Electrostatic effects in short superhelical DNA

Radial distribution function of semiflexible oligomers with stretching flexibility

The radial distribution of the end-to-end distance R_ee is crucial for quantifying the global size and flexibility of a linear polymer. For semiflexible polymers, several analytical formulas have been derived for the radial distribution of R_ee ignoring the stretching flexibility. However, for semiflexible oligomers, such as DNA or RNA, the stretching flexibility can be rather pronounced and can significantly affect the radial distribution of R_ee. In this study, we obtained an extended formula that includes the stretch modulus to describe the distribution of R_ee for semiflexible oligomers on the basis of previous formulas for semiflexible polymers without stretching flexibility. The extended formula was validated by extensive Monte Carlo simulations over wide ranges of the stretch modulus and persistence length, as well as all-atom molecular dynamics simulations of short DNAs and RNAs. Additionally, our analyses showed that the effect of stretching flexibility on the distribution of R_ee becomes negligible for DNAs longer than ∼130 base pairs and RNAs longer than ∼240 base pairs.

Influence of BII Backbone Substates on DNA Twist: A Unified View and Comparison of Simulation and Experiment for All 136 Distinct Tetranucleotide Sequences

Reliable representation of the B-DNA base-pair step twist is one of the crucial requirements for theoretical modeling of DNA supercoiling and other biologically relevant phenomena in B-DNA. It has long been suspected that the twist is inaccurately described by current empirical force fields. Unfortunately, comparison of simulation results with experiments is not straightforward because of the presence of BII backbone substates, whose populations may differ in experimental and simulation ensembles. In this work, we provide a comprehensive view of the effect of BII substates on the overall B-DNA helix twist and show how to reliably compare twist values from experiment and simulation in two scenarios. First, for longer DNA segments freely moving in solution, we show that sequence-averaged twists of different BI/BII ensembles can be compared directly because of approximate cancellation of the opposing BII effects. Second, for sequence-specific data, such as a particular base-pair step or tetranucleotide twist, can be compared only for a clearly defined BI/BII backbone conformation. For the purpose of force field testing, we designed a compact set of fourteen 22-base-pair B-DNA duplexes (Set 14) containing all 136 distinct tetranucleotide sequences and carried out a total of 84 μs of molecular dynamics simulations, primarily with the OL15 force field. Our results show that the ff99bsc0εζ_OL1χ_OL4, parmbsc1, and OL15 force fields model the B-DNA helical twist in good agreement with X-ray and minicircle ligation experiments. The comprehensive understanding obtained regarding the effect of BII substates on the base-pair step geometry should aid meaningful comparisons of various conformational ensembles in future research.

The energy of naturally curved elastic rods with an application to the stretching and contraction of a free helical spring as a model for DNA

We give a contemporary and direct derivation of a classical, but insufficiently familiar, result in the theory of linear elasticity-a representation for the energy of a stressed elastic rod with central axis that intrinsically takes the shape of a general space curve. We show that the geometric torsion of the space curve, while playing a crucial role in the bending energy, is physically unrelated to the elastic twist. We prove that the twist energy vanishes in the lowest-energy states of a rod subject to constraints that do not restrict the twist. The stretching and contraction energies of a free helical spring are computed. There are local high-energy minima. We show the possibility of using the spring to model the chirality of DNA. We then compare our results with an available atomic level energy simulation that was performed on DNA unconstrained in the same sense as the free spring. We find some possible reflections of springlike behavior in the mechanics of DNA, but, unsurprisingly, the base pairs lend a material substance to the core of DNA that a spring does not capture.

Torque-induced deformations of charged elastic DNA rods: thin helices, loops, and precursors of DNA supercoiling

We study the deformations of charged elastic rods under applied end forces and torques. For neutral filaments, we analyze the energetics of initial helical deformations and loop formation. We supplement this elastic approach with electrostatic energies of bent filaments and find critical conditions for buckling depending on the ionic strength of the solution. We also study force-induced loop opening, for parameters relevant for DNA. Finally, some applications of this nano-mechanical DNA model to salt-dependent onset of the DNA supercoiling are discussed.

