THE JOURNAL OF BIOLOGICAL CHEMISTRY Vol. 266, No. 30, Issue of October 25, pp. 20567-20573,1991 0 1991 by The American Society for Biochemistry and Molecular Biology, Inc. Printed in U.S.A.

Supercoiled DNA-directed Knotting by T4 Topoisomerase* (Received for publication, April 25, 1991)

Steven A. WassermanSQ and Nicholas R. Cozzarellill From the $Department of Biochemistry, University of Texas Southwestern Medical Center, Dallas, Texas 75235 and the YDepartment of Molecular Biology, University of California, Berkeley, California 94720

The mechanism by which the type 2 topoisomerase from bacteriophage T4 mediates knotting of negatively supercoiled DNA was deduced from an analysis of product topology. The knotted products were nicked and then subjected to electrophoresis in order to sepa- rate species on the basis of the minimum number of crossings in the knotted form. Knots with defined num- bers of crossings were purified and the configuration of these crossings determined in the electron micro- scope by the RecA coating method. The product knots were exclusively of the twist form, in which an inter- wound region is entrapped by a single interlock of two looped ends. The interwound region was of negative sign in >98% of the molecules examined, whereas the single interlock was equally likely to be positive or negative. These results are interpreted in terms of a model for knot formation in which random strand pas- sage mediated by the topoisomerase links bent or branched portions of a superhelix that has a specific interwound geometry. Superhelix interwinding and DNA contacts stabilized by excess enzyme molecules explain the very high frequency of knotting.

Topoisomerases, by carrying out DNA strand passage re- actions, fulfill a vital role in the replication and segregation of double helical DNA (1-4). In vitro, topoisomerases readily knot and unknot as well as catenate and decatenate DNA (5- 11). In uiuo, however, knotted and catenated DNAs accumu- late to significant levels only in cells deficient for topoisom- erase activity (2-4, 12). Although the active segregation of chromosomes might be postulated to drive decatenation in the cell, the same hypothesis could not explain the near absence of knots in wild-type cells, nor the rapid unlinking of catenated plasmids generated by recombination (13, 14). Rather, it seems likely that the intracellular state of the DNA is the predominant influence on the outcome of topoisomer- ase-mediated strand passage events, particularly for intra- molecular processes. In order to investigate the influence of DNA structure on the action of topoisomerases, we have therefore undertaken a study of DNA knotting.

Topoisomerase-mediated knotting of duplex DNA in vitro has been well characterized for the Escherichia coli topoisom- erase I (15, 16). The reaction, which requires a nicked or gapped substrate, is a simple strand passage reaction. Topoi- somerase I breaks one strand of the duplex opposite a preex- isting interruption in the other, allows a duplex segment to

* This work was supported by a grant from the Lucille P. Markey Charitable Trust (to S. A. W.) and by grants from the National Institutes of Health (to N. R. C.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accord- ance with 18 U.S.C. Section 1734 solely to indicate this fact.

!j Lucille P. Markey scholar.

pass through the transient double-stranded break, and then rejoins the broken strand. The form of the knot is determined not by the enzyme, but by the random folds and twists of the DNA that become locked in place by strand passage. The resulting catalogue of products contains each entry of a math- ematician’s knot table.

In light of the substantial insight into topoisomerase I action gained from studies of its knotting reactions (15-18), we set out to investigate the knotting of DNA by a type 2 enzyme from T4. Type 2 topoisomerases pass entire duplexes through each other and usually require ATP. In contrast to topoisomerase I, high concentrations of T4 topoisomerase can efficiently knot covalently closed DNA, provided that the substrate is supercoiled and no ATP is added to the reaction (6). If ATP is added, the T4 topoisomerase carries out multiple rounds of reaction, relaxing the substrate and untying any knots formed. Thus knotting by the T4 enzyme reflects a limited reaction with a supercoiled substrate, resulting, as we demonstrate here, in a unique family of products.

Our studies reveal a fundamental similarity between the type 1 and type 2 reactions; both enzymes knot DNA by carrying out random strand passage reactions. Both enzymes also augment greatly the frequency of knotting by what we interpret as a bridging of segments of the DNA chain. Striking dissimilarities in product distribution arise, nonetheless, due to conformational differences between relaxed and super- coiled DNA substrates. Moreover, a detailed analysis of the product array from the T4 topoisomerase reaction serves to solidify our picture of the structure of supercoiled DNA in solution as a branched interwound superhelix.

EXPERIMENTAL PROCEDURES

DNA and Enzymes-Plasmids pBNW3.8d, pRR51, and pA2 have been described (19-21). T4 topoisomerase partially purified from an extract of phage-infected cells by DNA cellulose and hydroxyapatite chromatography was a gift of Ken Kreuzer (Duke University, Dur- ham, NC). It was purified to homogeneity by chromatography on Sephacryl S-300 as previously described (22).

