A coarse-grain three-site-per-nucleotide model for DNA with explicit ions

Simulating the Lyotropic Phase Behavior of a Partially Self-Complementary DNA Tetramer

DNA oligomers in solution have been found to develop liquid crystal phases via a hierarchical process that involves Watson-Crick base pairing, supramolecular assembly into columns of duplexes, and long-range ordering. The multiscale nature of this phenomenon makes it difficult to quantitatively describe and assess the importance of the various contributions, particularly for very short strands. We performed molecular dynamics simulations based on the coarse-grained oxDNA model, aiming to depict all of the assembly processes involved and the phase behavior of solutions of the DNA GCCG tetramers. We find good quantitative matching to experimental data at both levels of molecular association (thermal melting) and collective ordering (phase diagram). We characterize the isotropic state and the low-density nematic and high-density columnar liquid crystal phases in terms of molecular order, size of aggregates, and structure, together with their effects on diffusivity processes. We observe a cooperative aggregation mechanism in which the formation of dimers is less thermodynamically favored than the formation of longer aggregates.

Explicit ion modeling predicts physicochemical interactions for chromatin organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono- and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Explicit Ion Modeling Predicts Physicochemical Interactions for Chromatin Organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Investigating the Hydrogen Bond-Induced Self-Assembly of Polysulfamides Using Molecular Simulations and Experiments

In this paper, we present a synergistic, experimental, and computational study of the self-assembly of N,N'-disubstituted polysulfamides driven by hydrogen bonds (H-bonds) between the H-bonding donor and acceptor groups present in repeating sulfamides as a function of the structural design of the polysulfamide backbone. We developed a coarse-grained (CG) polysulfamide model that captures the directionality of H-bonds between the sulfamide groups and used this model in molecular dynamics (MD) simulations to study the self-assembly of these polymers in implicit solvent. The CGMD approach was validated by reproducing experimentally observed trends in the extent of crystallinity for three polysulfamides synthesized with aliphatic and/or aromatic repeating units. After validation of our CGMD approach, we computationally predicted the effect of repeat unit bulkiness, length, and uniformity of segment lengths in the polymers on the extent of orientational and positional order among the self-assembled polysulfamide chains, providing key design principles for tuning the extent of crystallinity in polysulfamides in experiments. Those computational predictions were then experimentally tested through the synthesis and characterization of polysulfamide architectures.

Cation valence dependence of hydrogen bond and stacking potentials in DNA mesoscopic models

Monovalent and divalent cations play a crucial role in living cells and for molecular techniques such as PCR. Here we evaluate DNA melting temperatures in magnesium (Mg²⁺) and magnesium‑potassium (Mg²⁺+ K⁺) buffers with a mesoscopic model that allows us to estimate hydrogen bonds and stacking interaction potentials. The Mg²⁺ and Mg²⁺+ K⁺ results are compared to previous calculations for sodium ions (Na⁺), in terms of equivalent sodium concentration and ionic strength. Morse potentials, related to hydrogen bonding, were found to be essentially constant and unaffected by cation conditions. However, for stacking interactions we find a clear dependence with ionic strength and cation valence. The highest ionic strength variations, for both hydrogen bonds and stacking interactions, was found at the sequence terminals. This suggests that end-to-end interactions in DNA will be strongly dependent on cation valence and ionic strength.

Interaction between two polyelectrolytes in monovalent aqueous salt solutions

We use the recently developed soft-potential-enhanced Poisson-Boltzmann (SPB) theory to study the interaction between two parallel polyelectrolytes (PEs) in monovalent ionic solutions in the weak-coupling regime. The SPB theory is fitted to ion distributions from coarse-grained molecular dynamics (MD) simulations and benchmarked against all-atom MD modelling for poly(diallyldimethylammonium) (PDADMA). We show that the SPB theory is able to accurately capture the interactions between two PEs at distances beyond the PE radius. For PDADMA positional correlations between the charged groups lead to locally asymmetric PE charge and ion distributions. This gives rise to small deviations from the SPB prediction that appear as short-range oscillations in the potential of mean force. Our results suggest that the SPB theory can be an efficient way to model interactions in chemically specific complex PE systems.

