.=) 1992 Oxford University Press

Nucleic Acids Research, Vol. 20, No. 10 2447-2452

Field inversion gel electrophoresis in denaturing polyacrylamide gels Christoph Heller* and Stephan Beck Imperial Cancer Research Fund, 44 Lincoln's Inn Fields, London WC2A 3PX, UK Received March 5, 1992; Revised and Accepted April 16, 1992

ABSTRACT The velocities of single stranded DNA molecules in denaturing polyacrylamide gels during symmetric and asymmetric field inversion were measured at different pulse times and gel concentrations. Under the conditions chosen in our study, pulse times as short as a few milliseconds lead to a retardation of DNA molecules larger than 400 bases. We found that a field inversion with an electric field in the forward direction of about double the strength of that applied in the backward direction is a good compromise between the degree of retardation, the temperature control requirements and the run time of the gel. INTRODUCTION Field inversion gel electrophoresis (FIGE) was first introduced in 1986 (1) for separating large double stranded DNA molecules in agarose gels. Since then it has been widely used for a lot of applications and can be regarded as an established technique in molecular biology. In this method, a uniform electric field is periodically inverted. In order to achieve a net migration, the product of pulse time and amplitude of the pulse in the 'forward' direction must be larger than the one for the pulse in the 'backward' direction. This technique has been proven to be useful for the separation of DNA molecules with low (2-4), medium (1,5) and high (6) molecular weights, covering a range from a few thousand basepairs up to at least 6 Mbp. FIGE gives the opportunity to separate molecules over a wide range at a rather low resolution by using pulse time ramps, but can also achieve a very high resolution in a small window of separation by using constant pulse times (7). The FIGE system can be set up with a minimum of instrumentation and can also easily be combined with other techniques such as direct blotting electrophoresis (8). The mobility of DNA molecules in agarose gels under field inversion conditions has been well studied experimentally (2,4,5) and can also be reproduced by computer simulations based on theoretical models (9-11). Like agarose gels, denaturing polyacrylamide gels as they are used in DNA sequencing, suffer from poor separation of

molecules with higher molecular weight and therefore only up to about 300 bases can routinely and reliably be read from a standard sequencing gel. Only with considerable effort, such as very long or very thin gels (12), can this limit be extended to about 600 bases, but these techniques do not seem to be in general use. We assumed that if the separation of single stranded DNA molecules in denaturing polyacrylamide gels is based on a similar mechanism as for the separation of double stranded DNA in agarose gels, it should also be possible to enhance the separation limit of sequencing gels by using the field inversion technique. There have been few publications where inverted and intermittent fields were applied to sequencing gels (13- 15) but the improvements in separation seem to be rather small and the results do not give a clear picture about the behavior of single stranded DNA molecules in pulsed field sequencing gels. Therefore we have undertaken a systematic study, to achieve a better understanding about the mobility of single stranded DNA molecules in sequencing gels under non-stationary electrophoresis conditions and to achieve optimal and reproducible separation. As in non-stationary agarose gel electrophoresis, it can be assumed, that there are several parameters which influence the motion of the DNA molecules, such as electric field, pulse time, polyacrylamide concentration, buffer composition and temperature. In this study we have investigated the influence of the electric field, the pulse time and the gel concentration, whereas buffer composition and temperature were kept constant.

MATERIALS AND METHODS Apparatus As a switching interface between the gel and the power supply (Consort E 734; Consort, Turnhout, Belgium) we used the IBI Fiji HV3000 programmable switching device (IBI, New Haven, USA) which is able to deliver pulses as short as one millisecond and can be used for electric fields up to 3000 V. For experiments with different electric fields in the forward and in the backward direction a home made 'voltage divider' was used in connection with the switcher as shown in fig. 1. This voltage divider consists of ten high power zener diodes (BZY93 C75), each able to reduce the voltage by 75 Volts. This allows

* To whom correspondence should be addressed at Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris, Laboratoire de PhysicoChimie Th6orique, 10 rue Vauquelin, 75231 Paris cedex 05, France

