Packaging double-helical DNA into viral capsids: structures, forces, and energetics

Small, icosahedral double-stranded DNA bacteriophage pack their genomes tightly into preformed protein capsids using an ATP-driven motor. Coarse-grain molecular-mechanics models provide a detailed picture of DNA packaging in bacteriophage, revealing how conformation depends on capsid size and shape, and the presence or absence of a protein core. The forces that oppose packaging have large contributions from both electrostatic repulsions and the entropic penalty of confining the DNA into the capsid, whereas elastic deformations make only a modest contribution. The elastic deformation energy is very sensitive to the final conformation, whereas the electrostatic and entropic penalties are not, so the packaged DNA favors conformations that minimize the bending energy.     

Electrostatic contribution to the bending of DNA

A model is derived that accounts for the short-range electrostatic contribution to the bending of DNA molecule in solution and in complexes with proteins in terms of the non-linear Poisson-Boltzmann equation. We defined that the short-range electrostatic interactions depend on the changes of the polyion surface charge density under deformation, while the long-range interactions depend on the bending-induced changes in distances between each two points along the polyion axis. After an appropriate simplification of the Poisson-Boltzmann equation, the short-range term is calculated separately giving the lower limit for the electrostatic contribution to the DNA persistence length. The result is compared with the theoretical approaches developed earlier [M. Fixman, J. Chem. Phys. 76 (1982) 6346; M. Le Bret, J. Chem. Phys. 76 (1982) 6243] and with the experimental data. The conclusion is made that the results of Fixman-Le Bret, which took into account both types of the electrostatic interactions for a uniformly bent polyion, give the upper limit for the electrostatic persistence length at low ionic strength, and the actual behavior of the DNA persistence length lies between two theoretical limits. Only the short-range term is significant at moderate-to-high ionic strength where our results coincide with the predictions of Fixman-Le Bret. The bending of DNA on the protein surface that is accompanied by an asymmetric neutralization of the DNA charge is also analyzed. In this case, the electrostatic bending energy gives a significant favorite contribution to the total bending energy of DNA. Important implications to the mechanisms of DNA-protein interactions, particularly in the nucleosome particle, are discussed.     

Meta analysis of Chronic Fatigue Syndrome through integration of clinical, gene expression, SNP and proteomic data

The histone octamer induced bending of DNA into the super-helix structure in nucleosome core particle, is very unique and vital for DNA packing into chromatin. We collected 48 nucleosome crystal structures from PDB and applied a multivariate analysis on the nucleosome structural data. Based on the anisotropic nature of DNA structure, a principal conformational subspace (PCS) is derived from multiple properties to represent the most significant variances of nucleosome DNA structures. The coupling of base pair-oriented parameters with sugar phosphate backbone parameters presented in principal dimensionalities reveals two main deformation modes that have supplemented the existing physical model. By using sequence alignment-based statistics, a positiondependent conformational map for the super-helical DNA path is established. The result shows that the crystal structures of nucleosome DNA have much consistency in position-specific structural variations and certain periodicity is found to exist in these variations. Thus, the positions with obvious deformation patterns along the DNA path in nucleosome core particle are relatively conservative from the perspective of statistics.     

DNA structure: what's in charge?

DNA structure is well known to be sensitive to hydration and ionic strength. Recent theoretical predictions and experimental observations have raised the idea of the intrusion of monovalent cations into the minor groove spine of hydration in B-form DNA. To investigate this further, extensions and further analysis of molecular dynamics (MD) simulations on d(CGCCGAATTCGCG), d(ATAGGCAAAAAATAGGCAAAAATGG) and d(G(5)-(GA(4)T(4)C)(2)-C(5)), including counterions and water, have been performed. To examine the effective of minor groove ions on structure, we analyzed the MD snapshots from a 15 ns trajectory on d(CGCGAATTCGCG) as two subsets: those exhibiting a minor groove water spine and those with groove-bound ions. The results indicate that Na(+) at the ApT step of the minor groove of d(CGCCGAATTCGCG) makes only small local changes in the DNA structure, and these changes are well within the thermal fluctuations calculated from the MD. To examine the effect of ions on the differential stability of a B-form helix, further analysis was performed on two longer oligonucleotides, which exhibit A-tract-induced axis bending localized around the CpG step in the major groove. Plots of axis bending and proximity of ions to the bending locus were generated as a function of time and revealed a strong linear correlation, supporting the idea that mobile cations play a key role in local helix deformations of DNA and indicating ion proximity just precedes the bending event. To address the issue of "what's in charge?" of DNA structure more generally, the relative free energy of A and B-form d(CGCGAATTCGCG) structures from MD simulations under various environmental circumstances were estimated using the free energy component method. The results indicate that the dominant effects on conformational stability come from the electrostatic free energy, but not exclusively from groove bound ions per se, but from a balance of competing factors in the electrostatic free energy, including phosphate repulsions internal to the DNA, the electrostatic component of hydration (i.e. solvent polarization), and electrostatic effects of the counterion atmosphere. In summary, free energy calculations indicate that the electrostatic component is dominant, MD shows temporal proximity of mobile counterions to be correlated with A-track-induced bending, and thus the mobile ion component of electrostatics is a significant contributor. However, the MD structure of the dodecamer d(CGCGAATTCGCG) is not highly sensitive to whether there is a sodium ion in the minor groove.     

