Proc. Natl. Acad. Sci. USA 73 (1976) 2527

Addendum. To the paper "Purification of folate binding factorin normal umbilical cord serum" by Barton A. Kamen and J.Douglas Caston, which appeared in the November 1975 issueof Proc. Natl. Acad. Sci. USA 72,4261-4264, the following noteis added.The method for dissociation of endogenous bound folate from

the natural folate-binder complex was essentially that usedinitially in the isolation and characterization of folate binderfrom hog kidney (1, 2) and subsequently employed in the dis-covery of a folate-binder complex in serum (3). It is a modifi-cation of an approach used to dissociate the synthetically pro-duced folate-binder complex with the binder found in bovinemilk, which was shown by Ford et al. (4) to have a strong pHdependency for association-dissociation equilibrium.

1. Kamen, B. A. & Caston, J. D. (1974) J. Lab. CGn. Med. 83,164-171.

2. Kamen, B. A. & Caston, J. D. (1975) J. Biol. Chem. 250, 2203-2205.

3. Colman, N. & Herbert, V. (1974) CGun. Res. 22, 700A.4. Ford, J. E., Salter, D. N. & Scott, K. J. (1969) J. Dairy Res. 36,

435-466.

Correction. In the article "Affinity of myosin S-1 for F-actin,measured by time-resolved fluorescence anisotropy" by StefanHighsmith, Robert A&Mendelson, and Manuel F. Moralespublished in the January issue of Proc. Natl. Acad. Sci. USA 73,133-137, the authors have requested the following changes. Onpage 136 in Table 2 the association constant and invertedstandard error obtained by S. Marston and A. Weber (ref. 3) wasincorrectly quoted as (1.4 4 6) X 107 M-1 at 0.12 M KC1, andshould be (1.4 + 0.12) X 107M-' at 0.14 M KC1.

Correction. In the article "Antigen stimulation of prosta-glandin synthesis and control of immune responIses" by D. R.Webb and P. L. Osheroff, which appeared in the April 1976issue of Proc. Natl. Acad. Sci. USA 73, 1300-1304, the au-thors have requested the following change. On p. 1301, thefirst line of the second column should read .... Ro 20-5720,an irreversible inhibitor, ...."

Correction. In the article "A relativistic spherical vortex" byC. L. Pekeris, which appeared in the March 1976 issue of theProc. Natl. Acad. Sci. USA 73, 687-691, the author has re-quested the following changes. On page 690, at the top of theleft-hand column, the expressions [1 + 2nS(r) sin2 9]1/2 in therelativistic solutions should be replaced by [1 + 2772S(r) sin2O]1/2, and the last term should read F(I) = I + (1/2)17I2.

In Eq. 44, an editorial error was made. The correct equationis:

p(O) = p(a) - 2c2,uon2K2 > p(a) - (1/2)c2go [44]

In Eqs. 45 and A6, printer's errors were made. The correctequations are:

y = c-2p(a) + yu0[1 + qF - (1/2)v2(1 + 2,7F)] [45]F = -(3/2)a2V sin2 Of(r2/a2)

-[jj(#r/jI(X)]1/j2 -[-A1j(A)/1j(A)]L. [A6]

Correction. In the article "Intramolecular ciosslinking of tro-pomyosin via disulfide bond formation: Evidence for chainregister" by Sherwin S. Lehrer, which appeared in the Sep-tember 1975 issue of the Proc. Natl. Acad. Sci. USA 72,3377-3381, the author has requested the following changes. Onpage 3380, lines 10 and 11 in the right-hand column shouldread, "A mixture only of aa anda# chains would, .. On thesame page, lines 17 and 18 in the right-hand column shouldread, "For the aa, af3 model the ratios would be (0.5, 0.5) and(0.6, 0.4) for a/fl = 3 and 4, respectively."

Correction. In the article "Determination of the number ofsuperhelical turns in simian virus 40 DNA by gel electropho-resis" by W. Keller, which appeared in the December 1975 issueof Proc. Natl. Acad. Sct. USA 72, 4876-4880, the author hasrequested the following change. On page 4879, in the sentencebeginning on the tenth line of the right column, the two minussigns should be deleted. The corrected sentence is "For SV40DNA this amounts to a reduction of r by 0.62.5200/360 = 9turns."

