Internal motion of supercoiled DNA: brownian dynamics simulations of site juxtaposition

Bacterial nucleoid is a riddle wrapped in a mystery inside an enigma

Bacterial chromosome, the nucleoid, is traditionally modeled as a rosette of DNA mega-loops, organized around proteinaceous central scaffold by nucleoid-associated proteins (NAPs), and mixed with the cytoplasm by transcription and translation. Electron microscopy of fixed cells confirms dispersal of the cloud-like nucleoid within the ribosome-filled cytoplasm. Here, I discuss evidence that the nucleoid in live cells forms DNA phase separate from riboprotein phase, the "riboid." I argue that the nucleoid-riboid interphase, where DNA interacts with NAPs, transcribing RNA polymerases, nascent transcripts, and ssRNA chaperones, forms the transcription zone. An active part of phase separation, transcription zone enforces segregation of the centrally positioned information phase (the nucleoid) from the surrounding action phase (the riboid), where translation happens, protein accumulates, and metabolism occurs. I speculate that HU NAP mostly tiles up the nucleoid periphery-facilitating DNA mobility but also supporting transcription in the interphase. Besides extruding plectonemically supercoiled DNA mega-loops, condensins could compact them into solenoids of uniform rings, while HU could support rigidity and rotation of these DNA rings. The two-phase cytoplasm arrangement allows the bacterial cell to organize the central dogma activities, where (from the cell center to its periphery) DNA replicates and segregates, DNA is transcribed, nascent mRNA is handed over to ribosomes, mRNA is translated into proteins, and finally, the used mRNA is recycled into nucleotides at the inner membrane. The resulting information-action conveyor, with one activity naturally leading to the next one, explains the efficiency of prokaryotic cell design-even though its main intracellular transportation mode is free diffusion.

Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model's ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.

Traveling Salesman Finds Random Walk: A Curve Reconstruction Algorithm for Supercoiled DNA

DNA supercoiling plays an important role in a variety of cellular processes, including transcription, replication, and DNA compaction. To fully understand these processes, we must uncover and characterize the dynamics of supercoiled DNA. However, supercoil dynamics are difficult to access because of the wide range of relevant length and timescales. In this work, we present an algorithm to reconstruct the arrangement of identical fluorescent particles distributed around a circular DNA molecule, given their three-dimensional trajectories through time. We find that this curve reconstruction problem is analogous to solving the traveling salesman problem. We demonstrate that our approach converges to the correct arrangement with a sufficiently long observation time. In addition, we show that the time required to accurately reconstruct the fluorophore arrangement is reduced by increasing the fluorophore density or reducing the level of supercoiling. This curve reconstruction algorithm, when paired with next-generation super-resolution imaging systems, could be used to access and thereby advance our understanding of supercoil dynamics.

Stochastic curvature of enclosed semiflexible polymers

The conformational states of a semiflexible polymer enclosed in a compact domain of typical size a are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic "curvature" satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a telegrapher's equation whenever 2a/ℓ_{p}>1, where ℓ_{p} is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side a is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. 91, 166102 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.166102] where in this case the critical persistence length is ℓ_{p}^{*}≃a/8 such that the mean-square end-to-end distance exhibits an oscillating behavior for values ℓ_{p}>ℓ_{p}^{*}, whereas for ℓ_{p}<ℓ_{p}^{*} it behaves monotonically increasing.

Confinement induces helical organization of chromosome-like polymers

Helical organization is commonly observed for a variety of biopolymers. Here we study the helical organization of two types of biopolymers, i.e., DNA-like semiflexible and bottle-brush polymers, in a cell-like confined space. A bottle-brush polymer consists of a backbone and side chains emanating from the backbone, resembling a supercoiled bacterial chromosome. Using computer simulations, we calculate 'writhe' distributions of confined biopolymers for a wide range of parameters. Our effort clarifies the conditions under which biopolymers are helically organized. While helical organization is not easily realized for DNA-like biomolecules, cylindrical confinement can induce spiral patterns in a bottle brush, similarly to what was observed with bacterial chromosomes. They also suggest that ring-shape bottle brushes have a stronger tendency for helical organization. We discuss how our results can be used to interpret chromosome experiments. For instance, they suggest that experimental resolution has unexpected consequences on writhe measurements (e.g., narrowing of the writhe distribution and kinetic separation of opposite helical states).

