Electric and hydrodynamic properties of polypeptides in solution. 3. Aggregation of poly(L-glutamic acid) in aqueous methanol solvents studied by electric birefringence

The rise and decay of electric birefringence for poly(L -glutamic acid) (PLGA) in aqueous solvents containing 20 and 10 vol % methanol have been found to be unusual. The decay curves have been analyzed on the assumption that there exist two kinds of particles, namely, one (component I) with a shorter relaxation time exhibiting positive birefringence and the other (component II) with a longer relaxation time exhibiting negative birefringence at low fields. From the field strength dependence of the steadystate birefringence the permanent dipole moment, the anisotropy of electric polarizability, and the saturation value of birefringence have been determined for each component. Furthermore, from the relaxation time the length of component I and the diameter of component II have been computed on the models of cylindrical rod and oblate ellipsoid, respectively. The dipole moment, the anisotropy of electric polarizability, and the relaxation time of component II are much larger than those of component I. Both the anisotropy of electric polarizability and the optical anisotropy factor are positive in sign for component I and negative for component II. It is concluded that component I is the helical PLGA molecule itself and component II is the side-by-side (antiparallel) aggregate composed of many helical PLGA molecules. The optical anisotropy factor of each component has been discussed on the basis of Peterlin-Stuart theory.     

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.     

Decay processes of electric birefringence in chemically reacting system

Analytical and numerical calculations of the decay processes of the electric birefringence in an isomerizing system have been performed. Two modes of isomerization are considered: in the first mode, the direction of the axis (of the optical anisotropy) of a molecule is conserved during isomerization; in the second mode, it is not. In the first mode, if G_Ais not equal to G_B, and that, if k_A^op_A² is not equal to k_B^op_B² (when the orienting electric field is weak), in which G_A, G_B and p_A, p_b are the optical anisotropy and permanent electric dipole moments, of the molecule in two states A and B of the isomerization, and k_A^o and k_B^o are the rate constants for the transitions A → B and B → A, respectively, and if diffusion rates are very much slower than the chemical rates, the relaxation due to the chemical reaction can be detected in the decay of the electric birefringence. In the second mode, if diffusion rates are somewhat slower than the chemical rates, the relaxation due to the chemical reaction appears in the decay, even though there are no differences in optical anisotropy and electric moments in the two states. When the rotary diffusion coefficients are different in the two states, the decay process becomes almost one-component, bringing the chemical rate about ten times higher to diffusion coefficients in both modes.     

Electrical and hydrodynamical properties of polypeptides in solution. I. Poly(L-glutamic acid) in methanol-water mixtures

The electric birefringence of poly(L -glutamic acid) (PLGA) in methanol–water mixtures has been measured by the use of the rectangular pulse technique at 25°C. The permanent dipole moment, the anisotropy of electrical polarizability, and the optical anisotropy factor of PLGA in solution were obtained from the dependence of the steady-state birefringence on the electric field strength. Further, the mean length of PLGA in solution was calculated by a parameter method developed for analyzing the decay curve of electric birefringence. The permanent dipole moment per unit length obtained from these studies was 2.9₆, 2.4₈, 2.3₀, 2.6₆ D/Å in pure methanol, 10, 30, and 50 vol-% water, respectively. The increase of water content caused the decrease of the mean length and broadened the length distribution of PLGA. These results are discussed in relation to the viscosity and the electrical conductivity of PLGA solutions.     

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.     

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.     

Transient electric birefringence studies of T2 bacteriophage and T2 ghost

The transient electric birefringence behavior of bacteriophage T2 and the T2 ghost or protein coal was studied. The field free relaxation measurements show both the intact virus and its ghost to have two rotary diffusion coefficients. These coefficients have values of 555 ± 54 and 111 ± 22 sec.^?1 for the intact virus and 688 ± 89 and 161 ± 29 sec.^?l for the ghost. The equivalent ellipsoids for the fast and slow relaxation coefficients were obtained by use of Perrin's equation and were related to the bacteriophage structure in terms of a possible extension of the tail fibers or an enlargement of the head structure. The saturation of the specific birefringence of the phage and the ghost when compared with the specific birefringence of the free nucleic acid gave an average optical orientation of 10 to 18% of the nucleic acid parallel to the main axis of the phage. The analysis of the birefringence versus applied field strength in the Kerr region gave the following values for the anisotropy of the polarixability. α_e,33 – α_e,11 and intrinsic dipole, μ, of both phage and ghost : for T2 phage α_e,33 – α_e,11 = 5.0 × 10^?14 cm.³ and μ = 64,400 Debyes; for T2 ghost α_e,33 – α_e,11 = 7.9 × 10^?14cm.³ and μ = 57,200 Debyes. The high intrinsic dipole for phage and ghost is interpreted as to be associated with the mechanisms of the virus for attachment, to the host cell wall.     