2448 Nucleic Acids Research, Vol. 20, No. 10 the stepwise selection of different electric fields for the 'backward' direction in dependence of the electric field in the 'forward' direction (between 0 and 750 V). The performance of this setup in regard to square wave form, amplitude and length of the pulses was checked by an oscilloscope (data not shown). Electrophoresis Working solutions were prepared from a 40% (w/v) stock solution (with a 19:1 ratio of acrylamide to NN'-Methylenebisacrylamide, corresponding to a crosslinker concentration of 5%) by adding urea, lOxTBE buffer and water to the final concentrations of 6, 8 or 10% (total concentration) acrylamide, 1 xTBE and 7M urea, respectively. These were kept at 4°C not longer than 2 months and filtered before use. The TBE buffer was a modified version with a pH of 8.8, which prevents the buffer from precipitating. IOxTBE buffer is 162g/1 Tris Base, 27.5 g/l Boric acid and 9.2 g/l Na2EDTA. The gels were prepared by using 20 ml acrylamide solution, adding 40 Id N,N,N',N'-Tetramethylenediamine (TEMED) and 40 1l of a 25% Ammonium peroxodisulphate solution and pouring it between the assembled glass plates with the help of a syringe. All gel components were of 'Electran' grade (Merck-BDH, UK). As electrophoresis chamber we used the EV 220/221 slab gel unit (Cambridge Electrophoresis, Cambridge, UK) with 185 x200 mm large glass plates and 0.38mm thick spacers. Because of the 2 cm deep notch, the effective gel length was 165 mm. Before assembly, one glass plate was treated with 3-metacryloxypropyl-trimethoxysilane (GF 31, Wacker Chemie, Munich, Germany) in order to covalently bind the gel to this plate (16). The opposite glass plate was treated with Dimethylchlorosilane solution (Merck-BDH) as repellent. The gel was allowed to polymerize for at least one hour and then mounted into the electrophoresis unit. For electrophoretic separations without active temperature control, a 1mm thick aluminium plate was clamped onto the front glass plate in order to achieve a more uniform heat distribution.

The gel was pre-run at a constant voltage of 40 V/cm for 30 to 45 min. After this time the current was constant at 20-25 mA corresponding to a power of 13-16.5 Watts. By slightly

varying the pre-run time, we made sure that the gels had a temperature between 40 and 45°C at the beginning of the run. For gels with active temperature control, a plastic box was cut to size and glued to the front glass plate. Water was filled in and a cooling coil was immersed. In this case, the chosen prerun time was 30 minutes. The temperature of all gels was monitored with a 0.2 mm thick thermocouple (type K: Nickel-Chromium/Nickel-Aluminium), which was clamped between the back glass plate and the perspex support of the gel chamber. Test experiments with a second probe imbedded in the gel showed that the temperature difference between the inside and the outer surface of the glass plates was rather small (< 1.5°C). After the pre-run, the wells were washed, the samples loaded and the pulses applied. After the end of the electrophoresis, the glass plates were separated and the gel (bound to one plate) was immersed in 10% acetic acid for 20 minutes. After drying over night, the gels were exposed to an x-ray film.

DNA samples As length standards we used Sau3a digests from pBR 322 and pUC 18, labelled with Klenow end fill reaction in presence of 35S-dATP. A 123 bp ladder (Gibco BRL) was labelled with T4 DNA Polymerase and Klenow enzyme according to instructions of the manufacturer. Additionally, we used standard sequencing reaction products with M13mpl8 as a template and 35S-dATP as label. The samples were mixed with one volume loading buffer (10 mM EDTA, 0.05% Bromphenolblue, 0.05% Xylene Cyanol in deionized Formamide) and incubated at 80°C for 20 minutes before loading.

