Anomalies in sedimentation. IV. Decrease in sedimentation coefficients of chains at high fields

A theory is presented for the decrease of sedimentation coefficient at high centrifugal fields recently reported for samples of DNA by Rubenstein and Leighton and others. The theory uses the model of a chain of beads and springs to represent the molecule. Kirkwood's approximation is used for the sedimentation coefficient. The decrease in sedimentation coefficient with field comes about as a result of the uneven frictional forces in the chain, which on the average are less on segments near the center of the chain than on those near the ends. As a result the ends of the chain tend to drag behind the center, and the average intersegment distances are increased; consequently the hydrodynamic shielding of one segment by another is reduced, and the average friction is increased. The effect is thus characteristic of single molecules; intermolecular interaction is not involved. The sedimentation coefficient, S, varies as a power series in a parameter y that measures the distortion produced by the uneven friction: S = S⁰(1?D₂y² + D₄y⁴ ? ·). where S⁰ is the limiting value of S at zero centrifugal field and D₂ and D₄ are constants; y is proportional to the cen speed squared tunes the molecular weight squared divided by S⁰. It has been observed that the effects of centrifuge speed on S are negligible below certain critical values of the speed and molecular weight, but increase dramatically immediately above these values; this follows naturally from the high powers of the speed and molecular weight that appear in the above equation.     

A quantitative test of Zimm's model for the rotor-speed-department sedimentation of linear DNA molecules

In 1974, Zimm described a theory which predicts that the sedimentation coefficient of high-molecular-weight DNA will decrease as the rotor speed of measurement increases. In 1979, this theory was revised, and the new formula predicts speed-dependence effects that are substantially smaller than the predictions of the original version. This report describes the results of subjecting both the original and the revised versions of the theory to quantitative tests using a well-defined sucrose-gradient system and a DNA of known molecular weight (T4c DNA). T4c bacteriophage is a mutant, whose DNA contains the unmodified base cytosine, instead of the glucosylated hydroxymethylcytosine characteristic of the T-even bacteriophages, and has a molecular weight of 115 ± 3 × 10⁶. The DNA of the wild-type phage (T4D⁺) was also used in some experiments. In addition to the quantitative tests, the experiments test for an effect first observed by Rubenstein and Leighton, which showed that the sedimentation coefficient measured for T2 DNA depended on the composition of the centrifuge tube used for the measurement (tube composition effect). It can be inferred from this observation that an interaction occurs between particle and tube wall during sedimentation, and this leads to a reduction in sedimentation velocity independent of the reduction in S described by Zimm's theory. The results show that in the range of 25,000–50,000 rpm, the original but theoretically incorrect form of the theory quite accurately describes the sedimentation behavior of both T4c and T4D⁺ DNA, although T4D⁺ was a special case in some respects. The revised (corrected) form of the theory predicts much less of a speed-dependence effect than that actually observed. The discrepancy between corrected theory and observation suggests that other factors (perhaps arising from the use of the swinging bucket rotor geometry) are causing the additional observed reduction in S_20,w. However, the experiments show that the tube composition effect does not seem to be one of these.     

The flexibility of low molecular weight double-stranded dna as a function of length: I. Isolation and physical characterization of seven fractions

Sonicated calf thymus DNA was fractionated by rate zonal centrifugation into seven fractions with weight average molecular weights ranging from 0.28 to 1.3 × 10⁶ daltons, as determined by sedimentation equilibrium and light scattering measurements (the latter are described in the accompanying paper). Electron microscopy and sedimentation equilibrium analysis revealed these fractions to be narrowly disperse with M_w/M_n ratios averaging about 1.06. Intrinsic viscosities and sedimentation rates were measured and found to vary linearly with molecular weight in double-logarithmic plots in fair agreement with previously published functions relating these parameters for low molecular weight DNA. The average value for β from the Mandelkern— Flory equation was 2.59 × l0⁶, also agreeing with reported estimates of this parameter for short DNA. These data will be used in the second paper of this series to calculate the persistence length of the DNA fragments in each of the seven fractions by light scattering and hydrodynamic theories for the Kratky—Porod worm-like coil.     

