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

Pulsed Field Gel Electrophoresis: Past, present, and future

Pulsed Field Gel Electrophoresis (PFGE) has been considered for many years the 'gold-standard' for characterizing many pathogenic organisms as well as for subtyping bacterial species causing infection outbreaks. This article reviews the basic principles of PFGE and it includes the main advantages and limitations of the different electrode configurations that have been used in PFGE equipment and their influence on the DNA electrophoretic separation. Remarkably, we summarize here the most relevant theoretical and practical aspects that we have learned for more than 20 years developing and using the miniaturized PFGE systems. We also discussed the theoretical aspects related to DNA migration in PFGE agarose gels. It served as the basis for simulating the DNA electrophoretic patterns in CHEF mini gels and mini-chambers during experimental design and optimization. A critical comparison between standard and miniaturized PFGE systems, as well as the enzymatic and non-enzymatic methods for intact immobilized DNA preparation, is provided throughout the review. The PFGE current applications, advantages, limitations and future challenges of the methodology are also discussed.

Relationship between frequency and deflection angle in the DNA prism

The DNA prism is a modification of the standard pulsed-field electrophoresis protocol to provide a continuous separation, where the DNA are deflected at an angle that depends on their molecular weight. The standard switchback model for the DNA prism predicts a monotonic increase in the deflection angle as a function of the frequency for switching the field until a plateau regime is reached. However, experiments indicate that the deflection angle achieves a maximum value before decaying to a size-independent value at high frequencies. Using Brownian dynamics simulations, we show that the maximum in the deflection angle is related to the reorientation time for the DNA and the decay in deflection angle at high frequencies is due to inadequate stretching. The generic features of the dependence of the deflection angle on molecular weight, switching frequency, and electric field strength explain a number of experimental phenomena.

Capacitively-induced pulsed-field gel electrophoresis: a novel method for DNA separation

Present instruments used in pulsed field and conventional gel electrophoresis, encounter a number of real and conceived difficulties such as electrical hazard, ground leak current, electrical noises, formation of gas bubbles at the metal electrodes and production of Joule heat in the buffer-gel system. To overcome the above-mentioned problems a novel electrophoresis unit based on capacitively-induced pulsed field was designed and tested in which the applied high voltage is decoupled from the electrolyte (buffer-gel system). In order to achieve a higher performance, the primary pulse generator which has been fabricated to apply for capacitively-induced pulsed field electrophoresis was equipped with a modulating frequency pulse generator which produced a combination of low and high frequency waves. The newly designed electrophoresis unit was able to resolve the Lambda DNA fragments so that seven bands with an acceptable resolution were observed. By increasing the run time both the depletion of molecules from the wells and the resolution of the bands improved compare to the patterns obtained via conventional electrophoresis.

Reorientation of large DNA molecules in concentrated polyacrylamide solution during crossed-field electrophoresis

Recently, we found that, in concentrated neutral solutions, DNA molecules migrate in linear conformation under steady electric field. In this paper, we report the conformational change of DNA during 120 degree crossed-field electrophoresis in the same polymer solution. We found that, in concentrated polyacrylamide solutions, the reorientation process of DNAs becomes simple: the DNA goes back along the previous track and the reorientation time is longer for larger DNA. Such a backtrack motion has been thought to be an essential motion for the separation of DNA fragments in pulsed field gel electrophoresis. We expect that this phenomenon is useful for a more efficient separation technique of large DNAs than the current pulsed field gel electrophoresis.

