Irreversible trapping of DNA during crossed-field gel electrophoresis.

Using an original protocol with a rotating gel electrophoresis apparatus, it is shown that duplex DNA undergoing crossed-field electrophoresis in agarose gets trapped in the gel when the field is increased above a threshold value which decreases with the chain length and depends on the angle between the fields in a non-monotonous manner. This trapping is irreversible, i.e. once trapped at a high field strength, chains are unable to resume their motion when the field is returned to a lower value at which they moved prior to trapping. A model of trapping by "tight knots" is proposed. It predicts a trapping threshold proportional to the inverse square of the electric field, in qualitative agreement with the data. The implications of our results for the separation of large DNA molecules are discussed.     

Influence of electric field intensity, ionic strength, and migration distance on the mobility and diffusion in DNA surface electrophoresis

In order to increase the separation rate of surface electrophoresis while preserving the resolution for large DNA chains, e.g., genomic DNA, the mobility and diffusion of Lambda DNA chains adsorbed on flat silicon substrate under an applied electric field, as a function of migration distance, ionic strength, and field intensity, were studied using laser fluorescence microscope. The mobility was found to follow a power law with the field intensity beyond a certain threshold. The detected DNA peak width was shown to be constant with migration distance, slightly smaller with stronger field intensity, but significantly decreased with higher ionic strength. The molecular dynamics simulation demonstrated that the peak width was strongly related with the conformation of DNA chains adsorbed onto surface. The results also implied that there was no diffusion of DNA during migration on surface. Therefore, the Nernst-Einstein relation is not valid in the surface electrophoresis and the separation rate could be improved without losing resolution by decreasing separation distance, increasing buffer concentration, and field intensity. The results indicate the fast separation of genomic DNA chains by surface electrophoresis is possible.     

DNA electrophoresis in confined, periodic geometries: a new lakes-straits model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimm's approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.     

Activation energy of single-stranded DNA moving through cross-linked polyacrylamide gels at 300 V/cm effect of temperature on sequencing rate in high-electric-field capillary gel electrophoresis

In DNA sequencing, single-stranded DNA fragments are separated by gel electrophoresis. This separation is based on a sieving mechanism where DNA fragments are retarded as they pass through pores in the gel. In this paper, we present the mobility of DNA sequencing fragments as a function of temperature; mobility is determined in 4% T LongRanger gels at an electric field of 300 V/cm. The temperature dependence is compared with the predictions of the biased reptation model. The model predicts that the fragment length for the onset of biased reptation with stretching increases with the square of temperature; the data show that the onset of biased reptation with stretching decreases with temperature. Biased reptation fails to model accurately the temperature dependence of mobility. We analyzed the data and extracted the activation energy for passage of sequencing fragments through the gel. For fragments containing less than ca. 200 bases, the activation energy increases linearly with the number of bases at a rate of 25 J/mol per base; for longer fragments, the activation energy increases at a rate of 6.5 J/mol per base. This transition in the activation energy presumably reflects a change in conformation of the DNA fragments; small fragments exist in a random coil configuration and larger fragments migrate in an elongated configuration.     

Comparison of RNA, single-stranded DNA and double-stranded DNA behavior during capillary electrophoresis in semidilute polymer solutions

We present a study of the separation of RNA, single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) in semidilute linear hydroxyethylcellulose (HEC) solution. Our results strive to provide a better understanding of the mechanisms of nucleic acid migration during electrophoresis in polymer solutions under native and denaturing conditions. From a study of the dependence of mobility on chain length and applied electric field, we found that RNA and ssDNA show better separation and higher resolution over a larger range of sizes compared to dsDNA. In addition, RNA reptation without orientation extends to longer chain lengths in comparison to ssDNA, possibly as a result of different type of short-lived secondary structure formations. Such a comparative study between nucleic acid capillary electrophoresis helps to optimize RNA separation and provides better understanding of RNA migration mechanisms in semidilute polymer solutions under denaturing conditions.     

Universal interpolating function for the dispersion coefficient of DNA fragments in sieving matrices

The separation of DNA fragments by (slab or capillary) gel electrophoresis has been studied extensively. To characterize the separation achieved by such systems, one needs to understand the impact (and their dependency upon the experimental quantities) of two physical parameters: the electrophoretic mobility mu and the diffusion coefficient D. Three different regimes have been shown to exist for both mu and D: the Ogston regime, the reptation regime and the reptation with orientation regime (note that separation is only possible for the first two regimes). In the small electric field limit, both mu and D are apparently well described by theories for all three regimes. Unfortunately this results in disjointed scaling laws and no theory-based general equations can apply to all regimes. Recently, an empirical interpolating formula has been proposed that adequately fits the low electric field mobility mu of dsDNA fragments across all three regimes and is compatible with accepted theories. In this article we review and clarify the current state of knowledge regarding the size dependence of the mobility and the diffusion coefficient and propose an interpolating formula for molecular size dependence of the low field diffusion coefficient D. With formulas for both the mobility and the diffusion coefficient as a function of the experimental conditions one could, in principle, optimize any gel/polymer matrix-based electrophoresis system for a wide range of DNA molecular sizes.     

