Early and late helix-coil transitions in closed circular DNA the number of superhelical turns in polyoma DNA

J. Mol. Biol. (1968) 33, 173-197

Early and Late Helix-Coil Transitions in Closed Circular DNA The Number of Superhelical Turns in Polyoma DNA JEROME VINOGRAD, JACOB LEBOWITZ~ AND ROBERT WATSON Norman

W. Church Laboratory for Chemical Biology California Institute of Technology Pasadena, Cali@rniu 91109, U.S.A. (Received 12 September 1967)

The titration of closed circular polyoma DNA with small amounts of hydroxyl ions causes an unwinding of the duplex and a simultaneous and quantitatively equivalent unwinding of the superhelices. The buoyant densities of both intact, I, and singly nicked, II, polyoma DNA were measured as a function of pH, and the fraction of the base pairs titrated was calculated from the buoyant density shifts. A small but sign&ant increase in buoyant density occurred in I prior to the onset of the titration of II. This early titration or early helix-coil transition was completed when 3.2% of the base pairs were titrated. We have calculated from the foregoing result and the molecular weight of polyoma DNA that the closed circular molecule contains - 15% 1 superhelical turns in buoyant cesium chloride at neutral pH. Each superhelical turn consists of an approximately 1000 A length of duplex DNA and contains about 300 base pairs. The remaining 97% of the alkaline titration of I occurs at pH values that are higher than the pH required completely to titrate singly nicked polyoma DNA II. The late alkdine titration curve is broad, has a midpoint at pH 12.28, and is not completed until the pH is 12.37 at 20%. The stabilization caused by the inability of the molecule to unwind was calculated to correspond to an elevation in the melting temperatures in standard saline citrate of 1’7“C at the midpoint, and 22°C at the completion of the titration. An absorbance study of the thermal melting of closed circular polyoma DNA in standard saline citrate confirmed that the melting temperature exceeded 104”C, while the singly nicked polyoma DNA II melted at 89°C. Thermal melting of both I and II in 7.2 M-NaClo4 was studied by absorbance methods. The melting curve of II was similar to the curve for T7 DNA. The curve for I was broad with a midpoint at 73°C compared with a midpoint of 48°C for II. It was estimated from the foregoing results that the melting temperature of polyoma I in standard saline citrate should be 107°C.

1. Introduction The covalently closed circular duplex DNA isolated from polyoma virus has been shown to assume a compact conformation in aqueous salt solutions (Vinograd, Lebowitz, Badloff, Watson & Laipis, 1965). The compact form, I, is converted to a slower sedimenting, nicked relaxed form, II, upon the introduction of one singlestrand scission into the molecule. The compact form is also converted to an intact relaxed form, I’, upon melting of a small fraction of the base pairs in the molecule. Both circular relaxed forms are characterized by a sedimentation coefficient of 16 s t Present address: Biological Research Laboratories, U.S.A. 173

Syracuse University,

Syracuse, N.Y.,

174

J. VINOGRAD,

J. LEBOWITZ

AND

R. WATSON

in 1 M-NaCl, as compared with 20 s for the compact form, and 14.5 s for the linea? form of the molecule. The conversion of the compact form into the relaxed intact form, I + I’, was observed in alkaline melting experiments monitored by sedimentation velocity analyses. The midpoint of the conversion occurred about O-2 pH unit below the pH at the midpoint of the sedimentation velocity-pH titration of II. At the completion of the latter titration, the singly nicked relaxed form dissociated into two single-stranded molecules, one linear and one circular. Crawford & Black (1964) examined a mixture of the nicked and intact forms that had been heated to various temperatures in formaldehyde and cooled for the sedimentation analyses. Their results showed that the midpoint of the I -+ I’ conversion occurred about ten degrees below the temperature at the midpoint of the S versus T curve for II. More recently a similar set of conversions was observed by Mickel in an acid titration monitored by sedimentation velocity analyses (Vinograd & Lebowitz, 1966a). Three interrelated proposals were offered by Vinograd, Lebowitz, Radloff, Watson & Laipis (1965) to explain the foregoing results. (1) Component I owes its compact conformation to the presence of superhelical turns in the molecule. (2) The superhelical turns unwind spontaneously at a swivel located in the intact strand opposite the site of the fist single-strand scission introduced into the molecule. (3) The superhelical turns unwind completely when a small but definite number of the base pairs are melted in the initial stages of the helix-coil transition. The present paper is concerned with the quantitative aspects of these proposals and presents a study of the alkali and the thermally induced helix-coil transitions of the intact and the singly nicked molecules. The study of the alkali-induced transitions was carried out with the buoyant density method. This method is considerably more sensitive than the sedimentation velocity method previously used for monitoring the transition. A buoyant density shift of the order of 0.25% of the total shift in the titration can be detected. The buoyant density shifts may be quantitativel? related to the degree of titration of the DNA. A small but significant increase in the buoyant density of the compact form occurs a few tenths of a pH unit below the pH value required to induce the large and abrupt buoyant shift that takes place when the nicked form undergoes titration and strand separation. This rise in the buoyant density occurs at essentially the same pH value as the dip in the sedimentation velocity titration reported previously. We consider the early buoyant density shift to be a manifestation of an early alkaline t,itration. The buoyant density titration of the nicked molecule closely resembles that of linear DNA (Vinograd, Morris, Davidson & Dove, 1963; Baldwin & Shooter, 1963). The early titration in the closed circular molecule represents an early helix-cd transition driven by the positive free energy qf superhelix formation. Implied in proposal (2) is the statement that the superhelical molecule has a higher free energy than the equivalent nicked relaxed molecule or an identical closed molecule having no superhelical turns. The superhelix free energy ,which is stored in the molecule in the form of bending energy and a reduced conformational entropy, is available to lower the melting temperature or pH value of the first base pairs that undergo the helix-coil transition. An estimate of the number of superhelical turns in the compact form has been obtained from the magnitude of the early buoyant shift. For the calculation we

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

175

make use of the observation that there is a one-to-one correspondence between the unwinding of secondary and tertiary turns in closed circular duplex DNA (Vinograd 81 Lebowitz, 1966b). The correspondence is expressed by the relation 7=a-j3

(1)

between three winding numbers: the topological winding number, a, is the number of revolutions made by one strand about the duplex axis when the axis is constrained to lie in a plane ; the duplex winding number, /3, is the number of revolutions made by one strand about the duplex axis in the unconstrained molecule; the superhelix winding number, 7, is the number of revolutions made by the duplex about the superhelix axis. An analytical proof for equation (1) has recently been presented by Glaubiger & Hearst (1967). The geometric consequences of equation (1) are illustrated in Figure 1 for two

(a)

!b)

Cdl

Fro. 1. An illustration of the formation of superhelical turns in a closed duplex consisting of two non-interwound strands. The topological winding number, CC,in this Figure has a value of zero. (a) Two non-interwound strands. The duplex winding number, /I, and the superhelical winding number, 7, have values of zero. (b) Three right-hrmded duplex turns and three left-handed duplex turns have been wound into the duplex in (a). The right- and left-handed duplexes cancel eaoh other; CL=fi =r = 0. (c) Three right-handed duplex turns and three left-handed superhelical turns have been introduced into the duplex in (a). The separate strands in the superhelical region rotate about eaoh other. In this arrangement CL= 0, fl= + 3, and 7 = - 3. The superheliocrl turns may be regarded as forming a section of a toroidal superhelix. (d) Three right-handed duplex turns and three right-handed interwound superhelical turns have been introduced into the duplex in (a). The paired strands in the interwound superhelix do not rotate around each other. In this arrangement CL= 0, g = + 3, and + = - 3. See text for the explanstion of the sign convention for I in interwound superhelices.

impenetrable strands that are topologically unlinked, in which case a is equal to zero. Figure l(a) shows the two strands in the arrangement a=/3 = T= 0. Figure Z(b) presents an arrangement generated from the model in Figure l(a) by simultaneously winding in three right-handed and three left-handed duplex turns. We

176

J. VINOGRAD,

J. LEBOWITZ

AND

R. WATSON

now adopt the sign convention that right-handed duplex turns are positive. Over thr whole model, a =/l = 7 = 0. The model in Figure l(c) is generated from the model in Figure 1 (a) by simultaneously winding in three right-handed duplex turns and three left-handed super3. helical turns which have a negative sign. In this model a= 0, /3 = 3, and 7 =: The duplex and superhelical turns may be lengthened and extended over the whole model to form a toroidal superhelix. An alternative superhelical arrangement, the interwound superhelix or twisted structure, Figure l(d), is formed by simultaneously winding into the model in Figure l(a) three right-handed duplex turns and three right-handed interwound superhelical turns. The interwound superhelix contains two pairs of strands that cross over the superhelical axis one and one-half times. The interwound superhelical turns are seen to be right-handed in contrast to the turns in the non-interwound superhelix in Figure l(c) which are left-handed. This change in handedness is associated with a 90” change in the viewing axis. We will adopt the convention that left-handed interwound superhelical turns are positive. Again, in this model, a = 0, /3 = 3, and 7 = -3. The alkaline titration of duplex DNA causes the well-known helix-coil transition in which denatured loops are formed and sections of the Watson-Crick duplex are unwound. Under the condition that the titration of ten base pairs causes the complete unwinding of one duplex turn,

B = B” (1 -PI, where j?O is numerically equal to one-tenth and p is the fractional degree of titration. characterized by the relation

the number of base pairs per molecule The untitrated superhelical molecule is

7. = a -PO

(3)

where 7. is the number of superhelical turns and PO is the number of duplex turns in the untitrated molecule. We will assume that /30=j30 in the untitrated molecule. The superhelix density, c, at any degree of titration is defined by the relation

Equations

(1) to (4) are combined

to obtain

the relation

u = uo -c p,

(5)

where o. is the superhelix density in the untitrated molecule. In accordance with proposal (2), there will be a state at a critical degree of titration, pC, in which the molecule contains no superhelical turns, c = 0. Equation (5) becomes uo =

-pc.

