Monte Carlo simulations of supercoiled DNAs confined to a plane

Fully integrated Monte Carlo simulation for evaluating radiation induced DNA damage and subsequent repair using Geant4-DNA

Ionising radiation induced DNA damage and subsequent biological responses to it depend on the radiation’s track-structure and its energy loss distribution pattern. To investigate the underlying biological mechanisms involved in such complex system, there is need of predicting biological response by integrated Monte Carlo (MC) simulations across physics, chemistry and biology. Hence, in this work, we have developed an application using the open source Geant4-DNA toolkit to propose a realistic “fully integrated” MC simulation to calculate both early DNA damage and subsequent biological responses with time. We had previously developed an application allowing simulations of radiation induced early DNA damage on a naked cell nucleus model. In the new version presented in this work, we have developed three additional important features: (1) modeling of a realistic cell geometry, (2) inclusion of a biological repair model, (3) refinement of DNA damage parameters for direct damage and indirect damage scoring. The simulation results are validated with experimental data in terms of Single Strand Break (SSB) yields for plasmid and Double Strand Break (DSB) yields for plasmid/human cell. In addition, the yields of indirect DSBs are compatible with the experimental scavengeable damage fraction. The simulation application also demonstrates agreement with experimental data of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}γ-H2AX yields for gamma ray irradiation. Using this application, it is now possible to predict biological response along time through track-structure MC simulations.

Calculation of π and Classification of Self-avoiding Lattices via DNA Configuration

Numerical simulation (e.g. Monte Carlo simulation) is an efficient computational algorithm establishing an integral part in science to understand complex physical and biological phenomena related with stochastic problems. Aside from the typical numerical simulation applications, studies calculating numerical constants in mathematics, and estimation of growth behavior via a non-conventional self-assembly in connection with DNA nanotechnology, open a novel perspective to DNA related to computational physics. Here, a method to calculate the numerical value of π, and way to evaluate possible paths of self-avoiding walk with the aid of Monte Carlo simulation, are addressed. Additionally, experimentally obtained variation of the π as functions of DNA concentration and the total number of trials, and the behaviour of self-avoiding random DNA lattice growth evaluated through number of growth steps, are discussed. From observing experimental calculations of π (π_exp) obtained by double crossover DNA lattices and DNA rings, fluctuation of π_exp tends to decrease as either DNA concentration or the number of trials increases. Based upon experimental data of self-avoiding random lattices grown by the three-point star DNA motifs, various lattice configurations are examined and analyzed. This new kind of study inculcates a novel perspective for DNA nanostructures related to computational physics and provides clues to solve analytically intractable problems.

Efficient deformation algorithm for plasmid DNA simulations

BACKGROUND

Plasmid DNA molecules are closed circular molecules that are widely used in life sciences, particularly in gene therapy research. Monte Carlo methods have been used for several years to simulate the conformational behavior of DNA molecules. In each iteration these simulation methods randomly generate a new trial conformation, which is either accepted or rejected according to a criterion based on energy calculations and stochastic rules. These simulation trials are generated using a method based on crankshaft motion that, apart from some slight improvements, has remained the same for many years.

RESULTS

In this paper, we present a new algorithm for the deformation of plasmid DNA molecules for Monte Carlo simulations. The move underlying our algorithm preserves the size and connectivity of straight-line segments of the plasmid DNA skeleton. We also present the results of three experiments comparing our deformation move with the standard and biased crankshaft moves in terms of acceptance ratio of the trials, energy and temperature evolution, and average displacement of the molecule. Our algorithm can also be used as a generic geometric algorithm for the deformation of regular polygons or polylines that preserves the connections and lengths of their segments.

CONCLUSION

Compared with both crankshaft moves, our move generates simulation trials with higher acceptance ratios and smoother deformations, making it suitable for real-time visualization of plasmid DNA coiling. For that purpose, we have adopted a DNA assembly algorithm that uses nucleotides as building blocks.

