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Energetics of Coupled Twist and Writhe Changes in Closed Circular pSM1 DNA
J. Mol. Biol. (1995) 253, 438–452
Energetics of Coupled Twist and Writhe Changes in Closed Circular pSM1 DNA William R. Bauer1*, Hisako Ohtsubo2, Eiichi Ohtsubo2 and Craig J. Benham3 1
Department of Microbiology Health Sciences Center State University of New York Stony Brook, NY 11794-5222, USA 2 Institute of Applied Microbiology, University of Tokyo, Yayoi 1-1-1 Bunkyo-ku, Tokyo 113, Japan 3
Department of Biomathematical Sciences Box 1023, Mount Sinai School of Medicine, 1 Gustave Levy Place, New York, NY 10029 USA
The extent of local denaturation in closed circular pSM1 DNA depends upon the linking difference, DLk, and the temperature, t. We have determined the denaturation profiles, using gel electrophoresis, over the ranges −37 R DLk R +16 and 25 °C R t R 65 °C. We have applied statistical mechanical methods to these data to evaluate the free energies of superhelix formation, of the twisting of single strands around each other, and of the initration of local denaturation. Because the complete nucleotide sequence is needed for this analysis, the complete pSM1 DNA sequence was determined and is reported here. The values of the free energy parameters found in this work agree closely with those previously obtained from experiments with pBR322 DNA, suggesting that there is little dependence of these values on the particular DNA sequence. We find the temperature dependence of these free energies by the appropriate statistical mechanical analysis of the temperature-dependent denaturation profiles produced by supercoiling. Calculations of the transition probability profiles indicate that the course of local denaturation in pSM1 DNA involves a complex competition among several sites of comparable susceptibility. This contrasts with the melting of pBR322 DNA, in which one principal site dominates. In both molecules the sites of predicted denaturation occur at or near regulatory regions, suggesting that duplex destabilization may be associated with their biological activities. 7 1995 Academic Press Limited
*Corresponding author
Keywords: superhelical DNA; pSM1 DNA; gel electrophoresis; thermodynamics of supercoiling; DNA denaturation
Introduction Closed circular duplex DNA is subject to the constancy of the linking number, Lk, which couples together changes in twist, Tw, and writhe, Wr. This relationship is described in the well-known equation Lk = Tw + Wr (White, 1969). A useful variation of this fundamental equation is obtained by using nicked circular DNA as a reference. Then the (formal) linking number of the reference DNA, Lko , is given by Lko = N/ho (the ratio of the number of base-pairs to the helical repeat). Since Lk = Lko = Two when Wr = 0, it follows that DLk0Lk − Lko = DTw + Wr. Under defined environmental conditions, any plasmid DNA sample typically consists of a collection of topoisomers, differing from each other by integers in DLk. In general, DLk is a function of many environmental variables, such as temperature (Depew & Wang, 1975), ionic strength and composition (Anderson & Bauer, 1978). Thus, for a given topoisomer, DLk 0022–2836/95/430438–15 $12.00/0
varies slowly and smoothly with temperature due to underlying small temperature-dependent changes in Lko . In the event of a major change in duplex winding, however, a correspondingly large change in DTw is expected and will be accompanied by an equal and opposite change in Wr. This will, in turn, be reflected in a large change in the gel electrophoretic mobility of the topoisomer in question. In the present study we take advantage of this experimental finding, along with the appropriate statistical mechanical theory, to determine the thermodynamic properties of plasmid pSM1 DNA as it undergoes the initial stages of denaturation. pSM1 DNA was first isolated in our laboratory as one of a series of plasmids formed by internal recombination in drug resistance factor R12 (Mickel & Bauer, 1976). R12 is a copy number mutant of R100, a closed circular DNA of length 89.3 kbp, which confers resistance against a variety of antibiotics (Rownd et al., 1975). These autonomously replicating plasmids form a related series of closed 7 1995 Academic Press Limited
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Energetics of Superhelical DNA
circular DNA molecules ranging in length from 5.6 to 92 kbp (Mickel et al., 1977; Mickel & Bauer, 1976). These plasmids are incompatible with R12 but are homologous with the parent plasmid as shown by heteroduplex mapping experiments. Heteroduplex mapping experiments later showed that the pSM plasmids are formed by internal recombination between the IS1 insertion sequence and various other sites on the opposite side of an origin of replication (Mickel et al., 1977). The pSM series has been used in several important physical chemical studies of the properties of plasmid DNA. For example, it was employed to provide the first detailed description of the behavior in agarose gel electrophoresis of closed circular, nicked circular and linear DNAs as a function of length under various conditions of ionic strength, gel concentration and field strength (Mickel et al., 1977). pSM1 DNA, of length 5804 base-pairs, is the smallest plasmid of the series that consists of an uninterrupted segment of the original R12 genome. We made further use of pSM1 in the first study of the gel electrophoretic behavior of closed circular DNA as a function of temperature and linking number (Lee & Bauer, 1985). The biological properties of pSM1 and its relatives have also been extensively examined (Ohtsubo et al., 1986). pSM1 DNA replicates unidirectionally from the R12 origin, which occurs at 85.5 on the kilobase map of R100; this corresponds to the RTF replication origin of R12 (Ohtsubo et al., 1977). pSM1 DNA was also used for the first determination of the complete nucleotide sequence of the insertion element, IS1 (Ohtsubo & Ohtsubo, 1978). The genes required for several functions, including replication and incompatibility (Rosen et al., 1980, 1981) and copy number control (Burger et al., 1981), have been determined. In subsequent work, we characterized at least ten polypeptides larger that ten kilodaltons produced in minicells from pSM1 in vivo (Armstrong et al., 1986). Two of these, pemK and pemI, are responsible for stable maintenance of the parent plasmids R12 and R100 (Tsuchimoto et al., 1988). In the current study we have determined the complete nucleotide sequence of pSM1 DNA and we describe more fully its gel electrophoretic behavior as a function of temperature and ionic strength. We applied the statistical mechanical helix–coil transition theory described before (Bauer & Benham, 1993; Benham, 1990, 1992) to these experimental results. The calculations show that the energetics of superhelix formation, of the initiation of denaturation, and of the reverse twisting of denatured regions are similar for pSM1 and pBR322 DNAs. The denaturation transition profile in pSM1 DNA is, however, much more complex than that of pBR322. The latter DNA contains one principal region of early melting, while pSM1 DNA contains at least two, and perhaps as many as six, regions of comparable susceptibility to denaturation.
Theoretical Analysis Analytic methods We have analyzed local denaturation in closed circular pSM1 DNA using statistical mechanical methods (Bauer & Benham, 1993; Benham, 1990, 1992). The statistical mechanical calculations evaluate the equilibrium properties of the system from an approximate partition function. An energy threshold is specified, and all states whose energies exceed the minimum by no more than the threshold amount are found explicitly. The probability of transition of each base-pair in the sequence is found from these states, so the accuracy of the results increases with the threshold. Then the aggregate influence of the states whose energies exceed the threshold is estimated, which allows the precision of the transition probability profiles to be evaluated. In this analysis a state is determined by specifying the secondary structure of each base-pair in the molecule as being either paired or separated. Part of the imposed linking difference is thus absorbed in the change of twist consequent on separation. Because single strands of DNA are relatively flexible, the two strands comprising a separated region can twist around each other. The resulting change in duplex winding can absorb additional linking difference at a relatively small energy cost. The residual linking difference is the remainder of the imposed deformation not absorbed either by transition or by relative rotation of the separated regions. We assume that all rotational deformations have equilibrated with the residual linking difference. The energetics of local denaturation In the current formulation of the statistical mechanical theory, the energy of a state depends upon three empirical parameters. In particular, the denaturation transition energy depends upon the number of separated base-pairs, n; the number of these that are A or T, nAT ; and the number of runs of separation, r. The free energy of separation of any base-pair is then given by: DGsep = ar + bAT nAT + bGC (n − nAT ) Here a is the energy needed to start an additional run of separation. This parameter arises in large part from the extra stacking interaction that must be disrupted in opening the first base-pair in a run. Our previous analysis of DLk-dependent local denaturation in pBR322 DNA (Bauer & Benham, 1993) produced the value a = 10.2 kcal/mol. The parameters bAT and bGC are the energy required to separate an A·T (or G·C) base-pair. The values of these quantities are assumed to be known in the statistical mechanical treatment, as explained (Bauer & Benham, 1993; Benham, 1992). The free energy associated with the torsional deformation, t, of the strand-separated regions varies quadratically with t
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Energetics of Superhelical DNA
and linearly with the number n of separated, and hence torsionally deformed, base-pairs: DGt = (1/2)Ct nt 2 Here Ct is the effective torsional stiffness associated with this deformation. Local denaturation reduces the duplex winding number and produces a corresponding reduction in the extent in supercoiling. Operationally, the post-transition DNA behaves as if its linking difference, DLk, has been increased to that of the pre-transition comigrating species, having a linking difference DLkres . The free energy associated with residual superhelicity is quadratic in the residual linking difference, DLkres : DGres = K(DLkres )2 Here K is the supercoiling free energy coefficient, which has the form K = qRT/N, where N is the number of base-pairs. The three unknown parameters, K, Ct and a, are evaluated at various temperatures from the measured changes in gel electrophoretic mobility as a function of DLk. In the present analysis, as in all previous ones, we assume that there is no sequence or position dependence of the initiation energy parameter, a.
