We have investigated the phase behaviour of pUC18 plasmid solutions with
phase separation experiments and polarized light microscopy. Furthermore,
the configuration of the superhelix is monitored with small-angle neutron
scattering. The phase diagram is interpreted with liquid crystal theory including
the effects of charge, orientation entropy, excluded volume, as well as the elastic,
entropic and electrostatic contributions to the molecular free energy

Backendorf, C

Egelhaaf, Stefan U

Jesse, W

Lapp, A

van der Maarel, J R C

Zakharova, S S

Edinburgh Research Archive

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTERJ. Phys.: Condens. Matter 15 (2003) S183–S189 PII: S0953-8984(03)54871-8Supercoiled DNA; plectonemic structure and liquidcrystal formationJ R C van der Maarel1, S S Zakharova1, W Jesse1, C Backendorf1,S U Egelhaaf2 and A Lapp31 Leiden Institute of Chemistry, Leiden University, 2300 RA Leiden, The Netherlands2 Department of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK3 Laboratoire Léon Brillouin, CEA/CNRS, 91191 Gif-sur-Yvette Cedex, FranceReceived 16 October 2002Published 16 December 2002Online at stacks.iop.org/JPhysCM/15/S183AbstractWe have investigated the phase behaviour of pUC18 plasmid solutions withphase separation experiments and polarized light microscopy. Furthermore,the configuration of the superhelix is monitored with small-angle neutronscattering. The phase diagram is interpreted with liquid crystal theory includingthe effects of charge, orientation entropy, excluded volume, as well as the elastic,entropic and electrostatic contributions to the molecular free energy.1. IntroductionClosed circular DNA usually exists in a supercoiled configuration, in which the duplex is woundaround another part of the same molecule to form a higher-order helix (see figure 1). Theplectonemic supercoiling, with a right-handed interwinding, is the most likely conformationin vivo. Supercoiling is utilized in many cellular mechanisms. Examples include the replicationand transcription of DNA, the formation of protein complexes on DNA and altered primarystructures such as cruciforms.The organization of DNA in biological structures is largely unknown, but bears someresemblance to liquid crystalline phases observed in vitro [1]. The formation of the anisotropicphase results from the competition between orientation entropy and the volume excluded bya DNA molecule to another molecule [2]. The boundary concentrations are roughly inverselyproportional to this excluded volume, which is related to the molecular weight and the rangeof interaction. In the case of supercoiled DNA, topology is anticipated to be a key factorin controlling the phase behaviour. Apart from its effect on the molecular free energy, thetopological constraint sets the dimensions of the superhelix and, hence, determines the excludedvolume. Indeed, supercoiling has been reported to be a major compaction mode for plasmidDNA in the cytoplasm of bacteria [3].Here, we explore the extent to which supercoiling controls the compaction of pUC18bacterial plasmid (2686 base pairs) in a liquid crystal [4, 5]. The nature of the phase transition,0953-8984/03/010183+07$30.00 © 2003 IOP Publishing Ltd Printed in the UK S183S184 J R C van der Maarel et alFigure 1. A plectonemic helix with length L , radius r , pitch p and opening angle α.the critical boundaries and the characterization of the anisotropic phase are investigated withpolarized light microscopy and phase equilibrium experiments. Furthermore, the configurationof the superhelix is monitored with small-angle neutron scattering (SANS) through the phasetransition. Finally, the phase diagram is interpreted with lyotropic liquid crystal theoryincluding the effects of charge, orientation entropy, excluded volume, as well as the elastic,entropic and electrostatic contributions to the molecular free energy. The effect of the molecularfree energy comes in through the effect on the balance of chemical potentials pertaining to thecoexisting phases.2. TopologyThe topological constraint is characterized by the linking number deficit Lk, which isthe number of turns the duplex is turned by before closure to form a ring. As shownby gel electrophoresis, our DNA preparation contains a broad topoisomer distribution withpredominant Lk = −7 and deviation ±3 [4]. Lk is conserved and is distributed betweenthe writhe Wr and excess twist Tw exerted on the duplex according to [6]Lk = Wr + Tw. (1)For a right-handed, regular supercoil without end loops, Wr is proportional to the number ofcrossings n when viewed perpendicular to the superhelical axis: Wr = −n sin α, with thepitch angle α as in figure 1. It is convenient