Reptation theories of electrophoresis

In this review, we present the main aspects of the reptation theory, which has provided an essential insight into the processes at work during DNA electrophoretic separation in gels. We avoid mathematical developments, and rely as much as possible on an intuitive description. We first present the original biased reptation model, which assumes that the DNA threads its way as a "worm" of fixed length among the fibers of the gel. We then introduce a more recent version, the model of Biased Reptation with Fluctuations (BRF), which allows for longitudinal flexibility along the DNA. We then propose a quantitative comparison with experiments performed in constant field, and discuss the application of reptation theories to pulsed field techniques either with crossed fields or with field inversion. We also discuss at some length the different experiments that led to a criticism of reptation ideas, such as orientation measurements and videomicroscopy. Finally, we use these experiments together with various computer simulations developed recently for gel electrophoresis, to propose a more realistic qualitative description of DNA motion in gels, and we discuss what elements in this motion are relevant to reptation and what processes are not included in present analytical models.

Pulsed-field electrophoresis in microlithographic arrays

Transverse pulsed-field electrophoresis of DNA has been conducted in a silicon array engineered by optical lithography and the motion of individual molecules observed by fluorescence microscopy. In strong fields, the molecules can be maintained in highly stretched, linear conformations. When the field is switched through an obtuse angle, they head off in the new direction led by what was formerly their tail end. This backtracking gives rise to fractionation that is linear with molecular weight. A simple prescription exists for choosing the field parameters to obtain a particular range of separation. Since the molecular motions are much more uniform than those that occur in a gel, it is anticipated that the arrays will permit more efficient fractionation than traditional pulsed-field gel electrophoresis. Arrays suitably scaled down in size may be useful for pulsed-field sequencing.

Two-dimensional motion of DNA bands during 120 degrees pulsed-field gel electrophoresis

The position and velocity of a band of double-stranded, linear DNA from bacteriophage G were measured during 120 degrees pulsed-field gel electrophoresis, using a video micrometer. Both the x and y coordinates were determined simultaneously in the plane of a 1% agarose gel; x is the mean drift direction. For pulse durations T greater than the tube renewal time T*, the path traced by the band of 670 kb DNA in the xy plane was in remarkably good accord with that predicted by Southern's ratchet model. However, the measured instantaneous velocity vx showed a sharp backward spike each time the field changed direction, with amplitude about twice the mean drift velocity. This spike is not consistent with models which assume a constant curvilinear velocity of DNA in a tube, nor with the biased reptation model without fluctuations. The corresponding measurements of vy showed a sharp positive spike with amplitude more than 3 times the plateau velocity in the y direction; neither model predicted this. The sharp velocity spikes are consistent with the idea that, for T > T*, a large fraction of the DNA chains are stretched into U-shaped or herniated configurations. When the field changes direction, the arms of the U's and the hernias recoil rapidly in response to intramolecular DNA chain tension. Because the base of a U or hernia is fixed by gel fibers, the center of mass of the chain recoils backward every time the field changes direction.

Gel electrophoresis of an end-labeled DNA. I. Dynamics and trapping in constant fields

A theory for the gel electrophoresis of a flexible polyelectrolyte, bearing an uncharged bulky label or an uncharged section at one end, is presented. We first consider a gel that is fully permeable to the label: we calculate the degree of stretching of the polyelectrolyte and its mobility as a function of chain size, electric field and label friction. Various regimes are identified, and their "existence domains" are calculated. For increasing friction, we predict a transition from a mobility decreasing with chain size to a mobility increasing with chain size. Secondly, we consider the possibility that the label may get trapped at some locations of the gel, a situation relevant to a method of "trapping electrophoresis" recently proposed by Ulanovsky et al. for DNA sequencing. A molecular model for detrapping by thermally activated "backward reptation" is constructed and solved using the Kramers rate-equation theory. Different closed analytical expressions and approximate scaling laws corresponding to different regimes of stretching and field strengths are predicted. The most striking result is a mobility which exponentially decreases past a critical size Np*, which decreases with increasing field. In the regime relevant to the experiments by Ulanowsky et al., we predict Np* approximately E-2/3. The predictions are in good qualitative agreement with presently available experiments, but further experimental investigations are suggested.