Effect of crowding on the conformation of interwound DNA strands from neutron scattering measurements and Monte Carlo simulations

With a view to determining the distance between the two opposing duplexes in supercoiled DNA, we have measured small angle neutron scattering from pHSG298 plasmid (2675 base pairs) dispersed in saline solutions. Experiments were carried out under full and zero average DNA neutron scattering contrast using hydrogenated plasmid and a 1:1 mixture of hydrogenated and perdeuterated plasmid, respectively. In the condition of zero average contrast, the scattering intensity is directly proportional to the single DNA molecule scattering function (form factor), irrespective of the DNA concentration and without complications from intermolecular interference. The form factors are interpreted with Monte Carlo computer simulation. For this purpose, the many body problem of a dense DNA solution was reduced to the one of a single DNA molecule in a congested state by confinement in a cylindrical potential. It was observed that the interduplex distance decreases with increasing concentration of salt as well as plasmid. Therefore, besides ionic strength, DNA crowding is shown to be important in controlling the interwound structure and site juxtaposition of distal segments of supercoiled DNA. This first study exploiting zero average DNA contrast has been made possible by the availability of perdeuterated plasmid.

Effect of probe characteristics on the subtractive hybridization efficiency of human genomic DNA

Background

The detection sensitivity of low abundance pathogenic species by polymerase chain reaction (PCR) can be significantly enhanced by removing host nucleic acids. This selective removal can be performed using a magnetic bead-based solid phase with covalently immobilized capture probes. One of the requirements to attain efficient host background nucleic acids subtraction is the capture probe characteristics.

Findings

In this study we investigate how various capture probe characteristics influence the subtraction efficiency. While the primary focus of this report is the impact of probe length, we also studied the impact of probe conformation as well as the amount of capture probe attached to the solid phase. The probes were immobilized on magnetic microbeads functionalized with a phosphorous dendrimer. The subtraction efficiency was assessed by quantitative real time PCR using a single-step capture protocol and genomic DNA as target. Our results indicate that short probes (100 to 200 bp) exhibit the best subtraction efficiency. Additionally, higher subtraction efficiencies with these probes were obtained as the amount of probe immobilized on the solid phase decreased. Under optimal probes condition, our protocol showed a 90 - 95% subtraction efficiency of human genomic DNA.

Conclusions

The characteristics of the capture probe are important for the design of efficient solid phases. The length, conformation and abundance of the probes determine the capture efficiency of the solid phase.

Prestressed nuclear organization in living cells

The nucleus is maintained in a prestressed state within eukaryotic cells, stabilized mechanically by chromatin structure and other nuclear components on its inside, and cytoskeletal components on its outside. Nuclear architecture is emerging to be critical to the governance of chromatin assembly, regulation of genome function and cellular homeostasis. Elucidating the prestressed organization of the nucleus is thus important to understand how the nuclear architecture impinges on its function. In this chapter, various chemical and mechanical methods have been described to probe the prestressed organization of the nucleus.

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.

Secondary structural characterization of oligonucleotide strands using electrospray ionization mass spectrometry

Differences in charge state distributions of hairpin versus linear strands of oligonucleotides are analyzed using electrospray ionization mass spectrometry (ESI-MS) in the negative ion detection mode. It is observed that the linear structures show lower charge state distribution than the hairpin strands of the same composition. The concentration of ammonium acetate and the cone voltage are major factors that cause the shift of the negative ions in the charge states. The ESI data presented here are supported by UV spectra of strands acquired at 260 nm wavelength in aqueous ammonium acetate solution. We will show that the strands that demonstrate a higher charge state distribution in the gas phase also have a higher melting temperature in solution.

