Protein Bandwidth in Gel Electrophoresis: A Primary Function of

By use of the fluorescent protein R-phycoerythrin, a number of factors have been investigated as potential sources of band broadening in agarose and ...
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J. Phys. Chem. B 1998, 102, 4813-4818

4813

Protein Bandwidth in Gel Electrophoresis: A Primary Function of Migration Distance§ Elena Yarmola†.‡ and Andreas Chrambach*,† Section on Macromolecular Analysis, Laboratory of Cellular and Molecular Biophysics, NICHD, National Institutes of Health, Bethesda, Maryland 20892-1580, and Laboratory of Biopolymer Physics, Engelhardt Institute of Molecular Biology, Russian Academy of Sciences, Moscow, Russia ReceiVed: December 10, 1997; In Final Form: April 1, 1998

By use of the fluorescent protein R-phycoerythrin, a number of factors have been investigated as potential sources of band broadening in agarose and polyacrylamide gels: temperature gradients, Joule heating, conductivity differences between analyte and buffer, electroendosmosis, microheterogeneity due to charge density differences, etc. It was found that none of these factors could be the major source of band broadening. Recently, it has been shown that diffusion is also not the predominant source of R-phycoerythrin band spreading in agarose gels and that the bandwidth depends linearly on migration distance and time (Yarmola, E.; Calabrese, P. P.; Chrambach, A.; Weiss, G. H. J. Phys. Chem. 1996, 101, 2381). The present data collected in agarose and polyacrylamide gels confirm the linear dependence of bandwidth on migration distance and describe the slope of this dependence as a function of electrophoretic conditions. Among all the factors studied that may impact on band spreading, only the interaction with the gel and microheterogeneity cannot be ruled out. This conclusion with regard to the mechanisms of band spreading agrees with that obtained recently by capillary electrophoresis in polymer solutions (Radko, S. P.; Weiss, G. H.; Chrambach, A. J. Chromatogr. A 1997, 781, 277-286).

I. Introduction Experimental data recently collected support present experts in the field (e.g., ref 1) in suggesting that diffusion is not the predominant source of band spreading of DNA fragments in agarose gels2-4 nor of phycoerythrin (PHYCO) in an un-crosslinked polyacrylamide solution in capillary zone electrophoresis (CE)5,6 or in an agarose gel.7 An alternative mechanism, interaction with the gel matrix (“interactive dispersion”), has been suggested recently and the new model has been shown to be in better accord with experiment than the conventional theory of gel electrophoresis based on diffusion.7 Other factors, however, such as Joule heating, temperature gradients, conductance discrepancies between analyte and buffer, electroendoosmosis, microheterogeneity due to charge density differences, and conformational microheterogeneity may also affect band spreading.1,8 Thus, all of those factors have to be checked as potential sources of band broadening. A recent study on the bandwidth of PHYCO under the conditions of CE6 was able to rule out diffusion, Joule heat, and the conductivity differences between the sample zone and the surrounding buffer as being determinants of band broadening under the conditions of CE used. Only adsorption to the capillary walls could not be ruled out as a determinant and was therefore hypothetically proposed as being responsible for the measured band spreading. The present study carried out on 3-mm thick gel slabs without significant “wall area” tests that hypothesis as well as various other factors as potential sources of band spreading. That has * Correspondence should be addressed to this author at Bldg. 10, Rm. 9D50, NIH, Bethesda, MD 20892-1580 (Tel. 301-496-4878; FAX 301402-0263; E-mail [email protected]). † NIH. ‡ Russian Academy of Sciences. § Abbreviations: AG, agarose; % C, cross-linking monomer/total monomers (% w/w); CE, capillary zone electrophoresis; PA, polyacrylamide; PHYCO, R-phycoerythrin; % T, total monomer concentration (% w/v).