(6)

It is shown, in this study of the alkaline buoyant density titration of polyoma DNA, that the critical degree of titration is 0.032 & 0.002 and that the superhelix density (I~ of the untitrated molecule is -0.032 l O-002. We then calculate from equation (4), written for the untitrated molecule, To = B OQO, that polyoma

DNA

contains

-15

+ 1 superhelical

@a) turns.

In the above calculation

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

177

the value /lo = 470 was computed from the average sodium nucleotide residue weight, 332 daltons, and the molecular weight, 3.1 x lo6 daltons. Using another method to determine superhelix density, Bauer & Vinograd (1968) found that a very similar closed circular DNA from SV40 virus also contains - 13 ‘,1 1.5 superhelical turns. This conclusion was reached in an analysis of the results of a buoyant density study of the binding of an intercalative dye, ethidium bromide. An analysis of the effect of such dye binding upon the sedimentation velocity properties of SV40 DNA yielded a comparable but less precise result. While this manuscript was in preparation, Crawford & Waring (1967) reported similar results obtained in a study of the effects of ethidium bromide on the sedimentation velocity behavior of polyoma DNA. When the pH-melting process is continued beyond the end of the early transition, two new effects are encountered that are not met in the melting of linear or nicked circular DNA. The unwinding of the duplex cannot occur without a simultaneous winding up of t’he disordered or the remaining ordered regions, so as to maintain a constant topological winding number. After the melting process is complete and all positive interstrand interactions disappear, the strands still cannot separate. The above restrictions diminish the gain in configurational entropy which occurs on denaturation of II or of a linear molecule. Covalently-closed duplex circular DNA, freed of tertiary turns, is therefore thermodynamically more stable than linear DNA and displays a lute helix-coil tramition. The enhanced stability in alkali was noted by Weil & Vinograd (1963) and Dulbecco & Vogt (1963). We report absorbance versus temperature studies which demonstrate the enhanced thermal stability of covalently closed DNA at neutral pH, and alkaline buoyant density versus pH studies which confirm and extend the previous observations. A preliminary description of part of the results obtained in this study was reported by Lebowitz, Watson & Vinograd (1966, 2nd Int. Biophys. Congr. Int. Org. Pure and Appl. Biophys. Abstr. 1.1.2) and by Vinograd Rt Lebowitz (1966).

2. Materials and Methods (a) Isolation and purification of polyonzu virus and polyonm Gwl DNA Methods described by Winocour (1963) and Murikami (1963) were used for the isolation and puri&&ion of the virus. The DNA was extracted with phenol as described by Weil (1963). The phenol was distilled and stored under argon. Polyoma DNA I was isolated from the phenol extract by sucrose density-gradient sedimentation. The sucrose was removed by dialysis u?ith SSC/lO (SSC is 0.15 M-NaCl, 0.015 x-sodium citrate, pH 7.4). II was prepared from sucrose density-gradient purified I by treatment with pancreatic DNaae : 0.039 ml. of the enzyme reaction mixture, 2 x 10m3 pg/ml. DNase (oncecrystallized, Worthington Biochemical Corp.), 2 rg/ml. bovine serum albumin, 0.024 M-MgCl,, 0.02 &xTris, pH 7.6, and 0.06 M-NaCl were added bo O-350 ml. of polyoma DNA I, 48 pg/ml., at 20°C. After about 20 min the reaction was halt,ed by freezing in acetone-dry ice. Just prior to freezing, a 25-~1. portion was withdrawn, added to 5 ~1. of 0.10 M-EDTA, pH 8.0, and analyzed by analytical band sedimentation t,o determine the ext,ent of reaction. When approximately 30% conversion had occurred, the reaction was t’erminated by thawing in the presence of 25 ~1. of 0.10 M-EDTA, pH 8.0. This polyoma DNA solut.ion was used in some of the alkaline buoyant density titrations. Pure II was isolated from the enzymically treated I (about 30% conversion) by sucrose density-gradient sedimentation. The linear sucrose density-gradients (5 to 20% sucrose, I.0 ~-Kc1 and 0.05 M-Tris, pH 8.0) were overlaid with 2 ml. of sample and centrifuged at 4% and 26,000 rev./min for 16 hr in an SW25.1 rotor in a Beckman model L preparative ultracentrifuge. Fractions were collected from the bot,tom of t,he tubes and assayed spectrophotomet,ricalIp. 1:’

178

J. VINOGRAD,

J. LEBOWITZ

AND

R. WATSOIV

(b) Marker DNA Micrococcus lysodeikticw DNA was prepared by the method of Kirby (1957) and was a, gift from T. W. Thompson. Crab dAT from Cancer antenna&us sperm was a gift from R. Hyman who isolated this DNA wit’h the Cs2S04, HgCle method (Davidson et al., 1965). (c) Buoyant den&y titration in the analytical ultracentri&ge The experiments were performed in 2- and 4.cell rotors at 44,770 or 44,000 rev./min and at 20°C for 48 hr in Beckman model E ultracentrifuges. Temperature, indicated by the RTIC control unit, was monitored with a Varian G14 recorder (Fessler & Vinograd, 1965) and normally was constant within &O*O.!J”C.The angular velocity was monitored periodically with an optical tachometer. The fluctuations from the average velocity did not exceed 0.05%. The ultracentrifuges were equipped either with monochromator set at 2654 ml*, or with Cl,, Br, and Corning no. 9863 filters. The results of the experiments were recorded on Eastman Kodak Co. contact process glass plates which were developed for 8 min at 20°C in Kodak Dl 1 developer. In order to obtain the maximum accuracy the plates were read on a Nikon 6 comparator equipped with a projection screen. The position of band center could be read in eight readings by any of the authors with a standard deviation of 10.03 mm on the plate or SO.017 mm in the cell. This corresponds to an uncertainty in a density difference, relative to a marker, at the 60% confidence limit of 10.2 mg/ml. Errors caused by dust spots or oil droplets on optical elements in the ultracentrifuge can be avoided with this method of evaluating the results. The densities of the solutions were adjusted so that the marker band was always at approximately the same position in the liquid column. The length of the liquid column, 12.1 mm, was also approximately constant. In each set of experiments, up to ten cells were partially assembled. They were equipped with type III band-forming centerpieces (Vinograd, Radloff & Bruner, 1965) fabricated from Kel-F or charcoal-filled Epon and the appropriate side and radial wedge windows. The solutions in the sample well contained 20 ~1. polyoma DNA, 40 pg/ml., and either 2 ~1. crab dAT, 160 pg/ml., or 5 ~1. M. lysodeikticue DNA, 80 pg/ml. Also, 5 ~1. of 1.9 g/ml. C&l containing 0.25 M-K,HPOI, pH 10, were added to the sample well. The assembling of the cells was completed and the sector space flushed with argon. A stock solution of C&l adjusted to p” = 1.76 g/ml., 0.05 M-K~PO~ and approximately pH 11.0, and a titrant solution of CsCl p” = 1.76 g/ml., 0.05 M-K~PO~, and I.0 M-KOH were prepared. The titrant was added with a Greiner micropipette to 10.0 ml. of the stock solution stirred under argon at 20°C. At each desired pH, a sample was transferred to a cell assembly with an argon-flushed l*O-ml. syringe fitted with a disposable needle. The cell assembly was promptly sealed. After transfer of the sample from the sample well, the cell content had a final density of 1.740 g/ml. and a constant concentration of 0.05 M-K,PO,. The cells and rotor were brought to 20°C in the ultracentrifuge before the sample solution was transferred to the alkaline buoyant solvent. At the completion of several of the experiments the temperature was raised to 25 and 30°C and the buoyant densities determined after 24 hr at each temperature. (d) Buoyant density calculations The density difference between the marker DNA and the polyoma DNA was calculated with the relation (Vinogrsd & Hearst, 1962) Ati = (l/p0 + I,+ oz)~2?o Ar, where l/PO is the coefficient of the buoyant density gradient, p” is the density of the buoyant solution at atmospheric pressure, o is the angular velocity, r. is the mean of the two radial band positions, Ar is the difference between the band positions and # is the pressure coefficient of the buoyant density. The relation for the density difference may be written A0 = k?, Ar where k = 0.0192 and O-0198 g/cm5 at 44,000 and 44,700 rev./mm respectively. In hhc calculations of k, the following numerical values were used: l/j30 = 8.3 x lo-lo c.g.8. for p” = 1.74 and # = 23.3 x lo-la c.g.s., the value for native T4 DNA. The value for k and thus for the density gradient is valid at 25OC. It has, however, been used without modification in the evaluation of results at 20°C. The temperature coefficient, of the composition