Results Nucleotide sequence of pSM1 DNA The complete nucleotide sequence of pSM1 DNA, as determined in the present study, is shown in Table 1. The DNA contains 5,804 nucleotide pairs and has 49.83% A + T. The superhelix density of the native DNA under standard conditions is so = −0.063, or DLk o = −35.2 (Bauer, 1978). The region inclusive of nucleotide pairs 3917 to 4151 has not been reported previously and completes the sequence determination of the plasmid. Table 2 lists the sources for the previous determinations of portions of the plasmid DNA sequence; in all cases, our redetermination agrees with those in the literature wherever overlap occurs. Characteristic features of the secondary structure Plasmid pSM1 DNA is remarkably flat in terms of the distribution of A·T base-pairs along the contour. Figure 1 presents a plot of % A + T within a moving window of 25 base-pairs on each side of the base-pair at the location indicated (net 51 base-pairs). Although the plot is presented in linear form, the calculations were actually done with the circular representation. There are six regions with A + Te72%, and none with A + T < 27%. The six regions of highest average % A + T, and the locations of the base-pairs at which they are centered, are: AT-1, base-pair 1815 (80% A + T); AT-2, base-pair 3167 (78% A + T); AT-3, base-pair 5080 (76% A + T); AT-4, base-pair 2408 (75% A + T);
AT-5, base-pair 5747 (75% A + T); and AT-6, base-pair 4062 (73% A + T). The minimum value of A + T, as calculated with this window, is 27% and is centered on base-pair 1139. A corresponding analysis for pBR322 DNA (data not shown) shows the presence of only one region of average A + T > 75% at 3180 to 3301 base-pairs, at which early melting takes place (Bauer & Benham, 1993; Kowalski et al., 1988). The next most readily denaturable region of pBR322 is 72% A + T (located at 4100 to 4250 base-pairs), with all other regions being below 66% A + T. Thus, pSM1 DNA contains six regions that are candidates for early denaturation, in contrast to a maximum of two in pBR322 DNA. We have examined the sequence of pSM1 in order to determine the presence of candidate sequences for the formation of cruciforms. No region could be found that could reasonably be expected to extrude into a stable cruciform, with most possible sequences containing two or more mismatched bases in the putative stem. Region 826 to 857 contains a perfect inverted repeat of length ten, involving base-pairs 826 to 835 and 848 to 857. The loop size here is excessive, however, being 12 bases in length. A second possibility is located in the region 2011 to 2027. Here the stem contains seven base-pairs, but the loop is only three bases long. This, too, is not expected to extrude a cruciform. We conclude that cruciform formation does not occur with increasing superhelix density in pSM1 DNA, at least in the absence of divalent cations. The sequence was also examined for the presence of possible Z-DNA-forming sequences. Strikingly, only two stretches of alternating G·C were found, and these contained only (dG-dC)2·(dC-dG)2 . This is clearly inadequate to form a Z-DNA structure at any reasonable level of supercoiling. The base sequence (dT-dG)n·(dC-dA)n has also been reported to form a Z structure at physiological values of supercoiling (Nordheim & Rich, 1983), but pSM1 DNA contains no such sequence. The longest alternating PyPu sequence in pSM1 DNA is 20 base-pairs long and is centered at nucleotide 2390. This sequence contains a stretch of alternating (dT-dA)3·(dT-dA)3 base-pairs and is not surrounded by a region of high G + C content, hence is not likely to form a Z-DNA structure at any reasonably attainable level of supercoiling (McLean et al., 1986; Nejedly et al., 1993). Finally, we have examined the nucleotide sequence for the occurrence of stable (intrinsic) bends. Although the DNA contains numerous sequences of four contiguous A (or T) bases, as might be expected, in every case but one these are either isolated or separated by 14 to 16 base-pairs. This arrangement does not result in the formation of a net bend (Nadeau & Crothers, 1989). The one exception is from 4828 to 4851 base-pairs, which has the sequence 5'-TTTTGCGCAGTTTT-3'. This location is not associated with any of the early melting regions identified above.
Table 1. Complete nucleotide sequence of pSM1 DNA
Energetics of Superhelical DNA
441
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Energetics of Superhelical DNA
Table 1 (continued)
Energetics of Superhelical DNA
443
The sequence is numbered from the BglII restriction enzyme cutting site, and the EcoRI site is also indicated. The bar indicates the portion of the sequence newly determined in the present study.
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Table 2. Sequence information for pSM1 DNA Nucleotide sequence 1–3917 2835–3917 3917–4151 4150–4919 4920–5804
Reference(s) for determination Burger et al., 1981; Ryder et al., 1982; Ohtsubo et al., 1986 Tsuchimoto et al., 1988 This report; horizontal bar in Table 1 Ohtsubo & Ohtsubo, 1978 Armstrong et al., 1986
Determination of the energy parameters The results of the two-dimensional gel electrophoretic analysis of pSM1 DNA have been reported previously (Lee & Bauer, 1985) for temperatures from 25 to 65°C in increments of 5 deg.C. We have also determined the mobility profiles at two intermediate temperatures, 37°C and 62.5°C. The data from both sources are plotted in Figure 2(a) for temperatures of 40°C and less, and in Figure 2(b) for temperatures in excess of 40°C. The results are presented as distance migrated at each value of DLk, the offsets being due to the temperature dependence of the absolute gel electrophoretic mobility. Since the analysis does not require correction of the mobilities for this effect, we have retained it in the Figures. These experimental results were used to estimate values of the energy parameters K, Ct and a, using the methods described by Bauer & Benham (1993). Briefly, the residual linking difference, DLkres , for each topoisomer was determined by interpolation between the locations of the unmelted topoisomers of smaller =DLk =. The melting of a run of n base-pairs produces a decrease in duplex winding of n (1/ho − t/2p), and DLkres becomes less negative by the same amount (note that t < 0). The plots of distance migrated versus DLk are
Figure 1. Plot of % A + T versus axial position, measured in base-pairs, for pSM1 DNA. A moving window of width i − 25 to i + 25 was established for every base-pair position, i, and the % A + T was calculated for the resulting 51 base-pair sequence. Although the representation shown here is linear, the calculations were performed for the corresponding circular DNA. The upper and lower broken lines indicate the positions of 75% A + T and 70% A + T, respectively.
generally symmetric in the vicinity of DLk = 0. The curves in Figure 2 show, in addition, a reproducible vertical downward displacement of the one to three
(a)
(b)
Figure 2. Distance migrated versus DLk for pSM1 DNA topoisomers. The distance migrated at each temperature was measured from the initial position of the DNA sample in the first-dimension electrophoresis. The data at 37°C and at 62.5°C were determined in the present study, and the remaining curves were determined previously (Lee & Bauer, 1985). (a) Results for temperatures of 40°C and less: (Q) 25°C; (W) 30° C; (R) 35°C; (R) 37°C; (q) 40°C. The agarose gel concentration was 0.7%, the voltage was 50 V, and the gels were run for 18 hours. Both dimension gels were run in E buffer, and the second-dimension gels contained 2.0 mM chloroquine. (b) Results for temperatures greater than 40°C: (+) 45°C; (q) 50°C; (R), 55°C; (R) 60°C; (Q) 62.5°C; (w) 65°C. The conditions were the same as in (a), except that the concentration of chloroquine in the second-dimension gel was 1.5 mM.
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Energetics of Superhelical DNA
Table 3. Best-fit values of the energy parameters as a function of temperature t (°C)
q (bp)
Ct (kcal bp/rad2 )
a (kcal/mol)
Fita
40 45 50 55 60 62.5
1090 990 925 995 860 995
1.2 0.8 0.7 0.7 0.4 0.5
11.1 10.6 10.2 10.9 10.5 10.9
0.587 0.361 0.434 0.492 0.171 0.274
a The r.m.s. deviation of the best fit values of DLkr versus DLk relative to the experimental values.
topoisomers closest to the relaxed state. Preliminary analysis shows that this displacement is insignificant below 40°C and thereafter increases with increasing temperature. This phenomenon is probably not associated with a simple bend, since at most one intrinsically bent sequence occurs in pSM1 DNA (see above). In any event, bent sequences would be melted out in the higher temperature regions used here (Diekmann & Wang, 1985). The origin of this phenomenon is obscure, and it does not occur in pBR322 DNA (Bauer & Benham, 1993). However, since the symmetry of the plots is unaffected, the determination of DLkres is also unaffected.
Figure 3. Plots of DLkres − DLk versus −DLk for five different temperatures: (D) 40°C; (Q) 45°C; (q) 50°C; (R) 55°C; (w) 60°C. The continuous lines give the transition behavior at the values of the energy parameters giving the best fit at each temperature.
Topological state of the DNA The general expression for the free energy of a closed circular DNA, expressed per base-pair, was shown by Bauer & Benham (1993) to be: Dg(s, T ) =
Variation of the energy parameters with temperature The values of the free energy parameters giving the best fit to the data over the temperature range 40°C to 62.5°C were determined as described immediately above and are listed in Table 3, along with the goodness-of-fit expressed as the r.m.s deviation between the observed and calculated values of DLkres . The denaturation profiles at temperatures less than 40°C contain too little transition data to be useful in the curve fitting and are omitted from the Table. Both q and Ct decrease with increasing temperature, while a is independent of temperature. Figure 3 shows plots of −(DLk − DLkres ) as a function of −DLk for each value of t as calculated using the energy parameters listed in Table 3. The results calculated at temperatures greater than 60°C were not plotted because the transition profiles are too complex to permit fitting to an all-or-none transition model. As pointed out above, pSM1 DNA contains significantly more candidate sites than pBR322 DNA at which melting transitions are expected to occur. This is clearly evident in the experimental plots of Figure 2, where at least four distinct transitions are evident at some of the temperatures shown. At the current level of sophistication, the theoretical analysis is capable of fitting only the first transition, hence the theoretical curves stop at this point. At most temperatures, the goodness of fit into the second transition ranges from good to adequate.
