Model simulations of DNA dynamics

Melting and Bubble Formation in a Double-Stranded DNA: Microscopic Aspects of Early Base-Pair Opening Events and the Role of Water

Despite its rigid structure, DNA is a remarkably flexible molecule. Flexibility is essential for biological functions (such as transcription and gene repair), which require large-amplitude structural changes such as bubble formation. The bubbles thus formed are required to have a certain stability of their own and survive long on the time scale of molecular motions. A molecular understanding of fluctuations leading to quasi-stable structures is not available. Through extensive atomistic molecular dynamics simulations, we identify a sequence of microscopic events that culminate in local bubble formation, which is initiated by base-pair (BP) opening, resulting from the cleavage of native BP hydrogen bonds (HBs). This is followed by the formation of mismatched BPs with non-native contacts. These metastable structures can either revert to their original forms or undergo a flipping transition to form a local bubble that can span across 3-4 BPs. A substantial distortion of the DNA backbone and a disruption of BP stacking are observed because of the structural changes induced by these local perturbations. We also explored how water helps in the entire process. A small number of water molecules undergo rearrangement to stabilize the intermediate states by forming HBs with DNA bases. Water thus acts as a lubricant that counteracts the enthalpic penalty suffered from the loss of native BP contacts. Although the process of bubble formation is reversible, the sequence of steps involved poses an entropic barrier, preventing it from easily retracing the path to the native state.

Twist-stretch relations in nucleic acids

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules.

Non-linear Hamiltonian models for DNA

Nucleic acids' physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse-grained models, e.g., the worm-like-chain, taken from polymer physics. In this review article, I discuss an intermediate (mesoscopic) approach and show how to build a three-dimensional Hamiltonian model which accounts for the main interactions responsible for the stability of the helical molecules. While the 3D mesoscopic model yields a sufficiently detailed description of the helix at the level of the base pair, it also allows one to predict the thermodynamical and structural properties of molecules in solution. Relying on the idea that the base pair fluctuations can be conceived as trajectories, I have built over the past years a computational method based on the time-dependent path integral formalism to derive the partition function. While the main features of the method are presented, I focus here in particular on a newly developed statistical method to set the maximum amplitude of the base pair fluctuations, a key parameter of the theory. Some applications to the calculation of DNA flexibility properties are discussed together with the available experimental data.

Base pair fluctuations in helical models for nucleic acids

A statistical method is developed to estimate the maximum amplitude of the base pair fluctuations in a three dimensional mesoscopic model for nucleic acids. The base pair thermal vibrations around the helix diameter are viewed as a Brownian motion for a particle embedded in a stable helical structure. The probability to return to the initial position is computed, as a function of time, by integrating over the particle paths consistent with the physical properties of the model potential. The zero time condition for the first-passage probability defines the constraint to select the integral cutoff for various macroscopic helical conformations, obtained by tuning the twist, bending, and slide motion between adjacent base pairs along the molecule stack. Applying the method to a short homogeneous chain at room temperature, we obtain meaningful estimates for the maximum fluctuations in the twist conformation with ∼10.5 base pairs per helix turn, typical of double stranded DNA helices. Untwisting the double helix, the base pair fluctuations broaden and the integral cutoff increases. The cutoff is found to increase also in the presence of a sliding motion, which shortens the helix contour length, a situation peculiar of dsRNA molecules.

Statistical mechanics of a double-stranded rod model for DNA melting and elasticity

The double-helical topology of DNA molecules observed at room temperature in the absence of any external loads can be disrupted by increasing the bath temperature or by applying tensile forces, leading to spontaneous strand separation known as DNA melting. Here, continuum mechanics of a 2D birod is combined with statistical mechanics to formulate a unified framework for studying both thermal melting and tensile force induced melting of double-stranded molecules: it predicts the variation of melting temperature with tensile load, provides a mechanics-based understanding of the cooperativity observed in melting transitions, and reveals an interplay between solution electrostatics and micromechanical deformations of DNA which manifests itself as an increase in the melting temperature with increasing ion concentration. This novel predictive framework sheds light on the micromechanical aspects of DNA melting and predicts trends that were observed experimentally or extracted phenomenologically using the Clayperon equation.