Disentanglement and reptation during dissolution of rubbery polymers

The dissolution mechanism of rubbery polymers was analyzed by dividing the penetrant concentration field into three regimes that delineate three distinctly different transport processes. The solvent penetration into the rubbery polymer was assumed to be Fickian. The mode of mobility of the polymer chains was shown to undergo a change at a critical penetrant concentration expressed as a change in the diffusion coefficient of the polymer. It was assumed that beyond the critical penetrant concentration, reptation was the dominant mode of diffusion. Molecular arguments were invoked to derive expressions for the radius of gyration, the plateau modulus, and the reptation time, thus leading to an expression for the reptation diffusivity. The disentanglement rate was defined as the ratio between the radius of gyration of the polymer and the reptation time. Transport in the second penetrant concentration regime was modeled to occur in a diffusion boundary layer adjacent to the polymer-solvent interface, where a Smoluchowski type diffusion equation was obtained. The model equations were numerically solved using a fully implicit finite difference technique. The results of the simulation were analyzed to ascertain the effect of the polymer molecular weight and its diffusivity on the dissolution process. The results show that the dissolution can be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. © 1996 John Wiley & Sons, Inc.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

The electric field dependence of DNA mobilities in agarose gels: a reinvestigation

The electric field dependence of the electrophoretic mobility of linear DNA fragments in agarose gels was reinvestigated in order to correct the observed mobilities for the different temperatures actually present in the gel during electrophoresis in different electric field gradients. When corrected to a common temperature, the electrophoretic mobilities of DNA fragments less than or equal to 1 kilobase pairs (kbp) in size were independent of electric field strength at all field strengths from 0.6 to 4.6 V/cm if the gels contained less than or equal to 1.4% agarose. The mobilities of larger DNA fragments increased approximately linearly with electric field strength. If the agarose concentration was higher than 2%, the mobilities of all DNA fragments increased with increasing electric field strength. The electric field dependence of the mobility was larger in gels cast and run in Tris-borate buffer (TBE) than in gels cast and run in Tris-acetate buffer (TAE), and was more pronounced in gels without ethidium bromide incorporated in the matrix. Ferguson plots were constructed for the various DNA fragments, both with and without extrapolating the temperature-corrected mobilities to zero electric field strength. Linear Ferguson plots were obtained for all fragments less than or equal to 12 kbp in size in agarose gels less than or equal to 1.4% in concentration if the mobilities were first extrapolated to zero electric field strength. Concave upward curvature of the Ferguson plots was observed for DNA fragments greater than or equal to 2 kbp in size at finite electric field strengths. Convex downward curvature of the Ferguson plots was observed for DNA fragments greater than or equal to 1 kbp in size in agarose gels greater than or equal to 2% in concentration. The mobilities of the various DNA fragments, extrapolated to zero agarose concentration and zero electric field strength, decreased with increasing DNA molecular weight; extrapolating to zero molecular weight gave an "intrinsic" DNA mobility of 2.7 x 10(-4) cm2/Vs at 20 degrees C. The pore sizes of LE agarose gels cast and run in TAE and TBE buffers were estimated from the mobility of the DNA fragments.(ABSTRACT TRUNCATED AT 400 WORDS)     

Do orientation effects contribute to the molecular weight dependence of the free solution mobility of DNA?

The free solution mobility of DNA increases with increasing molecular weight and then levels off and becomes constant at molecular weights above approximately 400 bp (Stellwagen, N. C., Gelfi, C., Righetti, P. G., Biopolymers 1997,42, 687-703). To investigate whether the increase in mobility could be attributed to an increased orientation of the larger DNA molecules in the electric field, the free solution mobility of DNA was measured by capillary electrophoresis as a function of electric field strength. Mixtures containing 20-, 118- and 422-bp DNA molecules, and 20-, 422- and 2116-bp DNAs, were studied. If the larger DNA molecules in each mixture were oriented by the electric field, their mobilities should increase with electric field strength faster than the mobility of the 20-bp oligomer, which is too small to be oriented by the electric fields used in this study. Instead, the ratios of the mobilities of the 118-, 422- and 2116-bp fragments to the mobility of the 20-bp oligomer were independent of electric field strength. Hence, orientation effects are not important for DNA molecules up to 2 kbp in size, in electric fields up to 500 V/cm in amplitude. An explanation is suggested.     

