Brownian dynamics simulations of single-stranded DNA hairpins

Computational Modeling of DNA 3D Structures: From Dynamics and Mechanics to Folding

DNA carries the genetic information required for the synthesis of RNA and proteins and plays an important role in many processes of biological development. Understanding the three-dimensional (3D) structures and dynamics of DNA is crucial for understanding their biological functions and guiding the development of novel materials. In this review, we discuss the recent advancements in computer methods for studying DNA 3D structures. This includes molecular dynamics simulations to analyze DNA dynamics, flexibility, and ion binding. We also explore various coarse-grained models used for DNA structure prediction or folding, along with fragment assembly methods for constructing DNA 3D structures. Furthermore, we also discuss the advantages and disadvantages of these methods and highlight their differences.

Effect of backbone chemistry on hybridization thermodynamics of oligonucleic acids: a coarse-grained molecular dynamics simulation study

In this paper we study how varying oligonucleic acid backbone chemistry affects the hybridization/melting thermodynamics of oligonucleic acids. We first describe the coarse-grained (CG) model with tunable parameters that we developed to enable the study of both naturally occurring oligonucleic acids, such as DNA, and their chemically-modified analogues, such as peptide nucleic acids (PNAs) and locked nucleic acids (LNAs). The DNA melting curves obtained using such a CG model and molecular dynamics simulations in an implicit solvent and with explicit ions match with the melting curves obtained using the empirical nearest-neighbor models. We use these CG simulations to then elucidate the effect of backbone flexibility, charge, and nucleobase spacing along the backbone on the melting curves, potential energy and conformational entropy change upon hybridization and base-pair hydrogen bond residence time. We find that increasing backbone flexibility decreases duplex thermal stability and melting temperature mainly due to increased conformational entropy loss upon hybridization. Removing charges from the backbone enhances duplex thermal stability due to the elimination of electrostatic repulsion and as a result a larger energetic gain upon hybridization. Lastly, increasing nucleobase spacing decreases duplex thermal stability due to decreasing stacking interactions that are important for duplex stability.

Theory and simulation of DNA-coated colloids: a guide for rational design

By exploiting the exquisite selectivity of DNA hybridization, DNA-coated colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the fact that a proper choice of the grafted DNA sequences yields fine control over the colloidal interactions. Theory and simulations have an important role to play in the optimal design of self assembling DNACCs. At present, the powerful model-based design tools are not widely used, because the theoretical literature is fragmented and the connection between different theories is often not evident. In this Perspective, we aim to discuss the similarities and differences between the different models that have been described in the literature, their underlying assumptions, their strengths and their weaknesses. Using the tools described in the present Review, it should be possible to move towards a more rational design of novel self-assembling structures of DNACCs and, more generally, of systems where ligand-receptor are used to control interactions.

Melting dynamics of short dsDNA chains in saline solutions

DNA melting has attracted much attention due to its importance in understanding the life-reproduction and metabolism and in the applications of modern DNA-based technologies. While numerous works have been contributed to the determination of melting profiles in diverse environments, the understanding of DNA melting dynamics is still limited. By employing three-site-per-nucleotide (3SPN) double-stranded DNA (dsDNA) model, we here demonstrate the melting dynamics of an isolated short dsDNA under different conditions (different temperatures, ionic concentrations and DNA chain lengths) can be accessed by coarse-grained simulation studies. We particularly show that at dilute ionic concentration the dsDNA, regardless being symmetric or asymmetric, opens at both ends with roughly equal probabilities, while at high ionic concentration the asymmetric dsDNA chain opens at the A-T-rich end. The comparisons of our simulation results to available data are discussed, and overall good agreements have been found.

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.

