PRL 110, 148105 (2013)

week ending 5 APRIL 2013

PHYSICAL REVIEW LETTERS

Thermodynamics of Writhe in DNA Minicircles from Molecular Dynamics Simulations Jonathan S. Mitchell1 and Sarah A. Harris2 1

Section de Mathematiques, Ecole Polytechnique Federale de Lausanne, Lausanne 1015, Switzerland School of Physics and Astronomy and Astbury Centre for Structural and Molecular Biology, University of Leeds, Leeds LS2 9JT, United Kingdom (Received 13 November 2012; published 5 April 2013)

2

DNA supercoiling plays a role in genetic control by imposing torsional stress. This can induce writhe, which changes the global shape of the DNA. We have used atomistic molecular dynamics simulations to partition the free energy changes driving the writhing and unwrithing transitions in supercoiled minicircle DNA. The calculations show that while writhing is energetically driven, the unwrithing transition occurs because the circular state has a higher configurational entropy than the plectoneme. Writhing improves the van der Waals interactions between stacked bases, but can be suppressed by electrostatic repulsion within the negatively charged backbone strands in low salt conditions where electrostatic screening is poor. The free energy difference between circular and plectonemic DNA is determined by such a delicate balance of opposing thermodynamic terms that any perturbation in the environment, such as a change in salt concentration, can be sufficient to convert between these two states. This switchable behavior provides a mechanism for supercoiled DNA to store and communicate biological information physically as well as chemically. DOI: 10.1103/PhysRevLett.110.148105

PACS numbers: 87.15.La, 87.15.ap

The genetic information necessary to both build and operate a cell is encoded within its DNA sequence. To date, the genomes of around 2000 organisms, including humans, have been sequenced [1]. Although it is increasingly straightforward to determine the DNA sequence that comprises a genome, it is proving far more difficult to interpret this information in terms of the control and function of the cell at the molecular level. Consequently, the organization of the proteome cannot be predicted from the genome, even in genome-reduced bacteria [2]. In the smallest self-replicating genome Mycoplasma genitalium, none of the usual transcription factor proteins that switch genes on and off or the alternative sigma factors that specify which gene promoters are recognized by prokaryotic RNA polymerases have been identified [3,4]. The genome of this organism, within conventional schemes of regulation, therefore does not appear to contain sufficient chemical information in its DNA sequence to explain how it is controlled. One explanation for the complex regulatory behavior of relatively simple genomes such as M. genitalium is that information is not only stored by the chemical nature of the DNA bases, but also by the physical properties of the DNA itself, as may also be the case in more complex eukaryotic organisms [5]. In most bacteria, DNA is stored in an underwound supercoiled state [6]. First, this serves to package the genome because the torsional stress associated with this untwisting is relieved by writhe, which compacts the biopolymer. In closed DNA loops, the conversion of excess helical twist into writhe (Wr) is subject to the topological condition Lk ¼ Tw þ Wr, where the linking number Lk (the number of times the two backbone strands 0031-9007=13=110(14)=148105(5)

wrap around each other) is invariant unless strand passage occurs. Twist (Tw) describes the coiling of the strands around the central axis, whereas writhe quantifies the coiling of the central axis itself. Supercoiling may also be an essential method of transcriptional control. Although M. genitalium can function without many of the proteins present in more complex organisms, it does possess the enzymes common to most bacteria that control DNA superhelical stress, namely DNA gyrase and topoisomerase I [4]. DNA gyrase, which burns the energy rich molecule adenosine triphosphate (ATP) to introduce negative supercoils into bacterial DNA, connects the superhelical stress in the DNA to cellular metabolism, as it is more active when ATP is readily available [7]. Negative supercoiling in both prokaryotes and eukaryotes promotes the separation of the double helix into single strands, and can therefore control the ability of the transcriptional machinery to access the genetic code [8]. The process of transcription itself also changes the superhelical density, which provides a molecular mechanism for the cell to remember which genes have been recently transcribed, and for messages about transcription levels in individual genes to be communicated to other genes located nearby via the DNA itself [9]. Therefore, understanding the mechanical response of DNA to superhelical stress will be pivotal in quantifying the role of supercoiling in cellular control in all organisms, and in revealing the physical mechanisms by which this is achieved. Writhing is a dramatic consequence of DNA supercoiling which affects the global shape of the DNA and can bring previously distal sequences into close proximity. A cryo-electron microscopy (cryo-EM) study of DNA

148105-1

Ó 2013 American Physical Society

PRL 110, 148105 (2013)

