without noise (8). Test results for the instrument used in this work are present in Tables I to IV. The results are in good agreement with those reported earlier. The results presented in Tables I, 11, and 111 are for various ranges of synthetic slopes that were measured by the ratemeter. Each listed rate measurement is a single ratemeter readout of counted pulses. The synthetic slopes were generated by a n operational amplifier wired as an integration circuit. The time constant was approximately one second. No attempt was made to calibrate the slope generator, but rather, the input voltage to the slope generator was varied over a wide range of voltages with the slope generated by a 1-millivolt input to the integrator serving as unity for the relative inputs to the ratemeter. Computer evaluation of linear least squares fits to data in various ranges shows good linearity. Table I11 demonstrates decreased linearity. This may be attributed to the tracking speed of the voltage-to-frequency converter imposing its limitation on the accuracy of the rate determination.
To verify the noise immunity of the ratemeter, sine waves of various frequencies and amplitudes were summed with a synthetic slope of approximately 100 millivolts per second. Table IV presents the test results for these measurements. Good noise immunity is indicated with relative errors and standard deviations generally well below the 0.25% maximum. These results are in good agreement with those reported earlier. The successful application of the ratemeter to chemical analyses in a completely automated reaction-rate system will be described in a later report.
ACKNOWLEDGMENT The authors acknowledge the technical assistance of Gary Speas, Environmental Systems Engineering, Clemson University. Received for review December 13, 1972. Accepted March 20, 1973.
Composite Interference Optics for the Analytical Ultracentrifuge Charles H. Chervenka and Lee Gropper SDinco Division of Beckman Instruments, lnc., PaIo Alto, Calif. 94304
The Rayleigh interferometer of the analytical ultracentrifuge ( I ) forms an optical pattern of fringes by constructive and destructive interference of light passing through two channels of the spinning centrifuge cell. Differences in refractive index in the solutions contained in the cell cause shifts or bending of the fringes in the pattern, and measurement of these changes allows the quantitative analysis of refractive index changes in the cell. In typical physicochemical studies of the properties of a macromolecule in the ultracentrifuge, a dilute solution of the sample is placed in one channel of the cell and solvent is placed in the other. Changes in the distribution of the sample in the cell under the influence of high centrifugal forces can be followed during the experiment by measuring the resulting refractive index changes from the interference patterns formed. The interference patterns formed represent the total of refractive index changes in the centrifuge cell, which reflects changes in concentration of the sample solution plus a contribution due to any inhomogeneity in refractive index of the transparent optical windows used to enclose the cell. In order to make a correction for the contribution due to the windows, it is common practice to repeat a part of the experiment with only water in the cell; the fringes formed then represent a base line of zero refractive index change for the cell contents. We have been seeking ways to include information relative to the base-line fringes directly on photographs of the sample patterns recorded during an experiment. A procedure is described here in which sets of interference fringes
are superimposed on the photographic plate. One useful and direct way to accomplish this is to use a centrifuge cell with three sectorially oriented channels instead of the usual two. If two adjacent channels are filled with solvent and the third with sample solution, for example, then the conditions for interference are met twice during each revolution of the rotor-first when the two channels containing solvent are aligned in the optical system, and second when one solvent channel and the solution channel are aligned. The resulting photographic record is then a composite of the two sets of fringes, containing information about both the base-line conditions and the distribution of sample in the cell.
(1) E G Richards and H K Schachrnan, J Phys C h e m , 63, 1578
( 2 ) A. T. Ansevin, D. E. Roark, and D. A. Yphantis, Anal. Biochem., 34, 237 (1970).