A coarse-grained model for DNA-functionalized spherical colloids, revisited: effective pair potential from parallel replica simulations

We discuss a coarse-grained model recently proposed by Starr and Sciortino [J. Phys.: Condens. Matter 18, L347 (2006)] for spherical particles functionalized with short single DNA strands. The model incorporates two key aspects of DNA hybridization, i.e., the specificity of binding between DNA bases and the strong directionality of hydrogen bonds. Here, we calculate the effective potential between two DNA-functionalized particles of equal size using a parallel replica protocol. We find that the transition from bonded to unbonded configurations takes place at considerably lower temperatures compared to those that were originally predicted using standard simulations in the canonical ensemble. We put particular focus on DNA-decorations of tetrahedral and octahedral symmetry, as they are promising candidates for the self-assembly into a single-component diamond structure. Increasing colloid size hinders hybridization of the DNA strands, in agreement with experimental findings.

DNA translocation through a nanopore in a single-layered doped semiconductor membrane

Recently, we developed a computational model that allowed us to study the influence a semiconductor membrane has on a DNA molecule translocating through a nanopore in this membrane. Our model incorporated both the self-consistent Poisson-Nernst-Planck simulations for the electric potential of a solid state membrane immersed in an electrolyte solution together with the Brownian dynamics of the biomolecule. In this paper, we study how the applied electrolyte bias, the semiconductor membrane bias, and the semiconductor material type (n-Si or p-Si) affect the translocation dynamics of a single-stranded DNA moving through a nanopore in a single-layered semiconductor membrane. We show that the type of semiconductor material used for the membrane has a prominent effect on the biomolecule's translocation time, with DNA exhibiting much longer translocation times through the p-type membrane than through the n type at the same electrolyte and membrane potentials, while the extension of the biomolecule remains practically unchanged. In addition, we find the optimal combination for the membrane-electrolyte system's parameters to achieve the longest translocation time and largest DNA extension. With our single-layered electrically tunable membranes, the DNA translocation time can be manipulated to have an order of magnitude increase.

Biopolymer hairpin loops sustained by polarons

We show that polarons can sustain looplike configurations in flexible biopolymers and that the size of the loops depend on both the flexural rigidity of the polymer and the electron-phonon coupling constant. In particular we show that for single stranded DNA (ssDNA) and polyacetylene such loops can have as few as seven monomers. We also show that these configurations are very stable under thermal fluctuations and so could facilitate the formation of hairpin loops of ssDNA.

Modelling Nucleic Acid Structure and Flexibility: From Atomic to Mesoscopic Scale

This chapter surveys some of the recent developments in coarse-grained modelling of nucleic acids. We first discuss models based on pseudoatoms, effective spherical particles representing groups of atoms. A major part of the chapter is devoted to models in which bases or base pairs are represented as independent, interacting rigid bodies. Two popular definitions of internal coordinates, as implemented in the programs 3DNA and Curves+, are outlined from a common perspective. Recently developed rigid base and basepair models with nonlocal quadratic interactions are presented. A statistical mechanical description of the models on their full phase space yields exact relations between model parameters and expected values of some state functions. We estimated shape and stiffness parameters for nonlocal rigid base and basepair models of a DNA oligomer containing A-tract. The parameterization is based on atomic-resolution molecular dynamics simulation data. We found that the rigid base model is consistent with a local interaction pattern, while interactions in the rigid basepair model are visibly non-local, in agreement with earlier findings. Differences in shape and stiffness parameters obtained using Curves+ and 3DNA coordinates are found to be small for structures within the B-DNA family. Anharmonic effects, coarser models, and other approaches to describe nucleic acid structure and flexibility are discussed.

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.

Polymer translocation through an electrically tunable nanopore in a multilayered semiconductor membrane

We have developed a two-level computational model that enables us to calculate electrostatic fields created by a semiconductor membrane submerged in electrolytic solution and investigate the effects of these fields on the dynamics of a polymer translocating through a nanopore in the membrane. In order to calculate the electrostatic potentials and the ionic concentrations in a solid-state nanopore, we have self-consistently solved Poisson equation within the semiclassical approximation for charge carrier statistics in the membrane and electrolyte. The electrostatic potentials obtained from these simulations are then used in conjunction with Langevin (Brownian) dynamics to model polymer translocation through the nanopore. In this work, we consider single-stranded DNA (ssDNA) translocation through semiconductor membranes consisting of heavily doped p- and n-layers of silicon forming a pn-junction which is capable of creating strong electric fields. We show that the membrane electric field controls dynamics of a biomolecule inside the channel, to either momentarily trap it, slow it down, or allow it to translocate at will.