Energy patterns in twist-opening models of DNA with solvent interactions

Energy localization, via modulation instability, is addressed in a modified twist-opening model of DNA with solvent interactions. The Fourier expansion method is used to reduce the complex roto-torsional equations of the system to a set of discrete coupled nonlinear Schrödinger equations, which are used to perform the analytical investigation of modulation instability. We find that the instability criterion is highly influenced by the solvent parameters. Direct numerical simulations, performed on the generic model, further confirm our analytical predictions, as solvent interactions bring about highly localized energy patterns. These patterns are also shown to be robust under thermal fluctuations.

Twisting and bending stress in DNA minicircles

The interplay between bending of the molecule axis and appearance of disruptions in circular DNA molecules, with ∼100 base pairs, is addressed. Three minicircles with different radii and almost equal contents of AT and GC pairs are investigated. The DNA sequences are modeled by a mesoscopic Hamiltonian which describes the essential interactions in the helix at the level of the base pair and incorporates twisting and bending degrees of freedom. Helix unwinding and bubble formation patterns are consistently computed by a path integral method that sums over a large number of molecule configurations compatible with the model potential. The path ensembles are determined, as a function of temperature, by minimizing the free energy of the system. Fluctuational openings appear along the helix to release the stress due to the bending of the molecule backbone. In agreement with the experimental findings, base pair disruptions are found with larger probability in the smallest minicircle of 66 bps whose bending angle is ∼6°. For this minicircle, a sizeable untwisting is obtained with the helical repeat showing a step-like increase at T = 315 K. The method can be generalized to determine the bubble probability profiles of open ends linear sequences.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Coarse-grained model DNA: structure, sequences, stems, circles, hairpins

A coarse-grained model for DNA that is intended to function realistically at the level of individual bases is reported. The model is composed of residues with up to eight coarse-grained beads each, which is sufficient for DNA-like base stacking and base-base recognition by hydrogen bonding. The beads interact by means of short-ranged pair potentials and a simple implicit solvent model. Movement is simulated by Brownian dynamics without hydrodynamic coupling. The main stabilizing forces are base stacking and hydrogen bonding, as modified by the effects of solvation. Complementary double-stranded chains of such residues form stable double helices over long runs (~10 μs) at or near room temperature, with structural parameters close to those of B-form DNA. Most mismatched chains or mismatched regions within a complementary molecule melt and become disordered. Long-range fluctuations and elastic properties, as measured by bending and twisting persistence lengths, are close to experimental values. Single-stranded chains are flexible, with transient stretches of free bases in equilibrium with globules stabilized by intrastrand stacking and hydrogen bonding. Model DNAs in covalently closed loops form right- or left-handed supercoils, depending on the sign of overtwist or undertwist. Short stem-loop structures melt at elevated temperatures and reanneal when the temperature is carefully lowered. Overall, most qualitative properties of real DNA arise naturally in the model from local interactions at the base-pair level.

Breathing, bubbling, and bending: DNA flexibility from multimicrosecond simulations

Bending of the seemingly stiff DNA double helix is a fundamental physical process for any living organism. Specialized proteins recognize DNA inducing and stabilizing sharp curvatures of the double helix. However, experimental evidence suggests a high protein-independent flexibility of DNA. On the basis of coarse-grained simulations, we propose that DNA experiences thermally induced kinks associated with the spontaneous formation of internal bubbles. Comparison of the protein-induced DNA curvature calculated from the Protein Data Bank with that sampled by our simulations suggests that thermally induced distortions can account for ~80% of the DNA curvature present in experimentally solved structures.

Anharmonic stacking in supercoiled DNA

Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conformation, show an energetic advantage against the overtwisted ones. Accordingly moderately untwisted helices better sustain local fluctuational openings and make more unlikely the thermally driven complete strand separation.

