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Volume 3 no.11 November 1976 Nucleic Acids Research Sheared DNA fragment sizing: comparison of techniques Charles P.Ordahl, Thomas R.Johnson and Arnold I. Caplan Departments of Biology and Anatomy, Case Western Reserve University, Cleveland, OH 44106, USA Received 2 August 1976 ABSTRACT DNA fragmented by conventional French press shearing procedures (30,000 lbs/in^) has a number-average fragment size of 230 base pairs. This is considerably smaller than the 450 base pairs typically reported for DNA sheared by this method. Comparison of 5 sizing techniques indicates that sheared DNA fragment size is overestimated by either measurement of velocity sedimentation or Kleinschmldt Electron Microscopic visualization. Both adsorption grid electron microscopic visualization and gel electrophoresis yield the most reliable estimates of the mean size of small DNA fragment populations. In addition, the assessment of fragment size distribution (not possible from sedimentation analysis) potentially allows more critical evaluation of DNA hybridization and reassociation kinetic and measurement parameters. INTRODUCTION DNA reassociation and hybridization analysis requires the use of fragmented DNA . Precise information regarding the size of the DNA fragments is essential to interpretation of these kinds of experiments. Fragment size is not only an integral element in the kinetics of DNA reassociation and hybridization, but also affects the kinds of DNA-DNA or DNA-RNA duplexes obtained. For some experiments it is necessary to use long (>1000 base pair) fragments of DNA. Fragments of this size have been used to determine the extent of inter2 3 4 sperslon of repeated and nonrepeated sequences of DNA in eucaryotes ' ' In general, however, on kinetic and other grounds it is advantageous to use short DNA fragments less than 500 base pairs in length . This length not only permits separation of the repetitive and nonrepetitive components of most eucaryotlc genomes ' ' , but also reduces the amount of single strand tails 7 8 9 in reassociated and hybrid duplexes ' ' A variety of methods have been employed to shear high molecular weight DNA to fragments of a particular desired size . One of the most common methods is to force a DNA solution through the valve of a high pressure cell 2 5 at a constant pressure of between 30,000 and 50,000 lbs/in . DNA frag- mented in this manner i s typically reported to be 450 base pairs in length © Information Retrieval Limited 1 Falconberg Court London W1V5FG England 2985 Nucleic Acids Research 1 2 3 5 9 as determined from measurement of sedimentation velocity ' ' ' ' results presented here show that DNA sheared at 30,000 lbs/in ably smaller than the 450 base pairs typically reported. The is consider- DNA sheared in this manner has a mean fragment length of 220-235 base pairs as determined by gel electrophoresis and adsorption grid electron microscopy. Comparison of 5 sizing techniques indicates that both velocity sedimentation and Kleinschmidt electron microscopy overestimate mean fragment size in sheared DNA preparations. The implications of these observations are discussed as they relate to the current reassociation and hybridization technology. METHODS AND MATERIALS Preparation of DNA Nuclei were prepared by homogenizing chick embryonic brain tissue in 0.075 M NaCl, 0.025 M EDTA, pH 8 (Buffer A) at 4°C with 1% NP-40 (Shell) in a loose fitting dounce homogenizer. Cell breakage was virtually complete and nuclei were pelleted at 3,000 RPM for 10 min (Sorvall HB-4) and resuspended in Buffer A without NP-40 using a dounce homogenizer. The nuclei were again pelleted and resuspended in 0.1 M NaCl, 0.05 M Tris pH 7.4, 0.001 M EDTA (Buffer B ) ; SDS was added to a final concentration of 1% and the suspension homogenized. An equal volume of phenol saturated in Buffer B was added and the mixture shaken at room temperature for 20 minutes and then centrifuged at 5,000 RPM for 10 min at 20°C. The aqueous phase was removed and extracted twice more with phenol as above and then extracted once with chloroform: octanol (8:1) to remove phenol and precipitated overnight at -20°C with 2.5 volumes of ethanol. The DNA precipitate was pelleted at 10,000 RPM for 30 min at -10°C and redissolved in Buffer B at a concentration of <5 mg/ml (A 2 g. = 100). This solution was then loaded into a french pressure cell (Aminco) and expelled at a constant pressure drop of 30,000 psi using an Aminco french press at a rate of 1-5 mls/min. Sheared DNA was then treated with RNase B (Worthington 