The stretched intermediate model of B-Z DNA transition

There have been numerous attempts to describe the mechanism of B-Z transition. Our simulations based on the stochastic difference equation with length algorithm show that a short DNA oligomer will tend to unwind and overstretch during the transition. The overstretching of DNA is then understood from the Zhou, Zhang, and Ou-Yang model. Unlike the Harvey model, the stretched intermediate model does not pose any steric dilemma; we are able to show that the chain sense reversal progresses spontaneously using the stretched intermediate model. A nonlinear DNA model is used to describe the origins and mechanism of base rotation in the stretched intermediate state of DNA. We also propose an experiment that can verify the existence of a stretched intermediate state during B-Z transition, thus opening up fresh grounds for experimentation in this field.     

Evaluation of elastic properties of atomistic DNA models

A number of intriguing aspects in dynamics of double-helical DNA is related to the coupling between its macroscopic and microscopic states. A link between the elastic properties of long DNA chains and their atom-level dynamics can be established by comparing the worm-like chain model of polymer DNA with the conformational ensembles produced by molecular dynamics simulations. This problem is complicated by the complexity of the DNA structure, the small size of DNA fragments, and relatively short trajectory durations accessible in computer simulations of microscopic DNA dynamics. A careful study of all these aspects has been performed by using longer DNA fragments and increased durations of MD trajectories as compared to earlier such investigations. Special attention is paid to the necessary conditions and criteria of time convergence, and the possibility to increase the sampling by using constrained DNA models and simplified simulation conditions. It is found that dynamics of 25-mer duplexes with regular sequences agrees well with the worm-like chain theory and that accurate evaluation of DNA elastic parameters requires at least two turns of the double helix and approximately 20-ns duration of trajectories. Bond length and bond-angle constraints affect the estimates within numerical errors. In contrast, simplified treatment of solvation can strongly change the observed elastic parameters of DNA. The elastic parameters evaluated for AT- and GC-alternating duplexes reasonably agree with experimental data and suggest that, in different basepair sequences, the torsional and stretching elasticities vary stronger than the bending stiffness.     

Pulling-speed-dependent force-extension profiles for semiflexible chains

We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyart's stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.     

Probing the Elasticity of DNA on Short Length Scales by Modeling Supercoiling under Tension

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.     

Probing single-stranded DNA conformational flexibility using fluorescence spectroscopy

Single-stranded DNA (ssDNA) is an essential intermediate in various DNA metabolic processes and interacts with a large number of proteins. Due to its flexibility, the conformations of ssDNA in solution can only be described using statistical approaches, such as flexibly jointed or worm-like chain models. However, there is limited data available to assess such models quantitatively, especially for describing the flexibility of short ssDNA and RNA. To address this issue, we performed FRET studies of a series of oligodeoxythymidylates, (dT)N, over a wide range of salt concentrations and chain lengths (10 < or = N < or = 70 nucleotides), which provide systematic constraints for testing theoretical models. Unlike in mechanical studies where available ssDNA conformations are averaged out during the time it takes to perform measurements, fluorescence lifetimes may act here as an internal clock that influences fluorescence signals depending on how fast the ssDNA conformations fluctuate. A reasonably good agreement could be obtained between our data and the worm-like chain model provided that limited relaxations of the ssDNA conformations occur within the fluorescence lifetime of the donor. The persistence length thus estimated ranges from 1.5 nm in 2 M NaCl to 3 nm in 25 mM NaCl.     

Dynamics of Forced Nucleosome Unraveling and Role of Nonuniform Histone-DNA Interactions

