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.     

Electric and hydrodynamic properties of polypeptides in solution. II. Conformation of poly(L-glutamic acid) in various organic solvents

The electric birefringence of poly(L -glutamic acid) (PLGA) in methanol, dimethyl sulfoxide, dimethylformamide, N-methylacetamide, trifluoroacetic acid, dioxane–water mixtures (3:1 and 4:1 by volume), and dioxane–formamide mixture (1:1 by volume) has been measured by the use of the rectangular pulse technique at 30 °C. The intrinsic viscosity has also been measured at the same temperature. The magnitude of the specific Kerr constant and the intrinsic viscosity suggests that PLGA is helical and has a large dipole moment in methanol, dimethyl sulfoxide, dimelhylformamide, N-methylacetamide, and dioxane–water mixtures. In this case we have obtained the length distribution curve and the mean length of PLGA molecules from the decay of the electric birefringence, by applying the method recently developed for helical polypeptides. Furthermore, we have proposed and applied a method of obtaining the mean dipole moment and the optical anisotropy factor from the field strength dependence of the electric birefringence for polydisperse systems on the basis of the knowledge on the length distribution. The results show that PLGA may have a different helical conformation in dimethyl sulfoxide. The specific Kerr constant of PLGA in trifluoroacetic acid is very small, which suggests that PLGA is a random coil in this solvent.     

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.     

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.     

Electric birefringence of myosin subfragments.

Electric birefringence measurements have been made on aqueous solutions of myosin subfragments, heavy meromyosin, subfragments 1 and 2 (S-1 and S-2). All of these showed positive electric birefringence. Heavy meromyosin and S-2 showed a large intrinsic Kerr constant. From the analysis of the build up and decay process of the birefringence, the contribution of the slow induced dipole moment was concluded in heavy meromyosin and S-2, although the existence of the permanent dipole moment was not completely excluded. The decay process of the birefringence of heavy meromyosin was found to consist of two components; the fast one of which had a relaxation time of the same order as that of S-1. This is probably due to the presence of a flexible hinge in heavy meromyosin.     

Electric and hydrodynamic properties of polypeptides in solution. IV. A new conformational change of poly(L-glutamic acid) in dimethylsulfoxide–methanol mixtures

The electric birefringence of poly(L -glutamic acid) (PLGA) in dimethylsulfoxide (DMSO)–methanol mixtures has been measured by use of the rectangular pulse technique. The length distribution curve, the mean molecular length, and the mean apparent permanent dipole moment of PLGA in solution have been obtained from the decaycurve and field strength dependence of the steady-state birefringence according to the method developed for analyzing the electric birefringence of a polydisperse system. The length distribution curve exhibits one or two peaks. The length corresponding to a high peak and the mean length of PLGA undergo an abrupt change in the vicinity of 50 to 60 vol % DMSO at 30°C. Moreover, a sharp change of the Moffitt b₀ parameter with the solvent composition is observed. These results provide evidence for the existence of a solvent-induced transition from a helical conformation (presumably α-helix) to another helical conformation with shorter length per amino acid residue. Further, the temperature dependence of the length distribution of PLGA in 50 vol % DMSO suggests the existence of a temperature-induced helix ? helix transition.     

Electric birefringence of myosin subfragments

Electric birefringence measurements have been made on aqueous solutions of myosin subfragments, heavy meromyosin, subfragments 1 and 2 (S-1 and S-2). All of these showed positive electric birefringence. Heavy meromyosin and S-2 showed a large intrinsic Kerr constant. From the analysis of the build up and decay process of the birefringence, the contribution of the slow induced dipole moment was concluded in heavy meromyosin and S-2, although the existence of the permanent dipole moment was not completely excluded. The decay process of the birefringence of heavy meromyosin was found to consist of two components; the fast one of which had a relaxation time of the same order as that of S-1. This is probably due to the presence of a flexible hinge in heavy meromyosin.     

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).     