Free Energy Landscape and Dynamics of Supercoiled DNA by High-Speed Atomic Force Microscopy

DNA supercoiling fundamentally constrains and regulates the storage and use of genetic information. While the equilibrium properties of supercoiled DNA are relatively well understood, the dynamics of supercoils are much harder to probe. Here we use atomic force microscopy (AFM) imaging to demonstrate that positively supercoiled DNA plasmids, in contrast to their negatively supercoiled counterparts, preserve their plectonemic geometry upon adsorption under conditions that allow for dynamics and equilibration on the surface. Our results are in quantitative agreement with a physical polymer model for supercoiled plasmids that takes into account the known mechanical properties and torque-induced melting of DNA. We directly probe supercoil dynamics using high-speed AFM imaging with subsecond time and ∼nanometer spatial resolution. From our recordings we quantify self-diffusion, branch point flexibility, and slithering dynamics and demonstrate that reconfiguration of molecular extensions is predominantly governed by the bending flexibility of plectoneme arms. We expect that our methodology can be an asset to probe protein-DNA interactions and topochemical reactions on physiological relevant DNA length and supercoiling scales by high-resolution AFM imaging.

Energy required to pinch a DNA plectoneme

DNA supercoiling plays an important role from a biological point of view. One of its consequences at the supramolecular level is the formation of DNA superhelices named plectonemes. Normally separated by a distance on the order of 10 nm, the two opposite double strands of a DNA plectoneme must be brought closer if a protein or protein complex implicated in genetic regulation is to be bound simultaneously to both strands, as if the plectoneme was locally pinched. We propose an analytic calculation of the energetic barrier, of elastic nature, required to bring closer the two loci situated on the opposed double strands. We examine how this energy barrier scales with the DNA supercoiling. For physically relevant values of elastic parameters and of supercoiling density, we show that the energy barrier is in the k_{B}T range under physiological conditions, thus demonstrating that the limiting step to loci encounter is more likely the preceding plectoneme slithering bringing the two loci side by side.

Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

Jörg Langowski: his scientific legacy and the future it promises

Background

With the passing of Jörg Langowski 6 May 2017 in a sailplane accident, the scientific community was deprived of a strident and effective voice for DNA and chromatin molecular and computational biophysics, for open access publishing and for the creation of effective scientific research networks.

Methods

Here, after reviewing some of Jörg's key research contributions and ideas, we offer through the personal remembrance of his closest collaborators, a deep analysis of the major results of his research and the future directions they have engendered.

Conclusions

The legacy of Jörg Langowski has been to propel a way of viewing biological function that considers living systems as dynamic and in three dimensions. This physical view of biology that he pioneered is now, finally, becoming established also because of his great effort.

DNA Internal Motion Likely Accelerates Protein Target Search in a Packed Nucleoid

Transcription factors must diffuse through densely packed and coiled DNA to find their binding sites. Using a coarse-grained model of DNA and lac repressor (LacI) in the Escherichia coli nucleoid, simulations were performed to examine how LacI diffuses in such a space. Despite the canonical picture of LacI diffusing rather freely, in reality the DNA is densely packed, is not rigid but highly mobile, and the dynamics of DNA dictates to a great extent the LacI motion. A possibly better picture of unbound LacI motion is that of gated diffusion, where DNA confines LacI in a cage, but LacI can move between cages when hindering DNA strands move out of the way. Three-dimensional diffusion constants for unbound LacI computed from simulations closely match those for unbound LacI in vivo reported in the literature. The internal motions of DNA appear to be governed by strong internal forces arising from being crowded into the small space of the nucleoid. A consequence of the DNA internal motion is that protein target search may be accelerated.

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.

Computing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies

Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.

Modeling DNA Dynamics under Steady Deforming Forces and Torques

An algorithm is developed for modeling atom-level dynamics of DNA subjected to steady external torques. For completeness, simulations with steady stretching loads are also considered. The algorithms were tested in Brownian dynamics simulations of discrete wormlike chain models with calibrated elastic properties to confirm that the elastic responses induced are of desired type and magnitude and that no side effects appear. The same methods were next used in a series of 100-ns all-atom MD simulations of tetradecamer DNA fragments with explicit water and counterions. The results demonstrate the possibility of probing regular elastic responses in DNA under low, nearly physiological amplitudes of forces and torques.

