A coarse grain model for DNA

In silico study of DNA mononucleotide self-assembly

Recent experiments have demonstrated the self-assembly and long-range ordering of concentrated aqueous solutions of DNA and RNA mononucleotides. These are found to form Watson-Crick pairs that stack into columns that become spatially organized into a columnar liquid-crystalline phase. In this work, we numerically investigate this phase behavior by adopting an extremely coarse-grained model in which nucleotides are represented as semi-disk-like polyhedra decorated with attractive (patchy) sites that mimic the stacking and pairing interactions. We carry out Monte Carlo simulations of these patchy polyhedra by adapting algorithms borrowed from computer graphics. This model reproduces the features of the experimental phase behavior, which essentially depends on the combination of pairing and stacking interactions.

Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

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.

Anomalous Diffusion of Polyelectrolyte Segments on Supported Charged Lipid Bilayers

This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the "bead-spring" model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that "bead-spring" chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.

Force-induced melting of DNA hairpin: Unfolding pathways and phase diagrams

Using the exact enumeration technique, we have studied the force-induced melting of a DNA hairpin on the face centered cubic lattice for two different sequences which differ in terms of loop closing base pairs. The melting profiles obtained from the exact enumeration technique is consistent with the Gaussian network model and Langevin dynamics simulations. Probability distribution analysis based on the exact density of states revealed the microscopic details of the opening of the hairpin. We showed the existence of intermediate states near the melting temperature. We further showed that different ensembles used to model single-molecule force spectroscopy setups may give different force-temperature diagrams. We delineate the possible reasons for the observed discrepancies.

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

An associative memory Hamiltonian model for DNA and nucleosomes

A model for DNA and nucleosomes is introduced with the goal of studying chromosomes from a single base level all the way to higher-order chromatin structures. This model, dubbed the Widely Editable Chromatin Model (WEChroM), reproduces the complex mechanics of the double helix including its bending persistence length and twisting persistence length, and their respective temperature dependence. The WEChroM Hamiltonian is composed of chain connectivity, steric interactions, and associative memory terms representing all remaining interactions leading to the structure, dynamics, and mechanical characteristics of the B-DNA. Several applications of this model are discussed to demonstrate its applicability. WEChroM is used to investigate the behavior of circular DNA in the presence of positive and negative supercoiling. We show that it recapitulates the formation of plectonemes and of structural defects that relax mechanical stress. The model spontaneously manifests an asymmetric behavior with respect to positive or negative supercoiling, similar to what was previously observed in experiments. Additionally, we show that the associative memory Hamiltonian is also capable of reproducing the free energy of partial DNA unwrapping from nucleosomes. WEChroM is designed to emulate the continuously variable mechanical properties of the 10nm fiber and, by virtue of its simplicity, is ready to be scaled up to molecular systems large enough to investigate the structural ensembles of genes. WEChroM is implemented in the OpenMM simulation toolkits and is freely available for public use.

Mechanistic insight into the structure, thermodynamics and dynamics of equilibrium gels of multi-armed DNA nanostars

The unique sequence specificity rule of DNA makes it an ideal molecular building block for constructing periodic arrays and devices with nanoscale accuracy and precision. Here, we present the self-assembly of DNA nanostars having three, four and five arms into a gel phase using a simplistic coarse-grained bead-spring model developed by Z. Xing, C. Ness, D. Frenkel and E. Eiser (Macromolecules, 2019, 52, 504-512). Our simulations show that the DNA nanostars form a thermodynamically stable fully bonded gel phase from an unstructured liquid phase with the lowering of temperature. We characterize the phase transition by calculating several structural features such as the radial distribution function and structure factor. The thermodynamics of gelation is quantified by the potential energy and translational pair-entropy of the system. The phase transition from an arrested gel phase to an unstructured liquid phase has been modelled using a two-state theoretical model. We find that this transition is enthalpy driven, and loss of configuration and translational entropy is counterpoised by enthalpic interaction of the DNA sticky-ends, which gives rise to a gel phase at low temperature. The absolute rotational and translational entropy of the systems, measured using a two-phase thermodynamic model, also substantiates the gel transition. The slowing down of the dynamics upon approaching the transition temperature from a high temperature demonstrates the phase transition to a gel phase. A detailed numerical simulation study of the morphology, dynamics and thermodynamics of DNA gelation can provide guidance for future experiments, is easily extensible to other polymeric systems, and is expected to help in understanding the physics of self-assembly.

