[120] Sedimentation equilibrium in a buoyant density gradient

854

[119]

SPECIAL TECHNIQUES

line extending outward between the troughs from the point where the reactants are closest (Fig. 6). The angle (0) between the straight precipitin band and the antigen trough is such that tan 6 :- ( D J D b ) ~/2, where Dg and Db are the diffusion coefficients of antigen and antibody, respectively. The diffusion coefficient for all rabbit antibodies may be considered the same and taken as 3.8 X 10-7 cm.2/sec. The best straight line will be obtained if the amounts of antigen and antibody in the troughs are near optimal proportions. Gross deviations from these amounts will result in the band's curving and spreading toward the trough with the weaker reactant. With this technique, the diffusion coefficients of unrelated antigens may be measured in a mixture, as the precipitin bands form independently. The values obtained for several proteins, as measured in our laboratory, are listed in the table and compared with values obtained by free diffusion techniques. DIFFUSION COEFFICIENTS OF PROTEINS AS MEASURED BY Two-DIMENSIONAL IMMUNODIFFUSION D2OH20 Antigen H u m a n serum albumin Ts bacteriophage Thyroglobulin Rhodospirillum h e m e protein C y t o c h r o m e (Rhodospirillum rubrum) Pepsinogen P22 bacteriophage

Angle 0

Immuno

52.7 ° 9.7° 40.5 ° 58.0 ° 58.4 ° 56.6 ° 18.1 °

6.54 X 10 -7 0.11 X 10 -7 2.77 X 10 -7 9.73 X 10 -7 10.03 X 10 -7 8 . 7 X 10 -7 0 . 4 × 10 -7

[ 120] S e d i m e n t a t i o n E q u i l i b r i u m Density Gradient

Free 6.1 X 10 -7 0 . 3 X 10 -7 2.65 X 10 -7 8.65 × 10 -7 9.69 X 10 -7 (pepsin)

in a B u o y a n t

B y J E R O M E VINOGRAD

Introduction Equilibrium ultracentrifugation in a density gradient is a recently developed method I for the study of macromolecules, viruses, and particulate materials. A homogeneous mixture of a concentrated binary solvent and a dilute macrospecies are brought to sedimentation-diffusion equiI M. Meselson, F. W. Stahl, and J. Vinograd, Proc. Natl. Acad. Sci. U.S. 43, 58! (1957).

[120]

SEDIMENTATION EQUILIBRIUM IN A DENSITY GRADIENT

855

librium in the ultracentrifuge. The new distribution of the concentrated binary solvent presents a stable density gradient. At the same time the macrospecies concentrates to form a band in the redistributed binary solvent. After equilibrium is established, the macrospecies at band center is neutrally buoyant in the redistributed binary solvent. The buoyant density of the macrospeeies and the density of the binary solvent at band center are identical. With a homogeneous macrospecies a Gaussian concentration is formed about the center of the band. At this position centrifugal forces on the macrospecies vanish. Only diffusional forces cause the macrospecies to spread away from band center. The spreading is opposed by both centrifugal and centripetal forces, and an equilibrium concentration distribution results. Larger macromolecules diffuse less readily and form narrower bands than smaller macromolecules. The variance, a 2, of the Gaussian distribution has been shown to be given by Eq. (1). 2 The gas ~

=

RT M ,.o(dp/ dr ) e,.#8,o~2ro

(1)

constant, temperature, angular velocity, and radial distance to band center are R, T, ~o, and ro, respectively. The quantities Ms, o, (dp/dr)e,,o and 0~,,o are the solvated molecular weight, the effective density gradient, and the partial specific volume of the solvated species, respectively; all the foregoing quantities are given at band center as indicated by subscript zero. The quantity 08.o is identical with the reciprocal of the buoyant density, ps, o. Mixtures of materials of identical buoyant densities and differing molecular weights form symmetrical but non-Gaussian bands. From the shape of the bands, weight and number average molecular weights, both solvated and nonsolvated, may be evaluated. 1,2 A skewed band indicates buoyant density heterogeneity. Materials of sufficiently different buoyant densities in a mixture form bimodal or polymodal bands. We have, therefore, a general method for'recognizing heterogeneity among macromolecules. In a special but important exception, density heterogeneity may be contained within Gaussian bands and, at first sight, may not be recognized2 ,4 Since this procedure was first described, it has come into extensive use. Most of the applications derive from the fact that the macrospecies are separable and identifiable on the basis of buoyant density, a newly accessible physical property of a dissolved macrospecies. The procedures "~J. E. Hearst and J. Vinograd, Proc. Natl. Acad. U.S. 47, 999 (1961). 3 R. L. Baldwin, Proc. Natl. Acad. Sci. U.S. 45, 939 (1959). 4 N. Sueoka, Proc. Natl. Acad. Sci. U~. 45, 1480 (1959).

