J. Phys. Chem. 1995, 99, 4247-4251
4247
Internal Structure of the Agarose Gel Matrix? John Stellwagen and Nancy C. Stellwagen" Department of Biochemistry, University of Iowa, Iowa City, Iowa 52242 Received: October 11, 1994; In Final Form: January 5, 1995@
The intemal structure of agarose gels has been monitored by measuring their intrinsic birefringence. The sign and amplitude of the intrinsic birefringence vary from one gel to another and at different locations within each gel, suggesting that the intemal structure of the agarose matrix is macroscopically variable. The sign and amplitude of the electric birefringence, measured separately, also vary from one gel to another and at different locations within each gel. The average absolute amplitudes of the intrinsic birefringence and the electric birefringence increase linearly with agarose concentration, as expected. However, there is no correlation between the signs and amplitudes of the intrinsic and electric birefringence, suggesting that the electric field orients subdomains within the larger, intrinsically birefringent regions of the gel matrix.
Introduction Agarose is an alternating copolymer of 1,3-linked B-Dgalactose and 1P-linked 3,6-anhydro-a-~-galactose,' substituted at irregular intervals with sulfate esters, methyl ethers, andor pyruvate residues.2 The linear agarose molecules aggregate in dilute ~ o l u t i o n and ~ . ~ in the sol p h a ~ e , ~forming -~ large fiber bundles and microgel domains held together by noncovalent hydrogen bonds. Upon gelation, the fiber bundles and microgel domains aggregate into still larger structural units.',5,6,8-10 Electron micrographs indicate that the structure of agarose gels is very heterogeneous, containing large interstitial spaces bounded by fibrous areas of varying den~ity.I'-'~With increasing gel concentration, the microvoids remain relatively constant in size, while the fibrous regions between them become more densely packed. When long, low-voltage pulses, of the amplitude and duration used for pulsed field gel electrophoresis, are applied to agarose gels, the gels become strongly birefringent,l4-l7 indicating extensive orientation of agarose fiber bundles and/or microgel domains in the electric field.16*17 The fiber bundles and microgel domains range up to tens of micrometers in size, depending on pulse length and electric field strength.I6 One of the most unusual features of the electric birefringence of agarose gels in low-voltage electric fields is the fact that the sign and amplitude of the birefringence vary randomly from one gel to a n ~ t h e r , ' and ~ . ~ from ~ one location in the gel to another,I6suggesting that the direction of orientation of the fiber bundles in the electric field also varies randomly. This type of behavior is not observed for dilute aqueous solutions of agarose, which exhibit positive birefringence, indicating that the agarose molecules are orienting parallel to the electric field.394 The anomalous orientation behavior observed for agarose gels appears to be due to constraints imposed by the gel matrix, which prevent the fiber bundles from rotating freely in the electric field.I6 Hence, the direction of orientation is determined not by the intrinsic electric polarizability of the agarose fibers, as observed in dilute aqueous solutions, but by the random location of fiber bundles held in the matrix by weak junction zones.I6 Under pulsing conditions that cause extensivejunction zone breakdown, allowing the fiber bundles to orient freely in
' This is the third paper in a series entitled Electric Birefringence of
Agarose Gels. The previous papers appeared in Biopolymers 1994, 34, 187, 1259.
@Abstractpublished in Advance ACS Abstracts, March 1, 1995.
the electric field, positive birefringence is always observed,I7 indicating that the agarose fiber bundles would orient parallel to the electric field if they were freed from the constraints of the surrounding gel matrix. In addition to electric birefringence, agarose gels also exhibit intrinsic birefringence; that is, they rotate the plane of polarized light in the absence of an electric field because of the nonrandom arrangement of gel fibers in locally structured regions of the gel. In this report, the intrinsic birefringence is used to characterize the heterogeneous internal structure of the agarose gel matrix. The intrinsic birefringence was measured at several different locations within individual gels of various concentrations and at a single location in a large number of independently prepared gels. The results are compared with the electric birefringence of the same gels, measured at the same gel locations. The intrinsic birefringence suggests that structural heterogeneities occur over macroscopic distances in the gel. The implications of these results are discussed.