Knotting Reactions-Knotting was carried out in a mixture con- taining 50 mM Tris (pH 7.6), 60 mM KC1, 10 mM MgCl,, 20 pg/ml DNA, and 40 pg/ml bovine serum albumin (22). The solution was prewarmed to 32 “C prior to addition of 1.75 pg of T4 topoisomerase/ pg of DNA. After a 4-min incubation at 32 “C, the reaction was quenched by addition of EDTA to 10 mM. Following extraction of the mixture twice with phenol, the volume of the quenched reaction product was then reduced 2-fold by extraction with sec-butyl alcohol. The concentrated solution was then extracted twice with ether and the DNA precipitated with sodium acetate and ethanol. The precipi- tated DNA was resuspended to 0.1 reaction volume in TE buffer (10 mM Tris, pH 8.0, and 1 mM EDTA).

Nicking Reactions-After knotting, supercoils were removed from DNA by limited nicking (23) in a reaction containing 50 mM Tris (pH 7.61, 6 mM MgC12, 100 pg/ml each DNA and ethidium bromide, and 1.9 pg/ml DNase I. Electrophoretic analysis indicated that under these conditions, a 30-min reaction at 30 “C yielded approximately 90% nicked, 5% linear, and 5% supercoiled DNA. The reaction was quenched by addition of EDTA to 10 mM and NaCl to 150 mM. The

20567

20568 T4 Topoisomerase Knots mixture was then extracted twice with phenol, the volume reduced 4- fold by extraction with sec-butyl alcohol, and the concentrated solu- tion extracted twice with ether.

Gel Electrophoresis and Quuntitation-Nicked knotted DNA sam- ples (1 pg for analytical gels and 40 pg for preparative reactions) were subjected to agarose gel electrophoresis buffered with Tris-acetate containing 0.03% SDS' or with Tris-borate (89 mM Tris, 89 mM borate, 2.5 mM EDTA, pH 8.3) (2, 21). Following staining with 0.5 pg/ml ethidium bromide, the banding pattern was recorded on Pola- roid film and the negative scanned with a Molecular Dynamics densitometer.

Purification of Knotted DNA-Alternative methods (24) were used for the purification of knotted DNA with equivalent results. In one, samples were subjected to electrophoresis in a 0.7% agarose gel in Tris-borate for 38.5 h at 60 V. The gel was stained and a trough cut behind the trefoil species. The trough was filled with hydroxyapatite (Bio-Gel HTP) and electrophoresis carried out with reverse polarity for 2.25 h at 60 V. The hydroxyapatite was then packed into 0.5-ml columns, and each column was washed with a buffer of 10 mM potassium phosphate, pH 6.8, and 1 mM EDTA. The DNA was then eluted with 400 mM buffer and extracted sequentially with phenol, sec-butyl alcohol, and ether.

In the other procedure, samples were subjected to electrophoresis in a 0.75% agarose Tris-acetate gel for 43 h a t 42 V. The gel was washed twice in water to remove SDS and then stained. Agarose slices containing knotted species were cut from the gel and dissolved in 10 mM phosphate buffer saturated with potassium iodide. The DNA samples were then loaded onto 0.5-ml columns of hydroxyapa- tite (Bio-Gel HTP) equilibrated with 10 mM buffer. The DNA was eluted as above, extracted with phenol, and dialyzed twice against T E at room temperature.

Electron Microscow-Nicked, knotted DNAs were denatured by glyoxal treatment a t 62 "C for 90 min (25). The single-stranded DNA was desalted and coated with RecA in the presence of 5 mM ATP and 5 mM magnesium acetate, as described previously (26). The DNA- protein complexes were then fixed with glutaraldehyde and tungsten shadowed for electron microscopy (25). Criteria for tracing knots and scoring nodes were as reported previously (15).

RESULTS

To explore the mechanism of the T4 topoisomerase knot- ting reaction, we first characterized the products by gel elec- trophoresis. A supercoiled 3800-bp plasmid, pBNW3.8d, was knotted with purified T4 topoisomerase and singly nicked with DNase I; nicking removes supercoiling but leaves knot- ting intact. The DNA was then subjected to gel electrophoresis and stained with ethidium bromide (Fig. l.4). Under the conditions used, mobility in the gel was proportional to the minimum number of crossing, or nodes, in the knotted form.

Four features of the knotting reaction were evident from the electrophoretic analysis. 1) Topoisomerase-generated knots were generated with both odd and even numbers of crossings, forming a node ladder with steps-of-one spacing (Fig. IA, lune 3). By comparison, catenanes resulting from the same substrate by recombination mediated by the X inte- grase ( Int ) have even numbers of crossings exclusively (Fig. l.4, lanes 4 and 5). 2) The top rung of the T4 topoisomerase knot ladder was composed of trefoils, knots with 3 crossings. The trefoil (Fig. 2, a and b) is the simplest knot, since knot crossings are always integral and knots cannot be tied with fewer than 3 crossings. 3) The amount of a given product species declined with node number (Fig. L4, lane 3). 4) Knot formation in the T4 topoisomerase reaction required super- coiled substrate, since nicked or relaxed pBNW3.8d yielded less than 1% knotted product (data not shown).

