HALSALL
AND
SCHUMAKER
Zonal Diffusion, a New Technique. Application to the Determination of the Molecular Weight of M 13 Viral Deoxyribonucleic Acidy H. B. Halsall* and V. N. Schumaker?
ABSTRACT : Single-stranded D N A assumes a compact configuration in high ionic strength solvents at or near neutral pH. Using the recently developed method of zonal diffusion and band sedimentation, this property has been used advantageously to measure the molecular weight of the sodium salt of
M
13 is one of a class of small bacteriophages which infect male strains of Escherichia coli. The phage is a long rod in form, and its D N A consists of a single-stranded circle (Ray et a/., 1966a). The D N A molecular weights of these particles are low; they have been estimated as being about 2 million (Salivar et al., 1967). In view of the large amount of genetic information which is being gathered for this phage (Pratt et d,, 1969), we felt it would be useful to obtain a molecular weight by conventional hydrodynamic methods. This would normally be rather difficult because of boundary stability problems in obtaining reliable values for the diffusion coefficient of such a large molecule in the microgram per milliliter concentration range. Recently, however, we have developed a method (Halsall and Schumaker, 1970, 1971) which involves the examination of the diffusion profile of an initially very thin lamella of macromolecules which have been allowed to diffuse for known periods of time. Hydrodynamic stability of the diffusing zone is provided by a very shallow salt gradient. The experiments are performed in a zonal centrifuge rotor, and the diffusion profile is obtained by the direct analysis of fractions by any means appropriate for the molecule under study. Being single stranded, M13 D N A has very interesting hydrodynamic properties as a function of ionic strength. The molecule tends to collapse upon itself as the ionic strength of the medium is increased due t o the damping of the backbone charge. This causes pronounced changes in sedimentation and diffusion properties which tend to level off at high ionic strengths (>0.3 M). This property of the molecule may be used t o advantage in diffusion experiments, since such a collapsed molecule has a greatly increased diffusion coefficient, and hence is considerably easier t o measure. Materials and Methods M I 3 DNA. DNA was prepared from the M I 3 phage stock (the generous gift of Dr. Arleen Forsheit) by making it 0.2 From the Molecular Anatomy (MAN) Program, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830. Receiced July 24, 1972. Contribution 3013 from the Department of Chemistry, UCLA. The Molecular Anatomy Program is supported by the National Cancer Institute, the National Institute of General Medical Sciences, the National Institute of Allergy and Infectious Diseases, and the U. S . Atomic Energy Commission. Oak Ridge National Laboratory is oper-
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M13 viral DNA. With due account taken of possible sources of error, the value was estimated as 1.7 + 0.2 X lo6. Some observations are made regarding the most applicable situations for the zonal diffusion method.
in sodium dodecyl sulfate and bringing it t o 60'. Pronase was then added t o 100 pglml, and the mixture was incubated for 20 min at 60". A half-volume of 3 hi sodium perchlorate (pH 8-8.5) was added, followed by one volume of chloroform-octanol(9 :1). The mixture was then vortexed vigorously and centrifuged at low speed to separate the phases. The lower organic phase was discarded, and the aqueous phase was clarified by centrifugation at 15,000 rpm for 10 min. D N A preparations were stored in 0.05 M Tris buffer (pH 8.6). Sodium Bromide. Absorption of the concentrated sodium bromide solutions [analytical reagent grade (Baker Chemical Co.)] at 260 mp varied by a factor of ten when small batches were purchased. A uniformly low background was obtained by acquiring a 20-lb batch of a production lot of low absorbance. All solutions were filtered through a glass sinter before use. Diffusion Coeflcients. The techniques used were essentially those reported previously (Halsall and Schumaker, 1970, 1971). The underlay solution was 20% (w/w) sodium bromide, the zone solution was M13 D N A in 17% (w/w) sodium bromide, and the overlay solution was 15% (w/w) sodium bromide. Experiments were performed at a nominal temperature of 25", and results were corrected to this temperature when necessary (the largest correction required was 0.5"). All solutions were introduced into and removed from the rotor by gravity flow to avoid pulsation effects. Five-milliliter fractions were collected for assay a t 260 mp. Sample volumes were from 5 to 10 ml, with input concentrations of D N A from 23 to 100 pg per ml. R u n times were varied between 24 and 72 hr. Output concentrations a t peak maximum were from 1.8 t o 3.3 p g per mi. Sedimentation coeficients were measured by band centrifugation using Vinograd-type double-sector 12-mm charcoalfilled Epon centerpieces (Vinograd et al., 1965). The cell always held the following solutions: blank well, 15 pl of water; blank sector, 0.28 ml of sodium bromide a t molarity X;sample well, 15 p1 of M13 D N A in 0.002 M Tris (pH 8.6); sample sector, 0.28 m l of sodium bromide at molarity X. A Spinco Model E equipped with a split-beam photoelectric scanner
ated for the U. S . Atomic Energy Commission by Union Carbide Corporation Nuclear Division. Molecular Biology Institute and Department of Chemistry. U C L A , Los Angeles, Calif. 90024.