RT q(T )s2 ho2
(1)
where ho is the DNA helical repeat in base-pairs/ turn, equal to 10.5 for linear DNA in solution (Wang, 1979); s is the superhelix density, and Dg = DG/N, for a DNA containing N base-pairs. The coefficient q(T ) is a normalized form of the superhelix free energy coefficient K (Bauer & Vinograd, 1970), and q(T ) = NK/RT. The temperature dependence of q(T ) is shown in Figure 4. The data are fit by a straight line: q(T ) = A/T + B
(2)
Figure 4. Plot of q(T )versus 1/T. The values of q(T ) were taken from Table 3, and the continuous line is the best least-squares fit to the data. The datum at 62.5°C was not used in the fitting, as explained in the text.
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Energetics of Superhelical DNA
Figure 5. Plot of Ct /T versus 1/T. The values of Ct (T ) were taken from Table 3, and the continuous line is the best least-squares fit to the data. The datum at 62.5°C was not used in the fitting, as explained in the text.
which, when combined with equation (1), gives expressions for the supercoiling free energy, enthalpy and entropy as a function of the fitted coefficients, A and B, and the superhelix density, s: Dg(s, T ) =
Rs 2 (A + BT ) ho2
(3a)
Figure 6. Plot of a versus t. The values of a(t) were taken from Table 3, and the continuous line is the best least-squares fit to the data. The datum at 62.5°C was no used in the fitting, as explained in the text, although it falls well within the data plotted here. Erratum: for T, K read t, °C.
The free energy functions are then given in terms of the fitted coefficients by (Bauer & Benham, 1993): n 2 t (At + Bt T ) 2 DH(t) = (nAt /2)t2
(6b) (6c)
DG(t, T ) =
(6a)
ARs 2 Dh(s) = ho2
(3b)
DS(t) = −(nBt /2)t .
−BRs 2 ho2
(3c)
The numerical values of the fitted coefficients At and Bt from Figure 5 are:
Ds(s) =
The results of least-squares curve fitting to the data shown in Figure 4 are:
2
At = (8.221.7) × 10−13 erg bp/rad2 or (11.822.4) kcal bp/rad2 per mol Bt = −(0.03420.0052) × 10−13 erg bp/rad2 per deg or −(4927) cal bp/rad2 per deg per mol
A = (0.9520.36) × 106 bp deg B = −(2.021.1) × 103 bp,
Initiation of denaturation with a regression coefficient of 0.84.
Winding of denatured regions The expression for the free energy of denatured regions was derived previously (Bauer & Benham, 1993), and is given by: 1 DG(t, T ) = Ct nt 2 2
(4)
for a region containing n separated base-pairs in a denatured domain that is twisted to a helicity of t radians. Ct is the temperature-dependent force constant for interstrand winding of coiled regions. The values of Ct (T )/T are plotted as a function of 1/T in Figure 5. The data are well fit by a straight line, given symbolically by: Ct /T = At /T + Bt .
(5)
Figure 6 presents a plot of the temperature variation of the initiation free energy parameter, a. The result is that a is independent of and has average value (99% confidence level): a = 10.6620.72 kcal/mol This is remarkably similar to the result obtained previously with pBR322 DNA, where the value of a was 10.2220.67 kcal/mol. The close agreement of these two quite independent estimates strongly supports our working assumption that a is independent of base composition. The values of the entropy and enthalpy coefficients for all three processes have been tabulated in Table 4, along with the value of the free energy of superhelix formation at 37°C. For comparison, the Table includes the corresponding quantities calculated previously using data from pBR322 DNA (Bauer & Benham, 1993).
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Energetics of Superhelical DNA
Table 4. Compilation of thermodynamic quantities for closed circular DNA
DNA pSM1 pBR322a a
Dh(s)/s2 (kcal/mol)
Ds(s)/s2 (kcal/mol per deg)
Dg(s)/s2 (37°C) (kcal/mol)
DH(t)/nt 2 (kcal/mol)
DS(t)/nt 2 (kcal/mol per deg)
a (kcal/mol)
17.226.5 17.521.7
36220 34.625.5
624 6.821.2
5.921.2 4.5420.19
2423 1821
10.6620.72 10.2220.67
Taken from (Bauer & Benham, 1993).
Discussion Nature of the duplex transition in pSM1 DNA In general, the coupled change in twist that accompanies a change in DLk can arise from any process that brings about unwinding of the duplex. Among the processes commonly considered as possible mechanisms are cruciform extrusion, Z-DNA formation, H-DNA formation, and local denaturation. As pointed out above, a detailed analysis of the nucleotide sequence of pSM1 DNA allows us to rule out the first two possibilities. Likewise, pSM1 DNA lacks the extended homopurine-homopyrimidine tract required for H-DNA formation (Mirkin et al., 1987), which, in any case, requires a very high superhelix density to form at neutral pH (Lyamichev et al., 1985). We therefore argue that the observed duplex transitions can confidently be identified with local denaturation. We also emphasize that all DLk-dependent effects occur at linking deficiencies well within the physiological range for native pSM1 DNA (DLk o = −35.2). Denaturation profiles in pSM1 DNA Plasmid pSM1 DNA contains multiple candidate sites for the first denaturation region, as indicated by the base composition profile in Figure 1. The various regions melt, in order not yet determined, as =DLk = is increased at any temperature (see Figure 3). Having determined the various free energy coefficients, however, it is possible to calculate the probability p(x) that any particular base-pair is denatured, as a function of location along the DNA. Figure 7 shows how p(x) depends upon DLk at one particular temperature, taken to be 55°C. This particular temperature was chosen because the transitions are well developed and relatively easy to discern. Because of the thermodynamic equivalence of changes in t and in DLk (Lee & Bauer, 1985), the patterns at all other temperatures are very similar but displaced along the DLk axis. Figure 7(a) shows the variation in the p(x) curves as the linking number changes. Unlike pBR322, there are clearly two major and at least two minor competing transitions in pSM1 DNA. Interestingly, at relatively low values of −DLk, denaturation at AT-2 is dominant. A separate region, AT-1, centered at base-pair 1815, begins to melt shortly thereafter and is comparable to the first in the intermediate DLk range. At higher values of DLk AT-1 begins to
dominate, eventually overshadowing AT-2. The statistical mechanical analysis of the melting data allows us to predict the specific regions of the DNA at which melting is expected as a function of DLk and t, as illustrated in Figure 7(a) for a particular set of conditions. These regions can be detected by denaturation mapping using chemical probes at various temperatures, the results of which will be reported elsewhere. The transition probabilities in regions AT-1 and AT-2 are shown more clearly in Figure 7(b), at DLk = −16 and in Figure 7(c), at DLk = −21. The former shows a slight dominance of AT-2, while the latter shows a clear dominance of AT-1. Both show, in addition, a small transition, AT-3, centered at base-pair 5080. A fourth transition, centered at base-pair 2408, is insignificant compared to the others. The probability of denaturation as a function of location along the pSM1 genome is further analyzed in Figure 8. Here the maximum value of p(x) at each of the A·T regions is plotted as a function of −DLk, as is their sum. The results are shown for all four regions at 55° C in Figure 8(a). Figure 8(b) shows the probability curves for regions AT-1 and AT-2 at t = 40°C, 45°C, 50°C and 55°C, plotted through the first transition as determined experimentally. Similar behavior occurs at all temperatures, in that the AT-2 region takes the initial lead in melting, giving way to the AT-1 region at greater values of −DLk. Although two distinct regions of the DNA are comparably susceptible to denaturation, the population of DNAs is composed of a mixture of molecules melted in one region or the other, but not both. This is shown clearly in Figure 9, in which the probability of having r runs at 55°C is plotted as a function of −DLk. It is clear that the vast majority of DNA species either remain native or contain a single run of denatured bases, depending upon the change in DLk. The high energy cost of opening additional denatured regions dictates that, at equilibrium, the probability of a second run must be small except at high DLk. Thus, the equilibrium behavior of this molecule involves an average over competing species, each containing a single denatured region. In contrast, pBR322 DNA contains a single region that dominates the denaturation profile (Bauer & Benham, 1993). This means that the melting behavior of pSM1 DNA, even in the first transition, is more complex than that of pBR322, the molecule on which most previous experimental and theoretical work has been done. In particular, how the multiple susceptible sites in pSM1 compete depends sensitively on the energetics of transition at
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Energetics of Superhelical DNA
each. Only at the most extensive linking differences are a few molecules to be found that contain two simultaneously denatured regions. This corresponds to conditions in which the second transition begins. Thermodynamic parameters for pSM1 DNA The values of the thermodynamic parameters determined in this study with pSM1 DNA are remarkably similar to those determined previously with pBR322 DNA (Bauer & Benham, 1993), even though these two DNAs have little sequence in common. Although the uncertainties in the calculated values are greater in the present work, due in part to the complexity of the competition between alternative transition regions, agreement is excellent
in every case. The quantity least well determined is the entropy of superhelix formation, which is dependent upon a fairly long extrapolation (see Figure 4). The entropy of superhelix formation is clearly positive, however, reinforcing the conclusions reached earlier regarding the importance of solvent factors in understanding the structure of closed circular DNA in solution (Bauer & Benham, 1993). Relationship between denaturation regions and biological function Several of the functionally active gene locations have been determined for pSM1 DNA, and these are shown in Figure 10. Also indicated in the Figure are all of the seven most susceptible early melting
(a)
(b)
(c)
Figure 7. Variation of the probability of transition, p(x), versus location, x, as measured from the BglII cutting site in pSM1 DNA. The results are shown for 55°C, since the curves at other temperatures are similar in shape when appropriately displaced along the DLk axis. (a) Low-resolution plots of p(x) versus location for values of DLk between −13 and −21. The probability distributions are displaced vertically by an integer value, as indicated, for clarity of presentation. Four transitions can be seen at this resolution. From left to right in the figure these are: AT-1 (base-pair 1815 at center); AT-4 (base-pair 2408 at center); AT-2 (base-pair 3167 at center) and AT-3 (base-pair 5080 at center). (b) High-resolution plot of p(x) versus location for t = 55°C and DLk = −16. (c) High-resolution plot of p(x) versus location for t = 55°C and DLk = −21.