Evaluation of data The position of the bands relative to the wells were measured by digitizing the autoradiograms on a sonic digitizer (BioRad).


ziD z9


DC e.g 660V










n I\n1a


Z2 zi



1. 1 1


1 0,4

Molecular Weight (bases)

Fig. 1. Switcher and voltage divider for asymmetric FIGE. The electric field in the forward direction (arrow with broken line) remains constant, whereas the strength of the electric field in the backward direction is determined by the number of zener diodes between the switcher and the gel. A typical experimental situation is shown, together with the respective field strengths. The switcher reduced the input voltage of 660V to 640V output. Dl = 2* diode IN 5404 (parallel), ZI -Z10 = zener diode BZY93 C75.

Fig. 2. Velocities of single stranded DNA fragments under a constant electric field of 640 V (39 V/cm) and at 6% (O), 8% (/\) and 10% (x) total acrylamide concentration. The broken lines have a slope of -1. The dotted lines indicate the presumed transitions between Ogston sieving (I), reptation without stretching (II) and reptation with stretching (III).

Nucleic Acids Research, Vol. 20, No. 10 2449 The data were evaluated and processed by using home made and public domain software. All gels were run at least twice and all data are given as average values. As the applied field is not constant, we chose to give the velocity rather than the mobility. For expressing relative velocities we have chosen a DNA fragment with a length of 50 bases as a reference. This corresponds approximately to the distance between the SmaI site and the beginning of the primer, when a standard sequencing primer and pUC/M13 vectors are used. The applied voltage was measured at the electrodes. Assuming that the voltage drop in the buffer chamber can be neglected (conductivity of the buffer was 1150 /AS at 25°C), the values were divided by the gel length (16.5 cm) in order to obtain the electric field strength.

RESULTS Electrophoresis under constant electric field When plotting the logarithm of the velocity of single stranded DNA molecules in polyacrylamide gels versus the logarithm of molecular weight, a sigmoid curve is obtained (fig.2). This is essentially similar to the behavior of ds DNA in agarose gels, so we can assume that in principle the same mechanisms of interaction between the DNA and the gel are involved. As shown by Slater and Noolandi (17,18), this plot helps to identify the different regimes of separation: Small molecules form a kind of globule smaller than the pore size of the gel and are separated by a mechanism described as 'Ogston-sieving'. The velocity of the medium sized molecules is proportional to L-l (dotted lines with a slope of -1 in the log/log-plot) and can therefore be described as moving in a manner called 'reptationwithout-stretching' Larger molecules (> 500 bases) assume nearly the same velocity (plateau velocity), which can be explained by a stretching induced by the reptation process ('reptation-with-stretching'). It is this stretching which limits the electrophoretic separation of large molecules, but which we should be able to avoid by periodically inverting the electric field and therefore enhancing the separation limit. Our data are also in good qualitative agreement to the 'phase diagram' in (fig.1 of ref.18): The onset of reptation occurs at higher molecular weight with lower acrylamide concentration. However, the transition from the reptation-without-stretching mode to the reptation-with-stretching occurs approximately at the same molecular weight at all three gel concentrations, in contrast to the prediction. .


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200 400 600 800 1 000 1 2001 400

Asymmetric voltage field inversion Experiments under FIGE conditions can be described with a few parameters. These are the pulse times in the forward and backward direction (tf and tb) and the electric fields in these directions (Ef and Eb). The ratio between these parameters are given by R =tfltb and RE= E/Eb Furthermore, temperature and acrylamide concentration (%T) influence the mobility of the DNA molecules. It has been shown that field inversion gel electrophoresis with different electric fields in the forward and backward direction



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Molecular Weight (bases)



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Molecular Weight (bases)

weight for for giel concentration ofofVrel6,6, CO/St/vrel aelocity 8t atse argmn gel concentration and I8 10% and pule time t of I 8 and weight n at pulse Conditions fig.3.




