Electrophoretic Charge Density and Persistence length of DNA as Measured by Fluorescence Microscopy STEVEN B. SMITH’* and ARNOLD J. BENDICH’

Depirtments o f ’Genetics and *Botanyand Genetics, University of Washington, Seattle, Washington 981 95

SYNOPSIS

Individual ethidium-stained D N A molecules, embedded in a n agarose gel made with electrophoresis buffer (0.05 molar s a l t ) , are observed using a fluorescence microscope. I n t h e first experiment, open circular 66 kilobase pair ( k b p ) plasmids, immobilized by agarose fibers threaded through their centers, display entropic “rubber” elasticity. T h e charged molecules extend in a n electric field of several volts per centimeter and contract t o a compact random coil when t h e field is removed. T h e extension of t h e plasmids as a function of field strength is consistent with t h e freely jointed chain model when t h e effective electrophoretic charge density is set a t 15 e - per persistence length. In a second experiment, stained linear 48.5 kbp DNA molecules are observed a s random coils immobilized in agarose. A measure of their size, here named the “maximal-X-extent,” is taken for 100 molecules a n d found to average 1.47 F . A Monte Carlo computer simulation of random coils (freely jointed chain model) gives t h e same maximal-Xi-extent value when t h e persistence length is set at 0.08 ji.

I NTRODUCT10 N Many models of DNA electrophoresis use a n effective linear charge density p such that the net force per unit length on the molecule is p times the macroscopic electric field. Determination of p has been carried out using the electrophoretic mobility of free DNA in solution’ and making assumptions about the hydrodynamic drag on the molecule.2 Here we present an alternate method that employs a simpler theory and requires fewer assumptions. Individual double-stranded DNA molecules, stained with ethidium bromide, may be observed with a Buorescence microscope while undergoing gel electroph~resis.~Linear molecules often wrap around obstacles with both ends extending down-

(:

1990 J o h n Wiley & Sons, Inc.

CCC 000fi-3325/90/8/91167-0‘i $04.00 Biopol3--mers,Vol. 29, 1167-1173 (1990) * Present address: Dept. of Chemistry, University of New Mexico, Albuquerque, N M 87131. Plasrriid pSR.1409 is a transposon insertion derivative of t h e cosmid pVK257 (29.1 t 23 kbp ) 5 containing TN3HoHol ( 14.25 k h p ) .‘’

field, but they soon slip off the obstruction toward the side with the longer arm. Large open circles of plasmid DNA, however, become permanently caught on obstructions as long as the field remains constant and strong.* In the microscope, these plasmids appear as lines, anchored a t one end, whose lengths increase with electric field strength (Figures 1 and 2 ) . When the field is removed, they shrink back within a few seconds to random coil shapes centered a t the obstruction end. The elastic-restoring force is assumed t o be the so-called rubber elasticity of a freely jointed chain whose links are randomized in direction by thermal forces. By observing the extension of the molecules as a function of electric field strength, the electric force per unit length and the effective charge density of the molecules can be determined.

METHOD FOR CHARGE DENSITY DETERMINATION Plasmids, 66 kilobase pairs (kbp) in length (pSM409 from Escherichia coli C2110t), were extracted by the alkaline lysis method.’ The plasmids were fur1167

1168

SMITH AND BENDICH

Figure 1 These 66 kbp plasmids are permanently trapped inside the 1.5%agarose because some of the gel matrix formed through the loop when the agarose cooled. T h e electric field of 10 V / c m causes the molecules t o extend toward the right. Brightening on the left end is due t o random-coil entanglements formed when the gel polymerized. Brightening on the right is due t o lack of tension at the free end. This photomicrograph is a 20 s time exposure for which 1%2-mercaptoethanol was added t o the gel to prevent molecular breakage. Bar equals 10 1.

ther purified by casting them in a block of low melting point agarose (Bethesda Research Laboratory) and exposing the block to electrophoresis a t 6 V / cm for 5 h in l / 2 X T B E electrophoresis buffer (0.045 molar Tris base, 0.045 molar boric acid, 0.001 molar E D T A ) . All linear fragments left the block and only open circles remained trapped. A small piece (0.1 m L ) of the block containing 0.1 pg of plasmid was remelted in 1mL of molten (60°C) 1% SeaKem LE agarose made with 1 / 2 X TBE buffer and 0.5 pg/mL ethidium bromide. Gels 10-20 p thick were cast between a microscope slide and cover slip. An electric current was established between opposite edges of the 22 mm coverslip using platinum wire electrodes. The field inside the gel was measured using a high impedance voltmeter ( > 10 megohms) and platinum probe electrodes, 1 cm apart, which had been painted and fired onto the glass slide. The molecules were illuminated in green light and observed in red with a Nikon Microphot epifluores-