ZONAL DIFFUSION,
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A NEW
0.04
0.03 i E
1.2
0
N” 0.02
i
1
I
n 0
0.oj 4.4
0 5.2
4.8
4.4
r
5.6
(cm)
1: Diffusion profile of M13 viral DNA after 36 hr in the B-XV zonal rotor. Solvent conditions are described in the text.
FIGURE
1.0
I
c 1 1
0
0 2
01
03
V/ T
3: The noncorrelation between the observed diffusion coefficient, D15,n,the volume of the initial sample, V , and the run time,
FIGURE
T.
I
i
0 0
25
50
75
100
[DNA] ( p g / r n l )
FIGURE 2: Plot of D26,,vfor M13 viral DNA as a function of concentration. Extrapolation to zero concentration using weighted linear least-squares analysis yields a value of 0.95 =k 0.05 fick for
t -
O
D02h.
-1
i;
I
I
I
I
-
-
I
uiN
-
45
i
and a modified optical system (Breillatt et al., 1969) was used. All experiments were run with the RTIC unit switched off, temperature control being achieved with the refrigeration unit only. During the course of a n experiment the rotor temperature changed by no more than 0.2’. Runs were performed at a nominal temperature of 25’. Although our centrifuge is interfaced to a PDP-8/1 computer (Breillatt et al., 1969), in these experiments data records were obtained from an X-Y recorder giving a much larger trace than the strip recorder which is supplied with the scanner by Beckman. Generally seven t o ten “exposures” were made for a single experiment, and the observed sedimentation coefficients were extracted from the data using least-squares routines (weighted or unweighted) with standard errors. Corrections to s & w were made using standard procedures. Results
Diffusion Data. Figure 1 shows a typical diffused profile of MI3 D N A obtained from zonal diffusion experiments. During data analysis, points at the extreme edges of the zone were given the least weight, since it is here that artifacts caused by mixing a t the zone interfaces during layering have the greatest effect. Such diffusion profiles were analyzed as described previously’ (Halsall and Schumaker, 1970), and for a range of 1 Due to the large values of s and t in the experiment, it was necessary to include the correction term 01 in the calculations. See Halsall and Schumaker, 1970, eq 1.
to
I
I
l
l
I l l
4: Semilogarithmic plot of sodium bromide for M13 viral DNA.
FIGURE
1
,
I 1 I , , /
as a function of molarity of
concentrations yielded Figure 2. Weighted linear least-squares analysis of these data yielded a value of 0.95 f 0.05 X cm2/sec for D ; S , ~Diffusion . coefficients were measured for different lengths of time (2“) and different initial zone thickness ( V ) . No correlation between T, V, and D could be found (Figure 3). Sedimentation Data. Figure 4 shows a plot of s & wfor M13 D N A as a function of ionic strength of sodium bromide. This is very similar to that reported for single-stranded T7 D N A in solutions of sodium chloride (Studier, 1969), except for the decrease in sedimentation coefficient above 1 M NaBr due t o changes in water activity. It is apparent that the sedimentation coefficient is nearly independent of ionic strength above approximately 0.3 M NaBr. Three experiments in 1.891 M NaBr (the molarity a t which the diffusion experiments were performed) yielded a n s & , ~of 28.42 =k 0.30. As found earlier (Studier, 1969), no dependence of the sedimentation coefficient on concentration of the D N A could be demonstrated (Table 1). Calculations. All computations t o extract sedimentation and diffusion coefficients from the experimental data were performed with weighted or unweighted least-squares routines B I O C H E M I S T R YV,O L . 1 1 ,
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HALSALL
Values of the Sedimentation Constant of M I 3 Viral D N A Determined in 1.891 M NaBr at Three Concentrations; N o Concentration Dependence Is Seen. TABLE I :
28.42 i 0.40 28.62 k 0 . 1 5 28.41 + 0.15
1 2 3
10.5 25.7 49.4
yielding standard errors. The Svedberg equation may be rearranged to define the buoyant molecular weight, M(1 - ap) = sRT/D, where M is the molecular weight, s is the sedimentation coefficient in water at 25' (sec), R is the gas constant (8.314 X IOw7erg OK-' mol-'), T i s the temperature (OK), D is the diffusion coefficient in water a t 25' (cm2 sec-l), @ is the partial specific volume of the macromolecule (mi g-l), and p is the solvent density (g ml-l). Since the standard error on this quantity originates only from the parameters measured here, this standard error is important as an assessment of the precision of the hydrodynamic methods. Variance analysis gives this, since if M ( l - up) = f ( s , D)then 6 ~ ( 1-
i@)=
d(
dM(1 bs
up)
) ' W
+ (dM(1 - @p))*6 D 2
