Electric Dichroism

2.1 The Dichroism Amplitude

When DNA is aligned in the direction of the electric field, the absorbance of light, which is polarized parallel to the electric field, is decreased relative to the state, where the DNA is in the usual random spatial distribution The change of the absorbance of light polarized parallel to the field vector ΔA‖ is a measure of the degree of orientation. The theory predicts that the change of the absorbance of light polarized perpendicular to the field vector ΔA⊥ measured under the same conditions fulfills the relation.

(1)

The relative change of the absorbance defined by:

(2)

is the reduced electric dichroism, where A is the isotropic absorbance measured in the absence of an electric field.

The degree of molecular orientation and, thus, the magnitude of electric dichroism increases with the electric field strength E. Complete orientation in the direction of the electric field may be expected only in the limit of infinitely high E The dependence of ΔA/A on E is determined by the type and the magnitude of the electric dipole moment. The degree of orientation at a given field strength increases with the magnitude of the dipole moment. At low E-values the electric dichroism ΔA/A increases with E². The complete dependence of ΔA/A on the field strength E is described by the “orientation function” Φ according to ΔA/A = Φ ΔA/A _∞ (3) where ΔA/A _∞ is the limit value of the electric dichroism at infinite field strength. In the case of induced dipoles, the orientation function is given by: (4) where γ = (αE ²)/(2 kT), α is the polanzability, k the Boltzmann constant, and T the absolute temperature. In the case of permanent dipoles the orientation function is given by. (5) where β = µ_p. EkT and µ_p is the permanent dipole moment.

The orientation functions may be used to determine the limit value of the electric dichroism, corresponding to complete molecular orientation, by least-squares fitting of dichroism values measured at different field strengths. The limit value of the electric dichroism provides direct information about the orientation of the chromophors with respect to the dipole vector according to the following equation: (6) where ϕ is the angle of the transition dipole moment of the chromophor relative to the dipole vector. When the chromophor is bound to the surface of the DNA, and its transition dipole moment is oriented parallel to the long axis (cf. Fig. 2 ), corresponding to ϕ = 0, the limit value of the dichroism is +3. In the other limit case, where the chromophor is intercalated between the basepairs and the transition dipole moment is in perpendicular direction to the long axis (ϕ= 90), the limit value of the dichroism is —1.5 Thus, the limit value of the electric dichroism can be used to calculate the angle ϕ of the optical transition dipole with respect to the direction of the electric dipole, which corresponds to the long axis in the case of DNA (cf. Fig. 3 ). Actually the first evidence for the tilt of the basepairs in B-DNA double helices, i.e., the deviation of the basepair orientation from 90° relative to the helix axis, came from measurements of the electric dichroism (5).

When the electric dichroism of drug-DNA complexes is measured at wavelengths around 260 nm, where both the drug and the DNA contribute to the absorbance, the dichroism contains contributions from both components. Separation of these contributions may be difficult. However, most drugs absorb light at longer wavelengths than DNA. Thus, the electric dichroism of the drugs may be measured selectively in the long wavelength range and may be used to determine the orientation of the drug in the complex.

2.2 The Dichroism Decay Time Constant

When an electric field pulse is terminated, the molecules, which have been aligned under the influence of the electric field, turn back to their random distribution by rotational diffusion. The process of rotational diffusion is very strongly dependent on the molecular size the time required for the transition from the aligned to the random state increases with the cube of the length of rigid rodlike molecules Thus, the dichroism decay time constant, which reflects the rotational diffusion process, is a very sensitive indicator of the length.

Short DNA molecules up to chain lengths of ~100 bp behave like rigid rods. Rotational diffusion of these rigid rods is mainly determined by the length ℑ of the rod, whereas the width of the rod, described by the radius r, is of marginal influence only, except for very short rods. The dichroism decay time constant τ_d ^r _t for such rods may be described by ref. 6 and 7.

(1)

where q = ℑ/(2r), k the Boltzmann constant, T the absolute temperature, and ∌_o is the viscosity of the solvent. This equation may be used to calculate the length ℓ of a rigid rodlike molecule from its dichroism decay time constant.