Surface charge effects on the 2D conformation of supercoiled DNA

We have adsorbed plasmid pUc19 DNA on a supported bilayer. By varying the fraction of cationic lipids in the membrane, we have tuned the surface charge. Plasmid conformations were imaged by Atomic Force Microscopy (AFM). We performed two sets of experiments: deposition from salt free solution on charged bilayers and deposition from salty solutions on neutral bilayers. Both sets show similar trends: at low surface charge density or low bulk salt concentration, the internal electrostatic repulsion forces plasmids to adopt completely opened structures, while at high surface charge density or higher bulk salt concentration, usual supercoiled plectonemes are observed. We experimentally demonstrate the equivalence of surface screening by mobile interfacial charges and bulk screening from salt ions. At low to medium screening, the electrostatic repulsion at plasmid crossings is predominant, leading to a number of crossovers decreasing linearly with the characteristic screening length. We compare our data with an analytical 2D-equilibrated model developed recently for the system and extract the DNA effective charge density when strands are adsorbed at the surface.

Shape of adsorbed supercoiled plasmids: an equilibrium description

Inspired by recent atomic force microscope (AFM) images of plasmids deposited on oppositely charged supported lipid bilayers from salt free solution, we propose a model for strongly adsorbed supercoiled cyclic stiff polyelectrolytes. We discuss how the excess linking number Lk of the deposited cycle is shared between writhe Wr and twist Tw at equilibrium and obtain the typical number of self-crossings in the deposited cycle as a function of surface charge density. The number of crossings at equilibrium is simply determined by the crossing penalty which is a local quantity and by the excess linking number. The number of crossings is well defined despite versatile plasmid shapes. For moderate numbers of crossings the loops are rather small and localized along the primary cycle, as expected from entropic loops. In the regime of many crossings, the cycle takes the shape of a regular flat ply ruled by local stiffness. The model allows for a semiquantitative comparison with the AFM images of deposited plasmids which are strongly charged.

Atomic force microscopy of DNA at high humidity: irreversible conformational switching of supercoiled molecules

Three topologically different double-stranded DNA molecules of the same size (bps) have been imaged in air on mica using amplitude modulation atomic force microscopy (AM AFM) under controlled humidity conditions. At very high relative humidity (>90% RH), localized conformational changes of the DNA were observed, while at lower RH, the molecules remained immobile. The conformational changes occurred irreversibly and were driven principally by superhelical stress stored in the DNA molecules prior to binding to the mica surface. The binding mechanism of the DNA to the mica (surface equilibration versus kinetic trapping) modulated the extent of the conformational changes. In cases where DNA movement was observed, increased kinking of the DNA was seen at high humidity when more surface water was present. Additionally, DNA condensation behavior was also present in localized regions of the molecules. This study illustrates that changes in the tertiary structure of DNA can be induced during AFM imaging at high humidity on mica. We propose that AM AFM in high humidity will be a useful technique for probing DNA topology without some of the drawbacks of imaging under bulk solution.

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.

Estimation of the persistence length of DNA from the torsion elastic constant and supercoiling free energy: effect of ethylene glycol

Two different methods are proposed to estimate the persistence length ( P) of DNA from the measured torsion elastic constant (alpha) and the twist energy parameter ( E T ) that governs the supercoiling free energy. The first method involves Monte Carlo simulations and reversible-work calculations of E T for model DNAs that possess the measured alpha and selected trial values of P. Comparison of the computed E T values with the experimental value allows estimation of P (or equivalently the bending elastic constant (kappa beta)) by interpolation. A far simpler, though less accurate, alternative is to solve a previously conjectured analytical relation connecting E T , alpha, kappa beta (or P), and an unknown "constant" ( B). The present simulations are used to ascertain the optimum value of B and to assess the validity and accuracy of that relation. Within the simulation errors, P values obtained from the measured alpha and E T via this analytical expression agree with those determined from the simulations and E T values reckoned from the input alpha and kappa beta by this analytical expression agree with the corresponding simulated values. Although B is found to be insensitive to variation in alpha, it appears to decline slightly with increasing kappa beta. The original analytical expression is modified to take this apparent variation of B with kappa beta into account. By using this modified analytical relation to estimate P (from the measured alpha and E T ) or E T (from the input alpha and kappa beta), much closer agreement is obtained respectively with the values of P or E T obtained from the simulations. As specific examples, these methods are applied to determine P in 0 and 20 w/v % ethylene glycol, which has been shown to induce a structural transition in duplex DNA.

