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A semiempirical model for the electrophoretic mobilities of peptides in free-solution capillary electrophoresis
ANALYTICAL
BIOCHEMISTRY
179,28-33
(1989)
A Semiempirical Model for the Electrophoretic Mobilities of Peptides in Free-Solution Capillary Electrophoresis Paul D. Grossman, Joel C. Colburn, and Henk Applied Biosystems, Santa Clara, California 95050
Received
September
H. Lauer
21,1988
In this study an attempt is made to explore the effect of a peptide’s size, charge, and hydrophobicity on its electrophoretic mobility (11) as measured by free-solution capillary electrophoresis with the aim of developing a semiempirical model which incorporates these effects. The effects of peptide size (which is measured by the number of amino acids in the polypeptide chain (n)) and charge on p are independently determined by experiment in a single solvent system and combined to give the relationship ~ =
5.23
X
10m41dq no.43
+
1)
+
2
.
4,
x
1o-6
,
LA.11
where the constant 5.23 X 10m4 is postulated to depend on the solvent system used. The form of Eq. [A.11 was confirmed, and the values of the constants 5.23 X 10m4 and 2.47 X 10e6 were determined, by measuring the electrophoretic mobilities of 40 peptides varying in size from 3 to 39 amino acids and varying in charge from 0.33 to 14.0. Furthermore, the effect of noncharged neutral amino acids on mobility was investigated and shown to be present, but only as a minor perturbation on the effects of size and charge. c isss Academic PWS, IDC.
In a previous study from this laboratory, the effect of buffer pH on the electrophoretic mobilities of a series of model peptides using free-solution capillary electrophoresis (FSCE)’ was investigated (1). (The electrophoretic mobility is defined as the net migration velocity of the solute per unit of electrical field strength.) It was shown that the value of the electrophoretic mobilities of the peptides agreed qualitatively with those that would be predicted from calculated charges on the peptides at three different pH values: 2.5, 4.0, and 11.0. Furthermore, it was observed that neutral amino acids can affect ‘Abbreviation
used: FSCE,
free-solution
capillary
electrophoresis.
the electrophoretic mobility of peptides as measured by FSCE. In this study an attempt is made to explore further these and other structural factors, such as molecular size, on the electrophoretic mobility of peptides in FSCE with the aim of developing a semiempirical model relating the size and charge of peptides to their electrophoretic mobilities. The model should provide a usable means for predicting the approximate electrophoretic mobilities of peptides and should allow more information about the structure of the peptides to be inferred from the experimental data. As a starting point for the development of a model to relate the electrophoretic mobility (p) of a peptide to its molecular size and charge, we used the classical relationship V -=-
’ =E
9
PI
6xr7’
where g is the electrophoretic mobility, v is the migration velocity, E is the electric field strength, q is the net charge on the peptide, q is the solvent viscosity, and r is the apparent Stokes radius of the molecule. Equation [l] is derived by equating the force exerted on the charged solute by the electrical field to that caused by the viscous drag on the particle, assuming a spherical solute particle. Although Eq. [l] appears straightforward, the values for q and r for a solute in an aqueous electrolyte solution are difficult to evaluate, making Eq. [l] of little practical value. In an aqueous electrolyte solution the values of the net charge on a solute and its apparent size are complicated by the effects of the electrical double layer, the extent of hydration, and, in the case of large polymers, the rigidity of the polymer structure. In an electrolyte solution some fraction of the solute’s charge is shielded by the counter ions in the solution and by the dielectric properties of the solvent itself. Thus, the net charge which is seen by the electric field is less than the actual charge and is a complicated function of not only the charge on the sol0003.2697/89
28 All
$3.00
Copyright 0 1989 by Academic Press, Inc. rights of reproduction in any form reserved.
FREE-SOLUTION TABLE
CAPILLARY
29
ELECTROPHORESIS
1 6.0 -
Sequences, Calculated Charges, and Electrophoretic Mobilities of Peptides Used to Determine the Effect of Charge on Electrophoretic Mobility Calculated charge”
Sequence AFDDI AFDAI AFAAI AFKADNG AFKAI AF KKI LRRASLG RKRSRKE AFKKKKK AKKKKKK KKKKKKK
NG NG NG
0.33 0.37 0.41 1.37 1.41 2.41 2.41 5.31 5.33 6.33 7.33
NG NG
’ All charges
Electrophoretic mobility p X 10e4 (cm’/V. 5)
are calculated
1.03 1.10 1.16 2.17 2.21 3.01 3.00 4.38 4.58 4.95 5.07
assuming
I 1.0
FIG. 2. Measured electrophoretic mobility (a) vs ln(q + 1) of peptides from Fig. 1. See Eq. [4] and Table 1. Y intercept = 2.36 X 1O-5, slope = 2.31 X lo-“, r = 0.998.
pH 2.50.
ute, but also the concentration and composition of the solvent and the counter ions in solution. However, for a given set of solvent conditions, the net charge of a solute should be proportional to its actual charge. For a thorough discussion of electrical double-layer theory see Hiemenz (2). The determination of the molecular size of a polymer molecule in an aqueous solution is made complicated by the effects of hydration and conformational rigidity (3,4). Again, as is the case for the net charge, the conformation and extent of hydration are affected not only by the structure of the solute molecule, but they are also complicated functions of the properties of the solvent and counter ions. Therefore, in order to focus on the properties of the solute, in this study we will only look at one set of solvent conditions, namely an aqueous solution containing 20 mM monosodium citrate buffer at pH 2.50. For a thorough discussion of the effect
6
t
2
3
4
5
6
7
8
q FIG. 1. Measured (9) of model peptides
I 20
In (,?+I)
of buffer pH on the selectivity FSCE see Ref. (1).