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Energetics of Superhelical DNA
(a)
(b)
Figure 8. Plots of the maximum value of the probability of separation at a given denaturing region, p(tr, max) as a function of −DLk. (a) Probability distributions for each of the four denaturing regions shown in Figure 7, and their sum at 55°C. The symbols refer to: AT-1 (Q), AT-4 (W), AT-2 (R), AT-3 (w), and to the sum of all transition probabilities (q). (b) Probability distributions for the two most readily destabilized regions, AT-1 and AT-2 in Figure 10, for four different temperatures. The symbols for AT-1 are: (Q) 40°C; (R) 45°C; (q) 50°C; and (r) 55°C; the symbols for AT-2 are: (W) 40°C; (R|) 45°C; (w) 50°C; (r) 55°C.
regions, as determined in the present study. As indicated above, however, we can detect the possible melting of only AT-1 through AT-4 in the present study. The A·T-rich region that denatures most readily under most conditions, AT-1, is located within the origin of replication, ori. This is reminiscent of the situation at the Escherichia coli oriC origin of replication when present in a plasmid (Kowalski & Eddy, 1989). In the latter study it was found that initiation from this origin requires the presence of a sequence whose only necessary attribute is that it denatures when the DNA becomes sufficiently supercoiled. This does not appear to be the case, however, for pBR322. There the location of the origin of replication is considerably removed from both early melting regions (Sheflin & Kowalski, 1985). Altered DNA conformations detected by mung bean nuclease do
Figure 9. The probability that a given molecule contains exactly r runs, as a function of −DLk for t = 55°C. The three curves shown are for r = 0, 1 and 2. p(r) is negligible for r > 2.
occur, however, in promoter and terminator regions of supercoiled pBR322 DNA (Kowalski et al., 1988) We also note that two of the remaining early melting regions in pSM1 are closely associated with previously mapped open reading frames. Thus, AT-4 overlaps the beginning of ORF-1. AT-2, which is the second principal denaturation region, overlaps the beginning of the gene pemI, a gene whose product is involved in the stable maintenance of the plasmid (Tsuchimoto et al., 1988). Finally, AT-3 lies within approximately 50 base-pairs of the end of the IS1 region and overlaps the beginning of ORF-4; and AT-7 lies within RepA2. On the other hand, none of the other RepA genes appears to be associated with any of the principal A·T regions of expected reduced stability. The functional significance of these associations, if any, has not been determined.
Experimental Methods Plasmid DNA preparation Plasmid pSM1 DNA, a derivative of drug resistance factor R12, was prepared as described (Mickel & Bauer, 1976). Populations of topoisomers of the DNA were prepared by relaxing, under non-equilibrium conditions, a sample containing 0.2 mg DNA in 25 ml reaction buffer with 1.0 unit of calf thymus type I topoisomerase (Bethesda Research Laboratories) for 30 minutes at 2°C. The relaxation buffer contained 20 mM Tris-HCl (pH 8.0), 200 mM KCl, 0.5 mM dithiothreitol, 0.1 mM EDTA, and 30 mg/ml bovine serum albumin. The relaxation was stopped by adding 6.25 ml of a solution containing 5% SDS, 0.15% bromphenol blue, 50% glycerol, 10 mM Tris-HCl (pH 8.0), and 1 mM EDTA. Gel electrophoresis All procedures for gel electrophoresis were carried out as described (Bauer & Benham, 1993; Lee & Bauer, 1985). Briefly, first-dimension gel electrophoresis was conducted in tube gels of 0.7% agarose (type 1, Sigma Chemical Co.) in E buffer (90 mM Tris-borate, pH 8.4). The tube gels were
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Energetics of Superhelical DNA
Figure 10. Schematic representation of the genome of pSM1 DNA, showing the principal open reading frames including the mapped genes, the IS1 insertion sequence (Ohtsubo & Ohtsubo, 1978), and the origin of replication (Rosen et al., 1979), The gene and other open reading frame locations shown are pemI and pemK (Tsuchimoto et al., 1988); RepA1 through RepA4 (Rosen et al., 1980); and Orf1 and Orf4 (Armstrong et al., 1986). Also shown are the seven potential denaturing regions as determined in the present study. The actual boundaries of these regions depend upon DLk and temperature. For the example used in this figure, we took the positions where p(x) exceeded 0.001 when calculated at DLk = −19 and t = 55°C. prepared with 27 cm × 0.6 cm (i.d.) glass tubes, partially constricted at the bottom. Electrophoresis was performed for 18 hours at 50 V in a Buchler electrophoresis apparatus maintained at constant temperature (20.1 deg.C) by a Lauda model B-2 water incubator/circulator. The seconddimension gel electrophoresis was conducted by placing the appropriately sliced tube from the first dimension into the upper slot of a slab gel, also 0.7% agarose in E buffer and containing chloroquine at a concentration of 2.0 mM (40°C or less in the first dimension) or 1.5 mM (greater than 40°C). Second-dimension electrophoresis was conducted for 18 hours at 55 V and 25°C.
control gel to the distance between each topoisomer and the nicked form in the first-dimension gel. The linking difference for each band is defined as DLk = Lk − Lko , and values of DLk were obtained by the band-counting method (Keller, 1975). Determination of nucleotide sequence Nucleotide sequences were determined according to the methods of Maxam & Gilbert (1980).
Measurement of gels and calculations All procedures have been described (Bauer & Benham, 1993; Lee & Bauer, 1985). Absolute distances migrated were obtained by adding the distance traveled by the nicked DNA band in an ethidium bromide-stained
Acknowledgements This research was supported in part by grants from the National Institutes of Health and the National Science Foundation.
452
References Anderson, P. & Bauer, W. (1978). Supercoiling in closed circular DNA: dependence upon ion type and concentration. Biochemistry, 17, 594–601. Armstrong, K. A., Ohtsubo, H., Bauer, W. R., Yoshioka, Y., Miyazake, C., Maeda, Y. & Ohtsubo, E. (1986). Characterization of the gene products produced in minicells by pSM1, a derivative of R100. Mol. Gen. Genet. 205, 56–65. Bauer, W. R. (1978). Structure and reactions of closed duplex DNA. Annu. Rev. Biophys. Bioeng. 7, 287–313. Bauer, W. R. & Benham, C. J. (1993). The free energy, enthalpy and entropy of native and of partially denatured closed circular DNA. J. Mol. Biol. 234, 1184–1196. Bauer, W. & Vinograd, J. (1970). Interaction of closed circular DNA with inter-calative dyes. II. The free energy of superhelix formation in SV40 DNA. J. Mol. Biol. 47, 419–435. Benham, C. J. (1990). Theoretical analysis of heteropolymeric transitions in superhelical DNA molecules of specified sequence. J. Chem. Phys. 92, 6294–6305. Benham, C. J. (1992). Energetics of the strand separation transition in superhelical DNA. J. Mol. Biol. 225, 835–847. Burger, K. J., Steinbauer, J., Rollich, G., Kollek, R. & Goebel, W. (1981). Copy number control and incompatibility of plasmid R1: identification of a protein that seems to be involved in both processes. Mol. Gen. Genet. 182, 44–52. Depew, R. E. & Wang, J. C. (1975). Conformational fluctuations of DNA helix. Proc. Natl Acad. Sci. USA, 2, 4275–4279. Diekmann, S. & Wang, J. C. (1985). On the sequence determinants and flexibility of the kinetoplast DNA fragment with abnormal gel electrophoretic mobilities. J. Mol. Biol. 186, 1–11. Keller, W. (1975). Determination of the number of superhelical turns in simian virus 40 DNA by gel electrophoresis. Proc. Natl Acad. Sci. USA, 72, 4876–4880. Kowalski, D. & Eddy, M. J. (1989). The DNA unwinding element: a novel, cis-acting component that facilitated opening of the Escherichia coli replication origin. EMBO J. 8, 4335–4344. Kowalski, D., Natale, D. A. & Eddy, M. J. (1988). Stable DNA unwinding, not ‘‘breathing,’’ accounts for single-strand-specific nuclease hypersensitivity of specific A + T-rich sequences. Proc. Natl Acad. Sci. USA, 5, 9464–9468. Lee, F. S. & Bauer, W. R. (1985). Temperature dependence of the gel electrophoretic mobility of superhelical DNA. Nucl. Acids Res. 13, 1665–1682. Lyamichev, V. I., Mirkin, S. M. & Frank-Kamenetskii, M. D. (1985). A pH-dependent structural transition in the homopurine-homopyrimidine tract in superhelical DNA. J. Biomol. Struct. Dynam. 3, 327–338. Maxam, A. M. & Gilbert, W. (1980). Sequencing end-labeled DNA with base-specific chemical cleavages. Methods Enzymol. 65, 499–543. McLean, M. J., Blaho, J. A., Kilpatrick, M. W. & Wells, R. D. (1986). Consecutive A.T pairs can adopt a left-handed DNA structure. Proc. Natl Acad. Sci. USA, 83, 5884–5888.
