Modeling DNA structure, elasticity, and deformations at the base-pair level

DNAffinity: a machine-learning approach to predict DNA binding affinities of transcription factors

We present a physics-based machine learning approach to predict in vitro transcription factor binding affinities from structural and mechanical DNA properties directly derived from atomistic molecular dynamics simulations. The method is able to predict affinities obtained with techniques as different as uPBM, gcPBM and HT-SELEX with an excellent performance, much better than existing algorithms. Due to its nature, the method can be extended to epigenetic variants, mismatches, mutations, or any non-coding nucleobases. When complemented with chromatin structure information, our in vitro trained method provides also good estimates of in vivo binding sites in yeast.

Mechanical properties of DNA and DNA nanostructures: comparison of atomistic, Martini and oxDNA models

The flexibility and stiffness of small DNA molecules play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) with lengths ranging from 12 base-pairs (bp) to 56 bp, paranemic crossover (PX) DNA and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grained models - Martini and oxDNA. To calculate the persistence length (Lp) and the stretch modulus (γ) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for the DNTs, we implement our previously developed theoretical framework. We compare and contrast all of the results with previously reported all-atom molecular dynamics (MD) simulations and experimental results. The mechanical properties of dsDNA (Lp ∼ 50 nm, γ ∼ 800-1500 pN), PX DNA (γ ∼ 1600-2000 pN) and DNTs (Lp ∼ 1-10 μm, γ ∼ 6000-8000 pN) estimated using the Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces values of Lp and γ which are an order of magnitude higher. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. oxDNA captures the salt concentration effect on the small dsDNA mechanics. But it is found to be ineffective for reproducing the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA and DNA based nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.

Coarse-grained modelling of the structural properties of DNA origami

We use the oxDNA coarse-grained model to provide a detailed characterization of the fundamental structural properties of DNA origami, focussing on archetypal 2D and 3D origami. The model reproduces well the characteristic pattern of helix bending in a 2D origami, showing that it stems from the intrinsic tendency of anti-parallel four-way junctions to splay apart, a tendency that is enhanced both by less screened electrostatic interactions and by increased thermal motion. We also compare to the structure of a 3D origami whose structure has been determined by cryo-electron microscopy. The oxDNA average structure has a root-mean-square deviation from the experimental structure of 8.4 Å, which is of the order of the experimental resolution. These results illustrate that the oxDNA model is capable of providing detailed and accurate insights into the structure of DNA origami, and has the potential to be used to routinely pre-screen putative origami designs and to investigate the molecular mechanisms that regulate the properties of DNA origami.

Representation of DNA environment: Spiral staircase distribution function

In the present study, we investigated the local structure of DNA and its environment using a new visualization technique. The spiral staircase distribution function (SSDF) is determined as two-dimensional density distribution of atoms of water and ligands in local reference frames linked with each base pair of poly-DNA molecule, either GC or AT. This property of SSDF provides opportunity to study sequence-specific binding of ions, peptides, and other agents derived from a molecular dynamics computer simulation. The spatial structure of double-stranded DNA environment in water solution containing either Mg²⁺ or Na⁺ ions was investigated using of SSDF. The distributions of ions around GC and AT base pairs are shown separately. It is observed that Mg²⁺ ions interact with DNA atoms by means of the layer of water molecules and penetrate into the major groove only. Na⁺ ions have a direct contact with DNA atoms and penetrate both into the major and minor grooves of DNA. © 2018 Wiley Periodicals, Inc.

