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.     

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.     

Sizing of vesicles by electric birefringence

A study of the transient, electrically induced birefringence of aqueous suspensions of phospholipid vesicles (liposomes) has indicated a rapid and sensitive method of measuring the size and electrical polarizability anisotropy of these entities.     

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.     

Rotational dynamics of curved DNA fragments studied by fluorescence polarization anisotropy

The rotational dynamics of short DNA fragments with or without intrinsic curvature were studied using time-resolved phase fluorimetry of intercalated ethidium with detection of the anisotropy. Parameters determined were the spinning diffusion coefficient of the DNA fragments about the long axis and the zero-time ethidium fluorescence anisotropy. We find a significant decrease in the spinning diffusion coefficient for all curved fragments compared to the straight controls. This decrease is likewise evident in rotational diffusion coefficients computed from DNA structures obtained by a curvature prediction program for these sequences. Using a hinged-cylinder model, we can identify the change in rotational diffusion coefficient with a permanent bend of 13-16 degrees per helix turn for the sequences studied. Moreover, for some of the curved fragments an increased flexibility has to be assumed in addition to the permanent bend in order to explain the data.     

Rotational dynamics of surface probes in lipid vesicles

Translational and rotational diffusion of fluorescent molecules on the surface of small biological systems such as vesicles, proteins and micelles depolarize the fluorescence. A recent study has treated the case of the translational dynamics of surface probes (M.M.G. Krishna, R. Das, N. Periasamy and R. Nityananda, J. Chem. Phys., 112 (2000) 8502-8514) using Monte Carlo and theoretical methods. Here we extend the application of the methodologies to apply the case of rotational dynamics of surface probes. The corresponding fluorescence anisotropy decays were obtained using the Monte Carlo simulation methods for the two cases: surface probes undergoing rotational dynamics on a plane and on a sphere. The results were consistent with the theoretical equations which show that Monte Carlo methods can be used to simulate the surface diffusion problems. The anisotropy decay for the rotational diffusion of a molecule on a planar surface is single exponential and the residual anisotropy is zero. However, residual anisotropy is finite for the case of rotational diffusion on a sphere because of the spatial averaging of the anisotropy function. The rotational correlation time in both the cases is (4Drot)(-1) with Drot being the rotational diffusion coefficient. Rotational dynamics of a surface bound dye in a single giant liposome and in sonicated vesicles were studied and the results were explained according to the theoretical equations. A fast component of fluorescence depolarization was also observed for sonicated vesicles which was interpreted as wobbling-in-cylinder dynamics of the surface-bound dye.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering.

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation from the time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

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.     

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.     

Investigation of the flexibility of DNA using transient electric birefringence

In the preceding article, a Monte Carlo analysis was presented which provides a quantitative numerical relationship between the rotational diffusion coefficients, as measured by the decay of optical anisotropy following an electric field pulse, and the flexibility (persistence length) of short, wormlike chains. In the present article, the results of the foregoing analysis are applied to the observed rates of decay of birefringence for a series of sequenced DNA fragments ranging in size from 104 to 910 base pairs. Under the conditions used in this study, the DNA fragments exist as native, duplex molecules. Furthermore, conditions are defined in which the observed relaxation times are not dependent on DNA concentration, field strength, or the duration of the pulse. It is pointed out that the ionic atmosphere associated with a wormlike polyion does not exert any significant (direct) influence on the rotational diffusion of the polyion and, therefore, that the rotational relaxation times are a true measure of the configurations of the DNA molecules in solution. Moreover, excluded-volume effects are shown not to be significant for the moderately short molecules employed in this study. The major conclusion of this study is that there is no strong ionic strength dependence of the persistence length for ionic strengths above 1 mM and that the persistence length, under conditions where electrostatic contributions are negligible, is approximately 500 Å. For ionic strengths significantly lower than 1 mM, electrostatic contributions to the stiffness of DNA become significant.     

The size of the lactose permease derived from rotational diffusion measurements.

The lactose permease of Escherichia coli was labeled with eosinyl-maleimide, reconstituted into vesicles of dimyristoylphosphatidylcholine and subjected to time-dependent phosphorescence anisotropy measurements in order to determine the rotational diffusion coefficient. By comparison with bacteriorhodopsin, the diffusion coefficient is evaluated in terms of an effective radius of the lactose permease in the plane of the membrane. This radius amounts to 20 +/- 2 A which implies that the lactose permease is a monomer. The monomeric state is maintained in the presence of a membrane potential.     

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.     

