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1126 S. Blanco er a/. Electrophoresis 1996, 17, 1126-1 133
StCphane Blanco' Michael J. Clifton* Jean-Louis Joly' Gabriel Peltre3
'Laboratoire d'Etude des Systkmes et de I'Environnement Thermique de l'Homme, Universitd Paul Sabatier, Toulouse, France 'Laboratoire de Gdnie Chimique (CNRS URA 192), Universitd Paul Sabatier, Toulouse, France 31nstitut Pasteur, Paris, France
Protein separation by electrophoresis in a nonsieving amphoteric medium
A numerical model has been used to study the separation of protein mixtures by zone electrophoresis in a nonsieving amphoteric medium. An amphoteric buffer fixes the pH of the solution close to its isoelectric point, where the buffer molecules are uncharged: they thus contribute very little to the conduc- tivity of the solution. This means that high field strengths can be used for rapid separation without sacrificing resolution. The numerical study shows that in this process the band spreading that can reduce resolution is essentially due to differences in migration rate between protein-rich and low-protein zones: both differences in solution conductivity and in protein mobility are involved. Rules for judging the buffer capacity of amphoteric molecules are presented and it is shown how, for a given protein, the effectiveness of this technique varies with the range of pH in which it is applied.
1 Introduction
An amphoteric molecule in solution tends to fix the pH of the medium at its isoelectric point (or more strictly at its isoionic point). At this pH the amphoteric molecule is only slightly ionized and thus contributes very little to the conductivity of the solution. As an electrophoresis medium, it allows high field strengths to be used without causing excessive heating by the Joule effect. This is an advantage for zone electrophoresis because rapid separation can be obtained, avoiding loss of resolu- tion due to molecular diffusion. However, this technique has not been widely used so far because it has often been considered that the simple amphoteric molecules generally available did not offer sufficient buffer capacity and that they did not allow a suitably wide range of pH conditions in which to operate. Furthermore, it was noticed that the technique did not give good results under all conditions.
In the present study, a numerical model has been used to explore the separation mechanisms involved in amphoteric zone electrophoresis (AZE). We have sought to clarify the origin of phenomena that can lead to band spreading and thus hamper separation. A number of studies have already been devoted to band spreading in zone electrophoresis [I, 21. Hjertkn [3] has pointed out the particular importance of spreading due to differences in field strength and pH between the protein zone and the surrounding buffer. This mechanism is illustrated in Fig. 1. The migration velocity in the center of the protein zone, VPl, is generally lower than the velocity Vpo at the edges of the band where the protein concentration is vanishingly small. Where the protein is strongly present, it will modify the pH because of its acid-base equilibria, so its own electrophoretic mobility will be modified. Also, the protein itself is an extra charge carrier and it alters the state of charge of the buffer ions; the conduc-
Correspondence: Dr. Michael Clifton, Laboratoire de Genie Chimique et Electrochimie, Universite Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse cedex, France
Nonstandard abbreviation: AZE, amphoteric zone electrophoresis
Keywords: Ampholytes / Buffering capacity / Capillary electrophoresis / Numerical modeling
tivity in the protein zone will thus be different and this will mean a difference in field strength. Thus the migra- tion velocity, the product of field strength and mobility, will vary with the protein concentration and even slight variations are sufficient to cause the protein zone to spread. To keep the pH as uniform as possible, it is important to use an effective buffer solution. As doubts are often expressed as to the buffer capacity of ampho- teric molecules, particular attention has been given here to this aspect of the process.