Larger supercoiled substrates, pRR51 (5950 bp) and pA2 (6400 bp), yielded an even higher percentage of knotted prod- ucts, 50-75% in a standard reaction. Fig. 1B shows the PA' pattern. The distribution of knotted species for these larger

The abbreviations used are: SDS, sodium dodecyl sulfate; bp, base pair(s).

A.

n .-

i -

r -

1 2 3 4 5

Node 0.

-0

- 3

- 4

- 5

- 6 - 7 - a -9 - 10

FIG. 1. Electrophoretic analysis of DNA knots formed by T4 topoisomerase. A, pBNW3.8d was knotted with T4 topoisom- erase and nicked with DNase I to remove supercoils. It was then subjected to electrophoresis with markers in a 0.7% agarose gel in Tris-borate a t 70 V for 19 h. Lane I, 80 ng of supercoiled (sc) substrate. Lane 2, 65 ng of linear ( I ) substrate generated with BarnHI endonu- clease. Lane 3, 900 ng of nicked knots. Lanes 4 and 5, 1-pg marker ladders of catenanes generated by Int reaction with partially relaxed substrates. Nicked circles (n) and linearized substrate ( I ) in lanes 3- 5 are products of DNase I treatments, as is the free recombinant circle ( r ) in lanes 4 and 5. B, knotted and nicked pA2 subjected to electrophoresis in a 0.75% agarose gel in Tris-acetate with SDS for 43 h at 42 V.

plasmids was broad, ranging from 3-noded knots to knotted products with 18 or more crossings. The spacing of the ladder rungs remained one node.

These electrophoretic analyses indicated that, like E. coli topoisomerase I, the T4 type 2 enzyme could tie knots with variable numbers of crossings of odd or even number. How- ever, electrophoretic separation according to the minimum number of duplex crossings could not indicate whether the T4 enzyme produced all of the knots seen with topoisomerase I, since the number of crossings is an incomplete descriptor of all but the 4-noded knot. There is only a single knot with 4 nodes. There are, however, two enantiomeric knots with 3 nodes and eight knot isomers with 6 nodes. To determine which particular isomers arose in knotting reactions with the T4 topoisomerase, we undertook an electron microscopic analysis of the reaction products.

In order to visualize overlying and underlying DNA seg- ments at knot crossings, we thickened the DNA by coating it with RecA. Since RecA reacts more readily with single- than double-stranded DNA, gel-purified knots were denatured to separate the knotted single strand of each duplex from the nicked strand. This does not affect the topology of the knot. The single-stranded DNA was then reacted with RecA, ad- sorbed to carbon-coated grids, shadowed, and examined by electron microscopy.

We began our analysis with the 3-noded knots or trefoils. Trefoils can be of only two forms, distinguished by whether the three, irreducible nodes are of positive or negative sign (Fig. 2, a and b). The sign convention is explained in the legend to Fig. 2. The trefoils formed by T4 topoisomerase were overwhelmingly of one enantiometric form; 85 out of 87 trefoils examined were negative in sign; only two were posi- tive. Examples are shown in Fig. 3.

The strongly biased array of product trefoils formed by the T4 topoisomerase is in sharp contrast to the racemic mixture of (+) and (-) trefoils from an E. coli topoisomerase I knotting reaction (15). Our gel analysis revealed, however, that the T4 enzyme, like topoisomerase I, generated the 4-noded knot, which contains 2 (+) as well as 2 (-) nodes. Furthermore, the T4 topoisomerase is known to relax both positive and negative

