VOL. 14, 393-408 (1975)
BIOPOLYMERS
Characterization of Rodlike DNA Fragments M. THOMAS RECORD, JR., * and CHARLES P. WOODBURY, Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706; and ROSS B. INMAN, Biophysics Laboratory, University of Wisconsin, Madison, Wisconsin 53706
Synopsis Native calf thymus DNA was sheared by sonication in a viscous solvent to the molecular-weight range from 3 x lo4 to 3 x lo5 daltons, and fractionated by gel chromatography. Number and weight average molecular weights and were determined for individual fractions by electron microscopy; the ratio for the peak fraction is approximately 1.1. Sedimentation coefficients (so~o.,) of these fractionated samples show an approximately linear dependence on the logarithm of the molecular weight This behavior is that expected for rodlike molecules, and is in quantitative agreement for the with the theory ol Yamakawa and Fujii [(1973) Macromolecules 6, 407-4!5] sedimentajion coefficient of a wormlike chain with a per$stence length of 625 A, a diameter of 25 A, and a mass per unit length of 195 daltons/A. It appears that the wormlike coil model, without excluded volume, can represent the sedimentation behavior of DNA over the entire conformational range from rigid rod to flexible coil, using the above parameters. Equilibrium melting curves were determined for various fractions in aqueous 2.4 M tetraethylammonium bromide. A substantial broadening of the transition and decrease of the melting temperature were observed with decreasing molecular weight. Empirical expressions have been obtained relating both the transition temperature and breadth in this solvent to molecular weight.
(a, aw) a,,,/~@,,
a,.
INTRODUCTION The wormlike coil model provides a useful representation of the equilibrium and hydrodynamic properties of helical DNA molecules in tcrms of three parameters, the mass per unit length M,, the chain diameter d, and the persistence length 1/2k 1 (In addition, an excluded volume parameter may be necessary a t sufficiently high molecular weights.)* Hays et al.3and Yamakawa and Fujii4 have shown that sedimentation data on DNA samples in the molecular-weight range 3 X 105-l.lX lo8 daltons are accurately represented by a wormlike chain with a mass per unit length of 195 daltons/& a diameter of approximately 25 d, and a persistence length of approximately 600-650 d, corresponding to a statistical segment length (Kuhn length) of 1200-1300 d. Recent interest has focused on the extension of the range of data to higher molecular weights (chromosomal DNA5) where the wormlike coil approaches the limit of a flexible coil.
* To whom correspondence should be addressed. 393
@ 1975 by John Wiley & Sons, Inc.
394
RECORD, WOODBURY, AND INMAN
At sufficiently low molecular weight, the wormlike chain approaches the limiting behavior of a rigid rod. The early work of Doty et a1.6 on sonicated fragments of DNA in the molecular-weight range 3 x 105-7.4 106 daltons (weight average iLTWdetermined by light scattering) yielded a dependence of sedimentation Coefficient(SZO.,~) on the 0.37 power of the weight average molecular weight. Recently, Prune11 and Bernurdi,’ working with enzymatically degraded DNA fractionated on agarose columns, found that s O z O varied ,~ with the 0.32 power of the weight average molecular weight in the range 2.9 X 104-2.9 X lo5daltons. (Molecular weights AXw were evaluated by equilibrium ultracentrifugation). These exponents fall between those expected for flexible coils and rigid rods, and suggest a stiff but not yet rodlike configuration for DNA in this molecular-weight range. Cohen and Eisenberg8 chxamincd a single sonicate of molecular weight approximately 5 X lo5daltons by electron microscopy and light scattering, and found that the molecules were extended to approximately S9% of their contour length in solution. Eisenbergg showed that the sedimentation coefficients of the Cohen-Eisenbcrg sampltl and the lower molecular-weight Doty-McGill-Rice samples were in approximate agrec~mmtwith the predictions of the hydradynamic theory for cylindrical particles. However, the lack of quantitative agreement betn-een theory and experiment over this molecular-weight range for a unique choice of parametcrs (mass per unit length, cylinder diametcr) indicates that deviations from rodlike behavior exist in this region. The general theory for the Sedimentation coefficient of wormlike chains, as discussed most recently by Yamakawa and E ’ ~ j i ipredicts ,~ the functional form of the approach to rodlike behavior in the low-molecular-weight limit in terms of the same parameters ( M L , d, and 1/2h) used to characterize the wormlike chain a t higher molecular weights. Lack of data in the lowmolecular-weight region near and below that corresponding to one persistence length (-2.4 X lo5 daltons) has prcventcd a test of the predicted limiting behavior. In this paper we discuss thc preparation of fractionated DNA samples in t h r size range from 3 X 104-3 X lo5daltons, and the characterization of these DiYA fragments by electron microscopy, sedimentation velocity, and thermal denaturation. Thcse fragments, as we will show, define the rodlikc limit for DNA.
x
METHODS Sonication Calf thymus DNA (Sigma Chemical Company “highly polymerized”) was dissolved in BPES buffer (0.006 M Na2HP04,0.002 &f NaH2P04,0.001 M Na2EDTA,0.179 M NaCl) a t a DNA concentration of 25-75 mg/ml. A 6-ml sample was diluted with three volumes of glycerol and the resulting solution (solvent viscosity -500 cp) was sonicated for a total of 30 min with a Branson sonifier (WlS5,20 kHz). The sample was maintained in an
RODLTKE DNA FRAGMENTS
395
ice-salt bath a t -10°C. Bursts of 2-3-min duration a t 70 W power were alternated with pauses to permit cooling of the sample.
Fractionation Sonicated samples were fractionated by gel filtration on columns of agarose A-15m beads (Bio-Rad Laboratories). 1-ml samples of the sonicate were layered on columns 40-60 cm long and 1.8-2.8 cm diameter, and eluted with BPES buffer a t flow rates of 30-45 ml/hr. Pragress of fractionation was monitored by absorbance a t 260 nm. After elution of the void volume (-80 ml) the sample camp off in three peaks: an initial small peak (3% of the material or less, eluted in approximately 15 ml), the central peak, containing 97% of the DNA in a volume of 140 ml, and a final small peak (less than 0.1% of the material, eluted in approximately 10 ml). The leading and trailing peaks were discarded. Observation of the material in the central peak by electron microscopy showed the presence of a f w larger molecules, which should have eluted with the initial, excluded material but may havc adhered to the column walls and been washed off with later fractions. Consequently, the central peak fractions werc pooled, reconcentrated by dialysis against polyethylene glycol or by repeated evaporations a t 25°C in an air stream interspersed with dialysis into BPES (this process tool; approximately 48 hr zn toto) , and refractionated on a sccond A-13m column. Either 2- or 4-ml fractions were collected in the region of the broad cmtral peal;. These were used for electron microscopy, sedimcntation, and thermal denaturation studies. (Similar applications of gcl filtration to the fractionation of DNA fragments have been recently reported by Prune11 and Bernardi7and Britten et al.ln)
Electron Microscopy Refractionated samples from two different sonication experiments were examined in the electron microscope. The designations “peak” and “trailing” refer to fractions from one experiment; from a second, six fractions (15, 25, 37, 50, 61, and 70) mere chosen to span the width of the central peak. Each 2-ml fraction represented 1.3% of the elution volume of the central peak. Aliquots of these fractions (A260 > 0.25) were diluted with buffer at p H 9.9 to contain 0.02 M Ka?COa,0.0032 A 1 EDTA, 10% HCHO, 0.01% cytochrome c, and 0.5 pg/ml DNA. I n some cases P4 DNA was added as a n internal standard. I n other cases a sample of P4 DNA was prepared in parallel for microscopy, and measured as an external standard. All solutions were mixed with equal volumes of formamide before spreading. Details of the spreading procedure and the subsequent handling and shadowing operations are reviewed by Inman. l1 Samples were examined in a Philips EM-300 a t a nominal magnification of 33000X. Xolecules were measured from electron micrographs with a Sumonics Corporation digitizer, interfaced to a Hewlett-Packard 9820/9862A calculator/plotter for display of th(1length histogram for a given fraction (see Results).
396
RECORD, WOODBURY. AND INMAN
The lengths of phage DNA molecules used as primary and secondary molecular-weight standards are accurately reproducible under the spreading conditions used here. Younghusband et a1.12have measured the length of P4 DNA t o b r 4.1 f 0.07 pm, and calculate its molecular weight to be (7.35 =t0.14) X lo6daltons, based on 4X174RF and hCI857 DNA. This corresponds to a mass per unit length of 179 f 4 daltonsl8. Measurement of the length of P4 DNA as an internal standard in three samples resulted in a value of 4.09 f 0.05 pm. Since this is in close agreement with the value cited above, a mass per unit length of 179 daltonsl8 was used to convert measured fragment lengths to molecular weights. Length measuremrnts became ambiguous for thr smallest fragments. The width of a DNA molecule coated with cytochrome c and shadowrd with platinum was measured to be 61 f S 8. Molecules whose length w s! comparablc to their nidth (in practice, those with lengths below 100 A) could not be identified or measured with certainty because of the background grain structure, and so were omitted from the distributions. Fraction 70 appeared to contain a substantial number of thew molecules, and as a result a representative molecular-weight distribution could not be obtained for it. For larger molecules, it was assumed that the cytochrome c coated the ends as well as t hr length, and a visual correction was madr in the courw of measurement to comprnsate for the presence of the cytochrome c “caps.” Without this correction, molecular lengths could be overestimated by as much as 50 b. Icor the smallest fraction investigated (that designated as trailing) the weight average molecular length was approximately 250 8 aftrr correction, and as much as a 25% error could be introduced by ignoring the effect. We estimate that an uncertainty of approximately = t l 5 8 remains in the measurements. This results in an uncertainty of f2700 daltons in the molecular weights of the molecules, or an uncertainty of =t6% in the molecular weight of thr trailing fraction. For the highest molecular-weight fraction, the error due to the caps is only f 1%. Other minor errors, introducrd in the digitizing process, include a length-independent averagr error of +0.6%, and t h r resolution limit of approximately 6 8 (corresponding t o 0.25-mm digitizer resolution). Overall uncertainties in molecular-weight determinations therrfore range from +S% at 45,000 daltons to f3% a t 243,000 daltons.
