Macroscopic modeling and simulations of supercoiled DNA with bound proteins

A Hi-C data-integrated model elucidates E. coli chromosome's multiscale organization at various replication stages

The chromosome of Escherichia coli is riddled with multi-faceted complexity. The emergence of chromosome conformation capture techniques are providing newer ways to explore chromosome organization. Here we combine a beads-on-a-spring polymer-based framework with recently reported Hi-C data for E. coli chromosome, in rich growth condition, to develop a comprehensive model of its chromosome at 5 kb resolution. The investigation focuses on a range of diverse chromosome architectures of E. coli at various replication states corresponding to a collection of cells, individually present in different stages of cell cycle. The Hi-C data-integrated model captures the self-organization of E. coli chromosome into multiple macrodomains within a ring-like architecture. The model demonstrates that the position of oriC is dependent on architecture and replication state of chromosomes. The distance profiles extracted from the model reconcile fluorescence microscopy and DNA-recombination assay experiments. Investigations into writhe of the chromosome model reveal that it adopts helix-like conformation with no net chirality, earlier hypothesized in experiments. A genome-wide radius of gyration map captures multiple chromosomal interaction domains and identifies the precise locations of rrn operons in the chromosome. We show that a model devoid of Hi-C encoded information would fail to recapitulate most genomic features unique to E. coli.

Methods for modeling cytoskeletal and DNA filaments

This review summarizes the models that researchers use to represent the conformations and dynamics of cytoskeletal and DNA filaments. It focuses on models that address individual filaments in continuous space. Conformation models include the freely jointed, Gaussian, angle-biased chain (ABC), and wormlike chain (WLC) models, of which the first three bend at discrete joints and the last bends continuously. Predictions from the WLC model generally agree well with experiment. Dynamics models include the Rouse, Zimm, stiff rod, dynamic WLC, and reptation models, of which the first four apply to isolated filaments and the last to entangled filaments. Experiments show that the dynamic WLC and reptation models are most accurate. They also show that biological filaments typically experience strong hydrodynamic coupling and/or constrained motion. Computer simulation methods that address filament dynamics typically compute filament segment velocities from local forces using the Langevin equation and then integrate these velocities with explicit or implicit methods; the former are more versatile and the latter are more efficient. Much remains to be discovered in biological filament modeling. In particular, filament dynamics in living cells are not well understood, and current computational methods are too slow and not sufficiently versatile. Although primarily a review, this paper also presents new statistical calculations for the ABC and WLC models. Additionally, it corrects several discrepancies in the literature about bending and torsional persistence length definitions, and their relations to flexural and torsional rigidities.

A molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman's Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [J. Chem. Phys. 126, 084901 (2007)], can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

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.

Comparison of kinetic and dynamical models of DNA-protein interaction and facilitated diffusion

It has long been asserted that proteins such as transcription factors may locate their target in DNA sequences at rates that surpass by several orders of magnitude the three-dimensional diffusion limit thanks to facilitated diffusion, that is, the combination of one-dimensional (sliding along the DNA) and three-dimensional diffusion. This claim has been supported throughout the years by several mass action kinetic models, while the dynamical model we proposed recently (J. Chem. Phys. 2009, 130, 015103) suggests that acceleration of targeting due to facilitated diffusion cannot be large. In order to solve this apparent contradiction, we performed additional simulations to compare the results obtained with our model to those obtained with the kinetic model of Klenin et al. (Phys. Rev. Lett. 2006, 96, 018104). We show in this paper that the two models actually support each other and agree in predicting a low efficiency for facilitated diffusion. Extrapolation of these results to real systems even indicates that facilitated diffusion necessarily slows down the targeting process compared to three-dimensional diffusion.

Description of nonspecific DNA-protein interaction and facilitated diffusion with a dynamical model

We propose a dynamical model for nonspecific DNA-protein interaction, which is based on the "bead-spring" model previously developed by other groups, and investigate its properties using Brownian dynamics simulations. We show that the model successfully reproduces some of the observed properties of real systems and predictions of kinetic models. For example, sampling of the DNA sequence by the protein proceeds via a succession of three-dimensional motion in the solvent, one-dimensional sliding along the sequence, short hops between neighboring sites, and intersegmental transfers. Moreover, facilitated diffusion takes place in a certain range of values of the protein effective charge, that is, the combination of one-dimensional sliding and three-dimensional motion leads to faster DNA sampling than pure three-dimensional motion. At last, the number of base pairs visited during a sliding event is comparable to the values deduced from single-molecule experiments. We also point out and discuss some discrepancies between the predictions of this model and some recent experimental results as well as some hypotheses and predictions of kinetic models.

