Contribution of the intrinsic curvature to measured DNA persistence length1

doi:10.1006/jmbi.2001.5366 available online at http://www.idealibrary.com on

J. Mol. Biol. (2002) 317, 205±213

Contribution of the Intrinsic Curvature to Measured DNA Persistence Length Maria Vologodskaia and Alexander Vologodskii* Department of Chemistry New York University 31 Washington Place New York NY 10003, USA

The persistence length of DNA, a, depends both on the intrinsic curvature of the double helix and on the thermal ¯uctuations of the angles between adjacent base-pairs. We have evaluated two contributions to the value of a by comparing measured values of a for DNA containing a generic sequence and for an ``intrinsically straight'' DNA. In each 10 bp segment of the intrinsically straight DNA an initial sequence of ®ve bases is repeated in the sequence of the second ®ve bases, so any bends in the ®rst half of the segment are compensated by bends in the opposite direction in the second half. The value of a for the latter DNA depends, to a good approximation, on thermal ¯uctuations only; there is no intrinsic curvature. The values of a were obtained from measurements of the cyclization ef®ciency for short DNA fragments, about 200 bp in length. This method determines the persistence length of DNA with exceptional accuracy, due to the very strong dependence of the cyclization ef®ciency of short fragments on the value of a. We ®nd that the values of a for the two types of DNA fragment are very close and conclude that the contribution of the intrinsic curvature to a is at least 20 times smaller than the contribution of thermal ¯uctuations. The relationship between this result and the angles between adjacent base-pairs, which specify the intrinsic curvature, is analyzed. # 2002 Elsevier Science Ltd.

*Corresponding author

Keywords: DNA intrinsic curvature; DNA persistence length; DNA bending; DNA ¯exibility; DNA cyclization

Introduction Despite the rigidity and homogeneity of the double helix, typical conformations of DNA molecules look strongly bent on a scale of hundreds of base-pairs, and molecules containing thousands of base-pairs form a random coil. These bends result from both thermal ¯uctuations in the angles between adjacent base-pairs and the intrinsic curvature of DNA axis. In the large scale the conformational properties of high molecular weight DNA are speci®ed by the persistence length, a, which can be measured experimentally.1 It was suggested by Trifonov et al.2 and con®rmed by theoretical and computational analysis,3 ± 6 that the measured value of a always re¯ects both contributions, that from thermal ¯uctuations and from intrinsic, sequence-speci®c curvature. It is important, however, for a better understanding of many biological and physical properties of DNA to know the relaE-mail address of the corresponding author: [email protected] 0022-2836/02/020205±9 $35.00/0

tive contribution of these two factors. Knowledge of the contribution of intrinsic curvature is important for further improvement of the large-scale simulation of DNA conformational properties, especially dynamic properties that are much more sensitive to equilibrium bending.7 The data can provide an important test for different models of the sequence dependence of intrinsic curvature. If we knew the rules that specify the intrinsic curvature for a particular DNA sequence, we could simply calculate this contribution to the measured value of a. However, such rules are not well de®ned yet, although this problem has attracted considerable attention in the last two decades. Intensive studies of sequence-speci®c properties were initiated in late 1970 s early 1980 s by the discovery that certain DNA fragments show reduced electrophoretic mobility.8 ± 10 It was established in the following years that strong intrinsic bends of the double helix are associated with A-tracts of four or more base-pairs in length11 ± 14 (see also a careful NMR study of an A-tract related bend15). The intrinsic curvature originates in this case from the structure of dAn
dTn, which is notably different # 2002 Elsevier Science Ltd.