Quantitation of interactions between two DNA loops demonstrates loop domain insulation in E. coli cells

Eukaryotic gene regulation involves complex patterns of long-range DNA-looping interactions between enhancers and promoters, but how these specific interactions are achieved is poorly understood. Models that posit other DNA loops--that aid or inhibit enhancer-promoter contact--are difficult to test or quantitate rigorously in eukaryotic cells. Here, we use the well-characterized DNA-looping proteins Lac repressor and phage λ CI to measure interactions between pairs of long DNA loops in E. coli cells in the three possible topological arrangements. We find that side-by-side loops do not affect each other. Nested loops assist each other's formation consistent with their distance-shortening effect. In contrast, alternating loops, where one looping element is placed within the other DNA loop, inhibit each other's formation, thus providing clear support for the loop domain model for insulation. Modeling shows that combining loop assistance and loop interference can provide strong specificity in long-range interactions.

Tethered particle analysis of supercoiled circular DNA using peptide nucleic acid handles

This protocol describes how to monitor individual naturally supercoiled circular DNA plasmids bound via peptide nucleic acid (PNA) handles between a bead and a surface. The protocol was developed for single-molecule investigation of the dynamics of supercoiled DNA, and it allows the investigation of both the dynamics of the molecule itself and of its interactions with a regulatory protein. Two bis-PNA clamps designed to bind with extremely high affinity to predetermined homopurine sequence sites in supercoiled DNA are prepared: one conjugated with digoxigenin for attachment to an anti-digoxigenin-coated glass cover slide, and one conjugated with biotin for attachment to a submicron-sized streptavidin-coated polystyrene bead. Plasmids are constructed, purified and incubated with the PNA handles. The dynamics of the construct is analyzed by tracking the tethered bead using video microscopy: less supercoiling results in more movement, and more supercoiling results in less movement. In contrast to other single-molecule methodologies, the current methodology allows for studying DNA in its naturally supercoiled state with constant linking number and constant writhe. The protocol has potential for use in studying the influence of supercoils on the dynamics of DNA and its associated proteins, e.g., topoisomerase. The procedure takes ~4 weeks.

Chromatin fiber polymorphism triggered by variations of DNA linker lengths

Deciphering the factors that control chromatin fiber structure is key to understanding fundamental chromosomal processes. Although details remain unknown, it is becoming clear that chromatin is polymorphic depending on internal and external factors. In particular, different lengths of the linker DNAs joining successive nucleosomes (measured in nucleosome-repeat lengths or NRLs) that characterize different cell types and cell cycle stages produce different structures. NRL is also nonuniform within single fibers, but how this diversity affects chromatin fiber structure is not clear. Here we perform Monte Carlo simulations of a coarse-grained oligonucleosome model to help interpret fiber structure subject to intrafiber NRL variations, as relevant to proliferating cells of interphase chromatin, fibers subject to remodeling factors, and regulatory DNA sequences. We find that intrafiber NRL variations have a profound impact on chromatin structure, with a wide range of different architectures emerging (highly bent narrow forms, canonical and irregular zigzag fibers, and polymorphic conformations), depending on the NRLs mixed. This stabilization of a wide range of fiber forms might allow NRL variations to regulate both fiber compaction and selective DNA exposure. The polymorphic forms spanning canonical to sharply bent structures, like hairpins and loops, arise from large NRL variations and are surprisingly more compact than uniform NRL structures. They are distinguished by tail-mediated far-nucleosome interactions, in addition to the near-nucleosome interactions of canonical 30-nm fibers. Polymorphism is consistent with chromatin's diverse biological functions and heterogeneous constituents. Intrafiber NRL variations, in particular, may contribute to fiber bending and looping and thus to distant communication in associated regulatory processes.

DNA supercoiling enhances cooperativity and efficiency of an epigenetic switch

Bacteriophage λ stably maintains its dormant prophage state but efficiently enters lytic development in response to DNA damage. The mediator of these processes is the λ repressor protein, CI, and its interactions with λ operator DNA. This λ switch is a model on the basis of which epigenetic switch regulation is understood. Using single molecule analysis, we directly examined the stability of the CI-operator structure in its natural, supercoiled state. We marked positions adjacent to the λ operators with peptide nucleic acids and monitored their movement by tethered particle tracking. Compared with relaxed DNA, the presence of supercoils greatly enhances juxtaposition probability. Also, the efficiency and cooperativity of the λ switch is significantly increased in the supercoiled system compared with a linear assay, increasing the Hill coefficient.