Sedimentation Velocity sedimentation experimrnts were performed with a Spinco model E ultracentrifugr with absorption optics. Samples nere run a t concentrations of 5-20 pg/ml in BPES buffer using 12- or 30-mm cells at speeds in the range 36,500-44,770 rpm. Sedimentation coefficients were calculated from the motion of the midpoint of the sedimrnting boundary, using tracings of the films made on a Joyce-Loebl microdensitometcr. Boundaries remained symmetrical during the course of sedimentation, although broadening of the boundary due to diffusion and molecular-weight heterogeneity was observed as a function of timr. Within experimental error, no concentration
RODLIKE DNA FRAGMENTS
397
dependence of the sedimentation coefficients was noted in experiments a t 5, 10, and 20 pg/ml for a sample of molecular weight 110,000 daltons. This is in agreement with an estimate from the equation of Eigner and DotyL3that s and so differ by less than 1% over the range of molecular weights and concentrations investigated here. Sedimentation coefficients were corrected to the density and viscosity of water a t 20°C; the maximum correction was approximately 5%. Our estimate of the error in the determination of sedimentation coefficients, based on the reproducibility of individual measurements and the scatter of data points within a given run, is +0.4 S. This amounts to an error of + l o % in s ~ a t the ~ ~ lowest molecular weight investigated, and a n error of +S% a t the highest molecular weight. To examine the condition of the single strands of fragments produced by extended sonication, a n alkaline sample (0.1 M KaOH, 0.9 M NaC1) of a fraction of weight average molecular weight 110,000 (doubled stranded) was sedimented to equilibrium a t 10,589 rpm in an AnJ rotor (30-mm centerpiece, DNA concentration 7 pg/ml) . Equilibrium was attained in approximately 72 hr in the 1-em solution column; the run was continued for a n additional 30 hr beyond this point. At the speed selected, the equilibrium concentration of polymer a t the meniscus was essentially zero. Concentrations c as a function of radial distance r were determined using absorption optics and the linear film response region (the upper 80% of the cell). A plot of In c versus r 2 was linear over this region, and a n apparent molecular weight of 42,000 (intermediate between a weight and z average)' was obtained from the slope. Since the effects of high polyelcctrolyte charge, finite polymer concentration, and hydrolytic scissions a t the alkaline p H of the experiment would combine to reduce the apparent molecular weight from the ideal value, we interprct the correspondence between the observed and expected valurs (42,000 versus 55,000, ignoring the difference between the types of averages used) to indicate that there is less than one brcak per strand in the sonicated fragments. This is reasonable, since a single-strand break would be expected to bc a prime site for fragmentation of the molecule in the sonication experiment.
Denaturation Tetraethylammonium bromide (TEA, polarographic grade) was obtained from Southwestern Analytical Chemicals. TEA was dissolved in redistilled water to male a 4.0 M stock solution, clarified by sedimentation, titrated with HCl to p H 5.5, and mixed with fractions of calf thymus DNA (in 0.05 M phosphate buffer, p H 7.0) in a 3:2 ratio to produce solutions with a TEA concentration of 2.4 M and with DNA concentrations in the range 2 4 0 pg/ml. The pH of the final solution was 7.85 + 0.05 (meter reading). Melting curves a t this TEA concentration (for which Rlelchior and von Hippel14 have shown that effects of base composition on the transition temperature and transition breadth are eliminated) were determined on a
,
~
RECORD, WOODBURY, AND INMAN
398
Gilford 2400s spectrophotometer, using a calibrated platinum resistance probe in the cell compartment. Three samples and a blank were heated simultaneously in Teflon-stoppered cells a t a rate of 0.2O0C/min. (The rate of temperature rise was controlled with a geared drive on the thermoregulator of the circulating bath.) Transition temperatures T , were taken as the 50% transition point. Corrections were applied for linearly sloping baselines in the region of the transition. Transition breadths A were determined from the inverse of the transition slope a t the transition midpoint. (A = (be/bT);=,,,, where 0 is the fractional advancement of the transition.)
RESULTS AND DISCUSSION Electron Microscopy Histograms determined by electron microscopy showing the distribution of molecular lengths in high- and low-molecular-weight fractions (15 and 61) are shown in Figures 1 and 2. Number and weight average molecular weights computed from the histograms, the ratio aW/iiTn, and the number of molecules measured in each fraction are summarized in Table I. The fractionation obtained by gel filtration is quitr good, particularly in the leading (high-molecular-weight) half of t h r peak ($f,/AZn < 1.1).
(an, a,)
TABLE I Results of Electron JMicroscopy and Sedimentation Velocity Experiments Fraction Molecules M n li?, S020.w Number Counted x 10-4 x 10-4 2i?w (Svedbergs) 1.j 2.5 37 Peak 50 61 Trailing
22.9 17.7 10.6 8.0 7.2 6 .0 4.0
103 78 1-54 216 114 25 1 148
24.3 19.1 11.4 9.0 8.8 7.3 4 .5
F r o c l i o n 15 103 molecules
I -
n .06
.03
.09 .I2
1.06 1.08 1.08 1.12 1.22 1.22 1.12
.I5
.I8
2 1
.24
2 7
7.2 6 .3 5.7 6.4 5.4 4.7 3.9
-
.30
Length in microns
Fig. 1. Molecular-length distribution determined by electron microscopy for fraction 15 (of 70 2-ml fractions); A?, = 243,000, aW/a,, = 1.06.
399
RODLIKE DNA FRAGMENTS
.02
.04
.36
.08
.I0
Length in microns
Fig. 2. Molecular-length distribution determined by ele$oemicroscopy for fraction 61 (of 70 2-ml fractions); = 73,000, M w / M , = 1.22.
ivw
From Table I it is apparent that prolonged sonication in 75% glycerol produces a range of molecules with molecular weights as much as a n order of magnitude lower than those previously obtained by this technique. (Britten et al. have recently found a similar extent of degradation following highspeed stirring in glycerol-water mixtures, and Prunell and Bernardi have enzymatically degraded DNA to this size range.7) However, the distribution of molecular weights in our sonicate may be substantially broader than that obtained after sonication in aqutwus solution. Cohen and Eisenberg obtained X w / a n= 1.06 for a sonicate of molecular weight 5 X lo5.* Gel filtration is necessary to approach this degree of homogeneity in our samples. More than 1000 molecules in all were examined and measured by microscopy. The overwhelming majority of these had a rigid or gently curving appearance with no hairpin bends. There was no evidence of singlestranded (frayed) ends, though short single-stranded regions would not be detected. A few molecules of denatured DNA or RNA were observed in fraction 15; denatured molecules were not observed in other fractions.
Sedimentation Sedimentation coefficients SO^^,^) from boundary sedimentation experiments on the fractions examined by electron microscopy are included in Table I. The data are plotted in Figure 3 as a function of logarithm of the molecular weight (aw) of the fraction. Our sedimentation coefficients agree, within experimental error, with those calculated from the empirical equation of Prunell and Bernardi,’ determined for fractions of enzymatically degraded (and therefore nicked) DNA. This observed agreement gives further support to the conclusion of Hays and Zimml* that the presence of single-strand breaks does not affect the hydrodynamic properties of helical DhTA. I n addition, previously reported determinations of SO^^,^ for a variety of samples in the molecular-weight range 3 X 105-4 X lo6daltons are included in Figure 3. Of these, the measurements of Cohen and Eisenberg (soni-
RECORD, WOODBURY, AND JNMAN
400
Fig. 3. Variation of sedimentation coefficient S O ~ O , with ~ weight average molecular weight (plotted on a logarithmic scale). Filled data points refer to measurements on ? ' ~ Sinsheimer relatively homogeneous samples: ( 0 ) this work, (m) E i ~ e n b e r g , ~ (A) (@X174).'6*17 Other data are from (0)Eigner and I l ~ t y , (0) ' ~ Hays and Zimm (control and nicked samples),18( A ) Reinert, et a!. (corrected for polydispersity).lg The solid line is the theoretical relatio? of Yamakawaoand Fujii4for a wormlike cyldnder with mass per unit length 195 daltonslh, diameter 25 A, and persistence length 625 A.