2 Theoretical approach
2.1 Notation
B, specific buffer capacity of molecule i c, molar concentration of molecule i (mol m-3) D, diffusion coefficient of molecule i (m2 s-') E electric field strength (V m-') f, Henry function F Faraday constant (96485 C mol-') G velocity ratio h concentration of H' I current density (A m-') J molar flux (mol m-' s-') K, equilibrium constant for water dissociation r molecular radius (m) R gas constant (8.3144 J mol-' K-') t time (s) T temperature (K) u electrophoretic mobility (m2 V-' s-') v convection velocity (m s-') V migration velocity (m s-') x distance coordinate (m) Z mean charge number x electrical conductivity (S m-') xD Debye parameter (m-')
Subscripts a ampholyte B strong base i component i p protein w water 0 low-protein zone 1 protein-rich zone
0 VCH Verlagsgesellschaft mbH, 69451 Weinheim, 1996 0173-0835/96/0606-1126 $10.00+.25/0
Electrophoresis 1996, 17, 1126-1133 Protein separation in an amphoretic medium 1127
7 n
”I vp’ K
cannot be considered as giving a really accurate repre- sentation of the behavior of a particular protein, it does give a good representation of typical protein behavior.
The Henry equation for electrophoretic mobility can be combined with the Debye-Huckel theory to give this expression for the protein mobility [lo]:
( 3 ) I I -. b
X where j ; is the Henry function and the Debye parameter Figure 1. The mechanism of zone spreading by nonuniform migration velocity. Vpl: protein migration velocity at high protein concentration; Vpo: protein migration velocity at trace protein concentration.
xD is a function of the ionic strength of the solution. The electric field strength at any point can be expressed as follows:
2.2 Electrokinetic phenomena
The model used is similar in principle to the “Tucson- Princeton” model [4-71: it takes into account the acid- base equilibria of the various components and the transfer by migration and by diffusion. This model has already been generalized to treat a three-dimensional problem [8]. Here we shall consider electrophoresis either in a nonsieving gel or in an open capillary; the thermal contributions to band spreading are neglected. For these one-dimensional, transitory systems, the mass- conservation equation for any species i is given by the following expression:
(4) x where the conductivity x varies with both x and t , while the current density I is invariant. The second term in the numerator represents the diffusive contribution to the current: this term is generally small, though not always negligible [6]. The contribution of each species to the electrical conductivity is given by its concentration, its charge number and its mobility. For a solution con- taining one ampholyte, a, and several proteins, p , the conductivity is given by:
where J,,,, Jdlf and J, are the fluxes due to migration, dif- fusion and convection, respectively. In gel electro- phoresis, the convective velocity is generally negligible, whereas in capillary electrophoresis, there can be convec- tion by electroosmosis which superimposes a uniform velocity on the migrating, diffusing, and reacting system. In this study we shall assume that there is no convec- tion, but the effect of convection in the capillary system is ideally just a simple displacement of the nonconvec- tive behavior.
The overall electric charge density at any point in the solution must be zero: this is expressed by the electro- neutrality condition
K w h i
h - - + Eci Zi = 0
(1) where & is the conductivity of water and (2?)i is the mean square charge on the species i .
This constraint allows the charge number of each species to be calculated on the basis of a knowledge of its acid- base equilibria. Note that here the value Z represents the mean of the charge numbers (integer values) of the individual species in equilibrium. The variation of the protein charge number with pH (protein titration curve) was calculated from the amino-acid content of the pro- tein using the Linderstrcllm-Lang “smeared charge” model that takes into account the electrostatic interac- tions between sites [9]. Though such a simple approach
These equations were solved numerically: they were expressed in the TEF formalism (transfer-evolution for- malism) [ll] so as to allow use of the ZOOM software. This method of calculation can be used to gain access to the coupling between the various transfer variables. In this way any system presenting numerous complex inter- actions can be analyzed in terms of one-to-one relations between any two transfers. Analysis of the electro- phoresis process using this technique is still under way and will be the subject of a future paper. The grid had 121 space steps and the time step was varied according to the migration speeds so as to keep the Courant number sufficiently small [12]. The origin was moved progressively to keep the protein zone centered in the calculation window, and a “flux-corrected transport” (FCT) technique [12] was used to represent migration so as to eliminate “false-diffusion’’ errors.