Isolation and Characterization of Kinetoplast DNA Networks and Minicircles from Crithidia fasciculata*

SYNOPSIS. Covalently closed kinetoplast DNA networks have been isolated from stationary phase Crithidia fasciculata cells by a technic involving selective pelleting of the networks at a low centrifugal field. Approximately 62% of the kinetoplast DNA of the cell was recovered free of nuclear DNA by simple differential centrifugation. Purified kinetoplast DNA networks were visualized both in the electron microscope and in the light microscope. Closed networks sedimented as a homogeneous band both in neutral and alkaline sucrose, with an s_20w in neutral sucrose of approximately 5 × 10³. Closed monomeric minicircles were isolated from purified networks by mild sonication and band sedimentation in alkaline sucrose. Several physical properties of closed monomeric minicircles were measured. These included molecular weight, buoyant density in CsCl, superhelix density and sedimentation coefficient.     

Characterization of rodlike RNA fragments.

Native calf thymus DNA was sheared by sonication in a viscous solvent to the molecular-weight range from 3 × 10⁴ to 3 × 10⁵ daltons, and fractionated by gel chromatography. Number and weight average molecular weights (M?_n and M?_w) were determined for individual fractions by electron microscopy; the ratio M?_w/M?_n for the peak fraction is approximately 1.1. Sedimentation coefficients (s⁰_20,w) of these fractionated samples show an approximately linear dependence on the logarithm of the molecular weight M?_w. This behavior is that expected for rodlike molecules, and is in quantitative agreement with the theory of Yamakawa and Fujii [(1973) Macromolecules 6 , 407–415] for the sedimentation coefficient of a wormlike chain with a persistence length of 625 Å, a diameter of 25 Å, and a mass per unit length of 195 daltons/Å. 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.     

Isolation and characterization of kinetoplast DNA from Leishmania tarentolae

Kinetoplast DNA (? = 1.703 g/ml.) was isolated by preparative cesium chloride ultracentrifugation in a fixed-angle rotor from total cell DNA of Leishmania tarentolae and examined in terms of sedimentation properties, melting characteristics, and appearance in the electron microscope. It consisted of several molecular types, either free or bound together in associations of variable size: minicircles (molecular weight = 0.56 ± 0.03 × 10⁶), catenated minicircles, “figure 8” molecules, and long molecules. The associations seem to be held together by the long molecules threading through the smaller circles and catenanes. The large associations could be broken down by sonication, DNase II-treatment, or shear forces. Minicircles, catenated dimers, trimers, and small linear fragments were separated on preparative sucrose gradients of sonicated DNA, and S_20,w values were assigned to each molecular type by band sedimentation in the analytical ultracentrifuge.     

Characterization of the Bacillus subtilis W23 genome by sedimentation

Sedimentation measurements of DNA gently extracted from stationary-phase cells of Bacillus subtilis demonstrated molecules large enough to account for the total genome. The observed sedimentation coefficient of the putative genome showed a strong dependence on centrifuge speed and was, therefore, measured at very low speeds. The value for the sedimentation coefficient extrapolated to zero speed was 159 ± 19 s, from which was calculated molecular weights of (2.5 ± ^1.2_0.8) × 10⁹ a.m.u. for linear molecules and (1.8±^0.8_0.7) × 10⁹ a.m.u. for circular molecules (relative to the following values for T2 DNA: 57 s and 132±12 × 10 daltons; Leighton &; Rubenstein, 1969). The genome also showed extreme shear sensitivity.     

Length distributions of single-stranded DNA in Chinese hamster ovary cells.

The distribution of lengths of single-strand DNA in Chinese hamster ovary cells in the G₁ phase of the cell cycle has been observed for various conditions of cell lysis and incubation of the lysates. The method of analysis was band sedimentation through a self-generating density gradient, a technique developed originally for the analytical ultracentrifuge, but modified here for the preparative ultracentrifuge so that measurements of sedimentation coefficients could be made under conditions that minimize shearing of the single-stranded DNA. The effect of rotor speed dependence of the sedimentation coefficient is considered in developing the relation between the sedimentation coefficient and molecular weight for this technique.Special precautions were taken to ensure that complete separation of long single strands took place upon alkaline denaturation, to preclude the possibility of anomalous sedimentation due to interstrand entanglement. Bromodeoxyuridine was incorporated into the DNA in the last round of replication. Advantage was taken of the increased sensitivity to ultraviolet irradiation for the production of single-strand breaks in DNA strands substituted with bromodeoxyuridine. After irradiation the bromodeoxyuridine-substituted strand could be completely separated from the complementary strand in alkaline sedimentation profiles without any apparent breakage in the unsubstituted strand.The conditions of lysis, chosen to minimize the degradation of DNA in the lysates, included lysis at pH 9.3 with Pronase and lysis at high pH (10.8 and 12.0). Sedimentation analysis was performed at various time intervals after incubation at 4 °C or 37 °C. Lysis and incubation at pH 12.0 produced a continuous single-strand breakdown of the DNA in the lysate. Analysis of the sedimentation profiles indicates that these alkaline-induced breaks are randomly distributed. However, lysis and incubation at pH 10.8 and at pH 9.3 with Pronase produced stable sedimentation profiles with number-average molecular weights of 1.7 × 10⁸ and 6.0 × 10⁷, respectively. Analysis of the single-strand DNA sedimentation profiles for these lysates indicates that the distribution of lengths of single-stranded DNA is non-random, i.e. that the distributions may represent regular subunits of chromosomal DNA structure. Suggestive evidence is presented that the approximately 60-μm units are structurally alternated in the two chains. The possible origin of the discontinuities between the subunits is also discussed.     