Experimental Section Agarose Gels. Seakem LE agarose (electroendosmosis = 0.10-0.15), purchased from FMC BioProducts, was used for all experiments described here. Several samples with different lot numbers were studied, with no difference in the observed results. All gels were prepared by dissolving the desired quantity of gel powder (usually 10-20 mg) in 1 mL of distilled deionized water (Nanopure 11, Bamstad) by boiling 2-3 min in a microwave oven. After replacing the water lost by evaporation, the agarose sols were mixed, cooled to -50 "C, and placed in the birefringence cell. After inserting the electrode assembly and placing the cell in the thermostated cell compartment, the gels were allowed to equilibrate at least 30-60 min before the measurements were begun. Gelation usually occurred within 5-10 min, accompanied by a noticeable increase in turbidity. Apparatus and Methods. The apparatus and methods used for the electric birefringence studies have been described previously.'6-18 The equation describing the optical system of the apparatus is
-N_ -- _AV - sin2(a + 6/21 - sin2 a Io
"0
sin2 a
+ K~~
(1)
where AI is the change in light intensity induced by the electric
0022-365419512099-4247$09.0010 0 1995 American Chemical Society
Stellwagen and Stellwagen
4248 J. Phys. Chem., Vol. 99, No. 12, 1995
field, l o is the light intensity observed with the analyzer rotated a degrees from the crossed position, AV and VO are the corresponding output voltages from the detector, 6 is the phase retardation of the sample, and KSLis the stray light constant with the sample in the light path. The retardation is related to the birefringence, An, the difference in refractive index parallel and perpendicular to the electric field, as
where 1 is the wavelength of the incident light and 1 is the path length. In limiting low-voltage electric fields, the amplitude of the birefringence increases as the square of electric field strength, E, according to the Kerr law: An = KspnCvE2
(3)
where Ksp is the specific Kerr constant, characteristic of each macromolecular species orienting in the electric field, n is the mean refractive index of the sample, and C , is the volume fraction of the sample, usually approximated as Vc, where C is the partial specific volume and c is the concentration. A more extensive discussion of the theory of electric birefringence is given e1se~here.I~ The orienting pulses, ranging from 0.5 to 20 V/cm in amplitude and 10 ms to 100 s in duration, were generated by a dual pulser and stimulator controller designed by Mr. Craig Fastenow of the University of Iowa Bioengineering Department (manuscript in preparation). Successive pulses were separated by at least 10-20 min, to allow the birefringence to decay to 0 between pulses. Results at different gel locations were obtained by moving the cell compartment in the laser beam. All results were obtained with single pulses, without signal averaging. Typical oscilloscope traces have been selected to illustrate the results. The decay of the birefringence was measured by recording traces at several different oscilloscope sweep speeds, to visualize various portions of the decay in detail. The decay curves were analyzed as a sum of exponentials using a nonlinear least-squares fitting program CURVEFIT,20 based on the Marquardt algorithm. The relaxation times obtained at different sweep speeds were averaged together to obtain composite values representative of the entire decay curve. Duplicate measurements of the relaxation times of the same gel usually agreed within 4 3 6%. The relaxation times obtained for different, independently prepared gels of the same composition usually agreed within rt10-30%.16 The relaxation times can be related to particle dimensions using the Broersma equation,21if some assumptions can be made about particle shape andor the particle radius is known.I6 The intrinsic birefringence is defined here as the apparent birefringence observed in the absence of an electric field. It is equal to half the angle through which the analyzer is rotated to minimize the light intensity when a gel is placed in the light beam. The intrinsic birefringence is not due to optical rotation, which cannot be detected by the optical arrangement used in the birefringence apparatus and, in any event, would be too small to measure for the gels described here. The intrinsic birefringence may be thought of as a strain birefringence that varies throughout the gel matrix, due to the nonrandom orientation of the gel fibers.
