ANALYTICALBIOCHEMISTRY70, 506-525 (1976)

Laser Doppler Spectroscopy as Applied to Electrophoresis in Protein Solutions R. MOHAN, R. STEINER, AND R. KAUFMANN University of Diisseldorf, Institut fur Klinische Physiologie, Universiti~tsstrasse 1, D-4000 Di~sseldorf, West Germany

Received April 28, 1975; accepted September 24, 1975 The application of Laser Doppler spectroscopy (LDS) to the electrophoretic migration of macromolecules in solution by heterodyne light beating technique, previously developed by Ware and Flygare, has been improved by the design of a new microelectrophoresis cell and a high resolution in the frequency power spectrum. A 1024-channel correlator was used in combination with a softwarecontrolled Fast Fourier transformation (FFT). This technique has been applied to singleprotein solution, bovine serum albumin (BSA), and to multicomponent systems, in particular to human blood serum. In comparison to normal free electrophoresis, LDS is more convenient and reveals more information in a much shorter period of time. L a s e r Doppler velocimetry (LDV) is now a fully developed technique in momentum flow fluid dynamics, either by coherent or incoherent detection of quasi-elastically scattered light (1). As an extension to optical heterodyning in the study o f diffusional (Brownian) motion, electrophoretic light scattering was developed theoretically and experimentally by Ware and Flygare (9), Bennett and Uzgiris (3), and Yoshimura et al. (4). A new technique is hence available that in principle has many advantages compared to classical electrophoretic methods, since the desired information is obtained in much less time and even with minute samples. Furthermore, not only the electrophoretic mobilities but also the diffusional properties can be obtained at the same time. Finally, it gives access to kinetic studies of interacting macromolecules in solution (5). This paper deals with the application of L D V to electrophoretic serum analysis and explores the basic prerequisites, the type of information obtainable, and the limitations involved. The laser Doppler method measures the "instantaneous v e l o c i t y " in contrast to the moving boundary method or gel electrophoresis, where the total displacement after the elapse of certain time is measured. The "instantaneous v e l o c i t y " is given as a Doppler shift in the spectrum of the scattered light. The time required for a single experiment, therefore, depends only on the signal-averaging time required due to the statistical nature of the optical signals. With particles o f cellular dimensions at 506 Copyright © 1976 by Academic Press, Inc. All rights of reproduction in any form reserved.

ELECTROPHORETIC LIGHT SCATTERING

507

extremely low concentrations, the problem of signal processing would be similar to "burst-type" signal processing in LDV. Light-scattering sensitivity scales as the particle size, and hence, extraneous matter is deleterious, as are also the presence of unwanted local fluctuations, hydrostatic or electroosmotic flow, and convection. Unlike the conventional optical methods, such as absorption or Schlieren-interferometric methods, the intensity fluctuation spectrum is angle dependent, the mobilities scaling as K (scattering vector), the diffusional line-broadening scale as K s (see Theoretical Introduction). This necessitates electrophoretic light scattering to be performed actually at low scattering angles, where one has now to deal with narrow signal bandwidth involving much lower frequencies than in the LDV of fluid flows. To make the directional velocities of the moving proteins as high as possible, higher voltages are required than in conventional electrophoresis; to avoid the consequent heating effects, the electrical conductance of the solution must be as low as possible. All these factors imply the importance of the design of a cell suitable for electrophoretic light scattering. Such a cell must be small and compact, free from electrode reactions, compositional changes of the medium and microbubbles, and stable against the slightest convection at the (optical) probe volume.

THEORETICAL INTRODUCTION The basic theory of quasi-elastic light scattering has been extensively reviewed by Cummins and Swinney (6) and by Dubin (7). For the ~eplication of optical heterodyning to electrophoretic light scattering of macromolecules and the resolution criterion involved, we refer to Ware and Flygare (9) where the basic equations also are developed for noninteracting systems. The pertinent equations that describe the autocorrelation function (ACF) and the power spectrum (PS) of pure translational diffusion motion (D, diffusion coefficient): Gz(K,~) = N E ~ z exp (-i6o0~-) exp ( - D K 2 ~ ")

[1]

DK 2 S(~,o,) = N E s 2

(a~ - COo)z + ( D K 2 ) 2

[2]

are, in the presence of external field as under electrophoretic conditions, extended to: G2(~,,) = N E ~ z exp (-ioJ0~-) exp (-iKva~-) exp (-DK2r)

