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collaboration in the execution and inspiration of our recent efforts with flow systems. References 1 Catsimpoola-s, N. (ed.) (1977) Methods of Cell Separation, Vol. 2, Plenum Press, New York 2 Catsimpoolas, N. (ed.) (1979) Methods of Cell Separation, Vol. 1, Plenum Press, New York 3 Prescott, D. M. (ed.) (1973-1979) Methods Cell Biol. Vols. 6--20 4 Melamed, M. R., Mullaney, P. F. and Mendelsohn, M.L. (eds) (1979) How Cytometry and Sorting, Wiley, New York 5 Fulv,3der, M. J. (1965)Science 150, 371-372 6 Arndt-Jovin, D. J. and Jo~Sn, T. M. (1978)Annu. Rev. Biophys. Bioeng. 7, 527-558 7 tloran, P. K. and Wheeless Jr., L. L. (1977) Science 198, 149-157 8 Herzenberg, L. A., Sweet, R. G. and Herzenberg, L. A. (1976)Sci.Am. 234, 108--117

9 J. Histochem. Cytochem. (1979) 27, 1-641 10 Hercher, M., Mueller, W. and Shapiro, H. M. (1979) J. IIi~tochem. Cytochem. 27, 350-352 11 Cram, L. S., Arndt-Jovin, D. J., Grimwade, B. G. and Jovin, T. M. (1980) Acta Path. Microbiol.

Scand. (in press) 12 Arndt-Jovin, D. J. and Jovin, T. M. (1977) J. lt~tochem. Cytochem. 25,585-589 13 Gray, J. W., Langlois, R. G., Carrano, A.V., Burkhart-Schultz, K. and Van Dilla, M. A. (1979) Chromosoma 73, 9-27 14 Lebo, R, V., Carrano, W. V., Burkhart-Sehultz, K., Dozy, A.M., Yu, L.-C. and Kan, Y.W. (1979) Proc. Natl. Acad. Sci. U.S.A. 76, 5804-5808 15 Krhler, G. and Milstein, C. (1975)Nature (London) 256,495-497 16 Parks, D. R., Bryan, V. M., Oi, V. T. and Herzenberg, L. A. (1979) Proc. Natl. Acad. ScL U.S.A. 76, 1962-1966

Superhelical DNA James C. Wang Since the finding of the late J. Vinograd and his co-workers 15 years ago that the D NA of the animal virus polyoma is superhelical, DNAs o f this class have emerged as the most abundant form o f genetic material Some unique properties o f such DNAs and the discovery o f enzymes that can relax or supercoil DNA are summarized in this review. In the well-known Watson-Crick structure of DNA, the two antiparallel strands are coiled around each other. A direct consequence of this intertwining is that if a double-stranded D N A molecule is in the form of a ring with no discontinuity in the backbone bonds of either strand, the complementary single-stranded rings are linked. The parameter that describes quantitatively the linking of the pair of singlestranded rings in such a DNA is the linking number a or Lk. Roughly speaking, ct or Lk is the number of times one strand goes around the other in the duplex ring; it is an integer. A more rigorous definition can be found in the review by Crick 1.

make a complete helical turn in the absence of any constraint, then it seems intuitively reasonable that the linking number a ~ of the DNA closed by ligase is n/h ~ This DNA will be referred to as the relaxed DNA. It should be noted that h ~ is dependent on temperature, counter-ion concentrations, hydration, the binding of intercalating agents etc. Therefore, a DNA relaxed under one set of conditions is usually not relaxed under a different set of conditions. The properties of a covalently closed DNA are much affected by its linking number. The difference between its linking number a and the linking number a ~ of the same DNA when it is relaxed, Aa = a - a ~ The appearance and hydrodynamic has been referred to in the literature as the properties of a covalently closed DNA is number of superhelical turnst. Frequently, strongly affected by its linking number the deviations of the properties of a superFor a circular DNA duplex containing coiled DNA from those of a relaxed DNA one or more single-chain scissions, there is are best correlated with Act/a ~ rather than no topological constraint on the linking Act itself. The quantity Aa/a ~ will be renumber; ct is not a topological invariant. ferred to as the superhelical density or the When all scissions are sealed by DNA lig- specific linking difference:L ase, the DNA becomes 'covalently closed' and t~ is an invariant so long as none of the ~The relation a ~ = n/h* results if the average writhing backbone bonds is broken either transi- number of the relaxed DNA is zero. See the review by ently or permanently. If there are n base Crick, Ref. I. pairs (bp) per DNA molecule and h ~ bp t Vinograd et aL originally det-med the number of James C. Wang is at the Department of Biochemistry and Molecular Biology, ttarvard University, Cambridge, MA 02138, U.S.A.

superhelical turns as a - / 3 , where fl is the number of 'helical turns'. The identification offl as a* provides a more rigorous definition of/3. :l:The superhelical density was originally defined as (ct - fl) per 10 bp.

