Sequence-dependent elastic properties of DNA

Harmonic elastic constants of 3-11 bp duplex DNA fragments were evaluated using four 5 ns unrestrained molecular dynamics simulation trajectories of 17 bp duplexes with explicit inclusion of solvent and counterions. All simulations were carried out with the Cornell et al. force-field and particle mesh Ewald method for long-range electrostatic interactions. The elastic constants including anisotropic bending and all coupling terms were derived by analyzing the correlations of fluctuations of structural properties along the trajectories. The following sequences have been considered: homopolymer d(ApA)(n) and d(GpG)(n), and alternating d(GPC)(n) and d(APT)(n). The calculated values of elastic constants are in very good overall agreement with experimental values for random sequences. The atomic-resolution molecular dynamics approach, however, reveals a pronounced sequence-dependence of the stretching and torsional rigidity of DNA, while sequence-dependence of the bending rigidity is smaller for the sequences considered. The earlier predicted twist-bend coupling emerged as the most important cross-term for fragments shorter than one helical turn. The calculated hydrodynamic relaxation times suggest that damping of bending motions may play a role in molecular dynamics simulations of long DNA fragments. A comparison of elasticity calculations using global and local helicoidal analyses is reported. The calculations reveal the importance of the fragment length definition. The present work shows that large-scale molecular dynamics simulations represent a unique source of data to study various aspects of DNA elasticity including its sequence-dependence.     

Dynamics of the Buckling Transition in Double-Stranded DNA and RNA

DNA under torsional strain undergoes a buckling transition that is the fundamental step in plectoneme nucleation and supercoil dynamics, which are critical for the processing of genomic information. Despite its importance, quantitative models of the buckling transition, in particular to also explain the surprising two-orders-of-magnitude difference between the buckling times for RNA and DNA revealed by single-molecule tweezers experiments, are currently lacking. Additionally, little is known about the configurations of the DNA during the buckling transition because they are not directly observable experimentally. Here, we use a discrete worm-like chain model and Brownian dynamics to simulate the DNA/RNA buckling transition. Our simulations are in good agreement with experimentally determined parameters of the buckling transition. The simulations show that the buckling time strongly and exponentially depends on the bending stiffness, which accounts for more than half the measured difference between DNA and RNA. Analyzing the microscopic conformations of the chain revealed by our simulations, we find clear evidence for a solenoid-shaped transition state and a curl intermediate. The curl intermediate features a single loop and becomes increasingly populated at low forces. Taken together, the simulations suggest that the worm-like chain model can account semiquantitatively for the buckling dynamics of both DNA and RNA.     

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.     

Dynamics and relative stabilities of parallel- and antiparallel-stranded DNA duplexes.

The dynamics and stability of four DNA duplexes are studied by means of molecular dynamics simulations. The four molecules studied are combinations of 4, 15 bases long, single-stranded oligomers, F1, F2, F3, and F4. The sequence of these single strand oligomers are chosen such that F1-F2 and F3-F4 form parallel (ps) DNA double helices, whereas F1-F4 and F2-F3 form antiparallel-stranded (aps) DNA double helices. Simulations were done at low (100 K) and room (300 K) temperatures. At low temperatures the dynamics are quasi-harmonic and the analysis of the trajectories gives good estimates of the low frequency vibrational modes and density of states. These are used to estimate the linear (harmonic) contribution of local fluctuations to the configurational entropy of the systems. Estimates of the differences in enthalpy between ps and aps duplexes show that aps double helices are more stable than the corresponding ps duplexes, in agreement with experiments. At higher temperatures, the distribution of the fluctuations around the average structures are multimodal and estimates of the configurational entropy cannot be obtained. The multi-basin, nonlinear character of the dynamics at 300 K is established using a novel method which extracts large amplitude nonlinear motions from the molecular dynamics trajectories. Our analysis shows that both ps DNA exhibit much larger fluctuations than the two aps DNA. The large fluctuations of ps DNA are explained in terms of correlated transitions in the beta, epsilon, and zeta backbone dihedral angles.     

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.     

Relative flexibility of DNA and RNA: a molecular dynamics study

State of the art molecular dynamics simulations are used to study the structure, dynamics, molecular interaction properties and flexibility of DNA and RNA duplexes in aqueous solution. Special attention is paid to the deformability of both types of structures, revisiting concepts on the relative flexibility of DNA and RNA duplexes. Our simulations strongly suggest that the concepts of flexibility, rigidity and deformability are much more complex than usually believed, and that it is not always true that DNA is more flexible than RNA.     