50 yg/ml 1 hr 37°C) and pronase (Sigma 50 ug/ml 1 hr 37°C) and phenol extracted and ethanol precipitated as above. After collecting the ethanol precipitated DNA, it was excluded on Sephadex G-100 (Pharmacia) to remove digested RNA fragments and phenol and stored as an ethanol precipitate at -20°C until needed. A A manner had an 260^ 280 = 1-83-1.85. bias nic fibroblast culture using 10 previously Sheared DNA purified in this DNA was radiolabeled in chick embryo- H-Thymidine (Amersham Searle) as described Sucrose Gradient Centrifugation Neutral linear 5-20% sucrose gradients were made using Buffer B in SW- 2986 Nucleic Acids Research 40 Ti (Beckman) cellulose nitrate tubes (final volume 13 mis). DNA dissolved in 200 yl of Buffer B was layered onto the top and the gradients centrifuged at 30,000 RPM for 16 hrs at 4°C. Alkaline sucrose gradients were identical except that sucrose gradients were prepared in 0.1 M NaOH (pH 13). The DNA was dissolved in 0.1 M NaOH and heated to 65°C for 5 min before layering onto gradients. Centrifugation conditions were identical to those of the neutral gradients. Gradients were analyzed for absorbance at 254 nm on an Isco Model UA-4 gradient fractionator and recorder. Fractions (0.375 ml) were collected and neutralized with HC1 where appropriate. Radioactively labeled DNA was quantitated in trlton based scintillation cocktail (33% V/V Triton, 66% V/V Toluene, 0.53% W/V Omnifluor [Beckman]) at 30% efficiency. Model E Centrifugation Sedimentation analysis was conducted in a Beckman-Spinco Model E analytical ultracentrifuge equipped with an RTIC unit, electronic speed control, photoelectric scanner and multiplexer. An AnF rotor was used which incorpo- rated 3 cells with 12 mm light paths for scanning at 260 nm with ultraviolet optics. Centrifugation was conducted at 52,000 RPM at 20°C. DNA was sedi- mented in 0.12 M sodium phosphate buffer (NaPB pH 6.8). Observed S values were corrected to S-Q, W in the manner described by Studier after deter- mining the density (1.0114 g/cc) and viscosity relative to water (1.044) of 0.12 M sodium phosphate buffer. Sedimentation coefficients were determined by the method of midpoints for all runs. The log of the distance of the sedimenting boundary from the axis of rotation at the half-height of the boundary was plotted against time (seconds) and the sedimentation coefficient calculated from the slope of the line of best fit. Electron Microscopy For the grid adsorption method, DNA was mounted on grids from 0.12 M phosphate buffer and stained exactly as described in Johnson & Caston Kleinschmidt spreadings (13) were performed using a distilled water hypophase. The final composition of the hyperphase was: DNA, about 2 ug/ml; 0.02 M Tris, pH 7; 1 M ammonium acetate; and 0.01% cytochrome c. Films were picked up on carbon-coated Colloidon films and contrasted by shadowing with Pt:Pd 80-20. SV40 DNA (m.w. = 3.1 x 10 6 daltons) (kindly provided by Dr. Peter Tegtmeyer) was included for both procedures to serve as a length standard. For the grid adsorption method, micrographs were taken at a magni- fication of 60,000 to 80,000; for Kleinschmidt preparations, at about 20,000. Microscopy was performed with a Siemens 101A, operated at 80kV. Magnifica- 2987 Nucleic Acids Research tions were calibrated with a diffraction grating replica (58,000 lines/inch; Polysciences). Disc Gel Electrophoresis Disc gel electrophoresis was performed essentially by the method of Carroll & Brown1 . Disc gels (2.4% acrylamide, .12% bisacrylamide, 0.5% Agarose; 200 mm) were run at 5mAMP/tube for 4-5 hrs. Hind III nuclease (Miles) fragments of lambda DNA (Miles) was prepared according to Danna, Sack and Nathans . After electrophoresis the gels were stained for 30 minutes in 5 ug/ml ethidium bromide and then were irradiated on a long wave ultraviolet light box and photographed on Polaroid transparencies . The migration dis- tances were measured on photographic prints (see Figure 5 ) . Other gels were scanned at 260nm on a Gilford linear transport gel scanner to quantitate and record the distribution of sheared DNA fragments in the gel. The correspond- ing position of the Hind III fragments of lambda DNA was plotted on the recording (as in Figure 5) to calibrate the scan for distance versus molecular weight. The calibrated recording was then divided into increments of 25 base pairs and the area under the ultraviolet profile at each increment cut out and weighed on an analytical balance. The weight is directly proportional to the area and is therefore a measure of the relative mass of DNA at each 25 base pair increment. 