Rhombic-Shaped Nanostructures and Mechanical Properties of 2D DNA Origami Constructed with Different Crossover/Nick Designs

DNA origami methods enable the fabrication of various nanostructures and nanodevices, but their effective use depends on an understanding of their structural and mechanical properties and the effects of basic structural features. Frequency-modulation atomic force microscopy is introduced to directly characterize, in aqueous solution, the crossover regions of sets of 2D DNA origami based on different crossover/nick designs. Rhombic-shaped nanostructures formed under the influence of flexible crossovers placed between DNA helices are observed in DNA origami incorporating crossovers every 3, 4, or 6 DNA turns. The bending rigidity of crossovers is determined to be only one-third of that of the DNA helix, based on interhelical electrostatic forces reported elsewhere, and the measured pitches of the 3-turn crossover design rhombic-shaped nanostructures undergoing negligible bending. To evaluate the robustness of their structural integrity, they are intentionally and simultaneously stressed using force-controlled atomic force microscopy. DNA crossovers are verified to have a stabilizing effect on the structural robustness, while the nicks have an opposite effect. The structural and mechanical properties of DNA origami and the effects of crossovers and nicks revealed in this paper can provide information essential for the design of versatile DNA origami structures that exhibit specified and desirable properties.

The "sugar" coarse-grained DNA model

More than 20 coarse-grained (CG) DNA models have been developed for simulating the behavior of this molecule under various conditions, including those required for nanotechnology. However, none of these models reproduces the DNA polymorphism associated with conformational changes in the ribose rings of the DNA backbone. These changes make an essential contribution to the DNA local deformability and provide the possibility of the transition of the DNA double helix from the B-form to the A-form during interactions with biological molecules. We propose a CG representation of the ribose conformational flexibility. We substantiate the choice of the CG sites (six per nucleotide) needed for the "sugar" GC DNA model, and obtain the potentials of the CG interactions between the sites by the "bottom-up" approach using the all-atom AMBER force field. We show that the representation of the ribose flexibility requires one non-harmonic and one three-particle potential, the forms of both the potentials being different from the ones generally used. The model also includes (i) explicit representation of ions (in an implicit solvent) and (ii) sequence dependence. With these features, the sugar CG DNA model reproduces (with the same parameters) both the B- and A- stable forms under corresponding conditions and demonstrates both the A to B and the B to A phase transitions. Graphical Abstract The proposed coarse-grained DNA model allows to reproduce both the B- and A- DNA forms and the transitions between them under corresponding conditions.

Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy

Using analytical approach and Monte Carlo (MC) simulations, we study the elastic behavior of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than three-dimensional (3D) conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in two dimensions, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the transient curvature increasing with a half helical turn periodicity along the bent polymer.

Extreme bendability of DNA double helix due to bending asymmetry

Experimental data of the DNA cyclization (J-factor) at short length scales exceed the theoretical expectation based on the wormlike chain (WLC) model by several orders of magnitude. Here, we propose that asymmetric bending rigidity of the double helix in the groove direction can be responsible for extreme bendability of DNA at short length scales and it also facilitates DNA loop formation at these lengths. To account for the bending asymmetry, we consider the asymmetric elastic rod (AER) model which has been introduced and parametrized in an earlier study [B. Eslami-Mossallam and M. R. Ejtehadi, Phys. Rev. E 80, 011919 (2009)]. Exploiting a coarse grained representation of the DNA molecule at base pair (bp) level and using the Monte Carlo simulation method in combination with the umbrella sampling technique, we calculate the loop formation probability of DNA in the AER model. We show that the DNA molecule has a larger J-factor compared to the WLC model which is in excellent agreement with recent experimental data.

Coupled binding-bending-folding: The complex conformational dynamics of protein-DNA binding studied by atomistic molecular dynamics simulations

BACKGROUND

Protein-DNA binding often involves dramatic conformational changes such as protein folding and DNA bending. While thermodynamic aspects of this behavior are understood, and its biological function is often known, the mechanism by which the conformational changes occur is generally unclear. By providing detailed structural and energetic data, molecular dynamics simulations have been helpful in elucidating and rationalizing protein-DNA binding.

SCOPE OF REVIEW

This review will summarize recent atomistic molecular dynamics simulations of the conformational dynamics of DNA and protein-DNA binding. A brief overview of recent developments in DNA force fields is given as well.

MAJOR CONCLUSIONS

Simulations have been crucial in rationalizing the intrinsic flexibility of DNA, and have been instrumental in identifying the sequence of binding events, the triggers for the conformational motion, and the mechanism of binding for a number of important DNA-binding proteins.