SUPERHELIX

DENSlTY

1N POLYOMA

DNA

179

density gradient for CsCl at p = 1.7 g/ml. is unknown. It has been estimated by Schumaker & Wagnild (1965) to be -O.So/o per degree. The buoyant density experiments were performed at 20°C so as to permit comparison with the .previously published sedimentation velocity titrations at 20°C in 2.8 M-CsCl. (e) Tl~ermalZ denaturation A stock solution of 9 an-NaClO,, containing 0.0188 ~-sodium citrate, pH 7.2, was prepared. A l/5 vol. of DNA solution in SSC/lO was mixed with a 4/b vol. of the perchlorate stock solution at 4°C to give a tial solution of 7.2 M-NaClG4, 0.015 M-sodium citrate, pH 7.2. DNA solutions in SSC, pH 7.4, were prepared by adding 15 x SSC to the DNA solutions in SSC/lO. All solutions were partially freed of dissolved air by bubbling with helium for 30 sec. The glass-stoppered quartz spectrophotometer cells, obtained from Pyrocell, Inc., New York, were sealed with Dow-Corning silicone stopcock lubricant. A Gilford 2000 multiple sample absorbance recorder was used to record temperature and absorbance. A H&e temperature-controlled circulating water bath, series F, with a 1 rev./min synchronous motor driving the contact thermoregulator, was used to provide a linear heating rate of 0*66’C/min. The temperature indicated on the recorder was checked in a calibration experiment with the readings of a thermocouple inserted into a f?lled cell in the sample compartment. All hyperchromicities were corrected for solvent expansion upon heating. The temperature dependence of the specific volume of a 7.2 M-NaClG, solution was determined dilatometrically with a 50-ml. dilatometer. (f) Measurement of pH A Beckman research model pH meter, a Beckman general purpose small probe glass electrode, and a calomel reference electrode modified with a ground-glass junction (Lebowitz & Laskowski, 1962) were used. The pH meter was standardized at 20°C with Beckman saturated Ca(OH), buffer at pH 12.63 before the titration was begun. The buffer was m-read after the titration. The drift generally did not exceed & 0.01 pH unit. The accuracy of the pH responses, E = 59 mv/pH unit, was checked by measuring the difference between a Beckman phosphate buffer at pH 6.88 and the Beckman saturated Ca(OH), buffer at pH 12.63. The range of error was 10.02 pH unit.

3. Results (a) Alkaline buo?/ant density titration of intact ad nicked polyoma DNA A comparison of the alkaline buoyant density titrations of I and II reveals the effects of both the tertiary structure and t’he covalent ring closures in intact polyoma DNA (Fig. 2(a) and (b)). The alkaline buoyant density titration of II, like that of linear DNA from Escherichia coli, T4 bacteriophage and M. 1ysodeikticu.s (Vinograd, Morris, Davidson & Dove, 1963; Baldwin BEShooter, 1963), consists of three regions, a very narrow region no greater than 0.05 pH unit in which the entire titration occurs and constant regions at levels of pH above and below the titration zone at pH 11-80 -f O-02,. The nicked molecule is similar to linear DNA in its ability to unwind and dissociate to form independent single strands in denaturing solvents. The shift in buoyant density upon complete titration is 57 mg/ml. at 20°C. As was noted earlier, we have used the buoyant density gradient at 25°C to evaluate these density differences from the experimental data. If a correction is made for the estimated temperature dependence of the composition density gradient, the shift in buoyant density upon alkaline denaturation of II is 60 mg/ml., in satisfactory agreement with the value of 61 mg/ml. previously observed with linear DNA.

180

J. VINOGRAD,

J. LEBOWITZ

AXD

It.

WATSOIU

400 300 $ d 200 ‘; ‘ii 100 ;

II.2

II.4

II.6

11.8

12.0

12.2

I24

Il.2

II.4

II 0

12.0

0 I 2

6:

PH (a)

(b)

Fro. 2. The buoyant density titration in alkeline ceeium chloride, at 2O”C, of intact polyoma DNA I (-O-O--), and singly nicked polyome DNA II (-@-a-). The buoyant density results are given 8a buoyant density differences between polyome DNA and two markers 8s discussed in the text. (a) The complete titration curve between pH 11.2 ctnd pH 12.6. The dashed lines enclose the region in which the abrupt titration of II occurs. The tails on the d8t8 points indicate the number of overlapping results. (b) An enl8rged graph of part of the results in (a). The overlapping points are indicated 88 multiple circles. The right-hand ordin8te gives the number of base pairs in polyoma DNA that have been titrated.

The buoyant density titration of the intact molecule is bimodal. In the first part of the titration, between pH 11.3 and 11.7, small but definite buoyant density changes occur. These early buoyant density changes represent an early helix-coil transition driven by the potential energy stored in the superhelix. At higher pH, between 11.7 and 12.4, .the main or late alkaline titration is observed. The buoyant density versus pH curve for the late titration differs from the curve for II in three respects. (1) The curve is broad and asymmetric. (2) The midpoint is at pH 12.28 compared with 11.80. (3) The buoyant density of the fully titrated form is 19 mg/ml. higher than the mean buoyant density of the fully titrated separate strands. The transition pH values at 25 and 30°C were obtained by raising the temperatures of several of the buoyant samples and noting the new equilibrium positions. The pH, for II at 20, 25 and 30°C occurred at pH 11.80 &0*03,11*45 f 0.03 and 11.27 5 0.03, respectively. The corresponding pH, values for I occurred at pH 12-28 i O-03, 12.02 rt 0.03 and 11.78 f 0.03. The titrations appeared to be complete at 12.37 h 0.03, 12.15 f 0.05 and Il.90 & O-05. The effect of temperature on pH of the alkaline CsCl solutions was measured in pilot experiments and the results used to evaluate the ambient pH at the elevated temperatures.

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

181

Several experiments were performed with I and II and an D1. lysodeikticus marker DNA at pH 7.4. The buoyant density differences between I and the marker and II and the marker were 25.0 & O-2 mg/ml. The latter value was also found for both DNA’s just prior to the onset of the titration of I at pH 11.3 (Fig. 2). The high order of accuracy desired in these experiments was obtained by measuring buoyant density differences between polyoma DNA and a marker DNA. The early as well as the late transitions in polyoma I occur over a wide range in pH, unlike the transitions for linear or nicked circular DNA’s. It was necessary therefore to use two markers which undergo the abrupt transition at different pH values. Titrated crab dAT which has a low pH,, 11.5, was used as the marker in all experiments above pH 11.70 and untitrated IIJ. lysodeikticus DNA, which has a high pH,, 11.9, was used in all experiments below pH 11.60. Several experiments were performed with each of the markers in the pH interval between 11.60 and 11.65. The results TABLE

1

Buoyant density differences between polyoma DNA I and fully titrated crab dAT and untitrated M. lysodeikticus DNA (CsCl, 20°C)

PH 11.60 11.60 11.63 11.65

Marker DNA M. .!ysodeikticua Crab dAT -0.0230 -0.0232 -0*022q

-0.0230 -0.0232 -0.0231 -0*0230t

t These two results were obtained from an experiment in which the composition of the solutions w&s identical except for the nature of the marker. Paired cell assemblies were filled with the same volumes of solutions, and were centrifuged together in the same rotor.

