Transient electric birefringence study of the length and stiffness of short DNA restriction fragments

Transient electric birefringence measurements of the rotational diffusion constant of five short restriction fragments of the plasmid pBR322 show that the hydrodynamic length is independent of sodium ion concentration in the range of 0.2 to 2.5 mM. The fragments are too stiff to be modeled as wormlike molecules. The rotational relaxation times of the fragments, which range from 64 to 124 base pairs, have been used to calculate the rise per base pair using six different theoretical expressions for the length dependence of the rotational diffusion coefficient of straight cylinder. The best estimate for the rise per base pair of Na-DNA in solution is 3.3 ± 0.1 Å.     

DNA orientation in shear flow

The linear dichroism (LD) has been measured for DNA molecules 239–164,000 base pairs long oriented in shear flow over a large range of velocity gradients (30–3,000 s ^?1) and ionic strengths (2–250 mM). At very low gradients, the degree of DNA orientation increases quadratically with the applied shear as predicted by the Zimm theory [J. Zimm, (1956) Chemical Physics, Vol. 24, p. 269]. At higher gradients, the orientation of fragments ≥ 7 kilobase pairs (kbp) increases linearly with increasing shear, whereas the orientation of fragments ≥ 15 kbp shows a more complicated dependence. In general, the orientation decreases with increasing ionic strength throughout the studied ionic strength interval, owing to a decrease in the persistence length of the DNA. The effect is most dramatic at ionic strengths below 10 mM, and is more pronounced for longer DNA fragments. For fragments ≥ 15 kbp and velocity gradients ≥ 100 s^?1, the orientation can be adequately described by the empirical relation: LD^r= –(k₁-G)/(k₂ + G), where k₁is a linear function of the square root of the ionic strength and k₂ depends on the DNA contour length. Since the DNA persistence length can be represented as a linear function of the reciprocal square root of the ionic strength [D. Porschke, (1991) Biophysical Chemistry, Vol. 40, p. 169], extrapolation of the empirical relation provides information about the stiffness of the DNA fibers. © 1993 John Wiley & Sons, Inc.     

DNA persistence length revisited

DNA restriction fragments ranging from 79 to 789 base pairs in length have been characterized by transient electric birefringence (TEB) measurements at various temperatures between 4 and 43 degrees C. The DNA fragments do not contain runs of four or more adenine residues in a row and migrate with normal electrophoretic mobilities in polyacrylamide gels, indicating that they are not intrinsically curved or bent. The low ionic strength buffers used for the measurements contained 1 mM Tris Cl, pH 8.0, EDTA, and variable concentrations of Na(+) or Mg(2+) ions. The rotational relaxation times were obtained by fitting the TEB field-free decay signals with a nonlinear least-squared fitting program; the decay of the birefringence was monoexponential for fragments < or = 241 base pair (bp) in length and multiexponential for larger fragments. The terminal relaxation times, characteristic of the end-over-end rotation of the DNA molecules, were then used to determine the persistence length (p) and hydrodynamic radius (r) of DNA as a function of temperature and ionic strength, using several different hydrodynamic models. The specific values obtained for p and r are model dependent. The wormlike chain model of P. J. Hagerman and B. H. Zimm (Biopolymers 1981, Vol. 20, pp. 1481-1502) combined with the revised Broersma equation (J. Newman et al., Journal of Mol Biol 1997, Vol. 116, pp. 593-606) appears to be the most suitable for describing the flexibility of DNA in low ionic strength solutions. The values of p and r obtained from the global least squares fitting of this equation are independent of DNA length, and the deviations of the individual values from the average are reasonably small. The consensus r value calculated for DNA in various low ionic strength solutions containing 1 mM Tris buffer is 14.7 +/- 0.4 A at 20 degrees C. The consensus p values decrease from 814 approximately 564 A in solutions containing 1 mM Tris buffer plus 0.2-1 mM NaCl and decrease still further to 440 A in solutions containing 0.2 mM Mg(2+) ions. The persistence length exhibits a shallow maximum at 20 degrees C and decreases slowly upon either increasing or decreasing the temperature, regardless of the model used to fit the data. By contrast, the consensus values of the hydrodynamic radius are independent of temperature. The calculated persistence lengths and hydrodynamic radii are compared with other data in the literature.     