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Mickel, S. & Bauer, W. (1976). Isolation, by tetracycline selection, of small plasmids derived from R-factor R12 in Escherichia coli K-12. J. Bacteriol. 127, 644–655. Mickel, S., Arena, V., Jr & Bauer, W. (1977). Physical properties and gel electrophoresis behavior of R12-derived plasmid DNAs. Nucl. Acids Res. 4, 1465–1482. Mirkin, S. M., Lyamichev, V. I., Drushlyak, K. N., Dobrynin, V. N., Filippov, S. A. & Frank-Kamenetskii, M. D. (1987). DNA H form requires a homopurine-homopyrimidine mirror repeat. Nature, 330, 495–497. Nadeau, J. G. & Crothers, D. M. (1989). Structural basis for DNA bending. Proc. Natl Acad. Sci. USA, 86, 2622–2626. Nejedly, K., Lilley, D. M. & Palecek, E. (1993). Conformational junctions between left-handed DNA in (dA-dT)16 and contiguous B-DNA in a supercoiled plasmid contain chemically reactive bases. FEBS Letters, 315, 277–281. Nordheim, F. & Rich, A. (1983). The sequence (dCdA)n·(dG-dT)n forms left-handed Z-DNA in negatively supercoiled plasmids. Proc. Natl. Acad. Sci. USA, 80, 1821–1825. Ohtsubo, H. & Ohtsubo, E, (1978). Nucleotide sequence of an insertion element, ISl. Proc. Natl Acad. Sci. USA, 75, 615–619. Ohtsubo, E., Feingold, J., Ohtsubo, H., Mickel, S. & Bauer, W. (1977). Unidirectional replication in Escherichia coli of three small plasmids derived from R factor R12. Plasmid, 1, 8–18. Ohtsubo, H., Ryder, T. B., Maeda, Y. Armstrong, K. & Ohtsubo, E. (1986). DNA replication of the resistance plasmid R100 and its control. Adv. Biophys. 21, 115–133. Rosen, J., Ohtsubo, H, & Ohtsubo, E, (1979). The nucleotide sequence of the region surrounding the replication origin of an R100 resistance factor derivative. Mol. Gen. Genet. 171, 287–293. Rosen, J., Ryder, T., Inokuchi, H., Ohtsubo, H. & Ohtsubo, E. (1980). Genes and sites involved in replication and incompatibility of an R100 plasmid derivative based on nucleotide sequence analysis. Mol. Gen. Genet. 179, 527–537. Rosen, J., Ryder, T., Ohtsubo, H. & Ohtsubo, E. (1981). Role of RNA transcripts in replication incompatibility and copy number control in antibiotic resistance plasmid derivatives. Nature, 90, 794–797. Rownd, R. H., Perlman, D., Womble, D. D., Taylor, D. P., Morris, C. F. & Hill, W. E. (1975). Replication of R plasmids. In Microbial Drug Resistance (Mitsuhashi, S. & Hashimoto, J., eds), pp. 27–50, University Park Press, Baltimore, MD. Sheflin, L. G. & Kowalski, D. (1985). Altered DNA conformations detected by mung bean nuclease occur in promoter and terminator regions of super coiled pBR322 DNA. Nucl. Acids Res. 13, 6137–6154. Tsuchimoto, S., Ohtsubo, H. & Ohtsubo, E. (1988). Two genes, pemK and pemI, responsible for stable maintenance of resistance plasmid R100. J. Bacteriol. 170, 1461–1466. Wang, J. C. (1979). Helical repeat of DNA in solution. Proc. Natl Acad. Sci. USA, 76, 200–203. White, J. H. (1969). Self-linking and the Gauss integral in higher dimensions. Am. J. Math. 91, 693–728.
Edited by B. Honig (Received 10 March 1995; accepted 8 August 1995)
Energetics of Coupled Twist and Writhe Changes in Closed Circular pSM1 DNA William R. Bauer1*, Hisako Ohtsubo2, Eiichi Ohtsubo2 and Craig J. Benham3 1
Department of Microbiology Health Sciences Center State University of New York Stony Brook, NY 11794-5222, USA 2 Institute of Applied Microbiology, University of Tokyo, Yayoi 1-1-1 Bunkyo-ku, Tokyo 113, Japan 3
Department of Biomathematical Sciences Box 1023, Mount Sinai School of Medicine, 1 Gustave Levy Place, New York, NY 10029 USA
The extent of local denaturation in closed circular pSM1 DNA depends upon the linking difference, DLk, and the temperature, t. We have determined the denaturation profiles, using gel electrophoresis, over the ranges −37 R DLk R +16 and 25 °C R t R 65 °C. We have applied statistical mechanical methods to these data to evaluate the free energies of superhelix formation, of the twisting of single strands around each other, and of the initration of local denaturation. Because the complete nucleotide sequence is needed for this analysis, the complete pSM1 DNA sequence was determined and is reported here. The values of the free energy parameters found in this work agree closely with those previously obtained from experiments with pBR322 DNA, suggesting that there is little dependence of these values on the particular DNA sequence. We find the temperature dependence of these free energies by the appropriate statistical mechanical analysis of the temperature-dependent denaturation profiles produced by supercoiling. Calculations of the transition probability profiles indicate that the course of local denaturation in pSM1 DNA involves a complex competition among several sites of comparable susceptibility. This contrasts with the melting of pBR322 DNA, in which one principal site dominates. In both molecules the sites of predicted denaturation occur at or near regulatory regions, suggesting that duplex destabilization may be associated with their biological activities. 7 1995 Academic Press Limited
*Corresponding author
Keywords: superhelical DNA; pSM1 DNA; gel electrophoresis; thermodynamics of supercoiling; DNA denaturation
Introduction Closed circular duplex DNA is subject to the constancy of the linking number, Lk, which couples together changes in twist, Tw, and writhe, Wr. This relationship is described in the well-known equation Lk = Tw + Wr (White, 1969). A useful variation of this fundamental equation is obtained by using nicked circular DNA as a reference. Then the (formal) linking number of the reference DNA, Lko , is given by Lko = N/ho (the ratio of the number of base-pairs to the helical repeat). Since Lk = Lko = Two when Wr = 0, it follows that DLk0Lk − Lko = DTw + Wr. Under defined environmental conditions, any plasmid DNA sample typically consists of a collection of topoisomers, differing from each other by integers in DLk. In general, DLk is a function of many environmental variables, such as temperature (Depew & Wang, 1975), ionic strength and composition (Anderson & Bauer, 1978). Thus, for a given topoisomer, DLk 0022–2836/95/430438–15 $12.00/0
varies slowly and smoothly with temperature due to underlying small temperature-dependent changes in Lko . In the event of a major change in duplex winding, however, a correspondingly large change in DTw is expected and will be accompanied by an equal and opposite change in Wr. This will, in turn, be reflected in a large change in the gel electrophoretic mobility of the topoisomer in question. In the present study we take advantage of this experimental finding, along with the appropriate statistical mechanical theory, to determine the thermodynamic properties of plasmid pSM1 DNA as it undergoes the initial stages of denaturation. pSM1 DNA was first isolated in our laboratory as one of a series of plasmids formed by internal recombination in drug resistance factor R12 (Mickel & Bauer, 1976). R12 is a copy number mutant of R100, a closed circular DNA of length 89.3 kbp, which confers resistance against a variety of antibiotics (Rownd et al., 1975). These autonomously replicating plasmids form a related series of closed 7 1995 Academic Press Limited
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circular DNA molecules ranging in length from 5.6 to 92 kbp (Mickel et al., 1977; Mickel & Bauer, 1976). These plasmids are incompatible with R12 but are homologous with the parent plasmid as shown by heteroduplex mapping experiments. Heteroduplex mapping experiments later showed that the pSM plasmids are formed by internal recombination between the IS1 insertion sequence and various other sites on the opposite side of an origin of replication (Mickel et al., 1977). The pSM series has been used in several important physical chemical studies of the properties of plasmid DNA. For example, it was employed to provide the first detailed description of the behavior in agarose gel electrophoresis of closed circular, nicked circular and linear DNAs as a function of length under various conditions of ionic strength, gel concentration and field strength (Mickel et al., 1977). pSM1 DNA, of length 5804 base-pairs, is the smallest plasmid of the series that consists of an uninterrupted segment of the original R12 genome. We made further use of pSM1 in the first study of the gel electrophoretic behavior of closed circular DNA as a function of temperature and linking number (Lee & Bauer, 1985). The biological properties of pSM1 and its relatives have also been extensively examined (Ohtsubo et al., 1986). pSM1 DNA replicates unidirectionally from the R12 origin, which occurs at 85.5 on the kilobase map of R100; this corresponds to the RTF replication origin of R12 (Ohtsubo et al., 1977). pSM1 DNA was also used for the first determination of the complete nucleotide sequence of the insertion element, IS1 (Ohtsubo & Ohtsubo, 1978). The genes required for several functions, including replication and incompatibility (Rosen et al., 1980, 1981) and copy number control (Burger et al., 1981), have been determined. In subsequent work, we characterized at least ten polypeptides larger that ten kilodaltons produced in minicells from pSM1 in vivo (Armstrong et al., 1986). Two of these, pemK and pemI, are responsible for stable maintenance of the parent plasmids R12 and R100 (Tsuchimoto et al., 1988). In the current study we have determined the complete nucleotide sequence of pSM1 DNA and we describe more fully its gel electrophoretic behavior as a function of temperature and ionic strength. We applied the statistical mechanical helix–coil transition theory described before (Bauer & Benham, 1993; Benham, 1990, 1992) to these experimental results. The calculations show that the energetics of superhelix formation, of the initiation of denaturation, and of the reverse twisting of denatured regions are similar for pSM1 and pBR322 DNAs. The denaturation transition profile in pSM1 DNA is, however, much more complex than that of pBR322. The latter DNA contains one principal region of early melting, while pSM1 DNA contains at least two, and perhaps as many as six, regions of comparable susceptibility to denaturation.