of these latter experiments, Table 1, show that at a given pH value and within experimental error, untitrated M. lysodeikticus DNA and titrated crab dAT have the same buoyant density. This is indicated by the constant buoyant density difference between these DNA’s and polyoma I. We have made the assumption that the buoyant densities of titrated crab dAT and untitrated ill. lysodeiktticus DNA remain constant above pH 11.60 and below pH 11.70, respectively. This constancy was previously observed for M. lysodeikticus DNA by Vinograd et al. (1963). The constancy of the buoyant density difference for polyoma II between pH 11.85 and 12.30 is consistent with the assumption of the constant buoyant density of titrated crab dAT. (b) Relationship between the degree of titration and the buoyant density shifts in the a&-dine titration of DNA In the course of titration, the ring protons of the thymine and guanine residues are neutralized to form charged bases which are unable to participate in the formation of A-T or G-C?base pairs. Upon completion of the titration, strand separation occurs unless the strands are covalently crosslinked or topologically bonded to each other. The loss of the duplex structure and the charging of the bases each contributes to an increase of the buoyant density of DNA. It has been estimated by Vinograd

183

J. VINOGRAD,

J. LEBOWlTZ

AKD

R. WATSON

et al. (1963) that approximately three-quarters of the alkaline buoyant shift is due to the incorporation of one-half mole of solvated cesium ion per mole of nucleotide residue in the electrically neutral buoyant complex. The remainder of the shift is attributed to hydration changes accompanying the loss of the duplex structure. We now assume that a partially titrated molecule consists of fully titrated segments and unchanged untitrated segments, and that each type of segment makes an independent contribution to the buoyant density of a partially titrated molecule. The buoyant density of the partially titrated molecule is then given by the relation

1 -=- wo WI 0, 8, +,

(7)

where 0, is the buoyant density of DNA titrated to the degree p, t?, and 0, are the buoyant densities of the untitrated and fully titrated DNA, and w,, and w1 are the weight fractions of the untitrated and titrated solvated residues. It is shown in the Appendix that the buoyant density of a partially titrated duplex DNA is related to the degree of titration by the relation f=-= e,- 0, 4 - 0,

kP l+ (k- 1)~

(f-9

where k = M,B,/M,B. The symbol M represents the solvated nucleotide residue weight. The subscripts again represent the degree of titration. The value of the dimensionless coefficient k in equation (8) is 1.14, a result obtained with B0 = l-76 g/ml., e1 = l-76 g/ml., M, = 565 daltons and M, = 672 daltons. The value for the solvated nucleotide residue molecular weight, M,, includes 123 daltons for the preferential solvation by water (Hearst 6 Vinograd, 1961). To obtain M, we first estimate t, the anhydrous partial specific volume of alkaline CsDNA, to be 0.427 ml./g. In this calculation we take 6.4 g/ml. (Ifft & Williams, 1967) as the reciprocal of the partial specific volume of the cesium ion which is incorporated into the buoyant species at high pH, and 2.12 g/ml. as the reciprocal of the partial specific volume of CsDNA (Hearst, 1962). The preferential solvation for alkaline CsDNA is then calculated to be 165 daltons per nucleotide residue. For the early stages of the titration in which p r 0.1, equation (8) takes on the simple form p = 0-87J.

(9)

The above relation was used to compute the fraction of base pairs titrated. The results are given for the first 8% of the titration on the enlarged graph of the first part of the buoyant density titration, Figure 2(b). The buoyant density of fully titrated component II was used in the calculation of the fractional buoyant density shift, f, observed in the early stages of the titration of the intact compact form I. The reason for this choice is given in the next section. (c) Early helix-coil

transition

in polyom

DNA

In order to visualize the unwinding problems that arise in the melting of closed circular DNA, we first consider a diagrammatic representation of the helix-coil transition in nicked-circular or, equivalently, linear DNA. The upper ends of the strands in Figure 3 are considered to be fixed to a non-rotatable support. The lower ends of the

SUPERHELIX

DENSITY

(a)

IN

POLYOMA

DNA

153

(b)

FIG. 3. A representation of the helix-coil traneition in nicked circular or linear DNA. The symbols, (0). m provided to eastit the reader in tmcking & psrticuler &rend. The duplex strands sre anchored clt the top to a tied support, 8nd et the bottom to e rotatable support. The melting of five base pairs in the W&son-Crick duplex in (8) results in a 180’ clockwiee rot&ion of the lower section of the duplex &B shown in (b) and an enlargement of the coil region by five base pairs.

strands are considered to be connected to a support which may rotate about the axis of the helix. We add a small amount of heat or alkali to induce a small increase in the fraction of the molecule in the coil or random form. This material is represented (in Fig. 3(b)) by a loop which is enlarged at the expense of a portion of the helical region. If five base pairs undergo the helix-coil transition, as in Figure 3, the lower helical section must rotate 180” clockwise, as viewed by an observer stationed at the position of the swivel. This geometric requirement for rotation presupposes that the axis of the molecule remains in a plane. A section of the polyoma I molecule is shown in Figure 4(a). The diagram represents the state of the molecule in which only a part of the early melting has occurred and a small coil region has formed. The helical regions contain interwound strands that are arranged to form a distorted duplex with an enlarged pitch, base pairs/turn. The lower ends of the strands in the diagrams in Figures 4 and 5 are shown attached to a bellows which may extend but cannot rotate. Such an arrangement, in which one end cannot rotate relative to the other end, properly represents the intrinsic restriction against rotation in closed circular DNA. The addition of heat or alkali again enlarges the coil region (Fig. 4(b)). The mass required to enlarge the coil is derived from the material made available upon decreasing the pitch of the duplex. This process reduces the stress in the duplex and increases the thermodynamic stability of the duplex regions. As the early melting proceeds, the distortion of the duplex falls off until finally the relaxed circular duplex molecule, I’, contains two familiar DNA conformations-an undistorted helical duplex and a circular coil region in which the DNA is fully unwound. At the end

184

J. VINOGRAD,

J. LEBOWITZ

(a)

AND

R. WATSON

(b)

FIQ. 4. A representation of the early helix-coil transition in closed circular DNA. The symbols, strand. The duplex strands are ( l ), are provided to assist the reader in tracking a partioulrtr anchored at the top to a fixed support and at the bottom to 8 support which may stretch but not rotate. The superhelical molecule is represented in (a) by a distorted duplex having 8 linear axis. The melting of five base pairs results in a decrease in the pitch (base pairs per turn) of the distorted duplex and an enlargement of the coil region by five base pairs shown as in (b). In a superhelicrd molecule with a normal duplex pitch the pitch of the superhelix (base pairs per superhelical turn) increases when five base pairs are transferred to the coil region.

of the early transition the molecule contains denatured base pairs and an unstressed duplex. The fully titrated closed molecule has, as shown in Figure 2(a), a greater buoyant density than that of the fully titrated single strands. The abnormally high buoyant density of I at high pH, noted previously by Weil & Vinograd (1963) is apparently a general property of closed duplex DNA (Vinograd & Lebowitz, 1966aJ). The observed difference in buoyant density between the fully titrated intact molecule and the mean of the single strands from the nicked molecule is 195 mg/ml. This result corresponds to 20.5 mg/ml. at 25°C. The explanation for this increment is not established. It has been observed (Laipis & Vinograd, unpublished results) that alkaline linear DNA at 20°C is hypochromic at 270 m/L relative to the same solution at 60°C and thus contains stacked bases. This residual base stacking may be expected to lower the buoyant density at 20°C relative to a molecule in which base stacking is absent. Uncharged cytosine and adenine residues contained in a linear polynucleotide strand in alkaline solution can participate in stacking with the formation of loops or a hairpin-like structure. The spatial restrictions in intact polyoma DNA limit the ability of the single strands to assume the conformations necessary for stacking. The abnormally high buoyant density may be, at least in part, due to a sterica.lly imposed restriction on base stacking in the fully titrated double-stranded molecule. Since the denatured regions at the end of the early transition have the structure of a completely titrated single polynucleotide strand, we normalize our results by the total buoyant) density-shift for the nicked molecule II. 57 mg:/ml. at 20°C.