PHYSICAL REVIEW LETTERS

minicircles showed that an underwound 178 bp DNA loop adopted a circular configuration in low salt, but buckled into a plectoneme in high salt [10]. Based on these experimental observations, we have used atomistic molecular dynamics (MD) simulations to quantify the thermodynamic changes in negatively supercoiled DNA minicircles that occur both when the DNA writhes and when it opens up into an undertwisted circular structure using an in silico model system that switches reversibly between these two states in a controllable manner through changes in salt concentration, as is observed by cryo-EM. In the experiments, however, the DNA was of random sequence, and it was not possible to identify which sections formed the apices of the plectoneme, or even whether certain motifs were favored over others. Therefore, we have designed a simplified 178 bp sequence which folds in a predictable manner. The designed loop contains four distinct quarters by using the sequence dðGCÞ45 dðGGÞ44 dðGCÞ45 dðGGÞ44 , as shown in Fig. 1(a). Sequence-dependent stiffness analysis on the proteinDNA crystal structure database [11], as well as explicit and implicit solvent molecular dynamics simulations have all shown poly d(GG) to be stiffer than poly d(GC) [12,13]. Furthermore, recent magnetic tweezers experiments have suggested that the position of plectoneme formation in long supercoiled DNA molecules is not random but depends on the sequence-dependent mechanical properties [14]. It is therefore expected that the dðGCÞ45 quarters will reproducibly occupy the highly curved apices of any plectoneme formed. The choice of more stable GC-rich sequences minimizes the possibility of denaturation or defect formation due to underwinding contributing to the thermodynamics of writhing in this study [15].

FIG. 1 (color online). (a) DNA configurations sampled from the MD trajectory in alternating high and low salt conditions. GpC quarters are colored white and GpG quarters black. (b) DNA writhe as a function of time (blue, dark grey) and distance between the two base pairs at the center of the GpG quarters (red, light grey).

week ending 5 APRIL 2013

An implicit solvent model was used to carry out the MD simulations, since this allows the salt concentration to be easily controlled through adjustment of the Debye-Huckel screening parameter [16]. Simulation protocols using the AMBER suite of programs [16] were as described in the Supplemental Material [17] and in previous work [15,18]. We employed the parmbsc0 force field [19] which is widely used for simulating DNA and which has been shown to provide DNA flexibilities that are in good agreement with the alternative CHARMM27 forcefield [12]. The starting configuration of the loop was an undertwisted circle with the base pair step twist uniformly distributed. Initially the Debye-Huckel screening parameter was set to reproduce high (1 mol) monovalent salt conditions which ˚ . In this environequates to a Debye screening length of 3 A ment the loop immediately buckled into a plectonemic figure of eight [Fig. 1(a)]. The solvent conditions were then abruptly altered to reproduce low salt conditions (0.01 mol monovalent salt), which increased the Debye ˚ and resulted in a sharp transition screening length to 32 A back to a circular configuration. This process of altering the salt followed by 2 ns MD was repeated a further five times resulting each time in the same change in configuration [Fig. 1(a)]. This provided twelve independent sets of conformations, where six sets of writhed DNA configurations were obtained at high salt and six sets of unwrithed conformers were obtained under low salt conditions. Transitions between circular and plectonemic configurations were quantified by calculating the writhe [Fig. 1(b)]. The helical axis was determined from the base pair centres as defined by 3DNA [20], and the writhe of this curve was then calculated using the directional writhe method [21]. Clear transitions between unwrithed (open circular) and writhed (plectonemic) configurations at each change of salt concentration were observed [as shown in Fig. 1(b), in blue]. Measuring the distance between the two base pairs at the center of the dðGGÞ44 quarters showed that they approached each other whenever writhe was induced [as shown in Fig. 1(b) in red]. As expected the stiff dðGGÞ44 quarters formed the straight crossover segments and the more flexible dðGCÞ45 quarters reproducibly formed the apices. This demonstration that sequence-dependent flexibility is indeed capable of determining the tertiary structure of supercoiled DNA has important biological implications. While topology simplifying molecular motors such as topoisomerase II and DNA gyrase act nonspecifically on linear DNA sequences, they preferentially bind bent DNA [22,23]. Consequently, writhing can result in sequence selective recognition not present in relaxed DNA. Given the increasing appreciation that the physical as well as chemical responses of biomolecules are used to store and transfer information, it seems likely that this property of DNA may have been exploited by evolution in gene control [24]. Writhing relieves the torsional stress associated with supercoiling, but at the expense of introducing tight