Theoretical Analysis Analytic methods We have analyzed local denaturation in closed circular pSM1 DNA using statistical mechanical methods (Bauer & Benham, 1993; Benham, 1990, 1992). The statistical mechanical calculations evaluate the equilibrium properties of the system from an approximate partition function. An energy threshold is specified, and all states whose energies exceed the minimum by no more than the threshold amount are found explicitly. The probability of transition of each base-pair in the sequence is found from these states, so the accuracy of the results increases with the threshold. Then the aggregate influence of the states whose energies exceed the threshold is estimated, which allows the precision of the transition probability profiles to be evaluated. In this analysis a state is determined by specifying the secondary structure of each base-pair in the molecule as being either paired or separated. Part of the imposed linking difference is thus absorbed in the change of twist consequent on separation. Because single strands of DNA are relatively flexible, the two strands comprising a separated region can twist around each other. The resulting change in duplex winding can absorb additional linking difference at a relatively small energy cost. The residual linking difference is the remainder of the imposed deformation not absorbed either by transition or by relative rotation of the separated regions. We assume that all rotational deformations have equilibrated with the residual linking difference. The energetics of local denaturation In the current formulation of the statistical mechanical theory, the energy of a state depends upon three empirical parameters. In particular, the denaturation transition energy depends upon the number of separated base-pairs, n; the number of these that are A or T, nAT ; and the number of runs of separation, r. The free energy of separation of any base-pair is then given by: DGsep = ar + bAT nAT + bGC (n − nAT ) Here a is the energy needed to start an additional run of separation. This parameter arises in large part from the extra stacking interaction that must be disrupted in opening the first base-pair in a run. Our previous analysis of DLk-dependent local denaturation in pBR322 DNA (Bauer & Benham, 1993) produced the value a = 10.2 kcal/mol. The parameters bAT and bGC are the energy required to separate an A·T (or G·C) base-pair. The values of these quantities are assumed to be known in the statistical mechanical treatment, as explained (Bauer & Benham, 1993; Benham, 1992). The free energy associated with the torsional deformation, t, of the strand-separated regions varies quadratically with t
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and linearly with the number n of separated, and hence torsionally deformed, base-pairs: DGt = (1/2)Ct nt 2 Here Ct is the effective torsional stiffness associated with this deformation. Local denaturation reduces the duplex winding number and produces a corresponding reduction in the extent in supercoiling. Operationally, the post-transition DNA behaves as if its linking difference, DLk, has been increased to that of the pre-transition comigrating species, having a linking difference DLkres . The free energy associated with residual superhelicity is quadratic in the residual linking difference, DLkres : DGres = K(DLkres )2 Here K is the supercoiling free energy coefficient, which has the form K = qRT/N, where N is the number of base-pairs. The three unknown parameters, K, Ct and a, are evaluated at various temperatures from the measured changes in gel electrophoretic mobility as a function of DLk. In the present analysis, as in all previous ones, we assume that there is no sequence or position dependence of the initiation energy parameter, a.
Results Nucleotide sequence of pSM1 DNA The complete nucleotide sequence of pSM1 DNA, as determined in the present study, is shown in Table 1. The DNA contains 5,804 nucleotide pairs and has 49.83% A + T. The superhelix density of the native DNA under standard conditions is so = −0.063, or DLk o = −35.2 (Bauer, 1978). The region inclusive of nucleotide pairs 3917 to 4151 has not been reported previously and completes the sequence determination of the plasmid. Table 2 lists the sources for the previous determinations of portions of the plasmid DNA sequence; in all cases, our redetermination agrees with those in the literature wherever overlap occurs. Characteristic features of the secondary structure Plasmid pSM1 DNA is remarkably flat in terms of the distribution of A·T base-pairs along the contour. Figure 1 presents a plot of % A + T within a moving window of 25 base-pairs on each side of the base-pair at the location indicated (net 51 base-pairs). Although the plot is presented in linear form, the calculations were actually done with the circular representation. There are six regions with A + Te72%, and none with A + T < 27%. The six regions of highest average % A + T, and the locations of the base-pairs at which they are centered, are: AT-1, base-pair 1815 (80% A + T); AT-2, base-pair 3167 (78% A + T); AT-3, base-pair 5080 (76% A + T); AT-4, base-pair 2408 (75% A + T);
AT-5, base-pair 5747 (75% A + T); and AT-6, base-pair 4062 (73% A + T). The minimum value of A + T, as calculated with this window, is 27% and is centered on base-pair 1139. A corresponding analysis for pBR322 DNA (data not shown) shows the presence of only one region of average A + T > 75% at 3180 to 3301 base-pairs, at which early melting takes place (Bauer & Benham, 1993; Kowalski et al., 1988). The next most readily denaturable region of pBR322 is 72% A + T (located at 4100 to 4250 base-pairs), with all other regions being below 66% A + T. Thus, pSM1 DNA contains six regions that are candidates for early denaturation, in contrast to a maximum of two in pBR322 DNA. We have examined the sequence of pSM1 in order to determine the presence of candidate sequences for the formation of cruciforms. No region could be found that could reasonably be expected to extrude into a stable cruciform, with most possible sequences containing two or more mismatched bases in the putative stem. Region 826 to 857 contains a perfect inverted repeat of length ten, involving base-pairs 826 to 835 and 848 to 857. The loop size here is excessive, however, being 12 bases in length. A second possibility is located in the region 2011 to 2027. Here the stem contains seven base-pairs, but the loop is only three bases long. This, too, is not expected to extrude a cruciform. We conclude that cruciform formation does not occur with increasing superhelix density in pSM1 DNA, at least in the absence of divalent cations. The sequence was also examined for the presence of possible Z-DNA-forming sequences. Strikingly, only two stretches of alternating G·C were found, and these contained only (dG-dC)2·(dC-dG)2 . This is clearly inadequate to form a Z-DNA structure at any reasonable level of supercoiling. The base sequence (dT-dG)n·(dC-dA)n has also been reported to form a Z structure at physiological values of supercoiling (Nordheim & Rich, 1983), but pSM1 DNA contains no such sequence. The longest alternating PyPu sequence in pSM1 DNA is 20 base-pairs long and is centered at nucleotide 2390. This sequence contains a stretch of alternating (dT-dA)3·(dT-dA)3 base-pairs and is not surrounded by a region of high G + C content, hence is not likely to form a Z-DNA structure at any reasonably attainable level of supercoiling (McLean et al., 1986; Nejedly et al., 1993). Finally, we have examined the nucleotide sequence for the occurrence of stable (intrinsic) bends. Although the DNA contains numerous sequences of four contiguous A (or T) bases, as might be expected, in every case but one these are either isolated or separated by 14 to 16 base-pairs. This arrangement does not result in the formation of a net bend (Nadeau & Crothers, 1989). The one exception is from 4828 to 4851 base-pairs, which has the sequence 5'-TTTTGCGCAGTTTT-3'. This location is not associated with any of the early melting regions identified above.
Table 1. Complete nucleotide sequence of pSM1 DNA
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Table 1 (continued)
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443
The sequence is numbered from the BglII restriction enzyme cutting site, and the EcoRI site is also indicated. The bar indicates the portion of the sequence newly determined in the present study.
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Table 2. Sequence information for pSM1 DNA Nucleotide sequence 1–3917 2835–3917 3917–4151 4150–4919 4920–5804
Reference(s) for determination Burger et al., 1981; Ryder et al., 1982; Ohtsubo et al., 1986 Tsuchimoto et al., 1988 This report; horizontal bar in Table 1 Ohtsubo & Ohtsubo, 1978 Armstrong et al., 1986
Determination of the energy parameters The results of the two-dimensional gel electrophoretic analysis of pSM1 DNA have been reported previously (Lee & Bauer, 1985) for temperatures from 25 to 65°C in increments of 5 deg.C. We have also determined the mobility profiles at two intermediate temperatures, 37°C and 62.5°C. The data from both sources are plotted in Figure 2(a) for temperatures of 40°C and less, and in Figure 2(b) for temperatures in excess of 40°C. The results are presented as distance migrated at each value of DLk, the offsets being due to the temperature dependence of the absolute gel electrophoretic mobility. Since the analysis does not require correction of the mobilities for this effect, we have retained it in the Figures. These experimental results were used to estimate values of the energy parameters K, Ct and a, using the methods described by Bauer & Benham (1993). Briefly, the residual linking difference, DLkres , for each topoisomer was determined by interpolation between the locations of the unmelted topoisomers of smaller =DLk =. The melting of a run of n base-pairs produces a decrease in duplex winding of n (1/ho − t/2p), and DLkres becomes less negative by the same amount (note that t < 0). The plots of distance migrated versus DLk are
Figure 1. Plot of % A + T versus axial position, measured in base-pairs, for pSM1 DNA. A moving window of width i − 25 to i + 25 was established for every base-pair position, i, and the % A + T was calculated for the resulting 51 base-pair sequence. Although the representation shown here is linear, the calculations were performed for the corresponding circular DNA. The upper and lower broken lines indicate the positions of 75% A + T and 70% A + T, respectively.
generally symmetric in the vicinity of DLk = 0. The curves in Figure 2 show, in addition, a reproducible vertical downward displacement of the one to three
(a)
(b)
Figure 2. Distance migrated versus DLk for pSM1 DNA topoisomers. The distance migrated at each temperature was measured from the initial position of the DNA sample in the first-dimension electrophoresis. The data at 37°C and at 62.5°C were determined in the present study, and the remaining curves were determined previously (Lee & Bauer, 1985). (a) Results for temperatures of 40°C and less: (Q) 25°C; (W) 30° C; (R) 35°C; (R) 37°C; (q) 40°C. The agarose gel concentration was 0.7%, the voltage was 50 V, and the gels were run for 18 hours. Both dimension gels were run in E buffer, and the second-dimension gels contained 2.0 mM chloroquine. (b) Results for temperatures greater than 40°C: (+) 45°C; (q) 50°C; (R), 55°C; (R) 60°C; (Q) 62.5°C; (w) 65°C. The conditions were the same as in (a), except that the concentration of chloroquine in the second-dimension gel was 1.5 mM.