1
I
electrophoretic mobility (p) vs calculated having the same size. See Table 1.
charge
MATERIALS
AND
of peptide separations
by
METHODS
The apparatus used in these studies closely resembles that described by Jorgenson and Lukacs (5). A straight length of fused silica capillary (Polymicro Technologies Inc., Phoenix, AZ), 65 cm (45 cm to the detector) long with a 50-pm internal diameter and a 320-pm outside diameter, connected the anodic reservoir with the electrically grounded cathodic reservoir. A high-voltage power supply (O-36 kV, Hipotronics, Brewster, NY) was used to drive the electrophoretic process. Current through the system was measured over a l-kO resistor in the return circuit of the power supply. On-column uv detection at 200 nm was carried out using a modified variable-wavelength HPLC detector (Applied Biosystems Model 783, Foster City, CA). Samples were introduced into the capillary by applying a vacuum to the cathodic electrode reservoir at a specified level for a specified time, while the anodic end of the capillary was immersed in the sample solution. After the sample slug was introduced into the capillary, the anodic end of the capillary was then placed back into the electrophoresis buffer, along with the anodic electrode, and the electrophoretic voltage was applied. The temperature was maintained at 30.0 + O.l"C for all experiments. In order to measure the electrophoretic mobility of a solute by FSCE, one must first take into account the influence of electroendoosmosis on the measurements; electroendoosmosis is the bulk flow of liquid due to the effect of the electrical field on the electrical double layer adjacent to the capillary wall. What is measured in a FSCE experiment is an apparent mobility, PApp, which contains an electroosmotic component and an electrophoretic component. &,pp is defined as
30
GROSSMAN,
COLBURN, TABLE
AND 2
Sequences, Calculated Charges, Sizes, and Measured Electrophoretic the Effect of Size on Electrophoretic Average charge
Sequence
LAUER
Mobilities of Peptides Used to Determine Mobility
Charge”
Size
Electrophoretic mobility p X lo+ (cm’/V . 8)
1.34
ALK SAPLR AFKADNG
1.33 1.32 1.37
3 5 7
3.02 2.41 2.17
2.29
HIR AFKGKNG AGCKNFFWKTFTSC
2.32 2.41 2.14
3 7 13
3.90 3.24 2.14
3.29
RLRFH MEHFRWGK SYSMEHFRWGKPV
3.16 3.32 3.38
5 8 13
3.72 3.24 2.72
5.31
RKRSRKE GFLRRIRPKLK YGGFLRRIRPKLK YVNWLLAQKGKKNDWKHNITQ GGFMTSEKSQTPLVTLFKNAIIKNAY KKGE YGGFMTSEKSQTPLVTLFKNAIIKNA YKKGE
5.31 5.33 5.33 5.28 5.30
7 11 13 21 30
4.38 3.78 3.42 2.81 2.29
5.30
31
2.21
HFRWGKPVGKKRRPVKVYP SYSMEHFRWGKPVGKKRRPVKVYP SYSMEHFRWGKPVGKKRRPVKVYPN GAEDESAEAFPLEF
8.24 8.22 8.06
19 24 39
3.68 3.31 2.51
14.28 14.19 14.15 14.09
24 28 32 38
4.04 3.81 3.63 3.27
8.17
14.18
Proprietary
sequences
a All charges
are calculated
assuming
pH 2.50.
V net PaPP
=
-
E
ut =
-
tv
’
where vnet is the net (measured) migration velocity of the solute peak, E is the electrical field strength, Ld is the length of the capillary from the “sample” end of the capillary to the detector, & is the total length of the capillary, t is the net (measured) migration time of the solute peak, and V is the voltage across the capillary. The relationship between ll~p~ and the actual mobility of the solute, CL,is given by the equation =P+Peo, CLaPP where peOis the electroosmotic component ent mobility and is defined by the equation
[31 of the appar-
- V w-L&t ‘*
E
teoV’
where v, is the electroosmotic velocity and tea is the time required for an uncharged molecule to be carried past the detector window by the electroosmotic flow. One can determine the electroosmotic mobility directly by mea-
suring the migration time of an uncharged solute (where into Eq. [4]. AlternaP = 01, te,, and then substituting tively, one can use an “internal standard’ molecule whose p is known, measure its papp, and then use Eq. [3] to determine pea. If one performs a measurement of p using both methods simultaneously, the same value of LL results from both methods. However, the latter method is often preferable because if pea is very small, tea can be large; thus, the direct measurement can be very time consuming. The majority of the data presented in this work was collected using the internal standard method of measuring p, where the internal standard used was the 13-amino-acid peptide dynorphin 1-13 (p = 3.42 X low4 cm’/V s; see below for experimental conditions). It should be emphasized that p is the only parameter measured by FSCE that has any physical significance with regard to solute structure, and was thus the parameter that was chosen as a correlating parameter to describe the performance of FSCE separations. The experimental conditions for all electrophoresis experiments were as follows: field, 307 V/cm; current, 24 PA; buffer, 20 mM citric acid, pH 2.50; capillary length, 65 cm (45 cm to the detector); capillary internal diame-
FREE-SOLUTION
CAPILLARY
31
ELECTROPHORESIS
6
1
I 0.1
I
I
I
I
I
I
I
I
I
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
In (q+l) "0.43
FIG. 4. Electrophoretic mobility VB Dln(q + l)/r~‘.‘~ for 40 different peptides ranging in aixe from 3 to 39 amino acids and ranging in charge from 0.33 to 14. Y intercept = 2.47 X 10m5, slope = 5.23 X 10m4, r = 0.989. See Tables 1-3.