4, panel "f". The results of these determinations is shown in Figure To determine the relative number of DNA molecules at each gel position (Figure 4, panel " c " ) , the relative absorbence was divided by the calibrated number of base pairs (i.e., rel. ^QQIIIO. fragments). base pairs = rel. no. Thus, taking a given absorbence reading at the 200 base pair position of the gel as corresponding to x number of DNA fragments, then the same absorbence reading at the 100 base pair position would correspond to 2x number of DNA fragments. The molecular weights of the fragments of lambda DNA generated by Hind III nuclease fragments were determined by relative electrophoretic mobility and by electron microscopy. reported by Carroll and Brown The fragment lengths are identical to those except for the smallest fragment (VII) which was found to be 395 base pairs in length rather than 525 base pairs in length. The differences in fragment length probably reflect differences between the lambda DNA obtained from Miles Laboratories and that employed by Carroll and Brown rather than differences in measurement technique or accuracy. 2988 Nucleic Acids Research RESULTS I. Sedimentation Analysis Historically, the most commonly used method for sizing DNA has been sucrose gradient centrifugation which was used to estimate sedimentation coefficient (S value). Figure 1 shows the sedimentation of sheared native (undenatured) DNA relative to that of ribosomal RNA in a linear, neutral sucrose gradient. This sizing approach is advantageous in that it is rapid and readily accessible to most laboratories and it affords an approximation of the average size and homogeneity of DNA fragments. Under denaturing (0.1 M NaOH) conditions there is no broadening of the sheared DNA peak indicating that there are few, if any^ "cryptic" single strand sissions in the sheared native DNA fragments. The sharpness of the sheared DNA peak is misleading 28s Top 11 11 t i i • n \ i i i t i i : 0.1- 10 i o ; i i (M 1 1 1 iA• i ; i i• 1 i i \ i / f1 / 1\ t t 5sJ \ 1 1* \ I 1 i 18s l |, ! i i i i i t i » ; \ \ / \ / / / ^ ^ — " / . 10 20 FRACTION 30 Fig. 1 Sucrose Gradient Sedimentation of Sheared DNA. Solid line shows the absorbtion trace of sheared DNA sedimentation in a neutral 5-20% sucrose gradient. Inclusion of 3H-labeled DNA (closed circles) demonstrated that background absorbence at the tube bottom is not due to DNA. The broken line shows the absorbence tracing for ribosomal RNA sedimentation in a parallel gradient. For procedural details see Methods and Materials. 2989 Nucleic Acids Research because, as demonstrated below, there is considerable heterogeneity in fragment size. Comparing the rate of sedimentation of the sheared native DNA to that of the 5S, 18S and 28S ribosomal RNA species yields an approximate sedimentation coefficient of 7S. Using the Studier equation relating the sedimentation coefficient [S] to molecular weight [M] of native DNA under nondenaturing conditions; S = 0.0882 M yields a value of M = 3.1 x 10 per fragment. 0>346 ; or an average of approximately 475 base pairs As demonstrated below, this is a considerable overestimate of the true average size of these DNA fragments. This overestimate arises, in part, from inaccurate measurement of S value by sucrose gradient sedimentation. The measurement of S value can be made more accurately by direct measurement in Model E centrifugation. S-Q Figure 2 shows the change in value for sheared DNA as measured in 8 Model E centrifugations over a 10-fold concentration range. Extrapolation of this change in S tration yields a value of S.Q 20,w to zero concenof 6.7 which represents an estimate of the sedimentation velocity of the sheared DNA in the absence of intermolecular 0.2 0.1 10 20 30 40 ug DNA/ml Fig. 2 Sedimentation Analysis of Sheared DNA. Sheared DNA was sedimented in 8 -model E centrifuge runs at various concentrations and the observed S values corrected to S20 w as described in Methods and Materials. Extrapolation of the value l/S2o'w * 8 s n o w n a s a means of estimating the sedimentation velocity in the absence'of intermolecular interaction (S°,Q w ) . The value for 1 / S 2 Q w is 0.1475 corresponding to S§o,w = 6.7S. 2990 Nucleic Acids Research effects. Using the Studier equation, as above, this S value estimates the sheared DNA molecular weight to be 272,000 daltons or approximately 420 base pairs. It is clear that even slight inaccuracies in estimation of S can give rise to large inaccuracies in molecular weight estimation. Further experi- ments