The measurement of the rotational diffusion coefficient of bovine plasma fibronectin by electric birefringence technique

Although the conformation of fibronectin has been widely investigated by various techniques, there has not yet been any determination of its rotational diffusion coefficient. We report here this determination by the transient electric birefringence study of solutions of bovine plasma fibronectin at physiological ionic strength. The solutions showed a positive birefringence. A linear relationship was observed between the intensity of the birefringence at equilibrium and the square of the electric field within the range of fields applied (up to 12.5 kV.cm-1). The field-independent decay of the induced birefringence was described by a single exponential with a relaxation time of 0.76 (+/- 0.08) microsecond at 23 degrees C. This establishes fibronectin in solution as a globally rigid structure with a rotational diffusion coefficient, at 20 degrees C, of 202,000 s-1. This result allows the first rigorous determination of the low-resolution structure of fibronectin. It is important to notice that the analysis combines only results obtained in physiological conditions on native molecules and follows a strict hydrodynamic interpretation. The conclusion of this work is that a hollow sphere of about 20 nm external diameter can be proposed as a model for the three-dimensional structure of the fibronectin molecule in solution. This new model suggests the fibronectin could have the structure of a carrier protein.     

Analysis of time-resolved fluorescence anisotropy in lipid-protein systems

The subnanosecond fluorescence and motional dynamics of the tryptophan residue in the bacteriophage M13 coat protein incorporated within pure dioleoylphosphatidylcholine (DOPC) as well as dioleoylphosphatidylcholine/dioleoylphosphatidylglycerol (DOPC/DOPG) and dimyristoylphosphatidylcholine/dimyristoylphosphatidylglycerol (DMPC/DMPG) bilayers (80/20 w/w) with various L/P ratio have been investigated. The fluorescence decay is decomposed into four components with lifetimes of about 0.5, 2.0, 4.5 and 10.0 ns, respectively. In pure DOPC and DOPC/DOPG lipid bilayers, above the phase transition temperature, the rotational diffusion of the protein molecules contributes to the depolarization and the anisotropy of tryptophan is fitted to a dual exponential function. The longer correlation time, describing the rotational diffusion of the whole protein, shortens with increasing temperature and decreasing protein aggregation number. In DMPC/DMPG lipid bilayers, below the phase transition, the rotational diffusion of the protein is slowed down such that the subnanosecond anisotropy decay of tryptophan in this system reflects only the segmental motion of the tryptophan residue. Because of a heterogeneous microenvironment, the anisotropy decay must be described by three exponentials with a constant term, containing a negative coefficient and a negative decay time constant. From such a decay, the tryptophan residue within the aggregate undergoes a more restricted motion than the one exposed to the lipids. At 20 degrees C, the order parameter of the transition moment of the isolated tryptophan is about 0.9 and that for the exposed one is about 0.5.     

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.     

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

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

Quasielastic light scattering from solutions of filamentous viruses. II. Comparison between theories and experiments

We have compared four theoretical effects of rodlike macromolecules with the fast components, i.e., components other than translational diffusion, of our experimental data, which are presented as amplitude autocorrelation functions of electric field scattered from dilute solutions of monodisperse rodlike viruses with lengths from 3300 Å for tobacco mosaic virus to 20,000 Å for Pf1. The four effects are (1) the optic anisotropy treated by Aragón and Pecora, (2) coupled translational–rotational diffusion due to anisotropy in translational mobility recently reformulated by Gierke, (3) anisotropic rotational diffusion with respect to the direction of translational displacement first discussed by Berne and Pecora, and (4) the bending mode of a rod by Fujime and Maruyama. We show that both the first and second effects are required to explain the enhancement of amplitude of the translational diffusion at the expense of fast components. The experimental decay rates of the fast component exceed that of the rotational diffusions. In order to explain the excessive decay rate in the fast component, we need to include a minute amount (～1%) of bending mode of rodlike viruses, especially in longer viruses such as M13 and Pf1.     

Time-dependent rotational rates of excited fluorophores. A linkage between fluorescence depolarization and solvent relaxation

It is generally assumed that the rotational diffusion coefficients of fluorophores are independent of time subsequent to excitation, and that the rotational diffusion coefficients of the ground and the excited states are the same. We now describe a linkage between the extent of solvent relaxation and the rate of fluorescence depolarization. Specifically, if a fluorophore displays time-dependent solvent relaxation it may also show a time-dependent decrease in its rotational rate. A decreased rate of rotation could result from the increased interaction with polar solvent molecules which occurs as a result of solvent relaxation. The decays of anisotropy predicted from our model closely mimic those often observed for fluorophores which are bound to macromolecules. For example, the decays are more complex than a single exponential, and the time-resolved anisotropy can display a limiting value which does not decay to zero. The effect of solvent relaxation upon the rates of rotational diffusion is expected to be most dramatic for solvent-sensitive fluorophores in a viscous environment. These conditions are frequently encountered for fluorophore-macromolecule complexes. Consideration of the linkage between solvent relaxation and rotational diffusion leads to two unusual predictions. First even spherical fluorophores in an isotropic environment could display multi- or nonexponential decays of fluorescence anisotropy. Secondly, for the special case in which the fluorophore dipole moment decreases upon excitation, the theory predicts that the anisotropy decay rate may increase with time subsequent to pulsed excitation. The predictions of this theory are consistent with published data on the effects of red-edge excitation upon the apparent rotational rates of fluorophores in polar solvents.