856

SPECIAL TECHNIQUES

[120]

for carrying out these experiments are simple, involve relatively little personal skill, and are easy to reproduce. Density gradient experiments are performed in either preparative or analytical ultracentrifuges. The concentration distributions at equilibrium are independent of the shapes of the containers, and Eq. (1) is valid in both types of equipment. At the present time aqueous CsC1 is the most widely used buoyant solvent. Deoxyribonucleic acids, polypeptides, proteins, viruses, and ribosomes have been studied in CsC1 density gradients. Ribonucleic acids and some polynucleotides are too dense for even saturated aqueous CsC1 at 25% These macromolecules have been studied in aqueous cesium formate ~,6 and cesium sulfate 7 solutions. The choice of the medium depends on experimental and theoretical considerations which are discussed below. In the experimental section aqueous CsC1 will be regarded as the buoyant solvent unless otherwise stated. Experimental Procedure

1. Preparation o] Solutions. The solutions are prepared by volumetric combination of a concentrated CsC1 stock solution, water, buffer, and macromolecule solutions. Graduated serological pipets and micropipets are used. Occasionally when the maeromolecular material is available only in dilute solution, weighed amounts of solid dried salt are added. For volumetric work, additive mixing relations are satisfactory [Eqs. (2a) and (2b)]. The subscripts w and c refer to water and the concen(Pc - - P ° ) / ( P c - -

0.997)

(2a)

V= = r e ( p c - - p O ) / ( p O _

0.997)

(25)

Vl,= =

trated salt solution. The quantity po is the desired density. The subscript 1 in Eq. (2a) indicates the volume required to prepare 1 ml. of solution. Stock solutions are stored in plastic bottles, and solutions are made up in well-stoppered glass vials. Densities are checked ret~ractometrically before the experiments are set up. The relations between refractive index and density and between weight composition and density are useful aids in the preparation of solutions [Eqs. (3a) and (3b)]. These relapO,~5. = lO.8601nD~ o -- 13.4974

(3a)

Wt.% = 1 3 7 . 4 8 - 138.11(1/p °,~°)

(35)

~H. Dintzis, H. Borsook, and J. Vinograd, i n "Microsomal Particles and Protein Synthesis" (R. B. Roberts, ed.). Pergamon, New York, 1958. C. I. Davern and M. Meselson, J. M o l . B i o l . 2, 153 (1960). ' R. G. Wake and R. L. Baldwin, J. M o l . B i o l . submitted.

[120]

SEDIMENTATION EQUILIBRIUM IN A DENSITY GRADIENT

867

tions are valid in the density range 1.2 to 1.9 g./ml. Several such relations for other salts in water have been collected2 Densities accurate to ___0.001 g./ml, are easily measured with a pair of calibrated 0.3-ml. micropipets used as pycnometers. The pH of the solutions is adjusted with buffer solution or with acid or base and may be measured with standard glass and reference electrodes. Cesium chloride, like KC1, suppresses the liquid ]unction potential and does not interfere with the measurement of pH. The high salt concentrations affect the ionization constants of the buffer acids and bases. Shifts in pH of 0.5 unit have been observed 9 on dilution of some buffers into 7 molal CsC1 instead of water. The concentration of the macrospecies, Co, at band center in a Gaussian concentration distribution is related to the initial concentration, C~, of the uniform solution, the standard deviation o f the band, and the length of the liquid column, L [Eq. (4a)]. The extreme concentration Co = 0.40(L/~)C~

(4a)

gradients at the inflections are given by Eq. (4b). These equations were

(~r). = ~0.24(L/a~)Cu

(4b)

derived for cells with parallel walls but are sufficiently accurate for the preparation of solutions. The maximum concentration at band center is limited by experimental considerations and by the virial coefficients if molecular weights are desired. The minimum concentration detectable by absor~)tion optics in the analytical ultracentrifuge corresponds in the case of narrow bands in a 12-mm. centerpiece to an optical density of approximately 0.02. A suitable initial concentration of DNA is approximately 1 ~g./ml. 2. Time o] Approach to Equilibrium. The three-component solution is initially homogeneous. With the application of the field, redistribution of the binary medium to form the density gradient is followed by twodirectional accumulation of the macrospecies to form the band. The relative rates of the two processes depend on the sedimentation properties of the components. If the macrospecies has a large sedimentation coefficient, e.g., viruses, the species will within an hour or less find its buoyant position. The rate-limiting feature is then the time required for the medium to reach equilibrium. At 44,770 r.p.m., a 1.2-cm. liquid column of CsC1 at density 1.70 g./ml, is substantially at equilibrium at 8j. Vinograd and J. Hearst, Progr. in Chem. Org. Nat. Prod. 20, 372 (1962). 9j. Vinograd, J. Morris, N. Davidson, and W. F. Dove, Proc. Natl. Acad. Sci. U~. 49, 12 (1963).