NAFlex: a web server for the study of nucleic acid flexibility

We present NAFlex, a new web tool to study the flexibility of nucleic acids, either isolated or bound to other molecules. The server allows the user to incorporate structures from protein data banks, completing gaps and removing structural inconsistencies. It is also possible to define canonical (average or sequence-adapted) nucleic acid structures using a variety of predefined internal libraries, as well to create specific nucleic acid conformations from the sequence. The server offers a variety of methods to explore nucleic acid flexibility, such as a colorless wormlike-chain model, a base-pair resolution mesoscopic model and atomistic molecular dynamics simulations with a wide variety of protocols and force fields. The trajectories obtained by simulations, or imported externally, can be visualized and analyzed using a large number of tools, including standard Cartesian analysis, essential dynamics, helical analysis, local and global stiffness, energy decomposition, principal components and in silico NMR spectra. The server is accessible free of charge from the mmb.irbbarcelona.org/NAFlex webpage.

Dynamical simulations of DNA supercoiling and compression

In the present article, we summarize our recent studies of DNA dynamics using the generalized immersed boundary method. Our analysis of the effects of electrostatic repulsion on the dynamics of DNA supercoiling revealed that, after perturbation, a pre-twisted DNA collapses into a compact supercoiled configuration that is sensitive to the initial excess link and ionic strength of the solvent. A stochastic extension of the generalized immersed boundary method shows that DNA in solution subjected to a constant electric field is compressed into a configuration with smaller radius of gyration and smaller ellipticity ratio than those expected for such a molecule in a thermodynamic equilibrium.

IMPORTANCE OF EXCLUDED VOLUME AND HYDRODYNAMIC INTERACTIONS ON MACROMOLECULAR DIFFUSION IN VIVO

The interiors of all living cells are highly crowded with macromolecules, which results in a considerable difference between the thermodynamics and kinetics of biological reactions in vivo from that in vitro. To begin to elucidate the principles of intermolecular dynamics in the crowded environment of cells, employing Brownian dynamics (BD) simulations, we examined possible mechanism(s) responsible for the great reduction in diffusion constants of macromolecules in vivo from that at infinite dilution. In an E. coli cytoplasm modelcomprised of 15 different macromolecule types at physiological concentrations, where macromolecules were represented by spheres with their Stokes radii, BD simulations were performed with and without hydrodynamic interactions (HI). Without HI, the calculated diffusion constant of green fluorescent protein (GFP) is much larger than experiment. On the other hand, when HI were considered, the in vivo experimental GFP diffusion constant is almost reproduced without adjustable parameters. In addition, HI give rise to significant, size independent intermolecular dynamic correlations. These results suggest that HI play an important role on macromolecular dynamics in vivo.

On the origin of thermal untwisting of DNA

In aqueous solutions, the helical twist of DNA decreases with temperature. This phenomenon was noticed and studied experimentally several decades ago, but its physical origin remains elusive. The present paper shows that the thermal untwisting can be predicted from the specific properties of the torsional elasticity of the double helix revealed in recent computational studies. The temperature coefficient of untwisting estimated using coarse-grained models fitted to all-atom MD data accounts for the experimental results nearly quantitatively. The agreement is further improved with the computed torsional rigidity scaled to remove the discrepancy from experiment. The results confirm that the torsional rigidity of DNA is strongly anharmonic. They indicate that for random DNA, its value grows with small twisting and decreases with untwisting.

Bullied no more: when and how DNA shoves proteins around

The predominant protein-centric perspective in protein-DNA-binding studies assumes that the protein drives the interaction. Research focuses on protein structural motifs, electrostatic surfaces and contact potentials, while DNA is often ignored as a passive polymer to be manipulated. Recent studies of DNA topology, the supercoiling, knotting, and linking of the helices, have shown that DNA has the capability to be an active participant in its transactions. DNA topology-induced structural and geometric changes can drive, or at least strongly influence, the interactions between protein and DNA. Deformations of the B-form structure arise from both the considerable elastic energy arising from supercoiling and from the electrostatic energy. Here, we discuss how these energies are harnessed for topology-driven, sequence-specific deformations that can allow DNA to direct its own metabolism.

Comparison of Brownian dynamics algorithms with hydrodynamic interaction

The hydrodynamic interaction is an essential effect to consider in Brownian dynamics simulations of polymer and nanoparticle dilute solutions. Several mathematical approaches can be used to build Brownian dynamics algorithms with hydrodynamic interaction, the most common of them being the exact but time demanding Cholesky decomposition and the Chebyshev polynomial expansion. Recently, Geyer and Winter [J. Chem. Phys. 130, 1149051 (2009)] have proposed a new approximation to treat the hydrodynamic interaction that seems quite efficient and is increasingly used. So far, a systematic comparison among those approaches has not been clearly made. In this paper, several features and the efficiency of typical implementations of those approaches are evaluated by using bead-and-spring chain models. The different sensitivity to the bead overlap detected for the different implementations may be of interest to select the suitable algorithm for a given simulation.