T4 Topoisomerase Knots 20569 A

FIG. 2. Topology of DNA knots. Projection drawings of knotted molecules are shown. Knots are classified as to number and configu- ration of the irreducible number of nodes, or crossings. Knots a and b have 3 nodes, knot c has 4 nodes, knots d and g have 5 nodes, and knots e, f, and h have 6 nodes. If two molecules have an equal number of nodes, but one cannot be stretched to superimpose on the other or its mirror image, the two knots are distinct and diastereomeric. If one knot can only fit the mirror image of the other, the two are enantio- mers distinguished by node signs. Node sign, shown for a single node in the top row of knots, is determined separately for each crossing. Arrowheads denote an arbitrary orientation along the entire DNA axis. A node is negative in sign if the overlying arrow can be aligned with the underlying one by a clockwise rotation of less than 180". The node is positive if a counterclockwise rotation results in align- ment. Knots a and b are enantiomers. Knots e, j , and h are diastere- omers. Knots can also be grouped into families of related forms. Knots a-e are members of the twist family, which have an interwound region with 1, 2,3.. . n nodes and a single interlock made up of two nodes. The twist family is subdivided further according to whether there is an odd (a, b, d ) or even (c , e) number of nodes. For the former, the sign of all the nodes is the same; for the latter, the interlocking nodes have the sign opposite to that in the interwound region. Knot g is a member of the torus family. Knots of this family can be drawn without intersection on the surface of a torus, a doughnut-shaped solid, and are the most regular in structure of all knots. a, trefoil or 3-noded knot with 3 (-) nodes. b, trefoil with 3 (+) nodes. c, twist knot with 2 (-) and 2 (+) nodes (achiral). d, twist knot with 5 (-) nodes. e, twist knot with 4 (-) and 2 (+) nodes. f, a granny knot, a composite knot composed of two trefoils, each with 3 (-) nodes. g, torus knot with 5 (-) nodes. h, a 6-noded knot with 4 (-) and 2 (+) nodes that is not a twist knot.

supercoils (6) and can thus carry out binding and catalysis a t both (-) and (+) nodes. These facts, the topology of the 3- and 4-noded knots, and a catalytic mechanism that is blind with regard to node sign can all be accommodated by a model postulating random strand passage events between portions of a negatively interwound supercoiled DNA substrate, as illustrated in Fig. 4 and detailed below.

FIG. 3. Electron microscopy of trefoil knots. Purified trefoil knots made by T4 topoisomerase were denatured, coated with RecA protein, adsorbed to grids, shadowed with tungsten, and photographed in the electron microscope. A, pRR51 knots. B, pRR51 (left) and pA2 (right) knots. Each micrograph is accompanied by a tracing showing the relative overlay of strands at each crossing and by a redrawing of the knot with only the minimum number of crossings. Each knot has 3 irreducible (-) nodes.

If conformational fluctuations of the supercoiled substrate or topoisomerase-stabilized DNA bridges bring one loop of DNA across a second loop, a (+) node and a (-) node are formed. If the topoisomerase breaks one duplex at either the (+) or (-) node and allows the crossing duplex to pass through the gap before resealing the broken DNA, a knot of the twist family is produced (Fig. 4). The (-) sign of the crossings in the twisted region of the knot reflects the (-) supercoiling of the plasmid substrate. In the process of strand passage super- coils have been converted from geometric forms that can be unfolded to topological forms that cannot.

Two distinct classes of twist knots will arise depending on which of the overlap nodes is the site of reaction (Fig. 4). If the topoisomerase carries out strand passage at the (+) node, converting it to a (-) node, the knot will contain an odd number of nodes, all negative in sign. The 3- and 5-noded examples are shown, respectively, in Fig. 2, a and d. If the topoisomerase instead acts at the (-) overlap node to convert it into a (+) node, the knotted product will have a twist region containing an even number of (-) nodes and a linking region with two (+) nodes, as in the 4- and 6-noded knots in Fig. 2, c and e.

20570 T4 Topoison wrme Knots

FIG. 4. Proposed mechanism for twist knot formation by T4 topoisomerase. The substrate for knotting by T4 topoisomerase consists of an interwound, negatively supercoiled DNA. As the super- helix bends, two regions (bold lines) cross. As shown, two nodes result, one (-) and one (+). All other nodes of the superhelix are (-), but their sign is omitted for clarity. Knotting occurs by topoisomerase- mediated strand passage at either the (+) node (upper pathway) or the (-) node (lower pathway). The product of the upper pathway is a twist knot with an odd number of (-) nodes, two in the linking region and the rest in the intervening twist region. There is a total of 5 nodes in the example shown. The product of the lower pathway is a twist knot with 2 (+) linking nodes and an even number of intervening (-) nodes; there is a total of 4 nodes in the example shown. Note that unfolding removes any nodes not entrapped by knotting and that only a fraction of the original supercoiling contrib- utes to the knot structure. For illustrative purposes, unfolding is shown in two stages. In the first, the DNA is nicked but the regions where the topoisomerase has acted remain juxtaposed; in the second, this constraint is removed and the DNA rearranged into a more standard form for knots. A quantitative treatment of knotting by type 2 topoisomerases (27) describes the relationship of enzyme mecha- nism, substrate supercoiling, and product knotting.

By this model, product trefoils are of (-) sign not because the enzyme must invert a (+) node to form a knot, but because inversion of a (-) node will form a knot with an even number of nodes in its fully unfolded form. Rare (+) trefoils could be formed by the chance entrapment of a single (+) node by the enzyme and strand passage a t (-) node (27).