2.3 Buffer capacity
An essential aspect of this electrophoresis technique that needs to be considered is the buffering power of the amphoteric molecule. Here we shall follow the approach recently presented by Rilbe 1131. To illustrate this, let us consider the electroneutrality condition of Eq. (2) for an amphoteric buffer solution containing one protein:
(6) K w h
h - - +c,Z,+C,Z,=O
1128 S. Blanco et a / . Electrophoresis 1996, 17, 1126-1133
If a strong base is added at a low concentration c,, the pH will be raised by a small amount and the above equa- tion becomes
The buffer capacity of a solution has been defined as dc,/d(pH), for c, infinitesimally small, and in the present case it can be evaluated by differentiating the above expression:
From this expression it can be seen that the overall buffer capacity of the solution is the sum of three terms: the first due to the equilibrium of water, the second related to the amphoteric molecule and the third due to the protein. In the second and third terms, the deriva- tives correspond to the slopes of the titration curves. This value is related to the quantity defined by Rilbe as the “molar” buffer capacity for the molecule. As it is a dimensionless number, we prefer to avoid reference to any unit, so the term “specific buffer capacity” will be used:
(9)
For an amphoteric buffer molecule, therefore, its specific buffer capacity is given by the slope of its titration curve at its isoelectric pH. The contribution of this molecule to the overall buffer capacity is given by the quantity c,B,; this value has to be sufficiently high to counteract the buffer effect of the protein.
2.4 Differences in migration velocity
The last point can be made clearer by considering the ratio G of protein migration velocity in the protein-rich zone (V,,) to the protein velocity in a buffer zone con- taining only traces of protein (V,,), both of these veloci- ties being given by the product of the electrophoretic mobility and the field strength:
This ratio can be used as a measure of the difference in migration rate between the center of the protein zone and its edge; thus, the further that G is from the ideal value of 1, the worse the peak distortion that leads to a loss of resolution will be. Here E,, is the field strength outside the protein zone. As the current density outside the protein zone, Eo x, (assuming the diffusive contribu- tion is negligible), must be equal to the current density within the protein zone, El (x,, + Ax), the ratio of field strengths can be replaced by a ratio of conductivities:
where A x is the difference in conductivity between the protein zone and the surrounding medium.
The electrophoretic mobility of the protein is given by Eq. (3). We shall assume that the protein has little effect on the ionic strength of the solution, so that there is no difference in the Debye parameter between the protein zone and the surrounding buffer. The mobility can then be taken as proportional to the charge number of the protein Z,,, and we have the following expression:
From our definition of buffer capacity, we can consider that
z p i = Zpo - Bp (pH1 - PHJ = Z p o - B, A(PH) (13)
where A(pH) is the pH difference between the protein zone and the surrounding buffer; this linear relationship is justified for small values of A(pH).
If in Eq. ( 6 ) we assume that the charge concentration due to the water is negligible, then we obtain the fol- lowing expression for the charge on the ampholyte in the protein zone:
z a1 =-cp ’z P l (14) C d
Another expression can be given for this quantity on the basis of the buffer capacity of the ampholyte:
Equations (12) to (15) can be combined to give the fol- lowing expression for the ratio G:
(16) Bsca, KO G = BaC*l + B p c p 1 (KO + AX)
Alternatively, if Ax is small compared with q,:
Various approximations have been made in deriving these expressions, but they are suficiently accurate to be used as a guide in choosing suitable conditions for AZE. Equation (17) makes it clear that there are indeed two contributions to band spreading: one due to mobility dif- ferences and the other due to conductivity variations. The significance of these expressions will be discussed in light of the simulated separations.
3 Results
The first example of the application of this calculation procedure to ZE is the separation of a mixture of four proteins: soybean trypsin inhibitor (2.5 g/L), chicken ovalbumin (3 g/L), conalbumin (2.5 g/L) and equine
Electrophoresis 1996, 17, 1126-1133 Protein separation in an amphoretic medium 1129
charge
60
40
20
0
-20
-40
Figure 2. Calculated titration curves for four proteins: soybean trypsin inhibitor, chicken ovalbumin, conalbumin and equine myoglobin.