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.

Brownian dynamics simulations on CPU and GPU with BD_BOX

There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse-grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed-memory architectures, OpenMP for shared-memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU.

Dynamics of an electrostatically charged elastic rod in fluid

We investigate the effects of electrostatic and steric repulsion on the dynamics of a pre-twisted charged elastic rod immersed in a viscous incompressible fluid. Equations of motion of the rod include the fluid–structure interaction, rod elasticity and a combination of two interactions that prevent self-contact, namely the electrostatic interaction and hard-core repulsion. The governing equations are solved using the generalized immersed-boundary method. We find that after perturbation, a pre-twisted minicircle collapses into a compact supercoiled configuration. The collapse proceeds along a complex trajectory that may pass near several unstable equilibrium configurations, before it settles in a locally stable equilibrium. The dwell time near an unstable equilibrium can be up to several microseconds. Both the final configuration and the transition path are sensitive to the initial excess link, ionic strength of the solvent and the initial perturbation.

Dissecting protein-induced DNA looping dynamics in real time

Many proteins that interact with DNA perform or enhance their specific functions by binding simultaneously to multiple target sites, thereby inducing a loop in the DNA. The dynamics and energies involved in this loop formation influence the reaction mechanism. Tethered particle motion has proven a powerful technique to study in real time protein-induced DNA looping dynamics while minimally perturbing the DNA-protein interactions. In addition, it permits many single-molecule experiments to be performed in parallel. Using as a model system the tetrameric Type II restriction enzyme SfiI, that binds two copies of its recognition site, we show here that we can determine the DNA-protein association and dissociation steps as well as the actual process of protein-induced loop capture and release on a single DNA molecule. The result of these experiments is a quantitative reaction scheme for DNA looping by SfiI that is rigorously compared to detailed biochemical studies of SfiI looping dynamics. We also present novel methods for data analysis and compare and discuss these with existing methods. The general applicability of the introduced techniques will further enhance tethered particle motion as a tool to follow DNA-protein dynamics in real time.

Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects

We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri et al 2007 Phys. Rev. Lett. 99 088103). Our discrete helical wormlike chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite size effects in an experimental context, where polydA-polydT is clamped by two G-C strands, as well as for free polymers.

Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models

We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot probabilities of the more coarse-grained models with the wormlike model show that the behaviors of the random-flight model are similar to that of DNA molecules in a solution environment with high ionic strengths, whereas the behaviors of the cubic lattice model with excluded volume are akin to that of DNA molecules under low ionic strengths.

Dynamics and consequences of DNA looping by the FokI restriction endonuclease

Genetic events often require proteins to be activated by interacting with two DNA sites, trapping the intervening DNA in a loop. While much is known about looping equilibria, only a few studies have examined DNA-looping dynamics experimentally. The restriction enzymes that cut DNA after interacting with two recognition sites, such as FokI, can be used to exemplify looping reactions. The reaction pathway for FokI on a supercoiled DNA with two sites was dissected by fast kinetics to reveal, in turn: the initial binding of a protein monomer to each site; the protein–protein association to form the dimer, trapping the loop; the subsequent phosphodiester hydrolysis step. The DNA motion that juxtaposes the sites ought on the basis of Brownian dynamics to take ∼2 ms, but loop capture by FokI took 230 ms. Hence, DNA looping by FokI is rate limited by protein association rather than DNA dynamics. The FokI endonuclease also illustrated activation by looping: it cut looped DNA 400 times faster than unlooped DNA.

Predicting knot or catenane type of site-specific recombination products

Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. Here, we present a topological model of this process and characterize all possible products of the most common substrates: unknots, unlinks, and torus knots and catenanes. This model tightly prescribes the knot or catenane type of previously uncharacterized data. We also discuss how the model helps to distinguish products of distributive recombination and, in some cases, determine the order of processive recombination products.