Using DNA mechanics to predict in vitro nucleosome positions and formation energies

In eukaryotic genomes, nucleosomes function to compact DNA and to regulate access to it both by simple physical occlusion and by providing the substrate for numerous covalent epigenetic tags. While competition with other DNA-binding factors and action of chromatin remodeling enzymes significantly affect nucleosome formation in vivo, nucleosome positions in vitro are determined by steric exclusion and sequence alone. We have developed a biophysical model, DNABEND, for the sequence dependence of DNA bending energies, and validated it against a collection of in vitro free energies of nucleosome formation and a set of in vitro nucleosome positions mapped at high resolution. We have also made a first ab initio prediction of nucleosomal DNA geometries, and checked its accuracy against the nucleosome crystal structure. We have used DNABEND to design both strong and weak histone- binding sequences, and measured the corresponding free energies of nucleosome formation. We find that DNABEND can successfully predict in vitro nucleosome positions and free energies, providing a physical explanation for the intrinsic sequence dependence of histone–DNA interactions.     

DNA bending by bHLH charge variants

We wish to understand the role of electrostatics in DNA stiffness and bending. The DNA charge collapse model suggests that mutual electrostatic repulsions between neighboring phosphates significantly contribute to DNA stiffness. According to this model, placement of fixed charges near the negatively charged DNA surface should induce bending through asymmetric reduction or enhancement of these inter-phosphate repulsive forces. We have reported previously that charged variants of the elongated basic-leucine zipper (bZIP) domain of Gcn4p bend DNA in a manner consistent with this charge collapse model. To extend this result to a more globular protein, we present an investigation of the dimeric basic-helix–loop–helix (bHLH) domain of Pho4p. The 62 amino acid bHLH domain has been modified to position charged amino acid residues near one face of the DNA double helix. As observed for bZIP charge variants, DNA bending toward appended cations (away from the protein:DNA interface) is observed. However, unlike bZIP proteins, DNA is not bent away from bHLH anionic charges. This finding can be explained by the structure of the more globular bHLH domain which, in contrast to bZIP proteins, makes extensive DNA contacts along the binding face.     

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.     

A computational study of nucleosomal DNA flexibility

Molecular dynamics simulations of the nucleosome core particle and its isolated DNA free in solution are reported. The simulations are based on the implicit solvent methodology and provide insights into the nature of large-scale structural fluctuations and flexibility of the nucleosomal DNA. In addition to the kinked regions previously identified in the x-ray structure of the nucleosome, the simulations support the existence of a biochemically identified distorted region of the DNA. Comparison of computed relative free energies shows that formation of the kinks is associated with little, if any, energy cost relative to a smooth, ideal conformation of the DNA superhelix. Isolated nucleosomal DNA is found to be considerably more flexible than expected for a 147 bp stretch of DNA based on its canonical persistence length of 500 A. Notably, the significant bending of the DNA observed in our simulations occurs without breaking of Watson-Crick bonds. The computed relative stability of bent conformations is sensitive to the ionic strength of the solution in the physiological range; the sensitivity suggests possible experiments that might provide further insights into the structural origins of the unusual flexibility of the DNA.     

Charge neutralization and DNA bending by the Escherichia coli catabolite activator protein

We are interested in the role of asymmetric phosphate neutralization in DNA bending induced by proteins. We describe an experimental estimate of the actual electrostatic contribution of asymmetric phosphate neutralization to the bending of DNA by the Escherichia coli catabolite activator protein (CAP), a prototypical DNA-bending protein. Following assignment of putative electrostatic interactions between CAP and DNA phosphates based on X-ray crystal structures, appropriate phosphates in the CAP half-site DNA were chemically neutralized by methylphosphonate substitution. DNA shape was then evaluated using a semi-synthetic DNA electrophoretic phasing assay. Our results confirm that the unmodified CAP DNA half-site sequence is intrinsically curved by 26° in the direction enhanced in the complex with protein. In the absence of protein, neutralization of five appropriate phosphates increases DNA curvature to 32° (~23% increase), in the predicted direction. Shifting the placement of the neutralized phosphates changes the DNA shape, suggesting that sequence-directed DNA curvature can be modified by the asymmetry of phosphate neutralization. We suggest that asymmetric phosphate neutralization contributes favorably to DNA bending by CAP, but cannot account for the full DNA deformation.     