Corrections

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Proc. Natl. Acad. Sci. USA 73 (1976) 2527

Addendum. To the paper "Purification of folate binding factorin normal umbilical cord serum" by Barton A. Kamen and J.Douglas Caston, which appeared in the November 1975 issueof Proc. Natl. Acad. Sci. USA 72,4261-4264, the following noteis added.The method for dissociation of endogenous bound folate from

the natural folate-binder complex was essentially that usedinitially in the isolation and characterization of folate binderfrom hog kidney (1, 2) and subsequently employed in the dis-covery of a folate-binder complex in serum (3). It is a modifi-cation of an approach used to dissociate the synthetically pro-duced folate-binder complex with the binder found in bovinemilk, which was shown by Ford et al. (4) to have a strong pHdependency for association-dissociation equilibrium.

1. Kamen, B. A. & Caston, J. D. (1974) J. Lab. CGn. Med. 83,164-171.

2. Kamen, B. A. & Caston, J. D. (1975) J. Biol. Chem. 250, 2203-2205.

3. Colman, N. & Herbert, V. (1974) CGun. Res. 22, 700A.4. Ford, J. E., Salter, D. N. & Scott, K. J. (1969) J. Dairy Res. 36,

435-466.

Correction. In the article "Affinity of myosin S-1 for F-actin,measured by time-resolved fluorescence anisotropy" by StefanHighsmith, Robert A&Mendelson, and Manuel F. Moralespublished in the January issue of Proc. Natl. Acad. Sci. USA 73,133-137, the authors have requested the following changes. Onpage 136 in Table 2 the association constant and invertedstandard error obtained by S. Marston and A. Weber (ref. 3) wasincorrectly quoted as (1.4 4 6) X 107 M-1 at 0.12 M KC1, andshould be (1.4 + 0.12) X 107M-' at 0.14 M KC1.

Correction. In the article "Antigen stimulation of prosta-glandin synthesis and control of immune responIses" by D. R.Webb and P. L. Osheroff, which appeared in the April 1976issue of Proc. Natl. Acad. Sci. USA 73, 1300-1304, the au-thors have requested the following change. On p. 1301, thefirst line of the second column should read .... Ro 20-5720,an irreversible inhibitor, ...."

Correction. In the article "A relativistic spherical vortex" byC. L. Pekeris, which appeared in the March 1976 issue of theProc. Natl. Acad. Sci. USA 73, 687-691, the author has re-quested the following changes. On page 690, at the top of theleft-hand column, the expressions [1 + 2nS(r) sin2 9]1/2 in therelativistic solutions should be replaced by [1 + 2772S(r) sin2O]1/2, and the last term should read F(I) = I + (1/2)17I2.

In Eq. 44, an editorial error was made. The correct equationis:

p(O) = p(a) - 2c2,uon2K2 > p(a) - (1/2)c2go [44]

In Eqs. 45 and A6, printer's errors were made. The correctequations are:

y = c-2p(a) + yu0[1 + qF - (1/2)v2(1 + 2,7F)] [45]F = -(3/2)a2V sin2 Of(r2/a2)

-[jj(#r/jI(X)]1/j2 -[-A1j(A)/1j(A)]L. [A6]

Correction. In the article "Intramolecular ciosslinking of tro-pomyosin via disulfide bond formation: Evidence for chainregister" by Sherwin S. Lehrer, which appeared in the Sep-tember 1975 issue of the Proc. Natl. Acad. Sci. USA 72,3377-3381, the author has requested the following changes. Onpage 3380, lines 10 and 11 in the right-hand column shouldread, "A mixture only of aa anda# chains would, .. On thesame page, lines 17 and 18 in the right-hand column shouldread, "For the aa, af3 model the ratios would be (0.5, 0.5) and(0.6, 0.4) for a/fl = 3 and 4, respectively."

Correction. In the article "Determination of the number ofsuperhelical turns in simian virus 40 DNA by gel electropho-resis" by W. Keller, which appeared in the December 1975 issueof Proc. Natl. Acad. Sct. USA 72, 4876-4880, the author hasrequested the following change. On page 4879, in the sentencebeginning on the tenth line of the right column, the two minussigns should be deleted. The corrected sentence is "For SV40DNA this amounts to a reduction of r by 0.62.5200/360 = 9turns."