206 from the regular B form of DNA. Although this is the most pronounced case of the intrinsic curvature, and is well understood by now, its contribution to a is very small simply because the frequency of the A-tracts is relatively low in a typical DNA sequence (see Discussion). A larger contribution can result from the possibility of intrinsic bends associated with dimer steps. Our knowledge regarding this kind of bending is not suf®cient, however. The ®rst attempt to extract this information from the available experimental data was made by Bolshoy et al.16 Their analysis was based on the measured electrophoretic mobility and ef®ciency of cyclization of DNA fragments with different sequences. The analysis included several assumptions that are hard to test, however. Another set of similar data was deduced recently by statistical analysis of the protein-DNA crystal complexes.17 Although this set is based on the most detailed and accurate information available, the data correspond to crystals of the complexes rather than naked DNA molecules in aqueous solution. DNA conformations are certainly affected by the crystal packing18 and by protein-DNA interaction, so the conformational properties in solution may be different. In particular, it was shown directly that crystallization conditions can affect the conformations of A-tracts in DNA duplexes.19 The most direct way to study DNA conformational properties in solution is provided by NMR, but until the late 1990 s the accuracy of the method was not suf®cient to study small intrinsic bends of DNA axis.20 Recent breakthrough in the precision of the method has changed this situation, and the ®rst data obtained with the new technique look very promising.15,21 Certainly, the method will produce another set of parameters which specify the sequence dependence of DNA intrinsic curvature. In addition, a few groups are developing direct all-atom computer modeling of the duplexes in solution22,23 and in future a similar set of parameters might be obtained by computation. Meanwhile, the contribution of the intrinsic curvature to DNA large-scale conformational properties can be evaluated by macroscopic techniques. These methods allow one to measure the average properties over a particular sequence, importantly the DNA persistence length. To make a macroscopic approach successful one has to have a very accurate method to measure DNA persistence length for a particular sequence as well as a method to obtain DNA with a desired sequence. We demonstrate below that remarkably high accuracy can be achieved if the persistence length is extracted from measurements of the ef®ciency of cyclization for short DNA fragments. Study of the cyclization ef®ciency has been used for more than 20 years and has led to unique information about DNA conformational properties. It gave us extremely elegant proof of the helical nature of the double-stranded DNA24 as well as estimates of the DNA helical repeat and its bending and torsional rigidities.24,25 It is very important that for better

Static Persistence Length of DNA

accuracy the measurements should be performed on DNA fragments around 200 bp in length, and one can easy prepare fragments of this length with a desired sequence. Here we apply this approach to measure the average intrinsic curvature of the double helix, expressed in terms of static persistence length.2 We do this by comparing the measured persistence lengths of DNA fragments with a generic, ``typical'' sequence and specially designed fragments in which sequence eliminates possible intrinsic curvature, as suggested by Bednar et al.26 Unexpectedly, the results show that the contribution of the intrinsic bends into the value of a are many times smaller than the contribution of thermal ¯uctuations.

Results The contributions of thermal ¯uctuations and sequence-speci®c intrinsic bends into the value of a are speci®ed by dynamic and static persistence lengths, adyn and astat.2 Both adyn and astat can be de®ned in a similar way:  X  l1 li ; …1a† adyn ˆ lim i!1 l l1 X li i!1 l

astat ˆ lim

…1b†

where li is the vector of segment i of the chain and l is the length of the segments; the symbol h i corresponds to the averaging over thermal ¯uctuations of the chain conformations27 while the symbol corresponds to averaging over all possible sequences. The value of adyn assumes that the DNA is intrinsically straight. For astat the averaging in equation (1b) should be taken over the minimum energy conformations of the chains without accounting for thermal ¯uctuations. It was suggested initially by Trifonov et al.2 and con®rmed by theoretical and computational analysis3 ± 6 that the measurable persistence length of DNA, a, can be expressed as: 1 1 1 ˆ ‡ : a adyn astat

…2†

It is important to note that equation (1) does not depend on particular models of DNA bends, intrinsic or resulting from the thermal ¯uctuations. Nearly all methods of persistence length measurements give the value of a rather than adyn or astat. Therefore, to determine the intrinsic contribution to a we designed an ``intrinsically straight'' DNA. This consists of different segments each 10 bp in length. For each segment the sequence of the ®rst ®ve bases is repeated by the sequence of the second ®ve bases (Figure 1). If, in addition, all pentamers start from the same nucleotide, each two successive junctions between them will be identical as well. In such a DNA intrinsic bends in the ®rst

Static Persistence Length of DNA

207

Figure 1. Diagram of the sequence of an intrinsically straight DNA. For each ten base-pairs (shown by a particular color) the sequence of the ®rst ®ve base-pairs is repeated by the sequence of the second ®ve base-pairs. Since the helical repeat of the double helix is close to ten base-pairs per turn, intrinsic bends in the ®rst half of the helix turn are compensated by the bends in the opposite directions in the second half of the turn.