A coarse-grained model of the nucleosome is introduced to investigate the dynamics of force-induced unwrapping of DNA from histone octamers. In this model, the DNA is treated as a charged, discrete worm-like chain, and the octamer is treated as a rigid cylinder carrying a positively charged superhelical groove that accommodates 1.7 turns of DNA. The groove charges are parameterized to reproduce the nonuniform histone/DNA interaction free energy profile and the loading rate-dependent unwrapping forces, both obtained from single-molecule experiments. Brownian dynamics simulations of the model under constant loading conditions reveal that nucleosome unraveling occurs in three distinct stages. At small extensions, the flanking DNA exhibits rapid unwrapping-rewrapping (breathing) dynamics and the octamer flips ～180° and moves toward the pulling axis. At intermediate extensions, the outer turn of DNA unwraps gradually and the octamer swivels about the taut linkers and flips a further ～90° to orient its superhelical axis almost parallel to the pulling axis. At large extensions, a portion of the inner turn unwraps abruptly with a notable rip in the force-extension plot and a >90° flip of the octamer. The remaining inner turn unwraps reversibly to leave a small portion of DNA attached to the octamer despite extended pulling. Our simulations further reveal that the nonuniform histone/DNA interactions in canonical nucleosomes serve to: stabilize the inner turn against unraveling while enhancing the breathing dynamics of the nucleosome and prevent dissociation of the octamer from the DNA while facilitating its mobility along the DNA. Thus, the modulation of the histone/DNA interactions could constitute one possible mechanism for regulating the accessibility of the nucleosome-wound DNA sequences.     

Brownian dynamics simulation of probe diffusion in DNA: effects of probe size, charge and DNA concentration

We have used Brownian dynamics simulation to study probe diffusion in solutions of short chain DNA using our previously developed simulation algorithm. We have examined the effect of probe size, charge, and DNA concentration on the probe diffusion coefficient, with the aim of gaining insight into the diffusion of proteins in a concentrated DNA environment. In these simulations, DNA was modeled as a worm-like chain of hydrodynamically equivalent spherical frictional elements while probe particles were modeled as spheres of given charge and hydrodynamic radius. The simulations allowed for both short range Lennard-Jones interactions and long ranged electrostatic interactions between charged particles. For uncharged systems, we find that the effects of probe size and DNA concentration on the probe diffusion coefficient are consistent with excluded volume models and we interpret our results in terms of both empirical scaling laws and the predictions of scaled particle theory. For charged systems, we observe that the effects of probe size and charge are most pronounced for the smallest probes and interpret the results in terms of the probe charge density. For an ionic strength of 0.1 M we find that, below a critical probe surface charge density, the probe diffusion coefficient is largely independent of probe charge and only weakly dependent on the DNA charge. These effects are discussed in terms of the interactions between the probe and the DNA matrix and are interpreted in terms of both the underlying physics of transport in concentrated solutions and the assumptions of the simulation model.     

Applying the stochastic difference equation to DNA conformational transitions: a study of B-Z and B-A DNA transitions

Despite the existence of numerous models to account for the B-Z DNA transition, experimenters have not yet arrived at a conclusive answer to the structural and dynamical features of the B-Z transition. By applying the stochastic difference equation to simulate the B-Z DNA transition, we have shown that the stretched intermediate model of the B-Z transition is more probable than other B-Z transition models such as the Harvey model. This is accomplished by comparing potential energy profiles of various B-Z DNA transition models and calculating relative probabilities based on the stochastic difference equation with respect to length (SDEL) formalism. The results garnered in this article allow for new approaches in determining the structural transition of B-DNA to Z-DNA experimentally. We have also simulated the B-A DNA transition using the stochastic difference equation. Unlike the B-Z DNA transition, the mechanism for the B-A DNA transition is well established. The variation in the pseudorotation angle during the transition is in good agreement with experimental results. Qualitative features of the simulated B-A transition also agree well with experimental data. The SDEL approach is thus a suitable numerical technique to compute long-time molecular dynamics trajectory for DNA molecules.     

Simulating the Entropic Collapse of Coarse-Grained Chromosomes

Depletion forces play a role in the compaction and decompaction of chromosomal material in simple cells, but it has remained debatable whether they are sufficient to account for chromosomal collapse. We present coarse-grained molecular dynamics simulations, which reveal that depletion-induced attraction is sufficient to cause the collapse of a flexible chain of large structural monomers immersed in a bath of smaller depletants. These simulations use an explicit coarse-grained computational model that treats both the supercoiled DNA structural monomers and the smaller protein crowding agents as combinatorial, truncated Lennard-Jones spheres. By presenting a simple theoretical model, we quantitatively cast the action of depletants on supercoiled bacterial DNA as an effective solvent quality. The rapid collapse of the simulated flexible chromosome at the predicted volume fraction of depletants is a continuous phase transition. Additional physical effects to such simple chromosome models, such as enthalpic interactions between structural monomers or chain rigidity, are required if the collapse is to be a first-order phase transition.     