Origin of the intrinsic rigidity of DNA

The intrinsic rigidities of DNA and RNA helices are generally thought to arise from some combination of vertical base-stacking interactions and intra-helix phosphate–phosphate charge repulsion; however, the relative contributions of these two types of interaction to helix rigidity have not been quantified. To address this issue, we have measured the rotational decay times of a ‘gapped-duplex’ DNA molecule possessing a central, single-stranded region, dT₂₄, before and after addition of the free purine base, N⁶-methyladenine (^meA). Upon addition of ^meA, the bases pair with the T residues, forming a continuous stack within the gap region. Formation of the gapped duplex is accompanied by a nearly 2-fold increase in decay time, to values that are indistinguishable from the full duplex control for monovalent salt concentrations up to 90 mM. These results indicate that at least 90% of the rigidity of the dT_n–dA_n homopolymer derives from base pair stacking effects, with phosphate–phosphate interactions contributing relatively little to net helix rigidity at moderate salt concentrations.     

Chromatin ionic atmosphere analyzed by a mesoscale electrostatic approach

Characterizing the ionic distribution around chromatin is important for understanding the electrostatic forces governing chromatin structure and function. Here we develop an electrostatic model to handle multivalent ions and compute the ionic distribution around a mesoscale chromatin model as a function of conformation, number of nucleosome cores, and ionic strength and species using Poisson-Boltzmann theory. This approach enables us to visualize and measure the complex patterns of counterion condensation around chromatin by examining ionic densities, free energies, shielding charges, and correlations of shielding charges around the nucleosome core and various oligonucleosome conformations. We show that: counterions, especially divalent cations, predominantly condense around the nucleosomal and linker DNA, unburied regions of histone tails, and exposed chromatin surfaces; ionic screening is sensitively influenced by local and global conformations, with a wide ranging net nucleosome core screening charge (56-100e); and screening charge correlations reveal conformational flexibility and interactions among chromatin subunits, especially between the histone tails and parental nucleosome cores. These results provide complementary and detailed views of ionic effects on chromatin structure for modest computational resources. The electrostatic model developed here is applicable to other coarse-grained macromolecular complexes.     

Thermodynamic stability theory for DNA doughnut shapes induced by charge neutralization

A thermodynamic analysis of the bending free energy of DNA, initiated previously, is extended. It was demonstrated that the ionic-strength dependence of the persistence length of DNA in aqueous NaCl can be understood by postulating (1) a rigid-rod 60 base-pair unit and (2) a negative contribution from nonelectrostatic sources to the bending free energy of this unit. On electrostatic neutralization of the phosphate charge, the latter term alone survives, and bending becomes a spontaneous process. In this paper it is demonstrated from a theoretical analysis of the ionic-strength dependence of the rate of denaturation of DNA that the above statements are restricted in their validity to radii of curvature greater than 170 Å; beyond this limit, the steeply rising repulsive energy of tightly packed atoms dominates the bending free energy. Therefore, spontaneous bending on charge neutralization proceeds up to, but not beyond, this barrier to curvature. It is noted that doughnut forms of DNA induced by binding of cationic spermidine, or mixtures of Mg²⁺ and polyamines are observed to possess maximum curvatures, corresponding to the radius of the “hole in the middle,” in the range 1/150–1/200 Å.     

The helical model of the nucleosome core.

A model of the nucleosome core is proposed based on a topologically linear array of histones attached sequentially to DNA. The linear complex folds helically forming a spring-like particle. Different variants of the particle are discussed (cylindrical springs with and without histone-histone contacts between turns of the helix, solenoidal spring). The model is consistent with known data about the nucleosome structure. Histones H3 and H4 have a special role in the model which is related also to the superstructure of chromatin.     