presented below, however, also indicate that the Studier formula for relating S to DNA molecular weight also tends to overestimate the molecular weight of very small DNA fragments such as those being measured here (see Discussion). II. Electron Microscopic Visualization Visualization of DNA molecules in the electron microscope permits an essentially direct measurement of fragment size. This technique employs fewer correction factors and assumptions necessary to translate measurement into molecular weight. The most common technique for visualizing DNA is the Kleinschmidt procedure in which DNA embedded in a protein film is applied to a grid and rendered electron dense by staining or metal evaporation Figure 3a shows an electron micrograph of sheared native DNA as visualized by the Kleinschmidt procedure and Figure 4a and d shows the distribution of contour lengths (in base pairs) of 379 sheared native DNA fragments visualized by this technique. The number average length of the DNA fragments in this distribution is 333 base pairs. •m Fig. 3 Electron Micrographs of Sheared DNA. Panel "a" is a low magnification of sheared DNA as visualized in a Kleinschmidt preparation. Circular DNA molecule in "a" is SV-40 DNA included in all preparations as standard. Panel "b" is higher magnification of sheared DNA visualized by the adsorption grid procedure. The arrow in "b" indicates a 100 base pair fragment. Panel "c" is Kleinschmidt grid visualized at the same magnification as in panel "b". The bracketed bar spans 1000A in each panel. 2991 Nucleic Acids Research Figure 3b shows sheared DNA as visualized by the adsorption grid electron microscopic procedure. This technique differs significantly from the Kleinschmidt procedure in that visualization of the DNA is done by direct staining without intervention of a coating of cytochrome c. Briefly, DNA is adsorbed onto grids charged with the commercial disinfectant Zephiran and 12 stained with uranyl acetate . As a result, the visualized DNA fragments have a diameter of approximately 20A, closely approximating that expected for DNA in solution, and the DNA fragments are easily resolved above grid background (Figure 3b). Comparison, at the same magnification, of an adsorption grid micrograph (Figure 3b) to a Kleinschmidt micrograph (Figure 3c) demonstrates the increased resolution afforded by the grid adsoprtion procedure. For example, the 100 base pair fragment indicated by the arrow in Figure 3b CO 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 BASE PAIRS ( x i o o ) Fig. 4 Size Distribution of Sheared DNA Fragments. Panels a, b and c show the relative number of DNA molecules corresponding to given length increments (base pairs) as determined by Kleinschmidt EM, Adsorption EM and gel electrophoresis procedures, respectively. Panels d, e and f show the relative mass of DNA at each length increment as determined respectively by the Kleinschmidt EM,Adsorption EM and gel electrophoresis procedures. The vertical bar in a, b and c indicates the median fragment number. In d, e and f the vertical bars labeled "n" represent the number average length while that labeled "w" represents the weight average length. Relative number and mass units were used to facilitate comparisons between the 3 measurement techniques. The units for each panel were established by setting the arbitrary value of 10 at the measurement increment with the greatest abundance of DNA mass or number. This makes all distribution profiles have the same maximum height. The actual number of DNA fragments measured by electron microscopy was 379 in the Kleinschmidt preparation and 640 in the adsorption grid preparation. 2992 Nucleic Acids Research would be indistinguishable from grid background in Figure 3c. It is not sur- prising, therefore, that the distribution of fragment lengths as determined by adsorption grid microscopy (Figures 4c and 4f) demonstrates the presence of a large number of small (less than 100 base pair) DNA fragments which were not scored by the Kleinschmidt procedure. This, of course, has a considerable effect on the estimates of average fragment size obtained by the two methods (see Discussion). III. Gel Electrophoresis Gel electrophoresis permits highly precise estimates of DNA fragment size because DNA fragment standards of precisely known molecular weight are available by digestion of viral DNA with restriction nuclease. Figure 5 shows that the relative electrophoretic mobility of lambda DNA fragments resulting from Hind III nuclease digestion is linear with respect to the logarithm of the base pair