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DNA restriction fragments ranging from 79 to 789 base pairs in length have been characterized by transient electric birefringence (TEB) measurements at various temperatures between 4 and 43 degrees C. The DNA fragments do not contain runs of four or more adenine residues in a row and migrate with normal electrophoretic mobilities in polyacrylamide gels, indicating that they are not intrinsically curved or bent. The low ionic strength buffers used for the measurements contained 1 mM Tris Cl, pH 8.0, EDTA, and variable concentrations of Na(+) or Mg(2+) ions. The rotational relaxation times were obtained by fitting the TEB field-free decay signals with a nonlinear least-squared fitting program; the decay of the birefringence was monoexponential for fragments < or = 241 base pair (bp) in length and multiexponential for larger fragments. The terminal relaxation times, characteristic of the end-over-end rotation of the DNA molecules, were then used to determine the persistence length (p) and hydrodynamic radius (r) of DNA as a function of temperature and ionic strength, using several different hydrodynamic models. The specific values obtained for p and r are model dependent. The wormlike chain model of P. J. Hagerman and B. H. Zimm (Biopolymers 1981, Vol. 20, pp. 1481-1502) combined with the revised Broersma equation (J. Newman et al., Journal of Mol Biol 1997, Vol. 116, pp. 593-606) appears to be the most suitable for describing the flexibility of DNA in low ionic strength solutions. The values of p and r obtained from the global least squares fitting of this equation are independent of DNA length, and the deviations of the individual values from the average are reasonably small. The consensus r value calculated for DNA in various low ionic strength solutions containing 1 mM Tris buffer is 14.7 +/- 0.4 A at 20 degrees C. The consensus p values decrease from 814 approximately 564 A in solutions containing 1 mM Tris buffer plus 0.2-1 mM NaCl and decrease still further to 440 A in solutions containing 0.2 mM Mg(2+) ions. The persistence length exhibits a shallow maximum at 20 degrees C and decreases slowly upon either increasing or decreasing the temperature, regardless of the model used to fit the data. By contrast, the consensus values of the hydrodynamic radius are independent of temperature. The calculated persistence lengths and hydrodynamic radii are compared with other data in the literature.

The electrophoretic mobilities and diffusion coefficients of single- and double-stranded DNA molecules up to 50,000 bases or base pairs in size have been analyzed, using mobilities and diffusion coefficients either measured by capillary electrophoresis or taken from the literature. The Einstein equation suggests that the electrophoretic mobilities (mu) and diffusion coefficients (D) should be related by the expression mu/D = Q/k(B)T, where Q is the charge of the polyion (Q = ze(o), where z is the number of charged residues and e(o) is the fundamental electronic charge), k(B) is Boltzmann's constant, and T is the absolute temperature. If this equation were true, the ratio mu/zD should be a constant equal to e(o)/k(B)T (39.6 V(-1)) at 20 degrees C. However, the ratio mu/zD decreases with an increase in molecular weight for both single- and double-stranded DNAs. The mobilities and diffusion coefficients are better described by the modified Einstein equation mu/N(m)D = e(o)/k(B)T, where N is the number of repeat units (bases or base pairs) in the DNA and m is a constant equal to the power law dependence of the diffusion coefficients on molecular weight. The average value of the ratio mu/N(m)D is 40 +/- 4 V(-1) for 36 single- and double-stranded DNA molecules of different sizes, close to the theoretically expected value. The generality of the modified Einstein equation is demonstrated by analyzing literature values for sodium polystyrenesulfonate (PSS). The average value of the ratio mu/N(m)D is 35 +/- 6 V(-1) for 14 PSS samples containing up to 855 monomers.

