Properties of supercoiled DNA in gel electrophoresis

J. Mol. Biol. (1986) 192 645-660

Properties of Supercoiled DNA in Gel Electrophoresis The V-like Dependence of Mobility on Topological Constraint. DNA-Matrix Interactions Yvan Zivanovic, Isabelle Goulet and Ariel Prune11 Centre National de la Recherche Scienti$que Universite’ Paris VII, Institut Jacques Monod 2, place Jussieu. 75251 Paris, Ckdez 05, France (Received 9 May 1986, and in revised form 23 July 1986) The dependence of the electrophoretic mobility of small DNA rings on topological constraint was investigated in acrylamide or agarose gels as a function of DNA size (from approximately 350 to 1400 base-pairs), gel concentration and nucleotide sequence. Under appropriate adjustment between the size of the DNA and the gel concentration, this dependence was found to be V-shaped in a limited interval around constraint 0, the minimum mobility at the apex of the V being obtained for relaxed DNA. Analysis of the DNA size dependence of the V suggests that it is the result of a modulated compaction of the DNA rings by the gel matrix. Compaction appears to be maximum upon relaxation. and to decrease with increase in supercoiling. Consistent with this interpretation, gels were found to oppose structural departures from the B helix, such as Z transition and cruciform extrusion, which tend to relax the DNA molecule and make it more expanded. In contrast. when DNA size or gel concentration are large enough relative to one another, U shapes are observed instead of Vs, as a consequence of an increase in the mobility of the rings closer t’o relaxation. The relevance of these results to the situation of superhelical DNA in vivo is discussed. Application of the V to the measurement of the DNA helical twist is mentioned.

helical periodicity (Wang, 1979) and the determination of the double helix response to negative torsional stress, essentially through the B-Z transition (Singleton et al., 1982; Peck et al., 1982) and cruciform extrusion (Lilley, 1980; Panayotatos & Wells, 1981). In this work. the electrophoretic behaviour of small DNA rings was investigated as a function of DNA size, gel concentration and nucleotide sequence. It was found that the dependence of mobility on topological constraint may become V-shaped in a limited interval around constraint 0. the minimum mobilit,y at the apex corresponding to that of relaxed DNA. The results point to a modulated compaction of the molecules by the gel matrix, this compaction increasing, as expected, when the molecule is closer to relaxation. Consistently, the gel was found to oppose the structural transitions referred to above, which, in relaxing the molecule, tend to expand it. The notion that the environment may act directly, and not only indirectly through Tw, on the overall conformation of a supercoiled DNA molecule is discussed for DNA in vivo. Application of the V to the measurement of the DNA helical repeat is discussed.

1. Introduction Supercoiled DNA is commonly thought to be physico-chemically affected by its environment primarily at the level of its twist, Tw, and only secondarily at the level of its writhe, Wr. This is a consequence of the invariance of its topological linking number, Lk, as shown by the equation relating those three quantities: Lk=Tw+Wr

Cl)>

(White, 1969; Fuller, 1971; Crick, 1976). The effect on Tw of temperature (Wang, 1969; Depew & Wang, 1975; Pulleyblank et al., 1975), ionic strength and counterion (Anderson & Bauer, 1978), and ligand intercalation (Wang, 1974; Pulleyblank & Morgan, 1975) has been well-documented. An important tool for these studies has been gel electrophoresis, mostly of whole plasmid DNAs in agarose gels but also, more recently, of short DNAs in polyacrylamide gels (Shore et al., 1981; Shore & Baldwin, 1983aJ; Horowitz & Wang, 1984). It is noteworthy that this technique, applied to superhelical DNA, has contributed in a number of ways to the understanding of DNA structure and dynamics. These include the measurement of DNA 002%2836/86/2306445-

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C 1986 Academic

Press Inc.

(London)

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2. Materials and Methods (a) EnzynlP
fragmfdn

The 358, 66.5, 1374 and 506 bpt fragments. resprctively. originate from Sau3A and HinfI digests of pBR322 (Sutcliffe. 1978). Two fragment,s. 751 and 782 bp long. originated from a HhaI digest of phage IDNA. Thev span nucleotides 30.566 to 31.317 and 42,444 to 43.226. rrsp&irely. in the Sanger rt nl. (1982) sequence (EMBL srquener data library). 1 fragments were identified by mapping with BgZI (751 bp), &USA (782 bp) and Tag1 (751 and 782 bp) restriction endonurleases. whose (alravage sites were found at their expected locations. Other fragment,s contain inserts of either poly(dGd(‘) poly(dGdC1) (in the case of the 348 bp fragment) 01 poly(dA-dT) poly(dA-dT) (359. 709 and 738 bp fragments). The 348 and 359bp fragments were purified from Z’aqI digest’s of plasmids pLP32 (Peck ef al.. 1982) and pAT44 (Strauss et al.. 1981). respectively. The 709 and 738 bp fragments originate from Sau3A digests of plasmids pAT44 and pAT73, respectively (Strauss et al.. 1981). Plasmid pLP32 was obtained by insertion of 32 bp of poly(dG-dC) poly(dG-dC) at’ the filled-in RanlHI site of pBR322. pAT44 and pAT73 were also derived from l)l%R’322 after insertion of 40 and 69 bp of poly(dA-dT). poly(dA-dT). respect,ively. at the filled-in HindTTT sit)? of the parent plasmid. A11 fragments we’re purified by preparative gel electrophoresis as described bJ- Maxam 8r Gilbert (1977). They were subsequently dephosphorylated with alkaline phosphatase and labelled with [y-32P]ATl’ using T4 polynucleotide kinase to a specific activity of IO to 2 x 10’ cts/min per pg accsording to standard procedures.

thtx 665 bp fragment is shown it1 l;ig. were identified by their linking number with the slonrst migrating topoisomrt, the c,losrst therefore t>orelaxat ion. which reference. One has:

I. ‘i’ol~~~ihornc’~~s tlift;~rc~trc+~.Al,/,*. (tol)oisofrlf~t~ ( )i M’HS(*tlos+ltl ah it

AU = I!I;- I.k, in which I&

i?J

is the linking numbrr of topoisomrr

().

C’losrd circular products of the 665 bp t’ragmrnt obtained using T4 DPL’A ligase were used as substrat,e tin reverse gyrase from the arphaebacteriurn Sulfoloh~s acidocaldnrius (Kikuchi 8r Masai. 1984). This enzyme (a gift from Dr A. Kikuchi) has been pu’rified to homogeneit> (N, = 120,000) and has been found to havr a typp I activity (1Vakasu & Kikuchi. 1985: Forterrr of crl.. 1985). A total of 70 ng (700,000 c%s/min) of purified reaction products identical t*o t)hosr shown in Fig. 1 (lane 6) w(‘rtA incubated at 75”(! for 30 min with 84 np of enzyme in 300~1 of 50 mm-Tris.H(‘l (pH 7.5), 10 maI-KC’I. IO m>r-

1234567

((a) Circularizations

Circularizations were performed b!- incubating the lsbelled staggered-end fragments at a DNA concentration of 0.12 pg/ml (0.24 pg/ml for the 1374 bp fragment) in IO m&l-Tris. HCI (pH 7.5). 50 mM-Earl. 10 mM-MgCl,, 5 mw-dithiothreitol. 0.25 mM-ATP and 0.1 mg bovine serum albumin/ml, with 0.9 unit of ‘I’4 DNA ligase/ml for 2 to 5 h at 15°C’. Such caonditions for circularization are similar to those described by Shore et (~2. (1981): 10 FM-netropsin or various concentrat,ions of et,hidium bromide (as indicated thereaft.er) were added to the incubation buffer to increase (Malcolm & Snounou. 1982) or decrease (Wang, 1974) the apparent t’wist of the double helix, respectively. Aft,er incubation. samples were adjusted to 1% (w/v) sodium dodrcyl sulphate and 1 MSaCI, extracted with 1 vol. chloroform/isoamyl alrohol (24 : I, r/v) and DNAs were pre(Gpitated with ethanol. (:rl rlectrophorrsis of suc.h ligat,ion products with t Abbreviation

used: bp. base-pair(s).