3.1 General

As shown in Fig. 4 , measurements of the electric dichroism require a device for the generation of electric field pulses and a spectrophotometncal detection system with a sufficiently high time resolution, together with a system for transient storage of data and for subsequent processing of these data The details of the equipment depend very much on the type of the investigations. Measurements in the fast time range, corresponding to τ≪ 1 µs, require more sophisticated and, thus, also more expensive equipment than measurements in the range τ≥ 1 µs Because of the progress in electronics, the fast time domain is now more easily accessible than previously. Usually small molecules require higher electric field strengths for a sufficient degree of orientation than large molecules. Obviously, the difficulties and the expenses associated with the construction of pulse generators for high electric field strengths increase with decreasing rise and decay times of the pulses to be generated. The following summary presents a brief description of the standard equipment used in many different laboratories Unfortunately, a complete setup for measurements of the electric dichroism is not commercially available. However, the parts required for an instrument are available from various companies

3.2 Pulse Generator

Most of the electric dichroism data described in the literature have been obtained by use of commercial pulse generators These devices generate pulses with amplitudes up to a few kilovolts; the rise and the decay times of the pulses are in the range around 20 us. Generators of this type are distributed by, e.g., Velonex, Santa Clara, CA

3.3 The Measuring Cell

A relatively simple version of a cell for measurements of the electric dichroism consists of a standard cuvet with an insert machined from synthetic material, e.g., Teflon or Dynal, holding platinum electrodes. A picture of such a cell shown in Fig. 5 .

3.4 Spectrophotometric Detection

Standard commercial spectrophotometers are not sufficient for measurements of the electric dichroism, because their time resolution is usually limited to the range between s and ms. However, parts for the assembly of a fast spectroscopic detection system are available from various sources. For optimal signal-to-noise ratios, the light used for the measurements should be of high intensity. Light sources of high intensity are arc lamps, which are offered in many different variations. Monochromators, polarizers, and detector heads with appropriate power supplies are also offered in various forms by different companies.

Because the electric dichroism is induced by field pulses in the kilovolt range, whereas the absorbance changes after photoelectric conversion are usually in the millivolt range, the detection system has to be protected efficiently against perturbations by induction effects For this purpose the photomultipher is shielded in a cover made from µ-metal, protecting mainly against magnetic perturbations, and the multiplier head including the amplifier is mounted in another cover made from metal, protecting mainly against electric induction effects. The connection between the photomultipher head and the transient data storage unit has to be shielded as well.

3.5 Transient Data Storage and Data processing

Owing to the progress in electronics, transient digital storage of expenmental data in the time range of microseconds and below is not a problem anymore The transiently stored experimental data can be easily transferred to PCs, which are sufficient for evaluation of the data. Usually, the software required for the evaluation is prepared individually. (However, standard software for evaluation of exponentials may be obtained free from: Stephen Provencher, Max Planck Institut fur biophysikahsche Chemie, Am Fassberg 11, D-37077 Gottingen, Germany.)

3.6 Automatic Data Acquisition

Under many conditions, the electric dichroism of DNA is large enough, such that single shots are sufficient for data analysis. However, it is often useful to extend measurements to conditions of, e.g., low DNA concentration or low electric field strengths, where an increase of the signal to noise ratio by averaging of many transients is desirable. For this purpose, automatic acquisition of data is very useful. An instrument for automatic measurements of the electric dichroism may be constructed relatively easily.

Standard PCs are sufficient as control units for timing of the field pulses, activating, and reading of the transient data storage and averaging. For construction of an efficient automatic instrument, perturbations should be avoided by galvanic separation of the different units using optoelectronic coupling as much as possible. Application of many field pulses of a given polarity will lead to electrophoretic motion toward one electrode and, thus, the polarity of subsequent pulses should be changed. Another potential source of problems are photochemical reactions. These reactions may be avoided by using a shutter, which is opened only during recording of transients.

4.1 Preparation of Samples

The electric dichroism is usually measured at low salt concentrations in order to keep the electric conductivity of the samples as low as possible. At low conductivities the temperature increase of the samples caused by Joule heating during the pulses remains low; furthermore, the decay of the field strength resulting from current flow is also minimized; finally electric polarizabihties of polyelectrolytes are usually maximal at low salt concentrations. In most cases the requirement of low salt concentrations does not impose restrictions. DNA double helices, for example, are quite stable down to low salt concentrations. In most cases the binding of drugs to DNA is stabilized at low salt concentrations, because of an increase of electrostatic interactions.

Because the electric dichroism is very much dependent on the ionic strength, it is very important to do the experiments at a well-defined salt concentration. Of course, the pH of the solutions also must be well-defined Because of the high charge density of DNA, ions of different types are bound with high affinity The most effective procedure for removal of different ions, including other contaminations of low molecular weight, is dialysis. Because multivalent ions bind very strongly to DNA, in particular at low salt concentration, removal of these ions like Mg²⁺ or Ca²⁺ requires extensive dialysis against buffers containing EDTA. It is recommended either to exclude bivalent ions by dialysis and addition of a sufficient concentration of EDTA, or to add a well-defined concentration of bivalent ions, e.g., 100 µMMg²⁺ According to this procedure it is easily possible to get a sufficiently well-defined ionic milieu, which is important, because small variable residual bivalent ion concentrations may strongly affect electro-optical results. Among the different buffers available, cacodylate proved to be useful (pH range 5.3–7.3), because of the small temperature dependence of its pK and because of the strong suppression of bacterial growth.