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.

Torsional rigidities of weakly strained DNAs

Measurements on unstrained linear and weakly strained large (> or =340 bp) circular DNAs yield torsional rigidities in the range C = 170-230 fJ fm. However, larger values, in the range C = 270-420 fJ fm, are typically obtained from measurements on sufficiently small (< or =247 bp) circular DNAs, and values in the range C = 300-450 fJ fm are obtained from experiments on linear DNAs under tension. A new method is proposed to estimate torsional rigidities of weakly supercoiled circular DNAs. Monte Carlo simulations of the supercoiling free energies of solution DNAs, and also of the structures of surface-confined supercoiled plasmids, were performed using different trial values of C. The results are compared with experimental measurements of the twist energy parameter, E(T), that governs the supercoiling free energy, and also with atomic force microscopy images of surface-confined plasmids. The results clearly demonstrate that C-values in the range 170-230 fJ fm are compatible with experimental observations, whereas values in the range C > or = 269 fJ fm, are incompatible with those same measurements. These results strongly suggest that the secondary structure of DNA is altered by either sufficient coherent bending strain or sufficient tension so as to enhance its torsional rigidity.

Two-angle model and phase diagram for chromatin

We have studied the phase diagram for chromatin within the framework of the two-angle model. Only a rough estimation of the forbidden surface of the phase diagram for chromatin was given in a previous work of Schiessel. We revealed the fine structure of this excluded-volume borderline numerically and analytically. Furthermore, we investigated the Coulomb repulsion of the DNA linkers to compare it with the previous results.

Study of the DNA/ethidium bromide interactions on mica surface by atomic force microscope: influence of the surface friction

The influence of mica surface on DNA/ethidium bromide interactions is investigated by atomic force microscopy (AFM). We describe the diffusion mechanism of a DNA molecule on a mica surface by using a simple analytical model. It appears that the DNA diffusion on a mica surface is limited by the surface friction due to the counterion correlations between the divalent counterions condensed on both mica and DNA surfaces. We also study the structural changes of linear DNA adsorbed on mica upon ethidium bromide binding by AFM. It turns out that linear DNA molecules adsorbed on a mica surface are unable to relieve the topological constraint upon ethidium bromide binding. In particular, strongly adsorbed molecules tend to be highly entangled, while loosely bound DNA molecules appear more extended with very few crossovers. Adsorbed DNA molecules cannot move freely on the surface because of the surface friction. Therefore, the topological constraint increases due to the ethidium bromide binding. Moreover, we show that ethidium bromide has a lower affinity for strongly bound molecules due to the topological constraint induced by the surface friction.

Hyaluronan conformations on surfaces: effect of surface charge and hydrophobicity

Extended, relaxed, condensed, and interacting forms of the polysaccharide hyaluronan have been observed by atomic force microscopy (AFM). The types of images obtained depend on the properties of the surfaces used. We have investigated several different surface conditions for HA imaging, including unmodified mica, mica chemically modified with two different kinds of amino-terminated silanes (3-aminopropyltriethoxysilane and N-trimethoxysilylpropyl-N,N,N-trimethylammonium chloride), and highly oriented pyrolytic graphite. We found the degree of HA molecular extension or condensation to be variable, and the number of bound chains per unit area was low, for all of the mica-based surfaces. HA was more easily imaged on graphite, a hydrophobic surface. Chains were frequently observed in high degrees of extension, maintained by favorable interaction with the surface after molecular combing. This observation suggests that the HA macromolecule interacts with graphite through hydrophobic patches along its surface. AFM studies of HA behavior on differing surfaces under well-controlled environmental conditions provides useful insight into the variety of conformations and interactions likely to be found under differing physiological conditions.