Mechanism of spontaneous DNA-DNA interaction of homologous linear duplexes

Previously, we demonstrated the interaction of homologous linear duplexes with formation of four-way DNA structures on the model of five PCR products. We propose that homologous duplex interaction is initiated by the nucleation of several dissociated base pairs of the complementary ends of two fragments with Holliday junction formation, in which cross point migration occurs via spooling of DNA strands from one duplex to the other one, finally resulting in complete resolution into new or previously existing duplexes. To confirm that DNA-DNA interaction involves formation of four-way DNA structures with strand exchange at the cross point, we have demonstrated the strand exchange process between identical duplexes using homologous fragments, harboring either biotin label or (32)P-label. Incubation of the mixture resulted in the addition of (32)P-label to biotin-labeled fragments, and the intensity of (32)P-labeling of biotinylated fragments was dependent upon the incubation duration. DNA-DNA interaction is not based on surface-dependent denaturing, as Triton X-100 does not decrease the formation of complexes between DNA duplexes. The equilibrium concentration of Holliday junctions depends on the sequences of the fragment ends and the incubation temperature. The free energy of Holliday junction formation by the fragments with GC and AT ends differed by 0.6 kcal/mol. Electron microscopic analysis demonstrated that the majority of Holliday junctions harbor the cross point within a 300 base pair region of the fragment ends. This insight into the mechanism of homologous duplex interaction extends our understanding of different DNA rearrangements. Understanding of DNA-DNA interaction is of practical use for better interpretation and optimization of PCR-based analyses.     

Fuzzy cluster analysis of molecular dynamics trajectories.

We propose fuzzy clustering as a method to analyze molecular dynamics (MD) trajectories, especially of proteins and polypeptides. A fuzzy cluster analysis locates classes of similar three-dimensional conformations explored during a molecular dynamics simulation. The method can be readily applied to results from both equilibrium and nonequilibrium simulations, with clustering on either global or local structural parameters. The potential of this technique is illustrated by results from fuzzy cluster analyses of trajectories from MD simulations of various fragments of human parathyroid hormone (PTH). For large molecules, it is more efficient to analyze the clustering of root-mean-square distances between conformations comprising the trajectory. We found that the results of the clustering analysis were unambiguous, in terms of the optimal number of clusters of conformations, for the majority of the trajectories examined. The conformation closest to the cluster center can be chosen as being representative of the class of structures making up the cluster, and can be further analyzed, for example, in terms of its secondary structure. The CPU time used by the cluster analysis was negligible compared to the MD simulation time.     

A molecular dynamics study of the effect of G.T mispairs on the conformation of DNA in solution

The effect of G.T mispair incorporation into a double-helical environment was examined by molecular dynamics simulation. The 60-ps simulations performed on the two hexanucleotide duplexes d (G3C3)2 and d(G3TC2)2 included 10 Na+ counterions and first hydration shell waters. The resulting backbone torsional angle trajectories were analyzed to select time spans representative of conformational domains. The average backbone angles and helical parameters of the last time span for both duplexes are reported. During the simulation the hexamers retained B-type DNA structures that differed from typical A- or B-DNA forms. The overall helical structures for the two duplexes are vary similar. The presence of G.T mispairs did not alter the overall helical structure of the oligonucleotide duplex. Large propeller twist and buckle angles were obtained for both duplexes. The purine/pyrimidine crossover step showed a large decrease in propeller twist in the normal duplex but not in the mismatch duplex. Upon the formation of wobble mispairs in the mismatched duplex, the guanines moved into the minor groove and the thymines moved into the major groove. This helped prevent purine/purine clash and created a deformation in the relative orientation of the glycosidic bonds. It also exposed the free O4 of the thymines in the major groove and N2 of the guanines in the minor groove to interactions with solvent and counterions. These factors seemed to contribute to the apparently higher rigidity of the mismatched duplex during the simulation.     

