Electric birefringence of restriction enzyme fragments of DNA: optical factor and electric polarizability as a function of molecular weight

The electric birefringence of restriction enzyme fragments of DNA has been investigated as a function of DNA concentration, buffer concentration, and molecular weight, covering a molecular weight range from 80 to 4364 base pairs (bp) (6 × 10⁴–3 × 10⁶ daltons). The specific birefringence of the DNA fragments is independent of DNA concentration below 20 μg DNA/ml, but decreases with increasing buffer concentration, or conductivity, of the solvent. At sufficiently low field strengths, the Kerr law is obeyed for all fragments. The electric field at which the Kerr law ends is inversely proportional to molecular weight. In the Kerr law region the rise of the birefringence is accurately symmetrical with the decay for fragments ≤ 389 bp, indicating an induced dipole orientation mechanism. The optical factor calculated from a 1/E extrapolation of the high field birefringence data is ?0.028, independent of molecular weight; if a 1/E² extrapolation is used, the optical factor is ?0.023. The induced polarizability, calculated from the Kerr constant and the optical factor, is proportional to the square of the length of the DNA fragments, and inversely proportional to temperature. Saturation curves for DNA fragments ≤ 161 bp can be described by theoretical saturation curves for induced dipole orientation. The saturation curves of larger fragments are broadened, because of a polarization term which is approximately linear in E, possibly related to the saturation of the induced dipole in high electric fields. This “saturated induced dipole” is found to be 6400 D, independent of molecular weight. The melting temperature of a 216-bp sample is decreased 6°C in an electric field of 8 kV/cm, because the lower charge density of the coil form of DNA makes it more stable in an electric field than the helix form.     

Linear contour length dependence of electrical polarizability of nucleosomal DNA fragments: implications for the flexibility of DNA

The transient electric birefringence of monodisperse oligonucleosomal DNA ranging from 145 to 990 base pairs has been studied. The orientation of fragments can be described in terms of an induced dipole moment with a small contribution of a permanent dipole. The electrical polarizability delta alpha was found to increase linearly with the DNA contour length. This unexpected dependence might result from a bent structure of DNA already considerable for very short segments. The observed delta alpha values agree with a segmental orientation of rigid subunits of length 13-18 nm as estimated in the elastic model of DNA with a kink angle of about 41 degrees.     

Transient electric birefringence of two small DNA restriction fragments of the same molecular weight.

The transient electric birefringence of two small DNA restriction fragments of the same molecular weight, one of which migrates anomalously slowly on polyacrylamide gels, has been investigated. Both fragments exhibit negative birefringence. The decay of the birefringence of the anomalously slowly migrating fragment is 8-9% faster than that of the normally migrating fragment. The faster birefringence decay of the anomalous fragment 12A persists under a variety of buffer conditions, suggesting that it is due primarily to static bending and/or curvature of fragment 12A. In reversing electric fields the absolute amplitude of the birefringence of fragments 12A and 12B decreased about 26% before returning to the steady state value. The minimum in the birefringence occurred faster than expected from the birefringence decay times and decreased with increasing electric field strength, suggesting that the minimum is due to a slow polarization of the ion atmosphere. For both fragments, the rise of the birefringence in the Kerr region is about 10% slower than the field-free decay. The buildup of the negative birefringence is preceded either by an interval when no birefringence is observed or by a small positively birefringent transient, suggesting that a small transverse ionic polarizability is also present. Both DNA fragments exhibit Kerr law behavior over most of the range of electric field strengths investigated. Analysis of the shapes of the saturation curves suggests that differences may exist in the polarization mechanisms of the two fragments.     