The influence of rotor speed on the sedimentation behavior in sucrose gradients of high molecular weight DNA's

Anomalous sedimentation behavior has been observed for high molecular weight duplex DNA's in sucrose gradients. The sedimentation rate of DNA's having molecular weights of 10⁸ or higher is influenced by high centrifugal fields. The change in the sucrose sedimentation coefficient due to this effect, S^RPM_suc-S⁰_suc, is equal to 1 × 10^?48M^3.65( The anomalous behavior is not influenced by DNA concentration at sufficiently low concentrations. Because of the smallness of the coefficient this effect has not been previously detected for DNA's the size of T2 or smaller at rotor speeds below 40000 RPM. For example, the relative sedimentation coefficient of T2 DNA at 65 000 RPM is only 9% less than at 10000 RPM. However, the sedimentation profile of heterogeneous high molecular weight [(100 – 350) × 10⁶] E. coli DNA is severely altered even at moderate rotor speeds (37000 RPM). Therefore, it seems advisable to use low rotor speeds when sedimenting high molecular weight DNA's.     

Interlocked DNA rings. II. Physicochemical studies

Several species of topologically interlocked λb2b5c DNA rings (catenanes) have been prepared in vitro. The sedimentation behavior of dimeric catenanes containing 0, 1, or 2 covalently closed duplex rings has been studied as a function of the superhelical density of the covalently closed ring or rings. In general, if XtpY represents rings X and Y topologically interlocked, the sedimentation coefficient of this species, ^SXtpY, is related to the sedimentation coefficients ^SX and ^SY of the component rings by the empirical relationship ^SXtpY/^SY = [(M_X + M_Y)/M_Y] [1 + (M_X/M_Y)^1.78(^SY/^SX)^1.78]^?0.56 This equation can also be extended to the case where three monomeric rings are topologically linked in a chain. For two topologically interlocked monomeric rings with neither ring covalently closed, the sedimentation coefficient is 1.35 times that of the monomeric ring. This is different from results reported for mitochondrial and P22 catenanes by others. Several possibilities are discussed to account for this discrepancy. The sedimentation coefficient of a species containing one covalently closed duplex ring and a single-stranded ring was also measured in an alkaline medium. This species, which can be easily derived from a dimeric catenane containing two covalently closed duplex rings, is particularly useful for the identification of covalently closed dimeric catenanes. Some electron microscopic studies of these interlocked rings are presented in an accompanying paper.     

Sedimentation Rate as a Measure of Molecular Weight of DNA

Zone centrifugation of mixtures of two labeled DNA's at low concentrations in density gradients of sucrose permits accurate measurement of relative sedimentation rates. The individual rates are constant during the run. Measurements with DNA's from phages T2, T5, and lambda conform to the relation D₂/D₁ = (M₂/M₁)^0.35, where D and M refer to distances sedimented and molecular weights of the DNA pair. The results show that high molecular weight DNA's sediment artificially fast in the optical centrifuge, owing to a hitherto unknown effect of molecular interactions. The molecular weight of lambda DNA is 31 million, measured either from sedimentation rate or from tests of fragility under shear.     

The organization and repair of DNA in the mammalian chromosome. III. Determination of the molecular weight of a mammalian native DNA

The necessary conditions for a unique solution of the sedimentation vs DNA molecular weight equations are considered and applied to the native DNA of the L5178Y mouse leukemia cell. A brief review and critique of the literature of sedimentation anomalies is given to demonstrate that such anomalies are not present in the data reported here. It is shown that the chromosomal DNA of L5178Y cells comes in uniform packages of 1.0 (0.5–2.0) × 10¹⁰ daltons. All pieces are of an identical size which corresponds to the DNA content of about 1/13 the average chromatid. Both the size estimate and the number of such molecules/cell are confirmed by viscoelastometry. This DNA is shown to be free of radioactively demonstrable protein and/or lipid contaminants and of the same isopycnic density as T₄ DNA. Variance analysis is applied to determine the precision of all measurements and to pinpoint major sources of error. A relationship between [η] and M is derived for native DNA in 1.0M NaCl. A necessary conclusion from these data is that mammalian chromosome models requiring degrees of polynemy greater than 16-neme (in G₁) are incorrect (to the extent that the L5178Y cell is typical of mammalian cells).     