a,
cated calf thymus DXA, so20,m= 8.12 S,9ATrn = 4.92 X lo5 as determined by light scattering,15) and Sinsheimer and co-workers (4x174 DITA, S ~ Z O .= ~ 14.3 S for the linear double-stranded form 111,I'j iVrn = 3.4 X lo6as calculated from the light-scattering value for the singlc-stranded form17) were made with esseritially homogeneous samples. Other data are taken from the literature survcy and experiments of Eigncr arid Doty13 (molecular weights determined by light scattering or from the Flory-Rlandelkern equation), and the cxperiments of Hays and ZirnmI8 on nicked and control DNA (molecular weights determined from the Flory-Mandclkcrn equation) and of Rcinert et al.19 (molecular weights determined from the Svedberg equation). Only the data of Reinert et al. are corrected for polydispcrsity; as shown by Fujita et a1.20this correction becomes of increasing importance at low molecular weight. The uncorrected Sedimentation coefficient of a polydisperse sample is predicted t o be less than that of a homogeneous sample of thc same BW.Presumably this polydispersity effect is the cause of the observed systematic dcviations from the Yamakawa-Fujii curve in the molecular-weight range from 3-6 x lo5. The difficulties inherent in the determination of molecular weights of helical DKA samples by lightscattering measurements, even in this relatively low-molecular-weight range, have been discussed by Schmid ct a1.21 The 4x174 datum should be f r w of any uncertainty in this regard; however, a somewhat larger molecular weight (3.6 x lo6) has been recently reported for 4x174 DNA from length measurements relative to T 7 DNA in the electron Superimposed on the expcrimental points in Figure 3 is t h r theoretical curve of Yamakawa and Fujii4 for the dependence of sedimentation coefi-
RODLIKE DNA FRAGMENTS
401
cient on molecular weight f2r a wormlike cylinder with a persistence length of 625 8, a diameter of 25 A, and a mass per unit length of 195 daltons/8. This choice of parameters is within the range of persistence lengths (650 f 25 A) and diameters (25 f 1 8 ) found by Yamakawa and Fujii to give a satisfactory fit to sedimentation data in the molecular -weight range 3 X lo5 to 1.1 x 108 d a l t ~ n s . Hays ~ et al. also concluded that sedimentation data in this molecular-weight range could be ,fitwith a wormlike-coil model of persistence length 625 8 and diameter 25 A.3 From Figure 3 it is apparent that our sedimentation data on samples in the molecular-weight range 4 X lo4-3 X lo5daltons are consistent with the extrapolation of the Yamakawa-Fujii theoretical curve calculated using the above parameters. The equation for this curve, valid for molecular weights below 5.55 X lo5 daltons, is so20,u,= 1.525 In
A4
- 12.367
+ 1.043 X lop6M
+ 4.883 X 10-13 M 2 - 2.149 X 10-19 M 3 .
(1)
(Here, we have combined Eqs. 51,52, and 58 of the Yamakawa-Fujii paper, omitting higher order terms that contribute negligibly to the calculated sedimentation coefficient of a DNA model.) I n Eq. ( l ) , the first two terms on the right-hand side are independent of the choice of persistence length, and represent the functional dependence expected for rodlike particles of constant diameter and mass per unit length (see below). The final three terms depend also on the persistence length, and represent corrections to rodlike behavior that become increasingly important a t higher molecular weight. (Even a t 11.1 = 5.55 X lo5,however, these correction terms contribute only 9% of the calculated value of SO^^,^.) Above 5.55 X lo5,the valid relationship is sOZO,,
=
5.693 X lop3M”’
+ 4.351 + 1.043 X 1 0 2 h - ” * - 1.191 X
lo5 M-l - 5.506 X lo6 d4-”/‘. (2)
Here the first two terms represent the high-molecular-weight Gaussian limit, and the final three terms represent corrections for non-Gaussian behavior a t lower molecular weight. Excluded volume effects are not considered; a n excellent fit to published data is obtained without considering them, even up to molecular weights of 1.1 X los d a l t ~ n s . ~ I n Figure 4 we have replotted our sedimentation data and that of Cohen and Eisenberg on an expanded scale, and compared i t with theoretical curves calculated for various rodlike models. Again the Yamakawa-Fujii (YF) curve is included. As representations of rodlike behavior, we have plotted : the Riseman-Kirkwood (KR) expression for a chain of contiguous beadsz2(which is formally equivalent to the Perrin expression for a prolate ellipsoid of large axial ratioz3); the equation derived by Bloomfield et al. (BDH) for a cylindrical shell, neglecting end effects and retaining terms varying as the inverse first power of the axial ratio;24 and the expression of Broersma for a circular cylinder, including end effects and retaining terms of
RECORD, WOODBURY, AND INMAN
402
~
4.5X104
7.3~10~
I
1.l4xlO5
I
Mw
l.91~10~ 2.43~10~
I
I
4.92~10~
I
8
7-
6-
11.0
11.5
12.0
12.5
13.0
In ii, Fig. 4. The limiting rodlike region for DNA. The sedimentation data of Eisenberg9*16 ( 0 )and this work ( 0 ) (cf. Fig. 3 ) are plotted against In along with the theoretical
aw,
expression of Yamakawa and Fujii4 (YF) from Fig. 3. Plotted for comparison are three relationspps (shown as dashed lites) for stiff rods with a mass per unit length of 195 daltons/A and a diameter of 25 A: Riseman and Kirkwood fKR),22Bloomfield e t al. (BDH),24and Broersma (BLZ6
higher order in the inverse of the axial ratio.25 A mass per unit length of 195 daltons/i and a diameter of 25 were used throughout in these computations. From Figure 4 we conclude that the sedimentation behavior of DNA becomes indistinguishable from that of a rodlike molecule below a molecular weight of about lo5daltons. Below this point, the theoretical equations of Yamakawa and Fujii and Bloomfield et al. become virtually identical; these provide a somewhat better fit to the data than the equations of Riseman and Kirkwood or Perrin do. Surprisingly, the more exact treatment of Broersma does not fit the data in this region with a reasonable choice of cylinder diameter; a value in excess of 50 d is required to bring the Broersma equation into agreement with the experimental data. From the defining equations for the persistence length and end-to-end distance (h2)”’ of a flexible chain molecule, the ratio of the end-to-end distance to the contour length L can be evaluated for DNA of any molecular weight.26 At lo5 daltons, (h2)’,’/L= 0.87, or the molecule in solution is predicted to be extended to 87% of its contour length. This extent of curvature would not be a major deviation from the completely rodlike state. At 4.65 X lo5 daltons, the molecular weight of a sample examined by Cohen and Eisenberg,8 the DNA is calculated to extend to only 50% of its contour length. By comparison of light-scattering and viscosity estimates of the end-to-end distance for their sample (treated as a rod) with direct length measurement by electron microscopy, Cohen and Eisenberg con-
RODLIKE DNA FRAGMENTS
403
cluded that their sample was extended to S7-S9yO of its contour length in solution. This result would imply that the persistence length of DNA is substantially greater than 625 d in this molecular-weight range. * Schmid et aL2I have discussed potential sources of error in this result, and have taken the point of view that there is a unique persistence lcngth for DNA. Our present work supports the concept of a unique persistence length of 625 A for DNA, albeit indirectly. The DNA fragments we have investigated are too small to exhibit large deviations from rodlike behavior, and their sedimentation behavior can be fit by the Yamakawa-Fujii expression for a wide range of persistence lengths, since this parameter enters only into the corrections to rodlike behavior expressed in Eg. (1). It is however of significance that the Yamakawa-Fujii equation cxtrapolates correctIy into this rodlike region. One can therefore be confident that the excellence of its fit to the higher molecular-weight data (4 X 105-4 X lo6 daltons) is not accidental, but rather an indication that there is a unique persistence length for DNA.
Thermal Denaturation Studies Equilibrium melting curves were determined for unsonicated calf thymus DNA and for various fractionated DNA fragments in aqueous 2.4 M tetraethylammonium bromide (TEA), a solvent in which effects of base compositional heterogeneity are eliminated. l4 Wo were interested in the dependences of transition temperat.ure and breadth on molecular weight in this soIvcnt, as we11 as in dcrnonstrating the integrity of the double-helical structure under the conditions of our fragmentation experiments. As a result of previous theoretical and experiments with homop o l y r n e r ~ ~and ~ vnatural ~~ DNA,28t29 it is known that in the molecular-weight range where melting from the ends becomes a dominant mode of denaturation, a depression of the transition temperature and increase in transition breadth occur with decreasing molecular weight. Britten et a1.'0 have suggested that the T , depression be used to estimate the molecular weight of short DNA fragments used in hybridization or reannealing experiments. Wetmur has found that the tetraethyl quaternary salt solvent is very suitable for these renaturation experiments. 31 Hence a relationship between the T, depression and molecular weight in this solvent should prove useful. Figure 5 shows the gel filtration profile for the fractionation of samples (4-ml volumes) used in the denaturation experiments, and the sedimentation coefficicnts S O Z ~,lo determined for various fractions (A-G') across the peak. Since both s0pO,, and elution volume are approximately linear functions of the logarithm of the molecular weight in this range, it is not surprising that S O Z O , ~ varies linearly with the elution volume. Moleculsr weights for fractions were either determined directly from sedimentation coefficients * Recent unpublished work by Godfrey and Eisenberg [cited by Eisenberg, H. (1974) in Basic Principles i n Nucleic Acid Chemistry, Ts'o, P. O . , Ed., Acadoemic, New York, vol. 2, pp. 224-2251 gives a persistence length of approximately 600 A for sonicated, fractionated calf thymus DNA in the molecular-weight range 0.25 X 106-1.2 X lo6daltons.
RECORD, WOODBURY, AND INMAN
404
TABLE I1
Effect of
a,,, and Strand Concentration on Denaturation Parameters in TEABr
a,,,
Concentration (&ml)
Tm ("C)
13.2 1.5.4 27.1 -a3.3 9.1 18.4 36.7 38.2 2.2 18.8 34.0 9.0 20.7
67.9 67.9 67.8 67.8 6.5.4 65.3 64.7 66.4 61.2 61 . O 60.7 58.7 39 . 3
Unsonicated
78,000
40,000
30,000
I
/
A
("c) 1.2 1.1 1.1 1.1 2.7 2.8 2.0 2.7 6.6 5.1 5 .8 8.0 7.6
\ -\
0.50
Volume Collecled in ml.