to define the normalized length 2L/ l, with l beingthe length of the DNA molecule. From integration along the contour it follows that2L/ l = p/(p2 + r2)1/2, (2)if the end loops are neglected. The pitch angle α is given bytan α = p/r = (2L/ l)/(1 − (2L/ l)2)1/2 (3)and the writhe readsWr = −lp/(2π(p2 + r2)). (4)The local structure of the superhelix is fully characterized by p and r . These parametersdetermine α, Wr and 2L/ l. At a larger length scale, the superhelix can branch with an averageof 1.2 branch points per molecule [7].3. Phase diagramIf the plasmid concentration is increased beyond a certain critical concentration, the translucentsolution is seen to be composed of birefringent domains when observed through crossedpolarizers. Polarized light microscopy textures show that this observation is due to theSupercoiled DNA; plectonemic structure and liquid crystal formation S185Figure 2. (a) Critical boundaries versus salt concentration (T = 298 K). Open symbols: ci ;closed symbols: ca . The curves are calculated with the scaled particle description for hard-coreeffects and electrostatic interactions in the second virial approximation without (dashed curves)and with (solid curves) a change in molecular configuration through the phase transition. (b) Thetemperature-dependent phase diagram for 0.1 (), 0.2 (), 0.4 (♦) and 0.6 M () NaCl.formation of a liquid crystal rather than aggregation phenomena. In addition to lightmicroscopy, macroscopic phase separation experiments were carried out to obtain a preciseestimate of the phase boundaries.For phase equilibrium experiments, biphasic samples with coexisting isotropic and liquidcrystalline phases were prepared. The volume fraction of the anisotropic phase increaseslinearly from zero for isotropic samples to unity for the liquid crystal. The critical boundarieswere obtained by extrapolation to the concentrations at which the anisotropic phase firstappears ci and the isotropic phase completely disappears ca, respectively. As shown infigure 2, the transition is strongly first order with a broad gap between the phase boundaries.For concentrations below, say, 0.1 M NaCl, the boundaries are rather salt concentrationindependent; for higher salt concentrations they show a small increase with increasing ionicstrength. This behaviour is very different from the one observed for linear DNA, where thephase diagram shows a relatively narrow phase gap and a strong dependence on ionic strength.Furthermore, for the supercoil the boundaries are significantly lower than for linear DNA [8].In contrast to the weak salt dependence, the boundaries are very sensitive to temperature.At a sufficiently high, fixed DNA concentration, it is possible to convert the anisotropic intothe isotropic phase by raising the temperature; the liquid crystal reappears once the solution iscooled below the clearing point. We have checked that this clearing effect is fully reversible,so there are no irreversible changes involved. The clearing point depends on overall DNAconcentration as shown in figure 2. The temperature dependence of the phase diagram is verydifferent from the one observed for 50 nm length linear DNA, where the boundaries wereobserved to be weakly dependent on temperature only [9].The assignment of the anisotropic phase has caused some confusion in the literature,because non-aligned samples do not show the characteristic fingerprint-like textures expectedfor a cholesteric molecular organization (see figure 3(a)) [3, 10]. Due to the negativediamagnetic susceptibility of the bases, DNA arranges with its long axis perpendicular to thedirection of a magnetic field [11]. For linear DNA, this effect can be used to induce macroscopicalignment [12]. However, supercoiled DNA has a very weak diamagnetic anisotropy, becausethe axis of the duplex follows a classical plectonemic trajectory such that the anisotropy of thebases averages out [10]. We have succeeded in inducing macroscopic alignment by exposingthe preparation slide for more than 12 h in a 14 T field. As displayed in figure 3(b), a typicalS186 J R C van der Maarel et al(a) (b)Figure 3. Polarized light microscopy textures for 15 g of pUC18 dm−3 in 0.1 M NaCl. (a) Non-aligned; 1000×. (b) As (a), but after prolonged exposure to a 14 T magnetic field with directionparallel to the slide with the result that the cholesteric axis is perpendicular to the line of view.