Controlling the two components modified on nanoparticles to construct nanomaterials

Nanoparticle self-assembly technology has made great progress in the past 30 years. Many kinds of self-assembly strategies of modifiable nanoparticles have been developed and used to construct nano-aggregates by designing the shape, size and type of nanoparticles and controlling the components modified on nanoparticles. These strategies are widely used in many fields, such as medical diagnosis, biological detection, drug delivery, materials synthesis and sensors. The modified components can be DNA chains, polymer chains, proteins, and even organic molecules based on different molecular conformations and chemical properties. In recent years, the self-assembly of two-component modified nanoparticles has gradually attracted more attention. Nanoparticles modified with two components of different DNA strands can self-assemble to produce a variety of nano arrangement structures, such as BCC, FCC and other cubic crystals, which can be used in crystal materials. Two-component modification of hydrophilic and hydrophobic polymers can produce vesicular aggregates, which can be used for drug delivery. In this review, we summarize the latest experimental progress and theoretical simulation of self-assembly of two-component modified nanoparticles including different DNA chains, different polymer chains, DNA and polymer chains, proteins and polymer chains, and different organic molecules. Their self-assembly characteristics and application prospects were discussed. Compared with single-component modified nanoparticles, two-component nanoparticles have different tethered molecules or molecular chains, which can be multifunctional by regulating different modified components and types of nanoparticles and ultimately expand the scope of applications.

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions

The three-dimensional (3D) structure and stability of DNA are essential to understand/control their biological functions and aid the development of novel materials. In this work, we present a coarse-grained (CG) model for DNA based on the RNA CG model proposed by us, to predict 3D structures and stability for both dsDNA and ssDNA from the sequence. Combined with a Monte Carlo simulated annealing algorithm and CG force fields involving the sequence-dependent base-pairing/stacking interactions and an implicit electrostatic potential, the present model successfully folds 20 dsDNAs (≤52nt) and 20 ssDNAs (≤74nt) into the corresponding native-like structures just from their sequences, with an overall mean RMSD of 3.4Å from the experimental structures. For DNAs with various lengths and sequences, the present model can make reliable predictions on stability, e.g., for 27 dsDNAs with/without bulge/internal loops and 24 ssDNAs including pseudoknot, the mean deviation of predicted melting temperatures from the corresponding experimental data is only ~2.0°C. Furthermore, the model also quantificationally predicts the effects of monovalent or divalent ions on the structure stability of ssDNAs/dsDNAs.

To determine 3D structures and quantify stability of single- (ss) and double-stranded (ds) DNAs is essential to unveil the mechanisms of their functions and to further guide the production and development of novel materials. Although many DNA models have been proposed to reproduce the basic structural, mechanical, or thermodynamic properties of dsDNAs based on the secondary structure information or preset constraints, there are very few models can be used to investigate the ssDNA folding or dsDNA assembly from the sequence. Furthermore, due to the polyanionic nature of DNAs, metal ions (e.g., Na⁺ and Mg²⁺) in solutions can play an essential role in DNA folding and dynamics. Nevertheless, ab initio predictions for DNA folding in ion solutions are still an unresolved problem. In this work, we developed a novel coarse-grained model to predict 3D structures and thermodynamic stabilities for both ssDNAs and dsDNAs in monovalent/divalent ion solutions from their sequences. As compared with the extensive experimental data and available existing models, we showed that the present model can successfully fold simple DNAs into their native-like structures, and can also accurately reproduce the effects of sequence and monovalent/divalent ions on structure stability for ssDNAs including pseudoknot and dsDNAs with/without bulge/internal loops.