myoglobin (1 .O g/L). The calculated titration curves for these proteins are given in Fig. 2. The background buffer is a lysine solution (5 X mol/L): this imposes a pH of 9.7 (isoelectric pH) everywhere except where the ini- tial protein zone is located. These conditions were chosen to allow comparison with experimental data of HjertCn et a/. [I41 concerning capillary zone electro- phoresis. An initial zone width of 2 mm was chosen as corresponding approximately to the injection conditions used. Initially, the lysine is uniformly distributed. Figure 3 shows the distribution of the four proteins along the length of the capillary 40s after the application of the electric field. In this case the current density was kept constant at 280 Aim2 and the mean field strength was 620 V/cm. Here the protein peaks are already well separ- ated and remain fairly symmetrical, with a certain ten- dency for the fastest peak to take on the triangular form described by HjertCn [3]. The pH of the solution is quite uniform, with only small fluctuations due to the pres- ence of the proteins. The electric field shows some small fluctuations, with a dip corresponding to each protein peak. However, there is also a sharp dip in the field strength due to the presence of a zone of high lysine concentration. This is created when the lysine contained in the initial protein zone is “expelled” when the field is applied. In the initial state, only the lysine in the protein zone carries a significant charge, opposite in sign to the protein charge. When the field is applied, this charged ampholyte migrates in the direction opposite to the pro- tein migration and once it leaves the protein zone it returns to a state of low mobility.
In Fig. 4, results from the same system are presented in a different form. These graphs show the variation in time of the protein concentration at the detector, 11.5 cm from the injection point. These results are more directly comparable with the experimental data of Hjerten et al. (their Fig. 10, [14]), except that the latter give the UV absorption rather than the protein concentration. HOW-
0.2 0.1 Fi!vYLi 0 0 0 05 0 1 0.15 0 2 0 x 25 (m)
PROTEIN CONCENTRATIONS gEIW7, w
56000
54000 0 0 05 0 1 0 15 0 2 0 25
x (m) ELECTRIC FIELD
Figure 3. The separation of a mixture of four proteins, in the order slowest to fastest (left to right): equine myoglobin (1.0 g/L), conal- bumin (2.5 g/L), soybean trypsin inhibitor (2.5 g/L), and chicken oval- bumin (3 g/L). The background buffer is a lysine solution, whose con- centration is originally uniform (5 X mol/L). The distributions of protein concentration, field strength and pH are shown after 40s of migration with a constant current density of 280 A m-’ and a mean field strength of 620 V/cm.
ever, the migration times for the four proteins are close to the experimental values. The results are given for four different field strengths and it can be seen that, as in the experimental observations, the field strength has almost no effect on the resolution. This means that high field strengths can be used to obtain short measurement times. Of course the similarity in the calculated results is less surprising than in the experimental ones: it simply means that the system is dominated by migration. The experimental observations can be influenced by both thermal effects and by adsorption, though it should be noted that HjertCn etal. used a straight fused-silica tube coated with linear polyacrylamide to suppress adsorption and electroosmosis. In contrast, the model includes only one time-dependent effect other than migration, i. e., molecular diffusion, and in the present case the separa- tion times are too short for diffusion to be important. The model calculations can also be seen as suggesting that the coating used in the experiments was indeed effective in preventing adsorption.
Lysine is an interesting molecule to be used as an amphoteric buffer as it has a relatively high specific buffer capacity ( B = 0.55), i.e., its titration curve shows a strong gradient at the isoelectric point (pH 9.7). This is because the pKs on either side of the isoelectric point are quite close together (pK2 = 8.95, pK3 = 10.53). Figure 5 gives the calculated titration curve for lysine. To show the importance of buffer capacity in this system, the cal- culations for the first example were repeated using a dif- ferent amphoteric buffer; this was formed with a mole- cule similar to lysine except that its pKs on either side of the isoelectric point were moved symmetrically further
1130
0.45
3 v
0 0.4
0.35
0.3
0.25
0.2
0.1 5
0.1
0.05
i
n
...........
. . . . . .
i.. j .....
..........
S . Blanco ef al.