(This figure is in colour only in the electronic version)Figure 4. (a) Structure factor S versus momentum transfer q for 3 (), 6 (♦), 11 () and27 g DNA−3 (◦) in 0.05 M NaCl. (b) As (a), but for the normalized structure factor. Curvesrepresent a fit with parameters in table 1. To avoid overlap, the data are shifted along the y-axis.cholesteric, fingerprint-like texture is now observed, provided that the direction of the magneticfield was parallel to the slide with the result that the cholesteric axis is oriented perpendicularto the line of view. The cholesteric pitch, measured for twice the distance between the fringes,amounts to 4 µm, which is about twice the value observed for linear DNA [9].4. Neutron scatteringSANS from pUC18 plasmid in 0.05 M NaCl was measured at the Institute Laue-Langevin,Grenoble, and Laboratoire Léon Brillouin, CE de Saclay, France, and the results are displayedin figure 4.In our experiments, the range of momentum transfer q , which is defined by the wavelengthλ of the radiation and the angle θ between the incident and scattered beam according toq = 4π/λ sin(θ/2), exceeds L−1 by at least an order of magnitude. In this high-q range, thescattering is sensitive to interference over an extent of the order of r and p (qr ≈ 1 and qp ≈ 1)and effects of overall flexibility and/or branching of the supercoil are beyond observation. WeSupercoiled DNA; plectonemic structure and liquid crystal formation S187Table 1. Parameters resulting from the fit of the structure factor to the scattering data. Note thatthe margins are related to a variation in molecular shape.c (g dm−3) r (nm) p (nm) α (deg) 2L/ l Wr A2 (106 nm3)3 10 ± 4 21 ± 9 65 0.91 −6 ± 3 —6 9 ± 5 14 ± 7 57 0.84 −7 ± 4 0.5511 8 ± 4 13 ± 7 59 0.86 −9 ± 5 1.2227 5 ± 3 6 ± 4 52 0.79 −14 ± 10 1.92can accordingly use the high-q approximate form of the form factor of a regular superhelix [4]:P(q) = πq L[J 20 (qr) + 2qp/2∑k=1J 22k((q2 − 4k2/p2)1/2r)], q L  1. (5)The effect of the cross-sectional radius of gyration rp of the duplex is taken into account bymultiplication of equation (5) with the form factor pertaining to the cross-section:Pc(q) = [2J1(qrp)/(qrp)]2. (6)Note that P(q) is sensitive to the DNA density per unit length projected on the superhelicalaxis L−1. However, for qr  1 and qp  1 the scattering is essentially given by a singlestrand of the superhelix, which is proportional to the density per unit contour length l−1. Inboth regimes, the form factor displays the characteristic q−1-scaling for rodlike particles, butthe prefactor drops from L−1 to l−1. As we will see shortly, our data do not comply with suchidealized structure as depicted in figure 1. We will accordingly assume a Gaussian distributionin r with standard deviation σr and a distance of closest approach of the two opposing strandsin the superhelix 2rm (rm ≈ 2 nm). It is also assumed that α is constant, which implies that pis proportional to r with a proportionality factor given by equation (3). We have checked thata model in which p and r are allowed to fluctuate independently does not give a better fit.Interactions among supercoils are accounted for in the second virial approximation and thetotal scattering function takes hence the formS(q) = N P(q)/(1 + 2A2ρP(q)), (7)with N the number of bases, A2 the second virial coefficient and ρ the DNA density.The effect of interactions among supercoils on the structure factor is vanishing smallfor ρ less than, say, 3 g of DNA dm−3 (i.e. ρ A2 ≈ 0). For samples with higher plasmidconcentration, progressive interactions result in a suppression of the intensity at smaller q-values. The agreement with second virial theory and the absence of an interaction peakindicate that the supercoils do not interact too strongly. Due to the presence of a significantdistribution in r and p, the structure factors do not exhibit strong oscillatory behaviour. Theydo show, however, the anticipated q−1-scaling and the drop in prefactor from L−1 to l−1 withincreasing q . For q exceeding, say, 1 nm−1, the structure factors show the characteristicdeviation from q−1-scaling related to the cross-section of the duplex with rp = 0.8 nm.The plectonemic structure is most clearly demonstrated in figure 4(b), where the structurefactors are normalized in such a way that they go to unity at high q . The normalized structurefactor extrapolates to 2l/L for q → 0 and in the absence of interactions. In the fit procedure, wehave optimized r , its distribution width σr , α and A2. The other parameters are derived throughequation (3) and standard variance propagation. Note that the margins are not related to error,but rather to variation in molecular shape. The main contribution comes from the presence ofa distribution of topoisomers. Other sources are thermal fluctuations and partitioning of DNAover coexisting isotropic and liquid crystalline phases.S188 J R C van der Maarel et alWith increasing concentration through the phase transition, r and p are seen to