148105-2

PRL 110, 148105 (2013)

week ending 5 APRIL 2013

PHYSICAL REVIEW LETTERS

localized bends into the DNA. In addition, writhing incurs an electrostatic repulsion where the two nearby sections of the negatively charged sugar-phosphate backbone are forced to cross. The preference for writhed DNA structures in high salt and open circular conformations in low salt observed in the experiments by Bednar et al. was explained as being due to screening of the electrostatic repulsion at the crossover point of the plectoneme [10]. To test this hypothesis using our simulation data, we retrospectively calculated two separate sets of configurational energies (Etot ) for the DNA structures obtained during the 26 ns MD, one using high salt conditions to calculate the electrostatic interactions and the other using low, independent of the original conditions in which these structures occurred. We then compared the configurational energies of the writhed and unwrithed structures (e.g., those obtained using high and low salt in the original simulations, respectively) in each case, as shown in Fig. 2. The two sets of configurational energies as a function of time during the MD are shown in Fig. S2 in the Supplemental Material [17]. We obtained consistently lower total energies for the writhed structures relative to unwrithed in high salt (on average by 139  133 kB T, where the error quoted is the standard deviation, as explained in detail in section S4, in the Supplemental Material [17]), indicating that these were energetically favored. Therefore, the buckling transition from underwound circular to plectoneme on raising the salt concentration in the simulations can be explained in terms of the changing energetics of the minicircle. The preference for unwrithed structures in low salt was less clear, as the average energy difference was only 16:3  134 kB T less.

To provide a physical rationale for the difference in the total energies between writhed and unwrithed DNA conformations measured in both high and low salt, the nonbonded configurational energy was decomposed into the contributions from van der Waals (Evdw ) and electrostatics (Eel ), as shown in Fig. 2. The partitioned energetic components are plotted as a function of time during the MD simulations in Fig. S2 in the Supplemental Material [17], and the average values are provided in Table S2 [17]. The van der Waals energies (which are not affected by changes in electrostatic screening) favor writhing by an average of 257  86 kB T, because the release of torsional stress improves the base stacking interactions within the duplex. Conversely, electrostatics favors the open circle; in low salt, the plectoneme is 283  129 kB T higher in energy due to repulsive interactions within the DNA backbone, but at high salt, this is reduced by a factor of 2.2 by charge screening. These calculations show that optimizing the van der Waals interactions due to base stacking provides the energetic drive for the writhing transition observed at high salt. At low salt, however, this transition is suppressed by electrostatic repulsion, which is sufficiently large in the absence of Debye-Huckel screening that the total energy of writhed and open circular structures is indistinguishable. The salt-dependent electrostatic contribution is itself made up of two separate terms. The first is due to the electrostatic repulsion incurred at the crossing point (Eel-cp ), the second arises because the energetic cost of bending the DNA (Eel-b ) results partially from the negative charges on the backbone, which are screened in high salt. If we assume that most of the reduction in bending stiffness with increased screening will affect the electrostatic energy locally within the DNA circle (Elocal ), while a reduction in the electrostatic repulsion at the crossing point will change the global electrostatic energy (Eel ) of the DNA, then X Elocal ; (1) Eel-b ¼ quarters

Eel  Eel-b ¼ Eel-cp ;

FIG. 2 (color online). The average changes in total energy (Etot ), van der Waals energy (Evdw ), total electrostatic energy (Eel ), bending electrostatic energy (Eele-b ) and electrostatic energy associated with the crossing point (Ecp ) between writhed and unwrithed DNA conformations calculated in high (red, left) and low salt (blue, right). The zero of energy was arbitrarily defined as the average calculated over the first 1 ns of the simulation, which was performed at high salt, and a positive energetic contribution indicates that the plectonemic state was thermodynamically favorable.

(2)

where Elocal is the electrostatic energy calculated for each of the four separate quarters of the designed DNA sequence. Electrostatic energy can be simply mapped onto the DNA sequence in this particular circle because when the loop is writhed the two flexible dðGCÞ45 quarters occupy the bent apices consistently, leaving the stiffer dðGGÞ44 segments to form the crossing. Figure 2 and Fig. S2(e) show that while the electrostatic energy due to strand crossing Eel-cp is negligible in high salt conditions, regardless of whether the circle is writhed or open, in low salt this electrostatic repulsion raises the energy of the writhed conformation relative to the circular loop by 59  35 kB T. However, this is a factor of 3.8 times smaller than the corresponding change in bending energy (Eel-b ). Therefore, the cost of DNA bending at the apices is the