Fig. 5. Absorbance AZ60 (@) and sedimentation coefficient s~zo,,,, (0)as a function of the elution volume from an A-15 column. 4-ml fractions were collected; S O P O . ~ was measured on those labeled A-G.
using Eq. (l),or by interpolation of a plot of elution volume versus the logarithm of the molecular weight. (The molecular weights of samples F and G were estimated by extrapolation of this plot, since they fell below the range in which direct calibration by electron microscopy was possible.) Representative melting curves are plotted in Figure 6. Data obtained from experiments over a range of molecular weights and DNA concentrations are collected in Table 11. A depression of the melting temperature and increase in transition breadth are noted with decreasing molecular weight; however the expected dependence of the T , on DKA concentration, which is predicted to appear in this r e g i 0 n , ~ ~is, ~not 8 noticeable in our experiments. (A dependence of T , on polynucleotide concentration has been observed by Hayes et al. in experiments covering a wider concentration range and utilizing smaller fragments than those studied here. 30) An unexpected decrease in the hyperchromic effect accompanying the transition was observed with decreasing molecular weight. The high
RODLIKE DNA FRAGMENTS
405
Fig. 6. Normalized melting curves for unsonicated calf thymus DNA ( 0 )and various fractionated fragments (Fig. 5 ) in 2.4 M TEA; ( 0 ) = 78,000, ( A ) ii?u = 48,000, (0)ii?w = 40,000,(H)ii?w = 30,000.
a,
polymer gave a hyperchromicity of approximately 40%; values in the range 40-30y0 were observed for fractions from the leading through the central region of the peak, with some scattering in the data. The lowest molecular-weight fractions consistently gave hyperchromicities in the range 30-2070, with substantial scatter (even from sample to sample within a single fraction) in the data. We were able to ascribe part of this effect to the presence of dialyzable impurities in the lowrr molecular-weight fractions. However, since the true dependence of hyperchromicity on chain length should be minimal in this molecular-weight region,27it is possible that there are some denatured molecules or single-stranded regions (frayed ends) in the populations of fractionated fragments. For the fractions of lowest molecular weight, the presrnce of frayed ends in double-stranded molecules could cause systematic errors in the so20,10 versus M calibration. We have attempted to estimate the possible extent of such fraying from the hyperchromicity data. While the uncertainties in the data are large, it appears that the absolute amount of fraying would have to increase with decreasing molecular weight to give the hyperchroniicities observed. This appears unreasonable, and we are left without a satisfactory explanation for the observed trend. The variation of T , and the breadth A with l / M for all fragments investigated is plotted in Figure 7. The theory of Applequist and Damle27 (for melting from the ends in molecules small enough so that the transition occurs a t temperatures substantially below the transition temperature T," of the infinite polymer) prrdicts that the transition breadth and the quantity ( l / T m - l / T m m )should each be proportional to 1 / M . For small depressions of the T , as encountered here, the latter quantity is proportional to the depression of the T , itself, and both the breadth and the T , depression are therefore expected to be proportional to l / M . This prediction has been verified for the T , (though not for the transition breadth) in other syst e m ~ . ~ ,Our ~ ~data , ~can ~ be , ~fit~to such a dependence, but are better fit by the smooth curves drawn through the data in Figure 7. Moreover, the
RECORD, WOODBURY, AND INMAN
406
M I
I 0
6.7x10'
2x10'
lo5
I
I
I
I
I
0.5
1.0
5x10'
4x10'
I
I
I
I
I
1.5
2.0
2.5
3.3x10'
2.9x10'
I
I
3.0
I
I
19
I0
3.5
1 0 ~ 1 ~ Fig. 7. Transition temperature T, ( 0 )and transition breadth (0)as a function of the reciprocal of the molecular weight. All fragments are from the fractionation of Fig. 5. (Molecular weights are shown in the nonlinear upper scale.)
T,
Depression
("C)
Fig. 8. Relationship between the transition breadth and the depression of the T, for the data of Fig. 7. The least squares line is drawn through the data (see text).
breadth and transition temperature vary together, so that the breadth may be represented as a linear function of the transition temperature, as shown in Figure 8. Such a relationship was also observed by Hayes ct aL30 over the low-molecular-weight range, but is not interpretable in terms of current helix-coil transition theory. A least squares fit to the data of Figure S gives the following equation relating transition breadth to transition temperature : A = A"
+ 0.732 (T,"
-
T,)
where A" is the transition breadth of the infinite polymer. Equations for the smooth curves drawn through the data of Figure 7, which are consistent with the relationship obtained from Figure 8, are
RODLIKE DNA FRAGMENTS
T," - T, A - A m =
=
1.75 X lo5
1.2s
x
M
0.25 X 1Oln
-I-
M
407
M2
0.1s x
105 +
1010
M2
Because of the scatter in the data, these clearly can serve as only a n approximate measurc of the fragment. molecular weight. The authors thank Dr. R. R. Burgess for the use of his sonicator, Dr. W. T. Szybalski for the use of his microdensitometer, and Drs. R. L. Baldwin, V. A. Bloomfield, H. Eisenberg, J. A. Schellman, H. Yamakawa, and B. H. Zimm for their comments on this manuscript. This work was supported by grants from the NSF and the Wisconsin Alumni Research Foundation (to PI'ITR), and from the N I H and American Cancer Society (to RI).
References 1 . Kratky, 0. & Porod, G. (1949) Rec. Trav. Chim. 68,1106-1122. 2. Gray, Jr., H. B., Bloomfield, V. A. & Hearst, J. E . (1967) J . Chem. Phys. 46,14931498. 3. Hays, J. B., Magar, M. E. & Zimm, B. H. (1969) Biopolymers 8,531-536. 4. Yamakawa, H. & Fujii, M. (1973) Macrcmolecules6,407-415. 5. Appleby, D. W., Hearst, J. E . & Rall, S. C. (1974) (hbstract 333, Biochemistry/ Biophysics Meeting, Minneapolis, Minn.) Fed. Proc. 33,1282. 6. Iloty, P., McGill, B. B. & Rice, S. A. (1958) Proc. Nut. Acad. Sci. U.S. 44, 432438. 7. Prunell, A. & Bernardi, G. (1973) J . Bzol. Chem. 248,3433-3440. 8. Cohen, G. & Eisenberg, H. (1966) Bzopolymsrs 4,429-440. 9. Eisenberg, H. (1969) Biopolymers 8,545-551. 10. Britten, R. J., Graham, I). E. & Neufeld, B. R. (1974) in Methods in Enzymology, Grossman, L. & Moldave, K., Eds., Academic, New York, vol. 29, pp. 363-419. 11. Inman, R. B. (1974) in Methods i n Enzymology, Grossman, L. & Moldave, K., Eds., Academic, New York, vol. 29, pp. 451-458. 12. Younghusband, H. B., Egan, J. B., & Inman, R. B. (1975) in preparation. 13. Eigner, J. & Doty, P. (1965) J . Mol. Baol. 12,549-580. 14. R'felchior, Jr., W. B. & von Hippel, P. H. (1973) Pioc. Nut. Acud. Sci. U.S. 70, 298-302. 15. Cohen, G. & Eisenberg, H. (1969) Biopolymers 8,45-55. 16. Burton, A. & Sinsheimer, R. L. (1965) J . Mol. Biol. 14, 324-347 icf. Friefelder, D. (1970)J. Mol. Bid. 54,567-5771. 17. Sinsheimer, R. L. (1959) J . M o l . Biol. 1 , 4 3 4 3 . 18. Hays, J. B. & Zimm, B. H. (1970) J . M J ~Biol. . 48,297-317. 19. Reinert, K. E., Strassburger, J. & Treibel, H. (1971) Biopolymers 10,285-307. 20. Fujita, H., Teramoto, A., Yamashita, T., Okita, K. & Ikeda, S. (1966) Biopolymers 4,781-791. 21. Schmid, C. W., Rinehart, E. P. & Hearst, J. E. (1971) Biopolymers 10,883-893. 22. Riseman, J. & Kirkwood, J . G. (1956) in Rheology, Academic, New York, vol. 1, pp. 495-523. 23. Perrin, F. (1936)J. Phys. Radium7,1-11. 24. Bloomfield, V. A,, Dalton, W. 0. & van Holde, K. E. (1967) Biopolymers 5, 135148. 25. Broersma, S. (1960) J . Chem. Phys. 32,1632-1635. 26. Schellman, J. A. (1974) Biopolymers 13,217-226.
408
RECORD, WOODBURY, AND INMAN
27. Applequist, J. & Damle, V. (1965)J. Amer. Chem. Soe. 87,1450-1458. 28. Crothers, D. M., Kallenbach, N. R. & Zimm, B. H. (1965) J. MoZ. Biol. 11,802820. 29. Lazurkin, Yu. S., Frank-Kamenetskii, M. D., & Trifonov, E. N. (1970) Biopolymers 9,1253-1306. 30. Hayes, F. N., Lilly, E. H., Ratliff, R. L., Smith, D. A., & Williams, D. L. (1970) Biopolymers 9,1105-1117. 31. Chang, C. T., Hain, T. C., Hutton, J. R., & Wetmur, J. G. (1974) Biopolymers, 13, 1847-1858. 32. Wilson, D. A. & Thomas, C. A. (1974)J. Mol. Biol.84,115-144.