Corrections

Proc. Nat. Acad. Sci. USAVol. 72, No. 12, pp. 4876-4880, December 1975Biochemistry

Determination of the number of superhelical turns in simian virus 40DNA by gel electrophoresis

(DNA-relaxing enzyme/ethidium bromide/helix unwinding angle/chromatin structure)

WALTER KELLERCold Spring Harbor Laboratory, Cold Spring Harbor, New York 11724

Communicated by Barbara McClintock, September 30, 1975

ABSTRACT Closed-circular, superhelical DNA from sim-ian virus 40 (SV40 DNA I) was treated with an excess ofDNA-relaxing enzyme in the presence of increasing amountsof ethidium bromide (EtdBr). After removal of the ethidium,each sample consisted of a group of closed-circular DNAmolecules differing in their number of superhelical turns (r)around a mean value of i in a Gaussian-like distribution. TheDNA samples were analyzed by electrophoresis in agarosegels under conditions where the electrophoretic mobility wasa function of the number of superhelical turns. Since the dis-tributions around i of DNA molecules of different samplesoverlapped, the difference in the mean number of superheli-cal turns from sample to sample, AT, could be determinedand used to measure the mean number (T) for native SV40DNA I. By this criterion, SV40 DNA I contains a Gaussian-like distribution of molecules differing by integral numbersaround a mean value of i = -24 i 2 at 370C [in 0.2 M NaCl,10 mM Tris*HCI (pH 7.9), and 0.2 mM EDTAJ. The hetero-geneity in r is probably a consequence of thermal fluctua-tions in the DNA helix at the time when the last phospho-diester bond is closed in vivo.When correlated to the buoyant shift of completely relaxed

SV40 DNA in a CsCI-propidium diiodide gradient, the num-ber of AT = 24 + 2 of superhelical versus relaxed DNAimplies an unwinding of the DNA helix by 26-28° upon in-tercalation of one molecule of EtdBr.

The-presence of superhelical turns in all naturally occurringclosed-circular duplex DNAs has long been an intriguingpuzzle. (See ref. 1 for review.) The recent work of Germondet al. (2) provides the first plausible explanation for the exis-tence of superhelices in the DNAs of simian virus 40 (SV40)and polyoma virus. In these particles, DNA is associatedwith histones that are derived from their host cells (3-7).Such viral DNA-protein complexes have structural featuressimilar to those of cellular chromatin (8, 2). In the electronmicroscope, they appear as open-circular (relaxed) ringscontaining approximately twenty protein beads [v-bodies (9)or nucleosomes (10)]. Removal of the protein causes theDNA to assume superhelical configuration (2). After depro-teinization, superhelices occur only in closed-circular DNAand are a consequence of a topological constraint (1), whichprevents rotation of the strands in the double helix aroundthe helix axis. Determination of the number of superhelicalturns in SV40 DNA may help us to understand the organiza-tion of DNA in chromatin.To this end, I have prepared a series of DNA samples with

various degrees of superhelicity, by reacting SV40 DNA Iwith an excess of mammalian DNA-relaxing enzyme (11-15) in the presence of increasing concentrations of the inter-calating dye ethidium bromide (EtdBr). EtdBr reduces theaverage rotation angle in the double helix (16-19). Removalof the dye forces the enzymatically relaxed DNA to acquire

negative superhelical turns whose number is determined bythe concentration of EtdBr present during relaxation. Thisprocedure is analogous to the method of closing circularDNA containing at least one broken phosphodiester bond(nicked DNA, form II) by treatment with DNA ligase in thepresence of various amounts of EtdBr (20).SV40 DNA, enzymatically relaxed in the presence of