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

18.5

The value off,, the fractional buoyant density shift at the end of the early titration, is difficult to obtain accurately from the curve, Figure 2(a) and 2(b), which does not become flat before it begins to rise with an increasing slope at pH 11.70. At the onset of the early transition, the melting pH, pH,, of the A-T richest regions in the molecule is reduced by the large destabilizing effect of the high initial superhelix density. As the early titration continues, the superhelix density falls and the reduction in pH, becomes correspondingly smaller. Simultaneously the titration occurs in A-T poorer regions. These two anti-cooperative effects broaden the early t,itration curve. At the end of the early transition, the destabilizing effect of the superhelix falls to zero for all base pairs. Such a molecule contains coil regions rich in A-T and a remaining duplex depleted of the A-T richer segments. The titration curve for a hypothetical closed circular duplex DNA, having the same molecular weight and superhelix density as polyoma DNA I but containing 10 TVadjoining A-T base pairs and only G-C pairs in the remainder of the molecule, would be expected to contain a plateau region extending from the pH at a = 0 to the pH at which G-C pairs adjoining a coil region begin to titrate. In a natural closed DNA at D = 0, A-T base pairs are also contained in the duplex regions near the ends of the coil regions. The pH at the onset of late transition is therefore lowered, and the late transition may begin earlier than the onset of the titration of the nicked molecule, II, which must be nucleated by the formation of the first coil region. These considerations suggest that, in general, a true plateau region will not be observed with a naturally occurring DNA, but rather a change in slope near the end of the early titration. In Figure 2(b) the end of the early titration is characterized by an inflection point, at which the slope of the curve approaches but is not equal to zero. We take the height of the curve at this inflection point at pH 11.70 as the best measure of the maximum ext,ent of the early titration. The buoyant density increment at the inflection point is 2-l jO.1 mg/ml. This increment corresponds to a fractional buoyant density shift, fc, of O-037 and to the titration of 150&10 base pairs or to 3.2% of the 4700 base pairs in the molecule. Polyoma DNA in CsCl thus contains -15 -f 1 superhelical turns and has a superhelix density of --0.032 & 0*002 superhelical turns per duplex t’urn. The value, f O-1 mg/ml.. assigned to the uncertainty in the buoyant density shift represents our estimate of the error in evaluating the final result from the data points. It does not include a possible small over-estimate of u0 and T,, which may result from the observed overlap of the tails of the two transitions. The pH span over the middle 80% of the early transition is 0.25 pH unit, compared with less than 0.025 pH unit observed here for the nicked molecule. The onset of the early transition occurs at pH 11.35, 0.45 pH unit below the pH value for the abrupt transition of the nicked circular duplex. The latter increment in pH may be related to an increment in temperature with the aid of the results in Figures 2 and 7. The melting temperatures, T’,, of II and I in 7.2 M-N&JO, are 48°C and 73”C, respectively. The corresponding temperatures, T,, in standard saline citrate are 89°C and 107°C as shown below. The midpoints of the total buoyant density titrations of II and I are at pH 11.80 and 12.28. If we now assume that the temperature increment and the pH increment are linearly related, we calculate that O-45 pH unit corresponds to a temperature increment of 17°C in st’andard saline citrate, and that the onset of the early helix-coil transition should occur at 72°C. Similarly, the midpoint of the early helix transitsion, observed a,t pH 11.48. would occur at, 77°C.

186

J. VIKOGRAD,

J. LEBOWITZ

(d) Late Relix-coil transition

AND

R.

WATSON

in ~olymna DNA

The main helix-coil transition in closed circular DNA, Figure 2, occurs at a higher pH than is required for the nicked molecules. The initial state for this t,ransition is represented as a normal duplex DNA which contains a coil region consisting of two lengths of single-stranded DNA, each 150 nuoleotides long (Fig. 5(a)). The

(a)

(b)

FILL 5. A representation of the onset of the l&e helix-coil transition in closed circular DNA. The symbols, (a), are provided to assist the reader in tracking 8 part&&r strand. The duplex strands are anchored to supports 88 in Fig. 4. The melting of five base paira in the Watson-Crick duplex in (a) results in a 180’ clockwise rotation of the two strands in the coil region about each other and enlargement of the coil region by five base pairs as in (b).

contour length of such a loop is 2200 A. We now allow five base pairs to pass from the helical to the coil region without rotation of the helical segments as in Figure 4. The transfer of five base pairs results in the formation of one crossover in the coil region. The crossover has the effect of reducing the configurational entropy of the coil region of the molecule. Each further melting of five base pairs introduces another crossover. As the transition proceeds, the density of crossovers in the coil regions increases and approaches a value of one per five nuoleotide pairs. In the intermediate stages of the transition we expect that the native and the denatured duplex regions will form positive superhelical turns. At the end of the transition the ordered duplex regions will have disappeared and the alkaline denatured double-stranded cyclic coil formed. It is to be expected that the strands in the double-stranded coil will form supercoils to relieve the tightness of the winding. induced late helix-coil transition In these studies it was necessary to ascertain that single-strand scissions did not occur upon heating. When polyoma DNA I was heated in standard saline citrate, the absorbance of the solution began to change at 90°C. At 104°C approximately one-fifth of the expected absorbance change had occurred (Fig. 6). A sedimentation velocity analysis of the product obtained after quick cooling revealed that approximately 30% of the DNA had undergone a scission reaction. It was therefore not known (e) Themndly

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

187

whether any of the intact polyoma DNA had indeed melted. The T, of the singly nicked form in SSC was 89°C in agreement with the estimate of the guanine-cytosine content (48%) from the buoyant density. In order to reduce the melting temperature and thereby reduce the incidence of single-strand scissions, the melting experiments were performed in SSC/lO. It was found that the scission rate increased markedly at low ionic strength. Meaningful data could therefore not be obtained in the above solvents. Hamaguchi & Geiduschek (1962) showed that T’, for linear DNA in 7.2 M-NaClO, is about 40°C lower than T, in SSC. The solid curves in Figure 6 represent the average 100

30

40

50

60 Temperature

70

80

I/ I

I

90

100

(“0

Fro. 6. The thermally induced helix-coil transition in intact, I, and singly nicked, II, polyoma DNA in two solvents. The ordinate gives the percentage of the total absorbance change at 260 rnp. The fractional absorbence changes observed are discussed in the text. The melting of II in standard saline citrate occum with a midpoint at 89°C. The indicated partial melting for I may actually represent the introduction of single-strand missions. In 7.2 n-NaClO,, the midpoint of the melting of II occum 26°C below the midpoint of the melting of I. The error bars on the curve for I represent the standard deviation observed in five separate experiments. ) 7.2 M(NaCIO,; (---) SEX.

of our results obtained with I and II in 7.2 M-NaClC,. At the completion of the experiments with I, the cuvettes were cooled in ice. Portions were then diluted with one volume of buffer and analyzed by analytical band centrifugation in 45 M-NaClO,. Less than 5% conversion of I to II was observed. The midpoints of the transitions for polyoma I and II occurred at 73 and 48”C, respectively. The average fractional change in the absorbance at 260 rnp in 7.2 M-NaClC, was 0.33 for I and 0.32 for II. Similar values were obtained for T7 DNA and the linear bacterial DNA’s listed in Figure 7 and for E. coli DNA in this solvent by Iyer & Szybalski (1963). The melting temperature in NaClO,, T’,, may be converted to the more familiar T, in SSC with the relations T, = 69.3 + 0.41 (G-C)

(12)

T’, = 19.0 + 0.56 (G-C)

(13)

obtained by Marmur & Doty (1962) and Hamaguchi & Geiduschek (1962) for the dependence of melting temperature on the base composition of DNA in SSC and 7.2 M-NaClO,, respectively. In the above equations (G-G) stands for the guaninecytosine content expressed in moles %. We have evaluated the intercept in equation

188

J. VINOGRAD,

J. LEBOWITZ

AND

H.

WATSOS

(13) from the line given by Hamaguchi & Geiduschek (1962). The above equations when combined yield the conversion formula T, = 55.4 + O-732 T’,.

(14)

T, = 53.9 + 0.732 T’,

(15)

A second conversion formula is based on the published slopes and our own results for polyoma II in both solvents. Our data for polyoma DNA and for other bacterial and viral DNA are summarized in Figure 7 and Table 2. The values of T, calculated with equation (15) are in someTABLE 2 Melting temperatures of intact and nicked polyoma DNA and otbr selected DNA’s in 7-2 ar-NaClO, and in standard saline &a& M&%tial

T, in SSC c8lcul8tedg

Measured

cloatridizlnt perfringe?l.a

81.8 90.1 90.4 90.9 99.0 108.6

82*0(80*5)$ 89.8(89*5)$ 89.0 -(90*5)$ 100*0(99*5)$ -

36.0 47*4(49.2)7 47.8 48*5(49)t 60*6(59+O)t 72.8

T7 Polyome II E. w&i M. ly8odeilcticua Polyoma I

C8lculated

11

82.3 88.7 90.0 98.3 107.3

t Hamaguchi & Geiduschek (1962). $ Marmur t Doty (1962). 5 Calculatid with equation (14). 11C&uIated with equation (15).