1.0
I
I
2.0
3.0
I
4.0
In n FIG. 3. Effect of peptide size on electrophoretic mobility for six sets of peptidee, each set containing peptidea of approximately the same charge: (~1 q = 1.34, slope = -0.39, r = -0.997; (Cl) q = 2.29, slope = -0.40, r = -0.956; (A) q = 3.29, slope = -0.32, r = -0.999; (A) q = 5.31, slope = -0.47, r = -0.990; (0) q = 8.17, slope = -0.54, r = -0.999; (0) q = 14.18, slope = -0.47, r = -0.990.
ter, 50 pm; temperature, 30 f O.l”C. A buffer pH of 2.5 was used to reduce electroosmotic flow and to practically eliminate any solute-wall interactions. Both these effects are reduced at low pH because of greatly reduced charge on the fused silica capillary wall at low pH (1). An
TABLE
3
Sequences, Calculated Charges, Sizes, and Measured Electrophoretic Mobilities of Peptides Used to Confirm Eq. [ll]”
sequence YAGFM SYSMEHFRWGKPV’ ILPWKWPWWPWRR GRTGRKNSIHDIL AFKAKNG AFKIKNG AFKWKNG AFKLKNG
Chard 0.38 2.98 3.32 4.38 2.41 2.41 2.41 2.41
Size
Electrophoretic mohilitv p x 10-i kmZ/v.s)
5 13 13 13 I I 7 7
“Also see Tables 1 and 2. * All charges are calculated aaauming pH 2.50. ’ Contains an amidated carboxy terminus and an acetylated terminus.
1.20 2.20 2.67 3.21 3.13 3.04 3.01 3.05
amino
example of a typical electropherogram used to measure p in this study is shown in Fig. 5. The peptides used in this study were synthesized on an automated peptide synthesizer using the solid-phase t-butyloxycarbonyl methodology (Applied Biosystems Model 430A, Foster City, CA) or purchased from Peninsula Laboratories (Belmont, CA) or Sigma Chemical Co. (St. Louis, MO). Buffers and other reagents were of AR grade or comparable quality. Buffer solutions were prepared with water of HPLC grade, and no bacterial growth inhibitors were added. All buffer solutions were adjusted to the appropriate pH with 1 M NaOH or 1 M HCI. RESULTS
AND
DISCUSSION
In order to explore the relationship between a peptide’s electrophoretic mobility and its charge, we investigated a series of 11 peptides all having the same size, as measured by the number of amino acids (n), but differing widely in charge (see Table 1). The method used in this study to calculate the charge on the peptides is a modified version of a method presented by Skoog and Wichman for the calculation of protein isoelectric points based on the pK, of the component amino acid side chain and terminal residues (6). To test whether cc is in fact directly proportional to q as Eq. [l] predicts, the electrophoretic mobility of each of the 11 peptides was plotted against their calculated charge. As can be seen clearly in Fig. 1, while p appears to be a linear function of q at low values of q (~0.51, at higher values of q the relationship between CLand q is clearly nonlinear. It should be noted here that electrophoretic mobility measurements such as those shown in Fig. 1 are repeatable to within 1% when conditions are properly controlled (data not shown). The data in Fig. 1 imply that as the total charge
32
GROSSMAN,
COLBURN,
AND
LAUER
pin = A X l,n(q + 1).
[71
When the data of Fig. 1 are replotted with In(q + 1) as the abscissa, a good linear correlation results (r = 0.998) and, as must be the case, as q approaches 0, P also approaches 0 (see Fig. 2). Furthermore, in the limiting case as q becomes much smaller than 1, dp/dq I ,, becomes constant, as is predicted by Eq. [ 11. That is
&v’clsI,=A/(l+q)~A
7
a
9 TIME
10
11
12
for
qel.
PI
The slope of the curve in Fig.. 2, and thus the value of A, is 2.31 X 10m4. To explore the dependence of electrophoretic mobility on molecular size, we chose to treat the peptide molecule as a classical polymer in solution. To describe the molecular size of the molecule, we used the simplest model available, that of a freely joined chain. In this case, the root-mean-square end-to-end distance (rO), a parameter roughly analogous to a particle radius, is given by the equation
13
(min)
FIG. 6. Electropherogram of endorphin peptides GGFMTSEKSQTPLVTLFKNAIIKNAYKKGE (2-31) and YGGFMTSEKSQTPLVTLFKNAIIKNAYKKGE (l-31) and the N-terminal acetylated endorphin (l-31). The “marker” peak is an internal standard used to measure electroosmotic flow. See Materials and Methods for experimental conditions.
on the analyte molecule increases, the effect of any additional charge on its electrophoretic mobility decreases. While this behavior can be described by very sophisticated electrical double-layer theories (7), this observation can be more simply described by an empirical relation of the form
7-o= BrP5,
PI
where n is the number of monomer units (in this case amino acids) in the chain, and B is the apparent size of an individual monomer unit (4). The value of B is a function of the bond angle between monomer units in the polymer and the quality of the solvent. According to Eq. [ 11, the mobility of a charged particle should be proportional to l/r, or given Eq. [9],
p j q = C/rP5,
WI
where C is a constant of proportionality containing B. To confirm the form of Eq. [lo], we looked at six sets of peptides, where the peptides within each set have ap-
where A is a constant of proportionality. Eq. [5] says that if the size of the peptide is held constant, as q becomes larger the sensitivity of ~1to changes in q becomes smaller. If Eq. [l] is differentiated with respect to q, it shows that the sensitivity of p to q is constant and not a function of q, a conclusion which is not consistent with the data shown in Fig. 1. Although Eq. [5] shows the proper behavior at high values of q, when Eq. [5] is integrated it does not satisfy the boundary condition that, as q goes to 0, p must also go to 0. In order to obtain this behavior, one must modify Eq. [5] as ddd(q
+ 1) In = A x l/h
Integrating Eq. [6] using the boundary q approaches 0, P approaches 0, results
+ 1).
b31
condition that as in the equation
FIG. 6. Effect of the hydrophobicity of substituted neutral amino acids on the electrophoretic mobility of five model peptides having the structure AFK-X-KNG, where X is G, A, I, L, or W. Yintercept = 3.21 X 10m4, slope _ = -2.21 X lo-‘. r = -0.965.