Lin.-

“I*; i

Figure 1. (lirrularizat.ion of a 665 bp l)XA fragment with ligase under different caondit,ions. The fragment originates from a A’au3A digest of pKR322 l>XA (Sutcliffe, 1978). Labelling of the fragment with 3’P using polynuclrot~ide kinase and Vircularizations wpre performed as described in Materials and Methods. Incubation conditions with ligase were: lane I. 10~~ netropsin: 2. no ligand: 3. 0.15; 4. 0.3: 5. W-15; 6, 0%; 7. 1.0 pg ethidium bromide/ml. After extraction and precipitation with ethanol the samples were electrophoresed in a 44, polyacrylamidr (ac,rylamide, bisacrylamide = 3O:l. U/W.) gel at 37°C. as described in Matrrlals and Methods. An autoradiograph is shown. Eacsh O(‘. open caircular DNA: T,in. linear 1)X4. topoisomer is identified by a number. This number measures its linking number difference (AU) rr&tivr t,o topoisomer 0. the uppermost in t,he gel and the cslosest to relaxation.

Supercoiled DNA in Gel Electrophoresis MgCl,, 0.5 m,n-dithiothreitol. 0.5 mM-ATP, and 0.05 mg bovine serum albumin/ml. Polyethylene glycol (10%) was added to the reaction mixture since this compound was found to stimulat,e reverse gyrase activity (Forterre rt nl.. 1985). I’ndrr t#hese conditions, the stimulation factor was found to be between 10 and 20. After incubat’ion. the sample was extracted with phenol/ chloroform (1: 1. TYV) and subsequently with ether. The DNA was finally precipitated with ethanol and topoisomers were purified by preparative gel electrophoresis as described below. The autoradiograph of the gel (not shown) revealed the presence, in addition to some amount of linear and open circular DPiAs, of positive topoisomers + 2. +3 and +4. wibh respective relative yields of 27, 66 and 7% (as determined by microdensitometry). (See t’he legend to Fig. 1 for the identification of the topoisomers.) In contrast, circularization of 665 bp linear DXA with T4 DKA ligase in the presence of netropsin at a concentration of 10~~ (Fig. 1) or above (not shown) did not lead to detectable amounts of topoisomers + 3 and + 4. Such improvement over netropsin appears. however. to strongly depend on the size of the DNA. Indeed. in our hands. reverse gyrase failed to posit,ively supercoil 358 bp topoisomers. (e) Characterization of eirc,lLlar products and topvisonrer puri$cation

Products of rircularizat’ion reactions include closed and open circular molecules and unreacted linear DiL’A (see Fig. 1). The label of the linear Dh’A is readily removed by alkaline phosphata,se treatment, while open circular molecules could be discriminated from closed circular ones by their ability to be destroyed by consecutive incubations with ExoITI (IL’ew England Biolabs) and S, nurlease (Sigma). Reverse gyrase products do not correspond to knotted or catenated circles. as shown by the observat’ion that nicking of purified topoisomer +3 generates the open circular DSA (results not shown). (Nicking was performed by incubation at 75°C for 2 h under paraffin oil in the above reverse gyrase buffer, including polyethylene glycol.) Individual topoisomers (506, 665, 709. 751. 782 and 1374 bp in size) were purified by preparative elrctrophoreses of reac%ion products in 4% (w/v) polyacrylamide (acrylamideibisacrylamide = 30: 1. w/w) gels at 4°C (“negative” topoisomers), or at room temperature in the presence of 0.25 11~ rthidium bromide/ml (“positive” topoisomers and topoisomer 0). The 358 bp topoisomers + 1 and - 1 were purified in a 5”,() polyacrylamide (acrylamide,‘bisacrylamide = 20:1, w/w) gel at room temperature. and 3.58 bp topoisomer 0 in a similar gel containing 2 pg ethidium bromide/ml. Topoisomers were further extracted and purified from gel slices as described by i’vIaxa,m & Gilbert (1977). (f) T~~~?~oemt~lrr-regl~latedgel electrophoresea They were performed in a Pharmacia GE 2/4LS apparatus. which had been modified to improve caontrol. The temperature regulation temperature achieved by the system after an equilibration period of about, 1 h, performed during pre-electrophoresis of the gel. was within +O.l deg.{‘. The gel and electrode buffer was 20 rnM-sodium acetate. 2 mu-EDTA and 40 mM-Trisacetate (pH 7.8) (Loening. 1967). The gel (0.12 cm x 17 cm x 20 cm) was pre-electrophoresed at about 250 V and electrophoresed at the same voltage generally until the xylene cyan01 dyr reached the vicinity of the bottom. The power output was about 50 W. Recommendations

647

which may be made to insure reproducible results include: (1) the removal of residual insoluble material from the acrylamide plus bisacrylamide stock solution: (2) the rinsing of t’he plates with water or with the buffer prior to their immersion; (3) the replacement of electrode buffer (4 1) at least after every other gel: (4) the prevention of buffer evaporation at higher trmperat,ures: (5) t)he minimal disturbation of the grl during its preparation for autoradiography. (a) (‘onstruction

of the I;, and determination location.

Dejinition

of’ thu apex

of the I.