length for fragments less than 3,000 base pairs long. These restriction fragments therefore serve to calibrate the gel to relate DNA electrophoretic mobility to DNA molecular weight and as a result a logarithmic base pair scale can be superimposed over the gel length (Figure 5 ) . Using this scale it can be seen that the majority of the sheared DNA fragments migrate at a rate indicating that they are between 200 and 300 base pairs in length. Examination of a gel as in Figure 5 does not, however, permit critical evaluation of the distribution of fragment lengths because the base pair scale is logarithmic and thereby tends to concentrate larger fragments and dilute smaller fragments. To assess the distribution of fragments, cali- brated gels were scanned at 260 nm and the U.V. profile replotted on a linear scale of fragment length (Figure 4f, and Methods and Materials). Here it can be seen that the mean fragment length (number average) is 233 base pairs and that there is a predominant mode of fragments centered at approximately 200 base pairs. The median fragment length is 200 base pairs as shown in Figure 6c by a plot of the same data in terms of the relative number of DNA fragments in each size class. The data in Figure 6c and f demonstrate that an electropherogram such as in Figure 5 does not readily permit assessment of either the distribution or mean length of heterodisperse DNA fragment populations such as those obtained by shearing processes. It is therefore advan- tageous to replot gel electropherograms to assess the distribution of fragment size in heterodisperse DNA fragment populations. This distribution profile also permits more critical comparison of the relative accuracy of the various sizing techniques studied (see Discussion). _ _ Nucleic Acids Research 8 5 BASE PAIRS (x 100)+ 9876 5 4 mi 3 i i i If ' J '——t ' Relative Migration g '— Fig. 5 1 Electrophoretic Mobility of Sheared DNA Relative to Hind III DigestedLambda BNA. Bottom panel shows position of Hind Ill-Lambda DNA markers (Gel A & C) relative to sheared DHA (Gel B) . Upper panel shows the line establishing the relationship between relative electrophoretic mobility of Hind III digested lambda DNA fragments as standards and molecular weight in base pairs. This line calibrates the gel permitting superimposition of the base pair scale above the gels. Closed circles show position of Hind III lambda fragments. Open circle shows apparent midpoint of sheared DNA band. Right angles along calibration line show the relationship between the horizontal base pair scale superimposed over the gels and base pair scale on the vertical axis. For details see Methods and Materials. DISCUSSION The purpose of the measurements reported here is to compare the estimates of sheared DNA fragment size obtained by a variety of techniques. The results indicate that conventional French press shearing techniques (30,000 2994 Nucleic Acids Research 9 lbs/in ) yields fragments approximately 230 base pairs in length. In most cases DNA fragmented by French press shearing is reported to be 450 base pairs 1 2 3 5 9 in length ' ' ' ' , as determined by sedimentation velocity analysis. Comparison of the data obtained from the sizing techniques employed here indicates that the average size of sheared DNA fragment populations is overestimated by either velocity sedimentation of Kleinschmidt electron microscopic analysis. Comparisons of average molecular weight estimates obtained by different techniques cannot always be made directly because some measurement techniques give disproportionate weight to the largest molecules in a DNA fragment population . This gives rise to different estimates of average molecular weight which are not related to measurement accuracy. Table I compares the esti- mates of sheared DNA fragment size which are obtained from each technique as they relate to weight average molecular and median molecular weight. velocity sedimentation only gives a weight average molecular weight Because , it is appropriate to compare this technique to the others only with respect to this value. Even when this is done, it can be seen that Model E centrifugation determination of S value gives an estimate of weight average molecular weight approximately 30% higher than that obtained by either gel electrophoresis or adsorption grid electron microscopy (Table I ) . While there is apparent Table I. Estimates of Average Molecular Weight in Base Pairs of Sheared DNA;* Measurement Technique Median Weight Mw Sucrose Gradient Centrifugation 475 Model E Centrifugation 420 Mn Median Number Kleinschmidt EM 360 393 333 295 Adsorption Grid EM 278 293 222 204 Gel Electrophoresis 260 312 233 222 * Molecular weight averages, expressed in base pairs, were calculated by the following formulas: £ n-j M-i M.T = „ 7 .,1 w Z n^_ M-; . ; and Where n^ is the number and M.