Sequence-dependent motions of DNA: a normal mode analysis at the base-pair level

Computer simulation of the dynamic structure of DNA can be carried out at various levels of resolution. Detailed high resolution information about the motions of DNA is typically collected for the atoms in a few turns of double helix. At low resolution, by contrast, the sequence-dependence features of DNA are usually neglected and molecules with thousands of base pairs are treated as ideal elastic rods. The present normal mode analysis of DNA in terms of six base-pair "step" parameters per chain residue addresses the dynamic structure of the double helix at intermediate resolution, i.e., the mesoscopic level of a few hundred base pairs. Sequence-dependent effects are incorporated into the calculations by taking advantage of "knowledge-based" harmonic energy functions deduced from the mean values and dispersion of the base-pair "step" parameters in high-resolution DNA crystal structures. Spatial arrangements sampled along the dominant low frequency modes have end-to-end distances comparable to those of exact polymer models which incorporate all possible chain configurations. The normal mode analysis accounts for the overall bending, i.e., persistence length, of the double helix and shows how known discrepancies in the measured twisting constants of long DNA molecules could originate in the deformability of neighboring base-pair steps. The calculations also reveal how the natural coupling of local conformational variables affects the global motions of DNA. Successful correspondence of the computed stretching modulus with experimental data requires that the DNA base pairs be inclined with respect to the direction of stretching, with chain extension effected by low energy transverse motions that preserve the strong van der Waals' attractions of neighboring base-pair planes. The calculations further show how one can "engineer" the macroscopic properties of DNA in terms of dimer deformability so that polymers which are intrinsically straight in the equilibrium state exhibit the mesoscopic bending anisotropy essential to DNA curvature and loop formation.

Monte Carlo simulations of supercoiled DNAs confined to a plane

Recent advances in atomic force microscopy (AFM) have enabled researchers to obtain images of supercoiled DNAs deposited on mica surfaces in buffered aqueous milieux. Confining a supercoiled DNA to a plane greatly restricts its configurational freedom, and could conceivably alter certain structural properties, such as its twist and writhe. A program that was originally written to perform Monte Carlo simulations of supercoiled DNAs in solution was modified to include a surface potential. This potential flattens the DNAs to simulate the effect of deposition on a surface. We have simulated transfers of a 3760-basepair supercoiled DNA from solution to a surface in both 161 and 10 mM ionic strength. In both cases, the geometric and thermodynamic properties of the supercoiled DNAs on the surface differ significantly from the corresponding quantities in solution. At 161 mM ionic strength, the writhe/twist ratio is 1.20-1.33 times larger for DNAs on the surface than for DNAs in solution and significant differences in the radii of gyration are also observed. Simulated surface structures in 161 mM ionic strength closely resemble those observed by AFM. Simulated surface structures in 10 mM ionic strength are similar to a minority of the structures observed by AFM, but differ from the majority of such structures for unknown reasons. In 161 mM ionic strength, the internal energy (excluding the surface potential) decreases substantially as the DNA is confined to the surface. Evidently, supercoiled DNAs in solution are typically deformed farther from the minimum energy configuration than are the corresponding surface-confined DNAs. Nevertheless, the work (Delta A(int)) done on the internal coordinates, which include uniform rotations at constant configuration, during the transfer is positive and 2.6-fold larger than the decrease in internal energy. The corresponding entropy change is negative, and its contribution to Delta A(int) is positive and exceeds the decrease in internal energy by 3.6 fold. The work done on the internal coordinates during the solution-to-surface transfer is directed primarily toward reducing their entropy. Evidently, the number of configurations available to the more deformed solution DNA is vastly greater than for the less deformed surface-confined DNA.