Extended, relaxed, and condensed conformations of hyaluronan observed by atomic force microscopy

The conformation of the polysaccharide hyaluronan (HA) has been investigated by tapping mode atomic force microscopy in air. HA deposited on a prehydrated mica surface favored an extended conformation, attributed to molecular combing and inhibition of subsequent chain recoil by adhesion to the structured water layer covering the surface. HA deposited on freshly cleaved mica served as a defect in a partially structured water layer, and favored relaxed, weakly helical, coiled conformations. Intramolecularly condensed forms of HA were also observed, ranging from pearl necklace forms to thick rods. The condensation is attributed to weak adhesion to the mica surface, counterion-mediated attractive electrostatic interactions between polyelectrolytes, and hydration effects. Intermolecular association of both extended and condensed forms of HA was observed to result in the formation of networks and twisted fibers, in which the chain direction is not necessarily parallel to the fiber direction. Whereas the relaxed coil and partially condensed conformations of HA are relevant to the native structure of liquid connective tissues, fully condensed rods may be more relevant for HA tethered to a cell surface or intracellular HA, and fibrous forms may be relevant for HA subjected to shear flow in tight intercellular spaces or in protein-HA complexes.

Monte Carlo simulations of locally melted supercoiled DNAs in 20 mM ionic strength

Mesoscopic models of unmelted and locally melted supercoiled DNAs in 20 mM ionic strength are simulated over a range of linking difference from deltal = 0 to -26 turns, or superhelix density from sigma = 0 to -0.062. A domain containing m = 0, 28, or 56 melted basepairs (out of 4349 total) is modeled simply by a region of suitable length with substantially reduced torsion and bending elastic constants. Average structural properties are calculated from the saved configurations, and a reversible work protocol is used to calculate the supercoiling free energy, The cross-writhe between duplex and melted regions (defined herein) is found to be negligibly small. The total writhe, radius of gyration, and ordered elements of the diagonalized inertial tensor are found to be nearly universal functions of the residual linking difference (deltal(r)) associated with the duplex region, independent of m. However, deformability of the tertiary structure, as manifested by the variance of those same properties, is not a universal function of deltal(r)), but depends upon m.delta (SC) varies with deltal(r)) more strongly than deltal(r)) (2)due to the low ionic strength. The twist energy parameter, E (T) obtained from the simulated delta G(SC), deltal(r)), and net twisting strain of the melted region T (D), is found to be independent of m, hence also of the torsion and bending elastic constants of the melted region. However, E(T) increases linearly with -deltalr), which leads to 1). a small overestimation of E (T) for any given deltal(r)) when E(T) is determined from the observed deltal and deltal (r) by the protocol of Bauer and Benham; and 2). a significant enhancement of the apparent slope, -dE(T)/d(T), obtained via the protocol of Bauer and Benham, relative to the actual slope at fixed delta l(r). After taking these two effects into account, the theoretical and experimental values E(T) and -dE(T)/d(T) values agree rather well. For the larger deltal the melted regions are found preferentially in the linker domains between interwound arms, rather than in the apical regions at the ends of interwound arms.

Polylysine-coated mica can be used to observe systematic changes in the supercoiled DNA conformation by scanning force microscopy in solution

The conformations of supercoiled (sc) DNA and linear DNA bound to polylysine (PL)-coated mica were investigated by scanning force microscopy (SFM) in solution. From the polymer statistical analysis of linear DNA, we could distinguish between re-arrangements or trapping of the DNA on the surface. Conditions of re-arrangements to an almost equilibrated state can be achieved at appropriate PL surface concentrations. We could show that the ability of re-arrangements depends on the salt concentration of the adsorption/imaging buffer. Comparing the statistical analysis of the linear DNA with SFM images of scDNA suggested that irregular scDNA conformations are formed under conditions of trapping, whereas plectonemic structures are favoured under conditions of surface re-arrangements. Salt-dependent changes in the scDNA conformation over the range of 10-100 mM NaCl, as characterised by the parameters writhe and the superhelix radius r, are observable only under conditions that enable surface re-arrangements. The measured values of writhe suggest that the scDNA loses approximately one-half of the supercoils during the binding to the surface. At the same time r increases systematically with decreasing writhe, thus the scDNA topology remains determined by the constraints on supercoiling during the binding to PL-coated mica.