Stability and Existence of Noncanonical I-motif DNA Structures in Computer Simulations Based on Atomistic and Coarse-Grained Force Fields

Cytosine-rich DNA sequences are able to fold into noncanonical structures, in which semi-protonated cytosine pairs develop extra hydrogen bonds, and these bonds are responsible for the overall stability of a structure called the i-motif. The i-motif can be formed in many regions of the genome, but the most representative is the telomeric region in which the CCCTAA sequences are repeated thousands of times. The ability to reverse folding/unfolding in response to pH change makes the above sequence and i-motif very promising components of nanomachines, extended DNA structures, and drug carriers. Molecular dynamics analysis of such structures is highly beneficial due to direct insights into the microscopic structure of the considered systems. We show that Amber force fields for DNA predict the stability of the i-motif over a long timescale; however, these force fields are not able to predict folding of the cytosine-rich sequences into the i-motif. The reason is the kinetic partitioning of the folding process, which makes the transitions between various intermediates too time-consuming in atomistic force field representation. Application of coarse-grained force fields usually highly accelerates complex structural transitions. We, however, found that three of the most popular coarse-grained force fields for DNA (oxDNA, 3SPN, and Martini) were not able to predict the stability of the i-motif structure. Obviously, they were not able to accelerate the folding of unfolded states into an i-motif. This observation must be strongly highlighted, and the need to develop suitable extensions of coarse-grained force fields for DNA is pointed out. However, it will take a great deal of effort to successfully solve these problems.

Modified Poisson–Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions

We present a soft-potential-enhanced Poisson–Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulation with the explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1M and ion sizes ranging from small ions, such as Na+ or Cl−, to softer and larger ions with a size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface

The three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30 nm fiber.

The three-dimensional organization of chromatin plays critical roles in regulating genome function. Here the authors apply a near atomistic model to study the structure and dynamics of the chromatin folding unit - the tetra-nucleosome - to provide insight into how chromatin folds.

Linker DNA Length is a Key to Tri-nucleosome Folding

The folding of a nucleosome array has long been one of the fundamental and unsolved problems in chromatin biology. In this study, we address how nucleosome array folding depends on the length of linker DNA. We performed molecular dynamics simulations of a tri-nucleosome, a minimal model of chromatin folding, with various linker lengths (LLs) ranging from 20 to 40 base pairs (bps). We found that the tri-nucleosome folding strongly depends on LLs, and classified the structure ensemble into five classes, named from trinuc-1 to trinuc-5. As a function of LL, the different classes appear, on average, every 2 bps with a period of 10 bps, and are characterized by distinct inter-nucleosome interactions. The trinuc-1 conformation corresponds to LL ~ 10n, where n is an integer, and is stabilized by the tight packing between the first and the third nucleosomes, consistent with a zigzag fiber form. Structures of the other four classes are more diverse and distributed continuously in the space of possible configurations. Histone-DNA electrostatic interactions in the tri-nucleosome are further analyzed.

100th Anniversary of Macromolecular Science Viewpoint: Modeling and Simulation of Macromolecules with Hydrogen Bonds: Challenges, Successes, and Opportunities

Macromolecular materials with directional interactions such as hydrogen bonds exhibit numerous attractive features in terms of structure, thermodynamics, and dynamics. Besides enabling precise tuning of desirable geometries in the assembled state (e.g., programmable coordination numbers depending on the valency of the directional interaction), mixing in a blend/composite through stabilization via hydrogen bonds between the various components, hydrogen bonds can also impart responsiveness to external stimuli (e.g., temperature, pH). In biomacromolecules (e.g., proteins, DNA, polysaccharides), hydrogen bonds play a key role in stabilizing secondary and tertiary structures, which in turn define the function of these macromolecules. In this Viewpoint, I present the challenges, successes, and opportunities for molecular modeling and simulations to conduct fundamental and application-focused research on macromolecular materials with hydrogen bonding interactions. The past successes and limitations of atomistic simulations are discussed first, followed by highlights from recent developments in coarse-grained modeling and their use in studies of (synthetic and biologically relevant) macromolecular materials. Model development focused on polynucleotides (e.g., DNA, RNA, etc.), polypeptides, polysaccharides, and synthetic polymers at experimentally relevant conditions are highlighted. This viewpoint ends with potential future directions for macromolecular modeling and simulations with other types of directional interactions beyond hydrogen bonding.