GENERAL SIGNIFICANCE

Molecular dynamics simulations are an important tool for understanding the complex binding behavior of DNA-binding proteins. With recent advances in force fields and rapid increases in simulation time scales, simulations will become even more important for future studies. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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.

Rupture mechanism of liquid crystal thin films realized by large-scale molecular simulations

The ability of liquid crystal (LC) molecules to respond to changes in their environment makes them an interesting candidate for thin film applications, particularly in bio-sensing, bio-mimicking devices, and optics. Yet the understanding of the (in)stability of this family of thin films has been limited by the inherent challenges encountered by experiment and continuum models. Using unprecedented large-scale molecular dynamics (MD) simulations, we address the rupture origin of LC thin films wetting a solid substrate at length scales similar to those in experiment. Our simulations show the key signatures of spinodal instability in isotropic and nematic films on top of thermal nucleation, and importantly, for the first time, evidence of a common rupture mechanism independent of initial thickness and LC orientational ordering. We further demonstrate that the primary driving force for rupture is closely related to the tendency of the LC mesogens to recover their local environment in the bulk state. Our study not only provides new insights into the rupture mechanism of liquid crystal films, but also sets the stage for future investigations of thin film systems using peta-scale molecular dynamics simulations.

Presentation of large DNA molecules for analysis as nanoconfined dumbbells

The analysis of very large DNA molecules intrinsically supports long-range, phased sequence information, but requires new approaches for their effective presentation as part of any genome analysis platform. Using a multi-pronged approach that marshaled molecular confinement, ionic environment, and DNA elastic properties-but tressed by molecular simulations-we have developed an efficient and scalable approach for presentation of large DNA molecules within nanoscale slits. Our approach relies on the formation of DNA dumbbells, where large segments of the molecules remain outside the nanoslits used to confine them. The low ionic environment, synergizing other features of our approach, enables DNA molecules to adopt a fully stretched conformation, comparable to the contour length, thereby facilitating analysis by optical microscopy. Accordingly, a molecular model is proposed to describe the conformation and dynamics of the DNA molecules within the nanoslits; a Langevin description of the polymer dynamics is adopted in which hydrodynamic effects are included through a Green's function formalism. Our simulations reveal that a delicate balance between electrostatic and hydrodynamic interactions is responsible for the observed molecular conformations. We demonstrate and further confirm that the "Odijk regime" does indeed start when the confinement dimensions size are of the same order of magnitude as the persistence length of the molecule. We also summarize current theories concerning dumbbell dynamics.

Coarse-graining DNA for simulations of DNA nanotechnology

To simulate long time and length scale processes involving DNA it is necessary to use a coarse-grained description. Here we provide an overview of different approaches to such coarse-graining, focussing on those at the nucleotide level that allow the self-assembly processes associated with DNA nanotechnology to be studied. OxDNA, our recently-developed coarse-grained DNA model, is particularly suited to this task, and has opened up this field to systematic study by simulations. We illustrate some of the range of DNA nanotechnology systems to which the model is being applied, as well as the insights it can provide into fundamental biophysical properties of DNA.

Confinement dynamics of a semiflexible chain inside nano-spheres

We study the conformations of a semiflexible chain, confined in nano-scaled spherical cavities, under two distinct processes of confinement. Radial contraction and packaging are employed as two confining procedures. The former method is performed by gradually decreasing the diameter of a spherical shell which envelopes a confined chain. The latter procedure is carried out by injecting the chain inside a spherical shell through a hole on the shell surface. The chain is modeled with a rigid body molecular dynamics simulation and its parameters are adjusted to DNA base-pair elasticity. Directional order parameter is employed to analyze and compare the confined chain and the conformations of the chain for two different sizes of the spheres are studied in both procedures. It is shown that for the confined chains in the sphere sizes of our study, they appear in spiral or tennis-ball structures, and the tennis-ball structure is more likely to be observed in more compact confinements. Our results also show that the dynamical procedure of confinement and the rate of the confinement are influential parameters of the structure of the chain inside spherical cavities.