Moving beyond Watson-Crick models of coarse grained DNA dynamics

DNA produces a wide range of structures in addition to the canonical B-form of double-stranded DNA. Some of these structures are stabilized by Hoogsteen bonds. We developed an experimentally parameterized, coarse-grained model that incorporates such bonds. The model reproduces many of the microscopic features of double-stranded DNA and captures the experimental melting curves for a number of short DNA hairpins, even when the open state forms complicated secondary structures. We demonstrate the utility of the model by simulating the folding of a thrombin aptamer, which contains G-quartets, and strand invasion during triplex formation. Our results highlight the importance of including Hoogsteen bonding in coarse-grained models of DNA.

Lattice model of oligonucleotide hybridization in solution. I. Model and thermodynamics

A coarse-grained lattice model of DNA oligonucleotides is proposed to investigate the general mechanisms by which single-stranded oligonucleotides hybridize to their complementary strands in solution. The model, based on a high-coordination cubic lattice, is simple enough to allow the direct simulation of DNA solutions, yet capturing how the fundamental thermodynamic processes are microscopically encoded in the nucleobase sequences. Physically relevant interactions are considered explicitly, such as interchain excluded volume, anisotropic base-pairing and base-stacking, and single-stranded bending rigidity. The model is studied in detail by a specially adapted Monte Carlo simulation method, based on parallel tempering and biased trials, which is designed to overcome the entropic and enthalpic barriers associated with the sampling of hybridization events of multiple single-stranded chains in solution. This methodology addresses both the configurational complexity of bringing together two complementary strands in a favorable orientation (entropic barrier) and the energetic penalty of breaking apart multiple associated bases in a double-stranded state (enthalpic barrier). For strands with sequences restricted to nonstaggering association and homogeneous pairing and stacking energies, base-pairing is found to dominate the hybridization over the translational and conformational entropy. For strands with sequence-dependent pairing corresponding to that of DNA, the complex dependence of the model's thermal stability on concentration, sequence, and degree of complementarity is shown to be qualitatively and quantitatively consistent both with experiment and with the predictions of statistical mechanical models.

Analysis of a DNA simulation model through hairpin melting experiments

We compare the predictions of a two-bead Brownian dynamics simulation model to melting experiments of DNA hairpins with complementary AT or GC stems and noninteracting loops in buffer A. This system emphasizes the role of stacking and hydrogen bonding energies, which are characteristics of DNA, rather than backbone bending, stiffness, and excluded volume interactions, which are generic characteristics of semiflexible polymers. By comparing high throughput data on the open-close transition of various DNA hairpins to the corresponding simulation data, we (1) establish a suitable metric to compare the simulations to experiments, (2) find a conversion between the simulation and experimental temperatures, and (3) point out several limitations of the model, including the lack of G-quartets and cross stacking effects. Our approach and experimental data can be used to validate similar coarse-grained simulation models.

A Coarse Grained Model for Atomic-Detailed DNA Simulations with Explicit Electrostatics

Coarse-grain (CG) techniques allow considerable extension of the accessible size and time scales in simulations of biological systems. Although many CG representations are available for the most common biomacromolecules, very few have been reported for nucleic acids. Here, we present a CG model for molecular dynamics simulations of DNA on the multi-microsecond time scale. Our model maps the complexity of each nucleotide onto six effective superatoms keeping the "chemical sense" of specific Watson-Crick recognition. Molecular interactions are evaluated using a classical Hamiltonian with explicit electrostatics calculated under the framework of the generalized Born approach. This CG representation is able to accurately reproduce experimental structures, breathing dynamics, and conformational transitions from the A to the B form in double helical fragments. The model achieves a good qualitative reproduction of temperature-driven melting and its dependence on size, ionic strength, and sequence specificity. Reconstruction of atomistic models from CG trajectories give remarkable agreement with structural, dynamic, and energetic features obtained from fully atomistic simulation, opening the possibility to acquire nearly atomic detail data from CG trajectories.

A systematically coarse-grained model for DNA and its predictions for persistence length, stacking, twist, and chirality

We introduce a coarse-grained model of DNA with bases modeled as rigid-body ellipsoids to capture their anisotropic stereochemistry. Interaction potentials are all physicochemical and generated from all-atom simulation/parameterization with minimal phenomenology. Persistence length, degree of stacking, and twist are studied by molecular dynamics simulation as functions of temperature, salt concentration, sequence, interaction potential strength, and local position along the chain for both single- and double-stranded DNA where appropriate. The model of DNA shows several phase transitions and crossover regimes in addition to dehybridization, including unstacking, untwisting, and collapse, which affect mechanical properties such as rigidity and persistence length. The model also exhibits chirality with a stable right-handed and metastable left-handed helix.