cence microscope using a 60X ( N A 1.4) oil immersion objective, a n image intensifier, and a vidicon television camera.3 Each molecule was brought into focus and its length measured from a monitor screen that had been calibrated using a n objective micrometer. The molecules in Figure 1are poor subjects for analysis because of their crooked paths through the agarose pores. They always appear shorter than unimpaired molecules for a given field strength. Figure 2 shows plasmids on the surface of the agarose in a liquid layer just under the coverslip. Such molecules were usually caught a t just one end and free floating elsewhere. When the electric field was removed, they would retract and then come off their obstruction and tumble through the liquid in Brownian motion. When measuring the extension of molecules in a n electric field, as plotted in Figure 3, we selected the straightest and longest molecules, some of which were in the liquid layer above the gel and some of which were in large pores or crevices inside the gel.

ELECTROPHORETIC CHARGE DENSITY

1169

Figure 2 These plasmids had been free floating inside a thin liquid layer t h a t formed between the coverslip a n d t h e agarose. Each became hooked on a particular obstruction a n d remained there as long as t h e strong electric field was maintained. Thirty second time exposure. B a r equals 10 p .

Molecules inside solid gel, such as those in Figure 1. were not selected for measurement because our theory is not directly applicable to molecules winding through many pores in a gel.

30C

l

0

L

;a-

-

MODEL OF MOLECULAR EXTENSION IN AN ELECTRIC FIELD

4

-

1

1

2

I

I

I

4

6

8

I

10

I

I

12

14

Electric Field (vo1ts:crn) Figure 3 Extension vs electric field strength for selected (straightest) 66 kbp plasmids. Each dot is a different molecule. T h e experimentally measured extension does not fall to zero a t zero field since we then observed t h e random coil diameter (plus vidicon blooming). T h e curves plotted over t h e data are from Eq. ( 1) with L = 1 2 g. Three values for pb are plotted. T h e molecules were visually selected for straightness a n d many appeared t o be lying o n t h e surface of the gel.

When a plasmid is extended in the field it is assumed each half of the doubled-over loop is mechanically independent of the other half. Both halves are, in effect, attached to the gel at the anchored end, and they have the same mean extension and direction in the field, Therefore the mean extension of the loop is the same as that of a linear molecule, anchored at one end, with half of the loop's DNA. It is often possible, in zero field, to see the plasmids open up in loops. This observation suggests that the plasmids are open circles or only slightly twisted. The pertinent theory for linear molecules is presented in the preceding companion paper.8 The

1170

SMITH AND BENDICH

equivalent linear DNA molecule is regarded as a chain of Nfreely jointed bond vectors, or Kuhn links, each with length b. The Kuhn length b is twice the persistence length P , which is related to the bending rigidity K by P = K/ksT where k B T is thermal energ^.^ The DNA chain is assumed to be anchored to the gel a t the tail of the i = 1 link by a universal pivot and is subject to a uniform macroscopic electric field E . Each link bears an effective charge Q such that the force on that link exerted by the electric field is EQ. For a long DNA molecule containing many Kuhn links ( N % 1), the mean extension of the chain in the direction of the electric field ( R , ) is given by

R,

=

( l / a ) l n { (sinh NL)/NL}

(1)

where L = Nb is the contour length, N = Q E / k B T = Epb/k,T, and p is the effective charge per unit length. If aL > 2.5 then the mean extension can be approximated with less than 1% error by

It should be emphasized that Q ( o r p ) is not the actual charge because i t incorporates all effects due to differences between local and macroscopic electric fields, as well as the hydrodynamic forces exerted by small ions streaming by the polyion. However, EQ is the actual force exerted on the subunit (Kuhn link) by all processes associated with the electric field, except for the extension of the DNA.

RESULTS FOR EFFECTIVE CHARGE DENSITY Figure 3 shows the lengths of 66 kbp plasmids plotted vs field strength. The variety of lengths found a t a single field strength is presumably due to crooked paths inside pores of the gel. Therefore the high end of the distribution should represent the unobstructed molecules hooked a t one end. A few points are conspicuously high. These molecules were probably hooked at both ends while in a high electric field and then failed to contract when the field was lowered. Also plotted in Figure 3 are curves for the theoretical extension of the loops, from Eq. ( 1) . A value of 12 p was used for the contour length of the equivalent linear molecule. This value was chosen because three plasmids were found with triangular outlines, which had been mechanically stretched taut during the placement of the coverslip. These molecules had perimeters of 24 p and were stretched

tightly enough that they showed no visible deflection in an electric field of 20 V/cm. This puts the hasepair spacing (with intercalated ethidium) a t 3.6 A. The best fit to the top edge of the distribution occurs when the product p b equals the charge of 30 & 10 electrons, i.e., 15 -t 5 electrons per persistence length.