Role of loop entropy in the force induced melting of DNA hairpin

Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy plays a crucial role at high force. As a result, the force-temperature diagram differs significantly with the theoretical prediction.

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.

Structural, mechanical, and thermodynamic properties of a coarse-grained DNA model

We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson-Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an "average base" description of DNA. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization, and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.

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 of DNA with explicit solvation by water and ions

Solvation by water and ions has been shown to be vitally important for biological molecules, yet fully atomistic simulations of large biomolecules remain a challenge due to their high computational cost. The effect of solvation is the most pronounced in polyelectrolytes, of which DNA is a paradigmatic example. Coarse-grained (CG) representations have been developed to model the essential physics of the DNA molecule, yet almost without exception, these models replace the water and ions by implicit solvation in order to significantly reduce the computational expense. This work introduces the first coarse-grained model of DNA solvated explicitly with water and ions. To this end, we combined two established CG models; the recently developed mW-ion model [DeMille, R. C.; Molinero, V. J. Chem. Phys. 2009, 131, 034107], which reproduces the structure of aqueous ionic solutions without electrostatic interactions, was coupled to the three-sites-per-nucleotide (3SPN) CG model of DNA [Knotts, T. A., IV; et al. J. Chem. Phys. 2007, 126, 084901]. Using atomistic simulations of d(CGCGAATTCGCG)(2) as a reference, we optimized the coarse-grained interactions between DNA and solvent to reproduce the solvation structure of water and ions around CG DNA. The resulting coarse-grained model of DNA explicitly solvated by ions and water (mW/3SPN-DNA) exhibits base-pair specificity and ion-condensation effects and it is 2 orders of magnitude computationally more efficient than atomistic models. We describe the parametrization strategy and offer insight into how other CG models may be combined with a coarse-grained solvent model such as mW-ion.

DNA nanotweezers studied with a coarse-grained model of DNA

We introduce a coarse-grained rigid nucleotide model of DNA that reproduces the basic thermodynamics of short strands, duplex hybridization, single-stranded stacking, and hairpin formation, and also captures the essential structural properties of DNA: the helical pitch, persistence length, and torsional stiffness of double-stranded molecules, as well as the comparative flexibility of unstacked single strands. We apply the model to calculate the detailed free-energy landscape of one full cycle of DNA "tweezers," a simple machine driven by hybridization and strand displacement.

Coarse-Grained Brownian Dynamics Simulations of the 10-23 DNAzyme

Deoxyribozymes (DNAzymes) are single-stranded DNA that catalyze nucleic acid biochemistry. Although a number of DNAzymes have been discovered by in vitro selection, the relationship between their tertiary structure and function remains unknown. We focus here on the well-studied 10-23 DNAzyme, which cleaves mRNA with a catalytic efficiency approaching that of RNase A. Using coarse-grained Brownian dynamics simulations, we find that the DNAzyme bends its substrate away from the cleavage point, exposing the reactive site and buckling the DNAzyme catalytic core. This hypothesized transition state provides microscopic insights into experimental observations concerning the size of the DNAzyme/substrate complex, the impact of the recognition arm length, and the sensitivity of the enzymatic activity to point mutations of the catalytic core. Upon cleaving the pertinent backbone bond in the substrate, we find that the catalytic core of the DNAzyme unwinds and the overall complex rapidly extends, in agreement with experiments on the related 8-17 DNAzyme. The results presented here provide a starting point for interpreting experimental data on DNAzyme kinetics, as well as developing more detailed simulation models. The results also demonstrate the limitations of using a simple physical model to understand the role of point mutations.