been possible through use of automated intermittent scanning of the band during migration and therefore collection of a database of bandwidths at many migration distances which is not practically possible in CE. II. Materials and Methods Protein. The protein used was R-phycoerythrin (Polysciences, catalog no. 18188, lot 411701, and Sigma, catalog no. P-0159, lot 96H3800), a native fluorescent protein with Mr 240 000. It is designated as PHYCO. Gel. Both polyacrylamide [3% C(bis)] and agarose (SeaPrep, FMC, Rockland, ME) were used. Polyacrylamide was polymerized as described previously (section 5.5 of ref 3). The gelation of agarose followed the procedure described in ref 7. Apparatus. The automated gel electrophoresis apparatus with intermittent fluorescent scanning (HPGE-1000, LabIntelligence, Belmont, CA) was used. Gel thickness in the eight lanes of the gel tray of that apparatus was 3 mm. Electrophoresis. Gel electrophoresis was carried out at 5-20 °C, in 15 or 50 mM Tris-tricinate buffer, pH 8.2, or in 10 mM sodium phosphate buffer, pH 5.0-8.3, 2.5-20 V/cm, as described in the figure captions. Fluorescence intensity profiles constituting the gel pattern at selected intervals of migration time that are stored by the software of the HPGE-1000 apparatus were exported from the output in the form of ASCII data files and then read by the MATLAB program (Mathworks, Boston, MA). Then by use of MATLAB program files designed for that purpose (available upon request from the first author) experimental parameters such as bandwidth and band position, peak amplitude, peak area, and extent of asymmetry were computed. After completion of scanning, the PHYCO band was also visually observed under UV light on both the gel surface and transversely after sectioning across the band.

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TABLE 1: The Rate of Band Spreading of PHYCO, dw/dx, as a Function of Various Factors factor

gel AG

1 396 345 390

2 418

PA E (V/cm) 2.5 5.0 10.0 20.0 40.0

AG + 1% glycerol

temperature (°C) 5 10 15 20

AG

pH (phosphate) 5 5.9 7.1 8.3

PA

protein load (µg/lane) 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

AG + 1% glycerol

ionic strength 50 mM

AG

797 770 759 573

354 369 313 354

344 395 328 419

3 383

(dw/dx) × 104 at gel concentration (%) 4 5 6 7 382 330 398

503

600

668 749 616 608

755

336 400 310 377 772 714

8 590

9

10

417

304

498

459

424

350

336 395 316 368

357 363

292 357 408 540

250 347 365 343

286 297

565 766 560 673

557 676 506 699

722 826 770

566 811

648 685

546

580

332 513 847 767

811

613 604 637 580 607 610 574 568

448 447 465 a

AG, agarose; PA, polyacrylamide.

Evaluation of Band Spreading. Three main parameters were under investigation (1) Peak width at half-height w, determined as described in Section IV of ref 7 for the “first technique”. (2) Resolution efficiency x/w, where x is the migration distance. w/x is the square root of the number of theoretical plates, N, which, omitting the numerical coefficient 5.55, is defined as8

N ) x2/w2

(1)

(3) Rate of band spreading with migration distance, dw/dx, which is related to the resolution efficiency x/w. The first two parameters were investigated as functions of migration distance and time. The rate of band spreading with migration distance dw/dx was investigated as a function of electrophoretic conditions. III. Results A. Visually Observable Shape of the PHYCO Band in Gel Electrophoresis. The shape of the PHYCO band was observed to be straight and perpendicular to the direction of electrophoresis. After transverse sectioning of the gel, the shape of the PHYCO band appeared cylindrical with a distance of about 1 mm from top and bottom of the gel. This distance is the same as that between the bottom of the sample slot and the bottom of the gel. Thus, the position of the protein band corresponds to the bottom of the sample slot. B. Bandwidth and Resolution Efficiency as Functions of Migration Distance and Time. 1. Bandwidth as a Function of Migration Distance. Bandwidth of PHYCO in polyacrylamide and agarose gel electrophoresis is linearly related to

Figure 1. Proportionality between bandwidth and migration distance: 0.015 M Tris-tricinate, pH 8.2, 5 °C, 20 V/cm, PHYCO, 2 µg/lane. (O) 3% SeaPrep agarose; (*) polyacrylamide of 5% T, 2.6% C(bis).

migration distance. The linear dependence is maintained under all conditions investigated (see below). The representative cases of 5% polyacrylamide and of 3% agarose are shown in Figure 1. The slope of the line, dw/dx (Table 1) is related to the final number of theoretical plates (see Figure 3 and Discussion). Figure 2 illustrates the advantage of relating bandwidth to distance rather than time. In panel A, the dependence of bandwidth on time is shown. At 87 min migration time, the electric field strength was changed from 20 to 5.4 V/cm. The slope of the line depicting the dependence of bandwidth on migration time decreases with decreasing field strength. By

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Figure 3. Resolution efficiency (expressed as x/w) as a function of migration distance: conditions were as in Figure 1, except (O) 2% agarose and (*) 3% T polyacrylamide.