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total acrylamide concentration and at different pulse times. Conditions: tb, Ef = 640 V, Eb = 340 V, temp. = 430C, 1 xTBE. 10%





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2450 Nucleic Acids Research, Vol. 20, No. 10 (i.e. RE> 1, Rt=1, t=tf=tb) rather than two different pulse times is a very successful method for separating double stranded linear DNA in agarose gels, especially in the molecular weight range between 1 and 50 kbp (4,19). Also, the band inversion effect is less pronounced. Therefore it was suggested to use this technique for pulsing sequencing gels (13).

a) Dependence on pulse time and on acrylamide concentration. One of the most interesting parameters in this kind of separation is obviously the switch interval t. We have therefore undertaken a series of experiments with different pulse times and with three different acrylamide concentrations, but maintaining constant the electric fields (Ef=640 V corresponding to 39 V/cm and








E 10-1





Eb=340V corresponding to 20.5 V/cm) the ratio RE= 1.9 and the temperature. Pulsing with asymmetric electric fields has also the advantage that less electrical power is applied to the gel, resulting in a much lower heating of the gel. With the equipment used and under the conditions described, we were able to run these gels without active temperature control. The temperature in the gel rose only slowly, i.e. by 4°C during 5 hours run time. Therefore we were able to keep the temperature within the range of 43 +/-40C. Additionally, some runs were repeated with active temperature control (43 +-1° C), but these did not show a significant difference. As shown in fig.3, molecules larger than 400 bases are rtarde compared to their velocity under constant field conditions. This is in agreement with the assumption that only the molecules which are being stretched by the reptation mechanism will be influenced by the pulsing of the field. The onset of the retardation effect is at about 400 bases at all three gel concentrations. To demonstrate the amount of retardation we introduce a retardation factor r, which is the ratio between the relative velocity under constant field and the relative velocity under pulsed field conditions. A retardation factor of two for example, means that the fragment moves half as fast relative to the 50 base fragment under pulse conditions compared to its relative velocity in the constant field. Fig. 4 shows a plot of this retardation factor versus the molecular weight, determined for a pulse time of 1 ms and at all three gel concentrations. As the retardation effect obviously is a function of the pulse time, the data from the same experiments were used to show the dependence of the velocity of molecules of a particular size on the pulse time (log/log-plot, fig.5). This plot shows that the retardation of the molecules affected is constant below 10 ms but becomes gradually less with longer pulses until a plateau value is reached. This plateau value corresponds to a fourth of the velocity under constant field conditions. This is the expected value for RE=2, because in the low frequency regime molecules are not affected by the pulsing and their velocity is vpulse = vConst*((vf-vb)/2 vf). As the velocity at a constant field of 340 V is close to 1/2 v(E=64Ov) (data not shown), vpulse is 1/4 v,o,st.




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Pulse time (ms)

Re=3.5 A.Re=1.9 F e=1.3



Fig. 5. Absolute velocities of different single stranded DNA fragments in dependence of the pulse time and at different gel concentrations. The lengths are (O) 109 ;, (*) 211 ,(() 321 3, (o) 589(, (A) 959 , and (x) 1378 bases. The error bars show the standard deviations; electrophoresis conditions as in fig.3. The symbols at the far right indicate the velocity at constant field, corrected for the difference in velocity between constant and pulsed field. Note the different velocity scale for the 10% gel.

200 400

600 800

10001200 1400

Molecular Weight (bases)

Fig.6. Effect of varying the ratio of forward to backward electric field in asymmetric FIGE. Conditions: Ef = 640 V tf = tb = I mis, 8%T gel concentration, 43°C, 1 xTBE.

Nucleic Acids Research, Vol. 20, No. 10 2451 b) Dependence on the ratio between the electric fields, RE. We have also varied the ratio of the electric fields in the forward and backward direction by keeping Ef constant at 640 V and tf = tb = 1 ms but changing Eb. The values chosen were Eb = 490 V (30 V/cm), 340 V (20.5 V/cm), 185 V (11 V/cm) and 0 V corresponding to RE = 1.3, 1.9, 3.5 and infinite (intermittent field). As the net power applied to the gel varies with RE, an active temperature control had to be used for this series of experiments. Fig.6 shows that an intermittent field has less effect on the retardation of the molecules compared to the effect obtained when a reverse field is applied. In this case, the retardation is stronger with lower RE-