[3]

DK 2 S(~.o~) = N E f f

(w - K v . , cos 0/2) ~ + ( D K 2 ) 2

[4]

where N represents the number of independent spherical scatterers

508

MOHAN, STEINER AND KAUFMANN CELL A~

A:~L~

1

I~

'

I

A,L,

A~ -

1=4

---

FiG. 1. Block diagram of the experimental setup. A, apertures; L, lenses; PM, photomultiplier; PS, power supply; .~, preamplifier; S, oscilloscope; COR, correlator; HIST, signal analyzer; D, display; PL, plotter; TELE, teletype.

in the scattering volume, Es the amplitude factor of the scattered electric field, G2('r) the second-order correlation function of the time-dependent fluctuations in the scattered-light intensity, and S(K,to) the corresponding power spectrum. From these equations, the Doppler shift in frequency is" A~ = Kv d = tzEK

[5]

where the Doppler velocity Vd is equal to the electrophoretic mobility multipled by the electric field per centimeter. The shifted peak-line width is still Lorentzian with half-width at half-height equal to D K 2. Theoretically, the (electrophoretic) resolution R, is proportional to 1/O at small scattering angles (2), R = Vdho/2n'nDO

[6]

(h0, laser wavelength in vacuum; n, refractive index of the protein solution), and one would expect the best results for 0 to be near zero degree. Unfortunately, one has to find a compromise between a good resolution R and the ambiguity involved in the K vector at very low angles. We found optimum results at an angle of about 4°. An optimum resolution would also be set by the highest possible electric field E which can be applied to the cell with minimum disturbance from the joule heating effects.

INSTRUMENTAL SETUP

(a) The Electrophoretic Cell Several cell arrangements and methods were tested before we developed the present version, schematically shown in Fig. 2. The two outer buffer compartments (G), with a content of 4 ml each, were separated by semipermeable membranes and 0-rings from the sample compartments (H) both made of Perspex and rigidly attached to a 5-mm thick brass plate. The sample compartments (H) were each filled with 3-ml protein solutions and bridged to each other through a 15-mm long glass capillary with a uniform

ELECTRO PHORETIC LI GHT SCATTERIN G A

• ,.-/

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./..

~

B

F

509

"f"

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/ FIG. 2. Scheme of the electrophoresis cell. (a) A, palladium electrodes; B, platinum wire; C, silicone rubber; D, capillary; E, rubber O-ring; F, semipermeable membrane; G, buffer compartment; H, sample compartment. (b) Light path through the capillary. L, part of the scattering length seen by the phototube; 0, observation angle; On, observation angle corrected for the refractive index of the solution.

i.d. of 0.83 mm and a glass wall thickness of 0.4 mm. The special supporting silicone rubber retainer discs attached to the sample cells allow the capillary to be easily replaced when required. It is also possible to connect the sample compartments from above, with the capillary in an inverted U-tube form filled with the protein solution with no inferior performance, except that instead of the 1.5 cm long tube in the straight connection, a tube length of 3.5 cm would be required with consequent higher voltages to be applied to maintain the same electric field strength. The top plates covering (G) and (H), also made of Perspex, support the palladium electrodes (4 × 8 mm 2) for the high voltage supply, and the thin platinum needles submerged in the sample compartments measure the voltage drop across the capillary. More than 93% of the applied voltage drops across the capillary because of the high resistance due to the smaller cross section. During the experiment the voltage was stable for at least 1 hr, while most of the experiments were finished in a few minutes. Electrode phenomena. It is essential not only to keep the electrode phenomena to a minimum, but also that these reaction products and compositional changes do not reach the measurement area in view of the weak buffering (low ionic strength) of the medium, and further that these electrode reaction products be kept away from the Joule heating area. If not, then it is not possible to treat the electrode phenomena and the Joule heating due to the applied voltage separately, and this combination is easily susceptible to a variety of instabilities, irrespective of the cell geometry. In our cell system, the applied voltage is measured at the ends of the capillary, thereby bypassing the effects of electrode polarization in the