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.

Accurate Sequence-Dependent Coarse-Grained Model for Conformational and Elastic Properties of Double-Stranded DNA

We introduce MADna, a sequence-dependent coarse-grained model of double-stranded DNA (dsDNA), where each nucleotide is described by three beads localized at the sugar, at the base moiety, and at the phosphate group, respectively. The sequence dependence is included by considering a step-dependent parametrization of the bonded interactions, which are tuned in order to reproduce the values of key observables obtained from exhaustive atomistic simulations from the literature. The predictions of the model are benchmarked against an independent set of all-atom simulations, showing that it captures with high fidelity the sequence dependence of conformational and elastic features beyond the single step considered in its formulation. A remarkably good agreement with experiments is found for both sequence-averaged and sequence-dependent conformational and elastic features, including the stretching and torsion moduli, the twist–stretch and twist–bend couplings, the persistence length, and the helical pitch. Overall, for the inspected quantities, the model has a precision comparable to atomistic simulations, hence providing a reliable coarse-grained description for the rationalization of single-molecule experiments and the study of cellular processes involving dsDNA. Owing to the simplicity of its formulation, MADna can be straightforwardly included in common simulation engines. Particularly, an implementation of the model in LAMMPS is made available on an online repository to ease its usage within the DNA research community.

Nucleic acid folding simulations using a physics-based atomistic free energy model

Performing full-resolution atomistic simulations of nucleic acid folding has remained a challenge for biomolecular modeling. Understanding how nucleic acids fold and how they transition between different folded structures as they unfold and refold has important implications for biology. This paper reports a theoretical model and computer simulation of the ab initio folding of DNA inverted repeat sequences. The formulation is based on an all-atom conformational model of the sugar-phosphate backbone via chain closure, and it incorporates three major molecular-level driving forces-base stacking, counterion-induced backbone self-interactions, and base pairing-via separate analytical theories designed to capture and reproduce the effects of the solvent without requiring explicit water and ions in the simulation. To accelerate computational throughput, a mixed numerical/analytical algorithm for the calculation of the backbone conformational volume is incorporated into the Monte Carlo simulation, and special stochastic sampling techniques were employed to achieve the computational efficiency needed to fold nucleic acids from scratch. This paper describes implementation details, benchmark results, and the advantages and technical challenges with this approach.

Can one detect intermediate denaturation states of DNA sequences by following the equilibrium open-close dynamic fluctuations of a single base pair?

Melting of DNA sequences may occur through a few major intermediate states, whose influence on the melting curve has been discussed previously, while their effect on the kinetics has not been explored thoroughly. Here, we chose a simple DNA sequence, forming a hairpin in its native (zipped) state, and study it using molecular dynamic (MD) simulations and a model integrating the Gaussian network model with bond-binding energies-the Gaussian binding energy (GBE) model. We find two major partial denaturation states, a bubble state and a partial unzipping state. We demonstrate the influence of these two states on the closing-opening base pair dynamics, as probed by a tagged bond auto-correlation function (ACF). We argue that the latter is measured by fluorescence correlation spectroscopy experiments, in which one base of the pair is linked to a fluorescent dye, while the complementary base is linked to a quencher, similar to the experiment reported by Altan-Bonnet et al. [Phys. Rev. Lett. 90, 138101 (2003)]. We find that tagging certain base pairs at temperatures around the melting temperature results in a multi-step relaxation of the ACF, while tagging other base pairs leads to an effectively single-step relaxation, albeit non-exponential. Only the latter type of relaxation has been observed experimentally, and we suggest which of the other base pairs should be tagged in order to observe multi-step relaxation. We demonstrate that this behavior can be observed with other sequences and argue that the GBE can reliably predict these dynamics for very long sequences, where MD simulations might be limited.