As will be shown below. the plot relating the electrophoretic mobility of the topoisomrrs to their linking number difference, ALk. displays a singularity in the vicinity of the relaxed topoisomer wbirh often is V-like. but may also be IT-like. Construction of the V and (1) Positively generally includes 3 steps. negatively supercoiled topoisomers must first be discriminated from one another. This is straightforward for most of them. except somet,imes when t)he topoisomer is close to relaxation (topoisomer 0). It maa be useful in that case to slightly vary the elertrophorrsls temperature to find out n-hen topoisomer 0 is located at the apex of the V and may therefore be considered as relaxed. \Vhen this is achieved. adjacent topoisomrrs + 1 and - I usually show similar migrations (see an rxamplr of this in Fig. 2. below). As a consequence. a larger or a smaller mobility of topoisomer + 1 relative to topoisotnrr - 1 will as a rule br considered as a reflection of a positive ot negative supercoiling, respectively, of topoisomer 0. (This results from the known dependence of 7’~ on temprraturr (2) In thca and of eqn (1); see the Introduction.) second step. thr first two positively and nrgativel) supercoiled topoisomrrs are joined through straight lines which form the “positive“ and the “nepativr” branches of the \*. 13) Tn the last step. higher adjacent topoisomers that are not significantly off these lines arr incorporated into the branches of the Y through a leastsquares procedure. Topoisomrrs effect)ivrly usrd in thr construction will be joined through continuous straight lines. \vhile those excluded from it will br shown b? broken lines. Deviations of higher topoisomers from the st,raight lines in step (2) usually occur toward the out,sidr of t,hr 5. (see for example topoisomers -4. and +3 and +l in Fig. 2. below). Deviations toward the inside frotn either one of those straight lines or from both will be viewed as reflecting a c-like dependence of topoisomer mobility on ALk (examples are shown in Fig. 5(a), below-. for the 5.51 bp fragment: see topoisomers -3 and -2 relative to the straight line joining topoisomers 0 and - 1: and in Fig. 6 for the 506 bp fragment: see topoisomer $2 relative to the line specified by topoisomers 0 and + 1). Apex of the Vs was obtamed by extrapolating the branchrs until they intersect. If their equation is NOD = rc ALI; + 0. with Mob being t,he topoisomel mobility. then ALk at the apex is given by ALk, = (b- -h+)/(a+ --a-). where the + and - subscripts refer to the “positive” and “negative” brancahes. respect i rely.

3. Results (a) The V-like dependence of mobility OH topological constraint The 665 bp t,opoisomers -4 to +4 were electrophoresrd in duplicate in a gel similar to that

0.6

I -4

-3

I -2

I -I

I 0

I I

I 2

I 3

4

ALR (turns)

Figure 2. V-like dependence

of the electrophoretie mobility of supercoiled DKA on topological constraint. (a) 665 bp topoisomers were individually purified. appropriately mixed and elect,rophoresed in duplicate. along with the linear fragment, (Lin.). in 40/b polyacrylamide (acrylamide/bisacrylamide = 30 : 1. w/w) gels at the temperatures indicated. Minus and plus signs correspond to mixtures of topoisomers - 1. -2 and -3. and 0. + 1. +2 and +3. respectively. Topoisomers -4 and +4 were added t,o - and + mixtures, respectively, only in the left-hand duplicates. The xylem cyan01 dye showed the same migration in the 2 gels. Autoradiographs are shown. The radioactivity at the top of t,he gels was added after the electrophoreses were completed to show the position of the start. Topoisomers -4 to + 2 were obtained through circularizations with ligase. as shown in Fig. 1, while topoisomers + 3 and + 4 originated from t,he reaction of reverse gyrase on ligase-prepared negatively supercoiled topoisomers (see Materials and Methods). (b) Ratios between distances migrated from the start by the topoisomers and by the linear DNA were plotted at the 2 t,emperatures as a function of linking number differences (AU), for the left halves of the gels (topoisomers -4 to + 4). -3 to +3) were found to be virtually 1)ata for the duplicated migrations (right halves of the gels; topoisomers branches of the Vs were obtained as described in Materials and Methods indistinguishable from the former. “Positive” branches by joining positively supercoiled topoisomers + 1 and +2 (25°C 0) and 0. + 1 and +2 (45”C, 0). “Negative” were similarly obtamed with negatively supercoiled topoisomers -3. -2, - 1 and 0 (see below) (25°C) and -3 to - 1 -4 and +4 were not taken into account because they show significant deviations not only at 25 (45°C’). Topoisomers and 45°C. but also at other temperatures ranging from 21 to 60°C (not shown). The decision to also exclude topoisomer + 3 from the V may appear somewhat arbitrary since its actual deviation is small. Another reason to do so, however. is for the sake of homogeneity since reverse gyrase-produced topoisomers were not available for the other fragments studied in this work. The occurrence of a small negative supercoiling in topoisomer 0 at 25°C is suggested by the smaller mobility of t,opoisomer + 1 relative to topoisomer - 1 (see Materials and Methods). Consistently, topoisomer 0 appears to reach relaxation at a slightly higher temperature, as indicated by an electrophoresis at 27°C in which topoisomer 0 topoisomers + 1 and +2 than at 25°C. while keeping the same alignment showed a better alignment with “positive“ -1, -2 and -3. At the same time, topoisomers - 1 and + 1 were found to virtually with “negative” topoisomers comigrate (not shown). Computed apex abscissae (see Materials and Methods) were ALk, = + 0.054 and - 0.44’2 turn at’ 25 and 45°C. respectively.

Supercoiled DNA in Gel Electrophoresis displayed in Figure 1, at two temperatures (Fig, 2(a)). Topoisomer relative mobilities in these gels were plotted in Figure 2(b) as functions of ALk (see eyn (2) in Materials and Methods), and Vs (continuous st’raight lines) were constructed by joining positively and negatively supercoiled topoisomers, respectively, as described in Materials and Methods and in the Figure legend. The deviation observed for topoisomer -4 is typical of a structural transition from the regular B form double helix induced by negative torsional stress (see Introduction). An abrupt decrease in t,he resolution of the gel beyond a critical supercoiling would indeed be expected to affect positive topoisomers as well, which is not observed. concerning those Vs Several observat’ions (Fig. 2(b)) are of interest. (1) Their apexes correspond to virt’ua)lly identical mobilities at t’he two whether or not a topoisomer is temperatures, present at that particular location. This suggests that the mobility at the apex of the V may provide an estimat,e of that of relaxed DXA (this property will be used below in Fig. 4). (2) If ALk at the apex (ALk,) is necessarily integral when a topoisomer is it’ is fractional after the present (at -25°C). temperature increase (at 46°C). Interestingly. ALk, values derived from duplicate migrations within the same gel, such as t’hose in Figure 2(a) and others (not shown), were found to be within &-0*005 turn = & 1.8” in helix rotation at all temperatures tested (25. 37. 45 and SOY’). For this reason ALk, is generally given with three decimal places (see the Figure legend). Reproducibility in ALk, from one gel to another at the same temperature was, however, not as good, being within &-O-O3 turn = + 11” in helix rotaGot (results not shown). (3) “Negative” topoisomers - 1 to -4 on one hand. and “positive” topoisomers + 1 to +4 plus topoisomrr 0 on the other hand, appear to undergo approximately equal and opposite shifts in their mobility on going from 25 to 45°C. It is noteworthy that the polarity of those shifts was expected since topoisomer 0, presumably nearly relaxed at 25”C, must positively supercoil upon increase in the temperature, while supercoiling of “positive” and “negative” topoisomers must, respectively, become more positive and less negative. As a result, the net effect of t.he temperature increase appears to be a displacement’ of t,he V parallel to the ALk axis smaller values. That displacement, towards measured at the apex, is -0.49, turn (see the legend to Fig. 2). (b) DIVA size dependence of the 1’ Figure 3 shows the patt’erns obtained upon gel electrophoresis at two temperatures of topoisomers of 358, 506, 665 and 1374 bp pBR322 fragments, in gels identical to those displayed in Figures 1 and 2. Those gels were run until the dye had reached precisely the same position near the bottom. Mobility z’ersus ALk plots are shown in Figure 4 for 506 and 665 bp topoisomers. Data at 37°C were