ssDNA diffuses along replication protein A via a reptation mechanism

Replication protein A (RPA) plays a critical role in all eukaryotic DNA processing involving single-stranded DNA (ssDNA). Contrary to the notion that RPA provides solely inert protection to transiently formed ssDNA, the RPA-ssDNA complex acts as a dynamic DNA processing unit. Here, we studied the diffusion of RPA along 60 nt ssDNA using a coarse-grained model in which the ssDNA-RPA interface was modeled by both aromatic and electrostatic interactions. Our study provides direct evidence of bulge formation during the diffusion of ssDNA along RPA. Bulges can form at a few sites along the interface and store 1-7 nt of ssDNA whose release, upon bulge dissolution, leads to propagation of ssDNA diffusion. These findings thus support the reptation mechanism, which involves bulge formation linked to the aromatic interactions, whose short range nature reduces cooperativity in ssDNA diffusion. Greater cooperativity and a larger diffusion coefficient for ssDNA diffusion along RPA are observed for RPA variants with weaker aromatic interactions and for interfaces homogenously stabilized by electrostatic interactions. ssDNA propagation in the latter instance is characterized by lower probabilities of bulge formation; thus, it may fit the sliding-without-bulge model better than the reptation model. Thus, the reptation mechanism allows ssDNA mobility despite the extensive and high affinity interface of RPA with ssDNA. The short-range aromatic interactions support bulge formation while the long-range electrostatic interactions support the release of the stored excess ssDNA in the bulge and thus the overall diffusion.

Molecular dynamics simulations of alkaline earth metal ions binding to DNA reveal ion size and hydration effects

Classical molecular dynamics simulations reveal size-dependent trends of alkaline earth metal ions binding to DNA are due to ion size and hydration behavior.

Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins

Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (k_off) for complexes involving the former.

Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.

The Statistical Segment Length of DNA: Opportunities for Biomechanical Modeling in Polymer Physics and Next-Generation Genomics

The development of bright bisintercalating dyes for deoxyribonucleic acid (DNA) in the 1990s, most notably YOYO-1, revolutionized the field of polymer physics in the ensuing years. These dyes, in conjunction with modern molecular biology techniques, permit the facile observation of polymer dynamics via fluorescence microscopy and thus direct tests of different theories of polymer dynamics. At the same time, they have played a key role in advancing an emerging next-generation method known as genome mapping in nanochannels. The effect of intercalation on the bending energy of DNA as embodied by a change in its statistical segment length (or, alternatively, its persistence length) has been the subject of significant controversy. The precise value of the statistical segment length is critical for the proper interpretation of polymer physics experiments and controls the phenomena underlying the aforementioned genomics technology. In this perspective, we briefly review the model of DNA as a wormlike chain and a trio of methods (light scattering, optical or magnetic tweezers, and atomic force microscopy (AFM)) that have been used to determine the statistical segment length of DNA. We then outline the disagreement in the literature over the role of bisintercalation on the bending energy of DNA, and how a multiscale biomechanical approach could provide an important model for this scientifically and technologically relevant problem.

Structural Characterization of Bubbles Formed in DNA Melting: A Monte Carlo Simulation Study

Bubbles in DNA are involved in many important biological processes. In this work, a coarse-grained model is used for characterizing bubbles formed in DNA melting. The model resorts only to electrostatic interactions at the Debye-Hückel level, in combination with a short-ranged attractive interaction within a base pair. In spite of also omitting atomistic details, the model is able to capture experimentally established trends in persistence length and radius of gyration. By applying it on different systems, it is possible to conclude that there is a minimum size for stable bubbles, in the interval between 12 and 20 bp, which agrees well with previously published experimental findings. Simulated scattering data distinguishes between different bubbles and detects conformational changes in the melting process. Therefore, SAXS is regarded as useful for bubble formation studies, while simulations provide a molecular understanding.

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.