Time-lapse imaging of conformational changes in supercoiled DNA by scanning force microscopy

Most of the scanning force microscopy (SFM) images of supercoiled DNA on untreated mica thus far reported have not shown tight plectonemic structure seen by electron microscopy, but instead less coiled molecules and sometimes a partly "condensed" state with intimate chain-chain interactions. By observing time-lapse images of conformational changes of DNA induced by decreasing ionic strength of imaging buffer in solution SFM, we could show that the process of water rinsing, an indispensable step for preparation of dried samples, may be responsible for some of the conformational anomalies in the images previously reported. We have studied several protocols to observe supercoiled DNA molecules by SFM and discuss the merits and the demerits. Images obtained following uranyl acetate treatment may be ideal for the detection of DNA damage, as the supercoiled and nicked forms are easily distinguishable.

Electrostatic-undulatory theory of plectonemically supercoiled DNA

We present an analytical calculation of the electrostatic interaction in a plectonemic supercoil within the Poisson-Boltzmann approximation. Undulations of the supercoil strands arising from thermal motion couple nonlinearly with the electrostatic interaction, giving rise to a strong enhancement of the bare interaction. In the limit of fairly tight winding, the free energy of a plectonemic supercoil may be split into an elastic contribution containing the bending and torsional energies and an electrostatic-undulatory free energy. The total free energy of the supercoil is minimized according to an iterative scheme, which utilizes the special symmetry inherent in the usual elastic free energy of the plectoneme. The superhelical radius, opening angle, and undulation amplitudes in the radius and pitch are obtained as a function of the specific linking difference and the concentration of monovalent salt. Our results compare favorably with the experimental values for these parameters of Boles et al. (1990. J. Mol. Biol. 213:931-951). In particular, we confirm the experimental observation that the writhe is a virtually constant fraction of the excess linking number over a wide range of superhelical densities. Another important prediction is the ionic strength dependence of the plectonemic parameters, which is in reasonable agreement with the results from computer simulations.

Configurational transitions in Fourier series-represented DNA supercoils

A new Fourier series representation of supercoiled DNA is employed in Langevin dynamics simulations to study large-scale configurational motions of intermediate-length chains. The polymer is modeled as an ideal elastic rod subject to long-range van der Waals' interactions. The van der Waals' term prevents the self-contact of distant chain segments and also mimics attractive forces thought to stabilize the association of closely spaced charged rods. The finite Fourier series-derived polymer formulation is an alternative to the piecewise B-spline curves used in past work to describe the motion of smoothly deformed supercoiled DNA in terms of a limited number of independent variables. This study focuses on two large-scale configurational events: the interconversion between circular and figure-8 forms at a relatively low level of supercoiling, and the transformation between branched and interwound structures at a higher superhelical density.

Modeling protein-induced configurational changes in DNA minicircles

A method is offered for obtaining minimum energy configurations of DNA minicircles constrained by one or more DNA-binding proteins. The minicircles are modeled as elastic rods, while the presence of bound protein is implied by rigidly fixing portions of these chains. The configurations of the geometrically constrained circular rods are sampled stochastically and optimized according to a simple elastic energy model of nicked DNA. The shapes of the minimum energy structures identified after a simulated annealing process are analyzed in terms of relative protein orientation and writhing number. The procedure is applied to minicircles 500 base pairs in length, bound to two evenly spaced DNA-wrapping proteins. The presence of histone octamers is suggested by rigidly fixing the two protein-bound portions of each minicircle as small superhelices similar in dimension to nucleosomal DNA. The folded minimum energy forms of sample chains with different degrees of protein wrapping are noteworthy in themselves in that they offer a new resolution to the well-known minichromosome linking number paradox and point to future minicircle simulations of possible import.

Visualization of supercoiled DNA with atomic force microscopy in situ

Tertiary structure of supercoiled DNA is a significant factor in a number of genetic functions and is apparently affected by environmental conditions. We applied atomic force microscopy (AFM) for imaging the supercoiled DNA deposited at different ionic conditions. We have employed a technique for the sample preparation that permits high-resolution AFM imaging of DNA bound to the surface in buffer solutions without drying the sample (AFM in situ). The AFM data show that at low ionic strength, DNA molecules are loosely interwound supercoils with an irregular shape. Plectonemic superhelices are formed in high-concentration, near-physiological salt solutions. At such ionic conditions, superhelical loops are typically separated by regions of close helix-helix contacts. The data obtained show directly and unambiguously that overall geometry of supercoiled DNA depends dramatically on ionic conditions. This fact and the formation of close contacts between DNA helices are important features of supercoiled DNA related to its biological functions.