This model leads to the strong prediction that the knot8 formed by T4 topoisomerase should be restricted not only in node sign, but also in knot form. Only twist knots are expected to arise by the mechanism shown in Fig. 4. For knots with an odd number of crossings, all crossings should be (-) in sign; for knots of even node number, two nodes should be of (+) sign and the rest negative.

Among 5-noded knots, the proposed mechanism predicts that the T4 topoisomerase will produce only one of the four possible forms. The expected knot is a twist form with 5 (-) nodes (Fig. 2 4 , whereas the twist knot with 5 (+) nodes and the torus knots with 5 (-) nodes (Fig. 2g) or 5 (+) nodes should not appear. When 5-noded knots generated by T4 topoisomerase were examined, all 39 molecules were twist knots with 5 (-) nodes (Fig. 5). None of the three other possible 5-noded knots, all of which are formed by topoisom- erase I, were observed.

Although the analysis of the 5-noded knots offered substan- tial support for the supercoiled DNA-directed knotting model described above, an anomaly in the electrophoretic gel profile prompted us to extend our analysis to the 6-noded knots. Close examination of the electrophoretic ladders of T4 topo- isomerase knots revealed two knotted species in the region of the gel where 6-noded molecules migrate (Fig. 1B). A simple reaction of the type illustrated in Fig. 4 should give rise to only a single type of 6-noded knot, a twist knot with 2 (+)

FIG. 5. Electron microscopy of 5-noded knots. Electron mi- crographs of purified 5-noded knots of pA2, together with tracings and redrawings with the minimum number of crossings. Each knot has 5 irreducible (-) nodes.

TABLE I Product profile of knots made by T4 topoisomerose

The reaction products were nicked to remove supercoils, displayed by gel electrophoresis, and quantified by densitometric scanning of the ethidium bromide-stained gel.

Plasmid substrate Product Knot Profile

Name Size 3-noded 4-noded 5-noded 6-noded

bp % of total product

pBNW3.8d 3800 12.5 9.8 8.0 7.4 pRR51 5950 7.7 5.8 5.3 6.4 DA' 6400 11.1 ND" 8.4 9.9 Not determined (species comigrated with linear).

and 4 (-) nodes (Fig. 2e). We noted, however, that the total amount of 6-noded species was greater than that expected by extrapolation from the amount of knots with fewer crossings. The 3-noded, 4-noded, and 5-noded knots form a series of decreasing abundance (Table I). In contrast, the total amount of 6-noded knots from the two larger substrates, for which a second 6-noded species is more evident in gel profiles, is greater than the amount of 5-noded knots.

The relative overabundance of 6-noded species suggested that there might be a pathway for forming 6-noded knots that is inaccessible to knots with 3, 4, or 5 crossings. Mathemati- cally there is indeed such a distinction. A 6-noded species can be formed by knotting of a circle at two separate points. Furthermore, since the trefoil is the simplest knot, a 6-noded species composed of two trefoils is the simplest possible composite knot. Since the T4 topoisomerase was present in large excess, reaction could readily have occurred at more than one site on each substrate molecule.

The expected compound knot is the granny knot composed of 2 (-) trefoils whose form is illustrated in Fig. 2f. The granny knot and the 6-noded twist knot are diastereomers whose compaction in the gel could be distinct enough to result in differential mobility (26). Compound species are also ex- pected for knots with greater than 6 crossings. We did not, however, analyze more highly knotted species, because both the amount of knotted product and the resolving power of the gel decline with the number of knot crossings.

To test whether the two 6-noded species were indeed of the predicted configurations, the topology of the combined 6- noded species was examined directly by the RecA coating method, Out of 22 molecules, 10 molecules were 6-noded twist knots with 4 (-) and 2 (+) nodes; the remaining 12 molecules were compound 6-noded knots, granny knots, comprised of two (-) trefoils (Fig. 6). Given that there are eight different

T4 Topoisomerase Knots 20571

Ill Ill

FIG. 6. Electron microscopy of 6-noded knots. Electron mi- crographs of purified 6-noded knots of pA2, together with tracings and redrawings with the minimum number of crossings. The molecule on the left is a twist knot with 4 (-) and 2 (+) nodes. The molecule on the right is a granny, the compound knot composed of two trefoils, each with 3 (-) nodes.

TABLE I1 Topology of knots tied by T4 topoisomerase

The predicted knot topology is that derived from the scheme shown in Fig. 4.

Number of nodes

3 4 5 6

Total

Predicted knot node composition"

3 (-) (twist) 2 (-), 2 (+) (twist) 5 (-) (twist) 4 (-), 2 (+) (twist) or 3 (-), 3 (-) (granny)

predicted knots Number of

found/total knots scored

85/87 NDb 39/39 12/12 l o l l 0

146/148

Predicted knot form shown

Figs. 2a and 3 Fig. 2c Figs. 2d and 5 Figs. 2e and 6 Figs. 2f and 6

Knot type is indicated in parentheses. Not determined (only one possible structure).

possible 6-noded knots (4), yet only the two predicted forms were observed, we conclude that these knotted products in- deed result from random catalysis by T4 topoisomerase acting on an ordered DNA structure.