” 0 200 400 t (s)
330 Vlcm
.................
0 100 200 t (4
670 Vlcm
0 50 100 t (s)
1330 Vlcm
apart (pK, = 7.95, pK, = 11.53). The titration curve for this “modified lysine” is also given in Fig. 5. It can be seen that its slope at the isoelectric point is much smaller; its buffer capacity is thus much less ( B = 0.072).
Figure 6 shows results equivalent to those in Fig. 3, except that they were calculated with the “modified” buffer. It can be seen that the protein peaks are less well separated and their degree of spreading is not the same: the slowest peak shows little spreading while the fastest peak shows much more than in Fig. 3. The field strength here shows rises (zones of low conductivity) as well as falls. Also the variations in pH are much greater than in Fig. 3; for comparison, the pH profile from Fig. 3 has been reproduced here as a dashed curve. These differ- ences are due to the lower buffer capacity of the “modi- fied” buffer. This means that the presence of the protein causes a greater disturbance of the pH and the field strength: nonuniformities in either of these variables cause nonuniformities in migration velocity. Where the protein concentration is highest, the mobility tends to be lowest; the protein in advance of the peak thus runs on ahead, while the trailing protein catches up with the bulk of the protein. This asymmetry is also observed within the group of proteins: the slowest protein undergoes little spreading as it lies in a zone where the mobility decreases in the direction of migration (the proteins dis- place the pH from the buffer value towards their isoelec- tric points), whereas the fastest protein is in a pH gra- dient of the opposite tendency and so is subject to greater spreading.
charge 2
1.6
1.2
0.8
0.4
0
0 50
2000 Vlcm
-
...
....
...
. .
...
....
....
-
Electrophoresis 1996, 17, 1126-1133
Figure 4. For the same protein mixture as in Fig. 3 : protein concentration at a detector as a function of time for four different field strengths. The protein order from the slowest to the fastest (right to left) is: equine myoglobin, con-
(s) albumin, soybean trypsin inhibitor, and chicken ovalbumin. Detector position: 11.5 cm from injection point.
Figure 5. Calculated titration curves for lysine and a ‘modified lysine’ molecule having a lower buffer capacity at its isoelectric point.
Figure 7 gives calculated titration curves for horseradish peroxidase; the native form is shown together with three isotypes. These isotypes were formed by arbitrarily sup- pressing one or more amino acids from the native sequence. Such “families” of isotypes are observed in
Electrophoresis 1996, 17, 1126-1133 Protein separation in an amphoretic medium 1131
0 . 5 7 - I ::I A\*l , 1 0 1
0 0 0 05 0 1 0 15 0 2 0 25
PROTEIN CONCENTRATIONS x (m)
0 0.05 0.1 0.15 0.2 0.25 x (m) ELECTRIC FIELD
, w 9.4’ I I I
0 0.05 0.1 0.15 0.2 0.25 x (m) PH
Figure 6. The same separation as in Fig. 3, under the same conditions except that the amphoteric buffer molecule is now the ‘modified lysine’ at an initial concentration of 5 X mol/L. The dashed curve on the pH profile is the pH profile of Fig. 3.
charge 7 1
Figure 7. Calculated titration curves for native horseradish peroxidase and three hypothetical isotypes.
electrotitration gels of apparently pure proteins and it is interesting to see how they behave in an amphoteric medium, such as the lysine solution.
Figure 8 gives the distribution of four proteins (the native form and three isotypes) after 240s of migration with a current density of 600 A/mZ and a mean field strength of 750 V/cm. Here the buffer is a 10 mM lysine solution. The four proteins, differing in charge by about one unit, have been almost completely separated. The pH and the field strength (except for the dip due to
s - 0 111 t\fip1 j
0 0 0 05 0 1 0 15 0 2 0 25
PROTEIN CONCENTRATIONS x (m)
0 0 05 I 0 1 I 0 15 0 2 7 0 25
;;;;!