858

[120]

SPECIAL TECHNIQUES

12 hours. Procedures for calculating rate of attainment of equilibrium in two-component systems are given by Van Holde and Baldwin. 1° With macrospecies of lower sedimentation coefficients the rate of band formation is slower. A good estimate of the time required to attain equilibrium within 1% everywhere between band center and ___2a is given by the Eq. (5). TM The diffusion coefficient is D, and the length of ~ (L ) t* -- ~ In ~ -I- 1.26

L >> cr

(5)

the liquid column is L. Equation (5) was derived with the assumption that the equilibrium density distribution pre-exists before band formation begins. For globular proteins and most DNA samples, 24 hours is adequate at high angular velocities. At lower velocities the time required increases rapidly because the lead term, a 2, is inversely proportional to the fourth power of the angular velocity. 3. Equipment. Substantially standard commercial ultraeentrifuges are used for density gradient sedimentation. The machines should be well maintained so that they may be left unattended for the 12-hour to 4-day periods required for the runs. The schlieren light source with its water supply in the analytical ultracentrifuge is normally turned off during overnight runs. Metal centerpieces are avoided because of corrosion problems. Centerpieces fabricated from Kel-F and Epon resins are satisfactory for most runs. Cell leaks are avoided in experiments at high speeds and high densities by tightening with a torque of 115 inch-pounds. Cell parts are carefully cleaned and lubricated before assembly. In the author's laboratory it has been found that wear on the rotating parts of the ultracentrifuges is small in long runs, and that drives need replacement less frequently than in short-run operation. 4. Setting Up Runs. Standard procedures for sedimentation velocity experiments are used in setting up density gradient experiments in the analytical ultracentrifuge. The density gradient generates a prism in the liquid column, causing the light rays to be bent away from the axis of rotation. If the effective prism is large enough, the light is obstructed at the camera lens holder. A --1 ° quartz window at the top of the cell alleviates this problem but does not correct for errors in apparent concentration which arise from light rays passing through the cell at a small angle to the axis. 12 Window breakage traceable to high pressures, 56,100 r.p.m., density 2.05 g./m]., has not been encountered. Monochromaticity of the ultraviolet light is improved with a Corning No. 9683 filter. High'" K. E. Van Holde and R. L. Baldwin, J. Phys. Chem. 62, 734 (1958). " M. Meselson, Doctoral Dissertation, California Institute of Technology, 1957. 1, j . E. Hearst and J. Vinograd, J. Phys. Chem. 65, 1069 (1961).

[120]

SEDIMENTATION EQUILIBRIUM IN A DENSITY GRADIENT

859

quality double-cell runs are now performed with small light-source slits, side-wedge bottom quartz windows, a long exposure clock, and an alternator2 ~ Double-cell schlieren optical runs are routinely performed with upper windows differing in wedge angle by 1 ° . Double-sector cells of filled Epon or Kel-F have been routinely used at 56,100 r.p.m, and density 1.3 g./ml. Preparative ultracentrifuge runs are performed in swinging bucket rotors. The SW-39 rotor is normally filled with 2 ml. of liquid and overlayered with 2.5 ml. of light mineral oil to prevent tube collapse. The rotors are run at 35,000 r.p.m, to compensate for the increased load and to provide an extra safety factor. Three experiments can be run at once. 5. Recording o] Results. Three methods are available for recording results in the analytical ultracentrifuge. These are absorption optical photographs, schlieren optical photographs, and autoradiograms. ~4 Autoradiographic experiments may also be performed in the preparative ultracentrifuge with a modified analytical rotor. In the various kinds of experiment, different approaches are taken to the problem of recording results. When buoyant positions are sought, experiments may be performed at high speeds and at relatively high concentrations. When accurate band shapes are of interest, approximately optimum quantities of macrospecies must be introduced so as to obtain concentration distributions with accuracy. In the absorption optical system a maximum optical density change through the band should not exceed a value of 1.5, so that the image remains in the linear range of the characteristic curve of the film. According to Eq. (4a), the concentration at band center is inversely proportional to the square of the angular velocity. Similarly with the schlieren optical system the initial concentration is limited so that refractive index gradients do not exceed the limits of the optical system. Combining Eqs. (1), (4b), and (13), we obtain an expression for the magnitude of the extreme concentration gradients in the band [Eq. (6)]. An initial concentration of 0.1% bovine

dc) = =F0.24L M ~effoo4ro~ -~ ±~ poRT

(6)

mercaptalbumin is satisfactory for runs in CsC1, p ° = 1.3 g./ml., at 56,100 r.p.m. 15 A change in the molecular weight or in the buoyant medium will require the indicated change ih the angular velocity. Changes in refractive index increment also have to be considered with lSR. Inman and R. L. Baldwin, J. Mol. Biol. 5, 185 (1962). 14j. Vinograd and R. Kent, unpublished observations. 15j. B. Ifft and J. Vinograd, J. Phys. Chem. 66, 1990 (1962).