148105-3

PRL 110, 148105 (2013)

PHYSICAL REVIEW LETTERS

dominant electrostatic term suppressing writhe in low salt for circles of this size containing a single crossing within the simulations. The intracellular ionic environment in prokaryotes and eukaryotes varies during cell development, the cell cycle and due to environmental perturbations, which will affect the energy required to compact the nuclear material. Positively charged nucleoid associated proteins such as HU [25] in prokaryotes and the eukaryotic histone proteins [26] are able to control DNA packing by binding electrostatically to bent DNA [8]. Our analysis of the electrostatic changes on DNA writhing shows that this mechanism is so effective because the electrostatic repulsion due to bending, which is neutralized by these nuclear binding proteins, makes such a significant contribution to the thermodynamics of compacted DNA. Although we have successfully identified the energetic driving force for writhing at the atomistic level when the salt concentration is raised, the favorable energetic contribution that occurs in the transition from plectoneme to open circle when the salt concentration is lowered is a factor of 8.5 smaller (and less than the error). This suggests that the DNA is driven into the unwrithed state in low salt in the simulations primarily by an increase in entropy. Our energetic analysis places an upper bound on the entropy penalty of writhing of 139 kB T, otherwise the plectoneme would never be observed (since then the entropy penalty would always outweigh energetic terms that drive buckling). To compare the configurational dynamics of circular and plectonemic states at the level of the DNA sequence, we calculated the configurational entropies of successive 11=12 bp segments comprised of the stiff GpG and flexible GpC elements by separating the trajectory into writhed (observed at high salt) and unwrithed DNA conformations (observed at low salt) and analyzing the thermal fluctuations generated during the MD for these two separate states. Entropies were calculated using the Schlitter covariance matrix method [27], which is described in the Supplemental Material (S5) [17]. The difference in entropies between the writhed and unwrithed conformations for each of the individual GpG and GpC segments are shown in Fig. 3 in blue and red, respectively. For the stiff GpG segments (in blue), 7 out of the 8 segments have a higher entropy in the circular structures, where they are more bent than when forming the straight segments of the plectonemes. Conversely, 6 out of the 8 GpC segments (in red) have a higher entropy in the plectonemes where they form the highly curved apices. Consequently, DNA bending within minicircles is associated with a higher conformational flexibility at the atomistic level in the MD. We hypothesize that this is because bending increases the distance between stacked bases on the outside (long arc) of the DNA circle, which allows them additional room to move within the tightly stacked double helical structure of duplex DNA. Moreover, cyclization experiments carried out on minicircles over a range of temperatures have shown

week ending 5 APRIL 2013

FIG. 3 (color online). The difference in entropy S ¼ Suwr  Swr for each 11=12 bp sequence. Blue (segments 5–8 and13–16) and red (segments 1–4 and 9–12) indicate the stiff d(GG) and the more flexible d(GC) segments, respectively. Entropies were calculated by grouping all equilibrated plectonemic (e.g., the last 1 ns from each of the six sets of conformers) and unwrithed structures into one conformational sample, as described in section S5 of the Supplemental Material [17].

that the bending flexibility increases with temperature [28]. Comparing the total entropies Stot of open circles with plectonemes (which were estimated by summing the entropies of the individual 11=12 bp segments), shows that the circular structure is entropically favorable overall by Stot ¼ 44  21 kB T. Calculating the corresponding free energy differences F ¼ Etot  TStot (see also Fig. S3) shows that the free energy is lower for the circular structures (by 60  18 kB T) in low salt, but in high salt it is lower for the plectonemes (by 95  14 kB T), which demonstrates that our analysis of the underlying thermodynamics is consistent with the switchable salt-dependent behavior of the circles observed in the MD simulations. We have simulated the smallest minicircle (178 bp) shown to undergo a reversible writhing transition in response to changes in salt concentration in in vitro experiments to date. Smaller circles are more convenient computationally not only because their smaller size requires fewer computational resources, but also because they are restricted to two distinct states: open circular, and writhed with a single crossing point. In larger DNA circles additional variables, such as the tightness of the plectoneme, the relative size of the apical loops and the number of crossings, will also influence the free energy and consequently the global shape of the DNA, making it more difficult to unambiguously partition the various thermodynamic contributions. Our calculations show that the writhe of a supercoiled DNA minicircle is controlled at the atomistic level by a delicate balance between the contributions from the van der Waals interactions (which always favor writhe) weighed against the increased configurational entropy of the open circular DNA at the local level and electrostatic repulsion in the plectoneme (which both suppress writhe). The overall sign of the free energy