Direct measurements of the nucleosome-forming preferences of periodic DNA motifs challenge established models

Several periodic motifs have been implicated in facilitating the bending of DNA around the histone core of the nucleosome. For example, di-nucleotides AA/TT/TA and GC at ∼10-bp periods, but offset by 5 bp, are found with higher-than-expected occurrences in aligned nucleosomal DNAs in vitro and in vivo. Additionally, regularly oscillating period-10 trinucleotide motifs non-T, A/T, G and their complements have been implicated in the formation of regular nucleosome arrays. The effects of these periodic motifs on nucleosome formation have not been systematically tested directly by competitive reconstitution assays. We show that, in general, none of these period-10 motifs, except TA, in certain sequence contexts, facilitates nucleosome formation. The influence of periodic TAs on nucleosome formation is appreciable; with some of the 200-bp DNAs out-competing bulk nucleosomal DNA by more than 400-fold. Only the nucleotides immediately flanking TA influence its nucleosome-forming ability. Period-10 TA, when flanked by a pair of permissive nucleotides, facilitates DNA bending through compression of the minor groove. The free energy change for nucleosome formation decreases linearly with the number of consecutive TAs, up to eight. We suggest how these data can be reconciled with previous findings.     

Binding of ethidium to the nucleosome core particle. 2. Internal and external binding modes

We have previously reported that the binding of ethidium bromide to the nucleosome core particle results in a stepwise dissociation of the structure which involves the initial release of one copy each of H2A and H2B (McMurray & van Holde, 1986). In this report, we have examined the absorbance and fluorescence properties of intercalated and outside bound forms of ethidium bromide. From these properties, we have measured the extent of external, electrostatic binding of the dye versus internal, intercalation binding to the core particle, free from contribution by linker DNA. We have established that dissociation is induced by the intercalation mode of binding to DNA within the core particle DNA, and not by binding to the histones or by nonintercalative binding to DNA. The covalent binding of [3H]-8-azidoethidium to the core particle clearly shows that less than 1.0 adduct is formed per histone octamer over a wide range of input ratios. Simultaneously, analyses of steady-state fluorescence enhancement and fluorescence lifetime data from bound ethidium complexes demonstrate extensive intercalation binding. Combined analyses from steady-state fluorescence intensity with equilibrium dialysis or fluorescence lifetime data revealed that dissociation began when approximately 14 ethidium molecules are bound by intercalation to each core particle and less than 1.0 nonintercalated ion pair was formed per core particle.     

DNA sequence-dependent contributions of core histone tails to nucleosome stability: differential effects of acetylation and proteolytic tail removal

Modulation of nucleosome stability in chromatin plays an important role in eukaryotic gene expression. The core histone N-terminal tail domains are believed to modulate the stability of wrapping nucleosomal DNA and the stability of the chromatin filament. We analyzed the contribution of the tail domains to the stability of nucleosomes containing selected DNA sequences that are intrinsically straight, curved, flexible, or inflexible. We find that the presence of the histone tail domains stabilizes nucleosomes containing DNA sequences that are intrinsically straight or curved. However, the tails do not significantly contribute to the free energy of nucleosome formation with flexible DNA. Interestingly, hyperacetylation of the core histone tail domains does not recapitulate the effect of tail removal by limited proteolysis with regard to nucleosome stability. We find that acetylation of the tails has the same minor effect on nucleosome stability for all the selected DNA sequences. A comparison of histone partitioning between long donor chromatin, acceptor DNA, and free histones in solution shows that the core histone tails mediate internucleosomal interactions within an H1-depleted chromatin fiber amounting to an average free energy of about 1 kcal/mol. Thus, such interactions would be significant with regard to the free energies of sequence-dependent nucleosome positioning. Last, we analyzed the contribution of the H2A/H2B dimers to nucleosome stability. We find that the intact nucleosome is stabilized by 900 cal/mol by the presence of the dimers regardless of sequence. The biological implications of these observations are discussed.     

Molecular dynamics simulations reveal the balance of forces governing the formation of a guanine tetrad—a common structural unit of G-quadruplex DNA

G-quadruplexes (G4) are nucleic acid conformations of guanine-rich sequences, in which guanines are arranged in the square-planar G-tetrads, stacked on one another. G4 motifs form in vivo and are implicated in regulation of such processes as gene expression and chromosome maintenance. The structure and stability of various G4 topologies were determined experimentally; however, the driving forces for their formation are not fully understood at the molecular level. Here, we used all-atom molecular dynamics to probe the microscopic origin of the G4 motif stability. By computing the free energy profiles governing the dissociation of the 3′-terminal G-tetrad in the telomeric parallel-stranded G4, we examined the thermodynamic and kinetic stability of a single G-tetrad, as a common structural unit of G4 DNA. Our results indicate that the energetics of guanine association alone does not explain the overall stability of the G-tetrad and that interactions involving sugar–phosphate backbone, in particular, the constrained minimization of the phosphate–phosphate repulsion energy, are crucial in providing the observed enthalpic stabilization. This enthalpic gain is largely compensated by the unfavorable entropy change due to guanine association and optimization of the backbone topology.     

A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.