The Approach to Equilibrium in a Buoyant-Density Gradient

Transcription

1 BIOPOLY MERS VOL. 11, (1972) The Approach to Equilibrium in a BuoyantDensity Gradient CARL W. SCHMID and JOHN E. HEARST, Department of Chemistry, University of California Berkeley, California synopsis The theory for the approach to equilibrium in a buoyantdensity gradient is experimentally examined for the case of DNA in CsCl. INTRODUCTION The approach to equilibrium in a buoyantdensity gradient is a transport process in a centrifugal field and may be used to measure a sedimentation coefficient. This process is interesting for several reasons. Densitygradient sedimentation equilibrium can be used for the determination of the molecular weight of highmolecular weight DNA samples homogeneous in buoyant density. Furthermore, buoyantdensity centrifugation, in one form or another, has been one of the most important techniques in DNA experiments. With an understanding of the approach to equilibrium it would be possible to obtain a molecular weight, buoyant density, and sedimentation coefficient in the same experiment. A twocomponent theory for the approach to equilibrium was developed some time ago with considerable emphasis on the effects of both molecular weight and density heterogeneity. l v 2 In these early efforts considerable attention was also focussed on alternate methods of data analysis. However, an adequate description of this problem also requires consideration of the multicomponent nature of the system. Typically, the system might consist of three components: macromolecule, salt, and water. Hearst3 reconsidered this problem along lines similar to the original contributions, but with a proper description of the multicomponent system. As could be anti~ipated,~ the thermodynamic data required to evaluate the approach to equilibrium are the same as those required to evaluate the equilibrium distribution. Accurate thermodynamic data for DNA in buoyant cesium salts are now available5 and may be used to test this multicomponent theory by John Wiley & Sons, Inc.

2 1766 SCHMID AND HEARST THEORY For a macromolecular solute homogeneous in mass and density at infinite dilution Hearst3 has shown that the peak width changes with time, t, according to where d In [(P(t)) (P( ~))]/czt = 2D/a2 (1) (Wt)) = C(6) 62 d6 and Here 6 is the distance from the equilibrium band center, ro; C is the concentration; D is the socalled principle diffusion constant; and M3 is the molecular weight of dry neutral polymer, cesium DNA for the purposes of this investigation. The quantity (1 + I )/&f is needed to describe the buoyancy in a multicomponent buoyantdensity gradient and serves a function similar to the quantity (1 fip) encountered in conventional sedimentation in a twocomponent ~ystem.~*~ The derivation of Eq. (1) involves several assumptions similar to those used in deriving the equilibrium re~ult,~~ particularly that only firstorder terms in 6 need be carried in several expansions. While this assumption is good for narrow bands encountered in equilibrium work, it is less justifiable for the broad distributions occurring during the approach to equilibrium. For a more adequate description of the limitations of these assumptions, the original literature should be consulted. Particularly noteworthy, however, is the requirement that the lowmolecularweight components equilibrate rapidly to form the equilibrium density gradient. For low speeds and short columns the gradient equilibrates rapidly relative to the sedimentation of the and the required condition is satisfied. For a 1cm column about 10 hours are required for CSCI ~~ ~ solutions to reach equilibrum. EXPERIMENTAL Centrifugation was performed at 20 C with doublesector centerpieces on a Beckman Model E ultracentrifuge equipped with a photoelectric scanner. Harshaw optical grade CsCl dissolved in 0.01M Tris buffer ph 7.2 was used as the buoyant medium. Conventional boundary sedimentation velocity was performed by the methods of Gray and Hearst. DNA

3 BUOYANTDENSITY GRADIENT 1767 was isolated by phenol extraction of purified Pseudomonas phage D3 and B. megatherium phage a. RESULTS AND DISCUSSION Figure 1 is typical of the concentration distributions observed during the approach to equilibrium and may be analyzed by the secondmoment method according to Eq. (1). These results when plotted, as in Figure 2, fall on a reasonably straight line. Nonlinearity in Figure 2 might indicate either the importance of higher order terms in 6, neglected in deriving Eq. 1, or the effects of concentration on the sedimentation velocity. The linearity observed in Figure 2 does not preclude either of these effects. The slope of Figure 2 is a measure of the sedimentation coefficient. It is desirable to correct this quantity to a set of standard conditions, which will be taken as the sedimentation coefficient of sodium DNA in water at 20 C cm + i Fig. I. The approach to equilibrium of phage (Y DNA. This sample exhibited heterogeneity in boundary sedimentation which is also evident during the approach to equilibrium and in the equilibrium distribution. The times indicated on the traces are multiples of 32 min. Additional details are given in Figure 2 and Table I.

