A double coil chromatin sub-unit model

A model is proposed for the structure of DNA in chromatin sub-units. Each sub-unit is proposed to contain two turns of an inner coil, with a pitch of about 40and an external diameter of 70 . Around the inner coil is wound, in opposite handedness, a slightly larger amount of DNA at a diameter of about 150 . The total contour length consistent with the electron micrographs and X-ray scattering is 600–700 , or about 200 base pairs. It is suggested that the inner coil is protein rich and contains all of the histones except H1, which is associated with the outer coil. The double-coil model is consistent with previous biochemical and biophysical studies of chromatin. The existence of 200 and 100 base pair digestion fragments and a 6 to 1 DNA compaction are readily explained.This model is based upon the electron microscopic observation of replicas of frozen chromatin and X-ray and neutron scattering. Structural details of 25are preserved and visualized by the freeze fracture electron microscopy techniques employed.     

A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

A double coil chromatin sub-unit model.

A model is proposed for the structure of DNA in chromatin sub-units. Each sub-unit is proposed to contain two turns of an inner coil, with a pitch of about 40 A and an external diameter of 70 A. Around the inner coil is wound, in opposite handedness, a slightly larger amount of DNA at a diameter of about 150 A. The total contour length consistent with the electron micrographs and X-ray scattering is 600-700 A, or about 200 base pairs. It is suggested that the inner coil is protein rich and contains all of the histones except H1, which is associated with the outer coil. The double-coil model is consistent with previous biochemical and biophysical studies of chromatin. The existence of 200 and 100 base pair digestion fragments and a 6 to 1 DNA compaction are readily explained. This model is based upon the electron microscopic observation of replicas of frozen chromatin and X-ray and neutron scattering. Structural details of 25 A are preserved and visualized by the freeze electron microscopy techniques employed.     

Analysis of hydrodynamic data for denatured globular proteins in terms of the wormlike cylinder model.

Hydrodynamic data, i.e. intrinsic viscosity and sedimentation coefficient, for denatured globular proteins in 6 M guanidinium chloride have been re-analysed in terms of the Yamakawa-Fujii theory of the wormlike cylinder model. Molecular parameters thus obtained ((mean value of R2 0/M) infinity, the Kuhn statistical segment length and the molecular weight per unit contour length) are in better agreement with the values obtained theoretically or by other methods than those evaluated on the basis of the model of non-draining random coil.     

DNA sequencing and helix–coil transition. IV. Very long DNAs

Helix–coil transition in very long DNA (containing hundreds of thousands of nucleotides or more) is considered. Certain statistical information about DNA nucleotide sequence is obtained.     

Thermoadsorptive separation of DNA by size using a polymeric sorbent

The article describes theoretical aspects of isolation and separation of DNA fragments by size using a polymeric sorbent. On this basis we presented a theoretical model of thermal desorption of DNA fragments of different length. Assuming that, under certain pH, interaction of DNA with the polymer sorbent is of an ion-dipole character and moving dipoles interact with the sorbent according to the Boltzmann distribution with the total charge of the DNA fragment in its pore, the expression for the interaction energy as a function of temperature is obtained. Equating the thermal energy to the interaction energy of the ion-dipole character, we have found the critical temperature of DNA separation from the sorbent. Account of the conformation of single-stranded DNA in the coil form leads to the dependence of DNA separation temperature, i.e., desorption, on the length of the DNA chain. The temperature for desorption increases symbatically to the contour length of DNA.     

Flow birefringence of T7 phage DNA: Dependence on salt concentration

We have determined extinction angles and flow birefringence of T7 bacteriophage DNA over a wide range of shear, polymer concentration, and solvent ionic strength. From these data, information on the simple salt dependence of coil permeability to solvent and on short-range intrachain interactions (persistence length) was obtained. At all ionic strengths, our results are consistent with a partially draining coil in the Gaussian subchain dynamical theory of Rouse-Zimm-Tschoegl-Bloomfield. Salt dependence of persistence length is comparable to, although somewhat less than, that obtained previously using similar methods with a fivefold higher-molecular-weight DNA (T2 bacteriophage DNA). Possible reasons for observed discrepancies are analyzed, and the results of this work are compared in detail to other current studies of solvent ionic strength dependence in persistence length and hydrodynamic properties of DNA.     

Helix-coil transition in heterogeneous DNA.