Electric dichroism of DNA. Influence of the ionic environment on the electric polarizability

In order to test the diffuse ion atmosphere polarization model recently developed by us, the effects of ionic strength, titrating with Mg2+ and Co(NH3)3+6, and coion charge on the electric polarizability of short fragments of DNA are investigated. The results are consistent with the predictions of the theory and show that the diffuse ion atmosphere polarization contributes significantly to the overall orientation of DNA. At low ionic strengths, we attempt to separate the total dipole moment into two components: one that agrees well with the Debye-Hückel ion atmosphere calculations, while the other, presumably due to condensed counterion polarization, appears to be substantially independent of the ionic strength. At higher salt concentrations, however, a simple separation into dipole components is not possible, perhaps due to a significant coupling of ion flows between the diffuse atmosphere and the condensed counterion layer.     

Electro-optical studies on synthetic polyelectrolytes: IV. Electric polarizability and conformation of poly-N-methyl-2-vinylpyridinium bromide in aqueous solution

Measurements of the relaxation time on aqueous solutions of the title polyelectrolyte as a function of the concentration and of the molecular weight show that its conformation at very high dilution can be better accounted for by a weakly bending rod or worndike chain model, with persistence length ranging from 200 to 400 Å. The analysis of the field strength dependence of the electric birefringence yields electric polarizability values which increase sharply with the dilution and are not significantly dependent upon the molecular weight. This has been tentatively interpreted on the basis of the theories derived by Oosawa and by Mendel and Van der Touw. The partially flexible model proposed by the latter authors allow to identify the electric polarizability calculated from electro-optical data to the specific dielectric increment measured in the high frequency range; both parameters appear to be molecular weight independent. The electric polarizability obtained from the Kerr effect would be originated in the induced dipoles caused by the delocalization of the bound counterions along rigid subunits whose length seems however to differ from the persistence length.     

The optical birefringence of DNA solutions induced by oscillatory electric and hydrodynamic fields

The optical birefringence induced in DNA solutions by both oscillating hydrodynamic fields (flow birefringence) and oscillating electric fields (Kerr effect) is measured over a wide frequency range. The observed frequency response of the birefrigence is compared with theories for rigid ellipsoidal particles and for Gaussian chains. DNA at 6 × 10⁵ molecular weight is found to exhibit rigid particle hydrodynamic behavior, while DNA at 5 × 10⁶ molecular weight behaves like a flexible chain. Characterization of the hydrodynamic relaxation spectra for the DNA's by oscillatory flow birefringence allows precise comparison between theory and the experimental Kerr effect response. The dielectric model for DNA contains both permanent and dispersionless induced dipole moments. The dielectric behavior of DNA has the character of a permanent dipole but with anomalous low-frequency dispersion in the Kerr effect. The existing theories do not adequately describe this dispersion. A fluctuation dipole mechanism with relaxation times comparable to those associated with the hydrodynamic motion could possibly demonstrate the observed polar behavior.     

Dielectric behavior of polyelectrolytes. VI. Dynamic response of cylindrical biopolymers to electric fields

The time dependence of the orientation of a cylindrical biopolymer and the configuration of its counterion complement in the presence of an external electric field is found by solving a model forced diffusion equation. The solution is a high temperature expansion in the external field strength and is used to predict the nature of the dielectric relaxation and the dynamic Kerr effect for such systems. Specific application is made to the dynamic Kerr effect of a DNA oligomer for which experimental data appear in the literature. The analysis yields a value for the surface diffusion coefficient of a sodium ion on DNA at 20 degrees C of 3.8 x 10(-10) m2 s-1.     

Flexibility of nucleosomal DNA

In this study transient electric birefringence (TEB) has been used to investigate the molecular flexibility of short fragments of DNA. Nucleosomal DNA always exhibits negative birefringence and Kerr behavior was observed up to high field strengths (6 KV/cm). The value of the Kerr constant is 3.5 10^?2 e.s.u.. Birefringence decays were single exponentials and a field dependence of the molecular orientational relaxation time τ was found: it is explained by an inherent flexibility of the DNA molecule. A 20 % decrease in the calculated length was observed with fields applied as low as 2 KV/cm. The results obtained at very low fields establish TEB as a method well suited to calculate accurate values for the length of small fragments of DNA: the τ value of 4.3 μsec corresponds to a DNA length of 660 Å.     