Supercoiling and local denaturation of plasmids with a minimalist DNA model

We report molecular dynamics simulations of DNA nanocircles and submicrometer-sized plasmids with torsional stress. The multiple microseconds time scale is reached thanks to a new one-bead-per-nucleotide coarse-grained model that combines structural accuracy and predictive power, achieved by means of the accurate choice of the force field terms and their unbiased statistically based parametrization. The model is validated with experimental structural data and available all-atom simulations of DNA nanocircles. Besides reproducing the nanocircles' structures and behavior on the short time scale, our model is capable of exploring three orders of magnitude further in time and to sample more efficiently the configuration space, unraveling novel behaviors. We explored the microsecond dynamics of entire small plasmids and observed supercoiling and compaction in the overtwisted case. The stability of overtwisted nanocircles and plasmids is predicted up to macroscopic time scales. Conversely, in the undertwisted case, at physiological values of the superhelical density, after a metastable phase of supercoiling-compaction, we observe the formation and the complex dynamics of denaturation bubbles over a multiple microseconds time scale. Our results indicate that the torsional stress is involved in a delicate balance with the temperature to determine the denaturation equilibrium and regulate the transcription process.

Computer simulation study of probe-target hybridization in model DNA microarrays: effect of probe surface density and target concentration

We use lattice Monte Carlo simulations to study the thermodynamics of hybridization of single-stranded "target" genes in solution with complementary "probe" DNA molecules immobilized on a microarray surface. The target molecules in our system contain 48 segments and the probes tethered on a hard surface contain 8-24 segments. The segments on the probe and target are distinct, with each segment representing a sequence of nucleotides that interacts exclusively with its unique complementary target segment with a single hybridization energy; all other interactions are zero. We examine how surface density (number of probes per unit surface area) and concentration of target molecules affect the extent of hybridization. For short probe lengths, as the surface density increases, the probability of binding long stretches of target segments increases at low surface density, reaches a maximum at an intermediate surface density, and then decreases at high surface density. Furthermore, as the surface density increases, the target is less likely to bind completely to one probe; instead, it binds simultaneously to multiple probes. At short probe lengths, as the target concentration increases, the fraction of targets binding completely to the probes (specificity) decreases. At long probe lengths, varying the target concentration does not affect the specificity. At all target concentrations as the probe length increases, the fraction of target molecules bound to the probes by at least one segment (sensitivity) increases while the fraction of target molecules completely bound to the probes (specificity) decreases. This work provides general guidelines to maximizing microarray sensitivity and specificity. Our results suggest that the sensitivity and specificity can be maximized by using probes 130-180 nucleotides long at a surface density in the range of 7 x 10(-5)- 3 x 10(-4) probe molecules per nm(2).

Using theory and computation to model nanoscale properties

This article provides an overview of the use of theory and computation to describe the structural, thermodynamic, mechanical, and optical properties of nanoscale materials. Nanoscience provides important opportunities for theory and computation to lead in the discovery process because the experimental tools often provide an incomplete picture of the structure and/or function of nanomaterials, and theory can often fill in missing features crucial to understanding what is being measured. However, there are important challenges to using theory as well, as the systems of interest are usually too large, and the time scales too long, for a purely atomistic level theory to be useful. At the same time, continuum theories that are appropriate for describing larger-scale (micrometer) phenomena are often not accurate for describing the nanoscale. Despite these challenges, there has been important progress in a number of areas, and there are exciting opportunities that we can look forward to as the capabilities of computational facilities continue to expand. Some specific applications that are discussed in this paper include: self-assembly of supramolecular structures, the thermal properties of nanoscale molecular systems (DNA melting and nanoscale water meniscus formation), the mechanical properties of carbon nanotubes and diamond crystals, and the optical properties of silver and gold nanoparticles.