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obtained from a similar gel (not shown) Vs were constructed and subsequently shiRed relative t,o one another along the ALk axis by a fraction of a turn for their apexes t,o have the same abscissa (see the Figure legend). It is noteworthy that only four topoisomers could be used to construct the \’ for the 506 bp fragment, instead of six for the 665 bp fragment. Consistently, this number will be shown below (see Discussion) to further reduce to three for the 358 bp fragment, which prevents the construction of the V. As shown by the 25 and 37°C plots, the mobility of the larger topoisomers appears to increase regularly relative to that of the smaller upon decrease in the topological constraint. This effect reaches a maximum for topoisomers closer to the apex of the Vs. Interest’ingly. the two apexes have nearly t’he same mobility at’ 25’C. while the apex for the larger topoisomers passes that for the smaller at 37°C (Fig. 4). Those features are better shown in Figure 4, inset. where mobilities of either V apexes (for 506 and 665 bp topoisomers) or relaxed DNAs (358 bp topoisomer 0 and uppermost 1374 bp topoisomers) were represented as a function of DKA sizes at the three temperatures. These plots show that relaxed 1374 bp topoisomers always have a mobilit,y equal to or slightly larger than that of the apex of the V obtained wit’h 665 bp topoisomers. Such ability of the gel t’o make larger relaxed rings migrate relatively faster t,han smaller ones appears to be modulated by temperature in the 500 bp range. Xote the regularly increasing mobility of t,he V apex for 506 bp t)opoisomrrs upon decrease in the bemperature from 37 to 12”((. Finally. the mobility of a relaxed topoisotner of a size (358 bp) below that range appears c&lose to “normal” at all temperatures. These results can be summarized as follows. (1) The consequence of an increase in the size of closed circular DNA is a relative increase in its mobility. (2) This relative increase is larger at higher gel temperatures and smaller topological constraints, and reaches a maximutn upon UX’A relaxation. (c) The V-I!

transition

(i) Through increase in ring size The decreasing resolution observed between 1374 bp topoisomers closer to relaxation in Figure 3 (see particularly the 25°C gel) implies that, the mobility of these topoisomers no longer depends on a topological constraint) according to a V, as observed with 506 and 665 bp fragments, but rather according to a U (not shown: see the definition of U in Materials and Methods). The case of fragments only slightly longer than 665 bp is investigated below. Figure 5(a) shows mobility cersus ALk plots for two 751 and 782 bp fragments from 1 phage DKU’A. While t,he plot obtained with 665 bp topoisomers in the same gel (not presented) is V-like. as expected, those for 751 a,nd 782 bp topoisomers show an increasing U-like character. Such Us appear to be a consequence of a larger

0

.W :

.

-3 -4

358

506

665 .-

1374

bp

358

665

506 --

25OC I

0 4

i

I

+l 4-

-1 I

b2 -7 -3 7

I Figure 3. Comparative elertrophoretic migrations of topoisomers of different sizes in the same gel. 665 bp topoisomers are those shown in Fig. 2(a). The 506 bp fragment’ was purified from a HinfT digest of pBR322 and circularized as indicated in the legend to Fig. 1 for the 665 bp fragment. 358 and 1374 bp fragments originat*ed from a &~u3A digest of pBR322. The 358 bp fragment was circularized as described in the legend to Fig. 8, below. for the 348 bp fragment. (‘ircularizations of the 1374 bp fragment were performed using approximately half t’he ethidium bromide concentrations indicated in the legend to Fig. 1 for the 665 bp fragment. Topoisomers were purified by preparative gel electrophoresia as described in Materials and Methods appropriately mixed, and electrophoresed in 4c& polyacrylamide (acrylamidri bisacrylamide = 30 : 1. w/w) gels at the temperatures indicated, until the xylene cyan01 dye had reached precrsely the same posit’ion at about O..i cm from the bott,om. Autoradiographs are shown. The radioactivity observed at’ the top of the 12°C gel was added aft~er electrophoresis was completed to indicate the position of the start,. Diagrams of the bands ident,ifying the t>opoisomers of the 3 smaller fragments are shown on the right.

Supercoiled DNA in Gel filectrophoresis

651

r

0 506

DNA stze (bp)

Figure 4. DXA size dependence of the V. Top and bot’tom left: Distances migrated from the start by 506 and 665 bp topoisomers in the gels of Fig. 3 (12 and 25°C) and in another one (37°C) (not presented; the dye in t,hat gel showed the same migrat’ion as in the other 2) were plotted as functions of their linking number differences. Vs were const,ructed as described in Materials and Methods and in the legend to Fig. 2. and subsequently translated relative to one anot,her parallel to the ALk axis by the difference observed between the apex location, approximately 0.3 turn. for their apex t,o be posit,ioned at the same abscissa. It is important to note that t,his procedure preserves the position of the Vs relative

to the mobility axis. Linking number differences are indicated. Distances travelled by 358 bp topoisomer 0 (upper arrows) and uppermost 1374 bp topoisomers( lower arrows) are shown. Apex locations (seeMaterials and Methods) were for 506 and 665 bp topoisomers. respectively. ALk, = -0 and +0.320 (12”C), -0.230 and +0.092 (25°C). and -0.460 and -0.219 t,urn (37°C). Inset’: Mobilities of 358 bp topoisomer 0 and of uppermost 1374 bp topoisomers, as well as mobilities measured at apex locations for 506 and 665 bp topoisomers. were plotted as functions of ring sizes (on a logarithmic scale) for the different gel temperatures. The mobility of 358 bp topoisomer 0 was taken as that of the relaxed circle at all 3 temperatures, and not only at 25°C where topoisomers + 1 and - 1 nearly comigratr (see Fig. 3). and topoisomer 0 might indeed be expected to be relaxed (see Naterials and Met,hods). This procedure ix justified 1)~ the lack of a significant temperature dependence of the mobility of that topoisomrr. as shown in the Figure.

(6) 37°C; (m) 26Y’:-(n) 12°C.

-

mobility of topoisomers 0. which are located well above the apexes formed by extrapolating the straight lines (Fig. 5(a)), as well as above the apex obtained with the 665 bp fragment (arrow). Figure 5(b) shows similar plots for two derivatives of the 665 bp fragment obtained upon insertion of 40 bp (709 bp fragment) and 69 bp (738 bp fragment) of poly(dA-dT) . poly(dA-dT) at the same site. 709 bp topoisomers display a V and 738 bp topoisomers a IJ, which appears again t.o result’ from a larger mobility of topoisomer 0 (note tha,t 738 bp topoisomer 0, although closer to relaxation than 709 bp t,opoisomer 0, migrates faster). The V-C transition, therefore, appears to occur at a critical size comprised between approximately 700 and 750 bp under the present conditions. The results suggest that such a size may not significantly depend on the origin of the fragments nor on their nucleotide sequences. It is noteworthy that

the large mobility of topoisomer 0 characterizing the Us in Figure 5 is consistent with the previous conclusion that the tendency of the gel to increase topoisomer mobilities is maximal upon relaxation (see above and Fig. 4). (ii) Through increase in gel concentration Figure 6(a) displays the patterns obtained upon electrophoresis in a 5e/, polyacrylamide gel at 25°C’ of the DNA fractions previously shown in Figure 3. Figure 6(b) shows that topoisomer mobilities now depend in a IT-like fashion on topological constraint. indicating that an increase in gel concentration is equivalent. in this respec’t 1 to an increase in DNA size. This result prompted us to investigate hvhether 1374 bp topoisomers would show a V in a lower concentration gel. Because the acrylamide c&omentration of t’he gels in Figure 3 is already minimum.