1132 S. Blanco et a!. Electrophoresis 1996, 17, 1126-1133
Table 1. Various ampholyte molecules (amino acids and peptides) with their calculated buffer properties: isoelectric point and specific buffer capacity
Ampholyte molecule P I B
ASP 2.97 0.47 Glu 3.21 0.36
Asp-Glu-His 4.05 1.14 Glu-His 5.10 0.48
(GIu)z-(His)z 5.10 0.96 His 7.58 0.11 LY s 9.74 0.55
Lys-Arg 11.52 0.41 ( L Y s ) ~ - ( A ~ ~ ) z 12.50 1.20
point, as they would appear at a detector. It can be seen that the peaks now show unequal spreading: the fastest peak is least spread as it takes the least time to go past the detector.
4 Discussion Before applying this technique to separate a given mix- ture, the experimenter will want to ask a number of questions. At what pH can it be used? Is there a pre- ferred pH for the protein in question? What concentra- tion of the ampholyte is necessary? In fact, the character- ization of the amphoteric molecule is a relatively simple matter; on the other hand, estimating the possible behavior of a protein is not so easy. Even so, some rela- tively clear guidelines can be given. The candidate amphoteric molecules need to be characterized by their isoelectric points and by their buffer capacity at this pH. Table 1 gives a list of some amphoteric molecules, amino acids and peptides, with their isoelectric points and their specific buffer capacities. It can be seen that the isoelectric points cover a wide range of pH, so for the choice of pH many possibilities are available. The buffer capacities B, of all these molecules are reasonably high. It has been seen here, and demonstrated experi- mentally by Hjerten etal. [14], that lysine has a useful buffer capacity at a concentration of only 5 X mol/ L. To have a buffer capacity equivalent to a 5 mM lysine solution, the caBa value for the ampholyte has to be the same. Thus, for example, a histidine solution with a con- centration of 25 mM will have the same buffer capacity as a 5 mM solution of lysine. Note in Table 1 that the dimer peptides have a much higher buffer capacity than the corresponding monomers.
The tendency of proteins to spread out in this system can be characterized, as we have seen, by the parameter G, the ratio of the migration velocity in the protein zone to the velocity in the surrounding buffer. This ratio has been calculated for three proteins on the basis of the numerical model that was used for the simulations. Figure 10 shows how this ratio varies with the pH for a given molar concentration of protein (c, = lo-' mol/L) and for three different concentrations of ampholyte buffer: 2, 5 and 8 mM. The ampholyte here has the same properties as lysine (D = 0.75 X m2 s-', B = 0.55) except that its isoelectric point has been taken as a vari- able. It can be seen that this ratio shows a different type of variation for each protein. In particular, each protein shows a range of pH in which the ratio is closest to 1; this is where AZE should give good separations. In each
07 :f [,I, cwalbumin 1 I I I , I , , , I L I I
3 4 5 6 7 8 9 10 11 12 PH
1 1 7 , I
0 9 l i i l 0 7
, , , , , , , , , , , ~ , , , ~, , ,p:rqxlpase,, , , I 3 4 5 6 7 10 11 12
PH
Figure 10. Ratio (G) of migration velocity Vpl for protein at a finite molar concentration (c, = lo-' mol/L) to the migration velocity Vpo of the protein at trace concentration as a function of the pH maintained by a hypothetical ampholyte at its isoelectric point. The variation is given for three different ampholyte concentrations (2, 5 and 8 X lo-' mol/L) and for three different proteins: conalbumin, cytochrome c and peroxidase.
Kwj 1 d2
1 d3 ~
1 O4
Io5k
I I I I I .^ ~- (I
bH I"
Figure 11. Calculated electrical conductivity contributed by water as a function of the pH of the solution.
case the curves are generally raised when the ampholyte concentration increases, i.e., when the ampholyte buffer capacity increases. However, the rise is smaller when going from 5 to 8 mM than in going from 2 to 5 mM; this shows that beyond a certain threshold concentration any further rise in buffer concentration is not useful.