Composite model for DNA torsion dynamics

DNA torsion dynamics is essential in the transcription process; a simple model for it, in reasonable agreement with experimental observations, has been proposed by Yakushevich (Y) and developed by several authors; in this, the nucleotides (the DNA subunits made of a sugar-phosphate group and the attached nitrogen base) are described by a single degree of freedom. In this paper we propose and investigate, both analytically and numerically, a "composite" version of the Y model, in which the sugar-phosphate group and the base are described by separate degrees of freedom. The model proposed here contains as a particular case the Y model and shares with it many features and results, but represents an improvement from both the conceptual and the phenomenological point of view. It provides a more realistic description of DNA and possibly a justification for the use of models which consider the DNA chain as uniform. It shows that the existence of solitons is a generic feature of the underlying nonlinear dynamics and is to a large extent independent of the detailed modeling of DNA. The model we consider supports solitonic solutions, qualitatively and quantitatively very similar to the Y solitons, in a fully realistic range of all the physical parameters characterizing the DNA.

Computer simulation study of molecular recognition in model DNA microarrays

DNA microarrays have been widely adopted by the scientific community for a variety of applications. To improve the performance of microarrays there is a need for a fundamental understanding of the interplay between the various factors that affect microarray sensitivity and specificity. We use lattice Monte Carlo simulations to study the thermodynamics and kinetics of hybridization of single-stranded target genes in solution with complementary probe DNA molecules immobilized on a microarray surface. The target molecules in our system contain 48 segments and the probes tethered on a hard surface contain 8-24 segments. The segments on the probe and target are distinct and each segment represents a sequence of nucleotides ( approximately 11 nucleotides). Each probe segment interacts exclusively with its unique complementary target segment with a single hybridization energy; all other interactions are zero. We examine how the probe length, temperature, or hybridization energy, and the stretch along the target that the probe segments complement, affect the extent of hybridization. For systems containing single probe and single target molecules, we observe that as the probe length increases, the probability of binding all probe segments to the target decreases, implying that the specificity decreases. We observe that probes 12-16 segments ( approximately 132-176 nucleotides) long gave the highest specificity and sensitivity. This agrees with the experimental results obtained by another research group, who found an optimal probe length of 150 nucleotides. As the hybridization energy increases, the longer probes are able to bind all their segments to the target, thus improving their specificity. The hybridization kinetics reveals that the segments at the ends of the probe are most likely to start the hybridization. The segments toward the center of the probe remain bound to the target for a longer time than the segments at the ends of the probe.

Solitons in the Yakushevich model of DNA beyond the contact approximation

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation l0 --> 0, where l0 is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without l0 --> 0. The model still supports soliton solutions indexed by two winding numbers (n,m); we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively.

Mesoscopic modeling for nucleic acid chain dynamics

To gain a deeper insight into cellular processes such as transcription and translation, one needs to uncover the mechanisms controlling the configurational changes of nucleic acids. As a step toward this aim, we present here a mesoscopic-level computational model that provides a new window into nucleic acid dynamics. We model a single-stranded nucleic as a polymer chain whose monomers are the nucleosides. Each monomer comprises a bead representing the sugar molecule and a pin representing the base. The bead-pin complex can rotate about the backbone of the chain. We consider pairwise stacking and hydrogen-bonding interactions. We use a modified Monte Carlo dynamics that splits the dynamics into translational bead motion and rotational pin motion. By performing a number of tests, we first show that our model is physically sound. We then focus on a study of the kinetics of a DNA hairpin--a single-stranded molecule comprising two complementary segments joined by a noncomplementary loop--studied experimentally. We find that results from our simulations agree with experimental observations, demonstrating that our model is a suitable tool for the investigation of the hybridization of single strands.

A model for protein-DNA interaction dynamics

We map a simplified version of the protein-DNA interaction problem into an Ising-model in a random magnetic field. The model includes a "head" which moves along the chain while interacting with the underlying spins. The head moves by using the statistical fluctuations of base openings. A Monte Carlo (MC) simulation of this model reveals the possibility of biased diffusion in one direction, followed by sequence identification and binding. The model provides some insight into the mechanisms used by some repressor proteins to diffuse and bind to specific DNA-binding sites.