Sticky DNA: in vivo formation in E. coli and in vitro association of long GAA*TTC tracts to generate two independent supercoiled domains

The expanded GAA*TTC repeat sequence associated with Friedreich's ataxia (FRDA) adopts non-B DNA structures, (triplexes and sticky DNA). Sticky DNA is formed in plasmids by the association of two long GAA*TTC tracts at lengths that are found in the sequence of the frataxin gene in patients. Most FRDA patients have expanded GAA*TTC repeats (up to 1700 triplets), which inhibit the transcription of the gene, thus diminishing the synthesis of frataxin, a mitochondrial protein involved in iron-sulfur cluster biogenesis. Negative supercoiling and MgCl(2) (or MnCl(2)) are required to stabilize sticky DNA (a dumbbell-shaped structure) in plasmids with a pair of repeat tracts where n> or =60 in the direct repeat orientation in vitro. Since the triplet repeat sequences (TRS) were symmetrically positioned in the plasmids and because a number of unique restriction sites were present in the vector, studies were conducted to evaluate the influence of selectively linearizing one or the other supercoiled domains created by the DNA*DNA associated region, i.e. the stable complex at the pair of TRS's. The two domains behave independently, thus confirming the association of the two tracts and the dumbbell-shaped plasmid in our model for sticky DNA. Linking number investigations were performed on a family of plasmids harboring different lengths (30, 60, or 176 repeats), orientations and number of tracts (one or two) of a GAA*TTC repeat in Escherichia coli to evaluate the in vivo role, if any, of sticky DNA. Unexpectedly, this non-B DNA conformation elicited the formation of a TRS-length dependent change in the global topology of the plasmids, indicative of an apparent compression of the primary helices. Thus, linking number determinations confirm that sticky DNA has an important consequence in vivo.

Flexible histone tails in a new mesoscopic oligonucleosome model

We describe a new mesoscopic model of oligonucleosomes that incorporates flexible histone tails. The nucleosome cores are modeled using the discrete surface-charge optimization model, which treats the nucleosome as an electrostatic surface represented by hundreds of point charges; the linker DNAs are treated using a discrete elastic chain model; and the histone tails are modeled using a bead/chain hydrodynamic approach as chains of connected beads where each bead represents five protein residues. Appropriate charges and force fields are assigned to each histone chain so as to reproduce the electrostatic potential, structure, and dynamics of the corresponding atomistic histone tails at different salt conditions. The dynamics of resulting oligonucleosomes at different sizes and varying salt concentrations are simulated by Brownian dynamics with complete hydrodynamic interactions. The analyses demonstrate that the new mesoscopic model reproduces experimental results better than its predecessors, which modeled histone tails as rigid entities. In particular, our model with flexible histone tails: correctly accounts for salt-dependent conformational changes in the histone tails; yields the experimentally obtained values of histone-tail mediated core/core attraction energies; and considers the partial shielding of electrostatic repulsion between DNA linkers as a result of the spatial distribution of histone tails. These effects are crucial for regulating chromatin structure but are absent or improperly treated in models with rigid histone tails. The development of this model of oligonucleosomes thus opens new avenues for studying the role of histone tails and their variants in mediating gene expression through modulation of chromatin structure.

Do femtonewton forces affect genetic function? A review

Protein-Mediated DNA looping is intricately related to gene expression. Therefore any mechanical constraint that disrupts loop formation can play a significant role in gene regulation. Polymer physics models predict that less than a piconewton of force may be sufficient to prevent the formation of DNA loops. Thus, it appears that tension can act as a molecular switch that controls the much larger forces associated with the processive motion of RNA polymerase. Since RNAP can exert forces over 20 pN before it stalls, a 'substrate tension switch' could offer a force advantage of two orders of magnitude. Evidence for such a mechanism is seen in recent in vitro micromanipulation experiments. In this article we provide new perspective on existing theory and experimental data on DNA looping in vitro and in vivo. We elaborate on the connection between tension and a variety of other intracellular mechanical constraints including sequence specific curvature and supercoiling. In the process, we emphasize that the richness and versatility of DNA mechanics opens up a whole new paradigm of gene regulation to explore.