Modeling spatial correlation of DNA deformation: DNA allostery in protein binding

We report a study of DNA deformations using a coarse-grained mechanical model and quantitatively interpret the allosteric effects in protein-DNA binding affinity. A recent single-molecule study (Kim et al. Science 2013, 339, 816) showed that when a DNA molecule is deformed by specific binding of a protein, the binding affinity of a second protein separated from the first protein is altered. Experimental observations together with molecular dynamics simulations suggested that the origin of the DNA allostery is related to the observed deformation of DNA's structure, in particular, the major groove width. To unveil and quantify the underlying mechanism for the observed major groove deformation behavior related to the DNA allostery, here we provide a simple but effective analytical model where DNA deformations upon protein binding are analyzed and spatial correlations of local deformations along the DNA are examined. The deformation of the DNA base orientations, which directly affect the major groove width, is found in both an analytical derivation and coarse-grained Monte Carlo simulations. This deformation oscillates with a period of 10 base pairs with an amplitude decaying exponentially from the binding site with a decay length lD ≈10 base pairs as a result of the balance between two competing terms in DNA base-stacking energy. This length scale is in agreement with that reported from the single-molecule experiment. Our model can be reduced to the worm-like chain form at length scales larger than lP but is able to explain DNA's mechanical properties on shorter length scales, in particular, the DNA allostery of protein-DNA interactions.

RNA 3D structure prediction by using a coarse-grained model and experimental data

RNAs form complex secondary and three-dimensional structures, and their biological functions highly rely on their structures and dynamics. Here we developed a general coarse-grained framework for RNA 3D structure prediction. A new, hybrid coarse-grained model that explicitly describes the electrostatics and hydrogen-bond interactions has been constructed based on experimental structural statistics. With the simulated annealing simulation protocol, several RNAs of less than 30-nt were folded to within 4.0 Å of the native structures. In addition, with limited restraints on Watson-Crick basepairing based on the data from NMR spectroscopy and small-angle X-ray scattering (SAXS) information, the current model was able to characterize the complex tertiary structures of large size RNAs, such as 5S ribosome and U2/U6 snRNA. We also demonstrated that the pseudoknot structure was better captured when the coordinating Mg(2+) cations and limited basepairing restraints were included. The accuracy of our model has been compared favorably with other RNA structure prediction methods presented in the previous study of RNA-Puzzles. Therefore the coarse-grained model presented here offers a unique approach for accurate prediction and modeling of RNA structures.

Rigid-body molecular dynamics of DNA inside a nucleosome

The majority of eukaryotic DNA, about three quarter, is wrapped around histone proteins forming so-called nucleosomes. To study nucleosomal DNA we introduce a coarse-grained molecular dynamics model based on sequence-dependent harmonic rigid base pair step parameters of DNA and nucleosomal binding sites. Mixed parametrization based on all-atom molecular dynamics and crystallographic data of protein-DNA structures is used for the base pair step parameters. The binding site parameters are adjusted by experimental B-factor values of the nucleosome crystal structure. The model is then used to determine the energy cost for placing a twist defect into the nucleosomal DNA which allows us to use Kramers theory to calculate nucleosome sliding caused by such defects. It is shown that the twist defect scenario together with the sequence-dependent elasticity of DNA can explain the slow time scales observed for nucleosome mobility along DNA. With this method we also show how the twist defect mechanism leads to a higher mobility of DNA in the presence of sin mutations near the dyad axis. Finally, by performing simulations on 5s rDNA, 601, and telomeric base pair sequences, it is demonstrated that the current model is a powerful tool to predict nucleosome positioning.