Surface tension increment due to solute addition

Addition of solute into solvent may lead to an increase in surface tension, such as salt in water and water in alcohol, due to solute depletion at the interface. The repulsion of the solute from the interface may originate from electrostatic forces or solute-solvent attraction. On the basis of the square-well model for the interface-solute interaction, we derive the surface tension increment Deltagamma by both canonical and grand-canonical routes (Gibbs adsorption isotherm) for a spherical droplet. The surface tension is increased linearly with the bulk concentration of the solute c(b) and the interaction range lambda. The theoretical results are consistent with those obtained by experiments and Monte Carlo simulations up to a few molarity. For weak repulsion, the increment is internal energy driven. When the repulsion is large enough, the surface tension increment is entropy driven and approaches the asymptotic limit, Deltagamma approximately c(b)k(B)Tlambda, due to the nearly complete depletion of the solute at the interface. Our result may shed some light on the surface tension increment for electrolyte solutions with concentration above 0.2M.

Intersegmental interactions in supercoiled DNA: atomic force microscope study

Intersegmental interactions in DNA facilitated by the neutralization of electrostatic repulsion was studied as a function of salt concentration and DNA supercoiling. DNA samples with defined superhelical densities were deposited onto aminopropyl mica at different ionic conditions and imaged in air after drying of the samples. Similar to hydrodynamic data, we did not observe a collapse of supercoiled DNA, as proposed earlier by cryo-EM studies. Instead, the formation of the contacts between DNA helices within supercoiled loops with no visible space between the duplexes was observed. The length of such close contacts increased upon increasing NaCl concentration. DNA supercoiling was a critical factor for the stabilization of intersegmental contacts. Implications of the observed effect for understanding DNA compaction in the cell and for regulation DNA transactions via interaction of distantly separated DNA regions are discussed.

Monte Carlo simulation of the assembly of bis-biotinylated DNA and streptavidin

We present Monte Carlo simulations of the self-assembly of bivalent bis-biotinylated DNA molecules with the tetravalent biotin-binding protein streptavidin (STV). By fitting the STV binding probabilities for the four possible valencies, the modelling correctly reproduces the dependencies of various network parameters experimentally observed in an earlier study. The combined results from the experimental and theoretical studies suggest that the binding probability for divalent STV formation is about 50 times larger than for the formation of trivalent and about 200 times larger than for tetravalent STV. In accordance with the experimental results, the modelling also indicates that the mixture of an equimolar ratio of DNA and STV leads to a maximum in size of the oligomeric DNA-STV clusters formed. Furthermore, we found a percolation transition in which the DNA cluster size increases rapidly with increasing DNA concentration resulting in the formation of a single supercluster at elevated concentrations. This behaviour coincides with the occurrence of an immobile band previously observed in electrophoretic experiments, indicating the formation of extremely large DNA-STV aggregate networks.

Dimensions of plectonemically supercoiled DNA

With a view to determine the configuration and regularity of plectonemically supercoiled DNA, we have measured the small angle neutron scattering from pUC18 plasmid in saline solutions. Furthermore, we have derived the mathematical expression for the single chain scattering function (form factor) of a superhelical structure, including the longitudinal and transverse interference over the plectonemic pitch and radius, respectively. It was found that an interwound configuration describes the data well, provided interactions among supercoils are accounted for in the second virial approximation. The opening angle was observed to be relatively constant and close to 58 degrees, but it was necessary to include a significant distribution in radius and pitch. For diluted supercoils with vanishing mutual interaction, the derived structural results agree with independent measurements, including the distribution in linking number deficit as determined by gel electrophoresis. With increasing plasmid concentration, prior and covering the transition to the liquid-crystalline phase, the radius and pitch are seen to decrease significantly. The latter observation shows that compaction of negatively supercoiled DNA by confinement results in a decrease in writhing number at the cost of a positive twist exerted on the DNA duplex. It is our conjecture that the free energy associated with this excess twist is of paramount importance in controlling the critical boundaries pertaining to the transition to the anisotropic, liquid-crystalline phase.