Predicting the configuration and energy of DNA in a nucleosome by coarse-grain modelling

We present a novel algorithm which uses a coarse-grained model and an energy minimisation procedure to predict the sequence-dependent DNA configuration in a nucleosome together with its energetic cost.

Predicting genome organisation and function with mechanistic modelling

Fitting-free mechanistic models based on polymer simulations predict chromatin folding in 3D by focussing on the underlying biophysical mechanisms. This class of models has been increasingly used in conjunction with experiments to study the spatial organisation of eukaryotic chromosomes. Feedback from experiments to models leads to successive model refinement and has previously led to the discovery of new principles for genome organisation. Here, we review the basis of mechanistic polymer simulations, explain some of the more recent approaches and the contexts in which they have been useful to explain chromosome biology, and speculate on how they might be used in the future.

Potential of Mean Force for DNA Wrapping Around a Cationic Nanoparticle

Sharp bending and wrapping of DNA around proteins and nanoparticles (NPs) has been of extensive research interest. Here, we present the potential of mean force (PMF) for wrapping a DNA double helix around a cationic NP using coarse-grained models of a double-stranded DNA and a cationic NP. Starting from a NP wrapped around by DNA, the PMF was calculated along the distance between the center of the NP and one end of the DNA molecule. A relationship between the distance and the extent of DNA wrapping is used to calculate the PMF as a function of DNA wrapping around a NP. In particular, the PMF was compared for two DNA sequences of (AT)₂₅/(AT)₂₅ and (AC)₂₅/(GT)₂₅, for which the persistence lengths are different by ∼10 nm. The simulation results provide solid evidence of the thermodynamic preference for complex formation of a cationic NP with more flexible DNA over the less flexible DNA. Furthermore, we estimated the elastic energy of DNA bending, which was in good order-of-magnitude agreement with the theoretical prediction of elastic rods. This work suggests that the variation of sequence-dependent DNA flexibility can be utilized in DNA nanotechnologies, in which the position and dynamics of NPs are regulated on large-scale DNA structures, or the structural transformation of DNA is triggered by the sequence-dependent binding of NPs.

Base pair fluctuations in helical models for nucleic acids

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

Effect of DNA Flexibility on Complex Formation of a Cationic Nanoparticle with Double-Stranded DNA

We present extensive molecular dynamics simulations of a cationic nanoparticle and a double-stranded DNA molecule to discuss the effect of DNA flexibility on the complex formation of a cationic nanoparticle with double-stranded DNA. Martini coarse-grained models were employed to describe double-stranded DNA molecules with two different flexibilities and cationic nanoparticles with three different electric charges. As the electric charge of a cationic nanoparticle increases, the degree of DNA bending increases, eventually leading to the wrapping of DNA around the nanoparticle at high electric charges. However, a small increase in the persistence length of DNA by 10 nm requires a cationic nanoparticle with a markedly increased electric charge to bend and wrap DNA around. Thus, a more flexible DNA molecule bends and wraps around a cationic nanoparticle with an intermediate electric charge, whereas a less flexible DNA molecule binds to a nanoparticle with the same electric charge without notable bending. This work provides solid evidence that a small difference in DNA flexibility (as small as 10 nm in persistence length) has a substantial influence on the complex formation of DNA with proteins from a biological perspective and suggests that the variation of sequence-dependent DNA flexibility can be utilized in DNA nanotechnology as a new tool to manipulate the structure of DNA molecules mediated by nanoparticle binding.

ARGOS: An adaptive refinement goal-oriented solver for the linearized Poisson-Boltzmann equation

An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules in a solvent environment is developed and tested. At the heart of the solver is a goal-oriented a posteriori error estimate for the electrostatic coupling, derived and implemented in the present work, that gives rise to an orders of magnitude improved precision and a shorter computational time as compared to standard finite difference solvers. The accuracy of the new solver ARGOS is evaluated by numerical experiments on a series of problems with analytically known solutions. In addition, the solver is used to calculate electrostatic couplings between two chromophores, linked to polyproline helices of different lengths and between the spike protein of SARS-CoV-2 and the ACE2 receptor. All the calculations are repeated by using the well-known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver.