Results and Discussion Electric Birefringence. Agarose gels oriented by long, lowvoltage pulses exhibit complex electric birefringence signals
Figure 1. Typical oscilloscope traces of the birefringence signals observed for a 1% agarose gel under different pulsing conditions: (a) E = 10 Vlcm, pulse length, tp = 10 s; (b) E = 25 V/cm, tp = 2 s. In all oscilloscope traces, the horizontal line bounded by dashed vertical lines corresponds to the applied pulse; the noisier trace with the slower rise and decay times corresponds to the birefringence signal. The vertical scales are identical; the horizontal scale is indicated by the length of the orienting pulse. The direction of positive birefringence is up.
Figure 2. Variation of the electric birefringence observed at different locations within a single 1.0% agarose gel. E = 7.5 V/cm; t, = 5 s.
with both positively and negatively birefringent components, as shown in Figure 1. The sign of the birefringence is determined by the component with the longer relaxation time when two components are present (Figure la) or the intermediate relaxation time when three components are present (Figure lb). This component, called 72, which usually contributes 60-80% of the observed birefringence signal, most likely corresponds to the orientation of extended agarose fiber bundles.I6 The negatively birefringent component with the longer relaxation time, z3, observed upon increasing the pulse amplitude (Figure lb) or pulse length (not shown), is probably due to the orientation of clusters of fiber bundles or microgel domainsI6 that orient in the opposite direction. The reason for the change in the direction of orientation of macromolecular aggregates is not well understood, but similar results are observed in other systems.22 Even though the birefringence relaxation times are relatively constant from one gel to another, and virtually independent of gel concentration,I6 the sign and amplitude of the birefringence vary markedly from one gel to another, even when the gels are prepared under ostensibly identical condition^.'^,'^ Hence, the direction of orientation of the fiber bundles andor microgel domains and the extent of their orientation vary from one gel to another even though the sizes of the orienting particles are approximately constant. The sign and amplitude of the birefringence also vary at different locations within each gel, as shown in Figure 2, suggesting that the variable sign of the birefringence mirrors the internal heterogeneity of the agarose gel matrix. Despite the anomalous variation in the sign of the birefringence, in limiting low-electric fields the amplitude of the birefringence increases as the square of electric field strength, as shown in Figure 3, as expected from the Ken law, eq 1, for normal birefringent systems.
J. Phys. Chem., Vol. 99, No. 12, 1995 4249
Internal Structure of the Agarose Gel Matrix
loo
i
An x I O e
I
I
100
50
0
'
E', V'cm''
Figure 3. Dependence of the amplitude of the birefringence, An, on the square of electric field strength, E. Agarose concentration = 0.6%; tp = 5 s.
TABLE 1: Comparison of Birefringence within a Single 1.0% Agarose Gel" location
aint,deg
6,1, deg
T I ,s
ZZ,s
1 2 3 4 5 6
+1.3 -0.3 +0.8 -0.2 -0.5 +1.4
-0.7 -0.9 -0.3 +0.5 +2.1 -1.3
3.7 9.9
17 28
7.1
25 20 25
%A
t3,s
Figure 4. Dependence of the average absolute value of (A) the electric birefringence, (Id~l),and (B) the intrinsic birefringence, (Idl& on
38 34 46
) measured at agarose gel concentration, %A. The values of ( l d ~ lwere E = 7.5 V/cm, within the Kerr law region: (0)measured at different locations within a single gel; (0)measured at a single gel location in 6-49 gels of identical composition. The straight lines were calculated by linear regression; the correlation coefficients are 0.97 for (A) and 0.96 for (B).
E = 7.5 V/cm.