FREE-SOLUTION
CAPILLARY
proximately the same charge but differ in chain length, and each set differs in average charge (see Table 2). By plotting In(n) vs In(p) for each of the six sets of peptides, we were able to confirm the functional form of Eq. [lo]. Each of the curves is plotted in Fig. 3 along with its slope and correlation coefficient. The average value of the slopes of the six curves in Fig. 3 is -0.43 (s = 0.77 (18%)) rather than the value -0.5. Next, we combined Eqs. [7] and [lo], with the value 0.43 replacing 0.50 in Eq. [lo], to give a single relationship which includes both the effects of charge and size on the electrophoretic mobility of the peptides, P=
D ln(q + 1) no.43
3
WI
where D is a constant of proportionality. In order to test the validity of Eq. [ 111, and to determine the value of the constant D, the mobility of 40 different peptides ranging in molecular size from 3 amino acids to 39 amino acids and ranging in charge from 0.33 to 14 (see Tables 1-3) was plotted as a function of ln(q + l)/r~‘.~~. The results are shown in Fig. 4. The plot shows a good linear correlation (r = 0.989) and a Y intercept near 0 (2.47 X 10-5). Given the complexity of the system being described, the quality of this correlation is excellent, although clearly more work is required to thoroughly confirm the generality of this approach, particularly for different solvent systems. One would expect that for different solvent systems the value of the constant D in Eq. [ll] would vary due to the effects of charge shielding and polymer conformation, but that the general form would remain valid. Because the molecular weight of the amino acid monomer units vary, one is not able to express Eq. [ll] in terms of molecular weight. An example of a FSCE separation which highlights the effect of both size and charge on the separation of peptides is given in Fig. 5. In this figure, the effect of a change in size of only 1 amino acid out of 31 is illustrated by the separation of the two endorphin fragments 1-31 and 2-31, both of which nominally have the same charge. The effect of changing charge is demonstrated by resolution of peaks 1-31 and N-AC-1-31, both of which have nominally the same size but differ (in charge) by 1 charge unit. When one attempts to apply Eq. [ll] to predict the electrophoretic mobility of proteins, the predicted values of electrophoretic mobility are consistently lower than the measured values (data not shown). This could be because the conformation of proteins is more tightly folded than is the case for peptides, therefore affecting the value of the constant D in Eq. [ 111.
33
ELECTROPHORESIS
In our previous work, we observed that even uncharged amino acids could affect the electrophoretic mobility of peptides (1). We postulated that this effect was caused by the influence of the proximate neutral amino acid on the local dielectric of the solvent surrounding the dissociated ion pair, and thus the equilibrium. As stated by Conway, “The solvent determines the strength of an acid as much as does the HA bond strength” (3). To test this hypothesis, we studied a series of five peptides, each containing seven amino acids, which differ only in a single neutral amino acid. The neutral amino acid is located between two lysine residues. (The structure of the model peptides used is AFK-X-KNG, where X is G, A, I, L, or W.) The mobility of each of these peptides was measured and then plotted against a measure of the hydrophobicity of the substituted neutral amino acid. The hydrophobicity index that was used was that of Guo et al. (8). As can be seen in Fig. 6, the mobility of the peptides does in fact seem to be related to the hydrophobicity of the substituted amino acid, with the mobility decreasing as hydrophobicity increases. As discussed in our previous work (l), this is the trend that would be expected for a basic dissociation, such as that in lysine, as the local dielectric decreases. This effect would be difficult to include in a relation such as Eq. [ 111 because the position of the hydrophobic group relative to the charged side chains, as well as the total hydrophobic content, must be known. However, the shallow slope of the curve in Fig. 6 indicates that this effect is minor compared to the effects of size and charge on the electrophoretic mobilities of the investigated peptides, and it results in only a weak perturbation of Eq. [ 111. ACKNOWLEDGMENT We thank Dr. John Nickel for his invaluable assistance ing the computer program of Skoog and Wichman.
in modify-
REFERENCES 1. Grossman,
P. D., Wilson,
K. J., Petrie,
G., and Lauer,
H. H. (1988)
Anal. Biochem. 173,265-270. 2. Hiemenz, try, Chap.
P. C. (1977). 11, Dekker,
3. Conway, B. E. (1981). its, Chap. 10, Elsevier, 4. Rodriguez, Graw-Hill, 5. Jorgenson, 6. Skoog,
Principles New York.
of Colloid
Ionic Hydration Amsterdam.
in Chemistry
F. (1982). Principles New York.
of Polymer
J. N., and Lukacs,
K. D. (1983)
B., and Wichman,
A. (1986)
Systems, Science
Chemis-
andBiophysChap.
7, Mc-
222,266-272.
Trends And. C/tern. 6(4), 82.
7. Overbeek, J. (1967) in Electrophoresis l-52, Academic Press, New York. 8. Guo, D., Mant, C., Taneja, R. S. (1986) J. Chromotogr.
and Surface
A. K., Parker, 369,499~517.
(Bier,
M., Ed.),
Vol.