Received August 26, 1974 Accepted October 30, 1974
BIOPOLYMERS
Characterization of Rodlike DNA Fragments M. THOMAS RECORD, JR., * and CHARLES P. WOODBURY, Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706; and ROSS B. INMAN, Biophysics Laboratory, University of Wisconsin, Madison, Wisconsin 53706
Synopsis Native calf thymus DNA was sheared by sonication in a viscous solvent to the molecular-weight range from 3 x lo4 to 3 x lo5 daltons, and fractionated by gel chromatography. Number and weight average molecular weights and were determined for individual fractions by electron microscopy; the ratio for the peak fraction is approximately 1.1. Sedimentation coefficients (so~o.,) of these fractionated samples show an approximately linear dependence on the logarithm of the molecular weight This behavior is that expected for rodlike molecules, and is in quantitative agreement for the with the theory ol Yamakawa and Fujii [(1973) Macromolecules 6, 407-4!5] sedimentajion coefficient of a wormlike chain with a per$stence length of 625 A, a diameter of 25 A, and a mass per unit length of 195 daltons/A. It appears that the wormlike coil model, without excluded volume, can represent the sedimentation behavior of DNA over the entire conformational range from rigid rod to flexible coil, using the above parameters. Equilibrium melting curves were determined for various fractions in aqueous 2.4 M tetraethylammonium bromide. A substantial broadening of the transition and decrease of the melting temperature were observed with decreasing molecular weight. Empirical expressions have been obtained relating both the transition temperature and breadth in this solvent to molecular weight.
(a, aw) a,,,/~@,,
a,.
INTRODUCTION The wormlike coil model provides a useful representation of the equilibrium and hydrodynamic properties of helical DNA molecules in tcrms of three parameters, the mass per unit length M,, the chain diameter d, and the persistence length 1/2k 1 (In addition, an excluded volume parameter may be necessary a t sufficiently high molecular weights.)* Hays et al.3and Yamakawa and Fujii4 have shown that sedimentation data on DNA samples in the molecular-weight range 3 X 105-l.lX lo8 daltons are accurately represented by a wormlike chain with a mass per unit length of 195 daltons/& a diameter of approximately 25 d, and a persistence length of approximately 600-650 d, corresponding to a statistical segment length (Kuhn length) of 1200-1300 d. Recent interest has focused on the extension of the range of data to higher molecular weights (chromosomal DNA5) where the wormlike coil approaches the limit of a flexible coil.
* To whom correspondence should be addressed. 393
@ 1975 by John Wiley & Sons, Inc.
394
RECORD, WOODBURY, AND INMAN
At sufficiently low molecular weight, the wormlike chain approaches the limiting behavior of a rigid rod. The early work of Doty et a1.6 on sonicated fragments of DNA in the molecular-weight range 3 x 105-7.4 106 daltons (weight average iLTWdetermined by light scattering) yielded a dependence of sedimentation Coefficient(SZO.,~) on the 0.37 power of the weight average molecular weight. Recently, Prune11 and Bernurdi,’ working with enzymatically degraded DNA fractionated on agarose columns, found that s O z O varied ,~ with the 0.32 power of the weight average molecular weight in the range 2.9 X 104-2.9 X lo5daltons. (Molecular weights AXw were evaluated by equilibrium ultracentrifugation). These exponents fall between those expected for flexible coils and rigid rods, and suggest a stiff but not yet rodlike configuration for DNA in this molecular-weight range. Cohen and Eisenberg8 chxamincd a single sonicate of molecular weight approximately 5 X lo5daltons by electron microscopy and light scattering, and found that the molecules were extended to approximately S9% of their contour length in solution. Eisenbergg showed that the sedimentation coefficients of the Cohen-Eisenbcrg sampltl and the lower molecular-weight Doty-McGill-Rice samples were in approximate agrec~mmtwith the predictions of the hydradynamic theory for cylindrical particles. However, the lack of quantitative agreement betn-een theory and experiment over this molecular-weight range for a unique choice of parametcrs (mass per unit length, cylinder diametcr) indicates that deviations from rodlike behavior exist in this region. The general theory for the Sedimentation coefficient of wormlike chains, as discussed most recently by Yamakawa and E ’ ~ j i ipredicts ,~ the functional form of the approach to rodlike behavior in the low-molecular-weight limit in terms of the same parameters ( M L , d, and 1/2h) used to characterize the wormlike chain a t higher molecular weights. Lack of data in the lowmolecular-weight region near and below that corresponding to one persistence length (-2.4 X lo5 daltons) has prcventcd a test of the predicted limiting behavior. In this paper we discuss thc preparation of fractionated DNA samples in t h r size range from 3 X 104-3 X lo5daltons, and the characterization of these DiYA fragments by electron microscopy, sedimentation velocity, and thermal denaturation. Thcse fragments, as we will show, define the rodlikc limit for DNA.
x
METHODS Sonication Calf thymus DNA (Sigma Chemical Company “highly polymerized”) was dissolved in BPES buffer (0.006 M Na2HP04,0.002 &f NaH2P04,0.001 M Na2EDTA,0.179 M NaCl) a t a DNA concentration of 25-75 mg/ml. A 6-ml sample was diluted with three volumes of glycerol and the resulting solution (solvent viscosity -500 cp) was sonicated for a total of 30 min with a Branson sonifier (WlS5,20 kHz). The sample was maintained in an
RODLTKE DNA FRAGMENTS
395
ice-salt bath a t -10°C. Bursts of 2-3-min duration a t 70 W power were alternated with pauses to permit cooling of the sample.
Fractionation Sonicated samples were fractionated by gel filtration on columns of agarose A-15m beads (Bio-Rad Laboratories). 1-ml samples of the sonicate were layered on columns 40-60 cm long and 1.8-2.8 cm diameter, and eluted with BPES buffer a t flow rates of 30-45 ml/hr. Pragress of fractionation was monitored by absorbance a t 260 nm. After elution of the void volume (-80 ml) the sample camp off in three peaks: an initial small peak (3% of the material or less, eluted in approximately 15 ml), the central peak, containing 97% of the DNA in a volume of 140 ml, and a final small peak (less than 0.1% of the material, eluted in approximately 10 ml). The leading and trailing peaks were discarded. Observation of the material in the central peak by electron microscopy showed the presence of a f w larger molecules, which should have eluted with the initial, excluded material but may havc adhered to the column walls and been washed off with later fractions. Consequently, the central peak fractions werc pooled, reconcentrated by dialysis against polyethylene glycol or by repeated evaporations a t 25°C in an air stream interspersed with dialysis into BPES (this process tool; approximately 48 hr zn toto) , and refractionated on a sccond A-13m column. Either 2- or 4-ml fractions were collected in the region of the broad cmtral peal;. These were used for electron microscopy, sedimcntation, and thermal denaturation studies. (Similar applications of gcl filtration to the fractionation of DNA fragments have been recently reported by Prune11 and Bernardi7and Britten et al.ln)
Electron Microscopy Refractionated samples from two different sonication experiments were examined in the electron microscope. The designations “peak” and “trailing” refer to fractions from one experiment; from a second, six fractions (15, 25, 37, 50, 61, and 70) mere chosen to span the width of the central peak. Each 2-ml fraction represented 1.3% of the elution volume of the central peak. Aliquots of these fractions (A260 > 0.25) were diluted with buffer at p H 9.9 to contain 0.02 M Ka?COa,0.0032 A 1 EDTA, 10% HCHO, 0.01% cytochrome c, and 0.5 pg/ml DNA. I n some cases P4 DNA was added as a n internal standard. I n other cases a sample of P4 DNA was prepared in parallel for microscopy, and measured as an external standard. All solutions were mixed with equal volumes of formamide before spreading. Details of the spreading procedure and the subsequent handling and shadowing operations are reviewed by Inman. l1 Samples were examined in a Philips EM-300 a t a nominal magnification of 33000X. Xolecules were measured from electron micrographs with a Sumonics Corporation digitizer, interfaced to a Hewlett-Packard 9820/9862A calculator/plotter for display of th(1length histogram for a given fraction (see Results).
396
RECORD, WOODBURY. AND INMAN
The lengths of phage DNA molecules used as primary and secondary molecular-weight standards are accurately reproducible under the spreading conditions used here. Younghusband et a1.12have measured the length of P4 DNA t o b r 4.1 f 0.07 pm, and calculate its molecular weight to be (7.35 =t0.14) X lo6daltons, based on 4X174RF and hCI857 DNA. This corresponds to a mass per unit length of 179 f 4 daltonsl8. Measurement of the length of P4 DNA as an internal standard in three samples resulted in a value of 4.09 f 0.05 pm. Since this is in close agreement with the value cited above, a mass per unit length of 179 daltonsl8 was used to convert measured fragment lengths to molecular weights. Length measuremrnts became ambiguous for thr smallest fragments. The width of a DNA molecule coated with cytochrome c and shadowrd with platinum was measured to be 61 f S 8. Molecules whose length w s! comparablc to their nidth (in practice, those with lengths below 100 A) could not be identified or measured with certainty because of the background grain structure, and so were omitted from the distributions. Fraction 70 appeared to contain a substantial number of thew molecules, and as a result a representative molecular-weight distribution could not be obtained for it. For larger molecules, it was assumed that the cytochrome c coated the ends as well as t hr length, and a visual correction was madr in the courw of measurement to comprnsate for the presence of the cytochrome c “caps.” Without this correction, molecular lengths could be overestimated by as much as 50 b. Icor the smallest fraction investigated (that designated as trailing) the weight average molecular length was approximately 250 8 aftrr correction, and as much as a 25% error could be introduced by ignoring the effect. We estimate that an uncertainty of approximately = t l 5 8 remains in the measurements. This results in an uncertainty of f2700 daltons in the molecular weights of the molecules, or an uncertainty of =t6% in the molecular weight of thr trailing fraction. For the highest molecular-weight fraction, the error due to the caps is only f 1%. Other minor errors, introducrd in the digitizing process, include a length-independent averagr error of +0.6%, and t h r resolution limit of approximately 6 8 (corresponding t o 0.25-mm digitizer resolution). Overall uncertainties in molecular-weight determinations therrfore range from +S% at 45,000 daltons to f3% a t 243,000 daltons.