Figure 2. Advantage of relating bandwidth to migration distance rather than migration time: Agarose gel electrophoresis of PHYCO was carried out under the conditions of Figure 1, except that the field strength was changed from 20.0 to 5.4 during the migration. The change results in a change of the time-dependent rate of band spreading (panel A) but not in a change of the distance-dependent rate of band spreading (panel B).

contrast, the dependence of bandwidth on migration distance (panel B) remains the same, independently of field strength. This particular example demonstrates that the apparent effect of the electric field strength on the rate of band spreading with time, dw/dt, reflects a change of migration rate rather than a direct influence of the electric field on the process of band spreading. Moreover, it is the rate of band spreading with migration distance, dw/dx, that is related to the final number of theoretical plates, N (see Discussion). Thus, use of this parameter is advantageous for an elucidation of the roots of band spreading. 2. Resolution Efficiency (x/w) as a Function of Migration Distance. In both polyacrylamide and agarose gels, resolution efficiency, expressed as x/w (the square root of N, see eq 1), increases with migration distance until a plateau is reached (Figure 3). The plateau value is attained more rapidly in polyacrylamide than in agarose gel electrophoresis (Figure 3). Such behavior is connected with the linearity of the dependence of bandwidth on migration distance (see Discussion). C. Rate of Band Spreading with Migration Distance, dw/ dx, as a Function of Electrophoretic Conditions. 1. Gel Concentration. The dependence of bandwidth on migration

distance at all gel concentrations tested is linear, and the slope, dw/dx, of that linear relationship is not distinguishable within the limits of experimental scatter for all gel concentrations of polyacrylamide (Figure 4A,C) and agarose (Figure 4B,D) tested. An apparent decrease of dw/dx with increasing polyacrylamide concentration (Figure 4C) could be explained by the increased experimental error at elevated gel concentrations because of the correspondingly lower range of migration distances used to define the slope. It is seen from Figure 4A that the dependencies of w on peak position (migration distance) for all investigated gel concentrations nearly coincide. Thus, the observed apparent decrease is within the limits of experimental error. 2. Field Strength. The rate of band spreading, dw/dx, of PHYCO as a function of field strength is depicted for the representative cases of 2%, 3%, and 4% agarose gels in the range of 2.5-40 V/cm in Figure 5A. Clearly, the rate of band spreading does not increase with electric field strength within the range studied and within the limits of experimental error. 3. Temperature. In the representative case of agarose gel electrophoresis at 1-2.5% gel concentration and temperature in the range of 5-20 °C, no change in the rate of band spreading with temperature within the limits of experimental error is observed. At any one temperature tested, band spreading occurred at an identical rate independently of agarose concentration (Figure 5B). 4. Protein Load. The rate of band spreading in agarose gel electrophoresis is the same within the range of PHYCO loads of 0.4-3.2 µg/lane. That independence is demonstrated for the representative case of a gel concentration of 2% (Figure 5C). 5. pH and Ionic Strength. Figure 5D shows that the rate of band spreading remains the same within the range of pH 5-8.3 of the gel buffer sodium phosphate. Note that the rate of dispersion is higher for phosphate than for Tris-tricinate gel buffer at the same temperature (compare Figure 5D with Figure 4C; see Table 1) and that the resolution efficiency, x/w, of the phosphate gel is correspondingly less. D. Extent of Variability of dw/dx. Table 1 illustrates the limits of variability of the slope of the linear dependence of bandwidth on migration distance, where values of dw/dx, obtained under various conditions, are summarized. It is seen from the table that the value of dw/dx varies from 0.03 to 0.08 depending on conditions, i.e., it changes by a factor of 2.7. Although the rate of band spreading with migration distance holds nearly independently of temperature, field strength, gel

