Transcription-driven twin supercoiling of a DNA loop: A Brownian dynamics study

DNA superhelicity

Closing each strand of a DNA duplex upon itself fixes its linking number L. This topological condition couples together the secondary and tertiary structures of the resulting ccDNA topoisomer, a constraint that is not present in otherwise identical nicked or linear DNAs. Fixing L has a range of structural, energetic and functional consequences. Here we consider how L having different integer values (that is, different superhelicities) affects ccDNA molecules. The approaches used are primarily theoretical, and are developed from a historical perspective. In brief, processes that either relax or increase superhelicity, or repartition what is there, may either release or require free energy. The energies involved can be substantial, sufficient to influence many events, directly or indirectly. Here two examples are developed. The changes of unconstrained superhelicity that occur during nucleosome attachment and release are examined. And a simple theoretical model of superhelically driven DNA structural transitions is described that calculates equilibrium distributions for populations of identical topoisomers. This model is used to examine how these distributions change with superhelicity and other factors, and applied to analyze several situations of biological interest.

Two-phase dynamics of DNA supercoiling based on DNA polymer physics

DNA supercoils are generated in genome regulation processes such as transcription and replication and provide mechanical feedback to such processes. Under tension, a DNA supercoil can present a coexistence state of plectonemic and stretched phases. Experiments have revealed the dynamic behaviors of plectonemes, e.g., diffusion, nucleation, and hopping. To represent these dynamics with conformational changes, we demonstrated first the fast dynamics on the DNA to reach torque equilibrium within the plectonemic and stretched phases, and then identified the two-phase boundaries as collective slow variables to describe the essential dynamics. According to the timescale separation demonstrated here, we developed a two-phase model on the dynamics of DNA supercoiling, which can capture physiologically relevant events across timescales of several orders of magnitudes. In this model, we systematically characterized the slow dynamics between the two phases and compared the numerical results with those from the DNA polymer physics-based worm-like chain model. The supercoiling dynamics, including the nucleation, diffusion, and hopping of plectonemes, have been well represented and reproduced, using the two-phase dynamic model, at trivial computational costs. Our current developments, therefore, can be implemented to explore multiscale physical mechanisms of the DNA supercoiling-dependent physiological processes.

Nonequilibrium dynamics and action at a distance in transcriptionally driven DNA supercoiling

We study the effect of transcription on the kinetics of DNA supercoiling in three dimensions by means of Brownian dynamics simulations of a single-nucleotide-resolution coarse-grained model for double-stranded DNA. By explicitly accounting for the action of a transcribing RNA polymerase (RNAP), we characterize the geometry and nonequilibrium dynamics of the ensuing twin supercoiling domains. Contrary to the typical textbook picture, we find that the generation of twist by RNAP results in the formation of plectonemes (writhed DNA) some distance away. We further demonstrate that this translates into an "action at a distance" on DNA-binding proteins; for instance, positive supercoils downstream of an elongating RNAP destabilize nucleosomes long before the transcriptional machinery reaches the histone octamer. We also analyze the relaxation dynamics of supercoiled double-stranded DNA, and characterize the widely different timescales of twist diffusion, which is a simple and fast process, and writhe relaxation, which is much slower and entails multiple steps.

Requirements for DNA-Bridging Proteins to Act as Topological Barriers of the Bacterial Genome

Bacterial genomes have been shown to be partitioned into several-kilobase-long chromosomal domains that are topologically independent from each other, meaning that change of DNA superhelicity in one domain does not propagate to neighbors. Both in vivo and in vitro experiments have been performed to question the nature of the topological barriers at play, leading to several predictions on possible molecular actors. Here, we address the question of topological barriers using polymer models of supercoiled DNA chains that are constrained such as to mimic the action of predicted molecular actors. More specifically, we determine under which conditions DNA-bridging proteins may act as topological barriers. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. As a result, we find that DNA-bridging proteins must exert rather strong constraints on their binding sites; they must block the diffusion of the excess of twist through the two binding sites on the DNA molecule and, simultaneously, prevent the rotation of one DNA segment relative to the other one. Importantly, not all DNA-bridging proteins satisfy this second condition. For example, single bridges formed by proteins that bind DNA nonspecifically, like H-NS dimers, are expected to fail with this respect. Our findings might also explain, in the case of specific DNA-bridging proteins like LacI, why multiple bridges are required to create stable independent topological domains. Strikingly, when the relative rotation of the DNA segments is not prevented, relaxation results in complex intrication of the two domains. Moreover, although the value of the torsional stress in each domain may vary, their differential is preserved. Our work also predicts that nucleoid-associated proteins known to wrap DNA must form higher protein-DNA complexes to efficiently work as topological barriers.