®ve junctions are nearly compensated by the bends in the opposite directions in the second ®ve junctions. Thus, the persistence length of such a DNA depends, in good approximation, on thermal ¯uctuations only and is close to the value of adyn. To estimate astat we compared this value of adyn with the measured persistence length of regular DNA molecules, for which a includes contributions from both adyn and astat. To determine the DNA persistence length for a particular fragment we measured its j-factor, which de®nes the ef®ciency of the fragment cyclization.28 The j-factor equals the effective concentration of one end of the chain in the vicinity of the other end in the appropriate angular and torsional orientation. Joining the cohesive ends is a slow process, whose rate is not limited by the rate at which these ends diffuse;29 therefore, the j-factor also can be expressed as the ratio of the corresponding kinetic constants of irreversible ligation of DNA ends.24,30 On the other hand, the value of the j-factor is completely de®ned by the conformational parameters of the DNA fragment: the minimum energy conformation of its axis, the average bending rigidity of the fragment, its total equilibrium twist and its torsional rigidity. The value of the j-factor can be computed with high accuracy for both homogeneous and sequence-dependent models of the double helix, if the corresponding parameters are known.31 ± 33 It is important that j-factors of short DNA fragments depend very strongly on their lengths (Figure 2), in order that small changes of DNA persistence length cause very large change of j-factors for such DNA fragments. We calculated, using a theoretical equation for the j-factor,34 the variation of j-factor resulting from 2 % change in the value of a (Figure 3). One can see from the Figure that the variation is 25 % for 200 bp fragments. This sensitivity of the measurable variable to a allows us to determine the value a with remarkable accuracy. The dependence of the j-factor on the fragment length shown in Figure 2 does not account for the requirement of proper torsional orientation of DNA ends. In its closed circular form the double helix has to make an integer number of turns and this causes extra torsional stress in short DNA circles. As a results of this stress, the oscillations of j-

Figure 2. The j-factors for DNA fragments as a function of their length. The theoretical dependence for the worm-like chain model34 was converted to the dependence on DNA length assuming that a ˆ 50 nm.

factor with the fragment lengths are superimposed with the dependence shown in Figure 2.24 This oscillating dependence of the j-factor on the length of short DNA fragments is shown in Figure 4. The period of the oscillations corresponds to a DNA helical repeat which is close to 10.5.35 Its precise value depends on the DNA sequence and thus should be considered as an adjustable parameter during the analysis of experimental data. This means, that measurements of j-factor have to be performed for a few fragment lengths to cover one period of the oscillations. Although this is laborious, it makes determination of the persistence length more reliable and accurate.

Figure 3. Variation of j-factors for short DNA fragments resulting from a small change of DNA persistence length. The dependence corresponds to 2 % change of the value of a, from 49.5 to 50.5 nm. The plot is based on the theoretical equation for j-factor for the worm-like chain model.34

208

Static Persistence Length of DNA

Figure 4. Oscillations of j-factors with DNA length. The dependence was obtained by the analysis similar to one described,24 which was generalized to account for the writhing contribution to torsional ®t of the fragment ends.36 The contribution of writhing becomes notable for the fragments larger than 300 bp. The broken line reproduces the dependence shown in Figure 2.

determination. Typical distributions of ligation products for different ligation times are shown in Figure 5(a). Quantitative analysis of the gel allows reliable determination of j-factor (Figure 5(b)). It should be noted that the j-factor for 400 bp fragments is about 20 times larger than that for 200 bp fragments, and thus the rate of the cyclization is much higher for the dimers than for the original fragments. As a result, the majority of the dimers are present in circular form except the very beginning of the ligation reaction. Thus, to make more reliable extrapolation to zero reaction time, required by equation (3), we included into the value of D(t) both linear and circular dimers rather than only linear dimers.25 The values of j-factors obtained by accounting only for linear dimers or both for linear and circular dimers do not differ because only linear dimers appear at the very beginning of the ligation. However, accounting only for linear dimers requires us to work with

To obtain the j-factor experimentally we measured the ratio of the amounts of circular fragments, C(t), and linear and circular dimers of the fragments, D(t), formed during the early stage of fragment ligation:25 j ˆ 2M0 lim C…t†=D…t† t!0