EtdBr, does not migrate as a single homogeneous speciesduring electrophoresis in agarose gels (21). Instead, thisDNA is distributed into a group of about 10 closely spacedbands, with the most intense bands located at the middle ofthe distribution. This phenomenon was initially believed tobe a consequence of the presence of EtdBr during relaxa-tion. However, as Depew and Wang (22) and Pulleyblank etal. (23) have demonstrated, Gaussian-type distributions ofDNA bands are also observed in circular DNA closed byDNA ligase or by DNA-relaxing enzyme in the absence ofEtdBr and are the result of thermal fluctuation in the DNAhelix which leads to rotation of the two strands around thestrand opposite the nicks. Ligation locks the DNA into a setof molecules differing in their topological winding number,a (1), by small positive as well as negative integral values(22, 23). Molecules differing in their topological windingnumber will also differ in their number of superhelicalturns, T (see Results and Discussion). The shape of the re-sulting distribution is determined by the free energy of sup-erhelix formation and has been used to measure this quanti-ty (22, 23). In the experiments described here, I have takenadvantage of the distributions of DNA around i to count thenumber of superhelical turns in native SV40 DNA. Theuncertainties of our earlier attempts of measuring this num-ber by gel electrophoretic methods (13) were mainly due toinsufficient resolution. This difficulty has now been over-come.

MATERIALS AND METHODSSV40 virus was propagated in African green monkey cells(CV-1) and purified by standard procedures. Plaque-puri-fied wild-type virus (strain 777), was used at 0.4-1 plaque-forming units per cell. DNA was prepared from virions asdescribed (24). Radioactively labeled SV40 DNA was ob-tained by growing the virus in the presence of [3H]thym-idine or [32P]orthophosphate. DNA was stored in 0.01 MTris-HCl, pH 7.9; 0.2 M NaCl; 0.2 mM EDTA (buffer A) at00C or at -70'C. DNA concentrations were determinedspectrophotometrically. DNA-relaxing enzyme was purifiedfrom human tissue culture cells (KB-3) as previously de-scribed (15). For the experiments reported here, an aliquotof fraction 6 (15) was dialyzed into buffer A containing 10%(vol/vol) glycerol and 1 mM dithiothreitol. Ethidium bro-mide (EtdBr) and propidium diiodide (PrpI2) were pur-

4876

Abbreviations: SV40, simian virus 40; EtdBr, ethidium bromide;PrpI2, propidium diiodide.

Proc. Nat. Acad. Sci. USA 72 (1975) 4877

chased from Calbiochem. EtdBr concentrations were mea-sured spectrophotometrically at two different wavelengths.At 460 nm the specific absorptivity was taken as 4220 M-lcm 1 and 287 nm as 5.39 X 104 M-1 cm-' (25).

Treatment of SV40 DNA with DNA-relaxing enzyme wascarried out in reaction mixtures of 0.1 ml containing 10 mMTris-HCI (pH 7.9); 0.2 M NaCl; 0.2 mM Na2-EDTA; 0.05mM dithiothreitol; 0.5% (vol/vol) glycerol; 0.1 mM (nucleo-tide) SV40 DNA; approximately 100 units of DNA-relaxingenzyme (15); and EtdBr ranging from 0 to 6.9 X 10-6 M (seeFig. 3). A control mixture was included which did not con-tain relaxing enzyme and EtdBr. After incubation at 370Cfor 30 min, the mixtures were extracted twice with phenoland once with chloroform at 370C. The aqueous phaseswere recovered, diluted with H20, and adjusted to 10%(weight/volume) of sucrose and 0.008% (weight/volume) ofbromophenol blue in a final volume of 0.2 ml. Aliquots of 201Al were analyzed by gel electrophoresis.Gel Electrophoresis. Electrophoresis of DNA in agarose

(1.4% weight/volume; Sigma, no. A-6877) was performed inslabs (16 X 12 X 0.3 cm) as previously described (13, 15) ex-cept that the gels were formed between two glass plates.Sample wells were obtained by inserting a toothed plexiglasscomb into the top of the agarose immediately after pouring.The electrophoresis buffer was 40 mM Tris-HCl (pH 7.9), 5mM sodium acetate, and 1 mM Na2-EDTA. When appropri-ate, EtdBr was added to the melted agarose before the gelwas cast and to the electrophoresis buffer at concentrationsindicated in the legend to Fig. 1, from a 0.02 mg/ml of stocksolution (in H20) kept in the dark at 40. The electrophoresisbuffer was circulated between the electrode compartmentsat a rate of 2-5 ml/min. A constant voltage of 4 V/cm wasapplied for 18 hr. Unless otherwise indicated, electrophoresiswas carried out at room temperature. After electrophoresis,the gels were incubated for at least 1 hr in 500 ml of electro-phoresis buffer containing 0.5 ,g/ml of EtdBr. Photographsof fluorescent DNA bands were taken as described earlier(15). Each gel was photographed three times with exposuretimes of 15 sec. 30 sec. and 60 sec. Negatives were tracedwith a Joyce-Loebl microdensitometer.Mixed agarose (0.5% weight/volume)-polyacrylamide

(1.9% weight/volume) gels were run in slabs (17 X 18 X 0.3cm) at 2.5 V/cm for 85 hr in the buffer reported by Ger-mond et al. (2) and analyzed as described above. Additionalprocedures are detailed in Results and in the legends ofFigs. 1-5.