Covariance terms have been assumed to be zero. Thus the buoyant molecular weight was calculated to be 7.41 i 0.39 X IO5, a standard error of 5.2%. The absolute molecular weight may be obtained if the value of 1 - CP is known; however, as discussed below, uncertainty in the partial specific volume results in a large range of values possible for M . Using variance analysis, M was estimated t o be 1.7 i 0.2 x lo6for M I 3 viral NaDNA. Discussion Recently, several authors (Schmid and Hearst, 1969; Freifelder, 1970) have published excellent papers discussing in detail the problems of obtaining accurate molecular weights for DNA. With these in mind, we have attempted t o make a realistic analysis of the errors involved in our measurements and calculations. One of the basic problems in hydrodynamic measurements is the necessity for molecular homogeneity. In this case, there exists a possibility, despite due care, that we have been examining a mixed population of circular and linear molecules of the same molecular weight. Our use of high salt concentrations is a considerable advantage here, since the collapse of the molecules extends to the point that the two forms are indistinguishable hydrodynamically. The accuracy of our final result for the molecular weight depends on three quantities: sedimentation constant, diffusion constant, and partial specific volume. The technique of band sedimentation for the determination of sedimentation constants is well described (Vinograd et al., 1963, 1965; Schumaker and Rosenbloom, 1965). We chose to use the movement of the maximum ordinate of the sedimenting zone as characteristic of the velocity of all particles within the zone. It has been shown (Vinograd and Bruner, 1966; Dishon et a/., 1969) that this procedure gives results with precision similar
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to those obtained from second-moment calculations, therefore we may discount this as a source of error. It has also been demonstrated (Studier, 1969) that at sufficiently low concentrations of macromolecules, the value of the sedimentation coefficient obtained is equal to the sedimentation constant calculated by extrapolation to zero concentration of macromolecule in boundary sedimentation. Since determinations at three concentrations of D N A showed no concentration dependence (Table I), we have taken the weighted mean of these values as the sedimentation constant. Corrections to water as the solvent are, of course, hypothetical in this case, since the D N A has entirely different hydrodynamic properties in low or zero salt concentrations. The molecular weight calculations are not affected, however, since the correction terms for the sedimentation and diffusion constants cancel out. If solutions of macromolecules are layered upon density gradients or shelves containing a low molecular weight solute, then under certain conditions a hydrodynamic instability may develop, causing a phenomenon known as droplet sedimentation (Anderson, 1955; Nason et a / . , 1969). To avoid this, all band sedimentation solution concentrations were made so that previously determined stability criteria (Halsall and Schumaker, 1971) were not violated. The same stability considerations were invoked for all diffusion coefficient determination runs. The most general problem in measuring the diffusion coefficients of very large molecules is that the values obtained are somewhat high as a result of band spreading due to thermal effects and mixing on layering. Further, an approximation that is made here in analyzing the diffusion data is that the initial zone is infinitely thin. Our initial zone widths were between 1.5 and 3 . 5 x of the final zone width. If this finite width affects the results measurably, then an estimate of its magnitude combined with any mixing contributions to band spreading should be obtainable from measurements of the diffusion coefficient (D)using different initial zone widths ( V ) and/or different run times ( T ) and following D as the ratio V/T changes. Furthermore, the data should deviate from the theoretical model if such disturbances are important. Examination of the data in Figure 3 shows no trends attributable to mixing or the magnitude of initial zone widths, therefore the data appear to fit the theoretical model very well. This latter result is in full accord with previous work using cytochrome c and bovine serum albumin. The greatest problem is that of band spreading due to thermal effects. The errors these cause are probably reflected in the scatter of points in Figure 2 . The large volume and mass of the zonal rotor provide an appreciable heat sink, hence very precise temperature control is not absolutely necessary. Most undesirable are large fluctuations of temperature; in the centrifuge used in this work, the temperature was controlled to within *0.25". The