…3†

where M0 is the initial concentration of the fragments. Since it was shown that the ratio does not change over a wide range of the ligase concentration,25 we could adjust the concentration to have the characteristic time scale of the reaction in the convenient time interval. Two factors need to be considered when choosing the length of DNA fragments for the experiments. On one hand, the sensitivity of the j-factor to a increases as the fragment length shortens. On the other hand, the DNA concentration in the cyclization experiment should be about the value of jfactor to obtain comparable amounts of circular and dimeric products. Since the j-factor drops so fast with shortening DNA length (Figure 2), one has to work with very low DNA concentration if the fragments are too short. Keeping in mind these considerations we chose DNA fragments around 200 bp in length. First we performed measurements of j-factors and determined a for a set of 11 fragments with natural sequence taken from phage l DNA. The longest fragment consisted of 206 bp and each successive fragment was obtained by removing one base-pair from the previous one. The main goal of the experiment with these fragments was to show that the method and our experimental setup provide very high accuracy of the persistence length

Figure 5. Determination of j-factor from the ligation time course. (a) Typical result of agarose gel electrophoresis shows the linear monomers (LM) and dimers (LD), circular monomers (CM) and dimers (CD) obtained by ligation DNA fragments 198 bp in length. Quanti®cation of the bands was performed using a PhosphorImager. (b) The ratio C(t)/D(t) is extrapolated to zero ligation time to obtain the value of j-factor. Both linear and circular dimers were included in D(t).

209

Static Persistence Length of DNA

very small extent of the ligation reaction, and this complicates the measurements. The j-factors obtained for these 11 fragments are shown in Figure 6. We ®tted these data by the theoretical dependence of j-factor on DNA length obtained by Shimada and Yamakawa for the worm-like chain model.34 The theoretical dependence also accounted for the requirement of the proper torsional orientation of the fragment ends.24 The ®tting allowed us to determine three conformational parameters of the fragments: the effective persistence length, a, the DNA helical repeat, g, and the torsional rigidity of the double helix, C. It is important to emphasize that each parameter de®nes a different feature of the curve and thus can be determined unambiguously.24,25 The value of a found by this way, 48(1) nm, is in full agreement with the majority of published values (reviewed by;1 see also refs.25,36,37 In particular, Taylor and Hagerman found,25 using the same approach but longer DNA fragments, that a ˆ 45(1.5) nm, and from the similar data of Shore and Baldwin24 a is thought to be between 47 and 49 nm.33,34 To emphasize the accuracy of j-factor determination from these kind of experimental data we show in Figure 6, in addition to the theoretical curve that provides the best ®t to the experimental data, two more curves, for a ˆ 49 nm and a ˆ 47 nm. Clearly, these curves do not ®t the data. The values of two other adjusted parameters, g and C, were equal to 10.50(0.01) bp/(helix turn) and (2.4  0.1)  10ÿ19 erg cm, correspondingly. We obtained a second set of experimental data using 11 intrinsically straight DNA fragments (the precise sequences of the fragments are shown in Materials and Methods). Again, the longest

Figure 6. Dependence of j-factors on the length of DNA fragments with generic sequence. Experimental data (open circles;) were ®tted to the theoretical dependencies by adjusting the values of DNA helical repeat, g, torsional rigidity, C, and DNA persistence length, a. The best ®t (continuous line) corresponds to a ˆ 48 nm, g ˆ 10.50 bp/(helix turn), C ˆ 2.4  10ÿ19 erg cm. The broken lines show theoretical dependencies for a of 47 and 49 nm and the same values of g and C.

fragment consisted of 206 bp and each successive fragment was obtained by removing one basepair from the previous one. The fragments were obtained by chemical synthesis followed by cloning them into a plasmid to provide high homogeneity of the samples (see Materials and Methods). The measured values of j-factors and their theoretical ®t are shown in Figure 7. Comparing the data with the theoretical dependence we found that the best ®t corresponds to a ˆ 49.5 (1) nm, g ˆ 10.50(0.01) bp/(helix turn), C ˆ (2.4  0.1)10ÿ19 erg cm. Thus, the value of a for these intrinsically straight fragments, a2, hardly differs from the value of a for the ®rst set of fragments, a1. This means that the fragments with generic sequence are also, to a good approximation, intrinsically straight. Using the data obtained from these experiments and equation (2) we can estimate the value of the static persistence length, astat. The two sets of experiments correspond to the following equations: 1 1 1 ˆ ‡ a1 adyn astat 1 1 ˆ a2 adyn

…4†

Substituting measured values of a1 and a2 into these equations we ®nd that adyn ˆ 49.5(1) nm and astat  1600 nm. Since the estimation of astat is obtained as a difference of two very close values, the above estimation provides only a lower limit for astat with relatively large statistical error. We conclude that astat > 1000 nm, that is more than 20 times bigger than adyn.