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Figure 4. Independence of band spreading on gel concentration. Conditions were as in Figure 1. (A) Bandwidth w, pooled data from a range of polyacrylamide concentrations of 3-10% T. (B) Bandwidth w, pooled data from agarose concentrations ranging from 1% to 5% SeaPrep. (C) Rate of band spreading with migration distance, dw/dx, vs polyacrylamide concentrations; data as in panel A. (D) Rate of band spreading with migration distance, dw/dx, vs agarose concentration; data as in panel B, except the data point for Tris-tricinate concentration was raised from 15 to 50 mM (*).

concentration, pH, and protein load, one can observe differences in the rates of band spreading under the different conditions despite considerable scatter of the data. While that scatter does not allow us to accurately compare the rates of band spreading in agarose and polyacrylamide gels, it appears somewhat higher in the latter case than in the former one. The presence of glycerol in the gel, or the replacement of Tris-tricinate by phosphate buffer, double the rate of band spreading. IV. Discussion A. Resolution as a Function of Migration Distance. Constancy of the rate of band spreading, dw/dx, with time implies an independence of resolution efficiency x/w on migration distance and time at elevated values of the migration distance. This is due to the following: Experimentally it is found that dw/dx is constant with time and migration distance. Thus, bandwidth consists of the sum of initial bandwidth w0 and the value of kx, where k ) dw/dx. Accordingly, the resolution efficiency x/w equals

x/w ) x/(w0 + kx) ) 1/(w0/x + k)

(2)

When the migration distance x is small, w0/x . k. Therefore, k can be neglected. Thus at low values of x, x/w ) x/w0 and in the limit, x/w approaches 0. At large migration distances w0/x

, k. Therefore, w0/x becomes negligible compared to k, and the resolution efficiency x/w reaches a plateau at 1/k ) 1/(dw/ dx). Thus, the parameter dw/dx is the inverse of the plateau value of the resolution efficiency and has been used as the parameter by which the various factors determining bandwidth can be compared. B. Factors That May Affect Band Spreading in Gel Electrophoresis. 1. Diffusion. For R-phycoerythrin, diffusion has been demonstrated not to be the predominant source of band spreading for at least two reasons: (i) Bandwidth, not its square, is proportional to migration time (Figures 1 and 2 of this paper and Figure 5 of ref 7), and (ii) the rate of band spreading with time increases with field strength, while under conditions of diffusion it would remain independent of it. The observed linear dependence can also not be explained by the so-called “concentrational diffusion”, signifying that when the protein load is too high, band spreading due to diffusion could be increased and the effective diffusion coefficient would depend on protein concentration. The protein concentration under the band decreases when the band spreads, and accordingly in the case of concentrational diffusion the dependence of bandwidth on time cannot be linear but should be even more curved than the function of the square root of time. Moreover, the rate of band spreading should strongly depend on the protein load. Since no dependence of band dispersion on protein load is observed

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Figure 5. Rate of band spreading with migration distance, dw/dx, as a function of field strength, temperature, protein load, and pH: Conditions were as for agarose in Figure 1 except for the buffer in panel D. (A) (O) 2%, (*) 3%, (+) 4% agarose. (B) Dependence on temperature at 1% (O), 1.5% (*), 2% (+), and 2.5% (×) agarose. (C) Agarose, 2%; dependence on PHYCO load/lane. (D) Dependence on the pH of sodium phosphate buffer. Polyacrylamide of (O) 3% or 7%, (*) 4% or 8%, (+) 5% or 9%, or (×) 6% or 10% T.

in gel electrophoresis, no concentrational diffusion occurs under the conditions of the study. Thus, diffusion can be ruled out as being the main cause of band broadening. 2. Temperature Gradients. Temperature affects conductance, viscosity, and therefore mobility steeply. A vertical temperature gradient may lead to a vertical viscosity gradient, which increases band dispersion. It relates to apparatus design: in the HPGE-1000 apparatus, the horizontal gel is thermostated by Peltier cells from the bottom only, while the top of the gel is in contact with air at close to ambient temperature. Why, then, is it that variation of temperature of electrophoresis by a factor of 4 is without effect on band spreading? One reason appears to be that the protein is loaded into the sample slot in a dense medium (glycerol) and therefore migrates mostly close to the bottom of the gel, protected from atmospheric temperature. It is also protected by the fact that the heat conductivity of the gel buffer far exceeds that of air. It has been previously reported that, under the same conditions applied in the present report, asymmetry of the PHYCO peak remains constant (Figure 9B of ref 7) with time. Also, the particular asymmetrysa trailing ascending limbsis opposite to that produced by a vertical temperature gradient. For all of these reasons, temperature gradients cannot be a major cause of band spreading. That is also suggested by the results on band spreading of R-phycoerythrin on CE.6 The values of bandwidth at half-height obtained in ref 6 under conditions of CE were found to obey the law w ) AL0 + B, where L0 is the