148105-4

PRL 110, 148105 (2013)

PHYSICAL REVIEW LETTERS

difference depends on the near cancelation of these large, but opposing thermodynamic terms. Consequently, a small change in either one of these contributions can be sufficient to switch the most thermodynamically favorable state from writhed to open circular and vice versa. It is this exquisite sensitivity that enables duplex DNA to be highly responsive to changes in the environment, and provides a mechanism for DNA to store and transfer information not just through the chemistry of its sequence of nucleic acid bases but also by way of the physical properties that the sequence possesses. We acknowledge Charlie Laughton for providing the code to circularize the DNA and to perform the entropy analysis, Tony Maxwell for his advice on the biological aspects of the Letter, and we would like to thank Peter Olmsted and Agnes Noy for their helpful comments on the manuscript.

[1] K. Liolios, I. Chen, K. Mavromatis, N. Tavernarakis, P. Hugenholtz, V. Markowitz, and N. Kyrpides, Nucleic Acids Res. 38, D346 (2009). [2] S. Kuhner et al., Science 326, 1235 (2009). [3] C. Dorman, Mol. Microbiol. 81, 302 (2011). [4] W. Zhang and J. Baseman, Mol. Microbiol. 81, 327 (2011). [5] V. Ortiz and J. J. de Pablo, Phys. Rev. Lett. 106, 238107 (2011). [6] A. Bates and A. Maxwell, DNA Topology (Oxford University Press, New York, 1993). [7] L. Hsieh, J. Rouviere-Yaniv, and K. Drlica, J. Bacteriol. 173, 3914 (1991). [8] A. Travers and G. Muskhelishvili, EMBO Rep. 8, 147 (2007). [9] F. Kouzine, S. Sanford, Z. Elisha-Feil, and D. Levens, Nat. Struct. Mol. Biol. 15, 146 (2008).

week ending 5 APRIL 2013

[10] J. Bednar, P. Furrer, A. Stasiak, J. Dubochet, E. Egelman, and A. Bates, J. Mol. Biol. 235, 825 (1994). [11] W. Olson, A. Gorin, L. Xiang-Jun, L. Hock, and V. Zhurkin, Proc. Natl. Acad. Sci. U.S.A. 95, 11 163 (1998). [12] A. Perez, F. Lankas, F. Luque, and M. Orozco, Nucleic Acids Res. 36, 2379 (2008). [13] Y. Bomble and D. Case, Biopolymers 89, 722 (2008). [14] M. van Loenhout, M. de Grunt, and C. Dekker, Science 338, 94 (2012). [15] S. Harris, C. Laughton, and T. Liverpool, Nucleic Acids Res. 36, 21 (2007). [16] D. A. Case et al., AMBER 10, University of California, San Francisco (2008). [17] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.110.148105 for writhe calculation and a detailed analysis of the thermodynamic decomposition are provided. [18] J. Mitchell and S. Harris, Prog. Theor. Phys. Suppl. 191, 96 (2011). [19] A. Pe´rez, I. Marcha´n, D. Svozil, J. Sponer, T. Cheatmen, III, C. Laughton, and M. Orozco, Biophys. J. 92, 3817 (2007). [20] X.-J. Lu and W. Olson, Nucleic Acids Res. 31, 5108 (2003). [21] F. Fuller, Proc. Natl. Acad. Sci. U.S.A. 68, 815 (1971). [22] M. Oram, A. A. Travers, A. J. Howells, A. Maxwell, and M. L. Pato, J. Bacteriol. 188, 619 (2006). [23] K. Dong and J. Berger, Nature (London) 450, 1201 (2007). [24] D. Levens and C. Benham, Phys. Biol. 8, 035011 (2011). [25] K. Swinger, K. Lemberg, Y. Zhang, and P. Rice, EMBO J. 22, 3749 (2003). [26] K. Luger, A. Mader, R. Richmond, D. Sargent, and T. Richmond, Nature (London) 389, 251 (1997). [27] J. Schlitter, Chem. Phys. Lett. 215, 617 (1993). [28] S. Geggier, A. Kotlyar, and A. Vologodskii, Nucleic Acids Res. 39, 1419 (2011).

148105-5

Thermodynamics of writhe in DNA minicircles from molecular dynamics simulations.

DNA supercoiling plays a role in genetic control by imposing torsional stress. This can induce writhe, which changes the global shape of the DNA. We h...
334KB Sizes 2 Downloads 6 Views