Interconversion between Parallel and Antiparallel Conformations of a 4H RNA junction in Domain 3 of Foot-and-Mouth Disease Virus IRES Captured by Dynamics Simulations

RNA junctions are common secondary structural elements present in a wide range of RNA species. They play crucial roles in directing the overall folding of RNA molecules as well as in a variety of biological functions. In particular, there has been great interest in the dynamics of RNA junctions, including conformational pathways of fully base-paired 4-way (4H) RNA junctions. In such constructs, all nucleotides participate in one of the four double-stranded stem regions, with no connecting loops. Dynamical aspects of these 4H RNAs are interesting because frequent interchanges between parallel and antiparallel conformations are thought to occur without binding of other factors. Gel electrophoresis and single-molecule fluorescence resonance energy transfer experiments have suggested two possible pathways: one involves a helical rearrangement via disruption of coaxial stacking, and the other occurs by a rotation between the helical axes of coaxially stacked conformers. Employing molecular dynamics simulations, we explore this conformational variability in a 4H junction derived from domain 3 of the foot-and-mouth disease virus internal ribosome entry site (IRES); this junction contains highly conserved motifs for RNA-RNA and RNA-protein interactions, important for IRES activity. Our simulations capture transitions of the 4H junction between parallel and antiparallel conformations. The interconversion is virtually barrier-free and occurs via a rotation between the axes of coaxially stacked helices with a transient perpendicular intermediate. We characterize this transition, with various interhelical orientations, by pseudodihedral angle and interhelical distance measures. The high flexibility of the junction, as also demonstrated experimentally, is suitable for IRES activity. Because foot-and-mouth disease virus IRES structure depends on long-range interactions involving domain 3, the perpendicular intermediate, which maintains coaxial stacking of helices and thereby consensus primary and secondary structure information, may be beneficial for guiding the overall organization of the RNA system in domain 3.     

Force-extension formula for the worm-like chain model from a variational principle

Stiff polymers, such as single-stranded DNA, unstructured RNA and cellulose, are all basically extremely long rods with relatively short repeating monomers. The simplest model for describing such stiff polymers is called the freely jointed chain model, which treats a molecule as a chain of perfectly rigid subunits of orientationally independent statistical segments, joined together by perfectly flexible hinges. A more realistic model that incorporates the entropic elasticity of a molecule, called the worm-like chain model, has been proposed by assuming that each monomer resists the bending force. Some force-extension formulae for the worm-like chain model have been previously found in terms of interpolation and numerical solutions resulting from statistical mechanics. In this paper, however, we adopt a variational principle to seek the minimum energy configuration of a stretched molecule by incorporating all the possible orientations of each monomer under thermal equilibrium, i.e., constant temperature. We determine a force-extension formula for the worm-like chain model analytically. We find that our formula suggests new terms such as the free energy and the cut-off force of a molecule, which define a clear transition from the entropic regime to the enthalpic regime and the fracture of the molecule, respectively. In addition, we predict two possible phase changes for a stretched molecule, i.e., from a super-helix to a soliton and then from a soliton to a vertical twisted line. We show theoretically that a molecule must undergo at least one phase change before it is fully stretched into its total contour length. This new formula is used to fit recent experimental data and shows a good agreement with some current literature that uses a statistical approach. Finally, an instability analysis is adopted to investigate the sensitivity of the new formula subject to small changes in temperature.     