Low-frequency vibrational modes in G-quadruplexes reveal the mechanical properties of nucleic acids

Low-frequency vibrations play an essential role in biomolecular processes involving DNA such as gene expression, charge transfer, drug intercalation, and DNA–protein recognition. However, understanding the vibrational basis of these mechanisms relies on theoretical models due to the lack of experimental evidence. Here we present the low-frequency vibrational spectra of G-quadruplexes (structures formed by four strands of DNA) and B-DNA characterized using femtosecond optical Kerr-effect spectroscopy. Contrary to expectation, we found that G-quadruplexes show several strongly underdamped delocalized phonon-like modes that have the potential to contribute to the biology of the DNA at the atomic level. In addition, G-quadruplexes present modes at a higher frequency than B-DNA demonstrating that changes in the stiffness of the molecule alter its gigahertz to terahertz vibrational profile.

Low-frequency vibrations play an essential role in biomolecular processes involving DNA such as gene expression, charge transfer, drug intercalation, and DNA–protein recognition.

In silico prediction of the in vitro behavior of polymeric gene delivery vectors

Non-viral gene delivery vectors have increasingly come under the spotlight, but their performaces are still far from being satisfactory. Therefore, there is an urgent need for forecasting tools and screening methods to enable the development of ever more effective transfectants. Here, coarse-grained (CG) models of gold standard transfectant poly(ethylene imine)s (PEIs) have been profitably used to investigate and highlight the effect of experimentally-relevant parameters, namely molecular weight (2 vs. 10 kDa) and topologies (linear vs. branched), protonation state, and ammine-to-phosphate ratios (N/Ps), on the complexation and the gene silencing efficiency of siRNA molecules. The results from the in vitro screening of cationic polymers and conditions were used to validate the in silico platform that we developed, such that the hits which came out of the CG models were of high practical relevance. We show that our in silico platform enables to foresee the most suitable conditions for the complexation of relevant siRNA-polycation assemblies, thereby providing a reliable predictive tool to test bench transfectants in silico, and foster the design and development of gene delivery vectors.

Bottom-Up Coarse-Grained Modeling of DNA

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.

Thermodynamics of DNA Hybridization from Atomistic Simulations

Studying DNA hybridization equilibrium at atomistic length scales, either via molecular dynamics (MD) or through commonly used advanced sampling approaches, is notoriously difficult. In this work, we describe an order-parameter-based advanced sampling technique to calculate the free energy of hybridization, and estimate the melting temperature of DNA oligomers at atomistic resolution. The free energy landscapes are reported as a function of a native-topology-based order parameter for the Drew-Dickerson dodecamer and for a range of DNA decamer sequences of different GC content. Our estimated melting temperatures match the experimental numbers within ±15 °C. As a test of the numerical reliability of the procedures employed, it was verified that the predicted free energy surfaces and melting temperatures of the d- and l-enantiomers of the Drew-Dickerson dodecamer were indistinguishable within numerical accuracy.

Arbitrary Resolution with Two Bead Types Coarse-Grained Strategy and Applications to Protein Recognition

Molecular recognition is a fundamental step in essentially any biological process. However, the kinetic processes during association and dissociation are difficult to be efficiently sampled by direct all-atom molecular dynamics simulations because of the large spatial and temporal scales. Here we propose an arbitrary resolution with two bead types (ART) coarse-grained (CG) strategy that is adept in molecular recognition. ART is a universal user-customized CG strategy that can generate a system-specific CG force field anytime and be applied to any system with an arbitrary CG resolution according to research requirements. ART CG simulations can be very efficiently performed with implicit solvation in prevalent simulation packages and provide interfaces for any enhanced sampling method. We used three applications, HLA-HIV epitope recognition, barnase-barstar association, and trimeric TRAF2 self-assembly, to validate the feasibility of the ART CG strategy, its advantages in protein recognition, and its high performance in simulations. Regular CG simulations can successfully achieve valid protein recognitions without any prior bound structure.