Trivalent counterion condensation on DNA measured by pulse gel electrophoresis

Pulse gel electrophoresis was used to measure the reduction of mobilities of λ-DNA-Hind III fragments ranging from 23.130 to 2.027 kilobase pairs in Tris borate buffer solutions mixed with either hexammine cobalt(III), or spermidine³⁺ trivalent counterions that competed with Tris⁺ and Na⁺ for binding onto polyion DNA. The normalized titration curves of mobility were well fit by the two-variable counterion condensation theory. The agreement between measured charge fraction neutralized and counterion condensation prediction was good over a relatively wide range of trivalent cation concentrations at several solution conditions (pH, ionic strength). The effect of ionic strength, trivalent cation concentration, counterion structure, and DNA length on the binding were discussed based on the experimental measurements and the counterion condensation theory. © 1996 John Wiley & Sons, Inc.     

Dielectric properties of aqueous solutions of sonicated DNA above 40 MHz

The dielectric properties of sonicated calf-thymus DNA sodium salt in aqueous solutions have been studied in the frequency range from 40 MHz to 2 GHz by time domain spectroscopy (TDS). A dielectric dispersion not previously reported was found, which has a characteristic frequency of about 150 MHz. All of the dielectric parameters are insensitive to the size of DNA fragments and to helix-to-coil transitions. The study of this dispersion as a function of DNA concentration and temperature allows us to conclude that it may be due to counterion fluctuation on short sections, probably in a direction transverse to the macromolecular axis.     

The iso-competition point for counterion competition binding to DNA: calculated multivalent versus monovalent cation binding equivalence.

In this paper we introduce an important parameter called the iso-competition point (ICP), to characterize the competition binding to DNA in a two-cation-species system. By imposing the condition of charge neutralization fraction equivalence theta1 = ZthetaZ upon the two simultaneous equations in Manning's counterion condensation theory, the ICPs can be calculated. Each ICP, which refers to a particular multivalent concentration where the charge fraction on DNA neutralized from monovalent cations equals that from the multivalent cations, corresponds to a specific ionic strength condition. At fixed ionic strength, the total DNA charge neutralization fractions thetaICP are equal, no matter whether the higher valence cation is divalent, trivalent, or tetravalent. The ionic strength effect on ICP can be expressed by a semiquantitative equation as ICPZa/ICPZb = (Ia/Ib)Z, where Ia, Ib refers to the instance of ionic strengths and Z indicates the valence. The ICP can be used to interpret and characterize the ionic strength, valence, and DNA length effects on the counterion competition binding in a two-species system. Data from our previous investigations involving binding of Mg2+, Ca2+, and Co(NH3)63+ to lambda-DNA-HindIII fragments ranging from 2.0 to 23.1 kbp was used to investigate the applicability of ICP to describe counterion binding. It will be shown that the ICP parameter presents a prospective picture of the counterion competition binding to polyelectrolyte DNA under a specific ion environment condition.     

Charge structure and counterion distribution in hexagonal DNA liquid crystal

A hexagonal liquid crystal of DNA fragments (double-stranded, 150 basepairs) with tetramethylammonium (TMA) counterions was investigated with small angle neutron scattering (SANS). We obtained the structure factors pertaining to the DNA and counterion density correlations with contrast matching in the water. Molecular dynamics (MD) computer simulation of a hexagonal assembly of nine DNA molecules showed that the inter-DNA distance fluctuates with a correlation time around 2 ns and a standard deviation of 8.5% of the interaxial spacing. The MD simulation also showed a minimal effect of the fluctuations in inter-DNA distance on the radial counterion density profile and significant penetration of the grooves by TMA. The radial density profile of the counterions was also obtained from a Monte Carlo (MC) computer simulation of a hexagonal array of charged rods with fixed interaxial spacing. Strong ordering of the counterions between the DNA molecules and the absence of charge fluctuations at longer wavelengths was shown by the SANS number and charge structure factors. The DNA-counterion and counterion structure factors are interpreted with the correlation functions derived from the Poisson-Boltzmann equation, MD, and MC simulation. Best agreement is observed between the experimental structure factors and the prediction based on the Poisson-Boltzmann equation and/or MC simulation. The SANS results show that TMA is too large to penetrate the grooves to a significant extent, in contrast to what is shown by MD simulation.     