Conformational response of supercoiled DNA to confinement in a nanochannel

Monte Carlo simulations were done to study the conformation of supercoiled DNA confined in a nanochannel. The molecule has a superhelical density of around -0.05 and is bathed in a monovalent salt solution with an ionic strength of 2, 10, or 150 mM. The cross-sectional diameter of the circular shaped nanochannel was varied in the range of 10 to 80 nm. The conformational properties were characterized by the writhing number and the distribution in the distance between the two opposing strands of the superhelix. With increasing confinement, as set by a smaller tube diameter and/or decreased screening of the Coulomb interaction, the supercoil becomes more tightly interwound and long-range structural features such as branching and the formation of hairpins are progressively suppressed. Analysis of the energetics shows a concurrent increase in electrostatic energy and energy of interaction of the supercoil with the wall, but the elastic twisting energy decreases. Confinement in a nanochannel or otherwise hence results in a decrease in the absolute value of the twist exerted on the duplex. The bending energy remains approximately constant, which means that there are no significant deflections from the wall. The simulation results are interpreted with theory based on the wormlike chain model, including the effects of the wall, charge, elasticity, and configurational entropy. It was found that the theory is reasonably successful in predicting the structural response to the confinement at the local level of the diameter and pitch of the supercoil.

Models of protein linear molecular motors for dynamic nanodevices

Protein molecular motors are natural nano-machines that convert the chemical energy from the hydrolysis of adenosine triphosphate into mechanical work. These efficient machines are central to many biological processes, including cellular motion, muscle contraction and cell division. The remarkable energetic efficiency of the protein molecular motors coupled with their nano-scale has prompted an increasing number of studies focusing on their integration in hybrid micro- and nanodevices, in particular using linear molecular motors. The translation of these tentative devices into technologically and economically feasible ones requires an engineering, design-orientated approach based on a structured formalism, preferably mathematical. This contribution reviews the present state of the art in the modelling of protein linear molecular motors, as relevant to the future design-orientated development of hybrid dynamic nanodevices.

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.

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.

A coarse-grained model for double-helix molecules in solution: spontaneous helix formation and equilibrium properties

A new reductionist coarse-grained model is presented for double-helix molecules in solution. As with such models for lipid bilayers and micelles, the level of description is both particulate and mesoscopic. The particulate (bead-and-spring) nature of the model makes for a simple implementation in standard molecular dynamics simulation codes and allows for investigation of thermomechanic properties without preimposing any (form of) response function. The mesoscopic level of description--where groups of atoms are condensed into coarse-grained beads--causes long-range interactions to be effectively screened, which greatly enhances the efficiency and scalability of simulations. Without imposing local or global order parameters, a linear initial configuration of the model molecule spontaneously assembles into a double helix due to the interplay between three contributions: hydrophobic/hydrophilic interactions between base pairs, backbone, and solvent; phosphate-phosphate repulsion along the backbone; and favorable base-pair stacking energy. We present results for the process of helix formation as well as for the equilibrium properties of the final state, and investigate how both depend on the input parameters. The current model holds promise for two routes of investigation: First, within a limited set of generic parameters, the effect of local (atomic-scale) perturbations on overall helical properties can be systematically studied. Second, since the efficiency allows for a direct simulation of both small and large (>100 base pairs) systems, the model presents a testground for systematic coarse-graining methods.

Modeling DNA loops using the theory of elasticity

An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

The World of Non-Covalent Interactions: 2006

The review focusses on the fundamental importance of non-covalent interactions in nature by illustrating specific examples from chemistry, physics and the biosciences. Laser spectroscopic methods and both ab initio and molecular modelling procedures used for the study of non-covalent interactions in molecular clusters are briefly outlined. The role of structure and geometry, stabilization energy, potential and free energy surfaces for molecular clusters is extensively discussed in the light of the most advanced ab initio computational results for the CCSD(T) method, extrapolated to the CBS limit. The most important types of non-covalent complexes are classified and several small and medium size non-covalent systems, including H-bonded and improper H-bonded complexes, nucleic acid base pairs, and peptides and proteins are discussed with some detail. Finally, we evaluate the interpretation of experimental results in comparison with state of the art theoretical models: this is illustrated for phenol...Ar, the benzene dimer and nucleic acid base pairs. A review with 270 references.