The free solution mobility of DNA molecules of different molecular weights, the sequence dependence of the mobility, and the diffusion coefficients of small single- and double-stranded DNA (ss- and dsDNA) molecules can be measured accurately by capillary zone electrophoresis, using coated capillaries to minimize the electroosmotic flow (EOF) of the solvent. Very small differences in mobility between various analytes can be quantified if a mobility marker is used to correct for small differences in EOF between successive experiments. Using mobility markers, the molecular weight at which the free solution mobility of dsDNA becomes independent of molecular weight is found to be approximately 170 bp in 40 mM Tris-acetate-EDTA buffer. A DNA fragment containing 170 bp has a contour length of approximately 58 nm, close to the persistence length of DNA under these buffer conditions. Hence, the approach of the free solution mobility of DNA to a plateau value may be associated with the transition from a rod-like to a coil-like conformation in solution. Markers have also been used to determine that the free solution mobilities of ss- and dsDNA oligomers are sequence-dependent. Double-stranded 20-bp oligomers containing runs of three or more adenine residues in a row (A-tracts) migrate somewhat more slowly than 20-mers without A-tracts, suggesting that somewhat larger numbers of counterions are condensed in the ion atmospheres of A-tract DNAs, decreasing their net effective charge. Single-stranded 20-mers with symmetric sequences migrate approximately 1% faster than their double-stranded counterparts, and faster than single-stranded 20-mers containing A(5)- or T(5)-tracts. Interestingly, the average mobility of two complementary single-stranded 20-mers is equal to the mobility of the double-stranded oligomer formed upon annealing. Finally, the stopped migration method has been used to measure the diffusion coefficients of single- and double-stranded oligomers. The diffusion coefficients of ssDNA oligomers containing 20 nucleotides are approximately 50% larger than those of double-stranded DNA oligomers of the same size, reflecting the greater flexibility of ssDNA molecules. The methods used to carry out these experiments are also described in detail.

The mobilities of normal and anomalously migrating DNA fragments were determined in polyacrylamide gels of different acrylamide concentrations, polymerized with 3% N,N'-methylenebisacrylamide as the crosslinker. The DNA samples were a commercially available 123-bp ladder and two molecular weight ladders containing multiple copies of two 147-base pair (bp) restriction fragments, obtained from the MspI digestion of plasmid pBR322. One of the 147 bp fragments is known to migrate anomalously slowly in polyacrylamide gels. Ferguson plots were constructed for all multimer ladders, using both absolute mobilities and relative mobilities with respect to the smallest DNA molecule in each data set. If the retardation coefficients were calculated from the relative mobilities, and the rms radius of gyration was used as the measure of DNA size, the Ogston equations were obeyed and the gel fiber parameters could be calculated. The effective pore sizes of the gels were estimated from the gel concentration at which the mobility of a given DNA molecule was reduced to one-half its mobility at zero gel concentration. The estimated pore radii ranged from approximately 130 nm for 3.5% gels to approximately 70 nm for 10.5% gels. These values are much larger than the pore sizes previously determined for the polyacrylamide matrix.

SynopsisThe electric birefringence of restriction enzyme fragments of DNA has been investigated as a function of DNA concentration, buffer concentration, and molecular weight, covering a molecular weight range from 80 to 4364 base pairs (bp) (6 X lo4-3 X lo6 daltons). The specific birefringence of the DNA fragments is independent of DNA concentration below 20 pg DNA/ml, but decreases with increasing buffer concentration, or conductivity, of the solvent. At sufficiently low field strengths, the Kerr law is obeyed for all fragments. The electric field a t which the Kerr law ends is inversely proportional to molecular weight. In the Kerr law region the rise of the birefringence is accurately symmetrical with the decay for fragments 5 389 bp, indicating an induced dipole orientation mechanism. The optical factor calculated from a 1/E extrapolation of the high field birefringence data is -0.028, independent of molecular weight; if a 1/E2 extrapolation is used, the optical factor is -0.023. The induced polarizability, calculated from the Kerr constant and the optical factor, is proportional to the square of the length of the DNA fragments, and inversely proportional to temperature. Saturation curves for DNA fragments 5 161 bp can be described by theoretical saturation curves for induced dipole orientation. The saturation curves of larger fragments are broadened, because of a polarization term which is approximately linear in E, possibly related to the saturation of the induced dipole in high electric fields. This "saturated induced dipole" is found to be 6400 D, independent of molecular weight. The melting temperature of a 216-bp sample is decreased 6OC in an electric field of 8 kV/cm, because the lower charge density of the coil form of DNA makes it more stable in an electric field than the helix form.

