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.     

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.     

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.     

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.     

Electrooptical study of the electric polarizability of rodlike fragments of DNA

The anisotropy of electrical polarizability of rodlike fragments of DNA has been studied by a number of electro-optical methods: Kerr effect (combined with flow birefringence), light scattering, diehroism, and fluorescence in an electric field. The most sensitive technique (Kerr effect) has been used to study the variation of the polarizability with the nature and concentration of counteroins. DNA fragments constitute a truly rigid polyelectrolyte of known structure. The value obtained can then be quantitatively compared to the predictions of those of the theories of the longitudinal polarizability of rigid polyelectrolytes which are based on true molecular parameters. The comparison emphasizes the role of the counterion–counterion repulsion. Oosawa's theory seems to represent the best approach but fails to explain the differences observed between monovalent and divalent ions.     

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.     

Electroporation and electrophoretic DNA transfer into cells. The effect of DNA interaction with electropores.

It has been shown recently that electrically induced DNA transfer into cells is a fast vectorial process with the same direction as DNA electrophoresis in an external electric field (Klenchin, V. A., S. I. Sukharev, S. M. Serov, L. V. Chernomordik, and Y. A. Chizmadzhev. 1991. Biophys. J. 60:804-811). Here we describe the effect of DNA interaction with membrane electropores and provide additional evidences for the key role of DNA electrophoresis in cell electrotransfection. The assay of electrically induced uptake of fluorescent dextrans (FDs) by cells shows that the presence of DNA in the medium during electroporation leads to a sharp increase in membrane permeability to FDs of M(r) < 20,000. The permeability increases with DNA concentration and the effect is seen even if FD is added to the cell suspension a few minutes after pulse application. The longer the DNA fragment, the greater the increase in permeability. The use of a two-pulse technique allows us to separate two effects provided by a pulsed electric field: membrane electroporation and DNA electrophoresis. The first pulse (6 kV/cm, 10 microseconds) creates pores efficiently, whereas transfection efficiency (TE) is low. The second pulse of much lower amplitude, but substantially longer (0.2 kV/cm, 10 ms), does not cause poration and transfection by itself but enhances TE by about one order of magnitude. In two-pulse experiments, TE rises monotonously with the increase of the second pulse duration. By varying the delay duration between the two pulses, we estimate the lifetime of electropores (which are DNA-permeable in conditions of low electric field) as tens of seconds.(ABSTRACT TRUNCATED AT 250 WORDS)     

Study of the orientation of DNA molecules in an electrical field by anisotropy of electrical conductivity of their aqueous solution

Electro-conductive anisotropy of DNA solution caused by the molecular orientation in the external electric field was investigated. The dependence of a relative change of the conductivity of aqueous-salt DNA solution on the electric field in the amplitude range 0-700 V/cm and in the frequency range 100 Hz-10 kHz was studied. It was pointed out that the field thermal effect is an overcoming factor when the orientation of DNA molecules is investigated by field-free relaxation.     

Brownian dynamics simulation of rigid particles of arbitrary shape in external fields

We have developed a Brownian dynamics simulation algorithm to generate Brownian trajectories of an isolated, rigid particle of arbitrary shape in the presence of electric fields or any other external agents. Starting from the generalized diffusion tensor, which can be calculated with the existing HYDRO software, the new program BROWNRIG (including a case-specific subprogram for the external agent) carries out a simulation that is analyzed later to extract the observable dynamic properties. We provide a variety of examples of utilization of this method, which serve as tests of its performance, and also illustrate its applicability. Examples include free diffusion, transport in an electric field, and diffusion in a restricting environment.     

Kerr Constant of Vesicle-Like Droplets

The Kerr effect on vesicle-likedroplets (vesicles, cells or emulsion droplets) is described. Wegive a derivation of the Kerr constant for a dielectric fluiddroplet immersed in another fluid, assuming that the droplet in aweak electric field becomes a prolate ellipsoid. The Kerr constantis evaluated also for a droplet covered by a membrane of nonzerothickness. Comparing the theory with the experiment on dropletmicroemulsions from the literature, the bending rigidity constantof the surface layer is estimated.     

Electric shock-mediated transfection of cells. Characterization and optimization of electrical parameters.