I

-3

-2

I

-I

I

I

I

0

I

2 ALk

(al

i.

1

J

-3

-2

1

-I

/

I

0

I

2

(turns1 (b)

Figure 5. The V-U transition

through increase in ring size. (a) For i DNA fragments. (0) 751 and (0) 782 bp fragments were circularized as indicated for the 665 bp fragment in t’he legend to Fig. 1, and topoisomers purified as described in Materials and Methods. Electrophoresis was performed in a single 4qi, polyacrylamide (acrylamidei bisacrylamide = 30 : 1, w/w) gel at 30°C (not shown). For best results. topoisomers of the 2 fragments with identical ALk values were co-electrophoresed in the same lane of the gel. Distances migrated from the start were plotted as functions of ALk. Topoisomers - 1,0 and + 1 were connected smoothly. The arrow indicates the mobility at the apex of the T’ obtained in the same gel with 665 bp tjopoisomers; its abscissa was ALk, = -0.088 turn. (b) For poly(dA-dT) .poly(dA-dT)-containing fragments. (0) 709 and (0) 738 bp fragments were derived from the 665 bp fragment by insertion of 40 and 69 bp. respectively, of poly(dA-dT). poly(dA-dT) at the filled-in Hind111 site (see Materials and Methods). Circularizations were as described in the legend to Fig. 1 for the 665 bp fragment. Electrophoresis was performed in a gel identical to that in (a) at 23°C (not shown). Distances migrated from the start by topoisomers were plotted as functions of ALk. The V for the 709 bp DNA was constructed as indicated in Materials and Methods. 738 bp topoisomers - 1. 0 and + 1 were connected smoothly. Topoisomers -4 (not shown) migrated close to topoisomers - 1 (709 bp DNA) or 0 (738 bp DNA), p resumably because of cruciform extrusion from the inserts. The arrow indicates the mobility measured at the apex of the V obtained in the same gel with 665 bp t’opoisomers. Computed apex locations were ALk, = +0.083 and +0.179 turn for 665 and 709 bp fragments, respectively.

2.5% agarose gels, of presumably larger pore size, were used. Topoisomer mobilities obtained in such gels at two temperatures (not shown) were plotted in Figure 7 as functions of ALk, revealing Vs. As observed in Figure 2 for 665 bp topoisomers, increase in gel temperature also displaced the V is towards smaller ALk values. That displacement, equal to -0.20 turn (see the legend to Fig. 2). (d) Further

injluence

of gel concentration

(i) On the B-Z transition Figure 8(a) shows the electrophoreses at 25°C of circular products of a 348 bp poly(dG-dC). poly(dG-dC)-containing fragment in two gels of different) concentrations. The lower concentration gel (Fig. 8(a), top) shows a sharp decrease in the mobility of topoisomer -2 compared - 1. Upon further increase to that of topoisomer in the constraint, topoisomers comigrate with the open circular form. Such effects are consistent with a transition from the B to the 2 left-handed form of the poly(dG-dC) . poly(dG-dC)

insert (see the Introduction). In contrast. topoisomer -2 in the higher concentration gel (Fig. 8(a). bottom) is found to have a mobility much larger than t’hat of topoisomer - 1. This suggests that poly(dG-dC) poly(dG-dC) in t#opoisomer -2 is essentially in the R form in that gel, in contrast to the case of the lower concentration gel. The stabilizing effect of t’he concentrated gel appears, however, not to be sufficient’ to prevent -3 from undergoing the transition topoisomer (Fig. 8(a), bottom). Figure 8(b) shows a similar experiment performed with topoisomers of the 358 bp pBR322 fragment previously studied in Figure 3. This fragment contains alternating purine . pyrimidine two sequences, about 10 bp long, which are potential Z-forming sites (Konopka et al., 1985), but no palindrome (Sutcliffe, 1979). The Figure shows that the distance between topoisomers - 1 and -2 in the 8% gel is larger than the distance between topoisomers - 1 and 0 (the rat’io of those distances is 1.3), while the opposit’e is true in the 5% gel (the ratio becomes 0.75). Those results suggest, by

Supercoiled DNA in Gel Electrophoresis

653

i

ALL

(turns)

Figure 6. The \‘-1: transition through increase in gel concentration. (a) Same topoisomers as shown in Fig. 3 (12°C’ gel) were electrophoresed in a 5% polyacrylamide (acrylamide/bisacrylamide = 30: 1, w/w) gel at 25°C. An autoradiograph is shown. The radioactivity at the top of the gel indicates the position of the start, (b) Distances migrat,ed from the start by 506 (e) and 665 bp (0) topoisomers were plotted as functions of ALk. Topoisomers - I to + 1 were connected smoothly. Cs were subsequently shifted relative to one another parallel to the ALk axis by the same -0.3 turn as Vs obtained at the same temperature in the 4 9; polyacrylamide gel (Fig. 4. bottom left). Arrows indicate t,he distances travelled by the relaxed t’opoisomers.

analogy with the case of the 348 bp fragment, that, the smaller relative mobility of topoisomer -2 in the 50/b gel may result from a partial transition of one or both of the alternating stretches to the Z form. which can be delayed in the 8% gel. This also apphes to topoisomer -3, although the stabiliza-

tion exerted by the higher relatively smaller for that (ii)

Or1

concentration topoisomer.

gel may be

cruciform extrusion

Figure 9(a) shows electrophoreses of topoisomers of a 359 bp poly(dA-dT) . poly(dA-dT)-containing

- 2 migrat,r more anal muc~h more. rrspec%ively. iI1 thci higher conc*entration X”,, gel.

m1tl

Such cwnt,inuous topoisomrr - 2.

incwase

in

the

rnohility

10

a smaller

of’

Of to topoisomers $- 1. - 1 topoisomrar - 3. rrlativr and ~ 1. on going from the -1-“,, to t)hehHo0 gels i1lltl

txXtt~Ilt

(Fig, 9(b)). strongly suggests a cwrrelatirr reduct~ion in the size of tht pol\(d=\-dT) . poly(dA-dT) c+rucif’orm in those intermediate topoisomws. That

the c~ruriform start,s to ext,rudr in topoisomer -- 2 is actually caonsistent, in t)erms of superhelix density. n-it,h the observation that the same cruciform opens in topoisomer -4 of the 709 bp fragment (see t)hc legend to Fig. 5). t)aking into ac~c~ount that the 359 bp fragment is included in thai fragment. Finall!,. 0.7 1

I

Figure 7. V-like migration of a larger fragment in agarose gels. The same 137-Cbp topoisomers as shown in Fig. 3 were electrophoresed in 2~.%, agarose (BioRad laboratories) gels (not shown) at 2 temperatures. as indicated in Materials and Jlet,hods for polyacrylamide gels. Ratios between distances migrated from the start b> the topoisomers and by the linear DNA4 were plot’ted as funct,ions of ALk. ALI? values at the apex of the 1-s warp -0.13 and -0.33 turn at 25 (@) and 29’(‘ (0). respectively.

in two

gels (5’$o and

Wo)

identical

t,o

those in Figure 8, plus anot,her. more dilute. 4?, gel. In all gels, topoisomers - 3 and -4 (see identific*at)ion in Fig. 9(b)) show- a large upward shift in their mobility compared to topoisomer -2. This is presumably due to cruciform extrusion out of the alternating copolymer (see self-complementary Int,roduction) rather than to Z conversion in the pot’ential site existing in flanking DNA (Konopka et 01.. 1985), since topoisomers - 3 and -4 of the parental 315 bp pRR322 fragment show normal migrations below topoisomer -2 in a Eioi, gel (not prrsent)ed). At’ first, sight, band patt’erns as a whole appear

to

be very

similar

increase

in the

relative

mobility

ot

0 from the 1”,, to t)he So,, gels will apfwar to lIi1Vc’ it cjuiie differrnt origili (SW f>iscussion).