860

SPECIAL TECHNIQUES

[120]

Eq. (6) when the buoyant solvent is changed. Wales TM has shown that the second viral coefficient causes the band to widen with concentration. The band width derived from the separation between the maximum and minimum gradients for polystyrene in an organic binary buoyant solvent could be extrapolated to zero concentration in a linear plot of the standard deviation versus square root of the concentration. The ultraviolet optical system is usually chosen to record results in the analytical ultracentrifuge with nucleic acids and virus. Careful alignment of the optical elements so as to obtain light parallel with the optic axis and uniform illumination of the cell are required for accurate work. Optical elements must be clean. At the end of the run a series of exposures of increasing time is made; the film is developed and traced with a densitometer linear in optical density. Linearity is verified with the trace of an exposure made by an exponential aperture 17 in the rotor or the counterbalance. An alternative test is the superimposability of tracings from successive exposures. Pedersen TM has presented an extensive discussion of the ultraviolet optical system, and the reader is referred to this article for details. The problem of obtaining accurate records in density gradient experiments for molecular weight calculations is comparable with that encountered in two-component sedimentation equilibrium experiments. It is simpler in that base lines may be interpolated but more difficult in that smaller linear distances are involved. A density gradient experiment is essentially a short liquid-column experiment, with the length of liquid column corresponding to 4 to 6 a. It is free of difficulties normally encountered near the top and bottom bounds of the liquid. Photographic records from the schlieren optical system are of value in several types of experiment. DNA and viral bands may be located with precision. TM Banded precipitates and dissolved macrospecies may be easily differentiated.2° A main use is encountered in the study of small proteins 15 and nonabsorbing macrospecies. The requirements that the buoyant solvent not absorb at 265 m~, that the cells be uniformly illuminated, and that the films be linearly developed may be relaxed. For quantitative work, interference boundary-forming double-sector cells are usedJ 5 The reference sector is filled with a slight excess of salt 1~M. Wales, J. Appl. Polymer Scl. submitted. 1,E. Robkin, M. Meselson, and J. Vinograd, J. Am. Chem. Soc. 81, 1305 (1959). K. O. Pedersen, in "The Ultracentrifuge" (T. Svedberg and K. O. Pedersen, eds.). Clarendon, Oxford, 1940. loj. E. Hearst, J. B. Ifft, and J. Vinograd, Proc. Natl. Acad. Sci. U,8. 47, 1015 (1961). ~*J. Vinograd, J. Morris, and R. Greenwald, unpublished observations.

[120]

SEDIMENTATION E Q U I L I B R I U M IN A DENSITY GRADIENT

861

solution of the same density as the solution containing the macrospecies. Liquid levels become identical on acceleration of the rotor. An accurate base line is then superimposed in photographs taken at equilibrium. The photographic plate is traced under an enlarger, the base line is subtracted from the diphasic schlieren curve, and the concentration distribution is calculated by numerical integration procedures. The final photographs are exposed at phase plate angles of 85 ° to 55 ° . Disks of photograph film protected from the CsC1 solution by 0.5-rail Mylar can be centrifuged without distortion in standard analytical ultracentrifuge cell assemblies. 1~ The cell assemblies are provided with Dural windows and are filled under red light. Because the radioactive macrospecies is initially dilute relative to the final distribution in the band [c~. Eq. (4a)], it is a simple matter to adjust the time of ultracentrifugation and the dose of radioactive species so that clean bands appear on the photographic film. The experiments have been performed with standard 12-mm. Kel-F, double-sector 12-mm. Epon, double-sector 3-mm. Epon, and special triple-sector 1.5-mm. Kel-F centerpieces. No-screen X-ray film is used to form autoradiograms of p32_ labeled viruses and DNA. A direct image of the liquid column appears as a gray background when C14-1abeled leucine is present in the CsCl solution. Because of the long range of p~2 electrons, the resolution of bands is poorer than in photographic procedures. These experiments require 24 to 48 hours and need very small amounts of radioactive macrospecies 40 to 1800 c.p.m, or 1.7 to 2.5 c.p.m, per 0.001 ml. of solution. Approximately 250 to 500 c.p.m, of C14-1eucine per microliter are used. The entire experiment is easier to perform than the preparative ultracentrifuge experiments. In the analytical ultracentrifuge the maximum angular velocity is one and one-half times as great as in the preparative ultracentrifuge with swinging bucket rotors. Obvious advantages result in the shorter time of approach to equilibrium, narrow band width, higher concentrations at band center, and greater range of densities. The preparative ultracentrifuge with a modified analytical rotor may be used at 50,000 r.p.m, for autoradiogram experiments. Experiments in swinging bucket rotors are indicated whenever isolation of the materials is required for either preparative or analytical purposes. The plastic test tubes are removed from centrifuge containers and mounted in a rubber stopper sleeve on a ring stand. The plastic tubes are connected with a smaller rubber stopper to a container with variable air pressure so that the rate of drop formation is controllable. The plastic test tube is pierced with a sharp needle, and drops are collected individually or in groups in small test tubes previously lined up in racks. Three

862

SPECIAL TECHNIQUES

[120]

simple pressure-control systems used at the California Institute of Technology are shown in Fig. 1. Szybalski ~1 has described a somewhat more complicated device.