Studies on Transformations of Hemophilus influenzae : II. The molecular weight of transforming DNA by sedimentation and diffusion measurements

The sedimentation and diffusion coefficients have been determined for Hemophilus influenzae transforming activity and DNA using P³²-labeled DNA. The methods employed the Spinco fixed boundary separation cell for measurements of the sedimentation coefficient and the Northrop-Anson diffusion cell to determine the diffusion coefficient. There was a very close correlation between the amount of DNA and transforming activity sedimented or diffused. The sedimentation coefficient (s_20°), for both biological activity and DNA was 27 and the diffusion coefficient (D_20°) 1 x 10^-8 cm²/sec. The molecular weight calculated from these coefficients gave a value of 16 million. There was no difference in the sedimentation coefficients for the two unlinked markers, streptomycin and erythromycin resistance, and the diffusion coefficients for single markers or the linked markers, streptomycin and cathomycin, were the same.     

Fracture of DNA in transient extensional flow. A numerical simulation study

Using the Brownian dynamics simulation technique, we studied the fracture process of DNA chains subjected to transient extensional flow, letting the solution with DNA molecules pass through a very small orifice (radius = 0.0065 cm), thus experiencing extensional flow of the convergent (sink) type. The DNA molecules were modeled as FENE bead-spring chains with the springs obeying a modified Warner force law, as proposed by Reese and Zimm. The fracture yield was strongly dependent on flow rate and molecular weight, reaching, in our setup, a level of 100% at a flow rate of around 0.001 cm³/s for DNA with molecular weight 26 × 10⁶ (T7 DNA). There was found to exist a critical flow rate (Q_crit) below which fracture did not occur, in accordance with what was observed in studies on polystyrene in transient extensional flow. We found that for DNA, the critical flow rate depended on the molecular weight as Q_crit ∼ M⁻¹⁴ when the hydrodynamic interaction effect (HI) was not included in the simulations. When HI was accounted for, the relation was found to be Q_crit ∼ M^−1.1, close to the theoretical prediction for fracture of partly extended chains in transient extensional flow. © 1996 John Wiley & Sons, Inc.     

Mammary glucose 6-phosphate dehydrogenase. Molecular weight studies

Glucose 6-phosphate dehydrogenase was isolated from lactating rat mammary glands by a procedure extended and modified from one previously described. The sedimentation coefficient, S_20,W, was 10.3 in 0.01 m potassium phosphate, pH 6.9, containing 0.1 m NaCl at three protein concentrations between 0.51 and 1.45 mg/ml. The partial specific volume, v?, was 0.735 ml/g as determined by equilibrium sedimentation centrifugation in H₂O and D₂O containing buffers at pH(D) 6.5 containing 0.01 m potassium phosphate and 0.1 m NaCl. In the same buffer, but with 2.0 m NaCl, the apparent partial specific volume, φ′, was 0.756 ml/g. Equilibrium sedimentation of the enzyme at an initial concentration of 0.8 mg/ml was performed in 0.01 m potassium phosphate, pH 6.5, containing 1.0 mm EDTA, 7.0 mm mercaptoethanol, and various concentrations of NaCl between 0 and 2.0 m and with or without 0.1 mm NADP⁺. Weight-average and Z-average molecular weights were calculated and, from these values, the molecular weights of the monomer and dimer were derived. Under these conditions, the enzyme existed principally as a dimer, of molecular weight approximately 235,000, at low salt concentration, and as a monomer, of molecular weight approximately 120,000 in 1.0 m and 2.0 m NaCl. The subunit molecular weight was found to be 64,000 by polyacrylamide gel electrophoresis in sodium dodecyl sulfate. Equilibrium sedimentation in 6 m guanidine hydrochloride gave a subunit molecular weight of 62,000 (assuming v? was unaltered) or 58,000 or 54,000 (assuming v? is decreased by 0.01 or 0.02, respectively, in 6 m guanidine). We conclude that rat mammary glucose 6-phosphate dehydrogenase has a molecular weight similar to that of glucose 6-phosphate dehydrogenases isolated from various other mammalian sources with the notable exception of human erythrocyte glucose 6-phosphate dehydrogenase which, like the microbial glucose 6-phosphate dehydrogenases thus far examined, has a significantly lower molecular weight.     