17 Ledbetter, J. A. and Herzenberg, L. A. (1979) ImmunoL Rev. 47, 63-90 18 Schaap, G. H., Van l~er-Kamp, A. U. M., Ory, F. G. and Jongkind, J. F. (1979) Exp. Cell Res. 122,422--426 19 Jongkind, J. F., Verkerk, A. and Tanke, tt. (1979) Exp. Cell Res. 120. 444-448 20 Jongkind, J. F., Verkerk, A., Schaap, G. H. and Galjaard, H. (1980) Acta Path. Microbiol. Scand. (in press) 21 Mendelsohn, M. L., Bigbee, W. L., Branseomb, E. W. and Stamatoyannopoulos, G. (1980) Acta Path. MicrobioL Scand. (in press) 22 Molday, R. S., Yen, S. P. S. and Rembaum, A. (1977) Nature (London) 268,437-438 23 Antoine, J.-C., Thernynck, T., Rodrigot, M. and Avrameas, S. (1978) Immunochemistry 15, 443-453 24 Kronick, P. L., Campbell, G. LeM. and Joseph, K. (1978) Science 200, 1074-1076

As Act deviates from zero, the appearance of the D N A molecules changes. More crossovers are seen and the molecules appear twisted when viewed with an electron microscope (Fig. 1). The term supercoiled, superhelical, or supertwisted has been used to describe such molecules; depending on whether h a is positive or negative, the DNA is referred to as positively or negatively supercoiled. Th.e configuration changes of a DNA as Act deviates from zero are also reflected in changes in its hydrodynamic properties. Although sedimentation and viscosity measurements have been used extensively to monitor such changes, in recent years gel electrophoresis has become the method of choice for DNAs under 10 * daltons. Fig. 2 depicts the electrophoretic patterns of a family of four phage PM2 DNA samples with different Act values. The sample on the far left is highly negatively supercoiled, with a specific linking difference of about - 0 . 1 1 . The DNA migrates much faster than the nicked form, a trace of which is present in this sample and shows as a faint slower migrating band. The sample run in the second lane is less negatively supercoiled. Here the striking feature is that a series of discrete bands is seen. It has been shown that each of these is a DNA of a given linking numberL Within a certain range of IAct[/ct~ two topological isomers (topoisomers) which differ by 1 in their linking numbers are well-resolved. When I Act I/ct~is large, this fine resolution is lost and the topoisomers run as a single band, as is the case for the sample on the far left. When IActl/ct~ approaches zero, the resolution is again much reduced and the mobilities of the topoisomers approach that of the nicked species (Fig. 2, lanes 3 and 4). 9 Elsevier/North-HollandBiomedicalPress 1980

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lation of AGO from the Boltzmann distribution of topoisomers involves species Supercoiling of a D N A affects the stabil- with A a close to zero, the dependence of ity of the D N A with respect to strand sep- AG,~ on (As)" has been shown to be coraration and cruciform formation, as well as rect for IAsl[s~ at least as high as 0.1. T o illustrate how AGO affects the propits interactions with certain small and large erties of a DNA, consider the binding of molecules. The energctics of supercoiling a bacterial R N A polymerase to a D N A provides an important basis for underof a linking difference s - a ~ When a standing these effects3-6. The ability to resolve individual polymerase binds to a DNA, it unwinds the topoisomers by gel electrophoresis pro- double helix by about one turn, depending vides a direct method of examining free on the D N A and the counter-ion concentenergy differences, A G ~ (see Refs 7 and rations. It is therefore expected that a ~ will 8). If a nicked D N A is converted into the be reduced by about 1. The linking number covalent closed form by a D N A ligase, one or, being a topological invariant, is unwould expect a distribution of topoisomers affected. If the D N A is negatively superin the product if the difference in AG ~ be- coiled, a reduction in s ~ lowers (As) ~ and tween two topoisomers that differ by 1 in a therefore lowers AGO. In other words, the is of the same order of magnitude as the binding of the polymerase molecule is thermal energy RT. This turns out to be the favored by a lowering of AGO of the negacase. The free energy differences can be tively supercoiled D N A in addition to the deduced from the experimentally meas- favorable intrinsic binding free energy. For ured Boltzmann distribution, and it is a moderately supercoiled D N A with a found that AGO, the difference in AG ~ Aa/s ~of - 0 . 0 5 , the lowering oi~AG,~ between a particular topoisomer with a tributes about 6 kcal if the binding of an linking number s and the relaxed DNA, is RNA polymerase lowers a ~ by 1. This corequal to K(Aa) 2, where K is a constant responds to a factor of 1.7 x 104 in the relaroughly inversely proportional to s ~ It tive binding constants to the negatively should be noted that because of the dis- supercoiled and relaxed DNA. In general, tribution of topoisomers, the linking processes that lower ]Aa] are more number of the relaxed DNA should be favored for a supercoiled D N A substrate. taken as the population average < a* > ; it For a negatively supercoiled DNA, these need not be an integer. Although the calcu- include unpairing of bases or unwinding of supercoiling