Orientational interactions in low-concentration DNA solutions

The rotational relaxation tiem τ₃ of DNA molecules (M_w ? 5 × 10⁶) in solution has been determined by the transient electric birefringence method. The analysis of the birefringence decay makes it possible to study only the higher-molecular-weight fraction, the molecules being considered as rigid elongated particles in a short time scale. A marked concentration dependence of the relaxation time has been observed for DNA in low ionic strengths. Above a critical concentration c*, τ₃ increases with the DNA concentration, c. The value of c* increases with the ionic strength. For 10^?3 ionic strength (with NaCl), c* is about 10 μg/mL; then we observe the same strong concentration dependence of rotational relaxation times as recently reported for rodlike M-13 viruses [Maguire, J. F., McTague, J. P. & Rondelez, F. (1980) Phys. Rev. Lett. 45 , 1891–1894]. These results may be discussed in terms of the Doi-Edwards theory for rotational relaxation time of rigid macromolecules [Doi, M. (1975) J. Phys. 36 , 607–611; Doi, M. & Edwards, S. F. (1978) J. Chem. Soc. Faraday Trans. 74 , 918–932] and the critical concentration above which the interactions between the molecules begin to appear allows determining the corresponding molecular length. We observe a very good agreement between the DNA lengths obtained from the c* values and by using the infinite dilution value of τ₃ and Broersma's equation. Therefore, only highly diluted solutions can be used if intrinsic molecular properties based on the rotational diffusion of high-molecular-weight elongated molecules are studied.     

Monte Carlo approach to the analysis of the rotational diffusion of wormlike chains

A Monte Carlo analysis is presented which establishes a relationship between the rotational diffusion coefficients and the flexibility (persistence length, P) of short, wormlike chains. The results of this analysis are presented in terms of experimentally observable quantities; namely, the rotational relaxation times for the field-free decay of optical anisotropy. The pertinent theoretical quantity is R, defined as the ratio of the longest rotational relaxation time of a wormlike chain to the transverse rotational relaxation time of a rigid cylinder having the same axial length (L) and segmental volume. R, so defined, is essentially independent of the axial ratio of the cylinder for any value of L/P within the range of validity of the present analysis (axial ratio > 20; 0.1 < L/P < 5). It is pointed out that P can be determined with reasonable accuracy even in the absence of a precise knowledge of the local hydrodynamic radius of the chain.     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

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.     

Modeling the free solution electrophoretic mobility of short DNA fragments

Boundary element methods are used to model the free solution electrophoretic mobility of short DNA fragments. The Stern surfaces of the DNA fragments are modeled as plated cylinders that reproduce translational and rotational diffusion constants. The solvent-accessible and ion-accessible surfaces are taken to be coincident with the Stern surface. The mobilities are computed by solving simultaneously the coupled Navier–Stokes, Poisson, and ion-transport equations. The equilibrium electrostatics are treated at the level of the full Poisson–Boltzmann equation and ion relaxation is included. For polyions as highly charged as short DNA fragments, ion relaxation is substantial. At .11 M KCl, the simulated mobilities of a 20 base pair DNA fragment are in excellent agreement with experiment. At .04 M Tris acetate, pH = 8.0, the simulated mobilities are about 10–15% higher than experimental values and this discrepancy is attributed to the relatively large size of the Tris counterion. The length dependence of the mobility at .11 M KCl is also investigated. Earlier mobility studies on lysozyme are reexamined in view of the present findings. In addition to electrophoretic mobilities, the effective polyion charge measured in steady state electrophoresis and its relationship to the preferential interaction parameter γgG is briefly considered. © 1998 John Wiley & Sons, Inc. Biopoly 46: 359–373, 1998     

Quasielastic light scattering by biopolymers. V. Interparticle interactions between polynucleosomes

Quasielastic light scattering and electrophoretic light scattering experiments were performed on chicken erythrocyte polynucleosome solutions at various temperatures and ionic strengths. The apparent diffusion coefficient, D_app, was found to depend on the scattering vector K. In general, D_app can be described as a damped oscillatory function of K in the ionic strength range of 10 to 60 mM and over the temperature range of 10 to 40°C. Electrophoretic light scattering studies on total digest chromatin samples indicate the apparent charge on the polynucleosomes increases as the ionic strength is lowered from 10 to 1 mM. These data are interpreted in terms of fluctuations in the surface charge distribution of the polyion and subsequent inducement of an asymmetric distribution of small ions about the polyion. These fluctuation components lead to the formation of “clusters” of polyions.     