4.2 Measurements

Some of the technical precautions to be used for unperturbed measurements have been mentioned already above and are not repeated here For any measurement of the electric dichroism, first the sample should be at a well-defined temperature. An accurate control of the temperature is essential for evaluation of the time constants: the viscosity of aqueous solutions is very much dependent on the temperature and, thus, comparison of data and any quantitative evaluation require strict control of the temperature. Usually, the electric field pulse is adjusted to a length, which is sufficient to drive the dichroism to its stationary level. Evaluation of data by any orientation function requires stationary values of the electric dichroism. It is useful to collect data over a broad range of electric field strengths, as broad as possible under the given experimental conditions, which are defined by the pulse generator and the signal-to-noise ratio

Usually it is sufficient to determine the electric dichroism by measurements with light that is polarized parallel to the field vector. However, it is important to check whether the condition defined by Eq. 1 is satisfied. Thus, some transients should also be obtained with light polarized perpendicular to the field vector. Deviations from Eq. 1 may indicate either problems of the optical setup, e.g., strain in the windows of the measuring cell, or some field induced reaction, e.g., dissociation of a ligand or some change of the DNA structure. A further examination is possible by measurements at the “magic angle,” corresponding to an angle of 54.7° of the plane of polarized light with respect to the field vector (8). Under these conditions dichroism effects should disappear and, thus, any remaining field induced changes of the light intensity should be caused by reaction effects

The electric dichroism may be characterized at any wavelength that may be convenient for the measurements. One of the criteria for the selection of an appropriate wavelength is the availability of sufficient light intensity. The signal-to-noise ratio increases with the square root of the light intensity. The highest light intensities are provided at the mercury lines of xenon/mercury high pressure arc lamps. Mercury emission lines are at 248.2, 265 2, 280.4, 289.4, 302.2, 313.2, 334.2, 366.3, 404.7, 435.8, and 546 1 nm; thus useful lines are available for most applications A second cntenum is the position in the absorbance band. Usually (π* ↓ π)-transitions are polarized in the plane of aromatic chromophors, but there are also (π* ↓ ∌)-transitions that are usually polarized in perpendicular direction to the aromatic plane. Thus, the wavelength used for measurements should be selected carefully.

As usual the signal-to-noise ratio may be increased by averaging of transients. Because the signal-to-noise ratio value increases with the square root of the number of transients, an increase of signal-to-noise ratio by a factor of 5, for example, requires 25 transients In order to check for any potential damage of the solutions after a series of measurements, the first shot should be repeated at the end, and the results should be compared. Another useful control is a comparison of absorbance spectra before and after the measurements of the electric dichroism

4.3 Evaluation of Data

4.3.1 Stationary Dichroism

Measurements of the dichroism transients provide changes of an optical signal induced by application of an electric field pulse The difference ΔIbetween the optical signal approached during a pulse, which is sufficiently long to drive this signal to its stationary level, and the optical signal before the pulse may be determined by some computer graphics procedure Another parameter required for the evaluation is the (absolute) level of the optical signal I _o before pulse application Usually I _o is measured directly by some voltmeter, whereas ΔIis read from a digital recording with an unknown offset. Combination of these values, measured with light polarized parallel to the field vector, provides the absorbance change

(1)

Using the isotropic absorbance A measured at the same wavelength, the electric dichroism is given by These values are determined at different electric field strengths E, where E is the voltage of the applied pulse divided by the electrode distance.

4.3.2 Transients

Transients of the electric dichroism are evaluated in terms of exponentials:

(2)

where I(t) is the light intensity measured in mV or V at time t, n is the number of relaxation processes required to fit the data, I∞ is the light intensity at time is the change of the light intensity associated with the n ^th relaxation process and τ_n the relaxation time constant associated with the n ^th relaxation process. The data I(t) = f(t) are subjected to a least squares fitting procedure for evaluation of the parameters ΔI _n,and I∞. The decision on the number of relaxation processes may be based on visual inspection of the quality of the fit(s), but also on the sum of squared residuals:

(3)

where I _m(t) and I _f(t) are the measured and the fitted values of the light intensities at different times t, respectively. Usually S decreases for fits with an increasing number of relaxation processes n. The decision on the number of “significant” relaxation processes is usually simply operational: if S does not decrease significantly upon going from n to n + 1, the number n is selected as significant. As often in science, a decision on significance requires some experience. Usually a decrease of S by 50% is significant, at least if it is reproducible. If the decrease of S is smaller, the available experimental data may not be sufficient to define an additional relaxation process at a sufficient accuracy and then fitting of the additional process does not make sense. The program “Discrete,” written and distributed by Provencher (cf. above), offers an automatic decision on the number of relaxation processes.