Effect of nonparallel alternating fields on the mobility of DNA in the biased reptation model of gel electrophoresis

Chromosome-size DNA molecules can now be separated using a variety of pulsed field gel electrophoresis techniques. In this article, we study the predictions of the biased reptation model concerning the effect of two pulsed fields, making an arbitrary angle, on the power of separation of gel electrophoresis. Separation is predicted to be largely enhanced for obtuse angles, in agreement with experiments. Interestingly, very large molecules, which are not separated by pulsed fields, are predicted not to migrate along the gel diagonal for fairly long periods of time. Finally, we discuss the optimization of these techniques using the results of the theory, and the limitations of the latter when fluctuations and intramolecular modes probably dominate the system.     

Modeling ssDNA electrophoretic migration with band broadening in an entangled or cross-linked network

We use a coarse-grained model proposed by Graham and Larson based on the temporary network model by Schieber et al.. [1] to simulate the electrophoretic motion of ssDNA and corresponding band broadening due to dispersion. With dimensionless numbers reflecting the experimental physical properties, we are able to simulate ssDNA behavior under weak to moderate electric field strengths for chains with 8-50 entanglements per chain ( approximately 1000-8500 base pairs), and model smoothly the transition from reptation to oriented reptation. These results are fitted with an interpolation equation, which allows the user to calculate dimensionless mobilities easily from input parameters characterizing the gel matrix, DNA molecules, and field strengths. Dimensionless peak widths are predicted from mobility fluctuations using the central limit theorem and the assumption that the mobility fluctuations are Gaussian. Using results from previous studies of ssDNA physical properties (effective charge xiq and Kuhn step length b(K)) and sieving matrix properties (pore size or tube diameter a), we give scaling factors to convert the dimensionless values to "real" experimental values, including the mobility, migration distance, and time. We find that the interpolation equation fits well the experimental data of ssDNA mobilities and peak widths, supporting the validity of the coarse-grained model. The model does not account for constraint release and hernia formation, and assumes that the sieving network is a homogeneous microstructure with no temperature gradients and no peak width due to injection. These assumptions can be relaxed in future work for more accurate prediction.     

Mobility, diffusion and dispersion of single-stranded DNA in sequencing gels

Electrophoresis of single-stranded DNA in denaturing polyacrylamide gels is presently a standard procedure for the sequencing of DNA fragments. A thorough understanding of the factors that determine the resolution of DNA fractionated in polyacrylamide gels is necessary to optimize the performance of DNA sequencers. Significant research on the mobility of double-stranded (ds)DNA molecules in agarose and polyacrylamide gels has been performed, and the phenomenon of band broadening of single-stranded (ss)DNA fragments in DNA sequencing gels has received attention only recently. In this paper, we present a detailed study of mobility, diffusion and dispersion of ssDNA in sequencing gels as a function of molecular size, gel concentration and electric field strength. DNA mobility is shown to be essentially independent of electric field in the range of 0-60 V/cm. The band broadening is greatly enhanced in the presence of an electric field and the dispersion coefficient (DE) can be an order of magnitude higher than the field-free diffusion coefficient. The measured migration parameters approximately follow the predictions of the biased reptation including fluctuations (BRF) theory. However, deviations due to nonidealities of the separation conditions are observed. The measured migration parameters can be used to optimize the performance of separation systems.     

Gel electrophoretic mobility of single-stranded DNA: the two reptation field-dependent factors

The reptation model is the dominant theory in understanding the electrophoretic separation of single-stranded DNA molecules in gels or entangled polymer solutions. Recently, we showed that the Ogston and reptation regimes are separated by an entropic trapping regime at low field intensities. Here, we report the first comparison of the field-dependent part of the DNA mobility for both small and long reptating molecules. We show that both mobilities increase linearly with field intensity, with the mobility of the longer (comigrating) fragments increasing faster than that of the smaller ones. We compare our results to the predictions of the biased reptation model.     