The broadening of a helix–coil transition due to base pair heterogeneity is calculated on the basis of a cumulant perturbation expansion in the quasi-grand ensemble. In this ensemble the fictitious, homogeneous chain, to which the perturbation is referred, automatically decreases its correlation length as the heterogeneity increases. This “renormalization” seems to stabilize the perturbation expansion, in view of the good agreement between the present results and the exact theory of a heterogeneous polypeptide helix–coil transition. For the DNA model in which ring entropy is included, the transitions is found to be extremely narrow for an infinite random chain with conventional parameters. A tentative reconciliation of this result with contradictory calculations of some other workers is offered on the basis of end effects, coarse graining, or approximation to the ring entropy. An application of the new method to DNA with a non-random base pair distribution requires evaluation of the correlation function between molecular states (helix or coil), at different sites of the reference chain. The evaluation is reduced to quadrature, but numerical calculations have been made only for the random chain.     

Conformational transitions in polyelectrolyte adsorption

The mole fraction X of nucleic acid chromophores, adsorbed on cationic and anionic exchange chromatography paper disks, was calculated [O.L. H?rer and A. Grigorescu, Rev. Roum. Med. Virol., 43 (1992) 33] in terms of the standard Debye screening length D (in the 0.01 to 1.2 M ionic strength range), using data from MLSEA (multiple light scattering enhanced absorption) measurements. In contrast to the cases of mononucleotides or double-stranded and relatively rigid DNA structures, highly polymerized and single-stranded RNA shows sigmoidal-shaped X curves, suggesting that polymer adsorption may be regarded as a conformational transition from a three-dimensional statistical coil to a two-dimensional one.     

The dichroic tensor of flexible helices

A statistical theory of the linear dichroism of DNA-like chains is presented for two models which are discrete versions of the wormlike coil. In the final form the linear dichroism of the entire chain is related directly to the dichroic properties of a chain segment (base pair). Though the derivations are somewhat complicated, the result [Eq. (28)] is simple and the required statistical parameters can be easily calculated for either model from measured values of the persistence length. In fact, for molecules as stiff as double-stranded DNA, the results can be reduced with good accuracy to the form showing that the “optical persistence” given on the left is directly proportional to the structural persistence, P_∞/l. As in previous theories the results are restricted to chains in their Gaussian limit.     

Structure of collapsed persistent macromolecule: Toroid vs. spherical globule

We studied theoretically the behavior of a collapsed persistent macromolecule in poor solvent as a model of collapse transition of single double-stranded DNA chain, and constructed the diagram of states in the variables with contour length of a macromolecule and quality of the solvent. We found that the state of toroidal globule exists as an intermediate state between the states of elongated coil state and the spherical globule. Our theoretical result suggests that a single linear macromolecule with a high degree of polymerization can form a toroidal globule. However, the range in which the toroidal structure is stable decreases as the macromolecule length increases. Experimental observation with transmission electron microscopy has been performed to study the globular structure of single DNA chain (bacteriophage T4 DNA, λ-DNA) collapsed by hexammine cobalt (III) at different concentrations. We found that an extremely long chain of T4 DNA (166 kbp), with a contour length of 56 μm, actually forms a toroidal globule, and that isotropic spherical globule appears at higher hexammine cobalt concentration. © 1997 John Wiley & Sons, Inc.     

Electrophoretic charge density and persistence length of DNA as measured by fluorescence microscopy

Individual ethidium-stained DNA molecules, embedded in an agarose gel made with electrophoresis buffer (0.05 molar salt), are observed using a fluorescence microscope. In the first experiment, open circular 66 kilobase pair (kbp) plasmids, immobilized by agarose fibers threaded through their centers, display entropic "rubber" elasticity. The charged molecules extend in an electric field of several volts per centimeter and contract to a compact random coil when the field is removed. The extension of the plasmids as a function of field strength is consistent with the freely jointed chain model when the effective electrophoretic charge density is set at 15 e-per persistence length. In a second experiment, stained linear 48.5 kbp DNA molecules are observed as random coils immobilized in agarose. A measure of their size, here named the "maximal-X-extent," is taken for 100 molecules and found to average 1.47 mu. A Monte Carlo computer simulation of random coils (freely jointed chain model) gives the same maximal-X-extent value when the persistence length is set at 0.08 mu.     

Variance of writhe for wormlike DNA rings with excluded volume

We have calculated the variance of the equilibrium distribution of a circular wormlike polymer chain over the writhing number, less than (Wr)2 greater than, with allowance for the excluded volume effects. Within this model the less than (Wr)2 greater than value is a function of the number of Kuhn statistical segments, n, and the chain diameter, d measured in Kuhn statistical lengths, b. Simulated DNA chains varied from 200 to 10,000 base pairs and the d value varied from 0.02 to 0.2. Theory predicts a considerable ionic strength dependence of the DNA superhelix energy as a consequence of the change in the DNA diameter. A comparison with the available experimental data has yielded an estimate of the DNA torsional rigidity, the Kuhn statistical length, and the effective diameter of the double helix under conditions of the complete screening of the DNA electrostatic potential.     