Real-time observation of DNA looping dynamics of Type IIE restriction enzymes NaeI and NarI

Many restriction enzymes require binding of two copies of a recognition sequence for DNA cleavage, thereby introducing a loop in the DNA. We investigated looping dynamics of Type IIE restriction enzymes NaeI and NarI by tracking the Brownian motion of single tethered DNA molecules. DNA containing two endonuclease recognition sites spaced a few 100 bp apart connect small polystyrene beads to a glass surface. The position of a bead is tracked through video microscopy. Protein-mediated looping and unlooping is then observed as a sudden specific change in Brownian motion of the bead. With this method we are able to directly follow DNA looping kinetics of single protein–DNA complexes to obtain loop stability and loop formation times. We show that, in the absence of divalent cations, NaeI induces DNA loops of specific size. In contrast, under these conditions NarI mainly creates non-specific loops, resulting in effective DNA compaction for higher enzyme concentrations. Addition of Ca²⁺ increases the NaeI-DNA loop lifetime by two orders of magnitude and stimulates specific binding by NarI. Finally, for both enzymes we observe exponentially distributed loop formation times, indicating that looping is dominated by (re)binding the second recognition site.

Brownian dynamics simulation of knot diffusion along a stretched DNA molecule

Manipulation of individual DNA molecules by optical tweezers has made it possible to tie these molecules into knots. After stretching the DNA molecules the knots become highly localized. In their recent study, Quake and co-authors investigated diffusion of such knots along stretched DNA molecules. We used these data to test the accuracy of a Brownian dynamics simulation of DNA bending motion. We simulated stretched DNA molecules with knots 3(1), 4(1), and 7(1), and determined their diffusion coefficients. Comparison of the simulated and experimental results shows that Brownian dynamics simulation is capable of predicting the rates of large-scale DNA rearrangements within a factor of 2.

Electrostatic mechanism of nucleosomal array folding revealed by computer simulation

Although numerous experiments indicate that the chromatin fiber displays salt-dependent conformations, the associated molecular mechanism remains unclear. Here, we apply an irregular Discrete Surface Charge Optimization (DiSCO) model of the nucleosome with all histone tails incorporated to describe by Monte Carlo simulations salt-dependent rearrangements of a nucleosomal array with 12 nucleosomes. The ensemble of nucleosomal array conformations display salt-dependent condensation in good agreement with hydrodynamic measurements and suggest that the array adopts highly irregular 3D zig-zag conformations at high (physiological) salt concentrations and transitions into the extended "beads-on-a-string" conformation at low salt. Energy analyses indicate that the repulsion among linker DNA leads to this extended form, whereas internucleosome attraction drives the folding at high salt. The balance between these two contributions determines the salt-dependent condensation. Importantly, the internucleosome and linker DNA-nucleosome attractions require histone tails; we find that the H3 tails, in particular, are crucial for stabilizing the moderately folded fiber at physiological monovalent salt.

A computer-generated supercoiled model of the pUC19 plasmid

DNA models have become a powerful tool in the simulation of radiation-induced molecular damage. Here, a computer code was developed which calculates the coordinates of individual atoms in supercoiled plasmid DNA. In this prototype study, the known base-pair sequence of the pUC19 plasmid has been utilized. The model was built in a three-step process. Firstly, a Monte Carlo simulation was performed to shape a segment chain skeleton. Checks on elastic energy, distance and unknotting were applied. The temperature was considered in two different ways: (1) it was kept constant at 293 K and (2) it was gradually reduced from 350 K to less than 10 K. Secondly, a special smoothing procedure was introduced here to remove the edges from the segment chain without changing the total curve length while avoiding the production of overshooting arcs. Finally, the base pair sequence was placed along the smoothed segment chain and the positions of all the atoms were calculated. As a first result, a few examples of the supercoiled plasmid models will be presented, demonstrating the strong influence of appropriate control of the system temperature.

Enzyme-mediated DNA looping

Most reactions on DNA are carried out by multimeric protein complexes that interact with two or more sites in the DNA and thus loop out the DNA between the sites. The enzymes that catalyze these reactions usually have no activity until they interact with both sites. This review examines the mechanisms for the assembly of protein complexes spanning two DNA sites and the resultant triggering of enzyme activity. There are two main routes for bringing together distant DNA sites in an enzyme complex: either the proteins bind concurrently to both sites and capture the intervening DNA in a loop, or they translocate the DNA between one site and another into an expanding loop, by an energy-dependent translocation mechanism. Both capture and translocation mechanisms are discussed here, with reference to the various types of restriction endonuclease that interact with two recognition sites before cleaving DNA.