This review describes the electrophoresis of curved and normal DNA molecules in agarose gels, polyacrylamide gels and in free solution. These studies were undertaken to clarify why curved DNA molecules migrate anomalously slowly in polyacrylamide gels but not in agarose gels. Two milestone papers are cited, in which Ferguson plots were used to estimate the effective pore size of agarose and polyacrylamide gels. Subsequent studies on the effect of the electric field on agarose and polyacrylamide gel matrices, DNA interactions with the two gel matrices, and the effect of curvature on the free solution mobility of DNA are also described. The combined results suggest that the anomalously slow mobilities observed for curved DNA molecules in polyacrylamide gels are due primarily to preferential interactions of curved DNAs with the polyacrylamide gel matrix; the restrictive pore size of the matrix is of lesser importance. In free solution, DNA mobilities increase with increasing molecular mass until leveling off at a plateau value of (3.17 ± 0.01) × 10 -4 cm 2 /Vs in 40 mM Tris-acetate-EDTA buffer at 20°C. Curved DNA molecules migrate anomalously slowly in free solution as well as in polyacrylamide gels, explaining why the Ferguson plots of curved and normal DNAs containing the same number of base pairs extrapolate to different mobilities at zero gel concentration.Keywords agarose gels; capillary electrophoresis; DNA; free solution mobility; polyacrylamide gels Historical overviewThe study of DNA electrophoresis began in 1964, when three groups of investigators [1][2][3][4][5] measured the mobility in free solution using moving boundary methods. They found that the mobility was independent of size for DNA molecules larger than ∼400 base pairs (bp) [5], and varied with ionic strength [3,5] and the identity and valence of the cation in the background electrolyte [2,3]. At about the same time, inspired by the separation of proteins in synthetic gel matrices [6][7][8][9][10], other investigators began to use similar matrices to separate RNA [11][12][13][14][15][16][17][18][19] and DNA molecules [15,[20][21][22][23][24] by molecular mass. The separation matrices included agar [11,18,20,21], agarose [22,23], polyacrylamide [13,14,19,[24][25][26][27][28] and composite agarose-acrylamide [16,17] gels. As electrophoretic methods were improved by the purification of agarose [29][30][31] and the use of slab gels instead of tube gels [25,32], and as the discovery of restriction enzymes allowed the preparation of monodisperse DNA fragments of known size [33,34], it became apparent that the separation of DNA fragments by molecular mass depended on the gel matrix in which the separation was carried out Correspondence: Dr. Nancy C. Stellwagen, Department of Biochemistry, University of Iowa, Iowa City, IA 52242, USA, nancystellwagen@uiowa.edu, Fax: +319-335-9570. The author has declared no conflict of interest. NIH Public Access Author ManuscriptElectrophoresis. Author manuscript; available in PMC 2010 June 1. [33,35]. Electro...

The effect of monovalent cations on the thermal stability of a small model DNA hairpin has been measured by capillary electrophoresis, using an oligomer with 16 thymine residues as an unstructured control. The melting temperature of the model hairpin increases approximately linearly with the logarithm of increasing cation concentration in solutions containing Na(+), K(+), Li(+), NH(4)(+), Tris(+), tetramethylammonium (TMA(+)), or tetraethylammonium (TEA(+)) ions, is approximately independent of cation concentration in solutions containing tetrapropylammonium (TPA(+)) ions, and decreases with the logarithm of increasing cation concentration in solutions containing tetrabutylammonium (TBA(+)) ions. At constant cation concentration, the melting temperature of the DNA model hairpin decreases in the order Li(+) ∼ Na(+) ∼ K(+) > NH(4)(+) > TMA(+) > Tris(+) > TEA(+) > TPA(+) > TBA(+). Isothermal studies indicate that the decrease in the hairpin melting temperature with increasing cation hydrophobicity is not due to saturable, site-specific binding of the cation to the random coil conformation, but to the concomitant increase in cation size with increasing hydrophobicity. Larger cations are less effective at shielding the charged phosphate residues in B-form DNA because they cannot approach the DNA backbone as closely as smaller cations. By contrast, larger cations are relatively more effective at shielding the phosphate charges in the random coil conformation, where the phosphate-phosphate distance more closely matches cation size. Hydrophobic interactions between alkylammonium ions interacting electrostatically with the phosphate residues in the coil may amplify the effect of cation size on DNA thermal stability.