Magnetic birefringence study of the electrostatic and intrinsic persistence length of DNA

Magnetic birefringence experiments were performed on solutions of DNA of intermediate molecular weight at several concentrations (c_p) over a wide range of ionic strengths (of NaCl and MgCl₂). The specific Cotton-Mouton constant (CM/c_p) is found to be independent of c_p when contributions from c_p to the ionic strength (μ_eff) are taken into account according to the concept of counterion condensation. For μ_eff ? 10^?2M, CM/c_p is also independent of the ionic strength; the plateau value results in an acceptable value of the intrinsic persistence length, when a revised theoretical expression for the magnetic birefringence of wormlike chains is used, combined with new experimental data for the monomeric optical and magnetic anisotropy. For μ_eff < 10^?2M, CM/c_p strongly, or wealky, increases with decreasing μ_eff, depending on the valency of the counterion used (Na⁺ or Mg²⁺, respectively). This increase agrees quantitatively with the variation of the electrostatic persistence length as predicted by Odijk [(1977) J. Polym. Sci. Polym. Phys. Ed. 15 , 477–483], Odijk and Houwaart [(1978) J. Polym. Sci. Polym. Phys. Ed. 16 , 627–639], and by Skolnick and Fixman [(1977) Macromolecules 10 , 944–948]. A comparison with other experimental data seems to reveal the importance of excluded-volume effects, which are particularly pronounced in the low-salt regime.     

Semiflexibility of collagens in solution

The persistence length of lugworm cuticle collagen in 0.1M acetic acid was evaluated as 1600 ～ 1800 Å by Yamakawa-Fujii's model for a wormlike chain from the sedimentation constant and the intrinsic viscosity. The persistence length was further examined for a series of sample “collagen sonicates” produced by varying the duration of sonic irradiation. To estimate the salt effect on the persistence length, measurements were made over a range of NaCl concentrations from 0 to 0.1M. The results showed that the cuticle collagen and collagen sonicates had identical values of persistence length and that the neutral salt effect for the cuticle collagen was far smaller than that for DNA.     

Bending and flexibility of kinetoplast DNA

We have evaluated the extent of bending at an anomalous locus in DNA restriction fragments from the kinetoplast body of Leishmania tarentolae using transient electric dichroism to measure the rate of rotational diffusion of DNA fragments in solution. We compare the rate of rotational diffusion of two fragments identical in sequence except for circular permutation, which places the bend near the center in one case and near one end of the molecule in the other. Hydrodynamic theory was used to conclude that the observed 20% difference in rotational relaxation times is a consequence of an overall average bending angle of 84 +/- 6 degrees between the end segments of the fragment that contains the bending locus near its center. If it is assumed that bending results from structural dislocations at the junctions between oligo(dA).oligo(dT) tracts and adjacent segments of B DNA, a bend angle of 9 +/- 0.5 degrees at each junction is required to explain the observations. The extent of bending is little affected by ionic conditions and is weakly dependent on temperature. Comparison of one of the anomalous fragments with an electrophoretically normal control fragment leads to the conclusion that they differ measurably in apparent stiffness, consistent with a significantly increased persistence length or contour length in the kinetoplast fragments.     

Helix-coil transition in nucleoprotein. Effect of ionic strength on thermal denaturation of polylysine-DNA complexes

Thermal denaturation of direct-mixed and reconstituted polylysine–DNA complexes in 2.5 × 10^?4 M EDTA, pH 8.0 and various concentrations of NaCl has been studied. For both complexes, increasing ionic strength of the solution raises T_m, the melting temperature of free base pairs. The linear dependence of T_m on log Na⁺ indicates that the concept of electrostatic shielding on phosphate lattice of an infinitely long pure DNA by Na⁺ can be applied to short free DNA segments in a nucleoprotein. For a direct-mixed polylysine–DNA complex, the melting temperature of bound base pairs T_m′ remains constant at various ionic strengths. On the other hand, the T_m′ in a reconstituted polylysine–DNA complex is shifted to lower temperature at higher ionic strength. This phenomenon occurs for reconstituted complex with long polylysine of one thousand residues or short polylysine of one hundred residues. It is shown that such a decrease of T_m′ is not due to a reduction of coupling melting between free and bound regions in a complex when the ionic strength is raised. It is also not due to intermolecular or intramolecular change from a reconstituted to a direct-mixed complex. It is suggested that this phenomenon is due to structural change on polylysine-bound regions by ionic strength. It is suggested further that Na⁺ may replace water molecules and bind polylysine-bound regions in a reconstituted complex. Such a dehydration effect destabilizes these regions and lowers T_m′. This explanation is supported by circular dichroism (CD) results.     