Information on DNA conformation derived from transverse pore gradient gel electrophoresis in conjunction with an advanced data analysis applied to capillary electrophoresis in polymer media

Abnormally slow migration of DNA is conventionally viewed as being due to an abnormal conformation relative to "linear" standards. The evidence for this rests on a few instances where nonlinear DNA structures have been established by independent methods and yield low mobilities relative to standards. Transverse pore gradient gel electrophoresis of authentically bent kinetoplast DNA and of an upstream activator sequence (UAS) of an E. coli operon promoter shows in addition that curves of migration distance vs. gel concentration ("Ferguson curves") of such abnormally conformed DNA differ from those of "linear" standards. Since Ferguson curves are interpretable with regard to molecular size in concordance with a mathematical model (Ogston model), transverse pore gradient gel electrophoresis provides a simple means of correlating abnormally slow migration of DNA with molecular size. In addition, transverse pore gradient gel electrophoresis is able to distinguish between DNA banding which exhibits a steeper dependence on gel concentration than "linear" standards from one which shows the same dependence. The former appears characteristic of circularly bent DNA and gives rise to a substantial retardation, the latter of bending across a knot or kink in the DNA chain associated with a relatively minor retardation relative to standards. Circularly bent restriction fragments formed from kinetoplast DNA retain the characteristic intersecting Ferguson curves on the transverse pore gradient gel. Another authentically "abnormal" DNA structure recognizable on transverse pore gradient gels is supercoiled DNA derived from the reaction of topoisomerase with a plasmid. Different lengths of supercoiled sequences give rise to parallel Ferguson curves clearly intersecting with those of linear standards.(ABSTRACT TRUNCATED AT 250 WORDS)

Why can we not sequence thousands of DNA bases on a polyacrylamide gel?

Pulsed fields have been remarkably useful at extending the range of DNA molecular sizes that can be separated on agarose gels by controlling the field-induced molecular orientation that often limits the resolution of large molecules. Unfortunately, the same approach seems to be much less effective for DNA sequencing on polyacrylamide gels. We present an experimental and theoretical (modelling) study of DNA sequencing which shows that molecular orientation is indeed not the main limiting factor for sequencing devices that use moderate field intensities and polyacrylamide as a separating matrix. We examine the interplay between electric field intensity, molecular size and resolution, and we suggest different approaches to increase the resolution limit of standard and automated sequencing gels. The theoretical limits of high-field electrophoretic sequencing are also discussed. We conclude that new ideas will be needed to go beyond one kilobase.

Concave Ferguson plots of DNA fragments and convex Ferguson plots of bacteriophages: evaluation of molecular and fiber properties, using desktop computers

A desktop computer program evaluating physical properties of DNA and bacteriophages is presented. The analysis is based on data obtained from capillary and submarine-type agarose electrophoresis. Native molecular/particle properties and properties of the gel (or polymer) medium can be derived from electrophoresis at several gel concentrations. This is done conveniently by a computerized evaluation of the semi-logarithmic plot of mobility vs. gel concentration, designated the Ferguson plot. In application to most proteins, this plot is linear and computer programs exist to evaluate it. However, nonlinear Ferguson plots have assumed great importance in view of the fact that the plots are concave for DNA. Similarly, convex plots are important since they prevail in the electrophoresis of large particles in agarose. The computer program reported here is the first to (i) address concave Ferguson plots and (ii) allow for the evaluation of both cases using a desktop computer. Program ELPHOFIT version 2.0, a Macintosh application, is available upon request.

Bag model for DNA migration during pulsed-field electrophoresis

A model for pulsed-field electrophoresis was developed by picturing large DNA as a deformable "bag" that (i) moves with limiting mobility in a continuous electric field, (ii) adopts an orientation aligned with the field direction, and (iii) reorients after a change in field direction in a size-dependent manner. The model correctly predicted the resolution of large DNA in a pulsed field including the surprising phenomena of mobility inversion, lateral band spreading, and improved resolution for obtuse angles. A simple parametrization agreed with observations of two completely different aspects of DNA behavior: bulk mobility as measured during gel electrophoresis and molecular reorientation as measured by linear dichroism. The model also provides quantitative guidelines for setting experimental parameters in pulsed-field electrophoresis experiments.