RESULTS AND DISCUSSIONThe Measurement of i by Agarose Gel Electrophoresis.

The topological properties of closed-circular duplex DNAare defined by the relationship a = ,B + r (Eq. 1; see ref. 1for definitions). In brief, the topological winding number aof a DNA molecule is determined by the sum of its helicaltUrns ,B and its superhelical turns r. As shown by Depew andWang (22) and by Pulleyblank et al. (23), thermal fluctua-tion in the DNA helix at the time of ring closure causes het-etogeneity in the- topological winding number a of the re-sulting closed-circular molecules. After closure, the individ-ual DNA molecules within the distribution around a maystill fluctuate in their values for ,B and r, but the sum (a) ofthese two quantities will always be a constant and integralriumber. According to Depew and Wang (22), the electro-phoretic mobility of closed-circular DNA molecules is deter-mined by the time average of the absolute value of r, be-cause fluctuations around T are fast compared to the electro-

1233456?7891lollII

R I,

C i t4

ti tI z.~~~~~~~~~~~~~

e

1 23 4 5 6 7 8 910 11IIII .I

* .

,%..

d , H

..l .t

f

FIG. 1. Agarose gel electrophoresis of SV40 DNA containingincreasing numbers of superhelical turns. The DNA samples wereprepared as described in Materials and Methods. EtdBr concen-trations in the reaction mixtures are indicated in the lower abscis-sa of Fig. 3. Sample 11 was untreated SV40 DNA I. Gel b was runin a cold room at 4°C; all other gels were run at room temperature.Gels a and b had no EtdBr. Gels c-f contained the following con-centrations of EtdBr: c, 0.012 /Ag/ml; d, 0.016 tg/ml; e, 0.024 ,g/ml;f, 0.06 ,ug/ml. Staining and photography of the fluorescent DNAbands were performed as described in Materials and Methods.The slow migrating topmost band present in all samples is nicked-circular SV40 DNA.

phoresis time. Molecules differing in a have different valuesof r and will form separate bands during gel electrophoresis.A series of SV40 DNA samples differing in their average

number of superhelical turns i was prepared by treatmentof the DNA with an excess of DNA-relaxing enzyme in thepresence of increasing concentrations of EtdBr and subse-quent removal of the dye as described in Materials andMethods. At the time of ring closure, the average value ofthe topological winding number a will be different in dif-ferent samples, depending on the amount of EtdBr interca-lated into the DNA. Intercalation reduces the number of he-lical turns. Since a = ,B in a relaxed DNA, upon removal ofEtdBr after relaxation, the number of helical turns will in-crease. This increase must be compensated for by a corre-sponding number of negative superhelical turns because a =# + r (1). As a consequence of thermal fluctuations arounda during ring closure, each DNA sample consists of a set ofmolecules, differing in a and therefore in r around a meanvalue (T). After gel electrophoresis, adjacent bands within agiven set differ by one superhelical turn (22, 23), as suggest-ed earlier (13). The middle of the distributions of samplesthat differ in i will be found at different positions in a gel. Ifthe differences in T of samples in neighboring lanes of a gelare not too large, their distributions of bands around I will

Biochemistry: Keller

Proc. Nat. Acad. Sci. USA 72 (1975)

&;4.5

b3

b4

bS

®3 Distance Migrated 0FIG. 2. Densitometer tracings of lanes 3-5 of gel b (Fig. 1). See

text for explanation.