The effect of various parameters on the electric shock-mediated permeabilization and transfection of CHO cells has been investigated. Up to 70% of the cells can be maintained transiently permeable to erythrosin B for periods of at least 1 h at 20 degrees C. Electrical conditions optimal for transient permeabilization were also optimal for efficient DNA transfection by pSV2neo. However, the DNA must be present during exposure to the electric field for efficient transformation. The same requirement existed for voltage-induced DNA toxicity. The results suggest that DNA moves into the cells by electrophoresis, not by simple diffusion. Based on these observations a simple, rapid procedure for optimizing the conditions for electric shock-mediated DNA transfer into cells has been developed.     

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.     

Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

Radial migration of DNA molecules in cylindrical flow. I. Theory of the free-draining model

Inward radial migration of large DNA molecules undergoing concentric-cylinder shear flow has been previously observed in this laboratory during measurements of viscoelastic retardation times. In this paper a theoretical treatment of this effect is presented in the framework of the bead-spring model of polymer molecules. Equations of motion of the diffusion type are solved for the free-draining polymer in a solvent undergoing Couette flow. The results show an inward radial motion, essentially due to the curvilinear solvent flow field.     

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.     

Application of porous teflon tubing method to automatic fed-batch culture of microorganisms. I. Mass transfer through porous teflon tubing

For the purpose of a rational design for an automatic feedback control system incorporating a porous Teflon tubing sensor in semibatch culture, steady-state mass-transfer characteristics of tubing sensors have been investigated theoretically and experimentally, and also dynamic responses have been studied experimentally. A distributed mathematical model for steady-state diffusion has been solved numerically and its solution has been shown as useful for the sensor design. The overall mass-transfer resistance of radial diffusion has been shown to be the sum of external liquid-film mass-transfer resistance and membrane diffusion resistance. The steady-state experiments using ethanol dissolved in water revealed that its transfer into the tubing was controlled by the molecular diffusion within the tubing-wall membrane. Oxygen transfer from external water into the tubing was shown experimentally to be controlled by the liquid-film resistance outside the tubing. In general, the radial mass transfer of a substance having a small Henry's constant is controlled by the liquid-film resistance. The response of the tubing sensor-detector-recorder system for the stepwise addition of ethanol into the external water could not be represented by a simple combined system of the first-order delay with lag time. The responses depend on the characteristics of the tubing as well as flow rate of the carrier gas, etc., but they were quite excellent in all cases (e.g., 90% in 20 s).     

Structural aspects and orientation mechanism of mitochondrial F1 adenosinetriphosphatase. Evidence for a negative electric birefringence due to a permanent moment perpendicular to the long axes of the particle

The electric birefringence technique was used to investigate the steady-state birefringence, the orientational relaxation time, and the orientation mechanism of pig heart mitochondrial F1 adenosine-5'-triphosphatase (F1-ATPase). The electrooptical properties of this enzyme in solution were studied as functions of pH, protein concentration, and applied electric field. The F1-ATPase exhibits a surprising negative electric birefringence with a specific Kerr constant of -1.5 X 10(-3) esu cgs. The field-independent relaxation time was found to be 0.65 +/- 0.05 microseconds, corresponding to a rotational diffusion constant of 2.55 X 10(5) s-1. The overall size and shape of F1-ATPase have been calculated from both translational and rotational diffusion constants. The enzyme may be assumed to be an oblate ellipsoid of revolution with dimensions of about 170 X 170 X 70 A. The orientation mechanism of F1-ATPase was analyzed by fitting experimental birefringence rising curves with theoretical rising functions. The ratio of the permanent to induced dipole moment is found to be very high; therefore, the birefringence of F1-ATPase is due to a strong permanent dipole moment in a direction perpendicular to the long axes of the particle. These particular electric properties can be explained by the oligomeric structure of the protein and seem likely to play a role in its mechanism of functioning.     

