉⌬Lk͉ ϭ 1. However, even under these conditions we occa- permits one to deduce the enzymatic step size from a knowledge sionally saw steps corresponding to ͉⌬Lk͉ Ն 2. These larger steps of its mean velocity. At low rates (͗v͘ϭ2.27 nm͞s; i.e., an might occur because topo I is able to remove supercoils in steps enzymatic cycle of about 15 s; see Fig. 6A), we calculate that greater than 1. Alternatively, two or more independent step-of- ͗⌬Lk͘ϭ1.07 Ϯ 0.23, which is in agreement with the result one events could occur on a time scale faster than our temporal obtained from our real-time analysis and reconfirms that the resolution. This question was addressed by examining the kinet- statistical behavior of topo I follows a Poisson distribution. ics of relaxation by E. coli topo I. Moreover, the fluctuation analysis can equally well be applied to Ͻ The distribution of time between successive steps of relaxation relaxations under conditions (F 1 pN and 3 mM MgCl2)in at F ϭ 2.0 pN is shown in Fig. 6A. These data are well fit by a which a 10-fold increase in topo I relaxation rate prevents Poisson distribution with a mean time ␶ ϭ 15.4 Ϯ 3s.The real-time determination of steps. If we assume a Poisson distri- Poissonian nature of relaxation events indicates that the applied bution, the analysis yields a value of the step-size ͉͗⌬Lk͉͘ϭ force acts on a single rate-limiting step of topo I’s enzymatic 0.98 Ϯ 0.2. We conclude that our measurement of the enzymatic

Dekker et al. PNAS ͉ September 17, 2002 ͉ vol. 99 ͉ no. 19 ͉ 12129 Downloaded by guest on October 2, 2021 found that the number of steps-of-one predicted to occur on time scales faster than our temporal resolution, 13 Ϯ 4, was in agreement with the measured number of 12 fast steps-of-one contained in events contributing a ͉⌬Lk͉ Ն 2. This result shows that, as with the E. coli enzyme, the number of steps contributing ͉⌬Lk͉ Ն 2 is completely consistent with the strand-passage model. Analysis of the power spectrum of the fluctuations of T. maritima topo I activity yielded a step-size of 0.97 Ϯ 0.3, which is in excellent agreement with real-time analyses. Conclusions Our kinetic data along with past structural and biochemical results (9, 12–14) allow us to conclude that both E. coli and T. maritima type IA topoisomerases use an enzyme-bridged, strand-passage mechanism. Because these enzymes differ greatly in sequence, and the evolutionary divergence of these bacteria is large, it seems safe to conclude that the mechanism is conserved throughout type IA enzymes. This mechanism requiring enzyme binding to a single strand of DNA is well suited to the physio- logical roles of the two major type IA enzymes, topo I and topo III. Topo I is dedicated to removing (Ϫ) supercoils and thus complements DNA gyrase, which removes only (ϩ) supercoils, in maintaining the proper level of (Ϫ) supercoiling in bacteria (1, 2). Topo III does not play a role in relaxation of (Ϫ) supercoils in either or , but instead probably dis- entangles single strands produced during replication or recom- bination by the action of a DNA helicase (15, 16). The rotation mechanism proposed for type IB enzymes is much less controlled and is suited instead to the rapid removal of both (Ϫ) and (ϩ) supercoils. The latter activity is required during DNA replica- tion. The rotation mechanism cannot mediate disentanglement, (de)catenation, or (un)knotting of DNA as does the strand- Fig. 6. Kinetic analysis of E. coli topo I at a force of 2.0 pN. (A) Histogram of passage mechanism of type IA enzymes. When type IB enzymes times between steps in topo I activity, obtained by fitting the data in the Fig. carry out such reactions, another mechanism must be coming 5C Inset over a time window tav, where tav was allowed to vary between acquisitions. The exponential fit yields an enzymatic turnover time, ␶, of 15.4 Ϯ into play. There is a clear structural similarity between type II 3 s, corresponding to a mean rate of DNA elongation, ͗v͘, of 2.27 nm͞s. From and type IA, but not type IB, topoisomerases (28). Because type this fit, we estimated that topo I performed a total of 15 Ϯ 3 steps in a period II enzymes use an enzyme-bridged mechanism, it is clear that the faster than our time resolution tav. This result agrees well with the 17 fast similarity extends to the fundamentals of catalysis. Indeed, we steps-of-one contained in events contributing ͉͗⌬Lk͉͘ Ն 2 (Fig. 5C Inset). To can view a type II topoisomerase as one in which there is count these fast steps, a cutoff of ͉͗⌬Lk͉͘ϭ1.5 was applied to the Gaussian concerted type IA action on both strands of the double helix. distribution of the data. (B) Examples of the spectral distributions of the Finally, we note that our study depended critically on the fluctuations of DNA extension obtained with (red) and without (gray) topo I. advantages of single molecule enzymology over ensemble stud- The difference between these two curves was fit to the function A͞f 2 (blue ϩ curve), where f is the frequency and A is the amplitude. A is related to the ies. We capitalized on the ease of generating ( ) supercoils, the enzymatic rate v and the step-size S (in nm) by A ϭ Sv͞2␲2. From an average application of force to bring enzyme rate and noise within of over eight spectral distributions, we determined a value of ͗A͘ϭ4.30 nm2 bounds, and the quantification of fluctuations in the behavior of Hz. By using the mean velocity ͗v͘ϭ2.27 nm͞s, we deduced a step-size ͗⌬Lk͘ individual enzymes to calculate step sizes. ϭ 1.07 Ϯ 0.23. We thank T. Viard and C. Bouthier de La Tour for a gift of T. maritima enzyme, V. Holmes for help with Fig. 1, and J. Champoux, G. Charvin, step size is independent of the means used to slow down topo I R. DiGate, and J. Wang for a critical review of the manuscript. We activity. gratefully acknowledge support from the Centre National de la Recher- We applied the same analyses to relaxation by T. maritima che Scientifique, the Association pour la Recherche sur le Cancer, the topo I and found again that ͉͗⌬Lk͉͘ was uniquely equal to one Ecole Normale Supe´rieur, the National Science Foundation, and the National Institutes of Health (Grants GM31657 and GM63786). V.V.R. (data not shown). The distribution of step sizes obtained from acknowledges an award from the Research Corporation; N.H.D. ac- real-time analysis fit to a Gaussian distribution centered at a ͉͗⌬ ͉͘ϭ Ϯ ϭ knowledges an award from the Netherlands Organization for Scientific Lk 1.01 0.02 (n 213). The histogram of the times Research. This research has also been supported by a Marie Curie ϭ between successive steps (averaged over a time window tav 1s) fellowship of the European Community program Improving Human fit an exponential (Poisson) distribution with mean ␶ ϭ 4s.We Potential under Contract HPMF-CT-2000-00807.

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