The amplitude of the birefringence of a single 1.O% agarose gel, measured at the end of the pulse at different locations within the gel, is tabulated as the electric field retardation, delec,in column 3 of Table 1. The relaxation times measured at the same gel locations are given in columns 4-6. In each case, the sign of the component that decays with a relaxation time of t2 is the same as that of delec,while the components corresponding to TI and z3 have the opposite sign. Hence, the birefringence decay curves can be deconvoluted into their individual components, even though the absolute values of the relaxation times are similar. The various relaxation times are approximately constant throughout the gel, indicating that the sizes of the orienting fiber bundles and microgel domains are independent of gel location. Similar results are observed for gels of other concentrations. Therefore, differences in the sign and amplitude of the electric birefringence observed at different gel locations do not represent differences in the size of the orienting particles but differences in the direction of orientation in the electric field and the extent of orientation. The average absolute amplitude of the electric birefringence, measured at several locations in each gel (typically four to six), increases linearly with agarose concentration, as shown by the solid circles in Figure 4A. Similar results are obtained by averaging the absolute amplitudes of the electric birefringence of a large number of independently prepared gels (6-49 gels of each concentration), probed at a single gel location, as shown by the open circles in Figure 4A. The results indicate that the average amplitude of the electric birefringence of agarose gels increases linearly with gel concentration, as expected from eq 3. The virtually identical results obtained by the two methods of measuring the average absolute amplitude of the birefringence indicates that the random variation of the sign and amplitude of the electric birefringence observed for different independently prepared agarose gels mirrors the internal variation of the structure within each gel.
The Kerr constant calculated from the slope of the line in Figure 4 is 0.034 cgs esu (3.7 x lo-" m2 V-*). This value is somewhat smaller than the Kerr constants reported in ref 16, because of the variation of the individual values of delecwith gel location, as shown in Table 1. Intrinsic Birefringence. The intrinsic (strain) birefringence measured for agarose gels also varies randomly from one gel to another and at different locations within each gel. Typical values of the intrinsic birefringence of a 1% agarose gel, measured at the same gel locations as the electric birefringence, are given as dintin column 2 of Table 1. It is apparent that there is no correlation between the sign and amplitude of the intrinsic birefringence and the electric birefringence, indicating that the two parameters are sensitive to different aspects of gel structure. If the absolute value of the intrinsic birefringence is averaged at several (four to six) different locations within each gel, the average absolute value increases linearly with gel concentration, as shown by the solid circles in Figure 4B. The average absolute value of the intrinsic birefringence, measured at a single gel location in many (6-49) different gels of different compositions, also increases linearly with gel concentration, as shown by the open circles in Figure 4B. The correspondence of the two types of measurements indicates that the variation of the intrinsic birefringence from one gel to another is due to variations in the internal structure of the agarose gel matrix. The linear increase in the intrinsic birefringence with agarose concentration also indicates that the average absolute value of the intrinsic birefringence is proportional to the number of agarose chains in the gel matrix, as expected. The intrinsic birefringence of a 1.0% agarose gel was also measured systematically along a line through the central half of the gel, with the results given in Table 2. The sign and amplitude of the intrinsic birefringence vary almost sinusoidally throughout the gel, as shown schematically in Figure 5A. In each of the positively birefringent regions, the agarose fibers and/or fiber bundles must be oriented on average in the direction
Stellwagen and Stellwagen
4250 J. Phys. Chem., Vol. 99, No. 12, 1995
A
-
o
+
d
I
Figure 5. (A) Variation of the intrinsic birefringence of a 1.O% agarose gel as a function of gel height. (B) Schematic model of a portion of an agarose gel, showing how the variation of the orientation of agarose fiber bundles could lead to intrinsically birefringent domains of opposite sign, separated by regions with very little or no birefringence.