‘: P

fragment

the

tjopoisomrr

in the

different

gels,

although their distance from the start varies. Upon closer examination, however, differences appear at the level of topoisomer -2. This is better shown in the schemes of Figure 9(b), which show the superimposition of the bands corresponding to topoisomer - 1 in 5?/6 and 49/b gels (left-hand panel) panel). This and ’50’0 and 896 gels (right-hand Figure indeed reveals that’ two topoisomers. + 1 and - 4. coincide perfectly in 4% and 5% gels (in addition to topoisomer -l), while topoisomers 0. -2. and to a smaller extent -3, show a larger mobility in the 501” gel. Comparison between the 5°0 and Sl& gels shows a coincidence not only for the former three topoisomers, + 1. - 1 and -4. but also for topoisomer 0; similarly. topoisomers -3

4. Discussion

(a) ThP I’ as a reflection

of balanwl

interactions

o/

The elect rophoretic investigat’ion of the behariour of closed circular DNA as a fun&on of ring size has led to the unexpected result that its mobility does not always decrease upon a size increase. but ma>: be size-independent, or it ma! even increasc~ (Figs 4 and 5). Tnasmuc~h as its mobilit!. rrflccts the overall configuration of the molecwle. this suggests that, larger l>NAs may shrink relatively more than smaller Dh’As as a constyuenw of their interactions with the gel matrix. The result’s in Figure 4 further suggest that suc*h compact,ion of the DNA rings by the gel depends on their topological constraint and increases when they rome closer to relaxation. This feature was not unexpected since relaxed [)?;A must be more expanded than suprrcoiled I)SA and may therefore interact more with the gel. Such modulat)ed czornpaction of supercoiled DSA bv thr gel is pr~~sumably the basis for the i’-likr dependence of mobility on topological caonst’raint observed here (see section (e), below). ,An interesting feature of t,he Vs is to shift into l-s when the 1)NA size is large enough relative to the gel concentration and z*iw ~rsn. that is. when DN&matrix interactions increase beyond a critical level (see below). ,506 and 665 bp topciisomers give a \’ in 4O,) gets (Fig. 4). but’ a U in a 5?, gel (Fig. 6). Moreover, a 1‘ is found for 1374 bp topoisomrrs in a 40, gel (Fig. 3), but a 1. is obtained in agarose gels of presumably larger pore size (Fig. 7). (‘omposite polyacrylamidejagarose gels may also be suit’able for large I>XAs as suggested by t,he approximate \ obtained in such a gel by Dean et al. (1982) wit,h 1683 bp plasmid topoisomers. Finally. whether the I’s previously observed by I,ee & Rauer (1985) for a somewhat larger plasmid DNA (54 x IO3 bp) in agarose gels have the same origin is presentI> unknown. Our own investigation of the gJlert,ro-

Supercoiled

DNA

in Gel Electrophoresis

655

(b)

(a)

oc a,> -2

-I

2

3

I

4

5

6

2

7

3

4

I

5

oc

6

oc

0 -3 -4

-I

-I

-2

8% -3

348

bp

358

bp

Figure 8. Gel concentration

dependence of the R-Z transition. (a) In a poly(dG-dC). poly(dG-dC)-cont,aining fragment. The fragment,, 348 bp long, originates from a TapI digest of plasmid pLP32 [Peck et al., 1982), and contains a 32 bp insert of that copolymer. It was first labelled with 32P : then circularized bv incubation with T4 DNA ligase. as described in bfaterials and Methods, in: lane l? 10 PM-netropsin: 2, no ligand: 3. 0.15; 4. 0.3; 5. 0.6; 6, 0.9; 7, 1.2 pg rthidium bromide/ml. After extraction and precipitation with ethanol the samples were electrophoresed as described in ?vIaterials and Methods in SJ,~, (acrylamide/bisacrylamide = 20 : 1, w~jw) (top) and 8%; (acrylamide/bisacrylamide = 30 : 1, w/w) polyacrylamide gels (bottom) at 25°C. (b) In a pBR322 DNA fragment. The fragment, 358 bp long, originates from a Sau3A digest, of the plasmid and contains 2 - IO bp long alt.ernating purineepyrimidine sequences potentially susceptible to Z transition (Konopka et al., 1985). The 32P-labelled fragment, was circularized as indicated above for the 348 bp fragment. Two independently prepared series of samples were electrophoresed in 2 gels identical to those described in (a) for the 348 bp fragment. and at the same temperature. Autoradiographs are shown. Topoisomers are indicatcxd. OC. open circular DBA.

phoretic behaviour of topoisomers of pBR322 through two-dimensional gels, as described by those authors, has not revealed a significant tendency of the Us observed in 1.4% agarose gels to form Vs in @7?& gels (Y. Z.. unpublished results).

(b) Compaction of DNA rings by the gel matrix. The V-l-: transition and the stabilization. of R ,form DLVA . Speci$c features A compaction of closed circular DNA by the gel may occur through DNA bending at constant. Wr

1234567

I234567

1234567

8%

(b) 4

%

-._m_ 0

o5

%

-3

4

%

5

%

-4 -

5%

8%

--4

\ ---.

5

% H% 4

5

--_8%

% +---+ % 8

Figure 9. Gel concent,ration dependence of cruciform extrusion. (a) The fragment, 359 bp long, originates from a ‘kg1 digest of plasmid pAT44 (Strauss et al.. 1981), and contains a 40 bp insert of poly(dA-dT) .poly(dA-dT). The 321’-labelled fragment was circularized as indicated for the 348 bp fragment in the legend to Fig. 8(a), and electrophoresed in 4% (acrylamide/bisacrylamide = 30 : 1. w/w), 5 ?i, (acrylamide/bisacrylamide = 20 : 1. n/w) and 8?,, (acrylamidelbisacrylamide = 30 : l,, w/w) polyacrylamide gels at 25°C and 250 V for 3.2. 6.5 and 38 h. respectively. Autoradiographs are shown with the start (see radioactivity in 4% and 5% gels) aligned in the 3 gels. Topoisomers are indicated in the lower panels. Topoisomer 0 (the centre of t,he band) has migrated 0.1 cm from the start in the 8O; gel, as compared to 4.4 and 1.3 cm in 4O/, and 590 gels. respectively. (b) Bands corresponding t’o t,opoisomer - 1 were superimposed in 59, and 491, gels (left) and in 5% and 8% gels (right). The thick bars represent, the topoisomers which, in addit,ion to topoisomer - 1, are found to be superimposable in the 3 gels.