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APPARATUS AND PROCEDURES The Beckman/Spinco analytical ultracentrifuge was used in this work. The triple-sector concept in its simplest form can be used with no modification of the interferometric optical system of the ultracentrifuge. Only a special cell is required. One configuration of the cell-the unsymmetrical type-uses the standard double-sector cell housing and windows, but requires extra-wide aperture window holders and a special centerpiece as illustrated in Figure 1A. The clarity of the resulting fringes can be improved considerably if a three-slit limiting mask is used in the cell between the lower window and its holder. This mask can be machined from phosphor-bronze stock of 0.025-cm thickness, as shown in Figure l A , with 0.40-cm spacing between slits. Window distortion a t high speeds can be reduced by using polyvinyl chloride window liners, in place of the usual linen-bakelite liners (2). The cell is assembled so that one slit of the mask is over the narrower of the channels, and the other two are over the wider channel. Sample solution is placed in the narrower channel and
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
Figure 1. Centerpieces and masks used lor composi., Interference optics: (A) unsymmetrical type. (E) Symmetiicsl type
solvent in the other. The cell is then placed in a rotor along with an interference counterbalance and run in the ultracentrifuge as the conditions of the experiment require. Photographic records are made as needed. An example of the composite fringe patterns obtained in a sedimentation equilibrium experiment is shown in Figure ZA. The horizontal fringe pattern is generated as a result of interference between the two beams of light through the two slits over the solvent channel, the upward sloping fringes result from interference between beams through one solvent slit and the slit over the sample channel, and the diffuse vertical lines on the pattern result from mutual cancellation of the two overlapping fringe patterns. This cell can he used with schlieren optics in the same way that the usual double-sector interference cells are used. A more versatile version of the triple-sector cell can be made by using a Centerpiece with three sepslate channels, as shown in Figure 1B.One type of light-limiting mask for this cell has the three slits placed symmetrically around the centerline, with 0.40-cm spacing between slits. A special cell housing with three filling hole plugs can be used, or a standard housing can be used and the channels filled before the upper window and holder are assembled into the cell. This symmetrical cell can be used in the same way as the cell in the first example, and the same type of composite patterns is obtained. Several alternate procedures are possible with the symmetrical configuration, however. One interesting variation results when the sample is placed in the central channel and solvent in the other two. In this case, base-line fringes are not formed. Both sets of fringes are generated between solvent and solution, but the bending of the fringes is in opposite directions for the two sets. As shown in Figures 2 8 and ZC, this results in B deflection between conjugate fringes in the two sets equal to twice that for sample and hase-line fringes. Thus, the sensitivity of the interference optics for measuring changes in refractive index is effectively doubled. The symmetrical-type cell can he used also with a half-plane, half-wedge window to completely separate the two sets of fringes. In this case, a four-slit limiting mask is used to improve the clarity of the fringes. In this mask, the spacing between inner and outer slits of both sets is 0.40 em, and the spacing between the two inner s l i b is 0.2 em. In experiments using the available window, which has a 1" wedge, the fringes in the deviated image were somewhat distorted, however. The reason for this is not known, hut further investigation of this procedure is planned. Further variations are possible by changing the interference slit mask at the condensing lens of the optical system. Normally, this mask has two slits with B center-to-center spacing of 0.40cm. The fringe spacing at the image plane of the interference optical system is defined by
fringe apace =
Ad
S
where h is the wavelength of light used, d is the distance between the cell and the image plane of the condensing lens, and s is the distance between the interference slits. By using a slit mask with a spacing of 0.6 cm instead of 0.4 em, the fringe spacing will be deneased by one-third, and the number of fringes per millimeter on the photographic plate will be increased by one-half. Thus, for plate reading methods which depend upon the fringe density (an example will he described later), the number of experimental values obtained is increased proportionately. The four-slit cell mask used with the symmetrical centerpiece and plane windows
Figure 2. Representative composite fringe patterns (A) Sedimentation-diffusion equilibrium in the unsymmetrical-type cell. Lysozyme in initial concentration 01 2.0 mg/ml in 0.15M NaCI. Run at 20.000 rpm and 17.5- for 20 hr. (B) SedimBntation-diffUSion equilibrium in the symetrical-type cell. Lysozyme in initial Concentration of 1.0 mg/ml in 0.15M NaCI was placed in the middle channel 01 the cell. Run at 22.000 rpm for 21 hr. IC) Sedimentation Velocity in the symmelricaltype cell. y-Globulin in Initial Concentration of 2.0 mg/ml in 0.15M NaCI. Run at 56,000 rpm for 15 mi"
provides the 0.6-cm slit spacing required in the cell to match that of the eondensing lens mask. Use of a condensing lens mask with three slits allows still further variations in the patterns obtained. In this case. the unsymmetrical centerpiece was used with a cell mask with 0.20-cm slit spacing over the solvent channel and 0.40-cm slit spacing over the sample-solvent channels. The condensing lens mask had three slits with 0.20-em spacing. Thus. the sample fringes are normal, while the solvent-solvent fringes have twice the normal spacing, and are doubly exposed compared with the sample fringes.