Adaptive resolution simulation of oligonucleotides

Nucleic acids are characterized by a complex hierarchical structure and a variety of interaction mechanisms with other molecules. These features suggest the need of multiscale simulation methods in order to grasp the relevant physical properties of deoxyribonucleic acid (DNA) and RNA using in silico experiments. Here we report an implementation of a dual-resolution modeling of a DNA oligonucleotide in physiological conditions; in the presented setup only the nucleotide molecule and the solvent and ions in its proximity are described at the atomistic level; in contrast, the water molecules and ions far from the DNA are represented as computationally less expensive coarse-grained particles. Through the analysis of several structural and dynamical parameters, we show that this setup reliably reproduces the physical properties of the DNA molecule as observed in reference atomistic simulations. These results represent a first step towards a realistic multiscale modeling of nucleic acids and provide a quantitatively solid ground for their simulation using dual-resolution methods.

Multiscale coarse-grained modelling of chromatin components: DNA and the nucleosome

To model large biomolecular systems, such as cell and organelles an atomistic description is not currently achievable and is not generally practical. Therefore, simplified coarse-grained (CG) modelling becomes a necessity. One of the most important cellular components is chromatin, a large DNA-protein complex where DNA is highly compacted. Recent progress in coarse graining modelling of the major chromatin components, double helical DNA and the nucleosome core particle (NCP) is presented. First, general principles and approaches allowing rigorous bottom-to-top generation of interaction potentials in the CG models are presented. Then, recent CG models of DNA are reviewed and their adequacy is benchmarked against experimental data on the salt dependence of DNA flexibility (persistence length). Furthermore, a few recent CG models of the NCP are described and their application for studying salt-dependent NCP-NCP interaction is discussed. An example of a multiscale approach to CG modelling of chromatin is presented where interactions and self-assembly of thousands of NCPs in solution are observed.

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.

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.

A Solvent-Mediated Coarse-Grained Model of DNA Derived with the Systematic Newton Inversion Method

We present a new class of coarse-grained (CG) force fields (FFs) for B-DNA with explicit ions suited for large-scale mesoscale simulations at microsecond-micrometer scale using a wide spectrum of particle simulation methods from molecular dynamics to dissipative particle dynamics. The effective solvent-mediated pairwise interactions making up the FFs are obtained by inverting radial distribution functions and other particle-particle distributions obtained from all-atom simulations of numbers of octadecamer DNA fragments from the Ascona B-DNA library. The inverse Monte Carlo (IMC) method, later known as Newton inversion (NI) (Lyubartsev, A. P.; Laaksonen, A. Phys. Rev. E, 1995, 52, 3730-3737), was used together with the iterative Boltzmann inversion (IBI) scheme to compute the effective CG potentials. We show that this systematic structure-based approach is capable of providing converged potentials that accurately reproduce the structural features of the underlying atomistic system within a few percents of relative difference. We also show that a simple one-site-per-nucleotide model with 10 intramolecular pair interaction potentials is able to reproduce key features of DNA, for example, the persistence length and its dependence on the ionic concentration, experimentally determined around 50 nm at physiological salt concentration.

Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations

Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to emulate one ATP cycle of a molecular motor, kinesin. Second, nonspecific protein-DNA binding was studied by a combination of elaborate protein and DNA models. Third, a transcription factor, p53, that contains highly fluctuating regions was simulated on two perpendicularly arranged DNA segments, addressing intersegmental transfer of p53. Fourth, we simulated structural dynamics of dinucleosomes connected by a linker DNA finding distinct types of internucleosome docking and salt-concentration-dependent compaction. Finally, we discuss many of limitations in the current approaches and future directions. Especially, more accurate electrostatic treatment and a phospholipid model that matches our CG resolutions are of immediate importance.

Simple Elastic Network Models for Exhaustive Analysis of Long Double-Stranded DNA Dynamics with Sequence Geometry Dependence

Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately ∼150 bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.