Dynamics of DNA loop capture by the SfiI restriction endonuclease on supercoiled and relaxed DNA

The SfiI endonuclease is a prototype for DNA looping. It binds two copies of its recognition sequence and, if Mg(2+) is present, cuts both concertedly. Looping was examined here on supercoiled and relaxed forms of a 5.5 kb plasmid with three SfiI sites: sites 1 and 2 were separated by 0.4 kb, and sites 2 and 3 by 2.0 kb. SfiI converted this plasmid directly to the products cut at all three sites, though DNA species cleaved at one or two sites were formed transiently during a burst phase. The burst revealed three sets of doubly cut products, corresponding to the three possible pairings of sites. The equilibrium distribution between the different loops was evaluated from the burst phases of reactions initiated by adding MgCl(2) to SfiI bound to the plasmid. The short loop was favored over the longer loops, particularly on supercoiled DNA. The relative rates for loop capture were assessed after adding SfiI to solutions containing the plasmid and MgCl(2). On both supercoiled and relaxed DNA, the rate of loop capture across 0.4 kb was only marginally faster than over 2.0 kb or 2.4 kb. The relative strengths and rates of looping were compared to computer simulations of conformational fluctuations in DNA. The simulations concurred broadly with the experimental data, though they predicted that increasing site separations should cause a shallower decline in the equilibrium constants than was observed but a slightly steeper decline in the rates for loop capture. Possible reasons for these discrepancies are discussed.

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.

Analysis of Chemical and Enzymatic Cleavage Frequencies in Supercoiled DNA

Chemical and enzymatic probing methods are powerful techniques for examining details of sequence-dependent structure in DNA and RNA. Reagents that cleave nucleic acid molecules in a structure-specific, but relatively sequence-non-specific manner, such as hydroxyl radical or DNase I, have been used widely to probe helical geometry in nucleic acid structures, nucleic acid-drug complexes, and in nucleoprotein assemblies. Application of cleavage-based techniques to structures present in superhelical DNA has been hindered by the fact that the cleavage pattern attributable to supercoiling-dependent structures is heavily mixed with non-specific cleavage signals that are inevitable products of multiple cleavage events. We present a rigorous mathematical procedure for extracting the cleavage pattern specific to supercoiled DNA and use this method to investigate the hydroxyl radical cleavage pattern in a cruciform DNA structure formed by a 60 bp inverted repeat sequence embedded in a negatively supercoiled plasmid. Our results support the presence of a stem-loop structure in the expected location and suggest that the helical geometry of the cruciform stem differs from that of the normal duplex form.

Asymmetric Removal of Supercoils Suggests how Topoisomerase II Simplifies DNA Topology

Type-IIA topoisomerases consume ATP as they catalyse the interconversion of DNA topoisomers by transporting one DNA segment through a transient break in another. It remains unclear how their activity simplifies the topology of DNA below equilibrium values. Here we report that eukaryotic topoisomerase II narrows the thermal distribution of DNA supercoils, by mainly removing negative DNA crossings. Surprisingly, this asymmetry in supercoil removal is not due to deformation of the DNA before strand passage. Topoisomerase II neither bends nor alters the helical conformation of the interacting DNA. Rather, it appears to interact with a third DNA segment, in addition to the gated and the transported segments. Remarkably, the simultaneous interaction with three DNA segments accounts for the asymmetric removal of supercoils in relaxed DNA and gives a clue to how topoisomerase II simplifies the topology of DNA against the thermal drive.

Effect of DNA superhelicity and bound proteins on mechanistic aspects of the Hin-mediated and Fis-enhanced inversion

Using a recently developed inhomogeneous, macroscopic model for long DNA bound to proteins, we examine topological and geometric aspects of DNA/protein structures and dynamics on various stages of the Hin inversion pathway. This biological reaction involves exchange of DNA in a synaptic complex that brings together several DNA sites bound to Hin dimers as well as Fis enhancers. Brownian dynamics simulations in the millisecond timescale allow us to follow and analyze the DNA/protein dynamics trajectories and to examine the effects of DNA superhelicity and protein binding on various reaction steps. Analysis of the generated kinetic pathways helps explain mechanistic aspects regarding the process by which two or three protein-bound DNA sites come to close spatial proximity and show that how topological selectivity (two trapped supercoils), enhancer binding, and properties of supercoiled DNA play critical roles in regulating the inversion reaction. Specifically, a critical amount of DNA superhelicity (e.g., |sigma| > 0.02) leads to an optimal interplay for the first reaction step-two-site juxtaposition-between large-scale random rearrangements of Hin-bound DNA and local slithering within branches of plectonemes. The three-site juxtaposition, the second step, is significantly accelerated by the presence of an enhancer protein that, due to severe local bending, also alters juxtaposition mechanisms, especially for superhelical density magnitude greater than around 0.04.