Differences in the electric birefringence of spectrin dimers and tetramers as shown by the fast reversing electric pulse method

The electric birefringence of purified Spectrin has been examined in medium of low ionic strength ai 20°C and for electric fields smaller than 4 × 10⁴ V m^?1. using the reversing electric pulse method. This technique allows study of the permanent and induced dipole electric moment of macromolecules more easily than in measurements using only rectangular pulses. We show that spectrin heterodimers and heterotetramers have different electro-optical properties. The relaxation time of the tetramer (7 μs) is significantly longer than that of the dimer (4.5 μs). Tetramers and dimers have also different polarizability parameters.     

Transient electric birefringence of colloidal particles immersed in shear flow. Part II. The initial response under the action of a rectangular electric pulse and the behavior at a low alternating electric field

The time-dependent rotational diffusion equation for rigid macromolecules in solution has been approximately solved for two cases in order to extend the electric birefringence technique to streaming-electric birefringence. One is for the initial period through the application of a rectangular electric pulse to the solution immersed in a low shear flow. The purpose of this is expansion of the distribution function into a function series made by the product of the powers of reduced time (= Thetat) and hydrodynamic field alpha (= G Theta , G: velocity gradient, Theta: rotary diffusion constant) and a surface harmonic P(i)(j)cos jphi. The solution for the build-up process at arbitrary electric field strength is found, but is limited to low hydrodynamic fields. The other is for the response when an alternating electric field is applied to the solution in a shear flow. Here, instead of reduced time, the maximum electric field E(0) is chosen as a parameter for the expansion. The expressions for the intensity of the transmitted light through crossed Nicols are derived in two optical systems where the polarizer is set at an angle of 45 degrees and 0 degrees to the direction of the electric field. The results in the former case show that we can determine four parameters, the ratio of velocity gradient to rotary diffusion constant, the axial ratio of a particle, the anisotropy of electric polarizability, and the optical anisotropy factor, from four values observed in two optical systems, namely, two light intensities before applying an electric field and two initial slopes of the build-up after applying an electric field. On the other hand, when a low alternating electric field with extremely high frequency is applied, the build-up of the light intensity in the former case is the same as that of electric birefringence for pure induced dipole orientation. The build-up for the latter optical system is the same as the expression for pure induced dipole orientation of Eq. (38) shown in a previous work.     

Deconvolution can be used in electrooptic studies to correct for non-ideal electric excitation pulses only when the electric dipole moment of the studied molecules is predominantly induced

The electric field pulses used for most measurements of transient electrooptic properties such as birefringence and dichroism, are rectangular and assumed to be ideal, but in practice do all such pulses have non-zero rise and fall times. Claims have been made that this non-ideality may be taken into account by employing standard deconvolution techniques. We find that this approach yields exact results in the zero electric field limit when the electric dipole moment of the studied macromolecules is predominantly induced. However, for finite electric field strengths and/or macromolecules with partly or fully permanent electric dipole moments, we find that the deconvolution method yields erroneous estimates of the electrooptic relaxation times. When the decay time of the electric pulse and the electrooptic decay time are equal, and the system is operated in the Kerr domain, this systematic error for macromolecules with purely permanent electric dipole moment equals 37%. In a research field where the uncertainty of the reported relaxation times normally is assumed to be only a few percent this is an error that may seriously mislead unsuspecting users. We find that this systematic error can readily be avoided by employing standard numerical integration of a set of coupled first-order differential equations instead of the standard deconvolution techniques.     