Calculations on the effect of methylation on the electrostatic stability of the B- and Z-conformers of DNA

The three-dimensional Poisson–Boltzmann equation for the distribution of counterion charge density around double-helical DNA has been solved for solutions of .01M, .10M, and .20M monovalent salt. The polymers, poly[d(CpGp)] and poly[d(m⁵CpGp)], were studied in the B- and the Z-conformations. The effect of methylation on the relative stabilities of these conformers in solutions of different ionic strengths is known to favor the Z-form. Accumulation of charge density around the B- and the Z-conformers is compared in detail. The relative electrostatic stabilities of the B- and Z-conformers in .01M, .10M, and .20M solutions are compared and discussed in terms of the ion–DNA interactions and the self-energy of the structured ionic environment. The ion–DNA interaction energies, termed “phosphate screening,” monotonically decrease with ionic strength and are consistent with a B-to-Z conformation change induced in either polymer by increased electrolyte concentration. However, these calculated energies alone do not account for the fact that the ionic strength at the midpoint of the transition of the methylated polymer is substantially lower than that of its unmethylated analogues. The phosphate screening effect is counterbalanced by changes in the self-energy required for the creation of the structured counterion environment. This self-energy of the electrolyte environment monotonically increases with ionic strength. Methylation-induced shifts in the overall conformational equilibria depend on the relative changes of these competing effects. Increasing salt concentration is calcualted to favor the Z-conformer. The effect of methylation, lowering the ionic strength of the transition midpoint, is proposed to originate in minor structural changes in the Z-form of the polymer, making the groove more accessible to counterions in the G(3′ – 5′)C region. This allows a redistribution of counterion density and a lowering of the self-energy of the ionic environment, conferring added stability to the Z-conformation, as indicated by calculations of relative entropies. The experimentally observed temperature dependence of the B-to-Z transition, however, cannot be explained without assuming the release of bound water. Maps of the calculated three-dimensional structure at the counterion distribution near the surface of these molecules in both the B- and the Z-forms are also presented.     

Rotational diffusion of short DNA fragments in polyacrylamide gels: an electric birefringence study

Using electric birefringence we have examined the rotational diffusion of five short DNA fragments (55 to 256 base pairs) both in polyacrylamide gels as a function of gel concentration and in solution. The length dependence of the measured rotational relaxation times in the gels is in good agreement with the prediction from the Odijk theory for the dynamics of slightly flexible rods in a network. The rotational relaxation times were found to depend on the gel concentration, contrary to the prediction from the Odijk theory. Possible reasons for this observation are discussed. The birefringence decay curves for DNA fragments in the gel were single exponential only at small electric field strength.     

Dynamic light-scattering study of synthetic myosin filaments

Synthetic myosin filaments of rabbit were prepared. Electron microscopy showed that the number-average length (L_n = 470 nm) and sharpness in length distribution (L_w/L_n = 1.03₆) were independent of ionic strengths of 134, 74, and 44 mM, whereas the number ratio of M-filaments (about 15 nm in diameter at the bare zone) to m-filaments (about 10 nm) strongly depended on ionic strength (IS); the major filaments were M-filaments at IS = 134 mM, m-filaments at IS = 74 mM, and almost exclusively m-filaments at IS = 44 mM. Dynamic light scattering showed that the change in diameter with the change in ionic strength by 2-h dialysis was reversible. Combination of dynamic light scattering and sedimentation studies suggested a dynamic equilibrium between M- and m-filaments. Dynamic light-scattering spectra at IS = 134 and 74 mM could be analyzed by a theory for rigid rods, whereas those at IS = 44 mM only by introducing semiflexibility of filaments; m-filaments are more flexible at IS = 44 than at 74 mM.