starting zone width, A is a constant equal to approximately 0.5, and B is proportional to effective capillary length (Table 1 of ref 6). Thus, these results fully correspond to and could be presented exactly in the same form as the data obtained in gel electrophoresis: w ) w0 + kx, where w0 ) AL0, x ) migration distance ) effective capillary length, and k ) the rate of band spreading with migration distance. Note that under that consideration the value of k obtained from the data of CE6 is equal to the lowest k value obtained under conditions of gel electrophoresis, viz., k ) 0.03. It seems very unlikely that, under such different conditions as those of CE and gel electrophoresis, temperature gradients could cause the same gradients of mobility. Thus, temperature gradients cannot be a major cause of band spreading of R-phycoerythrin. 3. Joule Heating. An increase of temperature and the setting up of a temperature gradient by Joule heating, and the resulting band spreading, is ruled out since over a 16-fold increase of field strength, no increase in the rate of band spreading is observed (Figure 4A). This conclusion is suggested by the analogous result under conditions of CE.6 4. ConductiVity Difference. A discrepancy between the conductivity along the sample path and that of the surrounding sample-free gel buffer may affect bandwidth. This factor can be ruled out for two reasons: First, variation of PHYCO load by a factor of 16 did not produce any increase in band spreading (Figure 4C depicts an 8-fold increase). Moreover, if that effect on bandwidth were operative, one should observe an increase

4818 J. Phys. Chem. B, Vol. 102, No. 24, 1998 of band asymmetry with time. None could be measured.7 The analogous result has been obtained under conditions of CE.6 5. Electroendosmosis. It is well-known that electroendosmosis is close to zero in polyacrylamide gels and very low in agarose gels. In addition, some electroendosmotic flow will not affect bandwidth significantly. A contribution of electroendosmosis to band spreading can furthermore be ruled out since the rate of band spreading in agarose and polyacrylamide gels is about the same (Figure 4C,D) and since an increase in agarose concentration has no effect (Figure 4B,D). 6. Charge Density Differences. Charge density is dependent on pH since it is a function of the pKs of the functional groups of the protein. Thus, a microheterogeneity of the protein due to charge density differences could be a possible cause of band spreading. We have varied the pH from 5 to 8.3, i.e., the range in which carboxyl, imidazole, and R-amino residues are titrated. That variation in pH did not affect band spreading. We also tested the influence of ionic strength of the buffer on band spreading. Increasing the ionic strength from 15 to 50 mM (Figure 4D) does not affect the rate of band spreading. Thus microheterogeneity of the protein due to charge density differences can also not constitute the main cause of band spreading. 7. Interaction with the Gel Matrix. Recently a new mechanism of band spreading by interaction with the medium in contact with the particle (“interactive dispersion”) has been suggested.3,7 Under some assumptions, that theoretical model predicts a linear dependence of bandwidth on time.7 The basic idea underlying the model is that protein or DNA migration through the gel can be represented as a succession of periods during which the motion is unimpeded, randomly interrupted by periods during which it is arrested due to an entanglement with the surrounding medium, e.g., the gel fiber. The Giddings-Eyring-Weiss model of interactive dispersion3,7 does not provide an analytical expression that would predict the relation between the rate of band spreading and gel concentration. The experimental data do not reveal a dependence of dw/ dx on gel concentration or a significant difference with regard to dw/dx between agarose and polyacrylamide gels in the investigated concentration ranges. The data show that, taken at the same migration time, the bandwidth, w, as well as the peak position, x, are strong functions of gel concentration. But the dependencies of w and x on gel concentration are equally strong, and their effects on the derivative, dw/dx, cancel out. Data of CE6 show that the band of PHYCO spreads as a function of capillary length (migration distance) even in the absence of gel or polymer in the capillary, albeit a polyacrylamide coating of the inner capillary wall, at almost the same rate as the lowest rate obtained in gels (dw/dx ) 0.03). Only at relatively high concentrations of polymer (PEG) with high molecular weight does the rate of band spreading with migration distance increase. Under conditions of CE,6 the rate of band spreading as well as its sensitivity to polymer (PEG) concentration increase with decreasing starting zone length in the range of small values of that length (Figures 4 and 5 of ref 6). The starting zone lengths in gel electrophoresis are about 0.05-0.5 mm and thus correspond to the region of a rising rate of band spreading and higher sensitivity to polymer concentration in CE. The comparable properties of the CE and gel electrophoresis systems suggest that the mechanisms of band spreading observed in the absence of gels or polymers in CE may also apply to gel electrophoresis. However, one cannot exclude the possibility of interactive dispersion in CE by adsorption-desorption to the negatively charged capillary walls and/or their polymeric coating, entanglement-disentanglement with the polymer fiber