Modeling the mechanical properties of DNA nanostructures

We discuss generalizations of a previously published coarse-grained description [Mergell et al., Phys. Rev. E 68, 021911 (2003)] of double stranded DNA (dsDNA). The model is defined at the base-pair level and includes the electrostatic repulsion between neighbor helices. We show that the model reproduces mechanical and elastic properties of several DNA nanostructures (DNA origamis). We also show that electrostatic interactions are necessary to reproduce atomic force microscopy measurements on planar DNA origamis.

Definition of the persistence length in the coarse-grained models of DNA elasticity

By considering the detailed structure of DNA in the base pair level, two possible definitions of the persistence length are compared. One definition is related to the orientation of the terminal base pairs, and the other is based on the vectors which connect two adjacent base pairs at each end of the molecule. It is shown that although these definitions approach each other for long DNA molecules, they are dramatically different on short length scales. We show analytically that the difference mostly comes from the shear flexibility of the molecule and can be used to measure the shear modulus of DNA.

DNA Bending through Roll Angles Is Independent of Adjacent Base Pairs

We have studied DNA bending for a wide range of DNA sequences by two-dimensional adaptive umbrella sampling simulations on adjacent roll angles. Calculated free energy surfaces are largely additive and can be well approximated by the sum of the one-dimensional free energy surfaces. Cooperativity between adjacent roll angles was found to be negligible: less than 1.0 kcal/mol and a small fraction of the overall bending energy. Our calculations validate the assumptions underlying many popular coarse-grained models for DNA bending, and demonstrate their theoretical validity for investigating DNA bending.

BROMOC-D: Brownian Dynamics/Monte-Carlo Program Suite to Study Ion and DNA Permeation in Nanopores

A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion-ion and ion-DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)(n) and ss-poly(dC)(n). The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.

DNA Bending through Large Angles Is Aided by Ionic Screening

We used adaptive umbrella sampling on a modified version of the roll angle to simulate the bending of DNA dodecamers. Simulations were carried out with the AMBER and CHARMM force fields for 10 sequences in which the central base pair step was varied. On long length scales, the DNA behavior was found to be consistent with the worm-like chain model. Persistence lengths calculated directly from the simulated structures and indirectly through the use of sequence-independent coarse-grained models based on simulation data were similar to literature values. On short length scales, the free energy cost of bending DNA was found to be consistent with the worm-like chain model for small and intermediate bending angles. At large angles, the bending free energy as a function of the roll angle became linear, suggesting a relative increase in flexibility at larger roll angles. Counterions congregated on the concave side of the highly bent DNA and screened the repulsion of the phosphate groups, facilitating the bending.

Influence of mobile DNA-protein-DNA bridges on DNA configurations: coarse-grained Monte-Carlo simulations

A large literature exists on modeling the influence of sequence-specific DNA-binding proteins on the shape of the DNA double helix in terms of one or a few fixed constraints. This approach is inadequate for the many proteins that bind DNA sequence independently, and that are present in very large quantities rather than as a few copies, such as the nucleoid proteins in bacterial cells. The influence of such proteins on DNA configurations is better modeled in terms of a great number of mobile constraints on the DNA. Types of constraints that mimic the influence of various known non-specifically DNA binding proteins include DNA bending, wrapping, and bridging. Using Monte-Carlo simulations, we here investigate the influence of (non-interacting) mobile DNA-protein-DNA bridges on the configurations of a 1000 bp piece of linear DNA, for both homogeneous DNA and DNA with an intrinsic planar bend. Results are compared to experimental data on the bacterial nucleoid protein H-NS that forms DNA-protein-DNA bridges. In agreement with data on H-NS, we find very strong positioning of DNA-protein-DNA bridges in the vicinity of planar bends. H-NS binds to DNA very cooperatively, but for non-interacting bridges we only find a moderate DNA-induced clustering. Finally, it has been suggested that H-NS is an important contributor to the extreme condensation of bacterial DNA into a nucleoid structure, but we find only a moderate compaction of DNA coils with increasing numbers of non-interacting bridges. Our results illustrate the importance of quantifying the various effects on DNA configurations that have been proposed for proteins that bind DNA sequence independently.