DISCUSSION

Knotting Mechanism-When analyzed by gel electropho- resis, the products of E. coli topoisomerase I (15) and T4 topoisomerase knotting reactions (6) appear quite similar. Each reaction yields knotted products in which the trefoil is the most abundant species and the molecules form a steps-of- one electrophoretic ladder. Nonetheless, the knotted products of T4 topoisomerase reaction are clearly distinguishable from the knots tied by topoisomerase I. Whereas topoisomerase I produces every knot theoretically possible (13 , we have dem- onstrated here that the T4 topoisomerase reaction gives rise to a unique subset of the products seen with topoisomerase I. The results are summarized in Table 11.

The 3-, 4-, 5-, and 6-noded knots produced by T4 topoisom- erase are all either simple twist knots or composites of two twist knots. The odd-noded simple twist knots contained only (-) nodes; the even-noded simple knots also had 2 (+) nodes. Despite the topological sign difference the simple knots shared an overall geometry: in each there is a (-) interwound region of variable length held in place by a single interlock (see Fig.

2, a, c-e). Only two exceptional knots of (+) sign, both 3- noded, were found among 148 examined. Such molecules probably arise during those rare circumstances when the high concentration of bound topoisomerase captures a (+) node in the otherwise negatively supercoiled DNA substrate (27).

The knots formed by the T4 topoisomerase differ from those formed by the Int recombinase, which are exclusively (+) torus knots with an odd number of nodes (28), and those formed during processive recombination by Tn3 resolvase, which have only an even number of nodes and can be neither torus nor twist (26). Coincidentally, however, experiments in which the T4 topoisomerase knots served as topological stand- ards demonstrated that the products of processive recombi- nation by the Gin invertase constitute the same subset of knots as is produced by the T4 enzyme (29).

Paradoxically, the non-random nature of the T4 topoisom- erase products provides substantial support for a random strand passage mechanism for the enzyme. Our proposed mechanism, in which substrate configuration plays a critical role in determining knot structure, is illustrated in Fig. 4 for a single catalytic cycle. Of 148 molecules examined, 146 can be viewed as twist knots with (-) nodes in the interwound region (Table 11). This result can only be readily understood by assuming that the sign of the twist region reflects the supercoiling of the substrate. There is in fact evidence from electron microscopy, the structure of the Int products, and computer simulation of DNA structure that the linking deficit of DNA is expressed in the form of interwound (plectonemic) rather than solenoidal supercoils (28, 30-32). The current results confirm this important conclusion for DNA in solu- tion.

Knotted plasmid DNAs have also been analyzed from a mutant E. coli strain in which a deletion of the topoisomerase I gene and a compensatory mutation in the gyrase B gene lead to the accumulation of knotted DNAs at a level 10 times that of wild-type strains (12, 33). Those knots analyzed by the RecA coating method appear, like the T4 enzyme prod- ucts, to be (-) twist knots, but there is an unexplained preponderance of knots with an odd number of nodes. In- creased knotting has also been detected in wild-type strains upon addition of high concentrations of the DNA gyrase inhibitor, norfloxacin;' the structure of these knots is not known. The production of (-) twist knots in the mutant strain suggests a mechanism of knot formation similar to that proposed here for the in vitro reaction with T4 topoisomerase and further indicates that DNA inside of E. coli cells is a (-) interwound superhelix.

Knotting Frequency and Specificity-As pointed out origi- nally by Liu et al. (6), the efficiency of knotting (up to 75%) by T4 topoisomerase in vitro is far greater than expected on the basis of theoretical calculations. The probability of knot- ting can be estimated for molecules modeled as a series of connected but freely jointed (Kuhn) segments of sufficient length to account for the bending stiffness of the DNA. Each such Kuhn segment is twice the persistence length. Using the accepted valve for the length of the Kuhn segment of free DNA (1000 A) and for the effective diameter of DNA (36), we calculate that at equilibrium only about 1-2% of relaxed DNA would be knotted for plasmids in the size range (3800- 6400 bp) we used.

These calculations fail to take into account the presence of excess topoisomerase molecules and the supercoiling of the substrate. I t has been suggested that a restriction on the volume of the DNA chain imparted by both supercoiling and excess bound protein forces a more tortuous path for the

D. Adams and N. R. Cozzarelli, unpublished results.

20572 T4 Topoisomerase Knots chains. This is equivalent to a reduction in the effective Kuhn length and could, in turn, explain the observed high frequency of knotting (6). Indeed, Monte Carlo calculations show that the probability of knotting increases greatly with the number of Kuhn segments (34), reflecting the greater flexibility of a DNA composed of an increased number of segments. How- ever, we calculate that the effective Kuhn length would have to be reduced to an implausibly low value of less than two turns of the double helix to explain our pBNW3.8d results. Furthermore, if supercoiling and excess protein were simply equivalent to increasing the effective number of Kuhn seg- ments, knots of all topological types would be produced. Instead only a particular subclass of knot topoisomers are observed.