Fis protein forms DNA topological barriers to confine transcription-coupled DNA supercoiling in Escherichia coli

Previously, we demonstrated that transcription-coupled DNA supercoiling (TCDS) potently activated or inhibited nearby promoters in Escherichia coli even in the presence of all four DNA topoisomerases, suggesting that DNA topoisomerases are not the only factors regulating TCDS. A different mechanism exists to confine this localized DNA supercoiling. Using an in vivo system containing the TCDS-activated leu-500 promoter (Pleu-500 ), we find that the nucleoid-associated Fis protein potently inhibits the TCDS-mediated activation of Pleu-500 . We also find that deletion of the fis gene significantly enhances TCDS-mediated inhibition of transcription of three genes purH, yieP, and yrdA divergently coupled to different rrn operons in the early log phase. These results suggest that Fis protein forms DNA topological barriers upon binding to its recognition sites, blocks TCDS diffusion, and potently inhibits the TCDS-activated Pleu-500 .

Dynamical control of denaturation bubble nucleation in supercoiled DNA minicircles

We examine the behavior of supercoiled DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, in which supercoiling favors thermally assisted DNA denaturation bubbles of nanometer size and controls their lifetime. Mesoscopic modeling and accelerated dynamics simulations allow us to overcome the limitations of atomistic simulations encountered in such systems, and offer detailed insight into the thermodynamic and dynamical properties associated with the nucleation and closure mechanisms of long-lived thermally assisted denaturation bubbles which do not stem from bending- or torque-driven stress. Suitable tuning of the degree of supercoiling and size of specifically designed microDNA is observed to lead to the control of opening characteristic times in the millisecond range, and closure characteristic times ranging over well distinct timescales, from microseconds to several minutes. We discuss how our results can be seen as a dynamical bandwidth which might enhance selectivity for specific DNA binding proteins.

Transient and dynamic DNA supercoiling potently stimulates the leu-500 promoter in Escherichia coli

The inactive prokaryotic leu-500 promoter (P_leu-500) contains a single A-to-G point mutation in the -10 region of the leucine operon promoter, which causes leucine auxotrophy. This promoter can be activated by (-) DNA supercoiling in Escherichia coli topA strains. However, whether this activation arises from global, permanent, or transient, dynamic supercoiling is still not fully understood. In this article, using a newly established in vivo system carrying a pair of divergently coupled promoters, i.e. an IPTG-inducible promoter and P_leu-500 that control the expression of lacZ and luc (the firefly luciferase gene), respectively, we demonstrate that transient, dynamic (-) DNA supercoiling provided by divergent transcription in both wild-type and topA strains can potently activate P_leu-500 We found that this activation depended on the promoter strength and the length of RNA transcripts, which are functional characteristics of transcription-coupled DNA supercoiling (TCDS) precisely predicted by the twin-supercoiled domain model of transcription in which a (+) supercoiled domain is produced ahead of the RNA polymerase and a (-) supercoiled domain behind it. We also demonstrate that TCDS can be generated on topologically open DNA molecules, i.e. linear DNA molecules, in Escherichia coli, suggesting that topological boundaries or barriers are not required for the production of TCDS in vivo This work demonstrates that transient, dynamic TCDS by RNA polymerases is a major chromosome remodeling force in E. coli and greatly influences the nearby, coupled promoters/transcription.