Heat conductivity of DNA double helix

Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.

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.

Coarse-grained model for simulation of RNA three-dimensional structures

The accurate prediction of an RNA's three-dimensional structure from its "primary structure" will have a tremendous influence on the experimental design and its interpretation and ultimately our understanding of the many functions of RNA. This paper presents a general coarse-grained (CG) potential for modeling RNA 3-D structures. Each nucleotide is represented by five pseudo atoms, two for the backbone (one for the phosphate and another for the sugar) and three for the base to represent base-stacking interactions. The CG potential has been parametrized from statistical analysis of 688 RNA experimental structures. Molecular dynamic simulations of 15 RNA molecules with the length of 12-27 nucleotides have been performed using the CG potential, with performance comparable to that from all-atom simulations. For ~75% of systems tested, simulated annealing led to native-like structures at least once out of multiple repeated runs. Furthermore, with weak distance restraints based on the knowledge of three to five canonical Watson-Crick pairs, all 15 RNAs tested are successfully folded to within 6.5 Å of native structures using the CG potential and simulated annealing. The results reveal that with a limited secondary structure model the current CG potential can reliably predict the 3-D structures for small RNA molecules. We also explored an all-atom force field to construct atomic structures from the CG simulations.

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.

Conformational preference of ChaK1 binding peptides: a molecular dynamics study

TRPM7/ChaK1 is a recently discovered atypical protein kinase that has been suggested to selectively phosphorylate the substrate residues located in α-helices. However, the actual structure of kinase-substrate complex has not been determined experimentally and the recognition mechanism remains unknown. In this work we explored possible kinase-substrate binding modes and the likelihood of an α-helix docking interaction, within a kinase active site, using molecular modeling. Specifically kinase ChaK1 and its two peptide substrates were examined; one was an 11-residue segment from the N-terminal domain of annexin-1, a putative endogenous substrate for ChaK1, and the other was an engineered 16-mer peptide substrate determined via peptide library screening. Simulated annealing (SA), replica-exchange molecular dynamics (REMD) and steered molecular dynamics (SMD) simulations were performed on the two peptide substrates and the ChaK1-substrate complex in solution. The simulations indicate that the two substrate peptides are unlikely to bind and react with the ChaK1 kinase in a stable α-helical conformation overall. The key structural elements, sequence motifs, and amino acid residues in the ChaK1 and their possible functions involved in the substrate recognition are discussed.

PACS Codes: 87.15.A-

Insights on protein-DNA recognition by coarse grain modelling

Coarse grain modelling of macromolecules is a new approach, potentially well adapted to answer numerous issues, ranging from physics to biology. We propose here an original DNA coarse grain model specifically dedicated to protein-DNA docking, a crucial, but still largely unresolved, question in molecular biology. Using a representative set of protein-DNA complexes, we first show that our model is able to predict the interaction surface between the macromolecular partners taken in their bound form. In a second part, the impact of the DNA sequence and electrostatics, together with the DNA and protein conformations on docking is investigated. Our results strongly suggest that the overall DNA structure mainly contributes in discriminating the interaction site on cognate proteins. Direct electrostatic interactions between phosphate groups and amino acid side chains strengthen the binding. Overall, this work demonstrates that coarse grain modeling can reveal itself a precious auxiliary for a general and complete description and understanding of protein-DNA association mechanisms.

Twist-stretch correlation of DNA

We present an elastic model for B-form DNA with variable radius to study the elastic twist-stretch coupling of stretched DNA. In this model, only two strain variables as well as the changes in the energy of the hydrogen and covalent bonds of DNA during the deformation are considered. It is found that, depending on the elastic constants, the correlation between twisting and stretching of a helical molecule can be positive or negative. It is shown that for the suitable elastic constants in the model, the twist-stretch coupling of DNA behaves nonmonotonically, and contrary to intuition, the DNA twisting and stretching are positively correlated for small distortions. This result is entirely consistent with recent experimental results.

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).