FIG. 1. Three types of apparatus for pressure control in dropwise analysis of density gradient experiments. The fractions obtained with relatively little mixing are analyzed for macrospecies by optical density, radioactivity, and biological activity, and for density by refractive index. The combination of the former three measurements provides an elegant procedure ~2 for specifying density homogeneity of biologically active materials such as viruses and infective nucleic acids. Calculations and Theory 1. Buoyant Density Determinations. The buoyant density of a macrospecies was defined for Eq. (1) as the density of the medium at band center. This solution is normally at a pressure of 100 to 200 atm. and is several thousandths of a unit more dense than a solution of the same composition at atmospheric pressure. The error introduced by ignoring pressure effects, 1/~,,o = p~,, ~ po°, is less than 1% and at present is of no significance in applying Eq. (1). The quantity po° is the density at atmospheric pressure of the solution at band center. Buoyant densities have come to be of substantial importance in desig2~S. Szybalski, Experlentla 16, 164 (1960). L. Levintow and J. E. DarneU, Jr., J. Biol. Chem. 235, 70 (1960).

[120]

SEDIMENTATION EQUILIBRIUM IN A DENSITY GRADIENT

863

nating the composition and structure of DNA from various sources. Buoyant positions and buoyant densities can be measured with an accuracy of _+0.001 g./ml. Differences in buoyant density can be measured with still greater accuracy. It is important, therefore, that the nature of the pressure effects be understood. It has been shown 19 that increasing the hydrostatic pressure over a CsC1 density gradient causes the liquid column to compress. Otherwise the salt distribution does not change. Thus pressure merely adds a compression gradient to the composition gradient. The relative position in the liquid column for any salt composition is independent of pressure. A buoyant density may therefore be expressed as the composition or density at atmospheric pressure with no ambiguity arising from the effects of pressure on the gradient column. However, the buoyant species compresses differently than does the CsC1. Bands of DNA and TMV move toward the top of the liquid column when hydrostatic pressure is applied. TM There is no way of avoiding the specification of pressure in specifying a buoyant density. The buoyant density of reference DNA should be determined with cells that are about 90% full (0.70 ml. in a 4 ° sector) and run at a speed of 44,770 r.p.m. The pressure at the rootmean-square position in the liquid column is 150 arm. Alternatively, experiments at various pressures may be performed so that results can be expressed as the density of the salt solution at band center for a band which is itself at atmospheric pressure. This quantity is the reciprocal of the partial specific volume of the solvated species at atmospheric pressure. Pressure correction terms arising from variable speeds can now be made only for native T-4 DNA and for TMV. The next problem in expressing buoyant densities of DNA is to establish the isoconcentration position, re, in the gradient column. ~3 It is at this position that the original salt composition will be found. For DNA in CsC1 the isoconcentration distance is readily calculated with Eq. (7), r. --- %/(r, 2 ~- rb2)/2

(7)

where the subscripts t and b refer to the radial distances at top and bottom of the liquid column. For other densities and for other salts a general procedure for calculating re has been described. 23 In a 1.2-cm. liquid column in the analytical cell the isoconcentration distance is 0.03 cm. below the center of the liquid column. The choice of the center of the cell as the isoconcentration distance leads to buoyant densities which are 0.004 g./ml, too high with a density gradient of 0.12 g./ml. ~J. B. Ifft, D. H. Voet, and J. Vinograd, J. Phys. Chem. 65, 1138 (1961).

864

SPECIAL TECHNIQUES

[120]

For a new material, buoyant densities are best determined by using two solutions which form bands on either side of the isoconcentration distance and then interpolating. If the distances are not large, the assumption that the density gradient is constant over the interpolation is satisfactory. 2. The Density Gradient and the Use o] Density Markers. The sum of the composition density gradient and the compression density gradient is called the physical density gradient. In CsC1 solutions the compression gradient accounts for 8 to 10% of the total gradient, and this relative contribution is independent of the angular velocity. Whereas the physical gradient is used in calculating densities in the liquid column, and the composition gradient is used in calculating compositions in the column, the buoyancy density gradient 1~ [Eq. (8)] is used to calculate the

[1o

]

composition of the solution that bands the macrospecies at the isoconcentration distance from data relating the band position and solution density. The quantity flo° is the coefficient in the differential equation for sedimentation equilibrium in a two-component incompressible system [Eq. (9)]. The quantity po° is the density at band center, and ro is the (dp) o~'r ~rr ¢omp -- 80°

(9)

average of the radial distances to band center and the isoconcentration distance. The buoyancy density gradient is also obtained in a two-cell experiment from the distance between bands and the densities of the two solutions [Eq. (10)], where pc,2° and pc,1° are the densities of the initial

(dp)= -~r ~.o

p,.Op,.O (ro.~ -- r,.2) -- (ro.l -- r,.,)