^ is the base pair length of the DNA fragments at each measurement, ^ is the weight average molecular weight and M^ is the number average molecular weight^?. Median weight and median number show the midpoint of the fragment populations as assessed from total fragment weight and number, respectively. Sucrose gradient and Model E centrifugation estimates were made using Studier equation^-'-. All other estimates were calculated from the data shown in Figure 5. 2995 Nucleic Acids Research reasonable agreement between the Model E values and the Kleinschmidt electron microscopy value,other considerations, presented below, indicate the latter technique also overestimates the average size of heterodisperse populations of small DNA fragments. We conclude, therefore, that estimation of the molecular weight of small DNA fragments by either sucrose gradient or Model E centrifugation overestimates the true weight average size of the fragments. This is most probably due to the fact that Studier used DNA molecules over 100 times larger than those being measured here to formulate the equations relating S value to molecular weight for DNA . It would appear possible to re-calibrate the relationship between S and molecular weight for small DNA fragments using restriction endonuclease DNA fragments of known molecular weight. However, even if this were done, the use of sedimentation velocity measurement, although rapid and convenient, would remain less satisfactory for measuring small DNA fragments than the other methods discussed below because it is limited to estimation of weight average molecular weight alone. Because this average is strongly biased towards the molecules of highest molecular weight , it is less useful for calculation of the kinetic para- meters involved in DNA hybridization and reassociation as discussed below. The more useful number average molecular weight estimate is impossible to derive from the weight average without knowing the distribution of fragment lengths. Thus, even under ideal circumstances, the estimation of the average molecular weight of heterodisperse DNA fragment populations by sedimentation velocity is potentially less useful than estimates obtained by the other techniques described below. The use of electron microscopy to measure fragment size is, in general, a satisfactory method for measuring DNA fragment sizes. Both fragment length and number are directly measured and as a result reliable size distributions are obtained. This reliability depends upon first, measuring large numbers of fragments which is a laborious process; and second, insuring that no size bias is incurred during the measurement process which would tend to misrepresent the distribution. Two different electron microscopic sizing procedures gave significantly different size distributions (Figure 4) and molecular weight averages (Table I) for the sheared DNA fragments. Comparison of the fragment distribution obtained by the two methods (Figure 4) reveals that less than 18% of the Kleinschmidt visualized fragments are shorter than 200 base pairs as compared to 47% as visualized by the adsorption grid method. This indicates that DNA fragments shorter than 200 base pairs are visualized less effectively by the Kleinschmidt procedure and that fragments shorter 2996 Nucleic Acids Research than 100 base pairs are not resolved at all. This is visually illustrated in Figure 3b and 3c which compares an adsorption grid micrograph and a Kleinschmidt grid micrograph of sheared DNA at the same magnification. The 100 base pair fragment seen in the adsorption grid micrograph (Figure 3b, arrow) would obviously be difficult, or impossible, to visualize in the Kleinschmidt micrograph (Figure 3c). The fact that the smaller molecules are not visualized in Kleinschmidt preparations undoubtedly results from their being obscured, relative to grid background, by the coating of cytochrome f: and contrasting material. The size distribution in the two preparations are, however, remark- ably similar for fragments longer than 200 base pairs (Figure 4 ) . Thus, the higher average size estimates obtained by the Kleinschmidt procedure are entirely explained by the failure of this procedure to score the true relative proportion of fragments shorter than 200 base pairs. We conclude, there- fore, that