510

MOHAN, STEINER AND KAUFMANN

correct measurement of applied voltage. The arrangement of separating the buffer and sample compartments by membranes has several advantages: reaction of the proteins with the electrodes was inhibited, special coating of the electrodes was not necessary (pure palladium electrodes with high-current capacity were used), and the hydrodynamic disturbances and the false light-scattering measurements introduced by gas bubbles in the capillary minimized. This is in contrast to the situation with the narrow-gap electrodes system of Uzgiris, wherein the various instabilities are telescoped quickly to the initial time as soon as the experiment is started. Shadowgraph images (magnified) of such a cell quickly revealed convective turbulence involving microbubbles, polymerization, and adhesion of the proteins at the electrodes which coast down as soon as the modulated current was stopped. In addition, there is always some uncertainty involved in the applied voltage due to the capacitance effect at the electrodes. In Ware and Flygare (9) who used reversible electrodes, the bubbles are less severe and a closed system was possible. However, in both the Ware and Flygare system and the Uzgiris cell there is always the possibility of Ag- or Pt-black particles drifting through the cell. Joule heating. Once the electrode phenomena are kept away, the Joule heating can be discussed on its own, being the most important factor limiting high resolution. The effect of Joule heating in inducing the various transient and persistent instabilities and convective turbulences, i.e., the corresponding critical number (R number), depends strongly on cell geometry and dimensions. While in moving boundary electrophoresis, the Joule heating given by H = F/A2k (where i is the current, A the cross section, and k the specific conductance) is normally in the range of 0.1 W/cm 3, higher values are permissible in the light-scattering technique. In our case, we permitted up to 4 W/cm a (8 × l0 -a W dissipated through the length of 1.5-cm length of the capillary tube) continuously for up to 5 min. As opposed to the moving boundary method, here it is feasible to apply intermittent or square wave voltages (see also Ware and Flygare, and Uzgiris), although care must be taken in the signal processing of such intermittent signals. Ware and Flygare minimized Joule heating by cooling the system and by using a pulse mode of applied voltage (in the msec range) with long cooling periods between the pulses. In the narrow gap electrode method, minimization is due to the low voltages applied, while in our case, it is due to the very low cross section (5 × 10-z cm 2) of the cell used. Our cell constant was 126, which is 10-15 times higher than that of a Tiselius-type cell. Inhomogeneous media and their effects. Without cooling, thermal gradients will occur in the capillary. The radial temperature gradient is given by: AT = 0.24 12E2/8p~t

[7]

ELECTROPHORETIC LIGHT SCATTERING

511

where 1 is the length of the cell, E the applied voltage/cm, p the electrical resistance of the protein solution, and h its thermal conductivity. At 4 W/cm 3 dissipation, AT was 0.8°C (100 V/cm, 0.005 M buffer) in our capillary cell, with an additional I°C temperature difference between the cell wall and room temperature at the end of 5 min. The effect of this thermal gradient is to form a radial density distribution in the capillary which would tend to homogenize the medium by diffusional transport (when the system can be said to be stable) or by convective (drift) modes when instabilities occur. In the operative range for normal electrophoresis in our cell (i.e., to a maximum of 100-130 V/cm over a resistance of 644-k l) due to the 2% protein solution in 0.005 M veronal buffer), there are no additional drift modes other than the electrophoretic motion. There is much less contribution from the small refractive index gradients and thermal diffusion present since: (i) the Doppler shift is directionally sensitive only in the vectorial direction of flow along the capillary length, and (ii) a major part of the light-scattering signal comes from the cross-sectional middle of the capillary. Even beyond this safe normal-operative range for electrophoresis (i.e., above 4 W/cm 3 with longer experimental time), the only effect of the inhomogeneous medium observed is narrowing of the line-width at progressively higher voltages, with no effect on the electrophoretic Doppler shift itself. In this region, it is likely that the square-wave applied voltage (as in Uzgiris modulation spectroscopy) might make the drift modes operative with consequent inaccuracies in the Doppler shifts. We feel that in our capillary cell, the tendency of the heating effect is for the system to eventually go into the Btnard instability region before convective turbulence occurs (to be published). Electroosmosis and spatial velocity profiles. The facts that experimentally for a solution of a standard protein as BSA, we obtain consistently a Doppler shift, which corresponds to the known electrophoretic mobility, and that the linewidth corresponds to the diffusional motion of the protein, rule out any electroosmotic effect in our cell. The reasons are: (i) low conductivity of the medium, (ii) the cross-sectional area of the capillary (5 x 10-3 cm 2) is just above that required for electroosmosis, and (iii) the top plate covering the reservoirs was not completely closed, so that there was no hydrodynamic backflow in the capillary. It is also likely that the capillary force in the glass capillary is able to maintain a small pressure-head difference in the reservoirs due to the electroosmotic flow. Further, Poiseuille flow experiments in the same capillary under the same optical conditions gave a spectrum of velocity profiles (shown in Fig. 3) that was distinctly different from that of pure mass flow, as in electrophoresis. Here, the peak always corresponded to the maximum velocity in the center of the capillary, and the line shape to that of the spatial