TABLE 2: Systematic Variation of Intrinsic Birefringence with Gel Height vertical height, mm d,,,, deg vertical height, mm &, deg 0 0.5 1.o 1.5 2.0 2.5
-0.48 -0.22 -0.05 +0.10 +0.20 +0.12
3.0 3.5 4.0 4.5 5.0
0 -0.38 - 1.05 -1.18 - 1.52
perpendicular to that of the fiber bundles located in the negatively birefringent regions. The positively and negatively birefringent regions are separated by regions in which the birefringence is very small or 0, indicating either that the fibers are randomly oriented or that they are oriented on average at 45" with respect to the light beam, an orientation which would not give rise to an observable birefringence signal. A model of such a possible arrangement of the agarose fiber bundles is given in Figure 5B. The results suggest that the intemal structure of the agarose gel matrix may be similar to that of polymer liquid crystals, in which splay structures with quasiperiodic domains are separated by disinclination^.^^ The inhomogeneities in the intrinsic birefringence occur on a length scale of millimeters, much larger than the micrometer size of the fiber bundles and/or microgel domains that are oriented by low-voltage, pulsed electric fields.I6 Since there is no correlation between the sign and amplitude of the intrinsic and electric birefringence (Table l), it seems likely that the electric field transiently disrupts the larger intrinsically birefringent domains in the gel matrix, allowing smaller subunits to orient in the electric field. If low-voltage, unidirectional pulses are applied to the agarose gels, small but systematic changes in the intrinsic birefringence are usually observed, which remain for many hours after the electric birefringence has decayed to 0. However, the changes in the intrinsic birefringence are small in comparison with amplitude of the electric birefringence, suggesting that the agarose gel fibers return approximately to their original positions in the gel matrix after low-voltage pulses. Increasing the electric field strength or the duration of the applied pulses substantially, changing the polarity of the electric field, or applying asymmetric reversing field pulses usually caused large, apparently irreversible changes in the intrinsic birefringence to occur, consistent with extensive gel fiber rearrangements. Hence, these pulsing regimes appear to significantly disrupt the original
structure of the agarose gel matrix.I7 The spatial variation of these apparent structural changes, the threshold electric field strengths and pulse durations needed, and the time course for the relaxation of the altered gel structure to a more stable, apparently equilibrium structure24 remain to be determined quantitatively. Intrinsic Birefringence of Other Polymer Gels. The intrinsic birefringence of two other polysaccharide gels, HEEO agarose (a highly charged form of agarose) and P-carrageenan (a stereoisomer of agarose), also varies in sign and amplitude from one gel to another and within each individual gel, suggesting that a hierarchical domain structure may be common to all polysaccharide gels. Chemically cross-linked polyacrylamide gels apparently have a more uniform intemal gel structureI7and exhibit no intrinsic birefringence. Hence, intemal structural heterogeneities of the type described here for agarose gels are not found in all polymer gels.
Conclusions Several conclusions may be drawn from the results presented here. (1) Agarose gels contain macroscopic, intrinsically birefringent domains which vary approximately sinusoidally in sign and amplitude. In the birefringent domains of opposite sign the gel fibers must be oriented, on average, in perpendicular directions. ( 2 ) The intrinsically birefringent domains are separated by regions exhibiting little or no intrinsic birefringence, suggesting that the agarose fiber bundles in these regions are either randomly oriented or are oriented in an intermediate direction. (3) The agarose fiber bundles and microgel domains oriented by pulsed electric fields are much smaller than the intrinsically birefringent domains, suggesting that the agarose gel matrix is composed of a hierarchy of loosely connected substructures, held together by metastable hydrogen bonds. The transient orientation of the agarose fiber bundles and microgel domains in the electric field appears to overcome the intrinsic orientation of the agarose fibers in the gel matrix, because the sign and amplitude of the electric birefringence are independent of the sign and amplitude of the intrinsic birefringence. The original gel structure apparently re-forms when low-voltage, unidirectional pulses are applied to the gels, because the intrinsic birefringence retums approximately to its original value after the electric birefringence has decayed to 0. Other types of pulsing regimes significantly disrupt the original gel structure, causing large, apparently irreversible changes in the intrinsic birefringence. (4)The random sign of the intrinsic and electric birefringence observed for different independently prepared agarose gels mirrors the variable intemal structure of the gel matrix. (5) Other polysaccharide gels are also intrinsically birefringent and may contain a similar hierarchical array of intemal substructures. Chemically cross-linked polyacrylamide gels have a more uniform gel structure and exhibit no intrinsic birefringence.