Generalized coarse-grained model based on point multipole and Gay-Berne potentials

This paper presents a general coarse-grained molecular mechanics model based on electric point multipole expansion and Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic Gay-Berne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The Gay-Berne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the all-atom counterpart. The coarse-grained model has been applied to rigid-body molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with all-atom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers.

Unified description of poly- and oligonucleotide DNA melting: nearest-neighbor, Poland-Sheraga, and lattice models

We show that a simple lattice model can provide a unified description of the thermal denaturation of DNA oligomers and polymers. The model quantitatively reproduces experimental melting curves and reduces in limiting cases to the nearest-neighbor model and a suitable modified Poland-Sheraga model. Our results support the interpretation of the cooperativity parameter sigma for bubble opening in terms of an interfacial (forking) free energy which also affects chain opening from the ends. The lattice model treats long-ranged excluded volume interactions between all parts of the molecule explicitly, provides access to an ensemble of three dimensional structures (and hence the response to external mechanical forces), and includes fluctuations in situations without pre-determined secondary structure.

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.

Conservative spatial chaos of buckled elastic linkages

Buckling of an elastic linkage under general loading is investigated. We show that buckling is related to an initial value problem, which is always a conservative, area-preserving mapping, even if the original static problem is nonconservative. In some special cases, we construct the global bifurcation diagrams, and argue that their complicated structure is a consequence of spatial chaos. We characterize spatial chaos by the associated initial value problem's topological entropy, which turns out to be related to the number of buckled configurations.

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SMEs) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SMEs it is possible to manipulate molecules one at a time and measure distributions describing molecular properties, characterize the kinetics of biomolecular reactions and detect molecular intermediates. SMEs provide additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SMEs it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level, emphasizing the importance of SMEs to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SMEs from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOTs), magnetic tweezers (MTs), biomembrane force probes (BFPs) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation) and proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SMEs to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.

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.

Wringing out DNA

The chiral nature of DNA plays a crucial role in cellular processes. Here we use magnetic tweezers to explore one of the signatures of this chirality, the coupling between stretch and twist deformations. We show that the extension of a stretched DNA molecule increases linearly by 0.42 nm per excess turn applied to the double helix. This result contradicts the intuition that DNA should lengthen as it is unwound and get shorter with overwinding. We then present numerical results of energy minimizations of torsionally restrained DNA that display a behavior similar to the experimental data and shed light on the molecular details of this surprising effect.

Elastic correlations in nucleosomal DNA structure

The structure of DNA in the nucleosome core particle is studied using an elastic model that incorporates anisotropy in the bending energetics and twist-bend coupling. Using the experimentally determined structure of nucleosomal DNA [T. J. Richmond and C. A. Davey, Nature (London) 423, 145 (2003)], it is shown that elastic correlations exist between twist, roll, tilt, and stretching of DNA, as well as the distance between phosphate groups. The twist-bend coupling term is shown to be able to capture these correlations to a large extent, and a fit to the experimental data yields a new estimate of G = 25 nm for the value of the twist-bend coupling constant.

Nucleosome interactions in chromatin: fiber stiffening and hairpin formation

We use Monte Carlo simulations to study attractive and excluded volume interactions between nucleosome core particles in 30-nm chromatin fibers. The nucleosomes are treated as disklike objects having an excluded volume and short-range attraction modeled by a variant of the Gay-Berne potential. The nucleosomes are connected via bendable and twistable linker DNA in the crossed linker fashion. We investigate the influence of the nucleosomal excluded volume on the stiffness of the fiber. For parameter values that correspond to chicken erythrocyte chromatin, we find that the persistence length is governed to a large extent by that excluded volume whereas the soft linker backbone elasticity plays only a minor role. We further find that internucleosomal attraction can induce the formation of hairpin configurations. Tension-induced opening of such configurations into straight fibers manifests itself in a quasiplateau in the force-extension curve that resembles results from recent micromanipulation experiments. Such hairpins may play a role in the formation of higher-order structures in chromosomes like chromonema fibers.