Molecular dynamics simulations of the d(CCAACGTTGG)(2) decamer: influence of the crystal environment

Molecular dynamics (MD) simulations of the DNA duplex d(CCAACGTTGG)(2) were used to study the relationship between DNA sequence and structure. Two crystal simulations were carried out; one consisted of one unit cell containing two duplexes, and the other of two unit cells containing four duplexes. Two solution simulations were also carried out, one starting from canonical B-DNA and the other starting from the crystal structure. For many helicoidal parameters, the results from the crystal and solution simulations were essentially identical. However, for other parameters, in particular, alpha, gamma, delta, (epsilon - zeta), phase, and helical twist, differences between crystal and solution simulations were apparent. Notably, during crystal simulations, values of helical twist remained comparable to those in the crystal structure, to include the sequence-dependent differences among base steps, in which values ranged from 20 degrees to 50 degrees per base step. However, in the solution simulations, not only did the average values of helical twist decrease to approximately 30 degrees per base step, but every base step was approximately 30 degrees, suggesting that the sequence-dependent information may be lost. This study reveals that MD simulations of the crystal environment complement solution simulations in validating the applicability of MD to the analysis of DNA structure.     

Molecular dynamics simulation of Lewis blood groups and related oligosaccharides.

Molecular dynamics simulations without explicit inclusion of solvent molecules have been performed to study the motions of Lewisa and Lewisb blood group oligosaccharides, and two blood group A tetrasaccharides having type I and type II core chains. The blood group H trisaccharide has also been studied and compared with the blood group A type II core chain. The potential energy surface developed by Rasmussen and co-workers was used with the molecular mechanics code CHARMM. The lowest energy minima of the component disaccharide fragments were obtained from conformational energy mapping. The lowest energy minima of these disaccharide fragments were used to build the tri- and tetrasaccharides that were further minimized before the actual heating/equilibration and dynamics simulations. The trajectories of the disaccharide fragments, e.g., Fuc alpha- (1----4)GlcNAc, Gal beta-(1----4)GlcNAc, etc., show transitions among various minima. However, the oligosaccharides were found to be dynamically stable and no transitions to other minimum energy conformations were observed in the time series of the glycosidic dihedral angles even during trajectories as long as 300 ps. The stable conformations of the glycosidic linkages in the oligosaccharides are not necessarily the same as the minimum energy conformation of the corresponding isolated disaccharides. The average fluctuations of the glycosidic angles in the oligosaccharides were well within the range of +/- 15 degrees. The results of these trajectory calculations were consistent with the relatively rigid single-conformation models derived for these oligosaccharides from 1H-nmr data.     

End-to-end attraction of duplex DNA

Recent experiments [Nakata, M. et al., End-to-end stacking and liquid crystal condensation of 6 to 20 basepair DNA duplexes. Science 2007; 318:1276-1279] have demonstrated spontaneous end-to-end association of short duplex DNA fragments into long rod-like structures. By means of extensive all-atom molecular dynamic simulations, we characterized end-to-end interactions of duplex DNA, quantitatively describing the forces, free energy and kinetics of the end-to-end association process. We found short DNA duplexes to spontaneously aggregate end-to-end when axially aligned in a small volume of monovalent electrolyte. It was observed that electrostatic repulsion of 5'-phosphoryl groups promoted the formation of aggregates in a conformation similar to the B-form DNA double helix. Application of an external force revealed that rupture of the end-to-end assembly occurs by the shearing of the terminal base pairs. The standard binding free energy and the kinetic rates of end-to-end association and dissociation processes were estimated using two complementary methods: umbrella sampling simulations of two DNA fragments and direct observation of the aggregation process in a system containing 458 DNA fragments. We found the end-to-end force to be short range, attractive, hydrophobic and only weakly dependent on the ion concentration. The relation between the stacking free energy and end-to-end attraction is discussed as well as possible roles of the end-to-end interaction in biological and nanotechnological systems.     

Microscopic Basis for the Mesoscopic Extensibility of Dendrimer-Compacted DNA

The mechanism of DNA compaction by dendrimers is key to the design of nanotechnologies that can deliver genetic material into cells. We present atomistic simulations, mesoscopic modeling and single-molecule pulling experiments describing DNA dendrimer interactions. All-atom molecular dynamics were used to characterize pulling-force-dependent interactions between DNA and generation-3 PAMAM amine-terminated dendrimers, and a free energy profile and mean forces along the interaction coordinate are calculated. The energy, force, and geometry parameters computed at the atomic level are input for a Monte Carlo model yielding mesoscopic force-extension curves. Actual experimental single-molecule curves obtained with optical tweezers are also presented, and they show remarkable agreement with the virtual curves from our model. The calculations reveal the microscopic origin of the hysteresis observed in the phase transition underlying compaction. A broad range of ionic and pulling parameters is sampled, and suggestions for windows of conditions to probe new single-molecule behavior are made.     