overlap. DNA molecules in neighboring samples which havethe same electrophoretic mobility are identical in a andtherefore in r. Therefore, the difference in the mean num-ber of superhelical turns Ar in DNA samples from neigh-boring lanes of an agarose gel can be determined by measur-ing the distances from center to center of the various bandsets in units of r.The electrophoretic analysis of SV40 DNA molecules con-

taining different mean numbers of superhelical turns is illus-trated in Fig. 1. In each of the six panels, sample 1 repre-sents DNA which had been relaxed in the absence of EtdBr;samples 2-10 contained increasing concentrations of EtdBrduring enzymatic relaxation; sample 11 was untreated SV40DNA I. (Sample 1 consisted of molecules with a mean num-ber of i = 0, since its pattern upon electrophoresis was indis-tinguishable from the pattern obtained by treating nicked-circular SV40 DNA II with DNA-ligase.) From the patternof the gel in Fig. la, run under standard electrophoresis con-ditions (1.4% agarose, room temperature), it is clear thatonly some of the DNA samples (nos. 5-7) were resolved intotheir constituent Gaussian band sets. DNA samples whosevalue of i was below a certain level (nos. 1 and 2) ran as asingle band, together with nicked-circular (form II) DNA,which is the topmost band. Likewise, molecules whose X wasabove a certain range (nos. 8-11) formed a single fast mi-grating band during electrophoresis. To resolve the individ-ual DNA species in such samples, two modifications of thestandard electrophoresis conditions were employed: (a) low-ering the temperature during electrophoresis, and (b) addi-tion of various amounts of EtdBr to the gel matrix and theelectrophoresis buffer. Any change in temperature and/orionic strength will alter the average rotation angle (60) be-tween adjacent base pairs in the DNA helix (26-28). Inclosed-circular DNA this will cause an alteration in the helixwinding number j3 and lead to a corresponding shift in T(Eq. 1). Therefore, any change in A, from the reaction con-ditions during relaxation to the analysis conditions, will shiftthe mean number of superhelical turns i by some positive ornegative value: In Fig. lb, the effect of lowering the tem-perature during electrophoresis can be seen. Since a decreasein temperature leads to an increase in the average value ofthe helix rotation angle 00, all samples become more nega-tively supercoiled (Eq. 1), with a corresponding downfieldshift of the DNA bands during electrophoresis (compare, forexample, samples 2 and 3 in gels a and b of Fig. 1). The ef-

2 3 4 5 6 7Ethidium bromide concentration (pM)

FIG. 3. Plot of the differences in the mean number of superhe-lical turns (AS) in DNA samples of Fig. 1 as a function of EtdBrconcentration during enzymatic relaxation. The line through thedata points was calculated by the least squares method. The arrowindicates the relative position of untreated SV40 DNA I (sample11).

feet of adding EtdBr to the gels on the electrophoretic mo-bility of superhelical DNA is shown in gels c-f of Fig. 1.EtdBr unwinds the DNA helix upon intercalation. Thus, thehelix winding number ,3 was lowered, causing a correspond-ing positive shift in the superhelix winding number T of allclosed-circular DNA molecules. Therefore, DNA sampleswith low numbers of negative superhelical turns eventuallybecame positively supercoiled and those containing a highernumber of negative turns became less negatively super-coiled.Complete separation of all DNA samples into their com-

ponent band sets could be achieved by combining the resultsof gel electrophoresis in the presence of four different con-centrations of EtdBr (Fig. lc-f). The principle of the meth-od used to measure As between different band sets is shownin Fig. 2. Photographic negatives of the fluorescent DNAbands were traced with a microdensitometer. The middle ofeach distribution of bands was determined by calculatingtheir average intensity location, with the relative peakheights serving as a measure of DNA mass. Because adjacentpeaks within a group are separated by one superhelical turn,the difference between different DNA samples in the meannumber of superhelical turns (AT) could be counted directlyin units of turns. (Fractional values were rounded to thenearest half-turn.) Tracings of all six gels shown in Fig. 1were used to perform this analysis. When AT~was plottedagainst the concentration of EtdBr present during relaxa-tion, a straight line was obtained as illustrated in Fig. 3. Thehighest number of superhelical turns counted was X = -34I 3 (sample 10). By comparison, native SV40 DNA I had avalue of i = -24 ± 2 (sample 11). The reference state forthis value is 370C and buffer A (0.2 M NaCl, 10 mM Tris-HC1, pH 7.9, 0.2 mM EDTA). The error in determining Aibetween two DNA samples was estimated to be of the orderof +0.5-1.0 turn for each individual comparison. Thus theerror in the determination of 7 for SV40 DNA depends onthe number of overlaps that had to be counted from themiddle of sample 1 (Fig. 1) to the middle of native SV40DNA (sample 11, Fig. 1). As indicated by the data pointscontaining error bars in Fig. 3, the number of superhelicalturns in SV40 DNA could be determined by counting a min-imum of three overlaps: A-1_11 = Ai1-6 + AT6-8 + AT8-11(subscript numerals indicate sample numbers in Fig. 1). An