Simulation of DNA Supercoil Relaxation

Several recent single-molecule experiments observe the response of supercoiled DNA to nicking endonucleases and topoisomerases. Typically in these experiments, indirect measurements of supercoil relaxation are obtained by observing the motion of a large micron-sized bead. The bead, which also serves to manipulate DNA, experiences significant drag and thereby obscures supercoil dynamics. Here we employ our discrete wormlike chain model to bypass experimental limitations and simulate the dynamic response of supercoiled DNA to a single strand nick. From our simulations, we make three major observations. First, extension is a poor dynamic measure of supercoil relaxation; in fact, the linking number relaxes so fast that it cannot have much impact on extension. Second, the rate of linking number relaxation depends upon its initial partitioning into twist and writhe as determined by tension. Third, the extensional response strongly depends upon the initial position of plectonemes.

Stochastic Model of Supercoiling-Dependent Transcription

We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix and that these enzymes bind more favorably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter regime, the model displays transcriptional bursts, waves of supercoiling, and up regulation of divergent or bidirectional genes. It also predicts that topological enzymes which relax twist and writhe should provide a pathway to down regulate transcription.

Transcription-coupled DNA supercoiling in defined protein systems and in E. coli topA mutant strains

Transcription by RNA polymerases can stimulate (-) DNA supercoiling both in vitro and in Escherichia coli topA strains. This phenomenon has been successfully explained by a "twin-supercoiled-domain" model of transcription in which (+) supercoils are produced in front of the transcribing RNA polymerase and (-) supercoils behind it. Previously, it has been shown that certain sequence-specific DNA-binding proteins potently stimulate transcription-coupled DNA supercoiling (TCDS) in an in vitro protein system. These results are consistent with a topological barrier model where certain nucleoprotein complexes can form topological barriers that impede the diffusion and merger of independent chromosomal supercoil domains. Indeed, recent biochemical and single-molecule results demonstrated the existence of nucleoprotein-based DNA topological barriers, which are capable of dividing a DNA molecule into different topological domains. Additionally, recent in vivo studies showed that a transcriptional ensemble (including the transcribing RNA polymerase and the RNA transcript) alone is sufficient to cause a change in local DNA superhelicity. This topological change in local chromosome structure should have a great impact on the conformation and function of critical DNA sequence elements, such as promoters and DNA replication origins. In this article, we will also review recent progress by which TCDS is a critical stimulating force to activate transcription initiation from weak promoters, such as the Salmonella typhimurium leu-500 promoter.

Dependence of transcription-coupled DNA supercoiling on promoter strength in Escherichia coli topoisomerase I deficient strains

Transcription by RNA polymerase can induce the formation of hypernegatively supercoiled DNA in vitro and in vivo. This phenomenon has been nicely explained by a "twin-supercoiled-domain" model of transcription where a positively supercoiled domain is generated ahead of the RNA polymerase and a negatively supercoiled domain behind it. In Escherichia coli topA strains, DNA gyrase selectively converts the positively supercoiled domain into negative supercoils to produce hypernegatively supercoiled DNA. In this article, in order to examine whether promoter strength affects transcription-coupled DNA supercoiling (TCDS), we developed a two-plasmid system in which a linear, non-supercoiled plasmid was used to express lac repressor constitutively while a circular plasmid was used to gage TCDS in E. coli cells. Using this two-plasmid system, we found that TCDS in topA strains is dependent on promoter strength. We also demonstrated that transcription-coupled hypernegative supercoiling of plasmid DNA did not need the expression of a membrane-insertion protein for strong promoters; however, it might require co-transcriptional synthesis of a polypeptide. Furthermore, we found that for weak promoters the expression of a membrane-insertion tet gene was not sufficient for the production of hypernegatively supercoiled DNA. Our results can be explained by the "twin-supercoiled-domain" model of transcription where the friction force applied to E. coli RNA polymerase plays a critical role in the generation of hypernegatively supercoiled DNA.