2,
pp.
J. M. R., and Hodges,
BIOCHEMISTRY
179,28-33
(1989)
A Semiempirical Model for the Electrophoretic Mobilities of Peptides in Free-Solution Capillary Electrophoresis Paul D. Grossman, Joel C. Colburn, and Henk Applied Biosystems, Santa Clara, California 95050
Received
September
H. Lauer
21,1988
In this study an attempt is made to explore the effect of a peptide’s size, charge, and hydrophobicity on its electrophoretic mobility (11) as measured by free-solution capillary electrophoresis with the aim of developing a semiempirical model which incorporates these effects. The effects of peptide size (which is measured by the number of amino acids in the polypeptide chain (n)) and charge on p are independently determined by experiment in a single solvent system and combined to give the relationship ~ =
5.23
X
10m41dq no.43
+
1)
+
2
.
4,
x
1o-6
,
LA.11
where the constant 5.23 X 10m4 is postulated to depend on the solvent system used. The form of Eq. [A.11 was confirmed, and the values of the constants 5.23 X 10m4 and 2.47 X 10e6 were determined, by measuring the electrophoretic mobilities of 40 peptides varying in size from 3 to 39 amino acids and varying in charge from 0.33 to 14.0. Furthermore, the effect of noncharged neutral amino acids on mobility was investigated and shown to be present, but only as a minor perturbation on the effects of size and charge. c isss Academic PWS, IDC.
In a previous study from this laboratory, the effect of buffer pH on the electrophoretic mobilities of a series of model peptides using free-solution capillary electrophoresis (FSCE)’ was investigated (1). (The electrophoretic mobility is defined as the net migration velocity of the solute per unit of electrical field strength.) It was shown that the value of the electrophoretic mobilities of the peptides agreed qualitatively with those that would be predicted from calculated charges on the peptides at three different pH values: 2.5, 4.0, and 11.0. Furthermore, it was observed that neutral amino acids can affect ‘Abbreviation
used: FSCE,
free-solution
capillary
electrophoresis.
the electrophoretic mobility of peptides as measured by FSCE. In this study an attempt is made to explore further these and other structural factors, such as molecular size, on the electrophoretic mobility of peptides in FSCE with the aim of developing a semiempirical model relating the size and charge of peptides to their electrophoretic mobilities. The model should provide a usable means for predicting the approximate electrophoretic mobilities of peptides and should allow more information about the structure of the peptides to be inferred from the experimental data. As a starting point for the development of a model to relate the electrophoretic mobility (p) of a peptide to its molecular size and charge, we used the classical relationship V -=-
’ =E
9
PI
6xr7’
where g is the electrophoretic mobility, v is the migration velocity, E is the electric field strength, q is the net charge on the peptide, q is the solvent viscosity, and r is the apparent Stokes radius of the molecule. Equation [l] is derived by equating the force exerted on the charged solute by the electrical field to that caused by the viscous drag on the particle, assuming a spherical solute particle. Although Eq. [l] appears straightforward, the values for q and r for a solute in an aqueous electrolyte solution are difficult to evaluate, making Eq. [l] of little practical value. In an aqueous electrolyte solution the values of the net charge on a solute and its apparent size are complicated by the effects of the electrical double layer, the extent of hydration, and, in the case of large polymers, the rigidity of the polymer structure. In an electrolyte solution some fraction of the solute’s charge is shielded by the counter ions in the solution and by the dielectric properties of the solvent itself. Thus, the net charge which is seen by the electric field is less than the actual charge and is a complicated function of not only the charge on the sol0003.2697/89
28 All
$3.00
Copyright 0 1989 by Academic Press, Inc. rights of reproduction in any form reserved.
FREE-SOLUTION TABLE
CAPILLARY
29
ELECTROPHORESIS
1 6.0 -
Sequences, Calculated Charges, and Electrophoretic Mobilities of Peptides Used to Determine the Effect of Charge on Electrophoretic Mobility Calculated charge”
Sequence AFDDI AFDAI AFAAI AFKADNG AFKAI AF KKI LRRASLG RKRSRKE AFKKKKK AKKKKKK KKKKKKK
NG NG NG
0.33 0.37 0.41 1.37 1.41 2.41 2.41 5.31 5.33 6.33 7.33
NG NG
’ All charges
Electrophoretic mobility p X 10e4 (cm’/V. 5)
are calculated
1.03 1.10 1.16 2.17 2.21 3.01 3.00 4.38 4.58 4.95 5.07
assuming
I 1.0
FIG. 2. Measured electrophoretic mobility (a) vs ln(q + 1) of peptides from Fig. 1. See Eq. [4] and Table 1. Y intercept = 2.36 X 1O-5, slope = 2.31 X lo-“, r = 0.998.
pH 2.50.
ute, but also the concentration and composition of the solvent and the counter ions in solution. However, for a given set of solvent conditions, the net charge of a solute should be proportional to its actual charge. For a thorough discussion of electrical double-layer theory see Hiemenz (2). The determination of the molecular size of a polymer molecule in an aqueous solution is made complicated by the effects of hydration and conformational rigidity (3,4). Again, as is the case for the net charge, the conformation and extent of hydration are affected not only by the structure of the solute molecule, but they are also complicated functions of the properties of the solvent and counter ions. Therefore, in order to focus on the properties of the solute, in this study we will only look at one set of solvent conditions, namely an aqueous solution containing 20 mM monosodium citrate buffer at pH 2.50. For a thorough discussion of the effect
6
t
2
3
4
5
6
7
8
q FIG. 1. Measured (9) of model peptides
I 20
In (,?+I)
of buffer pH on the selectivity FSCE see Ref. (1).