Salt effects on internal motions of superhelical and linear pUC8 DNA. Dynamic light scattering studies

The plasmid pUC8 (2717 bp) has been studied in its native superhelical and Eco RI-linearized forms by dynamic light scattering at NaCl concentrations from 1.1 mM to 1 M. The data were analyzed using the biexponential model for the dynamic structure factor described by us in a previous paper (J. Langowski, U. Giesen and C. Lehmann, Biophys. Chem. 25 (1986) 191). As before, we could identify two decay components corresponding to the center-of-mass diffusion and to internal motions of the DNA, where the fast component could be identified as a rotational diffusion contribution in the case for superhelical, but not for linear DNA. We found that the conformation of superhelical pUC8 is not affected by changing the ionic strength, while the amplitude of the internal relaxation increases approx. 2-fold when [NaCl] is raised from 1.1 mM to 1 M. The linearized DNA shows an increase of the diffusion coefficient with ionic strength which is, however, not quite as pronounced as that found by others (Z. Kam, N. Borochov and H. Eisenberg, Biopolymers 20 (1981) 2671), and, together with the unchanged conformation of the superhelical DNA, suggests a persistence length which is not strongly dependent on ionic strength. In contrast to the increasing amplitude of internal relaxation for the superhelical DNA, this amplitude remains constant or decreases slightly for linear DNA on going from 1.1 mM to 1 M salt. Our findings are further discussed with respect to possible models of the interwound form of superhelical DNA.     

Transient electric birefringence of agarose gels. I. Unidirectional electric fields

The orientation of agarose gels in pulsed electric fields has been studied by the technique of transient electric birefringence. The unidirectional electric fields ranged from 2 to 20 V/cm in amplitude and 1 to 100 s in duration, values within the range typically used for pulsed field gel electrophoresis (PFGE). Agarose gels varying in concentration from 0.3 to 2.0% agarose were studied. The sign of the birefringence varied randomly from one gel to another, as described previously [J. Stellwagen & N. C. Stellwagen (1989), Nucleic Acids Research, Vol. 17, 1537–1548]. The sign and amplitude of the birefringence also varied randomly at different locations within each gel, indicating that agarose gels contain multiple subdomains that orient independently in the electric field. Three or four relaxation times of alternating sign were observed during the decay of the birefringence. The various relaxation times, which range from 1 to ～ 120 s, can be attributed to hierarchies of aggregates that orient in different directions in the applied electric field. The orienting domains range up to ～ 22 μm in size, depending on the pulsing conditions. The absolute amplitude of the birefringence of the agarose gels increased approximately as the square of the electric field strength. The measured Ker constants are ～ 5 orders of magnitude larger than those observed when short, high-voltage pulses are applied to agarose gels. The increase in the Kerr constants in the low-voltage regime parallels the increase in the relaxation times in low-voltage electric fields. Birefringence saturation saturation curves in both the low- and high-voltage regimes can be fitted by theoretical curves for permanent dipole orientation. The apparent permanent dipole moment increase approximately as the 1.6 power of fiber length, consistent with the presence of overlapping agarose helices in the large fiber bundles orienting in low-voltage electric fields, the optical factor is approximately independent of fiber length. Therefore, the marked increase in the Kerr constants observed in the low-voltage regime is due to the large increase in the electrical orientation factor, which is due in turn to the increased length of the fiber bundles and domains orienting in low-voltage electric fields. Since the size of the fiber bundles and domains approximates the size of the DNA molecules being separated by PFGE, the orientation of the agarose matrix in the applied electric field may facilitate the migration of large DNA molecules during PFGE. © 1994 John Wiley & Sons, Inc.     

High speed atomic force microscopy of biomolecules by image tracking.

An image-tracking procedure for atomic force microscopy is proposed and tested, which allows repeated imaging of the same area without suffering from lateral drift. The drift correction procedure is based on on-line cross-correlation of succeeding images. Using the image-tracking procedure allows zooming in on a small scan area over a long period and thus increases the frame rate inversely proportional to the scan area. Application of the procedure is demonstrated for diffusion of 5.4-kb DNA plasmids. With a scan area of 500 * 500 nm(2), a single plasmid can be imaged for more than 30 min at 4 s per frame, with a drift less than 10 nm. The high temporal resolution allows detailed analysis of the diffusion of DNA molecules. A diffusion coefficient of 30 nm(2)/s is found for most DNA molecules, though many molecules are temporally pinned to the mica surface, restricting diffusion.