A multiscale dynamic model of DNA supercoil relaxation by topoisomerase IB

In this study, we report what we believe to be the first multiscale simulation of the dynamic relaxation of DNA supercoils by human topoisomerase IB (topo IB). We leverage our previous molecular dynamics calculations of the free energy landscape describing the interaction between a short DNA fragment and topo IB. Herein, this landscape is used to prescribe boundary conditions for a computational, elastodynamic continuum rod model of a long length of supercoiled DNA. The rod model, which accounts for the nonlinear bending, twisting, and electrostatic interaction of the (negatively charged) DNA backbone, is extended to include the hydrodynamic drag induced by the surrounding physiological buffer. Simulations for a 200-bp-long DNA supercoil in complex with topo IB reveal a relaxation timescale of ∼0.1-1.0 μs. The relaxation follows a sequence of cascading reductions in the supercoil linking number (Lk), twist (Tw), and writhe (Wr) that follow companion cascading reductions in the supercoil elastic and electrostatic energies. The novel (to our knowledge) multiscale modeling method may enable simulations of the entire experimental setup that measures DNA supercoiling and relaxation via single molecule magnetic trapping.

DNA stress and strain, in silico, in vitro and in vivo

A vast literature has explored the genetic interactions among the cellular components regulating gene expression in many organisms. Early on, in the absence of any biochemical definition, regulatory modules were conceived using the strict formalism of genetics to designate the modifiers of phenotype as either cis- or trans-acting depending on whether the relevant genes were embedded in the same or separate DNA molecules. This formalism distilled gene regulation down to its essence in much the same way that consideration of an ideal gas reveals essential thermodynamic and kinetic principles. Yet just as the anomalous behavior of materials may thwart an engineer who ignores their non-ideal properties, schemes to control and manipulate the genetic and epigenetic programs of cells may falter without a fuller and more quantitative elucidation of the physical and chemical characteristics of DNA and chromatin in vivo.

Persistence lengths of DNA obtained from Brownian dynamics simulations

The persistence length of DNA has been studied for decades; however, experimentally obtained values of this quantity have not been entirely consistent. We report results from Brownian dynamics simulations that address this issue, validating and demonstrating the utility of an explicitly double-stranded model for mesoscale DNA dynamics. We find that persistence lengths calculated from rotational relaxation increase with decreasing ionic strength, corroborating experimental evidence, but contradicting results obtained from wormlike coil assumptions. Further, we find that natural curvature does not significantly affect the persistence length, corroborating cyclization efficiency measurements, but contradicting results from cryo-EM.

Brownian dynamics of double-stranded DNA in periodic systems with discrete salt

Numerical models of mesoscale DNA dynamics relevant to in vivo scenarios require methods that incorporate important features of the intracellular environment, while maintaining computational tractability. Because the explicit inclusion of ions leads to electrostatic calculations that scale as the square of the number of charged particles, such models typically handle these calculations using low-potential, mean-field approaches, rather than by considering the discrete interactions of ions. This allows approximation of the long-range, screened self-repulsion of DNA, but is unable to capture detailed electrostatic phenomena, such as short-range attractions mediated by ion-ion correlations. Here, we develop a dynamical model of explicitly double-stranded, sequence-specific DNA in a bulk environment consisting of other polyions and explicitly represented counterions and coions. DNA is represented as two interwound chains of charged Stokes spheres, and ions as free, monovalently charged Stokes spheres. Brownian dynamics simulations performed at salt concentrations of 0.1, 1, 10, and 100 mM demonstrate this model captures anticipated behaviors of the system, including increasing compaction of the polyion by the ionic atmosphere with increasing ionic strength. The decay of the distance dependence of the ion concentrations as one moves away from the polyion approaches their equilibrium values in quantitative agreement with predictions of Poisson-Boltzmann theory. The simulation results also demonstrate quantitative agreement with experimental measurements of the persistence length of B-DNA, which increases significantly at low ionic strengths. The model also captures behaviors intimating the importance of explicitly representing ionic and polyionic structure. These include penetration of the polyion interior by both coions and counterions, and counterion-mediated accumulation of coions near the surface of the polyion. Such phenomena are likely to play an important role in the formation of alternative DNA secondary structures, suggesting the present methods will prove valuable to dynamic models of superhelical stress-induced DNA structural transitions.