to as (such a mechanism may be referred constriction), and/or t)hrough increase in ) U’rl. No direct evidence has been found in this work in support of the latter mechanism (see. however, below). In contrast, constriction is presumably the

only mechanism by which relaxed DNA may be compacted, since Wr must remain equal t’o 0. This is probably relevant t’o the V-V transition which mav arise when compaction forces become sufficient to ““break” the DNA, through sharp bends for

Supercoiled DNA in Gel Electrophoresis example, so t’hat further compaction could be facilitated. Such a mechanism would be consistent with the observation that, the U results from an increase in the migrat’ion rate of the topoisomers close to relaxation (Fig. 5). If the gel compacts supercoiled DKA, it is quite st)ructural that it understandable opposes transitions of the double helix which tend t,o expand it? such as flipping of B to 2 forms (Fig. 8) extrusion (Fig. 9). LAlternative and cruciform explanations for the basic observation in Figures 8 and 9 that the relative mobility of topoisomer -% increases with t)he gel concentration may, however, be found. The first one mav be that the loss of resolution for highly supercoiled topoisomers is not as large in a concentrat’ed gel as in a dilute gel. This would hold for 358 and 359 bp fragments, but not poly(dG-dC) . poly(dG-dC)348 bp for the containing fragment where the effect is more dramatic (Fig. 8). In fact, such a possibility is not consistent, with the differential behaviour of highly positively and negatively supercoiled 665 bp topoisomers (see Fig. 2 and Results). which indicates mobilitp of smaller-than-expected that the “negative” topoisomers is not due to a decreased resolut)ion of the gel. (This could not’ be directly shown here because of the impossibility to prepare see topoisomer + 2 wit,h smaller fragments: Materials and Methods.) ,\nother explanation ma! call for gel concentration-dependent interactions of the ~rmiform (for example of its hairpin loop) and of Z D?r’A with the matrix. This is again inconsistent, with the observat’ion that the mobilit! of 348 hp (Fig. 8) a,nd 359 bp (Fig. 9) topoisomers -3 and -4 depends only slightly or does not depend at all on gel roncentration. alt’hough those toyisomers havcl presumably undergone larger transitions than topoisomer - 2. The mec~hanism by which the gel matrix may stabilize 11 form 1)N.A against Z or c.ruciform formation is interesting to csonsider in more detail. Indeed. if topoisomer -2 has undergone the transition in elect rode bufi~r before loading in the gels (see Figs X and 9). as is very likely, then a more accurate conclusion of those experiments is that the higher concentration gel, but not the lower. wa,s able t,o reverse it. It is not clear how pure (Lonstriction could do that. In contrast. a 1Wrl incnreased contributlion to compaction, such as that mentiont~d above. would decrease the overall torsional stress applied to the duplex (this is a consequence of ecln (1) in Tntroduct.ion). and would therefore provide an att,ract ive explanation. (c) Mobility

versus topoloyicnl constraint for smaller DNA ri rigs

Figure 10 shows the mobility versus ALk plot foi 359 bp topoisomers in the S?< gel displayed in Figure 9. Because topoisomer + 1 migrates more than topoisomer - 1, topoisomer 0 is expected to be positively supercoiled (see Materials and Methods). A 1’ could then be constructed by joining

657

,’

ALk (turns1 Figure 10. Dependenre of mobility on topological constraint for smaller DNA rings. Distances migrated from the start by 359 bp topoisomers in bhe PO gel in Fig. 9 were plotted as a function of ALL. The 1’ (continuous lines) was constructed bg joining positiveI> and negatively superroiled t,opoisomers together. rrspectively. The <- (see Discussion) was tentativeI>. drawn (broken curve).

topoisomers 0 and + 1, and - 1 and -2. respectively. ,4s shown in the Figure, the apex of t)hat V is located outside the gel by about 04 cm. which is significantly more than the distance migrated b> t,opoisomer 0 (see the legend to Fig. 9). The same feature is actually observed with the 1’ constructed with topoisomers of the 358 bp fragment in the X0,, gel of Figure 8(b) (not’ shown). The reason for such virtual apex location could not be a poor stabilization of the B form of poly(dX-dT) . poly(d;\-dT) in t,opoisomer -% since this, in decreasing the topoisomer mobility. would contribute to bringing the apex inside the gel but not, outside. i\ likelv reason therefore is a V--likcx dependence of mobility on topological constraint (Fig. 10. broken curve) as previously observed for larger fragments in Figures 5 and 6. The ohservation that t’he band pattern obtained in the 5(), gel is superimposable (except for t’opoisomers - 2 and -3) on that in t,he V& gel (Fig. 9(b)) strongly suggests the same U-like dependence in the 5”, gel. In the light of the above observntion that the Y-1’ tra,nsition for larger DNA rings o(‘curs as a consequence of an increase in gel concentration, it may be asked whether the Us observed here in WC, and 59 0 gels would t’end to \‘s in a lower concent,rat,ion gel. In fact, the smaller relative migration of topoisomer 0 observed in the -l(fo gel. as compared to 5?& and 83; gels (Fig. 9(b)). indicates just that. Whether this only sharpens t)hr r or transforms t.he U into an aut,hentic* \T is not known. Even if a 1’ is formed. however. it could not be constructed on only three topoisomrrs. + 1, 0

and - I, Indeed. the small mobilit:y, of tof)oisomvt ._ -. ,> resulting f’rotn the poor staf)tltzation against structural transitions afforded f)y this goal (src above). prevents its use in the 1..

According to the above results. a relaxed topoisomer must position itself at the apes of t’he V. The apex abscissa: ALk,

= ALk = I,&

12,

is then equal to the t’opofogical constraint of the tof)oisomcr (see rqn (2) in Materials a,nd Methods) and is integral. Making M’r = 0 in equation (I) in the Introduction gives: 7’0, = IX = IX, + ALli, The

helical

/rr/rorrstminPd

repeat’

(h)

of

the

torsionnlly

I)?;=\: h = S/Ttr

= Si( Lk, + ALP,)

(3)

(‘an therefore

f)r enfculst,ed from ALk, once Lk, is an approximate value of the ftrfic~af periodicit>- suffices to estimate Lk, when the> ring size. S. is not too large. It (‘an f>e shown that eyuation (3) act)ually holds (‘vett when ALk, is ftactional. providing a flexible and accutate met hod of measurement of t,he I)NX hrlicaf repeat (T. Coufet, Y. Zivanovic & A. Prunell. unpublished remits). This in turn explains in quantitative terms t.hr displacements observed f’or the V upon increase in gel t’emperat’ures in Figures 2 and 7 for 665 a,nd 1374 ftp Dh’As. respect,ively. Those shifts, -0.49, and -0.20 turn (see Results). respectively. indeed correspond to t)hrrmaf untwistings of 049, x 360/20 X 685 = 0.013, and 0.20 x 360/4 x 1374 = O.OlS,“/deg.(’ per hp. itt close ugrretnent wit*h values published hy I)epe\v B Wang (1975) (0~012”jdeg.(’ per bp) a,nd Pulleyblank 4 01. (I 975) (0.014”/deg.C per bp). krrokvn.