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Table 3. Best-fit values of the energy parameters as a function of temperature t (°C)
q (bp)
Ct (kcal bp/rad2 )
a (kcal/mol)
Fita
40 45 50 55 60 62.5
1090 990 925 995 860 995
1.2 0.8 0.7 0.7 0.4 0.5
11.1 10.6 10.2 10.9 10.5 10.9
0.587 0.361 0.434 0.492 0.171 0.274
a The r.m.s. deviation of the best fit values of DLkr versus DLk relative to the experimental values.
topoisomers closest to the relaxed state. Preliminary analysis shows that this displacement is insignificant below 40°C and thereafter increases with increasing temperature. This phenomenon is probably not associated with a simple bend, since at most one intrinsically bent sequence occurs in pSM1 DNA (see above). In any event, bent sequences would be melted out in the higher temperature regions used here (Diekmann & Wang, 1985). The origin of this phenomenon is obscure, and it does not occur in pBR322 DNA (Bauer & Benham, 1993). However, since the symmetry of the plots is unaffected, the determination of DLkres is also unaffected.
Figure 3. Plots of DLkres − DLk versus −DLk for five different temperatures: (D) 40°C; (Q) 45°C; (q) 50°C; (R) 55°C; (w) 60°C. The continuous lines give the transition behavior at the values of the energy parameters giving the best fit at each temperature.
Topological state of the DNA The general expression for the free energy of a closed circular DNA, expressed per base-pair, was shown by Bauer & Benham (1993) to be: Dg(s, T ) =
Variation of the energy parameters with temperature The values of the free energy parameters giving the best fit to the data over the temperature range 40°C to 62.5°C were determined as described immediately above and are listed in Table 3, along with the goodness-of-fit expressed as the r.m.s deviation between the observed and calculated values of DLkres . The denaturation profiles at temperatures less than 40°C contain too little transition data to be useful in the curve fitting and are omitted from the Table. Both q and Ct decrease with increasing temperature, while a is independent of temperature. Figure 3 shows plots of −(DLk − DLkres ) as a function of −DLk for each value of t as calculated using the energy parameters listed in Table 3. The results calculated at temperatures greater than 60°C were not plotted because the transition profiles are too complex to permit fitting to an all-or-none transition model. As pointed out above, pSM1 DNA contains significantly more candidate sites than pBR322 DNA at which melting transitions are expected to occur. This is clearly evident in the experimental plots of Figure 2, where at least four distinct transitions are evident at some of the temperatures shown. At the current level of sophistication, the theoretical analysis is capable of fitting only the first transition, hence the theoretical curves stop at this point. At most temperatures, the goodness of fit into the second transition ranges from good to adequate.
RT q(T )s2 ho2
(1)
where ho is the DNA helical repeat in base-pairs/ turn, equal to 10.5 for linear DNA in solution (Wang, 1979); s is the superhelix density, and Dg = DG/N, for a DNA containing N base-pairs. The coefficient q(T ) is a normalized form of the superhelix free energy coefficient K (Bauer & Vinograd, 1970), and q(T ) = NK/RT. The temperature dependence of q(T ) is shown in Figure 4. The data are fit by a straight line: q(T ) = A/T + B
(2)
Figure 4. Plot of q(T )versus 1/T. The values of q(T ) were taken from Table 3, and the continuous line is the best least-squares fit to the data. The datum at 62.5°C was not used in the fitting, as explained in the text.
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Energetics of Superhelical DNA
Figure 5. Plot of Ct /T versus 1/T. The values of Ct (T ) were taken from Table 3, and the continuous line is the best least-squares fit to the data. The datum at 62.5°C was not used in the fitting, as explained in the text.
which, when combined with equation (1), gives expressions for the supercoiling free energy, enthalpy and entropy as a function of the fitted coefficients, A and B, and the superhelix density, s: Dg(s, T ) =
Rs 2 (A + BT ) ho2
(3a)
Figure 6. Plot of a versus t. The values of a(t) were taken from Table 3, and the continuous line is the best least-squares fit to the data. The datum at 62.5°C was no used in the fitting, as explained in the text, although it falls well within the data plotted here. Erratum: for T, K read t, °C.
The free energy functions are then given in terms of the fitted coefficients by (Bauer & Benham, 1993): n 2 t (At + Bt T ) 2 DH(t) = (nAt /2)t2
(6b) (6c)
DG(t, T ) =
(6a)
ARs 2 Dh(s) = ho2
(3b)
DS(t) = −(nBt /2)t .
−BRs 2 ho2
(3c)
The numerical values of the fitted coefficients At and Bt from Figure 5 are:
Ds(s) =
The results of least-squares curve fitting to the data shown in Figure 4 are:
2
At = (8.221.7) × 10−13 erg bp/rad2 or (11.822.4) kcal bp/rad2 per mol Bt = −(0.03420.0052) × 10−13 erg bp/rad2 per deg or −(4927) cal bp/rad2 per deg per mol
A = (0.9520.36) × 106 bp deg B = −(2.021.1) × 103 bp,
Initiation of denaturation with a regression coefficient of 0.84.
Winding of denatured regions The expression for the free energy of denatured regions was derived previously (Bauer & Benham, 1993), and is given by: 1 DG(t, T ) = Ct nt 2 2
(4)
for a region containing n separated base-pairs in a denatured domain that is twisted to a helicity of t radians. Ct is the temperature-dependent force constant for interstrand winding of coiled regions. The values of Ct (T )/T are plotted as a function of 1/T in Figure 5. The data are well fit by a straight line, given symbolically by: Ct /T = At /T + Bt .
(5)
Figure 6 presents a plot of the temperature variation of the initiation free energy parameter, a. The result is that a is independent of and has average value (99% confidence level): a = 10.6620.72 kcal/mol This is remarkably similar to the result obtained previously with pBR322 DNA, where the value of a was 10.2220.67 kcal/mol. The close agreement of these two quite independent estimates strongly supports our working assumption that a is independent of base composition. The values of the entropy and enthalpy coefficients for all three processes have been tabulated in Table 4, along with the value of the free energy of superhelix formation at 37°C. For comparison, the Table includes the corresponding quantities calculated previously using data from pBR322 DNA (Bauer & Benham, 1993).
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Energetics of Superhelical DNA
Table 4. Compilation of thermodynamic quantities for closed circular DNA
DNA pSM1 pBR322a a
Dh(s)/s2 (kcal/mol)
Ds(s)/s2 (kcal/mol per deg)
Dg(s)/s2 (37°C) (kcal/mol)
DH(t)/nt 2 (kcal/mol)
DS(t)/nt 2 (kcal/mol per deg)
a (kcal/mol)
17.226.5 17.521.7
36220 34.625.5
624 6.821.2
5.921.2 4.5420.19
2423 1821
10.6620.72 10.2220.67
Taken from (Bauer & Benham, 1993).