Obviously, the most convenient systems are those, where the dichroism decay can be represented by single exponentials. The observation of more than a single relaxation process may indicate a special, nonsymmetric shape, internal flexibility, or heterogeneity of the sample under investigation The last possibility may be easily checked, e.g., by gel electrophoresis. A decision between the first two possibilities is usually more difficult. It should be mentioned that the theory predicts five exponentials for the dichroism decay of rigid particles without symmetry (9). However, usually most of these exponentials are associated with undetectably low amplitudes The number of clearly detectable processes obtained in many simulations in the author’s laboratory on rigid macromolecules of very different shape did not exceed two. Evidence for the case of internal flexibility may be obtained from a dependence of the observed amplitudes on the electric field strength, because flexible molecules may be stretched under the influence of high electric field pulses.

DNA double helices are known to behave like rigid rods up to chain lengths in the range around 100 bp. The decay of the electric dichroism of rigid rods is represented by single exponentials The observation of single exponential decays of the electric dichroism for much longer DNA chains reported in the literature appears to be partly because of experimental conditions (limited electric field strength) and partly because of a limited experimental accuracy.

4.3.3 Approximate Procedures

Although a complete characterization of the parameters of a system under investigation is always desirable, it often happens that this is rather difficult or even impossible for various reasons. Under such conditions, approximate procedures may be very useful. For the case of drug-DNA complexes such an approximate procedure has been used by Colson et al. (10) for the determination of the orientation of drugs relative to that of the DNA base pairs.

Colson et al. (10) did not determine the limit value of the electric dichroism, which requires the characterization of the orientation function by measurements over a broad range of electric field strengths They restricted their measurements to a given electric field strength E, but measured at this E value the dichroism for the free DNA in the absorbance band of the bases (ΔA/A) DNA and for the DNA-drug complex in the absorbance band of the (ΔA/A) drug. They define a dichroism ratio:

(1)

which is a measure of the orientation of the drug relative to that of the DNA base pairs. This procedure implies that the orientation function at the given E value is the same for the free DNA and for the DNA-drug complex, which is reasonable according to Colson et al. (10) at low degrees of drug binding. For the case of intercalation, the DR value is close to 1, as demonstrated, e.g., for ethidium and proflavine, whereas drugs bound to the outside of DNA like netropsin and distamycin show DR values in the range around-1. Colson et al. (10) have also demonstrated that the type of binding is dependent on the DNA sequence.

6.1 Electric Birefringence

The electric birefringence (1–4) is very similar to the electric dichroism. The only difference is the optical parameter used for detection of field-induced orientation. In the case of the birefringence, orientation of the molecules is detected by measurements of the anisotropy of the refraction, whereas the anisotropy of the absorbance is used in the case of the dichroism Measurements of the birefringence can be very sensitive; some authors even conclude that the birefringence is more sensitive than the dichroism; obviously the sensitivity depends very much on the technical details of the instrument used for the measurements and, thus, general statements are hardly justified. A clear advantage of the dichroism is the fact that its interpretation in terms of molecular structure is more simple and straightforward

6.2 Linear Dichroism Induced by Flow Velocity Gradients

Macromolecules may be aligned by flow velocity gradients and this alignment may be studied by measurements of the linear dichroism (16). Various forms of this technique have been used. An advantage of the method is the fact that it may be used at any salt concentration. However, applications are restricted to relatively long polymers. Furthermore, the flow dichroism cannot be used to get information about rotational diffusion in the time range below milliseconds.

6.3 Fluorescence Detected Dichroism

Drugs containing an aromatic component often emit fluorescence, which may be used for a selective measurement of the dichroism (17). Various experimental procedures are possible. One of them is use of polarized light for excitation, as usual in measurements of the dichroism, and detection of the dichroism by collection the fluorescence light under magic angle conditions, i.e., behind polarizers orientated at an angle of 54.7° with respect to the field vector (18). Use of magic angle conditions simplifies the evaluation to the standard procedure, because under these conditions the measured fluorescence intensity is dependent on the molecular orientation only because of the angular dependence of the excitation process, whereas the light intensity resulting from emission itself is independent of the molecular orientation.