Structural and thermodynamic features of spiroiminodihydantoin damaged DNA duplexes

Oxidation of guanine or 8-oxo-7,8-dihydroguanine can produce spiroiminodihydantoin (Sp) R and S stereoisomers. Both in vitro and in vivo experiments have shown that the Sp stereoisomers are highly mutagenic, causing G --> C and G --> T transversion mutations. Therefore, they are of interest as potential endogenous cancer causing lesions. However, their structural properties in DNA duplexes remain to be elucidated. We have employed computational methods to study the Sp lesions in 11-mer DNA duplexes with A, C, G, and T partners. Molecular dynamics simulations have been carried out to obtain ensembles of structures, and the trajectories were employed to analyze the structures and compute free energies. The structural and thermodynamic analyses reveal that the Sp stereoisomers energetically favor positioning in the B-DNA major groove, with minor groove conformers also low energy in some cases, depending on the partner base. The R and S stereoisomers adopt opposite orientations with respect to the 5' to 3' direction of the modified strand. Both syn and anti glycosidic bond conformations are energetically feasible, with partner base and stereochemistry determining the preference. The lesions adversely impact base stacking and Watson-Crick hydrogen bonding interactions in the duplex, and cause groove widening. The chemical nature of the partner base determines specific hydrogen bonding and stacking properties of the damaged duplexes. The structural characteristics may relate to observed mutagenic properties of the Sp stereoisomers, including possible stereoisomer-dependent differences.     

Structural insights into the effect of isonucleosides on B-DNA duplexes using molecular-dynamics simulations

Some structural insights into the conformations of the isonucleosides containing duplexes have been provided. Unrestrained molecular-dynamics simulations on 18-mer duplexes with isonucleosides incorporated at the 3'-end or in the center of one strand have been carried out with explicit solvent under periodic boundary conditions using the AMBER force field and the particle mesh Ewald method. The Watson–Crick hydrogen-bonding patterns of the duplexes studied remained intact throughout the simulation. For the modified duplexes, the changes observed in the inter-base pair parameters and backbone torsional angles were primarily localized at the isonucleoside-inserted area. All five structures studied remained in the B-form family. The decreased stacking abilities indicated by the large changes in inter-base pair parameters and the large changes in backbones made the modified duplexes show a minor thermal destabilization in comparison with native DNA. The MM_PBSA method for estimating binding free energies on two complementary strands was used. The results showed that the binding free energies of isonucleoside-incorporated DNA duplexes were lower than the native DNA duplex, which is in good agreement with experimental observations.      

Molecular dynamics structures of peptide nucleic acid x DNA hybrid in the wild-type and mutated alleles of Ki-ras proto-oncogene--stereochemical rationale for the low affinity of PNA in the presence of an AC mismatch

The low affinity of peptide nucleic acid (PNA) to hybridize with DNA in the presence of a mismatch endows PNA with a high degree of discriminatory capacity that has been exploited in therapeutics for the selective inhibition of the expression of point-mutated genes. To obtain a structural basis for this intriguing property, molecular dynamics simulations are carried out on PNA x DNA duplexes formed at the Ki-ras proto-oncogene, comprising the point-mutated (GAT), and the corresponding wild-type (GGT) codon 12. The designed PNA forms an A...C mismatch with the wild-type sequence and a perfect A...T pair with the point mutated sequence. Results show that large movements in the pyrimidine base of the A...C mismatch cause loss of stacking, especially with its penultimate base, concomitant with a variable mismatch hydrogen bond, including its occasional absence. These, in turn, bring about dynamic water interactions in the vicinity of the mismatch. Enthalpy loss and the disproportionate entropy gain associated with these are implicated as the factors contributing to the increase in free energy and diminished stability of PNA x DNA duplex with the A...C mismatch. Absence of these in the isosequential DNA duplex, notwithstanding the A...C mismatch, is attributed to the differences in topology of PNA x DNA vis-à-vis DNA duplexes. It is speculated that similar effects might be responsible for the reduced stability observed in PNA x DNA duplexes containing other base pair mismatches, and also in mismatch containing PNA x DNA duplexes.