PERSISTENCE LENGTH DETERMINATION When agarose polymerizes around a large DNA molecule, the molecule becomes relatively immobile and locked into a particular shape. Figure 4 is a photomicrograph showing linear A-phage DNA monomers (48.5 kbp) immobilized in agarose. To measure an ensemble of molecules, we focused on each molecule individually using the image intensifier and television system. The bright image blooming problem, as described previously," was avoided by using a lO0X (NA 1.2) oil immersion objective, which produced very large dim images. It was not possible to resolve the internal details of the random coils, so neither the end-to-end distances nor radii of gyration could be determined directly. The outlines of the coils were, however, resolvable. Taking measurements from the television monitor, it seemed possible to measure the width of the coils to within 0.3 p. The quantity measured was named the maximal-X-extent of the random coils. It is the horizontal displacement from the farthest left piece of a coil to the farthest right piece of that coil for all focal depths, i.e., while focusing up and down through the coil. Measurement of 100 stained Xphage DNA monomers put the mean maxima1-Xextent a t 1.47 p with an rms deviation of 0.49 p. We have made a computer simulation of these linear molecules using a freely jointed chain model. Ensembles, each of 100 coils, were created where each ensemble had a different Kuhn length but the contour length was held constant at 17.5 p (48.5 kbp times 3.6 A/bp for ethidium-stained D N A ) . Each coil was checked for volume exclusion of the molecule. If a coil intersected itself within a molecular, radius (including Debye layer) of 30 A, then that coil was discarded and another coil started until 100 nonintersecting coils were found. Both the mean maximal-X-extent and the rms deviation of' maximal-Xi-extent were recorded for each ensemble. It might seem that the mean maximal-X-extent would be proportional to the link length times the square root of the number of links, as is the mean end-toend distance and radius of gyration (all ignoring volume exclusion effects). Such a relation is nearly ( b u t not quite) the case. Figure 5 shows a plot of

E I J X T R O P H O R E T I C CHARGE DENSITY

Figure 4 T h e A-phage DNA monomers (recently heated t o 60'C) embedded in 1.5% agarose made with 1 / 2 X T B E buffer, 1% 2-mercaptoethanol, a n d 0.5 Fg/mL ethidium bromide. Many of the coils are slightly above or below the focal plane and appear indistinct. Thirty second time exposure. Bar equals 10 F.

I 0.1

0.2

0.3

04

05

Step Length (microns) Figure 5 T h e mean maximal-X-extents of computer-simulated random coil ensembles, each containing 100 random coils, are plotted (small dots) vs the Kuhn length. All simulated molecules have a constant contour length of 17.5 F . T h e rms deviation of maximal-Xextent is plotted above a n d below the mean ( b a r lengths 2 SD ) . T h e heavy square and bar represent t h e mean and rms deviation of maximal-X-extension for 100 actual plasmids.

1171

1172

SMITH AND BENDICH

the simulated mean maximal-X-extent and rms deviation vs Kuhn length for a contour length of 17.5 p. Placed on the graph is the measured microscope value. It is encouraging that the experimental mean and deviation both fit the model a t the same Kuhn length. In these experiments, the Kuhn length for ethidium-stained DNA appears to be 0.165 & 0.015 p , making the persistence length 825 t- 75 A.