(10)

solutions, to,2 and ro,1 are the distances at band center, and re,2 and re,1 are the isoconcentration distances. The term ¢ arises from the fact 2 that bands seek out slightly different salt compositions in buoyant media of different density, p°, because of the variation of band position with pressure. The pressure dependence of band position 2 results from the difference in the compressibility of the buoyant solvent and the apparent compressibility of buoyant macrospecies, and also from the variation of solvation with salt concentration. A convenient and accurate method of determining buoyant densities of DNA is to band a DNA together with a well-studied reference DNA

[120]

SEDIMENTATIONEQUILIBRIUM IN A DENSITY GRADIENT

865

in the same solution. ~ The difference in buoyant density is then given by ]~q. (11), where f~b,0° is the average value of fib,0°. The quantity Ar

AS= ~ o~oAr

(11)

is the distance between the bands. The assumption is made in the foregoing procedure that ~ for all DNA samples will be the same. The alternative procedure is to ignore the pressure contribution. This is equivalent to assuming that ~ ----0 in all cases. The equation then used is Eq. (12), where/~o ° is the term in brackets in Eq. (8). 1 Ap = ~0o ~2~0 Ar

(12)

3. Molecular Weight Determinations. Inspection of the derivation of Eq. (1) reveals that the net result of any phenomena affecting the buoyant density, 1/Vo,,, or the solvated molecular weight, Mo,,, linearly about band center is to change the density gradient, (dp/dr)~. The effective density gradient with two such variables taken into account-the dependence of solvation on salt composition and the effects of press u r e - h a s been shown ~,~5 to be (~r)~f,,o -- (~oO T ~bp°') ( 1 - a)oo~r

(13)

where

a = \-~al]~ \dp ° ]

and

~b = (1 - a)

where (~po°/~al)p is the slope of the plot of buoyant density versus water activity, and (dal°/dp °) is the reciprocal of the slope of the plot of solution density versus water activity. Both slopes are taken at the intersection of the plots. The quantity ~ is evaluated from the pressure dependence of band position. Curves for DNA in a variety of cesium salts 2e are shown in Fig. 2. In CsC1, a ----0.24, and ~po, _ 0.66 X 10-1° c.g.s. The effective density gradient, Eq. (13), is decreased 7% by ignoring the ~po, in the first term and increased 31% by ignoring the a in the second term. The solvated molecular weight will then be 23% too low. The solvation for T-4 bacteriophage DNA is, however, 28%. Thus by a coincidental cancellation of errors, Eq. (14) gives within 5% the ~ R. Rolfe and M. Meselson, Proc. Natl. Acad. Sci. U,8. 45, 1039 (1959). J. W. Williams, K. E. Van tIolde, R. L. Baldwin, and H. Fujita, Chem. Revs. 58, 715 (1958). Nj. E. Hearst and J. Vinograd, Proc. Natl. Acad. Sci. U~g. 47, 1005 (1961).

866

[120]

SPECIAL TECHNIQUES

RT M,~h (dp/ dr ) o. . . . p~,.~r

a2 =

(14)

anhydrous molecular weight of cesium DNA in CsC1. It is not to be expected that similar good fortune will attend the study of other systems. 4. Quantitative Analysis o] Macrospecies. The photographic record of absorbance may, after densitometry, be used to calculate the amount of macrospecies in a band. The calculation procedures require data from the simultaneous exposure of an exponential aperture in the rotor. Directions for carrying out these calculations have been published. 17 The accuracy of the procedure is limited by small effects due to the failure of the reciprocity law for photographic film.

2.2 ~'2.0 1.8

I

I

I

I

I

]

I

I

I

I

CsDNA

~~CsCI

CsBr

._<5 1.4

1.0

o'.2

3.4

o'.s

o'.6

o'.7

0'8

o19

,.o

a,~, water activity

FIG. 2. B u o y a n t density of T-4 bacteriophage D N A and solution density of various cesium salts versus water activity. ~

Concentrations may be calculated from schlieren photographs, providing the refractive index increment of the macrospecies in the buoyant solvent and the instrument constants are known. The evaluation of total infectivity, radioactivity, or optical density in a band in the preparative ultracentrifuge requires only simple summation of analytical results on the single drops. The hazardous assumption of constant drop volume is involved in the summation procedure. The assumption may be avoided by weighing the individual fractions. 5. Resolution o] Macrospecies. The resolution of two homogeneous macrospecies in a buoyant density experiment is independent of angular velocity. Increasing tl/e velocity narrows the bands but causes them to approach each other. Resolution, however, may be improved by using salts which give lower density gradients at a given speed. 8,23

[120]

SEDIMENTATION EQUILIBRIUM IN A DENSITY GRADIENT

867

Applications Several applications of equilibrium sedimentation in a density gradient have been developed in the last five years. Studies have been made of biological materials, of biological processes, of synthetic high polymers, and also of some physical-chemical phenomena uniquely revealed in the procedure. In this section only selected examples of the various applications are given to illustrate the range of the method. 1. Solvation. Unambiguous ther/nodynamic relations have been derived which permit the evaluation of the net solvation of the buoyant species. ~5 The solvation parameter, r, sometimes called the selective or preferential solvation, is the number of molecules of one of the two components of the binary solvent that acts in establishing the density of the macrospecies, as though it is attached. Cesium DNA has an anhydrous density of 2.12 g./ml. 2G,27 The buoyant density is approximately 1.70 g./ml. From numbers such as these, together with an assumption regarding the magnitudes of the specific or the partial specific volumes of water in the solvate layer, the quantity r ' is calculated from Eq. (15).

