Excess counterion binding and ionic stability of kinked and branched DNA.

We compute the excess number of counterions associated with kinked and branched DNA, and the ionic stabilities of these structures as a function of chain length and both sodium and magnesium salt concentration, using numerical counterion condensation theory. The DNA structures are modeled as two or more finite lines of phosphate charges radiating from the kink or junction center. The number of excess counterions around the (40-90 degrees) kinked duplex is very small (at most four). The geometries of large three- and four-way DNA junctions (with > 50 base pairs per arm) in solutions containing low to moderate NaCl concentrations, by contrast, accumulate a substantial number of excess sodium ions (> 20) but no more than 15 magnesium counterions. The excess number of counterions surrounding the kinked linear chain and the branched DNA structures either remains invariant or increases with chain length, tending to reach a plateau value. Open configurations, such as the planar Y-shaped three-way junction (with three 120 degrees inter-arm angles) and the 90 degrees cross-shaped four-way junction, are ionically more stable than compact geometries, such as pyramidal three-way junctions and X-shaped four-way junctions, over the entire range of salt concentration considered (10(-5)-10(-1) M NaCl or MgCl2). The ionic stabilities of the compact forms increase with increasing salt concentration and become comparable to those of the extended geometries at high salt (especially when magnesium is the supporting salt).

A theory of DNA dissociation from the nucleosome.

Previous analysis of an elastic model of the nucleosome indicated that 10 bp end segments of DNA can exist in a continuum of mechanically stable trajectories ranging from complete winding on the histone octamer to complete unwinding. Stable states of 20 bp and 40 bp end segments, however, are grouped in bands separated by gaps where DNA trajectories are unstable. We extend these results to cover the entire range up to a complete nucleosomal turn, 80 bp. We find that 10 to 60 bp segments have states intermediate between fully wound and fully unwound that are mechanically stable. In striking contrast, there is no stable intermediate trajectory for 70 bp or 80 bp segments. Segments of these lengths constitute a two-state system. A 70 or 80 bp segment is either fully wound or fully unwound, and the population of these states is governed by Boltzmann's thermal distribution. We have found a plausible dissociation pathway from the fully wound to the fully unwound state for the 80 bp segment. In a ponderous breathing motion that breaks all contacts with the histone ponderous breathing motion that breaks all contacts with the histone surface, the segment climbs to an activation peak of about 12 kcal/mol, then rapidly straightens away from the histone core to complete dissociation.

Flexing and folding double helical DNA.

DNA base sequence, once thought to be interesting only as a carrier of the genetic blueprint, is now recognized as playing a structural role in modulating the biological activity of genes. Primary sequences of nucleic acid bases describe real three-dimensional structures with properties reflecting those structures. Moreover, the structures are base sequence dependent with individual residues adopting characteristic spatial forms. As a consequence, the double helix can fold into tertiary arrangements, although the deformation is much more gradual and spread over a larger molecular scale than in proteins. As part of an effort to understand how local structural irregularities are translated at the macromolecular level in DNA and recognized by proteins, a series of calculations probing the structure and properties of the double helix have been performed. By combining several computational techniques, complementary information as well as a series of built-in checks and balances for assessing the significance of the findings are obtained. The known sequence dependent bending, twisting, and translation of simple dimeric fragments have been incorporated into computer models of long open DNAs of varying length and chemical composition as well as in closed double helical circles and loops. The extent to which the double helix can be forced to bend and twist is monitored with newly parameterized base sequence dependent elastic energy potentials based on the observed configurations of adjacent base pairs in the B-DNA crystallographic literature.

Configurational statistics of the DNA duplex: extended generator matrices to treat the rotations and translations of adjacent residues.

The base-to-base virtual bond treatment of nucleic acids used in statistical mechanical calculations of polynucleotide chain properties has been refined by incorporating the six parameters that relate the positions and orientations of sequential rigid bodies. The scheme allows for the sequence-dependent bending, twisting, and displacement of base pairs as well as for asymmetry in the angular and translational fluctuations of individual residues. Expressions are developed for the generator matrices required for the computation, as a function of chain length, of various parameters measuring the overall mean extension and shape of the DNA. Quantities of interest include the end-to-end vector r, the square of the end-to-end distance r2, the square radius of gyration s2, the center-of-gravity vector g, the second moments of inertia Sx2, and the higher moments of r and g. The matrix expressions introduced in the 1960s by Flory and co-workers for the determination of configuration-dependent polymer chain averages are decomposed into their translational and orientational contributions so that the methods can be extended to the rigid body analysis of chemical moieties. The new expressions permit, for the first time, examination of the effects of sequence-dependent translations, such as the lateral sliding of residues in A- and B-helices and the vertical opening of base pairs in drug-DNA complexes, on the average extension and shape of the long flexible double helix. The approach is in the following paper using conformational energy estimates of the base sequence-dependent flexibility of successive B-DNA base pairs.

Spatial translational motions of base pairs in DNA molecules: application of the extended matrix generator method.