1
I
electrophoretic mobility (p) vs calculated having the same size. See Table 1.
charge
MATERIALS
AND
of peptide separations
by
METHODS
The apparatus used in these studies closely resembles that described by Jorgenson and Lukacs (5). A straight length of fused silica capillary (Polymicro Technologies Inc., Phoenix, AZ), 65 cm (45 cm to the detector) long with a 50-pm internal diameter and a 320-pm outside diameter, connected the anodic reservoir with the electrically grounded cathodic reservoir. A high-voltage power supply (O-36 kV, Hipotronics, Brewster, NY) was used to drive the electrophoretic process. Current through the system was measured over a l-kO resistor in the return circuit of the power supply. On-column uv detection at 200 nm was carried out using a modified variable-wavelength HPLC detector (Applied Biosystems Model 783, Foster City, CA). Samples were introduced into the capillary by applying a vacuum to the cathodic electrode reservoir at a specified level for a specified time, while the anodic end of the capillary was immersed in the sample solution. After the sample slug was introduced into the capillary, the anodic end of the capillary was then placed back into the electrophoresis buffer, along with the anodic electrode, and the electrophoretic voltage was applied. The temperature was maintained at 30.0 + O.l"C for all experiments. In order to measure the electrophoretic mobility of a solute by FSCE, one must first take into account the influence of electroendoosmosis on the measurements; electroendoosmosis is the bulk flow of liquid due to the effect of the electrical field on the electrical double layer adjacent to the capillary wall. What is measured in a FSCE experiment is an apparent mobility, PApp, which contains an electroosmotic component and an electrophoretic component. &,pp is defined as
30
GROSSMAN,
COLBURN, TABLE
AND 2
Sequences, Calculated Charges, Sizes, and Measured Electrophoretic the Effect of Size on Electrophoretic Average charge
Sequence
LAUER
Mobilities of Peptides Used to Determine Mobility
Charge”
Size
Electrophoretic mobility p X lo+ (cm’/V . 8)
1.34
ALK SAPLR AFKADNG
1.33 1.32 1.37
3 5 7
3.02 2.41 2.17
2.29
HIR AFKGKNG AGCKNFFWKTFTSC
2.32 2.41 2.14
3 7 13
3.90 3.24 2.14
3.29
RLRFH MEHFRWGK SYSMEHFRWGKPV
3.16 3.32 3.38
5 8 13
3.72 3.24 2.72
5.31
RKRSRKE GFLRRIRPKLK YGGFLRRIRPKLK YVNWLLAQKGKKNDWKHNITQ GGFMTSEKSQTPLVTLFKNAIIKNAY KKGE YGGFMTSEKSQTPLVTLFKNAIIKNA YKKGE
5.31 5.33 5.33 5.28 5.30
7 11 13 21 30
4.38 3.78 3.42 2.81 2.29
5.30
31
2.21
HFRWGKPVGKKRRPVKVYP SYSMEHFRWGKPVGKKRRPVKVYP SYSMEHFRWGKPVGKKRRPVKVYPN GAEDESAEAFPLEF
8.24 8.22 8.06
19 24 39
3.68 3.31 2.51
14.28 14.19 14.15 14.09
24 28 32 38
4.04 3.81 3.63 3.27
8.17
14.18
Proprietary
sequences
a All charges
are calculated
assuming
pH 2.50.
V net PaPP
=
-
E
ut =
-
tv
’
where vnet is the net (measured) migration velocity of the solute peak, E is the electrical field strength, Ld is the length of the capillary from the “sample” end of the capillary to the detector, & is the total length of the capillary, t is the net (measured) migration time of the solute peak, and V is the voltage across the capillary. The relationship between ll~p~ and the actual mobility of the solute, CL,is given by the equation =P+Peo, CLaPP where peOis the electroosmotic component ent mobility and is defined by the equation
[31 of the appar-
- V w-L&t ‘*
E
teoV’
where v, is the electroosmotic velocity and tea is the time required for an uncharged molecule to be carried past the detector window by the electroosmotic flow. One can determine the electroosmotic mobility directly by mea-
suring the migration time of an uncharged solute (where into Eq. [4]. AlternaP = 01, te,, and then substituting tively, one can use an “internal standard’ molecule whose p is known, measure its papp, and then use Eq. [3] to determine pea. If one performs a measurement of p using both methods simultaneously, the same value of LL results from both methods. However, the latter method is often preferable because if pea is very small, tea can be large; thus, the direct measurement can be very time consuming. The majority of the data presented in this work was collected using the internal standard method of measuring p, where the internal standard used was the 13-amino-acid peptide dynorphin 1-13 (p = 3.42 X low4 cm’/V s; see below for experimental conditions). It should be emphasized that p is the only parameter measured by FSCE that has any physical significance with regard to solute structure, and was thus the parameter that was chosen as a correlating parameter to describe the performance of FSCE separations. The experimental conditions for all electrophoresis experiments were as follows: field, 307 V/cm; current, 24 PA; buffer, 20 mM citric acid, pH 2.50; capillary length, 65 cm (45 cm to the detector); capillary internal diame-
FREE-SOLUTION
CAPILLARY
31
ELECTROPHORESIS
6
1
I 0.1
I
I
I
I
I
I
I
I
I
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
In (q+l) "0.43
FIG. 4. Electrophoretic mobility VB Dln(q + l)/r~‘.‘~ for 40 different peptides ranging in aixe from 3 to 39 amino acids and ranging in charge from 0.33 to 14. Y intercept = 2.47 X 10m5, slope = 5.23 X 10m4, r = 0.989. See Tables 1-3.