1 ~3 + F'~I v3 + F'vl po= ~1 + F = 1 +F'

(15)

The quantity r ' is the net solvation expressed on a weight basis, po is the buoyant density, and O and v are the partial specific and specific volumes. The subscripts 3 and 1 refer to the anhydrous macrospecies and to the component in excess in the solvate layer. From the results in Fig. 2 the net hydration of buoyant cesium DNA from T-4 bacteriophage is about 10% by weight in cesium acetate solution, 28% in cesium chloride solution, and 68% in cesium sulfate solution. 26 Solvations of these magnitudes have been observed with bovine mercaptalbumin 2s and cesium poly-L-glutamate.~° 2. S t u d y of Structural Changes. Denaturation of DNA causes the buoyant density to increase. 29 On renaturation the original buoyant density is substantially restored. 3° Although the reasons for these changes are not understood at present, the density shifts provide a basis for recognizing the extent of denaturation of a DNA sample and for separating denatured from undenatured DNA. A similar density shift has been observed 31 after heat denaturation of bovine serum albumin. In ~ J . E. Hearst and J. Vinograd, Proc. Natl. Acad. Sci. U.S. 47, 825 (1961).

J. B. Ifft and J. Vinograd, unpublished observations. M. Meselson and F. W. Stahl, Proc. Natl. Acad. Scl. U~g. 44, 671 (1958). sop. Dory, J. Marmur, J. Eigner, and C. Schildkraut, Proc. Natl. Acad. Scl. U.8. 46, 461 (1960). alD. J. Cox and V. N. Schumaker, J. Am. Chem. Soc. 83, 2439 (1961).

868

SPECIAL TECHNIQUES

[120]

the latter case the density shift was observed in a three-component solvent--CsC1, (NH4) 2S04, and water. 3. Ef/ects of Camposition Changes. The two main factors governing buoyant density are the anhydrous density and the net solvation. The anhydrous density may be changed by an increment in mass without volume change by isotopic substitution; or, as in the substitution of adenine-thymine for guanine-cytosine pairs in DNA, the anhydrous density may be changed by an increment in volume with substantially no mass change. In both instances the density shifts are enhanced by shifts in net solvation. Buoyant density shifts also occur when simultaneous changes in mass and volume are introduced. Examples of these are (1) shifts occurring on acid-base titration of the macrospecies in CsCl (in this event hydrogen and cesium atoms are exchanged); (2) specific binding of anions to proteins; and (3) the biological substitution of bromines for methyl groups in thymine in DNA. Buoyant density is a property which may be readily changed in a variety of ways. Some of these variations have formed the basis for new areas of investigation. h. STABLEISOTOPESUBSTITUTIONS.The combined use of high concentrations of stable isotopes and density gradient sedimentation provides a procedure 29 for separating new from old biological macromolecules and cell particulates. In a series of trans]er experiments, Meselson and Stahl, ~9 Sueoka, 82 and Simon 3s demonstrated that DNA replicates semiconservatively and that, after one and two divisions, "hybrid" DNA exists. These experiments were performed with Escherichia coli B, Chlamydomonas reinhardi, and HeLa (human tissue culture) cells, respectively. The hybrid DNA most likely consists of a double-stranded DNA. The dense strand derives from the parent molecule, and the light strand is formed on replication after dilution with light isotope. The results of Meselson and Stahl and of Sueoka were obtained with the N 15 isotope, which changes the buoyant density by 0.015 g./ml. Simon's result was obtained with 5-bromouridine, which changes the buoyant density by approximately 0.10 g./ml. Davern and Meselson, ~ with C 1~ and N ~5 isotopes, showed that ribosomal RNA is conserved after two divisions of E. coll. The mixture of isotopes gave a density shift between new and old ribosomal RNA of 0.05 g./ml, in cesium formate. Brenner et al. 8~ also used both the isotopes C 18 and N ~5 to show that messenger RNA and new protein could be found in old ribosomes. These experiments were performed with CsC1 in the preparative ultracentrifuge, and the messenger RNA and new protein were recognized with ps2 and " N . Sueoka, Proc. Natl. Acad. Sci. U~. 46, 83 (1960). a E. H. Simon, J. Mol. Biol. 3, 101 (1961). " S . Brenner, F. Jacob, and M. Meselson, Nature 190, 576 (1961).