A generalized bead-rod model for Brownian dynamics simulations of wormlike chains under strong confinement

This paper is aimed to develop a Brownian dynamics simulation method for strongly confined semiflexible polymers where numerical simulation plays an indispensable role in complementing theory and experiments. A wormlike chain under strong confinement is modeled as a string of virtual spherical beads connected by inextensible rods with length varying according to the confinement intensity of the chain measured by the Odijk deflection length. The model takes hydrodynamic interactions into account. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. The model parameters are studied by quantitatively comparing the simulated properties of a double-stranded DNA chain with available experimental data and theoretical predictions.

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.

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.

Thermodynamic behaviors of polyampholytes at low temperatures

The thermodynamic properties of 6-mer polyampholyte chains were simulated with the multicanonical Monte Carlo method in a three-dimensional off-lattice model. The results demonstrate that the number of the charged monomers on the chain and the sequence significantly affect the transition behaviors of polyampholyte chains. In the case of the random distribution of the charged monomers, two oppositely charged monomers act as two stickers during a collapse process, due to which the movement of monomers is suppressed and the chains can more directly reach their solid state. Interestingly, in a proper arrangement of the charged monomers, the chains may have a proteinlike nondegenerate state, i.e., the chain is designable. The transition of such polyampholyte chains appears to be of a two-state, all-or-none type.

Deformations of promoter DNA bound to carcinogens help interpret effects on TATA-element structure and activity

The TATA-box binding protein (TBP) is required by eukaryotic RNA polymerases for correct transcription initiation. TBP binds to the minor groove of an 8 base pair (bp) DNA-promoter element known as the TATA box and severely bends the TATA box. The promoter-DNA substrate can be damaged by components present in the cell or the environment to produce covalent carcinogen-DNA adducts. These may lead to transcription blockage or unfaithful transcription. Benzo[a]pyrene (BP) is a widespread environmental chemical carcinogen which can be metabolically converted to DNA-reactive enantiomeric (+) and (-)-anti-benzo[a]pyrene diol epoxides (BPDEs). Recent experimental studies of a pair of stereoisomeric adenine adducts, derived from (+) and (-)-anti-BPDEs, have revealed how these lesions influence the complexation of TBP with the TATA box. Depending on the adduct's location in the TATA box and its stereochemistry, the stability of monomeric TATA-TBP complexes was found to increase or decrease relative to the unmodified DNA. We report here analyses of molecular-dynamics simulations to interpret these findings. Structural analyses of 12 DNA-protein systems representing different combinations of adduct stereoisomer type and placement within the promoter reveal that the location of the adduct within the TATA octamer determines whether the stability of TATA-TBP complexes is increased or decreased. The effect on binding stability can be interpreted in terms of conformational freedom and major-groove space available to BP due to the hydrogen bonds and inserted phenylalanines of the TATA-TBP complex; that is, depending on the position of the adenine to which BP is covalently bound, BP can be accommodated in an intercalated or major-groove orientation with ease or with difficulty (due to interference with TATA-TBP interactions). The unravelled structures and interactions thus reveal the effect of different adduct locations on TATA-TBP complex formation and suggest how transcription initiation may be affected by the presence of a bulky BP.

Unbiased rotational moves for rigid-body dynamics

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying the noncommuting rotational matrices in an arbitrary order. Our algorithm should thus replace standard approaches to rotate local coordinate frames in Langevin and Brownian dynamics simulations.

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.

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

The torque generated by RNA polymerase as it tracks along double-stranded DNA can potentially induce long-range structural deformations integral to mechanisms of biological significance in both prokaryotes and eukaryotes. In this paper, we introduce a dynamic computer model for investigating this phenomenon. Duplex DNA is represented as a chain of hydrodynamic beads interacting through potentials of linearly elastic stretching, bending, and twisting, as well as excluded volume. The chain, linear when relaxed, is looped to form two open but topologically constrained subdomains. This permits the dynamic introduction of torsional stress via a centrally applied torque. We simulate by Brownian dynamics the 100 micros response of a 477-base pair B-DNA template to the localized torque generated by the prokaryotic transcription ensemble. Following a sharp rise at early times, the distributed twist assumes a nearly constant value in both subdomains, and a succession of supercoiling deformations occurs as superhelical stress is increasingly partitioned to writhe. The magnitude of writhe surpasses that of twist before also leveling off when the structure reaches mechanical equilibrium with the torsional load. Superhelicity is simultaneously right handed in one subdomain and left handed in the other, as predicted by the "transcription-induced twin-supercoiled-domain" model [L. F. Liu and J. C. Wang, Proc. Natl. Acad. Sci. U.S.A. 84, 7024 (1987)]. The properties of the chain at the onset of writhing agree well with predictions from theory, and the generated stress is ample for driving secondary structural transitions in physiological DNA.

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.