Kerr effect of charged dipolar macromolecules without condensed counterions in conducting solution.

The theoretical treatment of the Kerr constant of rigid, dipolar, conducting ellipsoidal macromolecules of O'Konski and Krause (1970. J. Phys. Chem. 74:3243) has been extended to very low ionic strength solutions for charged macromolecules. The O'Konski and Krause theoretical treatment postulated a surface conductivity directly on the surface of each macromolecule. For charged macromolecules, this surface conductivity was generally assumed to be caused by movement of condensed counterions on the macromolecules. In the present work, it has been assumed that, at very low ionic strength, the average counterion is at the Debye characteristic distance from the surface of each charged macromolecule and contributes to surface conductivity at that distance, with no additional surface conductivity on the true surface of the macromolecule. Essentially, these considerations change the calculated interaction energy of the macromolecule with an externally applied electric field via a change in both the internal field components and in the reaction field of the macromolecular dipole. The new interaction energy is used to calculate the orientation distribution function of the macromolecules in solution and this distribution function can, in principle, be used to calculate the steady state electric linear or circular dichroism, electric light scattering, anisotropy of conductivity, etc., using the appropriate theoretical treatment for each of these quantities.     

Electric properties and structure of DNA-restriction fragments from measurements of the electric dichroism

The electric dichroism of 17 homogeneous DNA fragments, ranging in size from 43 to 4362 base-pairs, has been analyzed in high electric fields. The orientation of the small fragments can be described in terms of an induced dipole moment, whereas the large fragments are oriented according to a constant dipole mechanism. In the intermediate size range, DNA orients according to an induced dipole mechanism at low field strengths and according to a constant dipole mechanism at high field strengths. From these observations we propose an orientation mechanism with a saturating induced dipole. The induced dipole observed at low field strengths is saturated at a field strength Eo within a transition range Em to give a constant dipole moment at high field strengths. These parameters together with the polarizability and the limit reduced dichroism are evaluated by a least-squares analysis of the experimental data. Eo and Em are found to decrease with increasing chain length from Eo approximately 40 kV/cm (Em approximately 14 kV/cm) at 65 base-pairs to 10 kV/cm (6 kV/cm) at 194 base-pairs. The polarizability is found to increase with the square of the chain length, whereas the saturated dipole increases with chain length N at low N and goes to a limit value at high N. The temperature dependence of the orientation parameters is found to be very small. The values obtained for the limit dichroism are between -1.0 and -1.3 for chain lengths between 60 and 1000 base-pairs, whereas values around -1.4 are observed at chain lengths greater than 1000 base-pairs. These data indicate that electric fields extend the contour of DNA strands at high chain lengths from a weakly bent to a more linear form. The variations of the limit dichroism observed for short fragments suggest sequence-dependent differences in the secondary structure of the helix. The experimental results are compared with numerical calculations based on simple polyelectrolyte models. For short fragments the magnitude of several electrochemical parameters can be adequately explained by a polarization of the ion cloud around the DNA molecules. However, these polyelectrolyte models do not adequately describe the observed chain length dependence of the orientation phenomena.     