Discussion Nature of the duplex transition in pSM1 DNA In general, the coupled change in twist that accompanies a change in DLk can arise from any process that brings about unwinding of the duplex. Among the processes commonly considered as possible mechanisms are cruciform extrusion, Z-DNA formation, H-DNA formation, and local denaturation. As pointed out above, a detailed analysis of the nucleotide sequence of pSM1 DNA allows us to rule out the first two possibilities. Likewise, pSM1 DNA lacks the extended homopurine-homopyrimidine tract required for H-DNA formation (Mirkin et al., 1987), which, in any case, requires a very high superhelix density to form at neutral pH (Lyamichev et al., 1985). We therefore argue that the observed duplex transitions can confidently be identified with local denaturation. We also emphasize that all DLk-dependent effects occur at linking deficiencies well within the physiological range for native pSM1 DNA (DLk o = −35.2). Denaturation profiles in pSM1 DNA Plasmid pSM1 DNA contains multiple candidate sites for the first denaturation region, as indicated by the base composition profile in Figure 1. The various regions melt, in order not yet determined, as =DLk = is increased at any temperature (see Figure 3). Having determined the various free energy coefficients, however, it is possible to calculate the probability p(x) that any particular base-pair is denatured, as a function of location along the DNA. Figure 7 shows how p(x) depends upon DLk at one particular temperature, taken to be 55°C. This particular temperature was chosen because the transitions are well developed and relatively easy to discern. Because of the thermodynamic equivalence of changes in t and in DLk (Lee & Bauer, 1985), the patterns at all other temperatures are very similar but displaced along the DLk axis. Figure 7(a) shows the variation in the p(x) curves as the linking number changes. Unlike pBR322, there are clearly two major and at least two minor competing transitions in pSM1 DNA. Interestingly, at relatively low values of −DLk, denaturation at AT-2 is dominant. A separate region, AT-1, centered at base-pair 1815, begins to melt shortly thereafter and is comparable to the first in the intermediate DLk range. At higher values of DLk AT-1 begins to
dominate, eventually overshadowing AT-2. The statistical mechanical analysis of the melting data allows us to predict the specific regions of the DNA at which melting is expected as a function of DLk and t, as illustrated in Figure 7(a) for a particular set of conditions. These regions can be detected by denaturation mapping using chemical probes at various temperatures, the results of which will be reported elsewhere. The transition probabilities in regions AT-1 and AT-2 are shown more clearly in Figure 7(b), at DLk = −16 and in Figure 7(c), at DLk = −21. The former shows a slight dominance of AT-2, while the latter shows a clear dominance of AT-1. Both show, in addition, a small transition, AT-3, centered at base-pair 5080. A fourth transition, centered at base-pair 2408, is insignificant compared to the others. The probability of denaturation as a function of location along the pSM1 genome is further analyzed in Figure 8. Here the maximum value of p(x) at each of the A·T regions is plotted as a function of −DLk, as is their sum. The results are shown for all four regions at 55° C in Figure 8(a). Figure 8(b) shows the probability curves for regions AT-1 and AT-2 at t = 40°C, 45°C, 50°C and 55°C, plotted through the first transition as determined experimentally. Similar behavior occurs at all temperatures, in that the AT-2 region takes the initial lead in melting, giving way to the AT-1 region at greater values of −DLk. Although two distinct regions of the DNA are comparably susceptible to denaturation, the population of DNAs is composed of a mixture of molecules melted in one region or the other, but not both. This is shown clearly in Figure 9, in which the probability of having r runs at 55°C is plotted as a function of −DLk. It is clear that the vast majority of DNA species either remain native or contain a single run of denatured bases, depending upon the change in DLk. The high energy cost of opening additional denatured regions dictates that, at equilibrium, the probability of a second run must be small except at high DLk. Thus, the equilibrium behavior of this molecule involves an average over competing species, each containing a single denatured region. In contrast, pBR322 DNA contains a single region that dominates the denaturation profile (Bauer & Benham, 1993). This means that the melting behavior of pSM1 DNA, even in the first transition, is more complex than that of pBR322, the molecule on which most previous experimental and theoretical work has been done. In particular, how the multiple susceptible sites in pSM1 compete depends sensitively on the energetics of transition at
449
Energetics of Superhelical DNA
each. Only at the most extensive linking differences are a few molecules to be found that contain two simultaneously denatured regions. This corresponds to conditions in which the second transition begins. Thermodynamic parameters for pSM1 DNA The values of the thermodynamic parameters determined in this study with pSM1 DNA are remarkably similar to those determined previously with pBR322 DNA (Bauer & Benham, 1993), even though these two DNAs have little sequence in common. Although the uncertainties in the calculated values are greater in the present work, due in part to the complexity of the competition between alternative transition regions, agreement is excellent
in every case. The quantity least well determined is the entropy of superhelix formation, which is dependent upon a fairly long extrapolation (see Figure 4). The entropy of superhelix formation is clearly positive, however, reinforcing the conclusions reached earlier regarding the importance of solvent factors in understanding the structure of closed circular DNA in solution (Bauer & Benham, 1993). Relationship between denaturation regions and biological function Several of the functionally active gene locations have been determined for pSM1 DNA, and these are shown in Figure 10. Also indicated in the Figure are all of the seven most susceptible early melting
(a)
(b)
(c)
Figure 7. Variation of the probability of transition, p(x), versus location, x, as measured from the BglII cutting site in pSM1 DNA. The results are shown for 55°C, since the curves at other temperatures are similar in shape when appropriately displaced along the DLk axis. (a) Low-resolution plots of p(x) versus location for values of DLk between −13 and −21. The probability distributions are displaced vertically by an integer value, as indicated, for clarity of presentation. Four transitions can be seen at this resolution. From left to right in the figure these are: AT-1 (base-pair 1815 at center); AT-4 (base-pair 2408 at center); AT-2 (base-pair 3167 at center) and AT-3 (base-pair 5080 at center). (b) High-resolution plot of p(x) versus location for t = 55°C and DLk = −16. (c) High-resolution plot of p(x) versus location for t = 55°C and DLk = −21.
450
Energetics of Superhelical DNA
(a)
(b)
Figure 8. Plots of the maximum value of the probability of separation at a given denaturing region, p(tr, max) as a function of −DLk. (a) Probability distributions for each of the four denaturing regions shown in Figure 7, and their sum at 55°C. The symbols refer to: AT-1 (Q), AT-4 (W), AT-2 (R), AT-3 (w), and to the sum of all transition probabilities (q). (b) Probability distributions for the two most readily destabilized regions, AT-1 and AT-2 in Figure 10, for four different temperatures. The symbols for AT-1 are: (Q) 40°C; (R) 45°C; (q) 50°C; and (r) 55°C; the symbols for AT-2 are: (W) 40°C; (R|) 45°C; (w) 50°C; (r) 55°C.
regions, as determined in the present study. As indicated above, however, we can detect the possible melting of only AT-1 through AT-4 in the present study. The A·T-rich region that denatures most readily under most conditions, AT-1, is located within the origin of replication, ori. This is reminiscent of the situation at the Escherichia coli oriC origin of replication when present in a plasmid (Kowalski & Eddy, 1989). In the latter study it was found that initiation from this origin requires the presence of a sequence whose only necessary attribute is that it denatures when the DNA becomes sufficiently supercoiled. This does not appear to be the case, however, for pBR322. There the location of the origin of replication is considerably removed from both early melting regions (Sheflin & Kowalski, 1985). Altered DNA conformations detected by mung bean nuclease do
Figure 9. The probability that a given molecule contains exactly r runs, as a function of −DLk for t = 55°C. The three curves shown are for r = 0, 1 and 2. p(r) is negligible for r > 2.
occur, however, in promoter and terminator regions of supercoiled pBR322 DNA (Kowalski et al., 1988) We also note that two of the remaining early melting regions in pSM1 are closely associated with previously mapped open reading frames. Thus, AT-4 overlaps the beginning of ORF-1. AT-2, which is the second principal denaturation region, overlaps the beginning of the gene pemI, a gene whose product is involved in the stable maintenance of the plasmid (Tsuchimoto et al., 1988). Finally, AT-3 lies within approximately 50 base-pairs of the end of the IS1 region and overlaps the beginning of ORF-4; and AT-7 lies within RepA2. On the other hand, none of the other RepA genes appears to be associated with any of the principal A·T regions of expected reduced stability. The functional significance of these associations, if any, has not been determined.
Experimental Methods Plasmid DNA preparation Plasmid pSM1 DNA, a derivative of drug resistance factor R12, was prepared as described (Mickel & Bauer, 1976). Populations of topoisomers of the DNA were prepared by relaxing, under non-equilibrium conditions, a sample containing 0.2 mg DNA in 25 ml reaction buffer with 1.0 unit of calf thymus type I topoisomerase (Bethesda Research Laboratories) for 30 minutes at 2°C. The relaxation buffer contained 20 mM Tris-HCl (pH 8.0), 200 mM KCl, 0.5 mM dithiothreitol, 0.1 mM EDTA, and 30 mg/ml bovine serum albumin. The relaxation was stopped by adding 6.25 ml of a solution containing 5% SDS, 0.15% bromphenol blue, 50% glycerol, 10 mM Tris-HCl (pH 8.0), and 1 mM EDTA. Gel electrophoresis All procedures for gel electrophoresis were carried out as described (Bauer & Benham, 1993; Lee & Bauer, 1985). Briefly, first-dimension gel electrophoresis was conducted in tube gels of 0.7% agarose (type 1, Sigma Chemical Co.) in E buffer (90 mM Tris-borate, pH 8.4). The tube gels were
451
Energetics of Superhelical DNA
Figure 10. Schematic representation of the genome of pSM1 DNA, showing the principal open reading frames including the mapped genes, the IS1 insertion sequence (Ohtsubo & Ohtsubo, 1978), and the origin of replication (Rosen et al., 1979), The gene and other open reading frame locations shown are pemI and pemK (Tsuchimoto et al., 1988); RepA1 through RepA4 (Rosen et al., 1980); and Orf1 and Orf4 (Armstrong et al., 1986). Also shown are the seven potential denaturing regions as determined in the present study. The actual boundaries of these regions depend upon DLk and temperature. For the example used in this figure, we took the positions where p(x) exceeded 0.001 when calculated at DLk = −19 and t = 55°C. prepared with 27 cm × 0.6 cm (i.d.) glass tubes, partially constricted at the bottom. Electrophoresis was performed for 18 hours at 50 V in a Buchler electrophoresis apparatus maintained at constant temperature (20.1 deg.C) by a Lauda model B-2 water incubator/circulator. The seconddimension gel electrophoresis was conducted by placing the appropriately sliced tube from the first dimension into the upper slot of a slab gel, also 0.7% agarose in E buffer and containing chloroquine at a concentration of 2.0 mM (40°C or less in the first dimension) or 1.5 mM (greater than 40°C). Second-dimension electrophoresis was conducted for 18 hours at 55 V and 25°C.
control gel to the distance between each topoisomer and the nicked form in the first-dimension gel. The linking difference for each band is defined as DLk = Lk − Lko , and values of DLk were obtained by the band-counting method (Keller, 1975). Determination of nucleotide sequence Nucleotide sequences were determined according to the methods of Maxam & Gilbert (1980).
Measurement of gels and calculations All procedures have been described (Bauer & Benham, 1993; Lee & Bauer, 1985). Absolute distances migrated were obtained by adding the distance traveled by the nicked DNA band in an ethidium bromide-stained
Acknowledgements This research was supported in part by grants from the National Institutes of Health and the National Science Foundation.
452
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Edited by B. Honig (Received 10 March 1995; accepted 8 August 1995)