USE FOR MOLECULAR WEIGHT DETERMINATIONS The crosshatch t y p e p a t t e r n s obtained w i t h the triplesector cells m a k e possible a simple procedure for evaluating the composite interference images i n sedimentation
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equilibrium experiments. Each of the vertical shaded regions of the composite image, resulting from mutual cancellation between the two sets of fringes, marks a fringe shift in the sample set of one whole fringe relative to a n adjacent shaded region. Each shift of one fringe is proportional to an incremental change in refractive index in the sample channel relative to the solvent channel, and to a close approximation, each fringe shift is proportional to an incremental change in concentration in the sample channel ( I ) . Thus, by measuring the radial position of the center of each shaded region, one obtains a data set of relative concentration in the cell as a function of radius. With a knowledge of the initial sample concentration in fringes, solute molecular weights can be computed from these data by the usual methods ( I ) . For sedimentation equilibrium experiments in which the meniscus concentration is low, but not zero as in the meniscus depletion technique of labeling fringes ( 3 ) , fringe shifts can be related directly to zero concentration by the use of the triple-sector cell. In this case, white light photographs ( I ) are taken when the equilibrium condition is attained, in addition to the usual monochromatic light photographs. The vertical distance in fringes between the central fringe of the sample set and the central fringe of the solvent set is now proportional to concentration on a n absolute basis. An alternate procedure, which we have called the fringe slope method, allows the computation of reduced molecular weights from only the relative fringe positions us. radius data and a knowledge of rotor speed and temperature. Initial concentration need not be known, and measurements of the fringe patterns a t the extreme ends of the fluid column image are not normally required. By evaluating the slope of the fringes, which is dcldr, as a function of radial distance on the pattern, the molecular weight of the solute can be calculated by method I1 of Van Holde and Baldwin ( 4 ) . For ideal solutions, the following relation is used.
fringe can be computed by taking the reciprocal of the radial distance between each two adjacent fringes. The term on the right of Equation 2 is evaluated as the graphical slope of a plot of l / r A r us. N h c, where N is the sequential number of the fringe increment. The number of data points can be doubled by using increments of 0.5 fringe, in which case the same principles and methods of calculation apply. The additional radial measurements are made a t the center of each vertical region of enforcement between the two sets of fringes. For the experiment which yielded the fringe pattern shown in Figure 2A, a molecular weight for the protein lysozyme was determined to be 1.46 x lo4, using a value of 0.703 ml/g for the partial specific volume ( 5 ) and 1.005 g/ml for the solution density. This molecular weight can be compared with the value of 1.44 x lo4 reported by Sophianopoulos et al. ( 5 ) .
Here M and ij are the molecular weight and partial specific volume of the macromolecule, p is the density of the solution, R is the gas constant, T is the temperature in degrees Kelvin, w is the rotor speed in radians per second, r is the radius, and c and dc/dr are the concentration and concentration gradient of the macromolecular solute. For heterogeneous solutes, z average molecular weights are obtained. The fringe slope method depends upon the linear inverse relationship between the radial spacing of fringes and their slope. The concentration gradient a t the midpoint of each interval between two adjacent fringe positions can be approximated closely by Ac/Ar, where Ar is the radial distance between the two positions, and Ac is the increment of concentration between readings which is constant and equal to one fringe. Thus, the slope of the fringes at the midpoint of each radial increment of one
DISCUSSION This is a preliminary report on a new concept in interference optics for the ultracentrifuge. A wide variety of composite interference patterns is possible by varying the number of channels in the cell, by different cell fillings, and by using interference slit masks with different numbers, spacings, and widths of slits. Only a few of the possible combinations have been described here. Potentially, the best prospect for the use of the triplesector concept in interference optics would be to avoid the uncertainties in the measurements of fringe patterns due to cell distortion. The method described here for evaluating the composite patterns from the radial spacing between regions of fringe cancellation does compensate for deviations of the base-line fringes from straightness. That is, the slope of the fringes at points across the pattern is relative to the slope of the solvent-solvent fringes. What is unsure is whether or not a contribution to the sample fringe pattern due to window distortion is adequately represented by the shape of the solvent fringes. The obvious test-to fill all sectors with water and look for superimposition of the two sets of fringes-has been made with the two cells used in this study. The results were somewhat variable, although, in general, good superimposition of the patterns was found over the range of speeds normally used for sedimentation equilibrium experiments. More work along these lines and some additional considerations of centerpiece construction and design are needed, however, before it can be said that the problem of cell distortion has been circumvented. The fringe slope method which is described here has advantages in that the initial concentration need not be known, and the plate measurements and calculations are simple to make. This method can be applied also to the usual kinds of fringe patterns obtained when double-sector cells are used with interference optics, with the same advantages. For samples which are mixtures of species of different molecular weight, z average molecular weights are obtained. Received for review November 13, 1972. Accepted March 15, 1973.
(3) D. A. Yphantis, Bochemistry, 3, 297 (1964). (4) K . E. Van Holde and R. L. Baldwin, J. Phys. Chem., 62, 734 (1958).
(5) A. J. Sophianopoulos, C. K. Rhodes, D. N. Holcomb. and K. E. Van Holde, J. Bioi. Chem., 237, 1107 (1962).
.I1 dc\
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