512

MOHAN, STEINER AND KAUFMANN 1

05

0

~t'5

2~0 HZ

3"~5

5(X)

Fro. 3. Typicallight scatteringspectrumfor laminar liquid flow(0.2 ml/min)throughthe capillary. The peak corresponds to the maximalvelocityin the center of the tube.

distribution of velocities. Hence, the presence of electroosmosis in our electrophoretic experiments would have strongly affected the true peak position as well as distorted the line shape and narrowed the linewidth. This provides a quick check in sensing the presence of electroosmotic disturbance.

(b) Optics The optical design for low angle studies is shown in Fig. 1. A 15 mW H e - N e laser (Spectra Physics, Model 124B) was used as the coherent light source. The parallel beam of 1.1-mm diameter passed through two circular apertures A1, A2 of 1-mm diameter each to remove the incoherent part of the beam (which would otherwise contribute to 100-Hz and additional lower-frequency oscillations in the autocorrelation function). The laser beam was focused by the lens L1 (focal lengthfei = 8 cm) into the center of the capillary. A 1:1 image of the scattering volume was formed on the photomultiplier cathode by the lens L2 with the same focal length of 8 cm. While aperture A3 (0.3-0.7 mm) in front of the lens L~ restricted the field of view of the detector, the pinhole A4 (0.2 mm) in front of the multiplier cathode restricted the coherence area to one. In this optical configuration, the diameter (d) of the beam waist in the focal point is approximately

E L E C T R O P H O R E T I C LI GHT SCATTERIN G

513

d = fL, a./A2 and lies in the range of 100/~m. The cylindrical focusing effect of a capillary changes the circular cross section of the beam to an elliptical shape, the eccentricity varying with tube diameter. The scattering length L, as defined in (7), is L = (fL1/A3)~X and hence longer than the inner diameter of the capillary (0.83 mm). The depth seen by the multiplier decreases with the angle 0 according to 1 = da4/sin OR, where OR is the corrected scattering angle in accordance with Snell's law. If the angle 0 is smaller than 15°, light from the whole diameter of the capillary is scattered into the photomultiplier tube. Hence, enough scattered light from the cell wall enters the photomultiplier to form an efficient heterodyne signal. The presence of a row of antennas at the cell wall (speckle pattern) assures that the scattering volume is always centered in the middle of the goniometer when angular measurements are made. In our instrument, the chief cause for line broadening is the ambiguity of the vector K due to the focusing of the laser beam into the capillary and due to the acceptance angle spread of the detecting system. Both are angle dependent (7) and add up to a total uncertainty of about 4% in the Doppler shift for an observation angle of 5° . All optical parts are mounted on a heavy goniometer, 40 cm in diameter, with one fixed arm for the focusing system and another arm rotating around the center of the goniometer and carrying the detector system. The electrophoresis cell was screwed with its brass plate on a rotating table mounted in the center of the goniometer, and was adjustable in the X, Y, and Z directions by micrometer screws. The goniometer itself was horizontally aligned by three screws and rested on a 600-kg heavy metal table, which in turn was situated on isolator pads which efficiently damp vibrations communicated through the floor.