DISCUSSION If one accepts the most common value of the persistence length, namely 500 Atlo then the effective charge would be 0.1 electrons per base pair. If one uses our value of 825 A, then the effective charge would be only 0.06 electrons per base pair. When multiplied by the macroscopic electric field E , this charge yields the net force responsible for “spring” extension. By analyzing the electrophoretic mobility of free DNA in solution using a complex transport theory for uniformly charged cylinders, a value of 0.4-0.8 electrons per base pair is obtained for the actual excess charge inside the surface of shear.’,’ This bare charge governs the equilibrium surface potential. However, if it were simply multiplied by E , it would overestimate the net force responsible for spring extension because the effects of hydrodynamic interaction with the counterions and ionatmosphere polarization would be neglected. Thus it is expected to exceed the value obtained in the present experiment, as observed. The electrophoretic mobility of linear DNA is not greatly changed by staining with 0.5 pg/mL ethidium bromide. This result suggests that the effective charge is not changed much by ethidium staining either. If this is the case, then the effective charge for DNA, as determined here, whether stained or unstained, is much lower than the previous estimate of the actual excess inside the surface of shear. When observed on the television monitor, the trapped plasmids are slightly brighter a t their free ends than along their lengths. This brightening is barely evident in Figure 1 but hidden in Figure 2 because the latter was developed for maximum contrast (overexposed). The free ends are brighter because the molecules are under less tension there and the linear density of DNA is higher. If we arbitrarily define the “bright free end” as the region where the linear density of DNA is more than double its stretched-tight minimum value, then any link in the chain that is within the bright free end will have a mean extension in the electric field that is less than

b / 2 . For such a link, L ( N e d )< 0.5 where L is the Langevin function’ and N, is the number of Kuhn links downfield of that link to the free end. Assuming pb = 30e-, b = 0.1 p, and the base-pair spacing is 3.6 A, then the amount of DNA in a bright free end is equal to 4 2 k b p / E , where E is the electric field strength in V/cm. The size of the bright free end is independent of the overall length of the molecule provided the long molecule is anchored and a t rest. Whole linear chromosomal DNA molecules from yeast (250-1500 kbp) have been observed during gel electrophoresis with pronounced bright heads a t their leading ends.3 Such heads are a n order of magnitude larger than the bright free ends of extended stationary molecules. When a yeast DNA molecule is trapped for a relatively long time in a symetrical U shape, the very bright heads unravel into the less pronounced bright free ends. Some problems in our technique can now be solved by new experiments. In the measurement of extension vs field strength for trapped plasmids, many different plasmids were used because each molecule would break apart after about 30 s illumination. Yanagida and co-workers have discovered that the lifetime of a brightly illuminated stained DNA niolecule is dramatically extended by the addition of 1%2-mercaptoethanol to the buffer. Under these conditions, a single optimally placed molecule can be viewed for more than 5 min a t various field strengths. Molecules in the liquid layer between the agarose and coverglass ( a s in Figure 2 ) are subject to a convective fluid flow that is driven by the electric field. The direction of this flow aids the electric field in extending the molecules. Molecules inside the agarose are not affected by convection but have crooked paths through the pores. This dilemma may be avoided by selecting a plasmid that is under the surface but enclosed in a very large pore or liquid inclusion. A DNA molecule, anchored on the agarose wall of such a n inclusion and extended by the field into the liquid, would be a n ideal subject for study since it would not wind through gel pores and it would be shielded from convective flow. Yanagida has also used nonintercalating dyes, which apparently do not change DNA’s helicity or contour length.I2 With the aid of these improvements, the effect of different salt concentrations on the persistence length and charge could be explored.

‘‘J’

REFERENCES 1. Ross, P. D. & Scruggs, L. (1964) Biopolymers 2,231236.

ELECTROPHORETIC CHARGE DENSITY

2. Schellman, J. A. & Stigter, D. (1977) Biopolymers 16, 1415-1434. 3. Smith. S. B., Aldridge, P. A. & Callis, J. B. (1989) Science 243, 203-206. 4 . Levene, S. D. & Zimm, B. H. (1987) Proc. Natl. Acad. Sc,i. 84, 4054-4057. 5. Knauf, V. C. & Nester, E. W. (1982) Plasmid 8 , 4 5 54. ti. Srachel, S. E., An, G., Flores, C. & Nester, E. W. ( 1985) EMBO J . 4, 891-898. 7 . Maniatis, T., Fritsch, E. F. & Sambrook, J. (1982) Moi*.cular Cloning: A Laboratory Manual, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, p. 368. 8. Schurr, J. M. & Smith, S. B., preceding paper.

1173

9. Bloomfield, V. A., Crothers, D. M. & Tinoco, I., Jr. ( 1974) Physical Chemistry of D N A , Harper & Row,

New York. 10. Schurr, J. M. & Schmitz, K. S. (1986) Ann. Reu. Phys. Chem. 37, 271-305. 11. Yanagida, M., Hiraoka, Y. & Katsura, I. (1983) Cold Spring Harbor Symp. Quant. Biol. 47, 177-187. 12. Yanagida, M. et al. (1986) Applications of Fluorescence

i n the Biomedical Sciences, Alan R. Liss, New York, pp. 321-345.

Received April 10, 1989 Accepted J une 7, 1989