Studies on covalently closed DNAs led to the confirmation of the double-helix structure of D N A 2 and the development of two methods that can determine accurately the helical repeat of the number of base 9pairs per helical turn of a D N A segment of a given nucleotide sequence in solution 9"1~ The experimentally more simple method of the two, the band shift method, is described below. Suppose two nicked circular DNAs, one containingn bp/molecule and the other the same n bp plus an inserted sequence of x bp, are treated with ligase. The casex = 6 is taken as an example. As discussed in the section above, a distribution in s results for each DNA. Because of the integral nature of a, if the set of linking numbers of the ligase closed DNA with n bp/molecule is . . . . i - 1, i , i + 1 . . . . . the same set of integers must represent the linking numbers of the topoisomers in the D N A sample with n + 6 bp/molecule. The linking differences or the numbers of superhelical turns of the two samples during gel electrophoresis are not the same, however, since the population average linking hum-

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Fig. 2. Electrophoretie patterns of 4 phage PM2 DNA samples in O.7 % agarose gel. See text ]'or explanations.

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be corrected, however TM. For inserts of several different nucleotide sequences, the measurements so far show that at 37~ in a dilute aqueous buffer containing a few mM MgII, 10.5 • 0.1 bp makes a helical turn. The sequence d A , : d T , provides an exception: the measuredh ~ is 9.9 • 0.1 bp tt.

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Fig. 3. Electrophoretic pattern of a mixture o f two D N A samples that differ by 6 bp in their sizes, n is about 4300 bp. The bright band on top contains the nicked species; the length difference between the two samples is too small to be resoh'ed in this band. The m,o groups o f the covalently closed topoisomers are well-resolved. Three from each group are indicated in the figure. See Ref. 10 for more details.

An interesting outcome of studies on covalently closed DNAs is the discovery of enzymes that can relax or supercoil D N A I~-13. These enzymes can be subdivided into two categories 14"~5.The type I D N A topoisomerases require no energy cofactor such as ATP; they can reduce but cannot increase and a is changed in steps of • 1 by these enzymes. The type II D N A t0poisomerases usually require ATP. Some of the type II enzymes, the D N A gyrases, can catalyse the negative supercoiling of DNA, and is increased. Other type II enzymes, such as ~ahage T4 D N A topoisomerase or the ATP-dependent drosophila D N A t o p o isomerase, can only reduce [ A s [ at least under the assay conditions devised so far. The values of s are changed in steps of • 2 by the type II enzymes 15-17. The D N A topoisomerases not only eatalyse the reduction or increase in [ As I, but also interconversion between other types of topoisomers. Some of these reactions are depicted in Fig. 4. It is increasingly clear that the D N A topoisomerases play important roles in many vital processes involving D N A TM.The blocking of D N A gyrase in vivo leads to cessation of replicative D N A synthesis, inhibition of transcription of certain operons and certain repair processes. This multitude of effects might all result from the role of gyrase in maintaining the D N A in a negatively supercoiled state in vivo. The ATP-dependent T4 topoisomerase is required in replication. The phage k integrase, which is responsible for the integration of the viral D N A into the host genome, has a topoisomerase activity TM. T h e in v i v o roles of many other D N A topoisomerases are at present unknown, and their studies are likely to offer further insights into how nature deals with the topological problems of DNA.