Simulating DNA at low resolution

The past year has witnessed the development of several new mathematical approaches to analyzing the structure of double-helical DNA and to incorporating the sequence-dependent features of the chain in computer simulations of long polymers. Of special interest in this respect are the local and global structural changes induced by the binding of various proteins to DNA, ranging from subtle bending, untwisting and sliding motions at the base-pair level to the apparent organization of supercoiled structure in chains that are thousands residues long. The computational effort has also included both new ways to incorporate the polyelectrolyte character of DNA and other environmental forces in simulations of long chains and new methods to keep track of the multitude of configurations so generated. The collective advances are pointing to ways that will soon connect the sequences of base pairs in large genomes to folded three-dimensional structures based on natural bending, twisting and translational tendencies and in response to deformations produced by the binding of different proteins.

Effects of localized bending on DNA supercoiling

The DNA double helix is straight only in the idealized case. In reality, it bends, twists and stretches in response to local base sequence and to specific interactions with proteins and other bound ligands. Naturally occurring bends appear to promote the assembly of nucleosomes, and in some cases can effectively replace regulatory DNA-binding proteins in vivo. Recently, a computational method known as 'finite element analysis', which is used routinely by engineers to analyse the stability of buildings and bridges, has been applied to the quantitative assessment of natural curvature in supercoiled DNA structures, providing new insight into the relationship between local, sequence-dependent features and the overall topology of these chains.

Salt effects on nucleic acids

Salt-dependent electrostatic effects are a major factor in determining the stability, structure, reactivity, and binding behavior of nucleic acids. Increasingly detailed theoretical methods, especially those based on Monte Carlo and Poisson-Boltzmann methodologies, combined with powerful computational algorithms are being used to examine how the shape, charge distribution and dielectric properties of the molecules affect the ion distribution in the surrounding aqueous solution, and how they play a role in ligand binding, structural transitions and other biologically important reactions. These studies indicate that inclusion of detailed structural information about the nucleic acid and its ligands is crucial for improving models of nucleic acid electrostatics, and that better treatment of the ion atmosphere and dielectric effects is also of major importance.

Theory of electrostatic interactions in macromolecules

In the past year, substantial progress has been made in the modeling of electrostatic interactions in biomolecules. This review highlights advances in the following areas: first, the efficient computation of long-range electrostatic interactions in detailed molecular simulations; second, the application of the Poisson-Boltzmann electrostatic model in conformational analysis; third, the application of the Poisson-Boltzmann model in quantum chemistry calculations; fourth, the development of atomic parameters; and finally, the modeling of ionization equilibria in proteins.

Modeling superhelical DNA: recent analytical and dynamic approaches

During the past year, a variety of diverse and complementary approaches have been presented for modeling superhelical DNA, offering new physical and biological insights into fundamental functional processes of DNA. Analytical approaches have probed deeper into the effects of entropy and thermal fluctuations on DNA structure and on various topological constraints induced by DNA-binding proteins. In tandem, new kinetic approaches--by molecular, Langevin and Brownian dynamics, as well as extensions of elastic-rod theory--have begun to offer dynamic information associated with supercoiling. Such dynamic approaches, along with other equilibrium studies, are refining the basic elastic-rod and polymer framework and incorporating more realistic treatments of salt and sequence-specific features. These collective advances in modeling large DNA molecules, in concert with technological innovations, are pointing to an exciting interplay between theory and experiment on the horizon.