Effect of aliphatic alcohols on the conformation of poly (l-ornithine hydrobromide) as studied by square-pulse and reversing-pulse electric birefringence

The electric birefringence and circular dichroism spectra of poly(l-ornithine hydrobromide) have been measured in ethanol/water, 2-propanol/water and tertiary butyl alcohol/water mixtures of various compositions. This charged polypeptide underwent a transition from the coil conformation to the helical conformation at high alcohol content in every case tested. Anomalous birefringence signals, indicative of a field-induced helix-to-coil transition. were observed at high electric fields only in the case of ethanol/water mixtures. The reversing-pulse electric birefringence of this polypeptide has been studied in ethanol/water mixtures and in neutral aqueous solution. Upon rapid reversal of the pulse field, no transient could be observed. This confirms that the electric-field orientation of poly(l-ornithine hydrobromide) results predominantly from the contribution of the counterion-induced dipole moment, regardless of its molecular conformations. It is very probable that the backbone permanent dipole moment of the helical conformation is largely suppressed by the counterion-induced dipole moment in the ionized form.     

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.     

Electric birefringence of DNA and chromatin. Influence of divalent cations.

The effects of divalent cations on the DNA and chromatin conformation have been investigated by electric birefringence and birefringence relaxation measurements at low and constant ionic strength (0.001). An important decrease of the intrinsic optical anisotropy of DNA has been found in the presence of Mn2+ and Cu2+, but not with Mg2+. A complex variation of the mean relaxation time with the ratio I/P of ion to DNA-phosphate molar concentration has been evidenced in the presence of Mn2+ and Cu2+, while the mean relaxation time monotonously decreased in the presence of Mg2+. These observations are interpreted in terms of a specific organization of DNA in a compact, rigid structure, in the presence of Mn2+ and Cu2+, and a non-specific coiling in the presence of Mg2+. Drastic conformational changes encountered by chromatin in the presence of Mg2+ and Mn2+ cations have also been evidenced through electric birefringence measurements. They are interpreted by the formation of a superhelical compact arrangement of nucleosome strings which yielded a reversal of the birefringence sign with respect to the negative anisotropy observed in the presence of Na+ ions. The removal of the histone H1 prevented the appearance of this quaternary structure. More extended fragments of the chromatin chain obtained by ECTHAM chromatography of sonicated chromatin could not afford such compact arrangements.     

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.     

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.     

Electric Birefringence in Solutions of High Molecular Weight Ribonucleic Acid

The electric birefringence of low ionic strength solutions of high molecular weight ribonucleic acids from various sources was studied. RNA preparations with a high helical content were found to have negative electric birefringence as a result of the segment anisotropy of the helical portions of the RNA molecule. For completely unfolded molecules of RNA, the electric birefringence is positive and results from the orientation of the macromolecular coil. In intermediate cases, the observed electric birefringence is the sum of negative and positive birefringence. The negative birefringence is caused by the segment orientation of helical sections, and the positive birefringence is caused by the orientation of the macromolecular coil as a whole. Different relaxation times for the positive and negative birefringence permit the pulsed electric birefringence method to analyze these separate phenomena.     

Reversing-pulse electric birefringence of poly (γ-benzyl-L-glutamate). II. Field-strength dependence of steady-state and decay signals of well-fractionated samples

The electric field dependence (up to 21 kV/cm) of the steady-state and decay signals has been examined on the four well-fractionated samples of poly(γ-benzyl-L -glutamate), [Glu(OBzl)]_n, in N,N-dimethylformamide at 535 nm and 20°C. Together with the data previously obtained from the reversing-pulse electric birefringence [Ueda, K., Nomura, M. & Yamaoka, K. (1983) Biopolymers 22 , 2077–2090], the steady-state birefringence and field-free relaxation time were analyzed by a method that takes into account the polydispersity of the chain length. The weight-average chain length, (l_w), permanent dipole moment, (μ_w), electric polarizability anisotropy, (Δα_w), and the length-independent optical anisotropy factor were evaluated. The axial translation per residue was calculated for the [Glu(OBzl)]_n helix, but the uncertainly involved in the weight-average molecular weights, determined from light scattering by different investigators, makes the determination of the exact conformation of [Glu(OBzl)]_n difficult. The contribution of Δα_w to electric field orientation was found to be significant, since Δα_w was approximately proportional to l_w. A linear relationship also exists between μ_w and l_w, when the [Glu(OBzl)]_n helix is shorter than about 1200 Å.     

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 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.