30

40

50

60 Temperoture

70

80

90

100

K)

of intact polyoma DNA, I, FIG. 7. Melting curvee in SSC (---) and in 7.2 x-NaCIO1 (-) singly nicked polyome DNA, II, and three bacterial DNA’s: Cloattiwn perfringe~, P, M. Zyaodeikticlls, L, E. coli, C, and the viral DNA, T7. The results show that the melting of polyoma II is similar to that of T7 in both SSC and in N&10,. The transition of polyoma I in N&IO4 spans a temperature interval of 47°C compared with 8°C for polyoma II.

what better agreement with the experimental data than those obtained with equation (14), presumably because of the avoidance of a long extrapolation to f%ndthe intercept.. The main result of this work is that T, for polyoma DNA I in SSC is 107°C and that the stabilizing effect of the closure is 18°C. A melting temperature of 107°C corresponds, according t,o equation (12), to 93 moles y0 (G-C) for a linear DNA.

SUPERHELIX

DENSITY

IN

POLYOMA

189

DNA

We were unable to observe a hyperchromic effect associated with the early helixcoil transition. In order to detect this early hyperchromicity we would have had to have been able to observe a gradual change in absorbance of 0.01 optical density unit. Such effects would have been obscured by the noise level in our experiments. The thermally induced late helix-coil transition of I is much broader and thus less co-operative than that of II. The breadths of the transitions observed in Figure 7 are listed in Table 3. The breadths, AT’ and AT, give the temperature intervals in which TABLE

Tramition DNA

Cl. perfringelw T7 Polyoma II

E. coli M. lyaodeikttim Polyome t Temperature $ Temperature

interval interval

I

3

breadths in 7.2 nr-NaClO, and in SSC’ AT’i N&10, 7.2 3.7 5.6 7.4 3.6 19.0

ATi ssc 3.2 2.0 2.0 3.1 --

AT’d

AT’JAT

4.0 2.2 3.1 4.2 1.9 12.4

in which the middle 0*6Oth part of the transition in which the 0.20 to 0.50th part of the transition

0.55 0.59 0.56 0.57 0.53 0.65 occurs. occurs.

the central (l/l/e)th part of the transition occurs (Dove & Davidson, 1962). It should be noted that all of the transition breadths are larger in 7.2 M-NaClO, than in SSC, an effect observed earlier by Hamaguchi & Geiduschek. The breadth of the transition for polyoma DNA II in NaClO, is comparable with the breadth observed with linear DNA’s. The breadth for polyoma DNA I is 3.4 times larger than that observed for II. A similar ratio, 3.6, is obtained from the slopes of the curves taken at the midpoints of the transitions. We have noted earlier that the co&urational entropy of the coil region is substantial in closed circular molecules (Fig. 5). This effect is considered to be a major cause not only of the increased melting temperatures but also of the increased transition breadth. A more extensive analysis of the results obtained with I would appear to require modification of the Zimm (1960) theory for the helix-coil transition. It ie unlikely, for example, that the JacobsonStockmayer (1950) expression for the effect of ring formation on the configurational entropy of a chain will be applicable in the case of closed circular DNA, because of the presence of extensive interwinding of the two strands in the coil regions. The transition in I appears to be quite asymmetric in both t,he alkaline buoyant density titration, Figure 2(a), and the thermal melting in 7.2 nx-NaClO, (Fig. 6). Upon close inspection, the melting curves for II and for the ot’her linear DNA’s studied are also observed to be asymmetric. In Table 3 the asymmetries are characterized by the ratio, AT’JAT’. The quantities AT’, and AT’ are the temperature intervals in which the 0.20 to 0*50th part and 0.20 to 0*8Oth part of the transition occur, respectively. The mean asymmetry for II and for the four linear DNA’s is 0.56, compared with 0.65 for I. The melting curves for T7, polyoma I and II, and E. coli DNA in NaClO, are superimposed at the midpoints in Figure 8. Included also is a calculated curve for the first half of the melting of I. The calculated curve represents t*he expected

190

J. VIXCGRAD,

J. LEBGWITZ

AXD

H.

WATSON

AT FIG. 8. The cupves for polyome, I, and II, T7 (---), and E. di DNA ( . . . . ) in Fig. 7 was calcul&ed as exhave been shifted to a common abscissa, &t A!!’ = 0. The line -@-a-plained in the text from the upper half of the melting curve for polyoma I. The result shows that the first part of the melting of I occurs 0 to 5% below the cctlculated expected temper&urea. This lowering of the melting temperature in the first part of the late helix-coil transition is attributed to the presence of a coil region formed in the course of the early helix-coil transition.

melting pro6le in the absence of a distorting effect in I. The curve was calculated with the assumption that the broadening effect of the closure would be symmetrical about the midpoint of the transition. The quantity AT’(I)/AT’(II) was calculated at several levels in the second half of the transition. These factors were then multiplied by AT’(I1) at the conjugate levels in the first half of the transition of II to yield the calculated curve in Figure 8. The experimental curve is seen to be shifted to lower temperatures relative to the calculated curve. The shift is attributed to the presence of denatured regions in the molecule at the beginning of the late transition. These regions act as nucleation sites and lower the local transition temperatures. The melting of the A-T richer regions in the nicked molecule has to await the formation of the first nucleation sites, which occurs at somewhat higher temperatures.

4. Discussion The unique properties of closed circular DNA’s derive from the fundamental restriction against any change in the topological winding number, CLThis quantity, which is referred to as the linkage number in topology, describes the number of times one strand winds about the other in the closed molecule constrained to lie in a plane. The value of a in polyoma DNA is +455, the positive sign indicating that the winding occurs in a clockwise or right-handed sense when viewed by an observer along the helix axis. The value of a is fixed in the molecule at the time the last chain closure is made and remains invariant as long as both deoxyribophosphodiester chains remain intact. Three possibilities exist for the relation between CLand ,!l” at the time the final ring closure is made. (a) u = PO. The number of duplex turns in the molecule constrained to lie in a plane is exactly equal to the number required for the formation of the B form of the Watson-Crick duplex. Such a molecule will be free of superhelical turns in solvents such as 1 M-NaCl at neutral pH and room temperature in which the B form is stable. Gcllert (1967) apparently first prepared such molecules, aN/lO, by incubating viral

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

191

lambda DNA in crude extracts of E. wli B that contained the joining enzyme later isolated by Olivera & Lehman (1967), Zimmerman, Little, Oshinsky & Gellert (1967) and Gefter, Becker & Hurwitz (1967). (b) cc< /I’]. The topological winding number is smaller than the number of turns required in the B form. Such a molecule will wind up in order to form the stable structure and, to conserve the rule that a remain constant, will form a negative superhelical molecule, a right-handed interwound superhelix. All of the naturally occurring closed circular duplex DNA’s for which the sense of the superhelix has been determined appear to be negative superhelical molecules in saline solutions, and are therefore characterized by the relation, 0: < fl”. At the present time the list of such molecules includes polyoma DNA (Vinograd, Lebowitz, Radloff, Watson & Laipus, 1965), SV40 DNA (Bauer & Vinograd, 1968), human papilloma DNA (Crawford, 1965) and RF-+X DNA (Jansz & Pouwels, 1965). (c) a> /lo. Such molecules are overwound in comparison with DNA in the B form. They would be expected to form positive superhelical molecules, left-handed interwound superhelices, when placed in saline solutions. No such molecules have been reported. Positive superhelical molecules are, however, formed from molecules in which a ,: fl” when the average pitch of the duplex is adequately increased by a chemical reaction, as for example, with an intercalating dye, with hydroxyl ions, or with formaldehyde at elevated temperature. In these molecules the duplex winding number /3 is less than /3O,and r = a - /3 is positive. This result emphasizes that the sign of T and the sense of the interwound superhelix depend on the difference between the topological winding number a and the duplex winding number. The above relation, equation (l), is valid for any system of two impenetrable circles, which might bc lines or pieces of string. In DNA it is the chemical forces between the atoms in the different strands that are responsible for generating a structure having a particular value of p and, as a geometric consequence, a non-zero value of 7. (a) The superhelical structure and the early helix-coil transition (i) i5’tructure and homogeneity of superhelical closed circular polyoma DNA According to the results of this study, polyoma DNA in buoyant cesium chloride contains -15 f 1 superhelical turns and the superhelix density is -0.032 f 0902 superhelix per duplex turn. On the average there are about 300 base pairs and a length of about 1000 A of duplex DNA in each superhelical turn The distribution of superhelix densities among the molecules in polyoma DNA I appears to be narrow. The concentration profiles of polyoma DNA I and II in analytical band sedimentation velocity experiments broaden similarly. Spreading due to a marked heterogeneity in the sedimentation coefficient of component I has not been observed, nor was any increased band spreading observed in buoyant density experiments performed in the pH interval in which the early helix-coil transition occurred. We conclude from these two qualitative observations that the effect of any variation of the superhelix density among polyoma I molecules is small. The positive free energy of superhelix formation, AG, in the very similar DNA from SV40 virus has been evaluated by Bauer t Vinograd (manuscript in preparation). They found that AC at 7 = -15 and 0 = -0.032 is about 200 times greater than kT ; they also found that AG is approximately proportional to the square of 7. Large fluctuations of u along the duplex in any one native molecule are therefore relatively improbable. The molecule may. to a first approximation, be represented by an inter?