Acknowledgment. Partial financial support from Grant GM29690 from the National Institute of General Medical Sciences is gratefully acknowledged. References and Notes (1) Rees, D. A,; Moms, E. R.; Thom, D.; Madden, J. K. In The Polvsaccharides: Aminall. G. 0.. Ed.: Academic Press: New York. 1982, Voi. 1, pp 196-290: (2) Duckworth, M.; Yaphe, W. Carbohydr. Res. 1971, 16, 189-197. (3) Stellwagen, N. C.; Stellwagen, D. J.-Biomol. S t r u t . Dyn. 1990, 8, 583-600. (4) Dormoy, Y.; Candau, S . Biopolymers 1991, 31, 859-868. (5) Leone, M.; Sciortino, F.; Migliore, M.; Fomili, S . L.; Vittorelli, M. B. Biopolymers 1987, 26, 743-761.
Intemal Structure of the Agarose Gel Matrix (6) Emanuele, A.; DiStefano, L.; Giacomazza, D.; Trapanese, M.; Palma-Vittorelli, M. B.; Palma, M. U. Biopolymers 1991, 31, 859-868. (7) Bulone, D.; San Biagio, P. 0. Chem. Phys. Lett. 1991, 179, 339343. (8) Amott, S.; Fulmer, A,; Scott, W. E.; Dea, I. C. M.; Moorhouse, R.; Rees, D. A. J . Mol. Biol. 1974, 90, 269-284. (9) Pines, E.; Prins, W. Macromolecules 1973, 6, 888-895. (10) Feke, G . T.; Prins, W. Macromolecules 1974, 7 , 527-530. (11) Amsterdam, A,; Er-El, A.; Shaltiel, S . Arch. Biochem. Biophys. 1975, 171, 673-677. (12) Attwood, T. K.; Nelmes, B. J.; Sellen, D. B. Biopolymers 1988, 27, 201-250. (13) Griess, G. A,; Guiseley, K. B.; Senver, P. Biophys. J . 1993, 65, 138-148.
(14) Stellwagen, J.; Stellwagen, N. C. Nucleic Acids Res. 1989, 17, 1537-1548. (15) Sturm, J.; Weill, G. Phys. Rev. Lett. 1989, 62, 1484-1487. (16) Stellwagen, J.; Stellwagen, N. C. Biopolymers 1994,34, 187-201.
. I Phys. . Chem., Vol. 99, No. 12, 1995 4251 (17) Stellwagen, J.; Stellwagen, N. C. Biopolymers 1994, 34, 12591273. (18) Stellwagen, N. C. Biopolymers 1991, 31, 1651-1667. (19) Frederica. E.: Houssier. C. Electric Dichroism and Electric Birefri'ngence; Ciarendon Press: Oxford, 1973. (20) Swenson, C. A.; Stellwagen, N. C. Biopolymers 1988, 27, 11271141. (21) Broersma, S . J . Chem. Phys. 1981, 74, 6989-6990. (22) See, for example: Ookubo, N; Hirai, Y.; Ito, K.; Hayakawa, R. Macromolecules 1989, 22, 1359- 1366. Kramer, U.; Hoffmann, H. Macromolecules 1991, 24, 256-263. (23) Meyer, R. B. In Polymer Liquid Crystals; Cifeni, A., Krigbaum, W. R., Meyer, R. B., Eds.; Academic Press: New York, 1982; pp 133163. (24) Stellwagen, N. C.; Stellwagen, J. Electrophoresis 1993, 14, 355-368. JP94274OY