Pulsed-field electrophoresis of megabase-sized DNA

Success in constructing a physical map of the human genome will depend on two capabilities: rapid resolution of very large DNA and identification of migration anomalies. To address these issues, a systematic exploration of pulsed-field electrophoresis conditions for separating multimegabase-sized DNA was undertaken. Conditions were found for first liberating and then separating DNA up to 6 megabases at higher field strengths and more rapidly than previously reported. In addition, some conditions for transversely pulsed fields produced mobility inversion, in which increased size was accompanied by faster rather than slower migration. Importantly, anomalous migration could be identified by the presence of lateral band spreading, in which the DNA band remained sharply defined but spread laterally while moving down the gel. These results have implications for both practical applications and theoretical models of pulsed-field electrophoresis.

Pulsed-field electrophoresis of megabase-sized DNA

Success in constructing a physical map of the human genome will depend on two capabilities: rapid resolution of very large DNA and identification of migration anomalies. To address these issues, a systematic exploration of pulsed-field electrophoresis conditions for separating multimegabase-sized DNA was undertaken. Conditions were found for first liberating and then separating DNA up to 6 megabases at higher field strengths and more rapidly than previously reported. In addition, some conditions for transversely pulsed fields produced mobility inversion, in which increased size was accompanied by faster rather than slower migration. Importantly, anomalous migration could be identified by the presence of lateral band spreading, in which the DNA band remained sharply defined but spread laterally while moving down the gel. These results have implications for both practical applications and theoretical models of pulsed-field electrophoresis.

On the movement and alignment of DNA during 120 degrees pulsed-field gel electrophoresis

The displacement per pulse of lambda, T4, and G DNA during pulsed-field agarose gel electrophoresis has been measured for a fine mesh of pulse durations T between 0.02 and 120 s. The slopes of these curves show that the DNA moves by two distinct processes, designated 1 and 2, depending upon the pulse duration T. Process 1 operates at short T and causes dx/dT to decrease gradually with increasing T. This process is independent of molecular weight M. Process 2 is effective at longer T and causes dx/dT to rise sharply in sigmoidal fashion at a value of T which increases as M1.2, finally reaching a plateau of 1.4 microns/s for E = 4 V/cm. The shape of the dx/dT curve and its dependence on M lead directly to 4 zones of separation in plots of mobility vs M for different T. The alignment of the 3 DNAs during PFGE was measured by fluorescence-detected linear dichroism for E between 4 and 10 V/cm. These results are used in developing a molecular understanding of the mobility data.

Reptation-breathing theory of pulsed electrophoresis: dynamic regimes, antiresonance and symmetry breakdown effects

We apply the concepts of tube and reptation to the pulsed electrophoresis of DNA, considering both biased reptation and "breathing" modes (internal modes of the chain). Using suitable preaveraging approximations, analytical expressions are derived which relate displacement in crossed field electrophoresis to molecular weight, field strength, field period, pore size of the gel, and the angle between the field. These expressions provide scaling laws for the change of mobility when one (or more) of the parameters is varied as well as "universal" velocity versus molecular weight versus pulse time curves. These results are quantitatively compared with experiments. At some point which depends on field angle, field strength and chain length, however, we predict a failure of this model due to symmetry breakdown and loss of ergodicity. Qualitatively, this should lead to considerable band spreading and/or splitting of the highest DNA bands into two bands migrating sideways from the diagonal. The case of field inversion is also investigated. It is shown that only breathing modes can explain the strong differences in mobility experienced by chains of different length when opposite fields of equal amplitude are applied: the "trapping" of chains in conformations of low mobility is associated with an antiresonance-like coupling between the external field and the internal modes.