[120]

SEDIMENTATIONEQUILIBRIUM IN A DENSITY GRADIENT

869

S s5 radioactive isotopes. A twenty-drop interval occurred between the modes of the corresponding dense and light ribosomes. Hybrid DNA was first observed in the in vivo growth experiments of Meselson and Stahl. This hybrid has a buoyant density midway between N14-DNA and NI~-DNA and therefore contained equal amounts of each isotope. When the hybrid was heated to 100 ° for 30 minutes in 7 molal CsC1, two bands having buoyant densities of denatured NI~-DNA and N14-DNA were obtained. This result showed that the hybrid consisted of two subunits of DNA which were not definitely identified as DNA strands. Doty et al2 ° investigated this problem by the sedimentation velocity-viscosity method and concluded that the in vitro hybrid did indeed separate into single strands. These authors showed that the separate strands would recombine on slow cooling in dilute salt solution. Hybrid bands were observed to form between the closely related organisms E. coli and Shigella, but not between E. coli and DipIococcus pneumoniae or Serratia marcescens. Marmur and Lane, 85 in studies with transforming DNA, also concluded that heating and slow cooling lead to hybrid molecules. Schildkraut et al. 36 used deuterium and the N 1~ isotope to enhance greatly the buoyant density difference between labeled and unlabeled DNA. This difference was 0.040 g./ml. B. THE GUANINE--CYTOSINE DISTRIBUTION IN DNA. Sueoka et al. "7 and Rolfe and Meselson 2~ have shown that DNA from a variety of organisms, known from earlier work to contain widely different average guanine-cytosine contents, formed narrow bands of different buoyant density. Among the organisms studied, several of the DNA samples showed no detectable overlap in the concentration distribution in CsC1. This significant biological result has not yet been explained. The chemical result has been proposed as a method for base analyses? 4, 38 Only 1 ~g. of DNA is required for the analysis. Between 25 and 75% guaninecytosine content, the buoyant density varies linearly with guanine-cytosine content. The slope corresponds closely to 0.00100 g./ml, per % guanine-cytosine. DNA molecules from microbial sources are by no means necessarily homogeneous in base composition. Evidence in support of this view has been reported by Sueoka. ~ c. BUOYANT DENSITY TITRATIONS. When acidic hydrogens in a polyanion or polyampholyte are titrated with base and converted to salts, it is to be expected that the macrospecies will become more dense in u j . Marmur and D: Lane, Proc. Natl. Acad. Sci. 46, 453 (1960). s C. L. Schildkraut, J. Marmur, and P. Doty, J. Mol. Biol. 3, 595 (1961). N. Sueoka, J. Marmur, and P. Doty, Nature 183, 1429 (1959). P. Doty, J. Marmur, and N. Sueoka, Brookhaven Symposia in Biol. No. 12, 1 (1959).

870

SPECIAL TECHNIQUES

[120]

buoyant cesium chloride. 2° Such density shifts have been observed in alkaline CsC1 for DNA 9 and in acid CsC1 for poly-L-glutamic acid. 2° In the former case complete titration of guanine and thymine residues at pH 11.6 increases the buoyant density 0.063 g./ml. A density shift of 0.20 g./ml, was observed for poly-L-glutamic acid on titration of the ,/-carboxylic acid with base. These procedures appear to be general and include, for example, buoyant density changes on hydrolysis of ester side chains such as exist in pectins. 4. Isolation, Purification, and Characterization o] Macrospecies. Macrospecies can sometimes be readily separated from accompanying impurities by banding procedures. Viruses usually band rapidly and form narrow bands at characteristic buoyant densities different from those of host materials. Several reports of banding viruses in concentrated salt solutions with retention of biological activity have appeared. These include tobacco mosaic virus, 39 turnip yellow virus, 4° the bacterial viruses 6X-174, 41 T-4, and T-7, 42 ), and several transducing X viruses, 43 and the animal viruses polio ~a and rous sarcoma, r' For biological assay it is usually sufficient to dilute the recovered drops from preparative runs by a factor of 50 or 100, to avoid interfering effects of the salt. Purification from small molecules is less efficient than from large molecules. For nonsedimenting impurities the fraction remaining in the sample is 4alL with 95% recovery or 6alL with 99% recovery of the macrospeeies. In experiments with viruses, globular proteins, or globular particulates, the time required for an experiment may be considerably shortened by preforming the density distribution by layering of solutions or with a gradient-making machine. This is especially the case when long liquid columns are used. The desired density distributions may be calculated or interpolated from published data. 23 The numerical values of buoyant density at a given temperature and pressure are data that characterize materials. Such data may be expected to accumulate in the future. Investigators will do well to specify the purity of the buoyant solvent, the angular velocity, the length of the liquid column, the temperature, and the method of calculation. **A. Siegel and W. Hudson, Biochlm. et Biophys. Acta 34, 254 (1959). ~0R. E. F. Matthews, Nature 184, 530 (1959). ~1R. L. Sinsheimer, J. Mol. Biol. 1, 37 (1959). a M. Meselson, /n "The Cell Nucleus" (Proc. informal meeting by Faraday Soc., Cambridge, 1959). Butterworths, London, 1960. u j. Weigle, M. Meselson, and K. Paigen, J. Mol. Biol. 1, 379 (1959). L. V. Crawford, Virology 12, 143 (1960).