4 1768 SCHMID AND HEARST V 1.0 A N z 0.9 CQ A 0.8 m P P Time/32 min Fig. 2. The approach to equilibrium of phage 01 DNA. The moments, expressed in arbitrary chart units of dist,ance, are plotted according to Eq. (1). The initial data point is 40 hours into the run. The average concentration varied from 0.1 to 0.2 OD266,@,,, 1 em during the time sequence studied above. A sample calculation of the conversion of this slope to S20,w,NJ is summarized in Table I. The slope is converted to MID by Eq. (1) and the value of (1 + I )/&ff reported e1sewhe1e.~ The friction factor, f, is given by RT/D and is corrected to the viscosity of water at Z!0 C*2,13 to obtain the quantity MC~DNA/ fio,w. The molecular weight is corrected to that of the sodium salt upon multiplying by 0.75 and is then corrected by the buoyancy factor of sodium DNA in wateri4 to yield a fully corrected S~O,~,N~. TABLE I Sedimentation Velocity from the Approach to Equilibrium in a BuoyantDensit,y Gradient* Phage Phage Phage Phage DNA ff ff D3 D rl (C) OD265 mp. ~ cm d ln[(p) (6(m)2)]/dt X sec M CsDNA X lo+3 sec fz0.w M NaDNA (1 Op) f2o.w S20.w Svedberg units from boundary sedimentation f * The buoyant densities of phage CY and 1)3 DNAs were taken as and 1.722, respectively; centrifugation was performed at 24,960 rpm.

5 BUOYANTDENSITY GRADIENT 1769 These results are in fair agreement with those obtained by conventional boundary sedimentation velocity listed in Table I. This method is more laborious and less accurate than conventional boundary sedimentation velocity and will probably be useful for only certain special cases. The very high molecular weight DNAs currently being isolated in some laboratories may be such a case. For such samples both the anomalous speed effect15 and the large concentration dependence of sedimentation will pose some difficulties. The approach to equilibrium in a buoyant density gradient is a slow process and the anomalous speed effect should be suppressed under these conditions. In addition, the stabilizing influence of the density gradient makes it possible to work at lower concentrations than is possible with boundary sedimentation, eg, = 0.2 OD260mp,lcm. Phages a and D3 were a gift from Dr. David Freifelder. This work was supported in part by USPH Grant No. GbI Carl W. Schmid was supported by an NIH Predoctoral Fellowship No. 1FOlGM 46, References 1. M. Meselson and G. M. Nazarian, Ultracentrifugal Analysis, J. W. Williams, Ed., Academic Press, New York, 1963, p R. L. Baldwin and E. M. Shooter, Ultracentrifugal Analysis, J. W. Williams, Ed., Academic Press, New York, 1963, p J. E. Hearst, Biopolymers, 3, 1 (1965). 4. E. F. Casassa and H. Eisenberg, Adv. Protein Chem., 19,287 (1964). 5. C. Schmid and J. E. Hearst, Biopolymm, in press (1971). 6. G. Cohen and H. Eisenberg, Biopolymrrs, 8, 1077 (1968). 7. J. E. Hearst and J. Vinograd, Proc. Natl. Acad. Sci. U.S., 47,999 (1961). 8. J. E. Hearst and J. Vinograd, Proc. ivatl. Acad. Scz. U.S., 47, 1005 (1961). 9. J. E. Hearst, J. Ifft, and J. Vinograd, Z ruc. Null. Acad. Sci. U.S., 47, 1015 (1961). 10. J. A. Ifft, W. It. Martin, and K. Kinzie, Biopolymers, 9,597 (1970). 11. H. B. Gray and J. E. Hearst, J. Mol. Biol., 35, 111 (1968). 12. R. Bruner and J. Vinograd, Biochim. Biophys. Acta, 108, 18 (1965). 13. P. A. Lyons and J. F. Riley, J. Am. Chem. Soc., 76, 5216 (1954). 14. J. E. Hearst, J. MoZ. Biol., 4, 415 (1962). 15. J. E. Hearst and J. Vinograd, Arch. Biochem. Biophys., 92,206 (1961). 16. F. P. Rinehart, unpublished data. Received September 8, 1971