Figure 7. Dependence of j-factors on the length of intrinsically straight DNA fragments. Experimental data (open circles) were ®tted to the theoretical dependencies by adjusting the values of g, C and length, a. The best ®t (continuous line) corresponds to a ˆ 49.5 nm, g ˆ 10.50 bp/(helix turn), C ˆ 2.4  10ÿ19 erg cm. The broken lines show theoretical dependencies for a of 48.5 and 50.5 nm and the same values of g and C.

210

Static Persistence Length of DNA

Discussion We have measured the values of a for DNA fragments with generic sequences and with a sequence that practically eliminates intrinsic curvature. The values obtained for these fragments are very close, 48(1) nm and 49.5(1) nm, respectively. We conclude from these results that intrinsic curvature makes only a very small contribution to a of DNA molecules with a typical sequence. And speci®cally, we estimate that astat > 1000 nm. How does this result agree with previous data? There have been several attempts to measure static or dynamic components of a separately. Indirect approaches to the problem gave different results, although the authors of these articles concluded that astat < adyn.38 ± 41 It should be noted that the value of adyn measured in these ways re¯ects only the rapid dynamic component. Our estimation is related to the equilibrium distribution of DNA conformations, and thus the obtained value of adyn accounts for thermal ¯uctuations on all time scales. Bednar et al.26 were the ®rst to use synthetic intrinsically straight DNA to estimate adyn and astat. They measured persistence lengths of generic and intrinsically straight DNA molecules and concluded that astat ˆ 130 nm and adyn ˆ 80 nm. Certainly, these values do not agree with our results. We do not know the reasons for the discrepancy with this study, which was based on analysis of DNA conformations using cryo-electron microscopy. There have been also several attempts to calculate a full set of parameters that de®ne sequencespeci®c curvature for dinucleotide (wedge) models. Such sets of parameters allow one to calculate astat by applying equation (1b) to computed conformations of DNA molecules with different random sequences.42 The conformations contain only intrinsic bends which are completely speci®ed by the sequences of the molecules. We performed the calculations averaging over 100,000 random sequences 3-15 kb in length. The ®rst set of parameters16 gives astat ˆ 167 nm. The second set of parameters deduced by Olson et al.17 from proteinDNA crystal complexes corresponds to astat ˆ 1020 nm, in good agreement with our result. Our data correlate well with the ®rst NMR results on DNA bending, which show small values of wedge angles between adjacent base-pairs, yi.15,21 It is interesting to analyze how the wedge angles yi, both specifying the intrinsic curvature and resulting from thermal ¯uctuations, average out to de®ne astat and adyn. To get insight of the relationship we start from a simpler model, the freely rotating chain (see ref. (27), for example). In this model all angles between adjacent segments have the same value y and there is no correlation between directions of adjacent bends. The model corresponds to the worm-like chain in the limit of small y. There is a simple equation that connects a and the angle y: a ˆ l…1 ÿ cos y†  2l ˆ y2

…5†

where l is the length of one chain segment. To move closer to the wedge model let us now assume that wedge angles between adjacent basepairs, yi, depend on the corresponding dinucleotides. Equation (2) allows us to assume how to generalize equation (5) for the case when wedge angles are different. Indeed, equation (2) means that 1/a is a sum of two independent contributions, 1/adyn and 1/astat. If a polymer chain has several independent mechanisms of ¯exibility, 1/a equals the sum of corresponding contributions. Thus, considering the bends at each of 16 different dinucleotides as independent, we conclude that: 1=a ˆ

16 X iˆ1

pi y2i =2l;