decreasesignificantly. As a result of the (near) constancy of α, Wr decreases and the number ofsuperhelical turns increases (Wr = −n sin α). According to the fact that through equation (1)the sum of the excess twist and the writhe are conserved, this decrease in Wr should becompensated by a positive twist exerted on the duplex if Lk is conserved. Apart from thechange in physical size of the supercoil, the associated increase in molecular free energy is ofgreat importance in controlling the phase boundaries.5. Discussion and conclusionsThe phase behaviour is explained by considering the interplay between excluded volume andorientation order of a system of uniformly charged, wormlike cylinders. To decrease excludedvolume, the system increases anisotropy with a concurrent decrease in size of the supercoil.With a bending persistence length of the supercoil around 100 nm, we are in the very flexiblechain limit and effects of overall flexibility are expected to be moderate. Due to counterioncondensation, the effective charge of the supercoil is quite low. The electrostatic contributionis accordingly evaluated as a thermodynamic perturbation in the second virial approximation,whereas the hard-core contribution is evaluated with scaled particle theory to include higher-order terms [13]. In the analysis we will neglect branching of the supercoil, as its effect on thephase boundaries is unknown.We first assumed that the topology does not change through the phase transition, i.e. theboundaries are calculated with r = 10 nm and α = 65◦ pertaining to the isotropic phase. Asshown by the dashed curves in figure 2, the conventional narrow phase gap is obtained. Thepredictions can be improved if in the liquid crystal r and α are reduced to 7.5 nm and 58◦,respectively (solid curves), in accordance with the scattering results. Due to the decrease inexcluded volume and increase in molecular free energy through the effect on the chemicalpotentials, ca is shifted towards higher concentrations and is now in reasonable agreementwith the data. The prediction for ci is unaffected, however, because the dimensions in theisotropic phase were kept at their original values. With increasing temperature, the boundariesshift to higher concentrations, which indicates that the excluded volume decreases. Indeed,the shift can be reproduced by a small decrease in r . The solid curves in figure 2(b) connectthe predictions with optimized r = 7.5, 6.9 and 6.4 nm at 298, 308 and 328 K, respectively,so ca is reproduced.The broadening of the phase gap can be partially explained by theory including a decreasein size of the supercoil through the phase transition. The theoretical results compare favourablywith ca , but they fail to predict ci . This is probably related to branching in the isotropic phase,which results in an increase in excluded volume and shift of the corresponding boundariestowards lower concentrations. In the liquid crystal, branching is presumably suppressed dueto the spatial confinement. An explanation for the thermal phase diagram can be found in thetwist energy storing property of the supercoil and changes in flexibility of the duplex. Withincreasing temperature, the flexibility increases due to increased breathing of the base pairs.As a consequence of the associated decrease in elastic energy, the superhelix can be moretightly interwound, which results in a smaller excluded volume and a reversible shift of theboundaries towards higher packing fractions.References[1] Livolant F and Leforestier A 1996 Prog. Polym. Sci. 21 1115[2] Onsager L 1949 Ann. NY Acad. Sci. 51 627Supercoiled DNA; plectonemic structure and liquid crystal formation S189[3] Reich Z E, Wachtel J and Minsky A 1994 Science 264 1460[4] Zakharova S S, Jesse W, Backendorf C, Egelhaaf S U, Lapp A and van der Maarel J R C 2002 Biophys. J. 831106[5] Zakharova S S, Jesse W, Backendorf C and van der Maarel J R C 2002 Biophys. J. 83 1119[6] White J H 1969 Am. J. Math. 91 693[7] Boles T C, White J H and Cozzarelli N R 1990 J. Mol. Biol. 213 931[8] Kassapidou K, Jesse W, van Dijk J A P P and van der Maarel J R C 1998 Biopolymers 46 31[9] Rill R L, Strzelecka T E, Davidson M W and van Winkle D H 1991 Physica A 176 87[10] Torbet J and DiCapua E 1989 EMBO J. 8 4351[11] Maret G, Schickfus M V, Mayer A and Dransfeld K 1975 Phys. Rev. Lett. 35 397[12] Brandes R and Kearns D R 1986 Biochemistry 25 5890[13] Sato T and Teramoto A 1996 Adv. Polym. Sci. 126 85

Supercoiled DNA; plectonemic structure and liquid crystal formation

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Supercoiled DNA; plectonemic structure and liquid crystal formation

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