192

J. VINOGRAD,

J. LEBOWITZ

AND

R. WATSOS

wound superhelical structure of constant radius of curvature subject to small perturbations in the curvature induced by t,hermal motion. A set, of structures with different radii of curvature and correspondingly different superhelical dia,meters is described by Bauer & Vinograd (manuscript in preparation). (ii) Destabilizing effects of the superhelical turns The superhelical turns present in polyoma DNA destabilize the molecule in comparison with an equivalent closed molecule having no superhelical turns or in comparison with a nicked molecule. The destabilization revealed in this study, in which the helix-coil transitions in I and II have been compared, reduces the onset of the transition by 0.45 pH unit or equivalently by 17°C in standard saline citrate. The effect falls off as the superhelices unwind during t,he titration, until after 3.2% of the base pairs have been treated, the superhelices and the destabilizing effect disappear completely. The positive free energy associated with the superhelices is available to do work and to assist any process which requires unwinding of up to 3.2% of the duplex. Examples of such processes are the early melting, the early binding of dyes by intercalation, and possibly the binding of RNA polymerase at the initiation sites for transcription and the formation of transient hydrogen-bonded hybrids between the growing RNA and the hemplate DNA strand. (iii) Errors in the estimation of u. and 7. During the alkaline buoyant density titration of DNA, protons are removed from guanine and thymine residues and a corresponding number of solvated cesium ions are added to the buoyant complex in order to preserve electroneutrality. The buoyant density of a partially titrated molecule is regarded in this work as the appropriately weighted mean density of two attached buoyant complexes having different buoyant densities-the buoyant density of untitrated DNA and the buoyant density of fully titrated DNA. At the critical point p, in the titration curve, the 150 base pairs can form a ring approximately 2200 A in length, a size comparable to that estimated for the loop size in partially denatured high molecular weight DNA by Zimm (1960). The buoyant density of denatured regions of this size may be expected to be characteristic of the buoyant density of unrestrained fully titrated DNA strands. The titrated DNA in the coil regions at the critical point may be enriched in A-T base pairs, Such an enrichment, however, should have no significant effect on t,he observed fraction buoyant density shift. Vinograd et al. (1963) have previously shown that the fractional buoyant density shifts which occurred on complete titration of DNA’s of different base compositions were independent of base composition within the experimental error of about 2%. At the boundaries between the helix and coil regions the preferential solvation may deviate from the weighted mean characteristic of the two regions. The uncertainty associated with this effect, which in itself may not be large. is small if the number of boundary regions is small. The assumptions of a known buoyant density for the coil region and of a negligible effect due to a change in the preferential solvation at the helix-coil boundary regions become hazardous except in the neighborhood of the critical region in the titration curve. At the beginning of the early titration, the coil is small and both of the assumptions may be invalid. During the late helix-coil transition the buoyant density of the coil regions clearly changes from the value applicable at the beginning of the late Gtration, and indicat,ed by the upper plateau for polyoma DNA II, to the higher value

SUPERHELIX

DENSITY

IN

POLYOMA

DNA

193

at the upper plateau for polyoma DNA I. In this work we have avoided drawing quantitative conclusions which depend on the foregoing assumptions except at the critical point in the titration. (b) The late helix-coil transition The stabilizing effects of the closed structure delay the main helix-coil transition by 0.48 pH unit in the alkaline titration and by 18°C in thermal melting experiments. The midpoint of the thermally induced transition occurs at a temperature expected for a DNA having a 93 mole y0 G-C content, whereas the actual G-C content is approximately 48o/o. This stabilization is attributed to the effect of a reduction in the configurational entropy of the coil regions. At the midpoint of the late transition, the coil regions contain approximately one right-handed interstrand crossover for every five base pairs in a molecule having an axis constrained to lie in a plane. If we assume that the enthalpy of melting is not affected by the closure, the 5% enhancement of T, in SSC corresponds to a 5% decrease in AS,, the entropy change that occurs upon transferring a single base pair from the helix-coil boundary region to the coil region. DeVoe & Tinoco (1962) attributed about one fourth of the entropy change, AS,, to chain configurational effects and the remainder to solute-solvent interactiou effects. We conclude then that the configurational entropy change upon melt,ing a base pair is reduced by about 20% in the closed circular molecule. The stability of polyoma DNA against thermal- and alkaline-induced melting is a general property of closed circular duplex DNA. This property has been used as the basis for a method of separating closed circular from linear and nicked circular DNA (Jansz, Pouwels & Schiphorst, 1966). Heating to 100°C or exposure to pH 12.3 induces strand separation in linear DNA but only partially melts closed circular DNA. Upon cooling or neutralization the single strands re-associate slowly in a bimolecular reaction limited in rate principally by the slow rate of site recognition (Wetmur & Davidson, 1968) while the partially denatured closed circular molecules zip up rapidly by the type I renaturation mechanism described by Geiduschek (1962). (c) General properties of closed circular DNA molecules The superhelical structure and the requirement that the topological winding number a remains constant impart several general properties to all closed circular DNA’s. Completely base-paired superhelical molecules are more compact and thermodynamically less stable than the corresponding nicked relaxed molecules. The compactness accounts for the elevated sedimentation coefficient, s1 > su, at neutral pH and the higher resistance to shear reported by Weil t Vinograd (1963) and Young t Sinsheimer (1967). The reduced thermodynamic stability due to the superhelical structure destabilizes the molecule and explains the higher affinity for hydroxyl ions, intercalative dyes, and formaldehyde in reactions that occur with an obligatory unwinding of a small fraction of the duplex turns. The closed structure is also responsible for the appearance of twisted molecules in electron micrographs prepared by the method of Kleinschmidt & Zahn (1959). The number of superhelical turns, 7, in such electron micrographs may bear little relation to the value of r in the DNA solutions used in preparing the specimen grids. Three independent investigations (Kleinschmidt, Kass, Williams & Knight, 1965; Lang, Bujard, Wolff & Russell, 1967; Inman, 1967) have shown that the length of DNA and therefore the duplex winding number depends on the ionic strength of the 13

194

J. VINOGRAD,

J. LEBOWITZ

AND

R. WATSOS

substrate for the protein-DNA surface layer. The superhelices in polyoma DNA disappear completely when the average pitch of the duplex is increased by only 3% and appear again in accordance with equation (1) as positive superhelices when the average pitch is increased further. Unless conditions employed in specimen preparation are rigorously reproduced and the system calibrated with closed molrcules of known superhelix density, the electron micrographs may be regarded as evidence only for the existence of the closed structure and for the absence of a swivel. Nicked molecules usually take on the appearance of distorted circles with few if any crossovers (Vinograd, Lebowitz, Radloff, Watson & Laipis, 1965). The high T, and pH, observed in the late transition of closed polyoma DNA is a general property of all such molecules, depending as they do on the diminished entropy change that occurs on transferring a base pair from a helical to a coil region that already contains interwound denatured strands. The requirement that the denatured strands continue to be interwound accounts for the formation of the fast sedimenting fully titrated double-stranded cyclic coil described by Weil & Vinograd (1963) and Dulbecco & Vogt (1963). The sedimentation coefficient of this fast alkaline form is about 35 times greater than the sedimentation coefficient of the alkaline single strands in closed DNA’s ranging in molecular weight from 3 x lo8 to 3x IO7 daltons for polyoma and lambda DNA, respectively. The appearance of the fast alkaline form decisively demonstrates the absence in the molecule of both single-strand scissions and of depurinated sites. The backbone of DNA is known to hydrolyze rapidly at depurinated sites in the alkaline solutions, pH 12.5, in which these experiments are performed (Greer & Zamenhoff, 1962; Fiers & Sinsheimer, 1962). The elevated alkaline buoyant density, d8~0+02 g/ml., is also a general property of closed circular DNA. The detection of these abnormally dense buoyant molecules becomes more difficult as the molecular weight of the DNA increases. At pH 125 the phosphodiester deoxyribose strands hydrolyze at a slow enough rate so that apparently stable bands form with molecules having molecular weights in the range of 3 x lo6 daltons. After three days at 25”C, transfer of material from the dense to the light band was easily detected (Vinograd & Watson, unpublished results). The formation of the first hydrolytically induced single-strand scission in lambda DNA may be expected to occur ten times faster than in polyoma DNA. The restricted uptake of ethidium bromide at high ethidium concentrations is again the result of the obligatory formation of positive superhelices during the course of a reaction-intercalative binding-that causes unwinding of the duplex structure. The positive free energy stored in the superhelices effectively opposes the free energy change that drives the dye-binding reaction. The restricted ethidium uptake provides a useful and general preparative method for separating closed circular from nicked and linear DNA (Radloff, Bauer & Vinograd, 1967). (d) The origin and the biological significance of the superhelical turns in closed circular DNA At the present time it is not possible to decide between the two alternatives for t’he state of supercoiling of circular DNA molecules at the time of closure of the last polynucleotide ester bond. The superhelical molecule is in a high-energy state and would not be formed from a nicked molecule unless the latter were supercoiled as a result of an interaction with an organizer, such as viral core prot,ein, or with an as