Electric birefringence of bacterial flagellar protein filaments: evidence for field-induced interactions.

The time course for the build-up and decay of birefringence induced by a rectangular voltage pulse was measured on solutions of flagellar filaments from Salmonella equi-abortus (strain SJ25). These filaments are tubular polymers of protein (degree of polymerization ≈ 10³) constituted by non-covalent linkage of flagellin monomers of molecular weight 4 × 10⁴. The effect on electro-optical properties of solutions of filaments due to variations in temperature, concentration and mean length of protein filaments, and the duration and intensity of the applied electric field is described. Analysis of the field intensity dependence of the birefringence and comparison of the build-up and decay processes indicate that orientation in the field is due primarily to the existence of a permanent dipole moment in the filaments. At 18 °C the following values were obtained for a solution of filaments with mean length and standard deviation of 0.39 and 0.30 μm: specific Kerr constant (K_sp) = 6.14 × 10⁻³ electrostatic units; optical anisotropy factor (g₁ — g₂) = 5.66 × 10⁻³; dipole moment (μ) = 1.01 × 10⁵ Debye units; and mean relaxation time ($\text{}\text{̄}$gt) = 9.20 ms. At temperatures below 20 °C there is a marked increase in the optical anisotropy factor of the filaments which may be due to a change in their flexibility. The large values of K_sp obtained indicate the highly responsive nature of these filaments to an electric field. The birefringence decay curves were decomposed by computer into a specified number of exponential terms from which both the mean length and the size distribution of these polydisperse filaments were calculated. The results obtained were in substantial agreement with the values of these parameters observed by electron microscopy. A cumulative field effect dependent on field intensity and filament concentration was observed. Repeated pulsing of electric field, above threshold values of field intensity and filament concentration, produced decreases in the birefringence near 60% of its initial value. The effect was reversible with a time constant greater than two minutes. No appreciable change in the relaxation time for decay of birefringence was observed on multiple pulsing of these solutions. These results are interpreted consistently to arise from the sidewise aggregation of filaments induced by electrical impulses of sufficient intensity and duration. These properties appear relevant to bacterial motility: variations in electric potential along the membrane of the bacterium might serve first to orient these organelles and then to induce their coalescence to “bundles” of filaments. The latter structures are commonly observed in vivo. In this way the activity of flagella might be co-ordinated.     

Optical Properties of DNA in Aqueous Solution

In the study of DNA electric birefringence, it is usual to use theories that consider that molecules in solution are small in relation to the light wavelength. In this work, we study the DNA electric birefringence using a broken-rod macroion (BRM) model composed of two cylindrical arms which does not restrict the size of the molecules. To achieve this, we include the inhomogeneity effect of the light electric field through the molecule and the interaction between its different parts. To analyze the interaction between a molecule and the incident beam of light, we apply the discrete dipole approximation (DDA), according to which each molecule is described as a finite array of electronic coupled oscillators. The electric birefringence is calculated from the oscillator polarizability. This is obtained from experimental data of electric birefringence saturation and from the increment of the solution refraction index in relation to that of the solvent. Furthermore, the oscillator polarizability is also estimated from DNA absorption spectrum using the Kronig–Kramers relations. This allows us to analyze the contributions of the different absorption bands of DNA to the electric birefringence. We analyze the influence of the inhomogeneity of the light electric field and of the intramolecular interactions in the characterization of DNA optical properties using electric birefringence measurements.     

Dichroism of TMV in pulsed electric fields

The linear dichroism induced in a solution of electrically anisotropic molecules by a pulsed electric field has been studied. Equations have been obtained which express the dichroism as a function of dipole moment, excess polarizability, field strength, and the angle α between the dipole moment and the transition moment for the absorption band. These expressions have been related to the experimentally observed difference signal in such a way that when the dichroism is measured as a function of field strength the permanent moment, excess polarizability and angle a can be determined. Experiments have been carried out on tobacco mosaic virus (TMV), which is similar in its properties to the theoretical model. The polarizability anisotropy and rotary diffusion constant for the monomer and dimer of TMV have been obtained from these experiments. In addition to the molecular parameters mentioned above, the saturated electric dichroism of the virus was measured as a function of wave length and the presence of an n–π* transition in the tryptophan spectrum was indicated. Further experiments measuring dichroism as a function of pH demonstrated the general denaturation of the virus at high pH (10–11) but also the existence of a stable fraction which is not fragmented even at the high pH involved.     

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.     