Coarse-grained molecular dynamics simulations of poly(ethylene terephthalate)

We have constructed efficient coarse-grained (CG) models of poly(ethylene terephthalate) (PET), using three mapping schemes, in which a repeat unit is lumped into either three or four beads. The CG potentials are parameterized to reproduce target distributions of an underlying accurate atomistic model [H. Eslami and F. Müller-Plathe, Macromolecules 42, 8241-8250 (2009)]. The CG simulations allow equilibration of long PET chains at all length scales. The CG results on the density of PET in melt and glassy states, chain dimension, local packing, and structure factor are in good agreement with experiment. We have established a link between the glass transition temperature and the local movements including conformational transitions and mean-square displacements of chain segments. Temperature transferabilities of the three proposed models were studied by comparing CG results on the static and thermodynamic properties of a polymer with atomistic and experimental findings. One of the three CG models has a good degree of transferability, following all inter- and intra-structural rearrangements of the atomistic model, over a broad range of temperature. Furthermore, as a distinct point of strength of CG, over atomistic, simulations, we have examined the dynamics of PET long chains, consisting of 100 repeat units, over a regime where entanglements dominate the dynamics. Performing long-time (550 ns) CG simulations, we have noticed the signature of a crossover from Rouse to reptation dynamics. However, a clear separation between the Rouse and the reptation dynamics needs much longer time simulations, confirming the experimental findings that the crossover to full reptation dynamics is very protracted.

The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA

The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations resulting from mechanical perturbations in cells have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations showing sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulate overextension on different sequences of DNA ((AA)12, (AT)12, (CC)12 and (CG)12) with supercoiling densities at 200 and 50 mM salt concentrations. We find that DNA denatures in the majority of stretching simulations, surprisingly including those with over-twisted DNA. GC-rich sequences are observed to be more stable than AT-rich ones, with the specific response dependent on the base pair order. Furthermore, we find that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (CG)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20-30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.

Combination of coarse-grained molecular dynamics simulations and small-angle X-ray scattering experiments

The combination of molecular dynamics (MD) simulations and small-angle X-ray scattering (SAXS), called the MD-SAXS method, is efficient for investigating protein dynamics. To overcome the time-scale limitation of all-atom MD simulations, coarse-grained (CG) representations are often utilized for biomolecular simulations. In this study, we propose a method to combine CG MD simulations with SAXS, termed the CG-MD-SAXS method. In the CG-MD-SAXS method, the scattering factors of CG particles for proteins and nucleic acids are evaluated using high-resolution structural data in the Protein Data Bank, and the excluded volume and the hydration shell are modeled using two adjustable parameters to incorporate solvent effects. To avoid overfitting, only the two parameters are adjusted for an entire structure ensemble. To verify the developed method, theoretical SAXS profiles for various proteins, DNA/RNA, and a protein-RNA complex are compared with both experimental profiles and theoretical profiles obtained by the all-atom representation. In the present study, we applied the CG-MD-SAXS method to the Swi5-Sfr1 complex and three types of nucleosomes to obtain reliable ensemble models consistent with the experimental SAXS data.

Gō model revisited

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

A Biophysical Model for Curvature-Guided Cell Migration

The latest experiments have shown that adherent cells can migrate according to cell-scale curvature variations via a process called curvotaxis. Despite identification of key cellular factors, a clear understanding of the mechanism is lacking. We employ a mechanical model featuring a detailed description of the cytoskeleton filament networks, the viscous cytosol, the cell adhesion dynamics, and the nucleus. We simulate cell adhesion and migration on sinusoidal substrates. We show that cell adhesion on three-dimensional curvatures induces a gradient of pressure inside the cell that triggers the internal motion of the nucleus. We propose that the resulting out-of-equilibrium position of the nucleus alters cell migration directionality, leading to cell motility toward concave regions of the substrate, resulting in lower potential energy states. Altogether, we propose a simple mechanism explaining how intracellular mechanics enable the cells to react to substratum curvature, induce a deterministic cell polarization, and break down cells basic persistent random walk, which correlates with latest experimental evidences.