Molecular dynamics simulation for shape change of water-in-oil droplets

We performed molecular dynamics (MD) simulations of water-in-oil droplet shape transformations induced by the addition of polymer chains. In a prior experiment, transformations of spherical droplets to rod-like, worm-like and network-like droplets were observed. In our previous study, we reproduced rod-like droplets via coarse-grained MD simulations, and the mechanism for the droplet shape change was elucidated by considering the contact area between the chains and the surfactant head groups. However, in that simulation model, we could not reproduce the worm-like and network-like droplets. In this study, we improved the simulation model. For a small number of chains, several spherical droplets were obtained. As the number of chains increased, the spherical droplets were transformed to rod-like, worm-like and network-like shapes by coalescence of the droplets. The calculated and experimental results agreed well, and we verified that the mechanism for the droplet shape transformations observed in the present simulations could be explained by the mechanism suggested in the previous study.     

DNA sequence and methylation prescribe the inside-out conformational dynamics and bending energetics of DNA minicircles

Eukaryotic genome and methylome encode DNA fragments’ propensity to form nucleosome particles. Although the mechanical properties of DNA possibly orchestrate such encoding, the definite link between ‘omics’ and DNA energetics has remained elusive. Here, we bridge the divide by examining the sequence-dependent energetics of highly bent DNA. Molecular dynamics simulations of 42 intact DNA minicircles reveal that each DNA minicircle undergoes inside-out conformational transitions with the most likely configuration uniquely prescribed by the nucleotide sequence and methylation of DNA. The minicircles’ local geometry consists of straight segments connected by sharp bends compressing the DNA’s inward-facing major groove. Such an uneven distribution of the bending stress favors minimum free energy configurations that avoid stiff base pair sequences at inward-facing major grooves. Analysis of the minicircles’ inside-out free energy landscapes yields a discrete worm-like chain model of bent DNA energetics that accurately account for its nucleotide sequence and methylation. Experimentally measuring the dependence of the DNA looping time on the DNA sequence validates the model. When applied to a nucleosome-like DNA configuration, the model quantitatively reproduces yeast and human genomes’ nucleosome occupancy. Further analyses of the genome-wide chromatin structure data suggest that DNA bending energetics is a fundamental determinant of genome architecture.     

Effects of chain length on the aggregation of model polyglutamine peptides: molecular dynamics simulations

Aggregation in the brain of polyglutamine-containing proteins is either a cause or an associated symptom of nine hereditary neurodegenerative disorders including Huntington's disease. The molecular level mechanisms by which these proteins aggregate are still unclear. In an effort to shed light on this important phenomenon, we are investigating the aggregation of model polyglutamine peptides using molecular-level computer simulation with a simplified model of polyglutamine that we have developed. This model accounts for the most important types of intra- and inter-molecular interactions-hydrogen bonding and hydrophobic interactions-while allowing the folding process to be simulated in a reasonable time frame. The model is used to examine the folding of isolated polyglutamine peptides 16, 32, and 48 residues long and the folding and aggregation of systems of 24 model polyglutamine peptides 16, 24, 32, 36, 40, and 48 residues long. Although the isolated polyglutamine peptides did form some alpha and beta backbone-backbone hydrogen bonds they did not have as many of these bonds as they would have if they had folded into a complete alpha helix or beta sheet. In one of the simulations on the isolated polyglutamine peptide 48 residues long, we observed a structure that resembles a beta helix. In the multi-chain simulations we observed amorphous aggregates at low temperatures, ordered aggregates with significant beta sheet character at intermediate temperatures, and random coils at high temperatures. We have found that the temperature at which the model peptides undergo the transition from amorphous aggregates to ordered aggregates and the temperature at which the model peptides undergo the transition from ordered aggregates to random coils increase with increasing chain length. Our finding that the stability of the ordered aggregates increases as the peptide chain length increases may help to explain the experimentally observed relation between polyglutamine tract length and aggregation in vitro and disease progression in vivo. We have also observed in our simulations that the optimal temperature for the formation of beta sheets increases with chain length up to 36 glutamine residues but not beyond. Equivalently, at fixed temperature we find a transition from a region dominated by random coils at chain lengths less than 36 to a region dominated by relatively ordered beta sheet structures at chain lengths greater than 36. Our finding of this critical chain length of 36 glutamine residues is interesting because a critical chain length of 37 glutamine residues has been observed experimentally.     