Coarse-Grained Ions for Nucleic Acid Modeling

We present a general coarse-grained model of sodium, magnesium, spermidine, and chlorine in implicit solvent. The effective potentials between ions are systematically parametrized using a relative entropy coarse-graining approach [Carmichael, S. P. and M. S. Shell, J. Phys. Chem. B, 116, 8383-93 (2012)] that maximizes the information retained in a coarse-grained model. We describe the local distribution of ions in the vicinity of a recently published coarse-grained DNA model and demonstrate a dependence of persistence length on ionic strength that differs from that predicted by Odijk-Skolnick-Fixman theory. Consistent with experimental observations, we show that spermidine induces DNA condensation whereas magnesium and sodium do not. This model can be used alongside any coarse-grained DNA model that has explicit charges and an accurate reproduction of the excluded volume of dsDNA.

Molecular determinants of the interactions between proteins and ssDNA

ssDNA binding proteins (SSBs) protect ssDNA from chemical and enzymatic assault that can derail DNA processing machinery. Complexes between SSBs and ssDNA are often highly stable, but predicting their structures is challenging, mostly because of the inherent flexibility of ssDNA and the geometric and energetic complexity of the interfaces that it forms. Here, we report a newly developed coarse-grained model to predict the structure of SSB-ssDNA complexes. The model is successfully applied to predict the binding modes of six SSBs with ssDNA strands of lengths of 6-65 nt. In addition to charge-charge interactions (which are often central to governing protein interactions with nucleic acids by means of electrostatic complementarity), an essential energetic term to predict SSB-ssDNA complexes is the interactions between aromatic residues and DNA bases. For some systems, flexibility is required from not only the ssDNA but also, the SSB to allow it to undergo conformational changes and the penetration of the ssDNA into its binding pocket. The association mechanisms can be quite varied, and in several cases, they involve the ssDNA sliding along the protein surface. The binding mechanism suggests that coarse-grained models are appropriate to study the motion of SSBs along ssDNA, which is expected to be central to the function carried out by the SSBs.

Coarse-grained simulation study of sequence effects on DNA hybridization in a concentrated environment

A novel coarse-grained model is developed to elucidate thermodynamics and kinetic mechanisms of DNA self-assembly. It accounts for sequence and solvent conditions to capture key experimental results such as sequence-dependent thermal property and salt-dependent persistence length of ssDNA and dsDNA. Moreover, constant-temperature simulations on two single strands of a homogeneous sequence show two main mechanisms of hybridization: a slow slithering mechanism and a one-order faster zippering mechanism. Furthermore, large-scale simulations at a high DNA strand concentration demonstrate that DNA self-assembly is a robust and enthalpically driven process in which the formation of double helices is deciphered to occur via multiple self-assembly pathways including the strand displacement mechanism. However, sequence plays an important role in shifting the majority of one pathway over the others and controlling size distribution of self-assembled aggregates. This study yields a complex picture on the role of sequence on programmable self-assembly and demonstrates a promising simulation tool that is suitable for studies in DNA nanotechnology.

DNA Duplex Formation with a Coarse-Grained Model

A middle-resolution coarse-grained model of DNA is proposed. The DNA chain is built of spherical and planar rigid bodies connected by elastic virtual bonds. The bonded part of the potential energy function is fit to potentials of mean force of model systems. The rigid bodies are sets of neutral, charged, and dipolar beads. Electrostatic and van der Waals interactions are parametrized by our recently developed procedure [Maciejczyk, M.; Spasic, A.; Liwo, A.; Scheraga, H.A. J. Comp. Chem.2010, 31, 1644]. Interactions with the solvent and an ionic cloud are approximated by a multipole-multipole Debye-Hückel model. A very efficient R-RATTLE algorithm, for integrating the movement of rigid bodies, is implemented. It is the first coarse-grained model, in which both bonded and nonbonded interactions were parametrized ab initio and which folds stable double helices from separated complementary strands, with the final conformation close to the geometry of experimentally determined structures.

An experimentally-informed coarse-grained 3-Site-Per-Nucleotide model of DNA: structure, thermodynamics, and dynamics of hybridization

A new 3-Site-Per-Nucleotide coarse-grained model for DNA is presented. The model includes anisotropic potentials between bases involved in base stacking and base pair interactions that enable the description of relevant structural properties, including the major and minor grooves. In an improvement over available coarse-grained models, the correct persistence length is recovered for both ssDNA and dsDNA, allowing for simulation of non-canonical structures such as hairpins. DNA melting temperatures, measured for duplexes and hairpins by integrating over free energy surfaces generated using metadynamics simulations, are shown to be in quantitative agreement with experiment for a variety of sequences and conditions. Hybridization rate constants, calculated using forward-flux sampling, are also shown to be in good agreement with experiment. The coarse-grained model presented here is suitable for use in biological and engineering applications, including nucleosome positioning and DNA-templated engineering.