4878 Biochemistry: Keller

Proc. Nat. Acad. Sci. USA 72 (1975) 4879

II10-0 9

Proc. Nat. Acad. Sci. USA 72 (1975)

The value of Av on which our estimate of 0ke is based, ob-tained by the buoyant-separation method, is probably notvery accurate and should be measured by a more sensitiveprocedure. Nevertheless, the estimate derived here stronglysupports the value of 'e =-26 I 20 for the unwinding ofEtdBr reported by Wang (17, 19).

Heterogeneity of SV40 DNA I. Inspection of the electro-phoresis pattern obtained with SV40DNA I (Fig. 1; sample11 in gels c, e, and d) reveals that this DNA did not migrateas a single band. Instead, it showed a distribution of bandsquite similar to the patterns seen with enzymatically relaxedforms of DNA. That this was not caused by some artifactdue to the presence of EtdBr during electrophoresis is dem-onstrated in Fig. 5. Here; SV40 DNA I was subjected to elec-trophoresis in the absence of EtdBr in a mixed agarose-poly-acrylamide gel (2) as described in Materials and Methods.The DNA was distributed into a large number of bands.Bands 1-12 in Fig. 5 form a symmetrical Gaussian-like dis-tribution of intensities around band 7. In addition, there arealso some bands with very low intensities which correspondto DNA with a smaller number of superhelical turns (bands13-20, Fig. 5). Heterogeneity of SV40 DNA was first re-ported by Germond et al. (2). We take this heterogeneity inX as evidence that at the time of ring-closure in vivo theDNA is undergoing thermal fluctuations in its topologicalwinding number, 'a. Fluctuations in histone binding wouldtend to broaden the thermally induced distribution. This isin fact observed; compare, for example, the number ofbands per Gaussian set in enzymatically relaxed DNA (Fig.2) to the number of bands in SV40DNAI in Fig. 5.Chromatin Structure. Chromatin has been shown to con-

sist of repeating units, each of which is thought to contain180 to 200 base pairs of DNA (reviewed in ref. 32). If this isso, the SV40 mini-chromosome would have approximately26 such repeats. By electron microscopy, Griffith (8) andGermond et al. (2) have counted 21 to 26 nucleosomes innucleoprotein complexes containing SV40 DNA. There isclearly a conspicuous similarity in the number of repeatunits, the number of nucleosomes, and the number of su-perhelical turns found in SV40DNA after removal of theprotein. Assuming that the pitch of the helix in chromatinremains unchanged from that of the B form of naked DNA,the latter finding could be interpreted to indicate that theDNA helix in such complexes is wound around a histonecore as a condensed loop, giving rise to one negative su-perhelical turn per nucleosome. Whether the condensation isa consequence of bending,' folding, or kinking (33) of theDNA helix remains to be demonstrated.

I am grateful to Drs. J. Vinograd and J. C. Wang for sending metheir manuscripts prior to publication. I thank Bill Bauer, MavisShure, and Jim Wang for discussions concerning the experiment re-

ported in Fig. 4. Ingrid Wendel provided invaluable technical assis-tance. The work was supported by Grant CA 13106 from the Na-tional Cancer Institute.

1. Bauer, W. & Vinograd, J. (1974) in Basic Principles in Nule-ic Acid Chemistry, ed. T'so, P. 0. P. (Academic Press, NewYork and London), Vol. II, pp. 262-35.

2. Germond, J. E., Hirt, B., Oudet, P., Gross-Bellard, M. &Chambon, P. (1975) Proc. Nat. Acad. Sci. USA 72, 1843-1847.

3. Frearson, P. M. & Crawford, L. V. (1972) J. Cen. Virol. 14,141-155.

4. Lake, R. S., Barban, S. & Salzman, N. P. (1973) Biochem. Bio-phys. Res. Commun. 54,640-647.

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