1.0
I
I
2.0
3.0
I
4.0
In n FIG. 3. Effect of peptide size on electrophoretic mobility for six sets of peptidee, each set containing peptidea of approximately the same charge: (~1 q = 1.34, slope = -0.39, r = -0.997; (Cl) q = 2.29, slope = -0.40, r = -0.956; (A) q = 3.29, slope = -0.32, r = -0.999; (A) q = 5.31, slope = -0.47, r = -0.990; (0) q = 8.17, slope = -0.54, r = -0.999; (0) q = 14.18, slope = -0.47, r = -0.990.
ter, 50 pm; temperature, 30 f O.l”C. A buffer pH of 2.5 was used to reduce electroosmotic flow and to practically eliminate any solute-wall interactions. Both these effects are reduced at low pH because of greatly reduced charge on the fused silica capillary wall at low pH (1). An
TABLE
3
Sequences, Calculated Charges, Sizes, and Measured Electrophoretic Mobilities of Peptides Used to Confirm Eq. [ll]”
sequence YAGFM SYSMEHFRWGKPV’ ILPWKWPWWPWRR GRTGRKNSIHDIL AFKAKNG AFKIKNG AFKWKNG AFKLKNG
Chard 0.38 2.98 3.32 4.38 2.41 2.41 2.41 2.41
Size
Electrophoretic mohilitv p x 10-i kmZ/v.s)
5 13 13 13 I I 7 7
“Also see Tables 1 and 2. * All charges are calculated aaauming pH 2.50. ’ Contains an amidated carboxy terminus and an acetylated terminus.
1.20 2.20 2.67 3.21 3.13 3.04 3.01 3.05
amino
example of a typical electropherogram used to measure p in this study is shown in Fig. 5. The peptides used in this study were synthesized on an automated peptide synthesizer using the solid-phase t-butyloxycarbonyl methodology (Applied Biosystems Model 430A, Foster City, CA) or purchased from Peninsula Laboratories (Belmont, CA) or Sigma Chemical Co. (St. Louis, MO). Buffers and other reagents were of AR grade or comparable quality. Buffer solutions were prepared with water of HPLC grade, and no bacterial growth inhibitors were added. All buffer solutions were adjusted to the appropriate pH with 1 M NaOH or 1 M HCI. RESULTS
AND
DISCUSSION
In order to explore the relationship between a peptide’s electrophoretic mobility and its charge, we investigated a series of 11 peptides all having the same size, as measured by the number of amino acids (n), but differing widely in charge (see Table 1). The method used in this study to calculate the charge on the peptides is a modified version of a method presented by Skoog and Wichman for the calculation of protein isoelectric points based on the pK, of the component amino acid side chain and terminal residues (6). To test whether cc is in fact directly proportional to q as Eq. [l] predicts, the electrophoretic mobility of each of the 11 peptides was plotted against their calculated charge. As can be seen clearly in Fig. 1, while p appears to be a linear function of q at low values of q (~0.51, at higher values of q the relationship between CLand q is clearly nonlinear. It should be noted here that electrophoretic mobility measurements such as those shown in Fig. 1 are repeatable to within 1% when conditions are properly controlled (data not shown). The data in Fig. 1 imply that as the total charge
32
GROSSMAN,
COLBURN,
AND
LAUER
pin = A X l,n(q + 1).
[71
When the data of Fig. 1 are replotted with In(q + 1) as the abscissa, a good linear correlation results (r = 0.998) and, as must be the case, as q approaches 0, P also approaches 0 (see Fig. 2). Furthermore, in the limiting case as q becomes much smaller than 1, dp/dq I ,, becomes constant, as is predicted by Eq. [ 11. That is
&v’clsI,=A/(l+q)~A
7
a
9 TIME
10
11
12
for
qel.
PI
The slope of the curve in Fig.. 2, and thus the value of A, is 2.31 X 10m4. To explore the dependence of electrophoretic mobility on molecular size, we chose to treat the peptide molecule as a classical polymer in solution. To describe the molecular size of the molecule, we used the simplest model available, that of a freely joined chain. In this case, the root-mean-square end-to-end distance (rO), a parameter roughly analogous to a particle radius, is given by the equation
13
(min)
FIG. 6. Electropherogram of endorphin peptides GGFMTSEKSQTPLVTLFKNAIIKNAYKKGE (2-31) and YGGFMTSEKSQTPLVTLFKNAIIKNAYKKGE (l-31) and the N-terminal acetylated endorphin (l-31). The “marker” peak is an internal standard used to measure electroosmotic flow. See Materials and Methods for experimental conditions.
on the analyte molecule increases, the effect of any additional charge on its electrophoretic mobility decreases. While this behavior can be described by very sophisticated electrical double-layer theories (7), this observation can be more simply described by an empirical relation of the form
7-o= BrP5,
PI
where n is the number of monomer units (in this case amino acids) in the chain, and B is the apparent size of an individual monomer unit (4). The value of B is a function of the bond angle between monomer units in the polymer and the quality of the solvent. According to Eq. [ 11, the mobility of a charged particle should be proportional to l/r, or given Eq. [9],
p j q = C/rP5,
WI
where C is a constant of proportionality containing B. To confirm the form of Eq. [lo], we looked at six sets of peptides, where the peptides within each set have ap-
where A is a constant of proportionality. Eq. [5] says that if the size of the peptide is held constant, as q becomes larger the sensitivity of ~1to changes in q becomes smaller. If Eq. [l] is differentiated with respect to q, it shows that the sensitivity of p to q is constant and not a function of q, a conclusion which is not consistent with the data shown in Fig. 1. Although Eq. [5] shows the proper behavior at high values of q, when Eq. [5] is integrated it does not satisfy the boundary condition that, as q goes to 0, p must also go to 0. In order to obtain this behavior, one must modify Eq. [5] as ddd(q
+ 1) In = A x l/h
Integrating Eq. [6] using the boundary q approaches 0, P approaches 0, results
+ 1).
b31
condition that as in the equation
FIG. 6. Effect of the hydrophobicity of substituted neutral amino acids on the electrophoretic mobility of five model peptides having the structure AFK-X-KNG, where X is G, A, I, L, or W. Yintercept = 3.21 X 10m4, slope _ = -2.21 X lo-‘. r = -0.965.