The power of coarse graining in biomolecular simulations

Computational modeling of biological systems is challenging because of the multitude of spatial and temporal scales involved. Replacing atomistic detail with lower resolution, coarse grained (CG), beads has opened the way to simulate large-scale biomolecular processes on time scales inaccessible to all-atom models. We provide an overview of some of the more popular CG models used in biomolecular applications to date, focusing on models that retain chemical specificity. A few state-of-the-art examples of protein folding, membrane protein gating and self-assembly, DNA hybridization, and modeling of carbohydrate fibers are used to illustrate the power and diversity of current CG modeling.

Growth dynamics for DNA-guided nanoparticle crystallization

Spherical nucleic acid (SNA) nanostructures assemble into a large variety of well-defined crystalline superlattices via DNA-directed hybridization. Crystallities of SNA with various shapes emerge during the assembly process, which coalesce during coarsening, leading to polycrystalline materials. Here, we investigate the growth dynamics of SNAs into body-centered cubic superlattices and the coalescence of SNA aggregates using a colloidal model formulated from the competition of electrostatic core repulsions and localized DNA hybridization attractions. We find that the growth law of isolated SNA crystallities is well-described by the power law t(1/2), in agreement with experimental observations. At later times, coalescence slows the growth dynamics considerably and is dependent on the orientational mismatch (misorientation angle) of the coalescing crystallites. Molecular dynamics simulations show that the misorientation angle decreases continually during the coalescence, which is a signature of the grain rotation induced coalescence mechanism. This mechanism is followed by the coarsening of a "neck" that develops at the boundary between the coalescing crystallites. Remarkably, we find faster coalescence dynamics for larger SNAs compared to smaller SNAs due to their enhanced surface diffusion, which more effectively reduces curvature at the boundary of two superlattices. These findings provide fundamental insight into the relationship between nanoparticle surface chemistry and its crystallite growth and coalescence.

Counterion distribution surrounding spherical nucleic acid-Au nanoparticle conjugates probed by small-angle x-ray scattering

The radial distribution of monovalent cations surrounding spherical nucleic acid-Au nanoparticle conjugates (SNA-AuNPs) is determined by in situ small-angle x-ray scattering (SAXS) and classical density functional theory (DFT) calculations. Small differences in SAXS intensity profiles from SNA-AuNPs dispersed in a series of solutions containing different monovalent ions (Na(+), K(+), Rb(+), or Cs(+)) are measured. Using the "heavy ion replacement" SAXS (HIRSAXS) approach, we extract the cation-distribution-dependent contribution to the SAXS intensity and show that it agrees with DFT predictions. The experiment-theory comparisons reveal the radial distribution of cations as well as the conformation of the DNA in the SNA shell. The analysis shows an enhancement to the average cation concentration in the SNA shell that can be up to 15-fold, depending on the bulk solution ionic concentration. The study demonstrates the feasibility of HIRSAXS in probing the distribution of monovalent cations surrounding nanoparticles with an electron dense core (e.g., metals).

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.

Inferring bulk self-assembly properties from simulations of small systems with multiple constituent species and small systems in the grand canonical ensemble

In this paper, we generalize a methodology [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Phys.: Condens. Matter 22, 104102 (2010)] for dealing with the inference of bulk properties from small simulations of self-assembling systems of characteristic finite size. In particular, schemes for extrapolating the results of simulations of a single self-assembling object to the bulk limit are established in three cases: for assembly involving multiple particle species, for systems with one species localized in space and for simulations in the grand canonical ensemble. Furthermore, methodologies are introduced for evaluating the accuracy of these extrapolations. Example systems demonstrate that differences in cluster concentrations between simulations of a single self-assembling structure and bulk studies of the same model under identical conditions can be large, and that convergence on bulk results as system size is increased can be slow and non-trivial.