a more reliable DNA fragment size distribution and more accurate estimates of molecular weight averages are obtained by the adsorption grid method of electron microscopy. Gel electrophoresis is probably the most satisfactory method for sizing heterodisperse DNA fragment populations because it is rapid, easily calibrated with restriction fragment standards, and permits estimation of the distribution of fragment size. Figure 4 shows the electropherogram of sheared DNA on a gel calibrated with Hind III restriction nuclease fragments of lambda DNA. The sheared DNA migrates as a broad band the center of which is at a position corresponding to approximately 250 base pairs with extremes at approximately 400 base pairs and approximately 150 base pairs. This apparent distribution, however, is misleading because the correspondence between molecular weight and distance migrated is semilogarlthmic. To obtain a more meaningful distribution profile, a calibrated gel was scanned for A,gQ run to measure the relative amount of DNA throughout the gel and then the area under each 25 base pair increment of the optical density profile was determined. The results of this are shown in Figure 4f and in Figure 4c the relative number of DNA fragments at each increment is shown. On a linear scale the pattern of fragment length distribution is more readily assessed and further permits computation of the various estimates of average molecular weights shown in Table I. Both the distribution of fragment lengths (Figure 4) and the average molecular weight estimates (Table I) obtained by either gel electrophoresis or by adsorption grid electron microscopy are essentially identical. These data therefore mutually support the conclusion that the number average molecular weight (M ) of DNA sheared by conventional French —— Nucleic Acids Research press techniques is approximately 230 base pairs. In addition, it is most likely that previous reports that DNA sheared in this manner is 450 base pairs in length result from estimation of weight average molecular weight (Mw) and from inaccuracies relating S to molecular weight. Both the weight average (Mw) and number average (Mft) molecular weight are useful for computations involved with DNA reassociation and hybridization. The knowledge of both averages may prove useful in understanding the differences between the expected and observed rates of DNA hybridization or reassociation. For example, because the ratio of weight average molecular weight to number average molecular weight is 1.33, during DNA reassociation at the observed Cotl (Cot value at which 50% of the DNA mass is scored as duplex) one would expect approximately 67% of the DNA fragments to be in reassociated duplex. Since it is fragment number which kinetically drives the reassocia- tion of DNA, kinetic computations should ideally derive the concentration terms from M rather than M . Thus, it is potentially of great advantage in most cases to determine the distribution of sheared DNA fragment sizes in order to evaluate M and M . ACKNOWLEDGEMENTS We would especially like to thank Kenneth Neet and Chuck Starling for providing the Model E Centrifuge and the expertise to operate it. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 2998 Britten, R.J. and Kohne, D.E. (1968) Science 161, 529-540. Davidson, E.H., Hough, B.R., Amenson, C.S. and Britten, R.J. (1973) J. Mol. Biol. 77, 1-23. Graham, D.E., Neufeld, B.R., Davidson, E.H. and Britten, R.J. (1974) Cell 1, 127-137. Chamberlin, M.E., Britten, R.J. and Davidson, E.H. (1975) J. Mol. Biol. 96, 317-333. Britten, R.J., Graham, D.E. and Neufeld, B.R. (1973) in Methods in Enzymology 29(E) 363-418. Academic Press, New York. Davidson, E.H., Galau, G.A., Angerer, R.C. and Britten, R.J. (1975) Carnegie Inst. Wash. 4b 74, 673-678. Britten, R.J., Smith, M.J. and Davidson, E.H. (1975) Carnegie Inst. Wash. 4b 74, 699-711. Smith, M.J., Britten, R.J. and Davidson, E.H. (1975) Proc. Nat. Acad. Sci. USA 72, 4805-4809. Galau, G.A., Britten, R.J. and Davidson, E.H. (1974) Cell 2, 9-21. Ordahl, C.P. and Caplan, A.I. (1976) Develop. Biol. in press. Studier, F.W. (1965) J. Mol. Biol. 11, 373-390. Johnson, T.R. and Caston, J.D. (1975) Biopolymers 14, 1503. Kleinschmldt, A.K. (1968) in Methods in Enzymology 12(B), 361-377. Academic Press, New York. Carroll, D. and Brown, D.D. (1976) Cell 7, 467-475. Danna, K.J., Sack, G.H.,Jr. and Nathans, D. (1973) J. Mol. Biol. 78, 363-376. Nucleic Acids Research 16. Sharp, P.A., Sugden, B. and Sambrook, J. (1973) Biochemistry 12, 3055-3063. 2999 Nucleic Acids Research 3000