Brownian dynamics simulations of sequence-dependent duplex denaturation in dynamically superhelical DNA

The topological state of DNA in vivo is dynamically regulated by a number of processes that involve interactions with bound proteins. In one such process, the tracking of RNA polymerase along the double helix during transcription, restriction of rotational motion of the polymerase and associated structures, generates waves of overtwist downstream and undertwist upstream from the site of transcription. The resulting superhelical stress is often sufficient to drive double-stranded DNA into a denatured state at locations such as promoters and origins of replication, where sequence-specific duplex opening is a prerequisite for biological function. In this way, transcription and other events that actively supercoil the DNA provide a mechanism for dynamically coupling genetic activity with regulatory and other cellular processes. Although computer modeling has provided insight into the equilibrium dynamics of DNA supercoiling, to date no model has appeared for simulating sequence-dependent DNA strand separation under the nonequilibrium conditions imposed by the dynamic introduction of torsional stress. Here, we introduce such a model and present results from an initial set of computer simulations in which the sequences of dynamically superhelical, 147 base pair DNA circles were systematically altered in order to probe the accuracy with which the model can predict location, extent, and time of stress-induced duplex denaturation. The results agree both with well-tested statistical mechanical calculations and with available experimental information. Additionally, we find that sites susceptible to denaturation show a propensity for localizing to supercoil apices, suggesting that base sequence determines locations of strand separation not only through the energetics of interstrand interactions, but also by influencing the geometry of supercoiling.

Human topoisomerase IIalpha rapidly relaxes positively supercoiled DNA: implications for enzyme action ahead of replication forks

Movement of the DNA replication machinery through the double helix induces acute positive supercoiling ahead of the fork and precatenanes behind it. Because topoisomerase I and II create transient single- and double-stranded DNA breaks, respectively, it has been assumed that type I enzymes relax the positive supercoils that precede the replication fork. Conversely, type II enzymes primarily resolve the precatenanes and untangle catenated daughter chromosomes. However, studies on yeast and bacteria suggest that type II topoisomerases may also function ahead of the replication machinery. If this is the case, then positive DNA supercoils should be the preferred relaxation substrate for topoisomerase IIalpha, the enzyme isoform involved in replicative processes in humans. Results indicate that human topoisomerase IIalpha relaxes positively supercoiled plasmids >10-fold faster than negatively supercoiled molecules. In contrast, topoisomerase IIbeta, which is not required for DNA replication, displays no such preference. In addition to its high rates of relaxation, topoisomerase IIalpha maintains lower levels of DNA cleavage complexes with positively supercoiled molecules. These properties suggest that human topoisomerase IIalpha has the potential to alleviate torsional stress ahead of replication forks in an efficient and safe manner.

DNA Mechanics

We review the history of DNA mechanics and its analysis. We evaluate several methods to analyze the structures of superhelical DNA molecules, each predicated on the assumption that DNA can be modeled with reasonable accuracy as an extended, linearly elastic polymer. Three main approaches are considered: mechanical equilibrium methods, which seek to compute minimum energy conformations of topologically constrained molecules; statistical mechanical methods, which seek to compute the Boltzmann distribution of equilibrium conformations that arise in a finite temperature environment; and dynamic methods, which seek to compute deterministic trajectories of the helix axis by solving equations of motion. When these methods include forces of self-contact, which prevent strand passage and preserve the topological constraint, each predicts plectonemically interwound structures. On the other hand, the extent to which these mechanical methods reliably predict energetic and thermodynamic properties of superhelical molecules is limited, in part because of their inability to account explicitly for interactions involving solvent. Monte Carlo methods predict the entropy associated with supercoiling to be negative, in conflict with a body of experimental evidence that finds it is large and positive, as would be the case if superhelical deformations significantly disrupt the ordering of ambient solvent molecules. This suggests that the large-scale conformational properties predicted by elastomechanical models are not the only ones determining the energetics and thermodynamics of supercoiling. Moreover, because all such models that preserve the topological constraint correctly predict plectonemic interwinding, despite these and other limitations, this constraint evidently dominates energetic and thermodynamic factors in determining supercoil geometry. Therefore, agreement between predicted structures and structures obtained experimentally, for example, by electron microscopy, does not in itself provide evidence for the correctness or completeness of any given model of DNA mechanics.