(c) Electronic Equipment and Data Processing The output signal from an EMI 9558B photomultiplier tube, supplied by an extremely stabilized high-voltage power supply (KNOTT Electronics), was fed into anAC preamplifier ( K E I T H L E Y Mod. 103A) through a 100-kt~ photomultiplier load. According to the programmed sampling interval, r, and the number of channels used for the autocorrelation function, the bandwidth of the amplifier was adjusted for the high-frequency cutoff, while the low-frequency cutoff was maintained around 0.1 Hz. To avoid harmonics, the amplifier should not be saturated. The amplified signal was continuously displayed on an oscilloscope and controlled for its amplitude, quality, and stability. Autocorrelation was performed by a multichannel

514

MOHAN, STEINER AND KAUFMANN

signal analyzer (Histomat S, Intertechnique) after analog to digital conversion. The correlator was a 3-bit correlator with _+8 amplitude steps of 250 mV each. The number of channels could be selected from 128 to 1024. The continuous display of the developing autocorrelation function gave an additional possibility for control. As the autocorrelation function (ACF) was more stable than direct spectral analysis in the low frequency regions, the signal was first autocorrelated, after which the power spectrum was obtained by the Fast Fourier Transform (FFT). The resolution of the frequency spectrum, Af , is given by the relation A f = 1/rn. In most of the experiments A f w a s 0.5 Hz with 512 channels, but this was not enough for multicomponent systems such as human serum. Here, the resolution had to be increased to 0.125 Hz with 1024 channels at the expense of a much longer acquisition time.

(d) Performance Characteristics of the System In order to measure very low frequencies (corresponding to very slow electrophoretic drift velocities), many efforts must be made to eliminate mechanical and optical disturbances. To test the absence of mechanical vibrations and incoherent light in the laser beam, a frosted paper was mounted in the center of the goniometer as light scatterer and the signal autocorrelated. The autocorrelation and the power spectrum should represent shot noise. The frosted paper also allows to check the centering of the scattering volume and to estimate the volume as seen by the photomultiplier from the intensity variations as the frosted paper was moved by micrometer screws of 1/50-ram precision. Since our experiments were mostly in the forward direction, the heterodyning efficiency was high, as were also the signal intensities. The signal to noise ratio (Ps/Ps~) varied with the angles of scattering, the protein solutions used, and the general experimental conditions. The statistical signal-averaging (or the number of samples) required for the Doppler shift and for the linewidth is not the same, since the former is more coherent. Incomplete statistics would entail artificially narrowed linewidth, while the peaks may correspond to stable correct Doppler shifts. At still shorter times (a few cycles of signal averaging), while one could see well developed ACFs, the spectral peaks would wander from experiment to experiment. In multicomponent systems, the peaks and linewidths cannot be identified correctly with fewer points (or channels) for each peak. In principle, each diffusional line in the multicomponent system requires as many points (or channels) as used for the single component diffusional experiment, if "artificial" peaks are to be avoided. As a standard experiment to check the instrumental system, silica particles of70-and 140-/~ diameters were used (DU PONT, Ludox SM30

ELECTROPHORETIC

LIGHT SCATTERING

515

LUDOX diometer: 140A sompling_time 012 msec

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e= 1125"

~ 0~" " - - ~~X -

02°=312"107 cm2/sec

>, E~

i

T,:27 msec i 2

L

6

8

10

12

14

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t msec FiG. 4. Autocorrelation function of pure diffusion from LUDOX HS40 in veronal buffer (pH 8.6, I = 0.005), 128 channels, and sampling interval 0.125 msec. The solid line shows the

single exponential best fit.

and HS40, dilution 1:20). Figure 4 shows the ACF of pure diffusion. The calculated single exponential function fits the experimental values well. The PS (power spectrum) after FFT (see Fig. 5) again is in good agreement with the expected Lorentzian. The angular dependence of the half-width at half-height of the Lorentzian (DK 2) for Ludox and albumin solution (BSA) is shown in Fig. 6. With some experience, it was possible to see even the slightest leakage of the electrophoresis cell by the appearance on the oscilloscope of definite unsteady low-frequency oscillations in the photomultiplier current. With the electric field on, one could watch the pure waveforms corresponding to the Doppler-type waveform patterns. These useful diagnostic advantages are not available when the voltage is periodically interrupted or pulsed. MATERIALS

Bovine Serum Albumin (BSA), purchased from Behringwerke, Marburg, West Germany, contained about 2-4% dimers and polymers. For

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Laser Doppler spectroscopy as applied to electrophoresis in protein solutions.

ANALYTICALBIOCHEMISTRY70, 506-525 (1976) Laser Doppler Spectroscopy as Applied to Electrophoresis in Protein Solutions R. MOHAN, R. STEINER, AND R. K...
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