Frank-Kamenetskii and Vologodskii (35) proposed an al- ternative mechanism for the efficient knotting by T4 topoi- somerase. Knotting frequency varies inversely with effective DNA diameter (36), and they suggested that excess protein provides an attractive potential between DNA segments and thereby a smaller effective DNA diameter. An attractive po- tential does indeed increase greatly the calculated frequency of knotting (35). Their model, however, also does not account for the specificity of product knot structure.

In searching to explain both the efficiency and specificity of the T4 topoisomerase knotting reaction we first consider the consequences of high amounts of T4 topoisomerase. E. coli topoisomerase I is known to play a stoichiometric role in its knotting reaction; knotting requires a 20-fold greater level of topoisomerase I than is necessary for strand passage (15). High levels of topoisomerase are also needed for knotting by the T4, Drosophila, Bombyx mori, and HeLa type 2 enzymes (6,9,10); we routinely use a stoichiometry of 15-20 molecules of T4 topoisomerase (Mr = 260,000) per plasmid.

Since a topoisomerase must bind two separate DNAs in order to pass them through each other, it should act as a bidentate ligand and thus cross-link, or bridge, disparate points along the DNA axis. Indeed, the type 2 topoisomerase of Drosophila binds preferentially at crossovers (38), and in the absence of ATP the T4 topoisomerase efficiently brings together two or more segments of DNA (37). Furthermore, cross-linking promotes knotting, as demonstrated by the fact that a bidentate DNA binding protein that introduces only a single cross-link dramatically increases knotting by catalytic amounts of T4 topoisomerase in the presence of ATP (39).

In terms of polymer statistics, crosslinking by excess topo- isomerase can be considered as introducing a strong local attractive potential. However, under our conditions, excess T4 topoisomerase is insufficient by itself to bring about knot- ting in the absence of supercoiling; we do not observe knotting with relaxed DNA even at a stoichiometry of 22 to 1. Excess amounts of a Drosophila type 2 topoisomerase can knot nicked DNA in the presence of ATP (9); we predict that such knots would be random in form.

Preliminary calculations based on Monte Carlo simulations with a 3.5-kilobase pair DNA molecule indicate that super- coiling should increase the frequency of knotting of naked DNA roughly 7-f01d.~ The knots produced by simulation were all of the (-) twist form, exactly as found experimentally. Nevertheless, the level of knotting seen in these simulations is still an order of magnitude below that observed in uitro.

Thus, supercoiling alone cannot explain the high degree of knotting. Moreover, the requirements for a high amount of topoisomerase and the absence of ATP argue persuasively for some stoichiometric role of the protein. Just as persuasively, the (-) twist topology of the product knots clearly indicates

S. Levene and N. R. Cozzarelli, unpublished results.

that (-1 supercoiling supplies the interwound part of the knot. Our conclusion then is that the high frequency of knotting requires a structural contribution from both plecto- nemic supercoiling and protein cross-linking.

Given that bending of the superhelix to bring nearby points on the DNA into contact should be energetically disfavored, one would expect knots with many nodes to predominate among the products, contrary to what is observed. Rather it seems likely that the branching of interwound DNA (30) provides a ready means for facilitating contact between dis- parate points without requiring extensive bending of the superhelix, as shown in Fig. 4. The equation derived in the appendix that relates substrate supercoil structure to the number of nodes in the knots produced by a type-2 topoisom- erase confirms the reduction in knot complexity by branching. Moreover, the predicted (5.9) and measured (5.4) average number of knot nodes for pBNW3.8d are in very good agree- ment (see Appendix; Ref. 40).

In summary, the topology of the T4 topoisomerase knots is explained by the branched (-) plectonemic supercoiling of the substrate and random strand passages by the enzyme. The frequency of knotting is greatly increased over that calculated from random passage in relaxed molecules by both supercoiling and topoisomerase-induced crosslinking of the substrate.

REFERENCES 1. Cairns, J. (1963) J. Mol. Biol. 6 , 208-213 2. Sundin, O., and Varshavsky, A. (1980) Cell 2 1 , 103-114 3. DiNardo, S., Voelkel, K., and Sternglanz, R. (1984) Proc. Natl.

4. Wasserman, S. A., and Cozzarelli, N. R. (1986) Science 2 3 2 ,

5. Liu, L. F., Liu, C., and Alberts, B. M. (1979) Nature 2 8 1 , 456-

6. Liu, L. F., Liu, C., and Alberta, B. M. (1980) Cell 19,697-707 7. Tse, Y., and Wang, J. (1980) Cell 22,269-276 8. Brown, P. O., and Cozzarelli, N. R. (1981) Proc. Natl. Acad. Sci.