TacoxDNA: A user-friendly web server for simulations of complex DNA structures, from single strands to origami

Simulations of nucleic acids at different levels of structural details are increasingly used to complement and interpret experiments in different fields, from biophysics to medicine and materials science. However, the various structural models currently available for DNA and RNA and their accompanying suites of computational tools can be very rarely used in a synergistic fashion. The tacoxDNA webserver and standalone software package presented here are a step toward a long-sought interoperability of nucleic acids models. The webserver offers a simple interface for converting various common input formats of DNA structures and setting up molecular dynamics (MD) simulations. Users can, for instance, design DNA rings with different topologies, such as knots, with and without supercoiling, by simply providing an XYZ coordinate file of the DNA centre-line. More complex DNA geometries, as designable in the cadnano, CanDo and Tiamat tools, can also be converted to all-atom or oxDNA representations, which can then be used to run MD simulations. Though the latter are currently geared toward the native and LAMMPS oxDNA representations, the open-source package is designed to be further expandable. TacoxDNA is available at http://tacoxdna.sissa.it. © 2019 Wiley Periodicals, Inc.

1CPN: A coarse-grained multi-scale model of chromatin

A central question in epigenetics is how histone modifications influence the 3D structure of eukaryotic genomes and, ultimately, how this 3D structure is manifested in gene expression. The wide range of length scales that influence the 3D genome structure presents important challenges; epigenetic modifications to histones occur on scales of angstroms, yet the resulting effects of these modifications on genome structure can span micrometers. There is a scarcity of computational tools capable of providing a mechanistic picture of how molecular information from individual histones is propagated up to large regions of the genome. In this work, a new molecular model of chromatin is presented that provides such a picture. This new model, referred to as 1CPN, is structured around a rigorous multiscale approach, whereby free energies from an established and extensively validated model of the nucleosome are mapped onto a reduced coarse-grained topology. As such, 1CPN incorporates detailed physics from the nucleosome, such as histone modifications and DNA sequence, while maintaining the computational efficiency that is required to permit kilobase-scale simulations of genomic DNA. The 1CPN model reproduces the free energies and dynamics of both single nucleosomes and short chromatin fibers, and it is shown to be compatible with recently developed models of the linker histone. It is applied here to examine the effects of the linker DNA on the free energies of chromatin assembly and to demonstrate that these free energies are strongly dependent on the linker DNA length, pitch, and even DNA sequence. The 1CPN model is implemented in the LAMMPS simulation package and is distributed freely for public use.

Backmapping from Multiresolution Coarse-Grained Models to Atomic Structures of Large Biomolecules by Restrained Molecular Dynamics Simulations Using Bayesian Inference

Coarse-grained (CG) simulations have allowed access to larger length scales and longer time scales in the study of the dynamic processes of large biomolecules than all-atom (AA) molecular dynamics (MD) simulations. Backmapping from CG models to AA structures has long been studied because it enables us to gain detailed structure insights from CG simulations. Many methods first construct an AA structure from the CG model by fragments, random placement, or geometrical rules and subsequently optimize the solution via energy minimization, simulated annealing or position-restrained simulations. However, such methods may only work well on residue-level CG models and cannot consider the deviations of CG models. In this work, we describe, to the best of our knowledge, a new backmapping method based on Bayesian inference and restrained MD simulations. Restraints with log harmonic energy terms are defined according to the target CG model using the Bayesian inference in which the CG deviations can be estimated. From an initial AA structure obtained from either high-resolution experiments or homology modeling, a MD simulation with the aforementioned restraints is performed to obtain a final AA structure that is a backmapping of the target CG model. The method was validated using multiresolution CG models of the soluble extracellular region of the human epidermal growth factor receptor and was further applied to construct AA structures from CG simulations of the nucleosome core particle. The results demonstrate that our method can generate accurate AA structures of different types of biomolecules from multiple CG models with either residue-level resolution or much lower resolution than one-site-per-residue.

Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.

Toward Multiscale Modeling of Proteins and Bioagglomerates: An Orientation-Sensitive Diffusion Model for the Integration of Molecular Dynamics and the Discrete Element Method

Most processes involved in biological and biotechnological systems spread over many scales in space and time. For example, the interaction of multiple enzymes in heterogeneous enzymatic agglomerates or clusters, necessary for efficient enzymatic conversion, is of high interest for research and enzyme engineering. In order to understand and predict their overall behavior and performance, it is important to describe these scales as completely as possible, known as multiscale modeling. While many different approaches have been presented in recent years, knowledge about protein formation and bioagglomeration at the micro scale is still very limited. In an attempt to address such systems, we propose a bottom- up multiscale modeling methodology, bridging the gaps between molecular dynamics (MD) with an explicit solvent and the larger scale discrete element method (DEM) using an implicit solvent and abstracting macromolecules (e.g., proteins) as objects with anisotropic properties. We term this approach the molecular discrete element method (MDEM). For this, we present an orientation-sensitive diffusion model for DEM, which describes the dynamics of anisotropic translational and rotational diffusion, while implicitly considering solvent molecules and enforcing a canonical ensemble. A general-purpose model and parametrization approach is presented, which can be used to simulate any process involving diffusion of discrete particles. Effects of temperature and viscosity changes can be considered, and guidance is provided concerning time step selection. This model is generally applicable and serves as a precondition to enforce the proper dynamics (i.e., diffusion characteristics and canonical ensemble, similar to a thermostat in MD) for the proposed multiscale modeling methodology with anisotropic properties. Thereby, it presents a first step toward modeling at the micro scale and is integral to enforcing dynamics of such systems and therefore extensively validated. As a next step, interaction models are to be defined and added to the presented model. In comparison to atomistic and coarse-grained (CG) MD, a speedup of 5-7 orders of magnitude can be achieved. The approach is demonstrated on multiple components of the pyruvate dehydrogenase enzyme complex, a multienzymatic machinery that involves very different types of enzymes and is of high value to further elucidate the mechanisms of bioagglomeration and metabolic channeling.

DNA size in confined environments

For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders.

Monte Carlo simulation algorithm for B-DNA

Understanding the structure-function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small-angle X-ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all-atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub-ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B-DNA is represented using a wormlike bead-rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse-grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Force-extension behavior of DNA in the presence of DNA-bending nucleoid associated proteins

Interactions between nucleoid associated proteins (NAPs) and DNA affect DNA polymer conformation, leading to phenomena such as concentration dependent force-extension behavior. These effects, in turn, also impact the local binding behavior of the protein, such as high forces causing proteins to unbind, or proteins binding favorably to locally bent DNA. We develop a coarse-grained NAP-DNA simulation model that incorporates both force- and concentration-dependent behaviors, in order to study the interplay between NAP binding and DNA conformation. This model system includes multi-state protein binding and unbinding, motivated by prior work, but is now dependent on the local structure of the DNA, which is related to external forces acting on the DNA strand. We observe the expected qualitative binding behavior, where more proteins are bound at lower forces than at higher forces. Our model also includes NAP-induced DNA bending, which affects DNA elasticity. We see semi-quantitative matching of our simulated force-extension behavior to the reported experimental data. By using a coarse-grained simulation, we are also able to look at non-equilibrium behaviors, such as dynamic extension of a DNA strand. We stretch a DNA strand at different rates and at different NAP concentrations to observe how the time scales of the system (such as pulling time and unbinding time) work in concert. When these time scales are similar, we observe measurable rate-dependent changes in the system, which include the number of proteins bound and the force required to extend the DNA molecule. This suggests that the relative time scales of different dynamic processes play an important role in the behavior of NAP-DNA systems.

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system's electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.