Sedimentation Velocity sedimentation experimrnts were performed with a Spinco model E ultracentrifugr with absorption optics. Samples nere run a t concentrations of 5-20 pg/ml in BPES buffer using 12- or 30-mm cells at speeds in the range 36,500-44,770 rpm. Sedimentation coefficients were calculated from the motion of the midpoint of the sedimrnting boundary, using tracings of the films made on a Joyce-Loebl microdensitometcr. Boundaries remained symmetrical during the course of sedimentation, although broadening of the boundary due to diffusion and molecular-weight heterogeneity was observed as a function of timr. Within experimental error, no concentration
RODLIKE DNA FRAGMENTS
397
dependence of the sedimentation coefficients was noted in experiments a t 5, 10, and 20 pg/ml for a sample of molecular weight 110,000 daltons. This is in agreement with an estimate from the equation of Eigner and DotyL3that s and so differ by less than 1% over the range of molecular weights and concentrations investigated here. Sedimentation coefficients were corrected to the density and viscosity of water a t 20°C; the maximum correction was approximately 5%. Our estimate of the error in the determination of sedimentation coefficients, based on the reproducibility of individual measurements and the scatter of data points within a given run, is +0.4 S. This amounts to an error of + l o % in s ~ a t the ~ ~ lowest molecular weight investigated, and a n error of +S% a t the highest molecular weight. To examine the condition of the single strands of fragments produced by extended sonication, a n alkaline sample (0.1 M KaOH, 0.9 M NaC1) of a fraction of weight average molecular weight 110,000 (doubled stranded) was sedimented to equilibrium a t 10,589 rpm in an AnJ rotor (30-mm centerpiece, DNA concentration 7 pg/ml) . Equilibrium was attained in approximately 72 hr in the 1-em solution column; the run was continued for a n additional 30 hr beyond this point. At the speed selected, the equilibrium concentration of polymer a t the meniscus was essentially zero. Concentrations c as a function of radial distance r were determined using absorption optics and the linear film response region (the upper 80% of the cell). A plot of In c versus r 2 was linear over this region, and a n apparent molecular weight of 42,000 (intermediate between a weight and z average)' was obtained from the slope. Since the effects of high polyelcctrolyte charge, finite polymer concentration, and hydrolytic scissions a t the alkaline p H of the experiment would combine to reduce the apparent molecular weight from the ideal value, we interprct the correspondence between the observed and expected valurs (42,000 versus 55,000, ignoring the difference between the types of averages used) to indicate that there is less than one brcak per strand in the sonicated fragments. This is reasonable, since a single-strand break would be expected to bc a prime site for fragmentation of the molecule in the sonication experiment.
Denaturation Tetraethylammonium bromide (TEA, polarographic grade) was obtained from Southwestern Analytical Chemicals. TEA was dissolved in redistilled water to male a 4.0 M stock solution, clarified by sedimentation, titrated with HCl to p H 5.5, and mixed with fractions of calf thymus DNA (in 0.05 M phosphate buffer, p H 7.0) in a 3:2 ratio to produce solutions with a TEA concentration of 2.4 M and with DNA concentrations in the range 2 4 0 pg/ml. The pH of the final solution was 7.85 + 0.05 (meter reading). Melting curves a t this TEA concentration (for which Rlelchior and von Hippel14 have shown that effects of base composition on the transition temperature and transition breadth are eliminated) were determined on a
,
~
RECORD, WOODBURY, AND INMAN
398
Gilford 2400s spectrophotometer, using a calibrated platinum resistance probe in the cell compartment. Three samples and a blank were heated simultaneously in Teflon-stoppered cells a t a rate of 0.2O0C/min. (The rate of temperature rise was controlled with a geared drive on the thermoregulator of the circulating bath.) Transition temperatures T , were taken as the 50% transition point. Corrections were applied for linearly sloping baselines in the region of the transition. Transition breadths A were determined from the inverse of the transition slope a t the transition midpoint. (A = (be/bT);=,,,, where 0 is the fractional advancement of the transition.)
RESULTS AND DISCUSSION Electron Microscopy Histograms determined by electron microscopy showing the distribution of molecular lengths in high- and low-molecular-weight fractions (15 and 61) are shown in Figures 1 and 2. Number and weight average molecular weights computed from the histograms, the ratio aW/iiTn, and the number of molecules measured in each fraction are summarized in Table I. The fractionation obtained by gel filtration is quitr good, particularly in the leading (high-molecular-weight) half of t h r peak ($f,/AZn < 1.1).
(an, a,)
TABLE I Results of Electron JMicroscopy and Sedimentation Velocity Experiments Fraction Molecules M n li?, S020.w Number Counted x 10-4 x 10-4 2i?w (Svedbergs) 1.j 2.5 37 Peak 50 61 Trailing
22.9 17.7 10.6 8.0 7.2 6 .0 4.0
103 78 1-54 216 114 25 1 148
24.3 19.1 11.4 9.0 8.8 7.3 4 .5
F r o c l i o n 15 103 molecules
I -
n .06
.03
.09 .I2
1.06 1.08 1.08 1.12 1.22 1.22 1.12
.I5
.I8
2 1
.24
2 7
7.2 6 .3 5.7 6.4 5.4 4.7 3.9
-
.30
Length in microns
Fig. 1. Molecular-length distribution determined by electron microscopy for fraction 15 (of 70 2-ml fractions); A?, = 243,000, aW/a,, = 1.06.
399
RODLIKE DNA FRAGMENTS
.02
.04
.36
.08
.I0
Length in microns
Fig. 2. Molecular-length distribution determined by ele$oemicroscopy for fraction 61 (of 70 2-ml fractions); = 73,000, M w / M , = 1.22.
ivw
From Table I it is apparent that prolonged sonication in 75% glycerol produces a range of molecules with molecular weights as much as a n order of magnitude lower than those previously obtained by this technique. (Britten et al. have recently found a similar extent of degradation following highspeed stirring in glycerol-water mixtures, and Prunell and Bernardi have enzymatically degraded DNA to this size range.7) However, the distribution of molecular weights in our sonicate may be substantially broader than that obtained after sonication in aqutwus solution. Cohen and Eisenberg obtained X w / a n= 1.06 for a sonicate of molecular weight 5 X lo5.* Gel filtration is necessary to approach this degree of homogeneity in our samples. More than 1000 molecules in all were examined and measured by microscopy. The overwhelming majority of these had a rigid or gently curving appearance with no hairpin bends. There was no evidence of singlestranded (frayed) ends, though short single-stranded regions would not be detected. A few molecules of denatured DNA or RNA were observed in fraction 15; denatured molecules were not observed in other fractions.
Sedimentation Sedimentation coefficients SO^^,^) from boundary sedimentation experiments on the fractions examined by electron microscopy are included in Table I. The data are plotted in Figure 3 as a function of logarithm of the molecular weight (aw) of the fraction. Our sedimentation coefficients agree, within experimental error, with those calculated from the empirical equation of Prunell and Bernardi,’ determined for fractions of enzymatically degraded (and therefore nicked) DNA. This observed agreement gives further support to the conclusion of Hays and Zimml* that the presence of single-strand breaks does not affect the hydrodynamic properties of helical DhTA. I n addition, previously reported determinations of SO^^,^ for a variety of samples in the molecular-weight range 3 X 105-4 X lo6daltons are included in Figure 3. Of these, the measurements of Cohen and Eisenberg (soni-
RECORD, WOODBURY, AND JNMAN
400
Fig. 3. Variation of sedimentation coefficient S O ~ O , with ~ weight average molecular weight (plotted on a logarithmic scale). Filled data points refer to measurements on ? ' ~ Sinsheimer relatively homogeneous samples: ( 0 ) this work, (m) E i ~ e n b e r g , ~ (A) (@X174).'6*17 Other data are from (0)Eigner and I l ~ t y , (0) ' ~ Hays and Zimm (control and nicked samples),18( A ) Reinert, et a!. (corrected for polydispersity).lg The solid line is the theoretical relatio? of Yamakawaoand Fujii4for a wormlike cyldnder with mass per unit length 195 daltonslh, diameter 25 A, and persistence length 625 A.