Euler buckling and nonlinear kinking of double-stranded DNA

The bending stiffness of double-stranded DNA (dsDNA) at high curvatures is fundamental to its biological activity, yet this regime has been difficult to probe experimentally, and literature results have not been consistent. We created a ‘molecular vise’ in which base-pairing interactions generated a compressive force on sub-persistence length segments of dsDNA. Short dsDNA strands (<41 base pairs) resisted this force and remained straight; longer strands became bent, a phenomenon called ‘Euler buckling’. We monitored the buckling transition via Förster Resonance Energy Transfer (FRET) between appended fluorophores. For low-to-moderate concentrations of monovalent salt (up to ∼150 mM), our results are in quantitative agreement with the worm-like chain (WLC) model of DNA elasticity, without the need to invoke any ‘kinked’ states. Greater concentrations of monovalent salts or 1 mM Mg²⁺ induced an apparent softening of the dsDNA, which was best accounted for by a kink in the region of highest curvature. We tested the effects of all single-nucleotide mismatches on the DNA bending. Remarkably, the propensity to kink correlated with the thermodynamic destabilization of the mismatched DNA relative the perfectly complementary strand, suggesting that the kinked state is locally melted. The molecular vise is exquisitely sensitive to the sequence-dependent linear and nonlinear elastic properties of dsDNA.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

Effects of the cross-linkers on the buckling of microtubules in cells

In cells, the protein cross-linkers lead to a distinct buckling behavior of microtubules (MTs) different from the buckling of individual MTs. This paper thus aims to examine this issue via the molecular structural mechanics (MSM) simulations. The transition of buckling responses was captured as the two-dimensional-linkers were replaced by the three-dimensional (3D) ones. Then, the effects of the radial orientation and the axial density of the 3D-linkers were examined, showing that more uniform distribution of the radial orientation leads to the higher critical load with 3D buckling modes, while the inhomogeneity of the axial density results in the localized buckling patterns. The results demonstrated the important role of the cross-linker in regulating MT stiffness, revealed the physics of the experimentally observed localized buckling and these results will pave the way to a new multi-component mechanics model for whole cells.     

The folding pathway of ubiquitin from all-atom molecular dynamics simulations

The folding (unfolding) pathway of ubiquitin is probed using all-atom molecular dynamics simulations. We dissect the folding pathway using two techniques: first, we probe the folding pathway of ubiquitin by calculating the evolution of structural properties over time and second, we identify the rate determining transition state for folding. The structural properties that we look at are hydrophobic solvent accessible surface area (SASA) and Calpha-root-mean-square deviation (rmsd). These properties on their own tell us relatively little about the folding pathway of ubiquitin; however, when plotted against each other, they become powerful tools for dissecting ubiquitin's folding mechanism. Plots of Calpha-rmsd against SASA serve as a phase space trajectories for the folding of ubiquitin. In this study, these plots show that ubiquitin folds to the native state via the population of an intermediate state. This is shown by an initial hydrophobic collapse phase followed by a second phase of secondary structure arrangement. Analysis of the structure of the intermediate state shows that it is a collapsed species with very little secondary structure. In reconciling these observations with recent experimental data, the transition that we observe in our simulations from the unfolded state (U) to the intermediate state (I) most likely occurs in the dead-time of the stopped flow instrument. The folding pathway of ubiquitin is probed further by identification of the rate-determining transition state for folding. The method used for this is essential dynamics, which utilizes a principal component analysis (PCA) on the atomic fluctuations throughout the simulation. The five transition state structures identified in silico are in good agreement with the experimentally determined transition state. The calculation of phi-values from the structures generated in the simulations is also carried out and it shows a good correlation with the experimentally measured values. An initial analysis of the denatured state shows that it is compact with fluctuating regions of nonnative secondary structure. It is found that the compactness in the denatured state is due to the burial of some hydrophobic residues. We conclude by looking at a correlation between folding kinetics and residual structure in the denatured state. A hierarchical folding mechanism is then proposed for ubiquitin.