9. Hsieh, T. (1983) J. Biol. Chem. 258,8413-8420

Acad. Sci. U. S. A. 81,2616-2620

951-960

461

U. S. A. 78,843-847

10. Hirose, S., Tabuchi, H., and Yoshinaga, K. (1988) J. Biol. Chem.

11. Kreuzer, K. N., and Cozzarelli, N. R. (1980) Cell 20,245-254 12. Shishido, K., Komiyama, N., and Ikawa, S. (1987) J. Mol. Biol.

13. Bliska, J. B., and Cozzarelli, N. R. (1987) J. Mol. Biol. 194,205-

14. Bliska, J. B., Benjamin, H. W., and Cozzarelli, N. R. (1991) J.

15. Dean, F. B., Stasiak, A., Koller, T., and Cozzarelli, N. R. (1985)

16. Dean, F. B., and Cozzarelli, N. R. (1985) J. Bwl. Chem. 260,

17. Liu, L. F., Depew, R. E., and Wang, J. C. (1976) J. Mol. Biol.

18. Wang, J. C., and Liu, L. F. (1979) in Molecular Genetics (Taylor, J. H., ed) Part 3, pp. 65-88, Academic Press, New York

19. Wasserman, S. A., White, J. H., and Cozzarelli, N. R. (1988) Nature 334,448-450

20. Reed, R. R. (1981) Cell 2 5 , 713-719 21. Benjamin, H. W., Matzuk, M. M., Krasnow, M. A., and Cozzarelli,

22. Kreuzer, K. N., and Jongeneel, C. V. (1983) Methods Enzymol.

23. Greenfield, L., Simpson, L., and Kaplan, D. (1975) Biochim.

24. Smith, H. 0. (1980) Methods Enzymol. 66,371-380 25. Wasserman, S. A., and Cozzarelli, N. R. (1985) Proc. Natl. Acad.

Sci. U. S. A. 82,1079-1083 26. Wasserman, S. A., Dungan, J. M., and Cozzarelli, N. R. (1985)

Science 229,171-174 27. Cozzarelli, N. R., Krasnow, M. A., Gerrard, S. P., and White, J.

H. (1984) Cold Spring Harbor Symp. Quunt. Bwl. 49,383-400

263,3805-3810

195,215-218

218

Biol. Chem. 266,2041-2047

J. Biol. Chem. 260,4975-4983

4984-4994

106,439-452

N. R. (1985) Cell 4 0 , 147-158

100,144-160

Biophys. Acta 407,365-375

T4 Topoisomerase Knots 20513

28. Spengler, S. J., Stasiak, A., and Cozzarelli, N. R. (1985) Cell 4 2 , V. (1975) Nature 2 5 8 , 398-402

29. Kanaar, R., Klippel, A., Shekhtman, E., Dungan, J. M., Kah- Phys. USP. 24,679-696 mann, R., and Cozzarelli, N. R. (1990) Cell 6 2 , 353-366 36. Klenin, K. V., Vologodskii, A. V., Anshelevich, V. V., Dykhne, A.

30. Boles, T. C., White, J. H., and Cozzarelli, N. R. (1990) J. Mol. M., and Frank-Kamenetskii, M. D. (1988) J. Biomol. Struct. Biol. 213,931-951 Dynarn. 5,1173-1185

31. Klenin, K. V., Vologodskii, A. V., Anshelevich, V. V., Dykhne, A. 37. Kreuzer, K. N., and Huang, W. M. (1983) in Bacteriophage T4 M., and Frank-Kamenetskii, M. D. (1991) J. Mol. Bwl. 2 1 7 , (Matthews, C. K., Kutther, E. M., Mosig, G., and Berget, P. B.,

32. Adrian, M., ten Heggeler-Bordier, B., Wahli, W., Stasiak, A. Z., 38. Zechiedrich, E. L., and Osheroff, N. (1990) EMBO J. 9, 4555-

33. Shishido, K., Ishii, S., and Komiyama, N. (1989) Nucleic Acids. 39. Mukherjee, S., Erickson, H., and Bastia, D. (1988) Proc. Natl.

34. Frank-Kamenetskii, M. D., Lukashin, A. V., and Vologodskii, A. 40. White, J. H. (1991) J. Biol. Chrn. 266 , 20574-20575

325-334 35. Frank-Kamenetskii, M. D., and Vologodskii, A. V. (1981) Sou.

413-419 eds) American Society for Microbiology, Washington, D. C.

Stasiak, A., and Dubochet, J. (1990) EMBO J. 9,4551-4554 4562

Res. 17,9749-9759 Acad. Sci. U. S. A . 86,6287-6291