FREE-SOLUTION
CAPILLARY
proximately the same charge but differ in chain length, and each set differs in average charge (see Table 2). By plotting In(n) vs In(p) for each of the six sets of peptides, we were able to confirm the functional form of Eq. [lo]. Each of the curves is plotted in Fig. 3 along with its slope and correlation coefficient. The average value of the slopes of the six curves in Fig. 3 is -0.43 (s = 0.77 (18%)) rather than the value -0.5. Next, we combined Eqs. [7] and [lo], with the value 0.43 replacing 0.50 in Eq. [lo], to give a single relationship which includes both the effects of charge and size on the electrophoretic mobility of the peptides, P=
D ln(q + 1) no.43
3
WI
where D is a constant of proportionality. In order to test the validity of Eq. [ 111, and to determine the value of the constant D, the mobility of 40 different peptides ranging in molecular size from 3 amino acids to 39 amino acids and ranging in charge from 0.33 to 14 (see Tables 1-3) was plotted as a function of ln(q + l)/r~‘.~~. The results are shown in Fig. 4. The plot shows a good linear correlation (r = 0.989) and a Y intercept near 0 (2.47 X 10-5). Given the complexity of the system being described, the quality of this correlation is excellent, although clearly more work is required to thoroughly confirm the generality of this approach, particularly for different solvent systems. One would expect that for different solvent systems the value of the constant D in Eq. [ll] would vary due to the effects of charge shielding and polymer conformation, but that the general form would remain valid. Because the molecular weight of the amino acid monomer units vary, one is not able to express Eq. [ll] in terms of molecular weight. An example of a FSCE separation which highlights the effect of both size and charge on the separation of peptides is given in Fig. 5. In this figure, the effect of a change in size of only 1 amino acid out of 31 is illustrated by the separation of the two endorphin fragments 1-31 and 2-31, both of which nominally have the same charge. The effect of changing charge is demonstrated by resolution of peaks 1-31 and N-AC-1-31, both of which have nominally the same size but differ (in charge) by 1 charge unit. When one attempts to apply Eq. [ll] to predict the electrophoretic mobility of proteins, the predicted values of electrophoretic mobility are consistently lower than the measured values (data not shown). This could be because the conformation of proteins is more tightly folded than is the case for peptides, therefore affecting the value of the constant D in Eq. [ 111.
33
ELECTROPHORESIS
In our previous work, we observed that even uncharged amino acids could affect the electrophoretic mobility of peptides (1). We postulated that this effect was caused by the influence of the proximate neutral amino acid on the local dielectric of the solvent surrounding the dissociated ion pair, and thus the equilibrium. As stated by Conway, “The solvent determines the strength of an acid as much as does the HA bond strength” (3). To test this hypothesis, we studied a series of five peptides, each containing seven amino acids, which differ only in a single neutral amino acid. The neutral amino acid is located between two lysine residues. (The structure of the model peptides used is AFK-X-KNG, where X is G, A, I, L, or W.) The mobility of each of these peptides was measured and then plotted against a measure of the hydrophobicity of the substituted neutral amino acid. The hydrophobicity index that was used was that of Guo et al. (8). As can be seen in Fig. 6, the mobility of the peptides does in fact seem to be related to the hydrophobicity of the substituted amino acid, with the mobility decreasing as hydrophobicity increases. As discussed in our previous work (l), this is the trend that would be expected for a basic dissociation, such as that in lysine, as the local dielectric decreases. This effect would be difficult to include in a relation such as Eq. [ 111 because the position of the hydrophobic group relative to the charged side chains, as well as the total hydrophobic content, must be known. However, the shallow slope of the curve in Fig. 6 indicates that this effect is minor compared to the effects of size and charge on the electrophoretic mobilities of the investigated peptides, and it results in only a weak perturbation of Eq. [ 111. ACKNOWLEDGMENT We thank Dr. John Nickel for his invaluable assistance ing the computer program of Skoog and Wichman.
in modify-
REFERENCES 1. Grossman,
P. D., Wilson,
K. J., Petrie,
G., and Lauer,
H. H. (1988)
Anal. Biochem. 173,265-270. 2. Hiemenz, try, Chap.
P. C. (1977). 11, Dekker,
3. Conway, B. E. (1981). its, Chap. 10, Elsevier, 4. Rodriguez, Graw-Hill, 5. Jorgenson, 6. Skoog,
Principles New York.
of Colloid
Ionic Hydration Amsterdam.
in Chemistry
F. (1982). Principles New York.
of Polymer
J. N., and Lukacs,
K. D. (1983)
B., and Wichman,
A. (1986)
Systems, Science
Chemis-
andBiophysChap.
7, Mc-
222,266-272.
Trends And. C/tern. 6(4), 82.
7. Overbeek, J. (1967) in Electrophoresis l-52, Academic Press, New York. 8. Guo, D., Mant, C., Taneja, R. S. (1986) J. Chromotogr.
and Surface
A. K., Parker, 369,499~517.
(Bier,
M., Ed.),
Vol.
2,
pp.
J. M. R., and Hodges,