The denaturation transition of DNA in mixed solvents

The helix-to-coil denaturation transition in DNA has been investigated in mixed solvents at high concentration using ultraviolet light absorption spectroscopy and small-angle neutron scattering. Two solvents have been used: water and ethylene glycol. The "melting" transition temperature was found to be 94 degrees C for 4% mass fraction DNA/d-water and 38 degrees C for 4% mass fraction DNA/d-ethylene glycol. The DNA melting transition temperature was found to vary linearly with the solvent fraction in the mixed solvents case. Deuterated solvents (d-water and d-ethylene glycol) were used to enhance the small-angle neutron scattering signal and 0.1M NaCl (or 0.0058 g/g mass fraction) salt concentration was added to screen charge interactions in all cases. DNA structural information was obtained by small-angle neutron scattering, including a correlation length characteristic of the inter-distance between the hydrogen-containing (desoxyribose sugar-amine base) groups. This correlation length was found to increase from 8.5 to 12.3 A across the melting transition. Ethylene glycol and water mixed solvents were found to mix randomly in the solvation region in the helix phase, but nonideal solvent mixing was found in the melted coil phase. In the coil phase, solvent mixtures are more effective solvating agents than either of the individual solvents. Once melted, DNA coils behave like swollen water-soluble synthetic polymer chains.     

Bacterial Nucleoid: Interplay of DNA Demixing and Supercoiling

This work addresses the question of the interplay of DNA demixing and supercoiling in bacterial cells. Demixing of DNA from other globular macromolecules results from the overall repulsion between all components of the system and leads to the formation of the nucleoid, which is the region of the cell that contains the genomic DNA in a rather compact form. Supercoiling describes the coiling of the axis of the DNA double helix to accommodate the torsional stress injected in the molecule by topoisomerases. Supercoiling is able to induce some compaction of the bacterial DNA, although to a lesser extent than demixing. In this work, we investigate the interplay of these two mechanisms with the goal of determining whether the total compaction ratio of the DNA is the mere sum or some more complex function of the compaction ratios due to each mechanism. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. This work reveals that there actually exist different regimes, depending on the crowder volume ratio and the DNA superhelical density. In particular, a regime in which the effects of DNA demixing and supercoiling on the compaction of the DNA coil simply add up is shown to exist up to moderate values of the superhelical density. In contrast, the mean radius of the DNA coil no longer decreases above this threshold and may even increase again for sufficiently large crowder concentrations. Finally, the model predicts that the DNA coil may depart from the spherical geometry very close to the jamming threshold as a trade-off between the need to minimize both the bending energy of the stiff plectonemes and the volume of the DNA coil to accommodate demixing.     

X-ray scattering from randomly oriented superhelices. Circular superhelical DNA.

The scattering functions of randomly oriented filaments of finite length exhibiting two orders of helicity have been calculated. It is shown to a good approximation that each order scatters as if present alone as a first order helix of the same contour length and pitch angle. These results show that the measured scattering pattern from dissolved superhelical DNA molecules is consistent with the scattering pattern calculated for a coiled coil geometry.     

Solution and conformational properties of wheat beta-D-glucans studied by light scattering and viscometry

The solution properties of wheat beta-glucan were investigated by light scattering and viscometric methods. The hydrodynamic radius (R(h)), weight average molecular weight (M(w)), radius of gyration (R(g)), and the second virial coefficient (A(2)) of wheat beta-glucan were determined by both dynamic and static light scattering methods, whereas the critical concentrations (c) of the solution were derived from [eta] via viscometric method. The structure sensitive parameters, rho (1.52-1.62), the conformation parameter nu (0.62), and the Mark-Houwink-Sakurada exponents alpha (0.78) confirmed the random coil conformation of wheat beta-glucan in 0.5 M NaOH solution. The characteristic ratio (4.97) was obtained by the random flight model, and the statistical segment length (8.83 nm) was derived from the wormlike cylinder model. It was found that the wormlike cylinder model could explain the chain stiffness better than the random flight model, which suggested an extended random coil conformation of wheat beta-glucan in 0.5 M NaOH solution. The study also revealed that the structure feature of wheat beta-glucan; that is, the higher trisaccharide-to-tetrasaccharide ratio contributed to the stiffer chain conformation compared with other cereal beta-glucans.