Modeling of long-range electrostatic interactions in DNA

We used a Monte Carlo approach to compute the statistical properties of closed DNA chains with different descriptions of the electrostatic interactions. We compared these computed results with experimentally measured knotting probabilities, which are very sensitive to intersegment interactions. The calculated results based on the Debye-Hückel approximation of the solution of the Poisson-Boltzmann equation agreed very well with the published experimental data, while potential based on counterion condensation theory was clearly less satisfactory. We then compared the simpler hard-core approximation of electrostatic interactions to the Debye-Hückel potential. The hard-core approximation, specified in terms of a DNA effective diameter, gives the same conformational properties of random coils as the Debye-Hückel approximation. We found clear but relatively small differences between the two potentials for the conformational properties of supercoiled DNA.

The influence of salt on the structure and energetics of supercoiled DNA

We present a detailed computational study of the influence of salt on the configurations, energies, and dynamics of supercoiled DNA. A potential function that includes both elastic and electrostatic energy components is employed. Specifically, the electrostatic term, with salt-dependent coefficients, is modeled after Stigter's pioneering work on the effective diameter of DNA as a function of salt concentration. Because an effective charge per unit length is used, the electrostatic formulation does not require explicit modeling of phosphates and can be used to study long DNAs at any desired resolution of charge. With explicit consideration of the electrostatic energy, an elastic bending constant corresponding to the nonelectrostatic part of the bending contribution to the persistence length is used. We show, for a series of salt concentrations ranging from 0.005 to 1.0 M sodium, how configurations and energies of supercoiled DNA (1000 and 3000 base pairs) change dramatically with the simulated salt environment. At high salt, the DNA adopts highly compact and bent interwound states, with the bending energy dominating over the other components, and the electrostatic energy playing a minor role in comparison to the bending and twisting terms. At low salt, the DNA supercoils are much more open and loosely interwound, and the electrostatic components are dominant. Over the range of three decades of salt examined, the electrostatic energy changes by a factor of 10. The buckling transition between the circle and figure-8 is highly sensitive to salt concentration: this transition is delayed as salt concentration decreases, with a particularly sharp increase below 0.1 M. For example, for a bending-to-twisting force constant ratio of A/C = 1.5, the linking number difference (delta LK) corresponding to equal energies for the circle and figure-8 increases from 2.1 to 3.25 as salt decreases from 1.0 to 0.005 M. We also present in detail a family of three-lobed supercoiled DNA configurations that are predicted by elasticity theory to be stable at low delta Lk. To our knowledge, such three-dimensional structures have not been previously presented in connection with DNA supercoiling. These branched forms have a higher bending energy than the corresponding interwound configurations at the same delta Lk but, especially at low salt, this bending energy difference is relatively small in comparison with the total energy, which is dominated by the electrostatic contributions. Significantly, the electrostatic energies of the three-lobed and (straight) interwound forms are comparable at each salt environment. We show how the three-lobed configurations change slowly with ALk, resulting in branched interwound forms at higher salt. In longer chains, the branched forms are highly interwound, with bent arms. At low salt, the branched supercoils are asymmetric, with a longer interwound stem and two shorter arms. From molecular dynamics simulations we observe differences in the motions of the DNA as a function of salt. At high salt, the supercoiled chain is quite compact but fairly rigid, whereas at low salt the DNA is loosely coiled but more dynamic. Especially notable at low salt are the large-scale opening and closing of the chain as a whole and the rapid "slithering"of individual residues past one another. Toroidal forms are not detected under these conditions. However, the overall features of the open, loose supercoils found at low salt are more similar to those of toroidal than interwound configurations. Indeed,simulated x-ray scattering profiles reveal the same trends observed experimentally and are consistent with a change from closed to open forms as salt is decreased. Like the minimization studies, the dynamics reveal a critical point near 0.1 M associated with the collapse of loose to tight supercoils. Near this physiological concentration, enhanced flexibility of the DNA is noted. The collective observations suggest a potential regulatory role for salt on supercoiled DNA function, not only for closed circular DNA,but also for linear DNA with small looped regions.