a,
cated calf thymus DXA, so20,m= 8.12 S,9ATrn = 4.92 X lo5 as determined by light scattering,15) and Sinsheimer and co-workers (4x174 DITA, S ~ Z O .= ~ 14.3 S for the linear double-stranded form 111,I'j iVrn = 3.4 X lo6as calculated from the light-scattering value for the singlc-stranded form17) were made with esseritially homogeneous samples. Other data are taken from the literature survcy and experiments of Eigncr arid Doty13 (molecular weights determined by light scattering or from the Flory-Rlandelkern equation), and the cxperiments of Hays and ZirnmI8 on nicked and control DNA (molecular weights determined from the Flory-Mandclkcrn equation) and of Rcinert et al.19 (molecular weights determined from the Svedberg equation). Only the data of Reinert et al. are corrected for polydispcrsity; as shown by Fujita et a1.20this correction becomes of increasing importance at low molecular weight. The uncorrected Sedimentation coefficient of a polydisperse sample is predicted t o be less than that of a homogeneous sample of thc same BW.Presumably this polydispersity effect is the cause of the observed systematic dcviations from the Yamakawa-Fujii curve in the molecular-weight range from 3-6 x lo5. The difficulties inherent in the determination of molecular weights of helical DKA samples by lightscattering measurements, even in this relatively low-molecular-weight range, have been discussed by Schmid ct a1.21 The 4x174 datum should be f r w of any uncertainty in this regard; however, a somewhat larger molecular weight (3.6 x lo6) has been recently reported for 4x174 DNA from length measurements relative to T 7 DNA in the electron Superimposed on the expcrimental points in Figure 3 is t h r theoretical curve of Yamakawa and Fujii4 for the dependence of sedimentation coefi-
RODLIKE DNA FRAGMENTS
401
cient on molecular weight f2r a wormlike cylinder with a persistence length of 625 8, a diameter of 25 A, and a mass per unit length of 195 daltons/8. This choice of parameters is within the range of persistence lengths (650 f 25 A) and diameters (25 f 1 8 ) found by Yamakawa and Fujii to give a satisfactory fit to sedimentation data in the molecular -weight range 3 X lo5 to 1.1 x 108 d a l t ~ n s . Hays ~ et al. also concluded that sedimentation data in this molecular-weight range could be ,fitwith a wormlike-coil model of persistence length 625 8 and diameter 25 A.3 From Figure 3 it is apparent that our sedimentation data on samples in the molecular-weight range 4 X lo4-3 X lo5daltons are consistent with the extrapolation of the Yamakawa-Fujii theoretical curve calculated using the above parameters. The equation for this curve, valid for molecular weights below 5.55 X lo5 daltons, is so20,u,= 1.525 In
A4
- 12.367
+ 1.043 X lop6M
+ 4.883 X 10-13 M 2 - 2.149 X 10-19 M 3 .
(1)
(Here, we have combined Eqs. 51,52, and 58 of the Yamakawa-Fujii paper, omitting higher order terms that contribute negligibly to the calculated sedimentation coefficient of a DNA model.) I n Eq. ( l ) , the first two terms on the right-hand side are independent of the choice of persistence length, and represent the functional dependence expected for rodlike particles of constant diameter and mass per unit length (see below). The final three terms depend also on the persistence length, and represent corrections to rodlike behavior that become increasingly important a t higher molecular weight. (Even a t 11.1 = 5.55 X lo5,however, these correction terms contribute only 9% of the calculated value of SO^^,^.) Above 5.55 X lo5,the valid relationship is sOZO,,
=
5.693 X lop3M”’
+ 4.351 + 1.043 X 1 0 2 h - ” * - 1.191 X
lo5 M-l - 5.506 X lo6 d4-”/‘. (2)
Here the first two terms represent the high-molecular-weight Gaussian limit, and the final three terms represent corrections for non-Gaussian behavior a t lower molecular weight. Excluded volume effects are not considered; a n excellent fit to published data is obtained without considering them, even up to molecular weights of 1.1 X los d a l t ~ n s . ~ I n Figure 4 we have replotted our sedimentation data and that of Cohen and Eisenberg on an expanded scale, and compared i t with theoretical curves calculated for various rodlike models. Again the Yamakawa-Fujii (YF) curve is included. As representations of rodlike behavior, we have plotted : the Riseman-Kirkwood (KR) expression for a chain of contiguous beadsz2(which is formally equivalent to the Perrin expression for a prolate ellipsoid of large axial ratioz3); the equation derived by Bloomfield et al. (BDH) for a cylindrical shell, neglecting end effects and retaining terms varying as the inverse first power of the axial ratio;24 and the expression of Broersma for a circular cylinder, including end effects and retaining terms of
RECORD, WOODBURY, AND INMAN
402
~
4.5X104
7.3~10~
I
1.l4xlO5
I
Mw
l.91~10~ 2.43~10~
I
I
4.92~10~
I
8
7-
6-
11.0
11.5
12.0
12.5
13.0
In ii, Fig. 4. The limiting rodlike region for DNA. The sedimentation data of Eisenberg9*16 ( 0 )and this work ( 0 ) (cf. Fig. 3 ) are plotted against In along with the theoretical
aw,
expression of Yamakawa and Fujii4 (YF) from Fig. 3. Plotted for comparison are three relationspps (shown as dashed lites) for stiff rods with a mass per unit length of 195 daltons/A and a diameter of 25 A: Riseman and Kirkwood fKR),22Bloomfield e t al. (BDH),24and Broersma (BLZ6
higher order in the inverse of the axial ratio.25 A mass per unit length of 195 daltons/i and a diameter of 25 were used throughout in these computations. From Figure 4 we conclude that the sedimentation behavior of DNA becomes indistinguishable from that of a rodlike molecule below a molecular weight of about lo5daltons. Below this point, the theoretical equations of Yamakawa and Fujii and Bloomfield et al. become virtually identical; these provide a somewhat better fit to the data than the equations of Riseman and Kirkwood or Perrin do. Surprisingly, the more exact treatment of Broersma does not fit the data in this region with a reasonable choice of cylinder diameter; a value in excess of 50 d is required to bring the Broersma equation into agreement with the experimental data. From the defining equations for the persistence length and end-to-end distance (h2)”’ of a flexible chain molecule, the ratio of the end-to-end distance to the contour length L can be evaluated for DNA of any molecular weight.26 At lo5 daltons, (h2)’,’/L= 0.87, or the molecule in solution is predicted to be extended to 87% of its contour length. This extent of curvature would not be a major deviation from the completely rodlike state. At 4.65 X lo5 daltons, the molecular weight of a sample examined by Cohen and Eisenberg,8 the DNA is calculated to extend to only 50% of its contour length. By comparison of light-scattering and viscosity estimates of the end-to-end distance for their sample (treated as a rod) with direct length measurement by electron microscopy, Cohen and Eisenberg con-
RODLIKE DNA FRAGMENTS
403
cluded that their sample was extended to S7-S9yO of its contour length in solution. This result would imply that the persistence length of DNA is substantially greater than 625 d in this molecular-weight range. * Schmid et aL2I have discussed potential sources of error in this result, and have taken the point of view that there is a unique persistence lcngth for DNA. Our present work supports the concept of a unique persistence length of 625 A for DNA, albeit indirectly. The DNA fragments we have investigated are too small to exhibit large deviations from rodlike behavior, and their sedimentation behavior can be fit by the Yamakawa-Fujii expression for a wide range of persistence lengths, since this parameter enters only into the corrections to rodlike behavior expressed in Eg. (1). It is however of significance that the Yamakawa-Fujii equation cxtrapolates correctIy into this rodlike region. One can therefore be confident that the excellence of its fit to the higher molecular-weight data (4 X 105-4 X lo6 daltons) is not accidental, but rather an indication that there is a unique persistence length for DNA.
Thermal Denaturation Studies Equilibrium melting curves were determined for unsonicated calf thymus DNA and for various fractionated DNA fragments in aqueous 2.4 M tetraethylammonium bromide (TEA), a solvent in which effects of base compositional heterogeneity are eliminated. l4 Wo were interested in the dependences of transition temperat.ure and breadth on molecular weight in this soIvcnt, as we11 as in dcrnonstrating the integrity of the double-helical structure under the conditions of our fragmentation experiments. As a result of previous theoretical and experiments with homop o l y r n e r ~ ~and ~ vnatural ~~ DNA,28t29 it is known that in the molecular-weight range where melting from the ends becomes a dominant mode of denaturation, a depression of the transition temperature and increase in transition breadth occur with decreasing molecular weight. Britten et a1.'0 have suggested that the T , depression be used to estimate the molecular weight of short DNA fragments used in hybridization or reannealing experiments. Wetmur has found that the tetraethyl quaternary salt solvent is very suitable for these renaturation experiments. 31 Hence a relationship between the T, depression and molecular weight in this solvent should prove useful. Figure 5 shows the gel filtration profile for the fractionation of samples (4-ml volumes) used in the denaturation experiments, and the sedimentation coefficicnts S O Z ~,lo determined for various fractions (A-G') across the peak. Since both s0pO,, and elution volume are approximately linear functions of the logarithm of the molecular weight in this range, it is not surprising that S O Z O , ~ varies linearly with the elution volume. Moleculsr weights for fractions were either determined directly from sedimentation coefficients * Recent unpublished work by Godfrey and Eisenberg [cited by Eisenberg, H. (1974) in Basic Principles i n Nucleic Acid Chemistry, Ts'o, P. O . , Ed., Acadoemic, New York, vol. 2, pp. 224-2251 gives a persistence length of approximately 600 A for sonicated, fractionated calf thymus DNA in the molecular-weight range 0.25 X 106-1.2 X lo6daltons.
RECORD, WOODBURY, AND INMAN
404
TABLE I1
Effect of
a,,, and Strand Concentration on Denaturation Parameters in TEABr
a,,,
Concentration (&ml)
Tm ("C)
13.2 1.5.4 27.1 -a3.3 9.1 18.4 36.7 38.2 2.2 18.8 34.0 9.0 20.7
67.9 67.9 67.8 67.8 6.5.4 65.3 64.7 66.4 61.2 61 . O 60.7 58.7 39 . 3
Unsonicated
78,000
40,000
30,000
I
/
A
("c) 1.2 1.1 1.1 1.1 2.7 2.8 2.0 2.7 6.6 5.1 5 .8 8.0 7.6
\ -\
0.50
Volume Collecled in ml.