Discontinuous buffer system for polyacrylamide and agarose gel electrophoresis of DNA fragments

DNA fragments up to 9 kb in size were stacked and separated by polyacrylamide gel electrophoresis, and those up to 50 kb in size by agarose gel electrophoresis, using a discontinuous buffer system. Polyacrylamide gels at pH 8.9, 2 degrees C, 0.01 M ionic strength, yielded sharp bands with DNA loads of 8 micrograms/cm2 of gel of a mixture of 19 DNA fragments in the size range of 72-23130 bp, while agarose gels at pH 8.5, 25 degrees C, provided well-resolved, unperturbed bands at 0.04 M ionic strength with DNA loads of 1 microgram/cm2 of the same mixture. Note that the ionic strength of the agarose gels is comparable to the conventionally used 0.5 x TBE (Tris-borate-EDTA) buffer, while that successfully applied to polyacrylamide is seven-fold less than the ionic strength of conventionally used 1 x TBE buffer, with a substantially shorter duration of electrophoresis as a result. The application of a discontinuous buffer system to the gel electrophoresis of DNA results in (i) Band identification by Rf, the migration distance relative to a sharply defined "buffer front" (moving boundary). This is sufficiently labor saving, compared to determining absolute mobilities, so as to render practical the expression of bands as numbers, with benefits for data storage, statistical manipulations and physico-chemical exploitation of mobility data. The use of Rf's also circumvents loss of precision in mobility measurement resulting from progressive band spreading of dye bands used as a front. (ii) A uniformly and highly concentrated starting zone, beneficial to resolution, is obtained, without the losses by which separate concentration steps are usually burdened.(ABSTRACT TRUNCATED AT 250 WORDS)     

Computer simulation of DNA gel electrophoresis: influence of solid friction on linear and circular chains

The effect of solid friction between DNA molecules and gel fibres during gel electrophoresis has been studied using Brownian dynamics simulations. To investigate the effect of the topology of the polyelectrolyte chains, we have studied both linear and circular molecules. The results show that the migration properties of linear molecules seem to be almost uneffected by solid friction. There is, however, a significant effect on the mobility of circular molecules of the same size. Increasing the electric field strength increases the mobility of the linear molecules while for the circular chains, the mobility goes through a maximum when friction is included.     

Effect of bending and torsion rigidity on self-diffusion in polymer melts: a molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for NNe (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for NNe. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.     

Adhesion and friction of PDMS networks: molecular weight effects

The objective of this work is to find relations between adherence and friction behaviors of elastomer networks. The chosen approach is based on the parallel study of the initial molecular weight (i.e., the degree of cross-linking) dependence of both adherence and friction. The polymers used are cross-linked polydimethylsiloxane (PDMS) and the substrate is a smooth glass plate. The experimental procedure uses both friction (pin on disk tribometer) and adhesion (tack test) measurements, associated with surface analysis and mechanical and rheological characterizations. Tack results show that high molecular weight PDMS exhibits the greater adherence energy. This can be explained by the role of both chain length and free and pendant chains: more numerous and longer free chains favor the substrate wetting (at a molecular scale) and increases the energy dissipation during separation (extraction and reptation mechanisms). However, friction results indicate a higher friction resistance for low molecular weight PDMS. This result could be quite surprising. An explanation based on interfacial sliding properties of free and pendant chains can be proposed. Elsewhere, for the lower molecular weight polymer, elastic contact present during friction is able to act as a forced wetting, constraining the network and consequently leading to a greater energy dissipation.     

Interdiffusion of polymers across interfaces

Neutron Reflection (NR) and Dynamic Secondary Ion Mass Spectroscopy (DSIMS) experiments were conducted on symmetrically deuterated polystyrene triblock bilayers (HDH/DHD) which directly probed the interdiffusion dynamics of the chains during welding. The HDH chains had their centers deuterated 50%, the DHD chains had their ends deuterated (25% at each end) such that each chain contained approximately 50% D. During welding, anisotropic motion of the chains produces a time-dependent oscillation (ripple) in the H and D concentration at the interface, which bears the characteristic signature of the polymer dynamics. These oscillations were compared with those predicted by Rouse, polymer mode coupling (PMC), and reptation dynamics. The following conclusions can be made from this study. (a) During the interdiffusion of high molecular weight HDH/DHD pairs, higher mobility of the chain ends caused a concentration oscillation which increased to a maximum amplitude, and eventually vanished at times, t > τ_D. The amplitude, or excess enrichment found, was appreciably more than that predicted by Rouse and PMC simulations, and was only slightly less than that predicted from reptation simulations. (b) The oscillations were completely missing in the 30 and 50K HDH/DHD polymers, which are only weakly entangled. The lack of oscillations for the 30 and 50K pairs may be due to a combination of surface roughness and fluctuations of order 30 Å. (c) It was found that the position of the maximum in this ripple stayed at the interface during its growth. This is also consistent with reptation and has not been explained by other theories. (d) All dynamics models for linear polymers produce ripples, many of which are qualitatively similar to that predicted for reptation. However, each ripple bears the fingerprint of the dynamics in terms of its time-dependent shape, position, and magnitude, and the models are clearly distinguishable. Our results, in summary, support reptation as a candidate mechanism of interdiffusion at polymer(SINGLEBOND) polymer interfaces and its uniqueness is being further pursued. © 1996 John Wiley & Sons, Inc.