11~

praf~tif~r.

(e) .4 throrrticnl

mtionnlr

f~~~~~oriit+ :I \’ ii 1 I’ sharf)vtis. and subsequr~ntfy adequate gel eortc~t~ntratiott. with iftr> af)ex at AM = 0 1’pon f’urthrr increase in gel ~W~WIItration. the \’ t,akes the shape of a I)irtl’S wings wit.lt .\cyy)rdittg to the attt,hors, I he cliscvf)attcy,~ a fwf). with t ttv I’ c~sf)t~rimerrtall~- observetl frt~rt~ (Fig, G) may be a c~ottstyurnee of thr harmonica f)t~ttdittg anti twisting pot~eritials used in the simulation. I ft fatal. thosr f)otetttiafs may f~v~ntc~ atthwrntoni(~ upon large IIS. deformations. which has ttot f~vtt I alien irit,o ac*c*ount (81. f,e f
for

thr

I’

A computer sitnulation of t,he electrophoretic fjehaviour of stnall D?l;A rings (about 600 bp) has t)ern performed in the light of the present cbxperimental work by M. Le Bret and B. H. Zimm (unpublished results). A4t zero gel concentration. j IVrl appeared to depend on ALk according t,o a V centered at ALk = 0. This is consistent with a former rnodef described by Le Bret (1979. 1984), quoted by Shore & f!%aldwin (19836). which predicts t’hat 1W’rl of small circular DNA molecules in solution fjecotnes significant only at IALkl > 2 turns. The gel matrix was found to reduce the radius of gyration of the molecules. At the same time, while IWrl retnains equal to 0 at ALk = 0, it increases relative to its value in solution at (ALkJ > 0. As a result, the

f)NA itt the caeff. whether c~ornpfesetl or not u,ith proteins. torsionally stressed or not (WV revif I)) \\‘ang. 19X4: Lilley. 1983: Scott. fUS5). i:, tlot free to exfjantl t)ut is c~ortstrained in it cage. c~otistiir~trcl in tj>. ftrokar>.otes t)y the, (YII \ViIff. iitltl iii t~lt/iut~!‘f)tf~S the ttttc~lear membrane arid thv ttu(‘leitr matris (Berexttey. 1980: Fey of II/.. 19X1). The Ivtraviour 01’ supercoiled f)XA in ail ;trraJ. of’ f)~)Iv~tc~r\~latrtitf~ 01’ . . agarose threads may therefore have sotttts t’tllt’\.ittt(*t‘ to the functioning of DTv.4 it, j%icw. fti I);trtic~ttliir. sequettc*fJs \vhieh may flip to the % form III’ f~sttxflf~ into csruciform under the negative torsi~)ttal st t’c’ss f’ound ir/ vir*o when f’rec~ in solution ttta\- r101 (10 so in the cvll. The torsional stress rec$recf 1i1r t ttr, transition. if measured t hrongh gel efec*l rof)horesih. may also be o\-erestimatctt in the first pfuc,fl Wlilt ivfb to tftat tif~rtletl in sofut ion. Suc~fi bin:, tllil,V tlfw~t~\~f~ evaluation in quatititativr St utficxs. I+c*ause c~tianges in f)SI-I supervoilittg af)f)ear 10 affect the t~spressioti of f)N;\ gyras(~ getic5. at1 homeostatic control of’ f)SA\ suprtv)ilittg hits t)racslr f,ostulatetl in which the f)alattc*e f)etwethtt 1h(k two antagonistic enzymes (tof”‘isottiPt,as(~ I atitl y,xxtsf~) ;tcv)rdittgly (?1f~~ttzel6 (Mlrrt f983: for is adjttsted a review see also \Vang. t 9%). \l’hat is proposed here is that regulation of TIN,\ super(y~ilittg dotbs not actually Ilear on the sttpercoilitty of I ht. I)N,\ per 0). the

Supercoiled

DNA

659

in Gel Electrophoresis

negatively supercoiled DXA shrinks (A W’r < 0) and decreases it,s contact with t.he cage. Relaxation by topoisomerase I (ALk >O) may then increase the DNA interactions with the cage back to their original value if ALk = ATw (see the above equation). Similarly, if the temperature is increased, the twist decreases (ATw 0) and interacts more with the cage. Further supercoiling by gyrase (ALk < 0) may then reduce the interactions to their original level. A cent#ral question t.hen is how, in such a process, can the proper enzyme activity be stimulated? In fact, this may be explained if the cage exerts a direct influence on U’r. a,s suggested above and actually found in the computer simulation. Indeed, in that (1 ), case: the cage would. t’hrough equation indirectly influence the torsional stress of the duplex. and in t,urn modify the balance of activit’y between t.opoisomerase I and gyrase in case of a temperature modification. It can easily be shown that t,he change in torsional stress would have the right polarity to activate the proper enzyme relative to the other. An interesting aspect of such a model, therefore, is that it opens the possibility that regulation of supercoiling may not abvays require a modification of the weight ratio between the two t.opoisomerases. as implied by t.he horneostatic control referred to a’bove. (2) Dependence of supercoiling on DNA size, The second observation concerns a series of plasmids of different sizes propagated in Escherichia roli under identical conditions. The larger ones (18 x 10~ to 83 x 103 hp) were found to have. when compared to the smaller ones (5 x lo3 to 8x lo3 bp). a Zoo/e larger superhelix density (Nickel et al., 1977). The above cage regulation model may offer an attractive explanation for t,his trend. Indeed, larger DNAs are expected t’o require more super-coiling (in t,erms of superhelieal density), as compared t.o smaller DNAs. in order to be accommodated in the same cape. The real situation must be more complex, however. since the increase in superhelix density is not proportional to the increase in size. as implied in auc-h a simple model, but is only a small fraction of it. This in fa,ct supports t,he intuitive notion that biggctr DSA molecules get access to wider compartment’s of the cell. As a consequence. those DXAs do not have to be supercoiled as much as they uould if the cage was not expandable. which would probably not l)e compat,ible with their function.

Dr J. B. Le Pecq for his long-standing interest in t,he work. References Anderson. P. 6 Rauer. W. (1978). Hioch~r~/ist~y. 17. 591 601.

Berezney. R. (1980). J. Cell. Biol. 85. 641 -650. Crick. F. H. C. (1976). Prof. A’&. Act&. Sri.. l’.S..4. 73. "6X-3643.

Dean. F.. Krasnow. XI. 4.. Otter. R.. Jlatzuk. SI. >I.. Spengler. S. ,J. & C’ozzarelli. X. R. (198%). (‘o/d Spri7a.g Harbor

Syrup.

Quanf.

Biol.

47. 76% iii.

Depew. R. E. & iYang. J. p. (19i5). Proc. .Yc~f .1cad. Sri , I-.S..4.

Fey.

72. 427.!!-4279.

E. G.. N’an. Molecular

Biology

K.

?(I. & Penman.

S. (1981). In (‘old Press. (‘old Spring

of the C’ytoskel~fon.,

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Edited by C’. K. (‘antor