Association states of tubulin in the presence and absence of microtubule-associated proteins. Analysis by electric birefringence

Electric birefringence has been used to examine the states of association of tubulin in phosphocellulose-purified tubulin or depolymerized microtubule protein solutions at low temperature. In a high electric field (1000-4000 V/cm), tubulin could be orientated (owing to the existence of a permanent and/or induced dipole) and exhibited a positive birefringence (delta n), related to its intrinsic optical anisotropy. The analysis of the relaxation process (depending on hydrodynamic properties of molecules), by measurement of the time decay of delta n, revealed the existence of a multicomponent or polydisperse system, whatever the tubulin solution. Two relaxation times, representative of the smallest and the largest orientated species, were obtained by computer-fitting analysis. The mean values of relaxation time for phosphocellulose-purified tubulin were 0.8 and 8 microseconds. In microtubule protein solutions, large-sized macromolecular species with relaxation time up to 450 microseconds were detected. The largest species (relaxation times ranging from 50 to 450 microseconds) could be eliminated by centrifugation at 3000000 X g for 1 h. Addition of microtubule-associated protein to either pure tubulin or high-speed centrifuged microtubule protein led to a rapid formation of large species analogous to those present in microtubule protein. Molecular dimensions of the relaxing structures were estimated using simple hydrodynamic models and values of rotational diffusion constants calculated from the relaxation times, and compared to those of the structures described in the literature. In conclusion, we have found that (a) phosphocellulose-purified tubulin is not only composed of elementary species (dimers) but also contains tubulin-associated forms of limited size (up to 7-10 dimers), (b) depolymerized microtubule protein solutions contain ring oligomers and structures very much larger, the formation of which is dependent on the presence of microtubule-associated protein.     

Transient electric birefringence of T-even bacteriophages. IV. T2L0 and T6 with extended tail fibers

Transient electric birefringence measurements of the bacteriophages T2L0 and T6 were performed under such conditions that the tail fibers are extended. The data obtained are compared to previously reported data for T4B. For all T-even phages the degree of extension of the tail fibers is a function of pH, ionic strength, and temperature. For T4B, much higher ionic strengths are needed than for T2L0 and T6 to accomplish complete tail-fiber extension. The rotational diffusion coefficients of the phages with fully extended fibers are equal to 120 ± 3 sec^?1, 132 ± 5 sec^?1, 157 ± 4 sec^?1 for T2L0, T4B, and T6, respectively. The respective optical anistropies are ? (2.66 ± 0.05) × 10^?4, and ? (3.07 ± 0.15) × 10^?4. The differences in the rotational diffusion coefficient and optical anisotropy arise because the conformation of the fully extended tail fibers is different for the three phages. The tail fibers of T2L0 project further into the solution (away from the head) than do those of T4B and T6. The apparent permanent dipole moments of T2L0 and T6 decrease with increasing ionic strength. This decrease is caused by the screening of the surface charges on the phage body by the counter-ions in the solution. The biological relevance of this decrease is illustrated by the fact that the adsorption rate of T6 phages to E. coli B bacteria shows a similar dependence of ionic strength. Evidence is pressented that the tail fibers may move more or less independently of the phage body when an electric field is applied to the suspension.     

Transient electric birefringence of T-even bacteriophages. I. T4B in the absence of tryptophan and fiberless T4 particles

Measurements of the electric birefringence of suspensions of T4B in the absence of tryptophan and of fiberless T4 particles show that both kinds of particles are hydrodynamically equivalent. Their rotational diffusion coefficients corrected to 25°C and water viscosity (D_25,w) are 280 ± 9 sec^?1 and 295 ± 10 sec^?1, respectively. These corrected rotational diffusion coefficients are almost independent of buffer concentration and temperature. The sedimentation coefficient (s_20,w) of T4 B is equal to 1023 ± 12 S, a value which is likewise independent of buffer concentration. By analysis of the field strength dependence of the steady-state birefringence and by reversing pulse experiments it could be shown that the orientation in an electric field is largely due to a permanent dipole moment. This dipole moment is somewhat dependent on buffer concentration and amounts to about 24,000 debye for T4B and 95,000 debye for fiberless T4. An approximate calculation shows that the difference in dipole moment may be ascribed to positive charges on the fiber tip (at least ten per fiber), to negative charges along the fiber or (and) positive charges on the fiberless particle at those places where the fibers are attached in normal particles.     

