Problems and prospects in the theory of gel electrophoresis of DNA.
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Biomedical subjects
Publications and source records attributed to B H Zimm.
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The flow-induced degradation of T7 DNA (Molecular Size = 40 Kbp) was studied in a flow device that generates converging flow rather than simple shear flow. We discovered that the sizes of the degradation products were very broadly distributed, covering the range from 10 Kbp to 36 Kbp. An explanation for the broadness of the distribution is given based on a computer simulation of the experiment. The significance of converging flow to the routine handling of large DNA is emphasized.
In polyacrylamide gel electrophoresis, the retardation of DNA molecules containing regions of intrinsic curvature can be explained by a novel reptation model that includes the elastic free energy of the DNA chain. Computer simulations based on this model give results that reproduce the dependence of anomalous mobility on gel concentration, which is quantified by new experimental data on the mobilities of circularly permuted isomers of kinetoplast DNA fragments. Fitting of the data required allowing for the elasticity of the gel.
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The effect of high electric fields on the gel-electrophoretic mobility of open-circular DNA in agarose differs dramatically from that on linear molecules of the same molecular weight. At high fields, sufficiently large circular forms are prevented from migrating into the gel whereas linear molecules and smaller circular DNAs migrate normally. This effect is strongly field dependent, affecting circular molecules of decreasing size with increasing field strength. We have studied this effect with a series of plasmid DNAs ranging from 2.9 to 56 kilobase pairs using continuous and reversing-pulse electric fields. Application of reversing pulses abolishes the effect under certain conditions and supports the model for the gel electrophoresis of open-circular DNA where circular forms are trapped by engaging the free end of an agarose gel fiber.
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Condensation of the counter-ions around a highly charged infinitely long cylindrical molecule, such as DNA, can be described in detail in terms of the solutions of the Poisson-Boltzmann (Gouy-Chapman) equation. By using the Alfrey-Berg-Morawetz (1951) solution of this equation one can show that a certain fraction of the counter-ions remain within finite distances of the poly-ion even when the volume of the system is expanded indefinitely; these ions can be appropriately called "condensed". The fraction of the macromolecule's charge represented by these ions is just 1-1/xi, where xi is the linear charge-density parameter of the macromolecule; this is also the value given by Manning's theory. The question arises: Is this property unique to the infinite cylinder? Using the same PB equation, we can consider the infinite charged plane and a large finite charged sphere for comparison. In the case of the plane all of the counter-ions are condensed in the above sense, not just a fraction, for any surface charge density of the plane. These ions form the classical Gouy double layer. On the other hand, none of the counter-ions of the charged sphere are condensed in the above sense, no matter how high the surface charge density. Thus the cylinder is a unique intermediate case in which a fraction of the counter-ions are condensed if the linear charge density is higher than the critical value of unity.
We present a rheological separation method for DNA molecules in which their deformability is used to advantage. This is the "radial migration method"; here we present experimental verification of the principle, theory having been reported elsewhere. The main conclusions are: (1) the theory is reasonably good; (2) radial migration is highly sensitive to the molecular weight, as predicted, and (3) intact T2 DNA (1.25 X 108 daltons) can be made to migrate about three centimeters in less than three hours.
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The viscoelastic properties of T2 DNA solutions are used to determine the NaDNA molecular weight in four independent ways from the theory of the beads-springs model. The four molecular weights are 131.9, 132.7, 130.5, and 127.6 X 10(6). The average of these values, adjusted for the probable errors in viscoelasticity and concentration measurements, is (126 +/- 5) X 10(6). The four molecular weights are termed Mtaugamma11, Mtaueta, Mtaugamma, and MtauA; each is different in its sensitivity to molecular weight distribution. Their agreement suggests (1) that the theoretical equations relating each M to the corresponding measured properties are valid, (2) that T2 DNA behaves as a partially free-draining polymer chain, and (3) that our solutions were nearly homogeneous in DNA size. We show that serious errors can result if the viscoelastic properties are not extrapolated to their limits at zero shear rate, as well as at zero DNA concentration, before calculating molecular weight.
A concentric-cylinder flow-birefringence instrument is used to generate sufficient shear fields to break T2 DNA (M = 1.2 X 10(8)) and E. coli DNA (M = 2.5 X 10(9)) in dilute solution. Breakage is monitored in situ by measuring the change in birefringence relaxation after the flow has been stopped. The breakage of T2 DNA follows first-order kinetics. Rate constants are obtained as functions of shear rate and viscosity (varied by adding glycerol). The data are fitted by a modified Arrhenius equation, assuming that stess increases the rate by lowering the activation energy. The rate increases with temperature, pH, and water concentration, and appears to be a base-catalyzed hydrolysis of the phosphate-ester linkage. La3+ ions catalyze the reaction. E. coli DNA was reduced to half molecules at a shear stress of 0.4 dynes/cm2, which is about 2500 times less than that required for T2. The difference in rates is accounted for in part by the difference in size of the two, but may also reflect the presence of many single-strand nicks in the coli DNA.
The theory of a preceding paper [B.H. Zimm, Biophys, Chem. 1 (1974) 279] is used to calculate a numerical table for the change of sedimentation coefficient with centrifugal field for chain molecules. A simple formula is found to fit the results within 1.3% up to the centrifugal field at which S/So = 0.377; this formula is S/So=(1+0.1155y2)-1/4, where y is proportional to M2/So times the centripetal acceleration, M being the molecular weight and So the sedimentation coefficient at zero acceleration. Applying this formula to DNA, we conclude that at a given centrifuge speed the sedimentation coefficient must reach a maximum at a particular molecular weight and be smaller at higher molecular weights. The value of the maximum depends on the conditions, but can come at less than 150 S for DNA under typical conditions. When a maximum is present, the profile of a sedimenting non-homogeneous band is also severely distorted.
Single-stranded DNA released from E. coli wild type and mutant cells by alkaline-EDTA-detergent was analyzed using the recently developed biophysical technique of viscoelastometry. Under the lysis conditions used, it was possible to detect single strands of molecular weight approximately 2 times 10-9 daltons. Little difference was detected in the size of single-stranded DNA from log phase vs. stationary phase cultures, or from cells treated with chloramphenicol to allow completion of replicating chromosomes. The largest single strands from ligase overproducing, endonuclease minus, and pol A1 mutants were likewise of approximately the same size as wild type, but were present in smaller yields. The reduction in single-strand molecular weight as a result of heating intact cells was investigated as a function of time and temperature. Heating at 37 degrees C for up to 20 min produced no additional single-strand breaks, but temperatures from 45 to 65 degrees introduced breaks. Solutions maintained at pH 12.5 were not stable indefinitely, and the relative viscosity of such solutions was found to decrease over a period of several hours.
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