We have used the elementary generator matrices outlined in the preceding paper to examine the conformational plasticity of the nucleic acid double helix. Here we investigate kinked DNA structures made up of alternating B- and A-type helices and intrinsically curved duplexes perturbed by the intercalation of ligands. We model the B-to-A transition by the lateral translation of adjacent base pairs, and the intercalation of ligands by the vertical displacement of neighboring residues. We report a complete set of average configuration-dependent parameters, ranging from scalars (i.e., persistence lengths) to first- and second-order tensor parameters (i.e., average second moments of inertia), as well as approximations of the associated spatial distributions of the DNA and their angular correlations. The average structures of short chains (of lengths less than 100 base pairs) with local kinks or intrinsically curved sequences are essentially rigid rods. At the smallest chain lengths (10 base pairs), the kinked and curved chains exhibit similar average properties, although they are structurally perturbed compared to the standard B-DNA duplex. In contrast, at lengths of 200 base pairs, the curved and kinked chains are more compact on average and are located in a different space from the standard B- or A-DNA helix. While A-DNA is shorter and thicker than B-DNA in x-ray models, the long flexible A-DNA helix is thinner and more extended on average than its B-DNA counterpart because of more limited fluctuations in local structure. Curved polymers of 50 base pairs or longer also show significantly greater asymmetry than other DNAs (in terms of the distribution of base pairs with respect to the center of gravity of the chain). The intercalation of drugs in the curved DNA straightens and extends the smoothly deformed template. The dimensions of the average ellipsoidal boundaries defining the configurations of the intercalated polymers are roughly double those of the intrinsically curved chain. The altered proportions and orientations of these density functions reflect the changing shape and flexibility of the double helix. The calculations shed new light on the possible structural role of short A-DNA fragments in long B-type duplexes and also offer a model for understanding how GC-specific intercalative ligands can straighten naturally curved DNA. The mechanism is not immediately obvious from current models of DNA curvature, which attribute the bending of the chain to a perturbed structure in repeating tracts of A.T base pairs.

Influence of fluctuations on DNA curvature. A comparison of flexible and static wedge models of intrinsically bent DNA.

Matrix-generator and Monte Carlo methods have been employed to study the influence of thermal fluctuations on the overall sizes and shapes of curved pieces of DNA. The DNA model involves the independent angular parameters relating successive base-pair steps: the sequence-dependent equilibrium values and fluctuations of the twist, tilt, and roll angles. The curved sequence under study is the (A5X5)n repeating polymer, the AA and XX steps having different equilibrium roll and twist values. Both planar circles and superhelices are analysed. Detailed comparison is made between the rigorous statistical mechanical representation of the DNA and simplified static models currently used in the literature. That is, a more realistic "flexible wedge" model is contrasted with the existing "static wedge" model of DNA curvature, which is demonstrated to be inadequate. The size of the coils is described by the unperturbed root-mean-square end-to-end distance and the shape by a ratio of the principal moments of the radius of gyration. The moment ratios indicate that when DNA is relatively short (e.g. its length is shorter than half a turn of the static superhelix), the flexible chains are more "short and thick" than the static structure. The end-to-end distances, however, are practically the same in the two models. For longer DNA fragments, the flexible chain is more extended in terms of the end-to-end distance and more globular in terms of the moment ratio. Thus, fluctuations "blur" the curvature of longer DNA fragments compared with static models. Furthermore, the overall average shape of slightly curved DNA subject to natural bending and twisting fluctuations is essentially indistinguishable from that of the corresponding "straight" DNA. Such configurational similarities are apparently responsible for the relative insensitivity of the polyacrylamide gel matrix to small degrees of DNA curvature. These findings raise serious questions regarding the quantitative estimation of wedge angles in DNA from electrophoretic experiments, based on static models. Comparison between planar circles and superhelices shows that when fluctuations are considered, the flexible circles are more spherical than the superhelices. The results imply that when DNA bending is exactly "in phase" with the helical repeat (i.e. when the DNA loop is exactly planar at 0 K), the DNA coil is packed more tightly than when bending and twisting are "out of phase" (and a superhelix is formed at 0 K). This finding is consistent with polyacrylamide gel electrophoresis data testifying to an increase in DNA retardation when twisting is more precisely "tuned".(ABSTRACT TRUNCATED AT 400 WORDS)

The elastic resilience of DNA can induce all-or-none structural transitions in the nucleosome core particle.

DNA on the surface of the histone octamer in the native nucleosome core particle is modeled as a circumferentially wound elastic line on the surface of a cylinder. In a model for the radial transition, the line is allowed to straighten, and thus lose energy, by swinging off the surface, but it is impeded in such an excursion by a radial force field representing the attractive interaction between DNA and histone octamer. In a model for the axial transition, the line may straighten by becoming more parallel to a generator of the cylinder while remaining on the surface. In this mode of straightening, dimer-tetramer or tetramer-tetramer interfaces are disrupted, and the resulting energy gain impedes the transition. Both radial and axial transitions are predicted to occur in all-or-none fashion. We propose that these models are related to the abrupt transitions actually observed in the nucleosome core particle.