…6†

where pi is the probability of appearance of dinucleotide i and the sum should be taken over 16 types of dinucleotides. In particular, for a random sequence with equal frequencies of appearance of each nucleotide, pi equals 1/16. We tested equation (6) by comparing the calculated values of astat with the values obtained from equation (1b). Equation (1b) is a de®nition of astat and thus can be applied to any model, but its direct use requires computer simulation. We found that equation (6) works with remarkable accuracy for the model of independent intrinsic bends. However, equation (6) cannot be applied to calculate astat for the wedge model because in this model there is a strong correlation between the directions of the adjacent bends. The correlation originates from the fact that each bend depends on two adjacent base-pairs. In general, such correlation can increase or decrease astat. Equation (6) gives 86 nm and 200 nm for two sets of parameters mentioned above16,17 although the actual values of astat found from equation (1b) are 167 nm and 1020 nm, correspondingly. So, there is no simple relationship between the values of wedge angles and astat for the wedge model. In particular, if astat ˆ 1020 nm, according to equation (6) the root mean square average wedge angle is 1.5  . However, this set of parameters17 is characterized by the average wedge angle of 3.3  . Still, this average angle is two times smaller than the amplitude of the thermal ¯uctuation, 6.7  . Equation (6) can be used, however, to calculate adyn for the wedge model because thermal ¯uctuations eliminate correlations in the bend directions. In this case the values of y2i in equation (6) should be substituted by the variances of the wedge angles. In particular, the same value of adyn, 47 nm, is obtained by using either equation (1a) or equation (6) for the set of variances of the wedge angles.17 It is reliably established that 18-19  bends of the double helix are associated with sequences AAAA, and AATT and TTTT.13 ± 15 We chose for our experiments a fragment of l phage DNA without any such elements, so these intrinsic bends make no contribution to a1. It is not dif®cult, however, to

211

Static Persistence Length of DNA

estimate the contribution theoretically. The probability of appearance of each of the above three elements in a random sequence is 1/256, so they are separated by 85 base-pairs, on average. Since there is no correlation in the direction of successive bends in a random sequence, one can use equation (6) to evaluate their contribution to astat. The resulting value, 580 nm, is smaller than the contribution from other sequence motifs, so that A-tracts make a larger contribution to the intrinsic curvature of the double helix than all other elements. Still, their contribution to a is very small. We also estimated in this work the value of DNA torsional rigidity, C. We found that C ˆ 2.4  10ÿ19 erg cm, in good agreement with the results obtained from the same type of experiments.24,25 This value is notably lower, however, than the estimation obtained from the analysis of the equilibrium distribution of DNA topoisomers, 3.0  10ÿ19 erg cm.35,43 The discrepancy is not surprising since the value obtained in the cyclization experiments is speci®c to nicked DNA. Indeed, we measure here the rate of cyclization, and although two nicks at each circle are ligated, the ®rst ligation, that is ligation of DNA with one more nick, is the rate-limiting step of the process.24 So, the value obtained in such experiments has to be lower than the value for the intact double helix, and this is what we observe. Here we have estimated a from the properties of 200 bp DNA fragments. Is this length suf®ciently long to average out sequence-dependent conformational properties? To study this issue we calculated j-factors for 200 bp fragments with 20 different random sequences. The intrinsic curvature for these calculations was speci®ed by the wedge model16 for which astat ˆ 167 nm. Correspondingly, adyn was equal to 71 nm, to make a ˆ 50 nm. A recently developed ef®cient algorithm32 allowed us to calculate j-factors for each sequence with a good accuracy. The values of j-factors found in these calculations varies greatly (data not shown), corresponding to a values between 30 and 70 nm. On the other hand the values of a found from the experimentally measured j-factors for 200-250 bp fragments are equal to 48(1) nm (see above). These results are in good agreement with the data obtained on large DNA molecules35,36 for which sequence-dependent conformational properties have to be averaged out. One has to conclude that the experimental results on short fragments would be a rare coincidence if the contribution of intrinsic curvature to DNA conformational properties is comparable with the contribution of thermal ¯uctuations. Our estimation of astat shows that the contribution of intrinsic curvature is actually negligible and thus it is not surprising that the values of a obtained for two DNA fragments 200-250 bp in length are identical.