largest uncertainty is in the value of the partial specific volume factor. As with other workers (Hearst, 1962; Studier, 1965), we have chosen a value of 0.556 ml,'g. However, this was obtained for calf thymus D N A ; therefore in computing the molecular weight we imposed upon the partial specific volume an assumed error of 8%. This, of course, is reflected as a large error in the molecular weight. It is generally useful to compare experimental rcsults to values determined for the same quantity by other workers. The molecular weights of iM13 viral D N A and the natural mutants fd, f l , and ZJi2 have ranged from 1.5 X l o Gto 2.3 X IO6 (Marvin and Hoffmann-Berling, 1963; Zinder et ul., 1963; Marvin and Schaller, 1966; Ray et a/., 1966b). These values were obtained by chemical analysis of phage DNA content
ZONAL DIFFUSION,
A NEW TECHNIQUE
(Zinder et al., 1963), electron microscope contour length measurements of the double-stranded replicative form (Ray et nl., 1966b), and sedimentation and viscosity measurements (Marvin and Hoffmann-Berling, 1963; Ray et al., 196613). Of these, the sedimentation and viscosity results, which are perhaps the most reliable, give the molecular weight of fd viral D N A as 1.6 X lo6 t o 1.8 X lo6. Although all the mutants mentioned above are filamentous phages, similar comparisons may also be drawn between M13 viral D N A and that from the spherical phage aX174. The D N A from these two phages have similar sedimentation coefficients (Ray et al., 1966a; D. S . Ray, personal communication; Studier, 1965; this work), and thus it is consistent that the two molecules should have very similar molecular weights, a x 1 7 4 viral D N A being 1.7 =t0.1 X lo6 (Sinsheimer, 1959). We have now applied the zonal diffusion method to several macromolecular systems ranging from 1 t o 12 ficks, and have obtained a clearer understanding of the situations in which it is best used. In order to obtain a uniform precision, most diffusivity measuring techniques, including the zonal method, take progressively longer to perform the smaller the diffusion constant of the macromolecule. This is due to the time dependence of the band width, and can extend t o several days. For a purified, homogeneous macromolecular preparation, a lower practical limit for the zonal method might therefore be 1 fick, or the level reported here. This is not intended to imply, however, that experiments cannot be performed successfully below this value, although optical mixing spectroscopy (Dubin et al., 1967), would be more tractable. If a specific assay is available for the macromolecule of interest, e.g., radioactivity, enzymic activity, then because of the sampling nature of the zonal method, mixtures containing the macromolecule may be used. At low diffusivities in particular this offers a considerable advantage over optical mixing spectroscopy and the Gouy interference method (Strassburger and Reinert, 1971). References Anderson, N. G. (1955), Exp. CellRes. 9,446.
Breillatt, J., Willk, D. D., Bishop, B. S., Spragg, S. P., and Zapp, F. (1969), USAEC Report ORNL-4558 Special. Dishon, M., Weiss, G. H., and Yphantis, D. A. (1969), Ann. N. Y. Acad. Sci. 164, 33. Dubin, S. B., Lunacek, J. H., and Benedek, G. B. (1967), Proc. Nat. Acad. Sci. U. S. 57,1164. Freifelder, D. (1970), J. Mol. Biol. 54, 567. Halsall, H. B., and Schumaker, V. N. (1970), Biochem. Biophys. Res. Commun. 39,479. Halsall, H. B., and Schumaker, V. N. (1971), Biochem. Biophys. Res. Commun. 43,601. Hearst, J. E. (1962), J. Mol. Biol. 4,415. Marvin, D. A., and Hoffmann-Berling, H. (1963), Z . Naturforsch. B 18,884. Marvin, D. A., and Schaller, H. (1966), J. Mol. Biol. 1 5 , l . Nason, P., Schumaker, V. N., Halsall, H. B., and Schwedes, J. (1969), Biopolymers 7,241. Pratt, D., Tzagoloff, H., and Beaudoin, J. (1969), Virology 39,42. Ray, D. S., Bscheider, H. P., and Hofschneider, P. H. (1966a), J. Mol. Biol. 21,473. Ray, D. S., Preuss, A., and Hofschneider, P. H. (1966b), J . Mol. Biol. 21,485. Salivar, W. O., Henry, T. J., and Pratt, D. (1967), Virology 32,41. Schmid, C. W., and Hearst, J. E. (1969), J. Mol. Biol. 44, 143. Schumaker, V. N., and Rosenbloom, J. (1965), Biochemistry 4,1005. Sinsheimer, R . L. (1959), J. Mol. Biol. I , 43. Strassburger, J., and Reinert, K. E. (1971j, Biopolymers 10, 263. Studier, F. W. (1965), J. Mol. Biol. 11,373. Studier, F. W. (1969), J. Mol. Biol. 41,189. Vinograd, J., and Bruner, R. (1966), Biopolymers 4,131. Vinograd, J., Bruner, R., Kent, R., and Weigle, J. (1963), Proc. Nat. Acad. Sci. U. S. 49,902. Vinograd, J., Radloff, R., and Bruner, R. (1965), Biopolymers 3,481. Zinder, N. D., Valentine, R. C., Roger, M., and Stoeckenius, W. (1963), Virology 20,638.
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