Electrophoresis 1996, 17, 1126-1133 Protein separation in an amphoretic medium 1133
Obviously the use of much higher ampholyte concentra- tions should, in any case, be avoided as they imply higher conductivities and thus more intense Joule heating.
Note in Fig. 10 that in the case of cytochrome c and per- oxidase, the curve corresponding to the lowest ampho- lyte concentration rises above the other two at low pH. This is explained by the fact that in these cases the con- ductivity effect compensates the lack of buffer capacity: at this pH and these concentrations, the conductivity in the protein-free zone is higher because the conductivity of water is higher there. Figure 11 shows how the calcu- lated conductivity of water varies with pH: close to its minimum value (around pH of 7.15) the water conduc- tivity is extremely low, but at high or low pH values it may be appreciable in low-conductivity solutions such as those used in AZE.
The values for G calculated in this way have been compared with the approximate expression given by Eq. (17) and good agreement was found. This approximate expression for the ratio G can also be used to discuss the effect of protein properties in the quality of the separa- tion. The mobility effect is given by the first factor in this expression. Note that this term is always less than 1 and that it is further reduced when the protein concen- tration increases. In fact, this is the ratio of the ampho- lyte buffer capacity to the overall buffer capacity (ampho- lyte with protein) and its value improves as the buffer capacity of the ampholyte B,c, increases. Its value is also improved at pH values where the specific buffer capacity of the protein B, is low, i.e. in the parts of the protein titration curves where the slope is small. For example, the fact that the G values for peroxidase in Fig. 10 are close to 1 for a wide range of pH values is partially explained by the fact that its titration curve has a mod- erate slope in this range.
When these comments are applied to the results in Fig. 6, compared with Fig. 3, it is surprising that the separa- tion in Fig. 6 is so little different, although the buffer capacity of the ampholyte is much lower. Detailed anal- ysis of these results shows that the differences in mobility here all work in the direction of increased spreading, but they are partially compensated by a differ- ence in conductivity. The conductivity effect on G usu- ally works in the same direction as the mobility effect: the protein zone is generally higher in conductivity than the surrounding medium (AK positive) and spreading is enhanced. However, as has been noted in the above dis- cussion of Fig. 10 for cytochrome c and peroxidase at low pH, there are some rare cases in AZE where the opposite is true: Ax is negative and the conductivity dif- ference acts against spreading. This beneficial situation is really only possible in AZE when the water conductivity is involved but in traditional zone electrophoresis this can also happen when the protein shifts the pH in such a way that the state of ionization of the buffer is reduced. The overall effect can then be a reduction in conductivity in the protein zone. Hjerten [3] has, in fact, pointed out that in this case the change in conductivity can be strong enough to outweigh the mobility differ-
ences and cause zone spreading in the opposite direc- tion: with a sharp profile ahead of the peak and a diffuse zone behind the peak.
In Figure 8, the spreading of the peroxidase seems, at the stage shown, to be due mainly to molecular diffu- sion. This is illustrated by the fact that at a given time all the peaks show about the same spreading, even though it is possible that the initial high-concentration protein zone went through an early phase of spreading by elec- tromigration. Spreading due to differences in migration velocity over a long term increases with the distance migrated rather than simply with time. This is the behavior that is visible to some extent in Fig. 3 and more strongly in Fig. 6 .
In conclusion, this work has shown how numerical modeling can be used to explore new possibilities in electrophoresis. It can be considered as a means of improving understanding and as a way of testing princi- ples of techniques and not simply as a predictive tool. In the present case, we have been able to show that protein electrophoresis in an amphoteric medium can be a useful technique, allowing rapid separation while giving a satisfactory resolution. The main mechanism leading to a loss in resolution has been traced to differences in pro- tein migration velocity between protein-rich zones and the surrounding buffer. The criteria for choosing ampho- lyte molecules have been clarified in terms of their spe- cific buffer capacity at their isoelectric point. It has also been shown why, as for other electrophoresis techniques, this technique is not equally effective for all proteins and that, for a given protein, some ranges of pH are prefer- able to others; guidelines have been given that can help in making the right choice.
Received November 4, 1995
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