Materials and Methods DNA fragments The fragments with generic sequence Fragments were prepared by PCR ampli®cation of 205 bp l DNA segment starting from the nucleotide 29,853 and ending by the nucleotide 30,057. This sequence was chosen because it does not contain any known intrinsically curved elements of the double helix, AAAA, TTTT and AATT. PCR primers were extended by adding HindIII restriction sites. The upper strand primer was identical for all 11 fragments. The lower strand primers provided shortening of the fragments down from the maximum size in successive 1 bp steps. The 11 fragments obtained by PCR were digested by HindIII (New England Biolabs), puri®ed using the PCR Puri®cation Kit (QIAGEN), and cloned as HindIII fragments into pUC19 plasmids. The QIAGEN Miniprep Puri®cation Kit was used to extract DNA from Escherichia coli cells. We tested, for one fragment, that DNA puri®ed by the Plasmid Puri®cation Maxi Kit (QIAGEN) and subsequently puri®ed by equilibrium centrifugation in CsCl gives the same value of j-factor. The concentration of puri®ed DNAs were determined using a Hitachi Gene Spec I spectrophotometer. The fragments were obtained by treating the plasmids by HindIII restriction endonuclease. Our experimental design does not require separation of the large and small DNA fragments obtained by the restriction. The fragments with intrinsically straight sequence The second set of 11 fragments, in which intrinsic curvature of the double helix was essentially eliminated, was obtained by chemical synthesis of subfragments, assembling these in solution, and cloning. First, the variable parts of the fragments, about 40 bp in length, were inserted between PstI and HindIII sites of pUC19. The sizes of the inserts diminished in 1 bp steps. Second, XbaI/PstI-ended subfragment, common for all 11 fragments, was assembled by annealing six synthetic oligonucletides, about 50 bases each. The subfragment also contained a HindIII site near its left end which was used at the ®nal step of the fragment preparation. After cloning this XbaI/PstI fragment into pUC19 it was separated from the rest of the plasmid by agarose gel electrophoresis and inserted between XbaI and PstI sites in each of 11 plasmids carrying the variable subfragments. The desired fragments of 196-206 bp in length (Figure 8) were obtained by treating the plasmids with HindIII restriction endonuclease. All plasmids were maintained in E. coli DH-5a cells. The sequences of both sets of fragments were checked directly at the DNA sequencing facility. Radioactive labeling The mixture of two fragments, 200 bp and the rest of the plasmid, was labeled with 32P by incubation with [g-32P]ATP and T4 polynucleotide kinase (New England Biolabs). The mixture containing 0.5 picomol of each fragment, 7.5 ml of [g-32P]ATP (10 mCi/ml, 6000 Ci/ mmol ATP), and eight units of the kinase was incubated in 15 ml of kinase buffer (New England Biolabs) for one hour at 37  C. The reacting mixture was subsequently heated to 65  C for 20 minutes. Unincorporated label was removed using Sephadex G-50 column (Amersham-Phar-

212

Static Persistence Length of DNA

Figure 8. Nucleotide sequences of DNA fragments used in this study. Both fragments of l DNA (a) and intrinsically straight fragments (b) were cloned into pUC19 plasmids. Two sets of 11 HindIII-ended fragments were obtained by shortening down from the longest fragments, shown in the Figure, with 1 bp step. The orders of successive deletions indicated by the numbers at the right end of the sequence.

macia). These samples were used for the ligation experiments. We tested that the molecules thus prepared are fully phosphorylated: after two hours ligation at low DNA concentration about 95 % of the molecules were in closed circular form and only about 5 % in nicked circular form. We also found that phenol-extraction of the reaction mixture followed by ethanol-precipitation, performed for selected samples, does not change the experimental results. Ligation time course Ligations were performed in 62.5 ml of the ligation buffer (50 mM Tris-HCl (pH 7.6), 10 mM MgCl2, 10 mM DTT, 1 mM ATP, 100 mg/ml BSA) at 22  C. The concentration of the DNA fragments was 0.5-2 nM and 0.2 units/ml T4 DNA ligase (New England Biolabs) were used. At speci®c time intervals 12.5 ml portions were withdrawn from the reaction solution and quenched with 1 ml 0.5-M EDTA and heated (65  C, ten minutes). Gel electrophoresis and data analysis The ligation products were separated in 2.2 % (w/v) MetaPhor agarose (BioWhittaker) gels. The gels were run at room temperature in standard TBE buffer at 4 V/cm, for nine hours. Following electrophoresis, the gels were equilibrated in ethanol/glycerol solution, dried between cellophane sheets in a gel drying frame (Owl Separation Systems) and quanti®ed using Bio-Rad GS-525 Molecular Imager.

Acknowledgments We thank Dr N. Kallenbach for helpful advice during the preparation of this paper and Dr A. Stasiak for useful

discussion. This work was supported by NIH grant GM54215 to A.V.

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Edited by I. Tinoco (Received 12 October 2001; received in revised form 14 December 2001; accepted 17 December 2001)