Symmetric voltage field inversion We were also interested in the effect of the 'classic' field inversion gel electrophoresis, i.e. pulsing with two different pulse times but constant electric field. The parameters chosen were Ef=Eb=640 V (39 V/cm), 8%T and Rt=2. This pulse regime results in a substantial heating of the gel and therefore an active cooling was necessary. Again, a retardation of molecules larger than 400 bases is observed, but the effect is weaker than with two different fields (fig.7). The velocity of the retarded molecules is also dependent on the pulse time. Again, the dependence shows a sigmoid behavior, with a plateau value corresponding to a third of the velocity under constant field conditions (vpulse = Vconst (tf-tb)/(tf+tb)) (not shown). *

DISCUSSION The mobility function of ss DNA in denaturing polyacrylamide gels can be divided into three regimes, indicating different mechanisms of separation. This phenomenon seems to be universal for the electrophoretic mobility of flexible polymers in porous matrices (20). The electrophoretic behavior of ss DNA in polyacrylamide gels is in fairly good agreement with the predictions of the biased reptation model, especially concerning the onset of reptation. The rather long molecular weight range





Molecular Weight (bases)

Fig. 7. Denaturing acrylamide gel electrophoresis with symmetric field inversion. Conditions: Ef = Eb = 640 V, Rt = 2, 8%T gel concentration, 43°C, I xTBE.

with a slope of -1 in the double logarithmic plot of velocity vs molecular weight indicates that the movement of single stranded DNA in a polyacrylamide gel is a good example of a reptating chain. However, the onset of the reptation-with-stretching regime does not seem to follow the predicted law, but more measurements with molecules > 1000 bases would be necessary to precisely estimate the transition point between the two regimes. The most important parameters which influence the kind of motion of polymers in porous matrices are the size of the pores in the matrix and the flexibility of the polymer. The pore size of the polyacrylamide gels like the ones used in this study are about one order of magnitude smaller than the ones in agarose gels (21,22). However, recent publications indicate that the pore size in polyacrylamide gels might be larger as estimated earlier (23). The presence of urea can also play a role (24). To our knowledge, the persistence length of ss DNA has not been determined so far, but we can assume that it is much smaller than the persistence length of ds DNA. The ambiguities in the pore size and the unknown persistence length do not allow us to make exact predictions or even simulations of the motion of ss DNA in polyacrylamide gels, but it is likely that it is similar to that of ds DNA in agarose gels, but on a smaller scale. This means the molecules might also be able to assume stretched and relaxed conformations, as they are observed for large ds DNA molecules (25). If these assumptions are correct, then the stretching phenomenon, which hinders the electrophoretic separation, should be overcome by periodically turning off the electric field (intermittent field). This method was used by Daniels et al. (15) and was also tested in our study, but it seems to be not very effective. As the relaxation time of a reptating polymer chain is supposed to be proportional to the third power of molecular weight (26), it is possible that the zero-field intervals chosen (1 ms) are not long enough to allow a complete relaxation of the chain. But also on-off pulses as long as 20 msec did not improve the retardation (data not shown). By applying an electric field in the reverse direction, the retardation effect could be clearly enhanced, with the effect depending on the strength of the backward electric field. Presumably, this enforces the relaxation process and therefore reduces the stretching. Pulsing with symmetric electric fields works as well, but a smaller retardation effect was observed. As expected, the retardation is also dependent on the pulse time. The sigmoid velocity vs pulse time function is essentially similar to the one observed for short and medium sized ds linear DNA molecules in agarose (table 1 of ref.27, fig. 1 of ref. 28). A mobility minimum which would lead to a band inversion in the electrophoresis, has not been observed so far, but-in analogy to the agarose data-could be expected for longer molecules. However, it has to be pointed out, that the retardation effects which we could observe for ss DNA in polyacrylamide gels are very small compared to FIGE in agarose gels with ds DNA, where dramatic retardations are obtained. As pulsing, as well as a lower electric field reduces the stretching of the DNA, it is not possible to distinguish to what amount the retardation is due to the lower effective electric field and to what amount it is a result of the pulsing. The onset of the retardation was found to be the same at all three gel concentrations, but the effect is stronger with higher gel concentration. The retardation factor which we have