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bers of the DNAs relaxed under the electrophoresis conditions are clearly different. For the D N A with n bplmolecule, the distribution in A s i s . . . i - 1 - n / h ~ - n / h ~ i + 1 - n / h ~ . . . ; for the D N A with n + 6 bp/molecule, the distribution in A s is . . . i - 1 - (n + 6)/h ~ i - (n + 6)/h ~ + 1 - (n + 6 ) / h ~ Clearly, for a topoisomer with a given linking difference k in the first set, there is a corresponding topoisomer with a linking difference k - 6/h ~ in the second set. Since the spacing between two adjacent topoisomer bands of either sample represents a differe,ace of 1 in As, it follows that all topoisomer bands of the D N A with n + 6 bp/molecule are shifted from the qorresponding topoisomer bands of the D N A with n bp/molecule by a fraction 6/h ~ of the spacing between bands. This is indeed observed as indicated in Fig. 3. By extending this line of reasoning, it can be generalized that ifx = integer 9h ~ + y, w h e r e y < h ~ is the non-integral residue, all topoisomer bands in the D N A with n + x bp/molecule are shifted by a f r a c t i o n y / h ~ of the spacing between bands. This dependence on the non-integral residue is reminiscent of the interference phenomenon in optics. By using cloned inserts of larger and larger x, a high accuracy in the measured h ~ can be achieved. The conclusion above is arrived at by assuming that the only effect on mobility by the addition ofx bp is due to the dependence of the electrophoretic mobility on A s. The mobility is actually slightly affected also by the lengthening of the DNA. This length effect can

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References 1 Crick, F. H. C. (1976) Proe. Natl. Acad. Sci. U.S.A. 73, 2639-2643 2 Crick, F. H. C., Wang, J. C. and Bauer, W. R. (1979)J. Mol. Biol. 129,449-461

Fig. 4. Topoisomerization reactions that are catalysed by DNA topoisomerases. The thicker line represents double-stranded DNA and the thinner line single. stranded DNA. Reactions B and C as drawn are known to be catalysed by the type 1 enzymes; the doublestranded equivalent o f Reaction C is catalysed by the type H enzymes. The linking and unlinking of doublestranded DNA rings with or without gross sequence homology are catalysed by both types o f topoisomerases. The type I enzymes, however, require the presence of a pre-existing single-chain scission in one of the participating rings.

3 Bauer, W. R. and Vinograd, J. (1970) J. Mol. Biol. 47,419-435 4 Hsieh, T.-S. and Wang,J. C. (1975) Biochemistry 14, 527-535 5 Davidson,N. (1972)J. Mol. Biol. 66, 307 6 Vologodskii,A. V., Lukashin,A. V., Anshelevich, V. V. and F/ank-Kameneskii, M. D. (1979) Nucleic Acids Res. 6, 967-982 7 Depew, R. E. and Wang, J. C. (1975) Proc. Natl. Acad. Sci, U.S.A. 72, 4275-4279 8 PuUeyblank, D. E., Shure, M., Tang, D., Vinograd, J. and Vosberg, H. P. (1975) Proc. Natl. Acad. Sci, U.S.A. 72, 4280-4284 9 Wang, J. C. (1979) Cold Spring Harbor Syrup. Quant. Biol. 43, 29-33 10 Wang, J. C. (1979) Proc. Natl. Acad. Sci, U.S.A. 76, 200-203 11 Peck, L. and Wang,J. C. (to be published) 12 Reviewedin Wang, J. C. and Lin, L. F. (1979) in Molecular Genetics (Taylor, J. H., ed.), Part 3, pp. 65-88, AcademicPress, New York 13 Gellert, M., Mizuuchi, K., O'Dea, M. H. and Nash, H. A. (1976) Proe. Natl. Acad. Sci. U.S.A. 73, 3872-3876

14 Liu, L. F., Liu, C.-C. and Alberts, B. M. (1979) Nature (London) 281,456--461 15 Liu, L. F., Liu, C.-C. and Alberts, B. M. (1980) Cell. (in press) 16 Brown, P. O. and Cozzarelli,N R. (1979)Science 206, 1081-1083 17 Mizuuchi, K., Fisher, M., O'Dea, M. H. and Gellert, M. (1980) Proc. Natl. Acad. Sci. U.S.A. 77, 1847-1851 18 Reviewedin Cozzarelli,N. R. (1980) Science 207, 953-960 19 Kikuchi, Y. and Nash, H. A. (1979) Proc. Natl. Acad. Sci, U.S.A. 76, 3760-3764