Fig. 5. Absorbance AZ60 (@) and sedimentation coefficient s~zo,,,, (0)as a function of the elution volume from an A-15 column. 4-ml fractions were collected; S O P O . ~ was measured on those labeled A-G.
using Eq. (l),or by interpolation of a plot of elution volume versus the logarithm of the molecular weight. (The molecular weights of samples F and G were estimated by extrapolation of this plot, since they fell below the range in which direct calibration by electron microscopy was possible.) Representative melting curves are plotted in Figure 6. Data obtained from experiments over a range of molecular weights and DNA concentrations are collected in Table 11. A depression of the melting temperature and increase in transition breadth are noted with decreasing molecular weight; however the expected dependence of the T , on DKA concentration, which is predicted to appear in this r e g i 0 n , ~ ~is, ~not 8 noticeable in our experiments. (A dependence of T , on polynucleotide concentration has been observed by Hayes et al. in experiments covering a wider concentration range and utilizing smaller fragments than those studied here. 30) An unexpected decrease in the hyperchromic effect accompanying the transition was observed with decreasing molecular weight. The high
RODLIKE DNA FRAGMENTS
405
Fig. 6. Normalized melting curves for unsonicated calf thymus DNA ( 0 )and various fractionated fragments (Fig. 5 ) in 2.4 M TEA; ( 0 ) = 78,000, ( A ) ii?u = 48,000, (0)ii?w = 40,000,(H)ii?w = 30,000.
a,
polymer gave a hyperchromicity of approximately 40%; values in the range 40-30y0 were observed for fractions from the leading through the central region of the peak, with some scattering in the data. The lowest molecular-weight fractions consistently gave hyperchromicities in the range 30-2070, with substantial scatter (even from sample to sample within a single fraction) in the data. We were able to ascribe part of this effect to the presence of dialyzable impurities in the lowrr molecular-weight fractions. However, since the true dependence of hyperchromicity on chain length should be minimal in this molecular-weight region,27it is possible that there are some denatured molecules or single-stranded regions (frayed ends) in the populations of fractionated fragments. For the fractions of lowest molecular weight, the presrnce of frayed ends in double-stranded molecules could cause systematic errors in the so20,10 versus M calibration. We have attempted to estimate the possible extent of such fraying from the hyperchromicity data. While the uncertainties in the data are large, it appears that the absolute amount of fraying would have to increase with decreasing molecular weight to give the hyperchroniicities observed. This appears unreasonable, and we are left without a satisfactory explanation for the observed trend. The variation of T , and the breadth A with l / M for all fragments investigated is plotted in Figure 7. The theory of Applequist and Damle27 (for melting from the ends in molecules small enough so that the transition occurs a t temperatures substantially below the transition temperature T," of the infinite polymer) prrdicts that the transition breadth and the quantity ( l / T m - l / T m m )should each be proportional to 1 / M . For small depressions of the T , as encountered here, the latter quantity is proportional to the depression of the T , itself, and both the breadth and the T , depression are therefore expected to be proportional to l / M . This prediction has been verified for the T , (though not for the transition breadth) in other syst e m ~ . ~ ,Our ~ ~data , ~can ~ be , ~fit~to such a dependence, but are better fit by the smooth curves drawn through the data in Figure 7. Moreover, the
RECORD, WOODBURY, AND INMAN
406
M I
I 0
6.7x10'
2x10'
lo5
I
I
I
I
I
0.5
1.0
5x10'
4x10'
I
I
I
I
I
1.5
2.0
2.5
3.3x10'
2.9x10'
I
I
3.0
I
I
19
I0
3.5
1 0 ~ 1 ~ Fig. 7. Transition temperature T, ( 0 )and transition breadth (0)as a function of the reciprocal of the molecular weight. All fragments are from the fractionation of Fig. 5. (Molecular weights are shown in the nonlinear upper scale.)
T,
Depression
("C)
Fig. 8. Relationship between the transition breadth and the depression of the T, for the data of Fig. 7. The least squares line is drawn through the data (see text).
breadth and transition temperature vary together, so that the breadth may be represented as a linear function of the transition temperature, as shown in Figure 8. Such a relationship was also observed by Hayes ct aL30 over the low-molecular-weight range, but is not interpretable in terms of current helix-coil transition theory. A least squares fit to the data of Figure S gives the following equation relating transition breadth to transition temperature : A = A"
+ 0.732 (T,"
-
T,)
where A" is the transition breadth of the infinite polymer. Equations for the smooth curves drawn through the data of Figure 7, which are consistent with the relationship obtained from Figure 8, are
RODLIKE DNA FRAGMENTS
T," - T, A - A m =
=
1.75 X lo5
1.2s
x
M
0.25 X 1Oln
-I-
M
407
M2
0.1s x
105 +
1010
M2
Because of the scatter in the data, these clearly can serve as only a n approximate measurc of the fragment. molecular weight. The authors thank Dr. R. R. Burgess for the use of his sonicator, Dr. W. T. Szybalski for the use of his microdensitometer, and Drs. R. L. Baldwin, V. A. Bloomfield, H. Eisenberg, J. A. Schellman, H. Yamakawa, and B. H. Zimm for their comments on this manuscript. This work was supported by grants from the NSF and the Wisconsin Alumni Research Foundation (to PI'ITR), and from the N I H and American Cancer Society (to RI).
References 1 . Kratky, 0. & Porod, G. (1949) Rec. Trav. Chim. 68,1106-1122. 2. Gray, Jr., H. B., Bloomfield, V. A. & Hearst, J. E . (1967) J . Chem. Phys. 46,14931498. 3. Hays, J. B., Magar, M. E. & Zimm, B. H. (1969) Biopolymers 8,531-536. 4. Yamakawa, H. & Fujii, M. (1973) Macrcmolecules6,407-415. 5. Appleby, D. W., Hearst, J. E . & Rall, S. C. (1974) (hbstract 333, Biochemistry/ Biophysics Meeting, Minneapolis, Minn.) Fed. Proc. 33,1282. 6. Iloty, P., McGill, B. B. & Rice, S. A. (1958) Proc. Nut. Acad. Sci. U.S. 44, 432438. 7. Prunell, A. & Bernardi, G. (1973) J . Bzol. Chem. 248,3433-3440. 8. Cohen, G. & Eisenberg, H. (1966) Bzopolymsrs 4,429-440. 9. Eisenberg, H. (1969) Biopolymers 8,545-551. 10. Britten, R. J., Graham, I). E. & Neufeld, B. R. (1974) in Methods in Enzymology, Grossman, L. & Moldave, K., Eds., Academic, New York, vol. 29, pp. 363-419. 11. Inman, R. B. (1974) in Methods i n Enzymology, Grossman, L. & Moldave, K., Eds., Academic, New York, vol. 29, pp. 451-458. 12. Younghusband, H. B., Egan, J. B., & Inman, R. B. (1975) in preparation. 13. Eigner, J. & Doty, P. (1965) J . Mol. Baol. 12,549-580. 14. R'felchior, Jr., W. B. & von Hippel, P. H. (1973) Pioc. Nut. Acud. Sci. U.S. 70, 298-302. 15. Cohen, G. & Eisenberg, H. (1969) Biopolymers 8,45-55. 16. Burton, A. & Sinsheimer, R. L. (1965) J . Mol. Biol. 14, 324-347 icf. Friefelder, D. (1970)J. Mol. Bid. 54,567-5771. 17. Sinsheimer, R. L. (1959) J . M o l . Biol. 1 , 4 3 4 3 . 18. Hays, J. B. & Zimm, B. H. (1970) J . M J ~Biol. . 48,297-317. 19. Reinert, K. E., Strassburger, J. & Treibel, H. (1971) Biopolymers 10,285-307. 20. Fujita, H., Teramoto, A., Yamashita, T., Okita, K. & Ikeda, S. (1966) Biopolymers 4,781-791. 21. Schmid, C. W., Rinehart, E. P. & Hearst, J. E. (1971) Biopolymers 10,883-893. 22. Riseman, J. & Kirkwood, J . G. (1956) in Rheology, Academic, New York, vol. 1, pp. 495-523. 23. Perrin, F. (1936)J. Phys. Radium7,1-11. 24. Bloomfield, V. A,, Dalton, W. 0. & van Holde, K. E. (1967) Biopolymers 5, 135148. 25. Broersma, S. (1960) J . Chem. Phys. 32,1632-1635. 26. Schellman, J. A. (1974) Biopolymers 13,217-226.
408
RECORD, WOODBURY, AND INMAN
27. Applequist, J. & Damle, V. (1965)J. Amer. Chem. Soe. 87,1450-1458. 28. Crothers, D. M., Kallenbach, N. R. & Zimm, B. H. (1965) J. MoZ. Biol. 11,802820. 29. Lazurkin, Yu. S., Frank-Kamenetskii, M. D., & Trifonov, E. N. (1970) Biopolymers 9,1253-1306. 30. Hayes, F. N., Lilly, E. H., Ratliff, R. L., Smith, D. A., & Williams, D. L. (1970) Biopolymers 9,1105-1117. 31. Chang, C. T., Hain, T. C., Hutton, J. R., & Wetmur, J. G. (1974) Biopolymers, 13, 1847-1858. 32. Wilson, D. A. & Thomas, C. A. (1974)J. Mol. Biol.84,115-144.
Received August 26, 1974 Accepted October 30, 1974