Electro-optic scattering studies on deoxyribonucleic acid

Measurements have been made of the intensity of light scattered from aqueous solutions of calf thymus DNA with and without the application of electric fields. For fields approaching 150 V/cm and frequencies below 2.5 KHz, changes (ΔI) of up to 10% in the residual scattered intensity were observed. In agreement with previous dielectric and electric birefringence measurements, a low frequency dispersion of ΔI was observed, from which a rotary diffusion constant (D) of 1200 s^?1 was determined. Interpreting the electric field data in terms of the classical dipolar orientation theory led to values of 2.4 × 10^?25 cm (7.4 × 10^?14 esu) and 4.3 × 10^?25 cm (13 × 10^?14 esu) for the permanent dipole moment and the anisotropy of the electric polarisabilities respectively. Furthermore the permanent dipole moment was along the major molecular axis and the particles orientated in the field as rigid entities. The zero field data indicated a molecular shape which was not rodlike but corresponded to the Kratky-Porod “stiffness” parameter of x = 24 for the wormlike coil model. Although curved, the molecules appeared to orientate in low-intensity electric fields as rigid, but not rodlike molecules. The implications of this on recent discrepancies in D determined by two or more dynamic relaxation methods is briefly discussed.     

Electric birefringence of poly-L-lysine hydrobromide in methanol-water mixtures and helix-coil transition induced by high electric fields

The electric birefringence of poly-L -lysine hydrobromide in methanol–water mixtures has been measured at 25 °C over a wide range of field strengths by use of the rectangular pulse technique. An abrupt change in the specific Kerr constant was observed between 87 and 90 vol % methanol, corresponding to the solvent-induced helix–coil transition. The specific Kerr constant increased rapidly with dilution in the random coil form, and more slowly in the helical conformation. The field strength dependence of the bire fringence at various concentrations, for both the helical and coil conformations, can be described by a common orientation function, which resembles the theoretical one for the case of permanent dipole moment orientation. This is interpreted in terms of the saturation of ion–atmosphere polarization. The optical anisotropy for the helical conformation was much larger than that for the coil form. Anomalous birefringence signals were observed above a critical field strength (about 5 kV/cm) in 90 vol % methanol. The birefringence passed through a maximum and began to decrease slowly before the pulse terminated, reaching a steady-state value. This steady-state value was closer to that of the coil in the coil in the limit of very high fields. The results indicate that a transition from the charged helix to the charged coil is induced by high electric fields in the transition region. This effect can be explained on the basis of the polarization mechanism proposed by Neumann and Katchalasky.     

Electric birefringence studies on polyglutamic acid.

The electric birefringence for the aqueous solution of poly-L -glutamic acid (PGA) in the helical form was studied. PGA samples were fractionated by gel column chromatography. PGA showed a positive electric birefringence. The permanent dipole moment of the PGA molecule was suggested to be largely suppressed. The measurements of the intrinsic Kerr constants for various molecular lengths showed that the electric anisotropy (polarizability) of PGA is proportional to the 1.5 power of the length. The electric birefrigence measurement was also carried out in the helix–coil transition region. The Kerr constant of PGA was largely reduced on going from the helical form to the coiled form.     

A study of rhodopsin-detergent micelles by transient electric birefringence.

The hydrodynamic method of transient electric birefringence has been used to study bovine rhodopsin solubilized in two detergents, 0.02% Ammonyx LO and 0.045% digitonin. All measurements are interpreted as the sum of two exponentials by which the relaxation times yield the rotary diffusion coefficients for ellipsoids of revolution. The semi-major and minor axes for prolate ellipsoid models have been calculated and their axial ratio, 6.8, in both detergents, is in line with recent reports on the structure of rhodopsin. Studies on bleached rhodopsin showed a large increase in axial ratio in 0.02% Ammonyx LO.     

Reversing-pulse electric birefringence of poly(γ-benzyl-L-glutamate). III. The temperature dependence of the transient and steady-state behavior in cyclohexanone

The reversing-pulse electric birefringence (RPEB) technique was applied to the study of the temperature effect on the electrooptical and hydrodynamic properties of a fractionated [Glu(OBzl)]_n sample, which is molecularly dissolved in cyclohexanone. The aim was to develop a standard analytical method for thermal denaturation and temperature-induced conformational transitions. The field-on reverse and steady-state signal, and the field-off decay signal, were measured at 535 nm and at a constant low field strength (ca. 3 kV/cm) over a wide temperature range (5–90°C). The steady-state birefringence and the relaxation time in the decay process were also measured at two constant temperatures (5 and 70°C) over a wide field strength range (E ≤ 20 kV/cm). By the combination of these two different sets of RPEB measurements, the unwanted effect of the high pulse field on polymer conformation at elevated temperatures could be minimized. Together with the density and viscosity of cyclohexanone measured between 5 and 95°C, the following quantities could be evaluated: the weight-average permanent dipole moment and polarizability anisotropy, the reduced optical anisotropy factor (Δg/n), the weight-average length, and the degree of polydispersity. All these quantities, except for Δg/n, were found to be almost independent of temperature (5–90°C) and concentration (1.54–4.27 mM).