Yarmola and Chrambach in gel electrophoresis, and similar band spreading behavior in both cases despite divergent mechanisms. C. Why Do PHYCO Bands Spread in Gel Electrophoresis? Analysis of results on the PHYCO band spreading in gel electrophoresis shows that none of such factors as diffusion, temperature gradients, Joule heating, conductivity difference between sample zone and surrounding buffer, electroendosmosis, and charge density differences could be the main cause of band spreading. Coincidence of the results obtained for PHYCO in gel electrophoresis with those obtained in CE6 show that the main cause could be connected to the protein sample itself. Because the rate of band spreading depends on the type of buffer and on the presence of glycerol, one may speculate that conformational differences between protein molecules with relatively slow transition between conformations could be responsible for the band spreading of R-phycoerythrin. Three R-phycoerythrin species isolated from Ceramium rubrum of the same molecular weight, each with a specific ionic strength dependence of chromatographic elution behavior, have been reported.9 Tailing behind the dominant peak (Figures 1 and 3 of ref 7) also indicates that the PHYCO preparation is not entirely homogeneous. However, the measurement of bandwidth at half-height is taken from the main peak only and should not be affected. Another possible cause is aggregation of protein molecules during electrophoresis. Both cases could be described by the same mathematical model that was elaborated for the mechanism of interaction with gel matrix.3 Indeed, in all cases migration through the gel can be represented as a succession of periods during which migration occurs with the velocity corresponding to one state (faster moving species, monomers, or nonentangled molecules), randomly interrupted by periods during which it occurs with another velocity, corresponding to another state (slowly moving species, aggregates, or entangled molecules). The transition between two states cold be described by kinetic expressions or in terms of probability density for each state. In the case of aggregation the rate constant k (see ref 3) should be second-order and thus band spreading should depend on protein concentration. Since no dependence on protein load is found, aggregation of protein during electrophoresis is an unlikely cause of band spreading. Thus, microheterogeneity related to conformation or the localization of charge density on the molecular surface with relatively slow exchange between two or more states remain possible candidates for being a cause of PHYCO band spreading. To obtain theoretical linear dependence of bandwidth on migration distance one should suggest more complicated kinetics of transition between states than simple first-order kinetics.3,7 That possibility requires further investigation. References and Notes (1) Hjerten, S. Electrophoresis 1990, 11, 665. (2) Yarmola, E.; Chrambach, A. Electrophoresis 1995, 16, 345. (3) Weiss, G. H.; Sokoloff, H.; Zakharov, S. F.; Chrambach, A. Electrophoresis 1996, 17, 1325. (4) Yarmola, E.; Sokoloff, H.; Chrambach, A. Electrophoresis 1996, 17, 1416-1419. (5) Radko, S. P.; Chrambach, A. Electrophoresis 1998 (in press). (6) Radko, S. P.; Weiss, G. H.; Chrambach, A. J. Chromatography A 1997, 781, 277-286. (7) Yarmola, E.; Calabrese, P. P.; Chrambach, A.; Weiss, G. H. J. Phys. Chem. B 1997, 101, 2381. (8) Giddings, J. C. Dynamics of Chromatography; Marcel Dekker: New York, 1965. (9) Tiselius, A.; Hjerten, S.; Levin, Oe. Arch. Biochem. Biophys. 1956, 65, 132.