Hydrodynamic studies of a DNA-protein complex. Elongation of single stranded nucleic acids upon complexation with the gene 32 protein of phage T4 deduced from electric field-induced birefringence experiments

Short DNA and RNA fragments complexed with the helix destabilizing protein of bacteriophage T4, GP32, have been studied in solution by electric birefringence and circular dichroism. The birefringence of the complexes is positive and the magnitude indicates that the DNA and RNA fragments become linear and rigid upon protein binding. The field free decay is biphasic. On the basis of a rigid rod approximation the slow relaxation time leads to a base-base distance along the helix axis in the complex from 4.3 to 5.6 A, an elongation of at least 50% compared to single-stranded DNA.     

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.     

Thermodynamics of cation-induced DNA condensation.

An estimation of the various free energy contributions to DNA collapse into toroidal particles is made, considering DNA bending and segment mobility, electrostatic repulsions between DNA chains, and attractive forces resulting from correlated counterion fluctuations. It is shown that the process of DNA condensation becomes spontaneous in the presence of divalent cations in methanol, and in the presence of tri- or tetravalent cations in water media. This is a consequence of the large decrease in the electrostatic repulsion between charged DNA segments, allowing the attractive force resulting from correlated fluctuations of bound counterions to become dominant. Our calculations indicate that short DNA fragments would condense into multimolecular particles in order to maximize the attractive force due to counterion fluctuations.     

Electric properties of macromolecules. IX. Dipole moment, polarizability, and optical anisotropy factor of collagen in solution from electric birefringence

The electric birefringence of collagen solutions has been measured over a wide range of field strength with the pulse technique. The soluble collagen was from rat tail tendon. The solvent used was dilute acetic acid. Very pronounced saturation of the electric birefringence was observed, permitting calculation of the optical anisotropy factor. The Kerr constant was determined by extrapolation to zero field strength. From the dependence on field strength of the birefringence, the permanent dipole moment and the anisotropy of polarizability were separately determined. The contribution of the former to the Kerr constant was found to be twice as large as that of the latter. The same conclusion was obtained from the initial slope of the rise curves of the birefringence at low fields. The permanent dipole moment was 1.5 × 10⁴ Debye, and the anisotropy of polarizability was about 3 × 10^?15 cm.³. The magnitude of the latter indicates that the ion atmosphere polarization is important. Effects of added salt and thermal denaturation on the electric birefringence were explored.     

Effect of ions on the dielectric relaxation of DNA

The dielectric relaxation of DNA solutions has been investigated with and without extraneous ions covering a wide frequency range. The effect of monovalent ions such as Na, K, and Li as well as divalent ions such as Mg, Ca, and Hg have been included in the study. These ions are found to have a profound effect on the dielectric increment and the relaxation time without affecting the molecular dimension drastically. This dielectric effect is interpreted as indicating the importance of counterion fluctuation on the low frequency dielectric constant of DNA in solution. The effect of an organic ion, tetra-methylammoniun bromide, has also been studied. This ion has no noticeable effect. A simple theory is derived on the basis of a microscopic model to account for the effect of external ions on the dielectric behavior of solutions of DNA.     

Visualizing ion relaxation in the transport of short DNA fragments

Ion relaxation plays an important role in a wide range of phenomena involving the transport of charged biomolecules. Ion relaxation is responsible for reducing sedimentation and diffusion constants, reducing electrophoretic mobilities, increasing intrinsic viscosities, and, for biomolecules that lack a permanent electric dipole moment, provides a mechanism for orienting them in an external electric field. Recently, a numerical boundary element method was developed to solve the coupled Navier-Stokes, Poisson, and ion transport equations for a polyion modeled as a rigid body of arbitrary size, shape, and charge distribution. This method has subsequently been used to compute the electrophoretic mobilities and intrinsic viscosities of a number of model proteins and DNA fragments. The primary purpose of the present work is to examine the effect of ion relaxation on the ion density and fluid velocity fields around short DNA fragments (20 and 40 bp). Contour density as well as vector field diagrams of the various scalar and vector fields are presented and discussed at monovalent salt concentrations of 0.03 and 0.11 M. In addition, the net charge current fluxes in the vicinity of the DNA fragments at low and high salt concentrations are briefly examined and discussed.