SUPBRBELtiX

DENSl!i!P

IN

POltYOhfA

DNd

I!%

yet unknown core substance upon which duplex DNA is wound as it is synthesized in the cell. The alternative possibility is that the nicked molecule is partially unwound at the time of closure and that fi = a < /3”. This unwinding may be the result of a generalized increase in pitch over that assumed by the B form of the molecule, or may be the result of local interactions with proteins or small molecules that unwind DNA upon binding. Purification of the DNA then allows a perturbed Watson-Crick structure, 7 = CX-~ and B = p” > a to form. We thank W. R. Bauer for several valuable discussions and his critical comments on the manuscript. We thank L. Wenzel for her assistance in the growth of the polyoma virus and R. Kent for her assistance in the preparation of the manuscript. The research has been supported by grants HE03394 from the National Heart Institute and CA08014 from the National Cancer Institute, United States Public Health Service. This is contribution no. 3568 from the Department of Chemistry of the California Institute of Technology. REFERENCES Baldwin, R. L. & Shooter, E. (1963). J. Mol. Biol. 7, 511. Bauer, W. R. & Vinograd, J. (1968). J. Mol. BioZ. 33, 141. Crawford, L. V. (1965). J. Mol. Bid. 13, 362. Crawford, L. V. & Black, P. H. (1964). virology, 24, 388. Crawford, L. V. & Waring, M. J. (1967). J. Mol. Biol. 25, 23. Davidson, N. D., Widhohn, J. M., Nandi, U. S., Jensen, R. H., Glivera, B. M. & Wang, J. C. (1966). Proc. Nut. Acod. Sci., Wash. 53, 111. DeVoe, H. & Tinoco, I., Jr. (1962). J. MOE. BioZ. 4, 500. Dove, W. F. & Davidson, N. D. (1962). J. Mol. BioZ. 5, 467. Dulbecco, R. & Vogt, M. (1963). Proc. Nat. Acad. Sci., Wash. 50, 263. Fessler, J. & Vinograd, J. (1965). Biochim biophy~ Actu, 103, 160. Fiers, W. & Sinsheimer, R. L. (1962). J. Mol. BioZ. 5, 420. Gefter, M. L., Becker, A. & Hurwitz, J. (1967). Proc. Nat. Ad. Sk., Wash. 58, 240. Geiduschek, E. P. (1962). J. Mol. BioZ. 4, 467. Gellert, M. (1967). Proc. Nat. Acud. Sci., Wash. 57, 148. Glaubiger, D. & Hearst, J. E. (1967). Biopolymers, 8, 691. Greer, S. Bi Zamenhoff, S. (1962). J. Mol. BioZ. 4, 123. Hamaguchi, K. & Geiduschek, E. P. (1962). J. Amer. Chem. Sot. 84, 1329. Hearst, J. 13. (1962). J. Mol. BioZ. 4, 415. Hearst, J. E. & Vinograd, J. (1961). PTOC. Nat. Accd Sci., Wash. 47, 1005. Ifft, J. B. & Williams, A. (1967). B&him. biophys. Actu, 136, 151. Inman, R. B. (1967). J. Mol. BioZ. 18, 464. Iyer, V. N. & Szybalski, W. (1963). Proc. Nat. Acad. Sci., Wash. 50, 355. Jacobson, H. & Stockmayer, W. (1950). J. Chem. Phya. 18, 1600. Jansz, H. S. & Pouwels, P. H. (1966). B&hem. Biophya. Ra. Comm. 18, 589. Jansz, H. S., Pouwels, P. H. & Schiphorst, J. (1966). B&him. biophya. Act& 123, 626. Kirby, K. S. (1957). BiocRem. J. 66, 405. Kleinschmidt, A. K., Kass, S. J., Williams, R. C!. & Knight-, C. A. (1965). J. Mol. BioZ. 13, 74Q. Kleinschmidt, A. T. & Zahn, R. K. (1969). Z. Nuturf. 14b, 770. Lang, D., Bujard, H., Wolff, B. & Russell, D. (1967). J. Mol. BioZ. 23, 163. Lebowitz, J-. & Laskowski, M., Jr. (1962). Biochemistry, 1, 1044. Marmur, J. 8: Doty, P. (1962). J. Mol. BioZ. 5, 109. Murikami, W. (1963). Science, 142, 56. Olivera, B. M. & Lehman, I. R. (1967). Proc. Nat. Aead. Sci., Wash. 57, 1426. Radloff, R., Bauer, W. R. & Vinograd, J. (1967). Proc. Nat. Acad. Sci., Wah. 57, 1614. Schumaker, V. N. & Wagnild, J. (1965). Biophys. J. 5, 947. Vinograd, J. & Hearst, J. E. (1962). In Forkwhritte der Chemie organ&her Naturstoffe, ed. by L. Zechmeister, vol. 20, p. 372. Vienna: Springer-Verlag.

196

J. VINOGRAD,

J. LEBOWlTZ

Ai\‘D

R. WATSOS

Vinograd, J. C Lebowitz, J. (1966a). J. Gen. Physiol. 49, 103. Vinograd, J. & Lebowitz, J. (19663). In Macromolecular Metabolism, p. 103. Boston: Little, Brown & Co. Vinograd, J., Lebowitz, J., Radloff, R., Watson, R. & Laipis, P. (1965). Proc. Nat. Acad. Sci., Wash. 53, 1104. Vinograd, J., Morris, J., Davidson, N. & Dove, W. F. Jr., (1963). Proc. Nat. Acad. Sci., Wash. 49, 12. Vinograd, J., Radloff, R. & Bruner, R. (1965). B~iopoZymere, 3, 481. Weil, R. (1963). Proc. Nat. Acud. Sk, Wash. 49, 480. Weil, R. & Vinograd, J. (1963). Proc. Nut. Acad. Sci., Wash. 50, 730. Wetmur, J. & Davidson, N. D. (1968). J. Mol. BioZ., in the press. Winocour, E. (1963). %oology, 19, 158. Young, E. T., II, & Sinsheimer, R. L. (1967). J. Mol. BioZ. 30, 165. Zimm, B. (1960). J. Chem. Phye. 33, 1349. Zimmerman, S. B., Little, J. W., Oshinsky, C. K. & Gellert, M. (1967). Proc. Nat. Acad. Sci., Wueh. 57, 1841. Note added in proof. It has been recently pointed out (J. C. Wang, personal communication) that the average angle between two adjoining base pairs in the duplex may change with the unwinding of the superhelical turns which occurs in the alkaline titration. Such a change in the average angle of the untitrated duplex segments would result in an overestimate of the superhelix density aa calculated with equation (6). The effect of this suggestion is described in a “Note added in proof” in the paper by Bauer t Vinograd (1968). The quantities 0.67 Y and 0.67 y0 should be replaced by p and p,, respectively, in their equations (iii) and (iv) in order to be applicable to the alkaline titration.

APPENDIX Relationship between the Degree of Titration and Fractional Buoyant Density Shift in an Alkaline Buoyant Density Titration of DNA The weight fraction, wo, of untitra~ed titrated DNA molecule is

solvated cesium nucleotide residues in a

partially

(1 -PM,

w=

(1 -~Wo+z--,

(A-1 1

where r, is the degree of titration and &lo and Ml are the solvated molecular weights of untitrated and titrated cesium nucleotide residues. The partial specific volume of a partially titrated molecule is CD= woiio + WIGl

(A-2)

where wo, wl, and ii,, GI are the weight fractions and solvated partial specitk volumes of untitrated and titrated solvated residues. These equations are combined: 1-pM,, --=2, M,

C,,-17, B, - Gp

(A-3)

and the partial specific volumes replaced by the reciprocals of the buoyant densities

1 -PM, --=--

~9~0,- 0,

P

4 4 - 00

MI

(A-4)

SUPERHELIX

DENSITY

IN

POLYOMA

where the subscripts on 0 denote the degree of titration. fractional buoyant shift: f=S and obtain the 6nal result

f= M, 0,

where k = -.

Mo 4

197

We now introduce f, the

(A-5) 0

into (A4),

DNA

kp 1+p(k - 1)’