Fractionation of DNA from Bacillus subtilis and its transforming activity for various markers

The physical, chemical, and functional heterogeneity of tranforming DNA was studied by preparative fractionation techniques providing resolution with respect to differences in molecular weight (gel filtration, sucrose density gradient), base composition (CsCl density gradient), or both these parameters simultaneously (methylalbumin-coated celite 545 MAK column). A comparison of the basic characteristics of the obtained fractions (melting temperature, T _m; density, ; sedimentation coefficient, S _20,w; and transforming activity for ade, leu, and met markers) showed that the factor decisive for functional activity represents, in addition to the sequential arrangement of nucleotides in the chain, the average base composition. Hence, using the methylalbumin column or CsCl density gradient centrifugation, DNA fractions can be isolated which show a several times higher transforming activity for any of the markers examined. By contrast, the remaining fractionation methods, even though considerably decreasing the heterogeneity of the fractions as regards their molecular weight (such as zonal centrifugation), do not offer a possibility of fractionation of the activity for individual markers. This indicates a statistically random degradation of transforming DNA during its isolation. The order of the investigated markers according to their guanine-cytosine content is ade leu met and corresponds also to the order of their positions on the genetic map of Bacillus subtilis.     

Molecular weight of base plates of bacteriophage T4D.

Highly purified base plates of bacteriophage T4D were obtained from lysate of gene 19 am mutant of this phage by differential centrifugation and sucrose gradient. Base plates were studied by means of high speed sedimentation equilibrium. The molecular weight determined by this method is (6.7 plus or minus 0.2)-10-6.     

The flexibility of low molecular weight double-stranded dna as a function of length: II. Light scattering measurements and the estimation of persistence lengths from light scattering,sedimentation and viscosity

In the preceding paper are described the isolation and physical characterization of seven narrowly disperse fractions of calf thymus DNA in the molecular weight range 0.3 to 1.3 × 10⁶ daltons. Herein, we have determined by light scattering the molecular weights and root mean square radii of these fractions in a solvent comprising 0.2 M NaCl, 2 mM EDTA, 2m MNa-PO₄, pH 7. Measurements were made in a modified Wippler—Scheibling photometer to a 20° lower limit of scattering angle on solutions rendered virtually dust-free by procedures described. The optical aniso tropics of the DNA fractions were measured permitting the experimental molecular weights and root mean square radii to be corrected to their true values. From these values, with appropriate polydispersity corrections, we calculate a Kratky—Porod persistence length, a, of 54.0 ± 5.6 nm which is invariant over the molecular weight range examined. From the sedimentation coefficients (preceding paper) and the theory of Yamakawa and Fujii, we calculate a to be 66 nm, a value found to apply equally well to several DNA samples of various origins whose sedimentation rates are known in the molecular weight range from about 4 × 10⁴ to 10⁸ daltons. Similarly, from the intrinsic viscosities and the theory of Yamakawa and Fujii, we calculate a to be 59 nm, which again adequately applies to a number of DNA samples whose viscosities have been measured by other workers in the molecular weight range 3 × 10⁵ to 10⁸ daltons. The Flory—Mandelkern parameter, β, was found to vary with molecular weight in the manner predicted by the theory of Yamakawa and Fujii. The average value of a from the three sets of measurements is 60 ± 6 nm, which we believe applies to double-stranded DNA molecules, independent of chain length, over the whole range of molecular weights for which reliable data exist.     

Sedimentation coefficients of replicating and crosslinked DNA

The sedimentation coefficients of branched and cyclic replicating DNA structures have been calculated taking into account both chain stiffness and excluded volume effects. For branched DNA, the calculated ratio S⁰(α)/S⁰(0) of the sedimentation coefficient at degree of replication α to that at α = 0 increases from 1.000 to 1.331 as α goes from 0 to 1. For cyclic replicating DNA, S⁰(1)/S⁰(0) = 1.517. The considerable difference between these two ratios for α = 1 suggests that the two types of replicating structures may feasibly be distinguished by sedimentation velocity studies, A similar calculation has been made of the sedimentation coefficient of singly cross-linked DNA under denaturing conditions, as a function of placement of the crosslink. In 0.195M Na⁺, the ratio S⁰(α)/S⁰(0) varies from 1.000 at α = 0 to 1.124 at α = 0.5, where α is the fractional distance of the crosslink from the end of the chain.