2452 Nucleic Acids Research, Vol. 20, No. 10 determined, can be used to calculate the separation between two bands under pulsed field conditions. For example, in a 6% gel at constant field, a pair of fragments of 400 bases and 500 bases length, have a velocity of 0.65 mm/min and 0.53 mm/min, respectively. In five hours run time, they would travel 195 and 159 mm respectively, leading to a separation of 36 mm. If we run the same samples in a pulsed field gel with 1 ms (and under the conditions described in fig.3), so that the 50 base fragment travels the same distance as under constant field, then the 400 base fragment will also travel the same distance as before, but the 500 base fragment will be retarded by a factor of 1.17, i.e. it will only travel 136 mm, resulting in a separation between these two bands of 59 mm. If we assume a limit of readability of 25 bands/cm for a sequencing gel (15), the separation achieved at constant field will not be good enough for reading a sequence, but this should be possible with the pulsed field gel. The technique of periodically inverting the electric field leads to longer run times than under constant field conditions and therefore to more diffuse bands, especially in the low molecular weight range. The bandwidths of fragments smaller than 100-150 bases (10% gel), 200-250 bases (8% gel) and 300-350 bases (6% gel) were generally found to be larger compared to those obtained under constant electric field. Above these limits, we could not find any significant differences. It will have to be tested, to what amount this bandspreading can be compensated by a 'wedge gel' or an ionic strength gradient in the lower part of the gel. We have shown, that the use of two different electric fields in field inversion is an effective means to retard the velocity of molecules above a size of about 400 bases. The parameters used in our experiments (i.e. RE=2, E=40 V/cm pulse time 1-10 ms) are a good compromise between the degree of retardation achieved, the duration of the run and the temperature control requirements. Under these conditions, an active cooling, is not absolutely necessary, but is still advantageous. This technique can be established with few modifications to any standard equipment. It should therefore be useful to enhance the amount of data which could be read from a sequencing gel.

ACKNOWLEDGEMENTS We thank John Curtis for his help with the construction of the

voltage divider and Jean Louis Viovy for helpful discussions. REFERENCES 1. Carle,G.F., Frank,M. and Olson,M.V. (1986) Science 232, 65-68. 2. Bostock,C.J. (1988) Nucleic Acids Res. 16, 4239-4252. 3. Birren,B.W., Lai,E., Hood,L. and Simon,M.I. (1989) Analytical Biochemistry 177, 282-286. 4. Heller,C. (1990) 'Untersuchungen zur DNA-Bewegung im Agarose-Gel' Ph.D. Thesis, University of Constance, Hartung-Gorre Verlag, Konstanz. 5. Heller,C. and Pohl, F.M. (1989) Nucl. Acids Res. 17, 5989-6003. 6. Turmel,C., Brassard,E., Slater,G.W. and Noolandi,J. (1990) Nucleic Acids Res. 18, 569-575. 7. Heller,C. and Pohl,F.M. (1990) Nucleic Acids Res. 18, 6299-6304. 8. Heller,C. and Pohl,F.M. (1989) in Radola,B.J. (Ed.) Electophoresis Forum '89, Munchen, 194-198. 9. Smith,S., Heller,C. and Bustamante,C. (1991) Biochemistry 30, 5264-5274. 10. Zimm,B.H. (1991) J. Chem. Phys. 94, 2187-2206. 11. Duke,T.A.J. and Viovy,J.L. (1992) J. Chem. Phys., in press. 12. Ansorge,W. and Barker,R. (1984) J. Biochem. Biophys. Methods 9, 33-47 13. Birren,B.W., Simon,M.I. and Lai,E. (1990) Nucleic Acids Res. 18, 1481-1487. 14. Lai,E., Davi,N.A. and Hood,L. (1989) Electrophoresis, 10, 65-67.

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Field inversion gel electrophoresis in denaturing polyacrylamide gels.

The velocities of single stranded DNA molecules in denaturing polyacrylamide gels during symmetric and asymmetric field inversion were measured at dif...
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