In the Classroom
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A Graphical Approach to Determine the Isoelectric Point and Charge of Small Peptides from pH 0 to 14 Gabriele D’Andrea* and Giuseppe Di Nicolantonio Department of Biomedical Sciences and Technologies, University of L’Aquila, Coppito 2, I-67100 L’Aquila, Italy; *
[email protected] Background Depending on the pH value, many biomolecules may have both negatively and positively charged groups and are consequently referred to as ampholytes (amphoteric electrolytes) (1). Examples of well-studied amphoteric biomolecules of great interest include amino acids, peptides, and proteins. Amino acids possess an α-amino group (except proline, which is an imino acid) and an α-carboxyl group, and are ionized at all pH values as shown below: R α
CH
+
R
pKa1
α
NH3
+
pKa2
NH3
COO−
COOH
net positive charge
CH
R α
CH2 α
CH
NH2
net negative charge
1.95
It is noteworthy that a neutral species never exists in solution at any time. Moreover, at low pH values, an amino acid exists as a cation, and at high pH values, as an anion. At a particular intermediate pH, the amino acid carries no net charge although it is still ionized, and is called a zwitterion (or dipolar ion). The pH at which the zwitterion predominates in aqueous solution is referred to as the isoionic point, since the total number of negative charges is equal to the total number of positive charges (3). In the case of very small particles such as amino acids, the isoionic point is equal to the pI, that is, the pH value at which the net electric charge of an elementary entity is zero (4 ). As a consequence, in electrophoresis there is no net motion of the particles in an electric field at the pI. The numerical value of this pH for a monoamino, monocarboxyl amino acid is related to its acid strength (pKa value) by the equation pI = 1⁄2(pKa + pKa ) 2
where pKa and pKa are equal to the negative logarithm of the acid dissociation constants, Ka and Ka . In the case of glycine, or Gly (the three-letter designation for the amino acids will be used hereafter), pKa and pKa are 2.34 and 9.58, respectively, so that the isoionic or isoelectric point is 5.96 (pK values are from ref 2). At pH values below the pI, the cation and zwitterion will coexist in equilibrium in a ratio determined by the Henderson–Hasselbalch equation, whereas at higher pH values the zwitterion and anion will coexist in equilibrium. For dicarboxylic amino acids such as Asp, the ionization pattern is different owing to the presence of a second carboxyl group: 2
2
1
972
CH
3.71
α
cation (1 net positive charge)
CH
2
COO−
pKa3
CH2
+
NH3
COO−
CH2
+
NH3
9.66
α
COO−
zwitterion pH 2.83 (isoionic point)
CH
NH2
COO−
anion (1 net negative charge)
anion (2 net negative charges)
In this case, the zwitterion will predominate in aqueous solution at a pH determined by pKa and pKa , and the pI is the mean of pKa and pKa (pI = 2.83). In the case of diamino acids such as Lys, the pI is the mean of pKa and pKa (pI = 9.92): 1
2
2
3
2
+
+
+
N H3
N H3
N H3
CH
pKa1
(CH2)4
+
NH3
COOH
1
α
COOH
α
increasing pH
1
pKa2
CH2
+
NH3
(CH2)4
1
COO−
COOH
pKa1
1
CH
COO−
zero net charge ("zwitterion")
COOH
cation (2 net positive charges)
2.15
α
CH COO
pKa2
(CH2)4
+
NH3 −
cation (1 net positive charge)
9.16
α
CH COO
pKa3
NH2 −
zwitterion pH 9.92 (isoionic point)
N H2 (CH2)4 α
10.67 CH
NH2
COO−
anion (1 net negative charge)
Ionizable side groups other than amino or carboxylic acids exist in amino acids and are capable of ionizing in the physiological range. Such groups include the imidazoyl group of His (pKR = 6.04), the sulfhydryl group of Cys (pKR = 8.14), the phenolic group of Tyr (pKR = 10.10), and the guanidino group of Arg (pKR = 12.10), which may also contribute to the overall ionization of a protein. Posttranslational modifications, such as the addition of a phosphate group to a Tyr, Ser, or Thr, will further alter the ionizability of the protein. It is clear that the state of ionization of the main groups of amino acids (acidic, basic, neutral) will vary with pH. Moreover, even within a given group there will be minor differences due to the precise nature of the R group. These differences are dramatically important in the electrophoretic and ion-exchange chromatographic separation of mixtures of amino acids such as those present in a protein hydrolysate. With the exception of the two terminal amino acids, all the α-carboxyl and α-amino groups of a peptide are involved in peptide bonds and are not ionizable. However, amino, carboxyl, imidazoyl, sulfhydryl, phenolic, and guanidino groups in the side chains are free to ionize. The isoionic point of large peptides and proteins, unlike that of an amino acid, is generally not identical to the isoelectric point. In fact, for real macroions in aqueous solution the electric field experienced by the macromolecule will differ appreciably from that which we measure as being imposed by the
Journal of Chemical Education • Vol. 79 No. 8 August 2002 • JChemEd.chem.wisc.edu
In the Classroom 4
5
pI =
3
1 2
4
(pK3 + pK4)
pI =
1 2
(pK4 + pK5)
3
2
q
q
2 1
1 0
0 -1
-1
-2
-2 0
1
2
3
4
5
6
n Ionizable Group n /pK Value Lys carboxyl 1/2.15 Asp β - carboxyl 2/3.71 His imadazoyl 3/6.04 Gly amino 4/9.58 Lys ε - amino 5/10.67
0
1
2
3
4
5
6
7
n Ionizable Group n /pK Value Lys carboxyl 1/2.15 Asp β - carboxyl 2/3.71 His imadazoyl 3/6.04 Gly amino 4/9.58 Lys ε - amino 5/10.67 Arg guanidino 6/12.10
Figure 1. Plot of q vs n for the peptide Gly-His-Val-Ile-Asp-Lys (qi = +3 and qj = ᎑2) in the range from the first (lowest) pK value to the fifth (highest) pK value. This graph also applies for any other peptide that has the same qi and qj values (+3 and ᎑2, respectively). Moreover, for pI determination, it is valid for all other peptides that have the same qi value (+3) and a different qj value.
Figure 2. Plot of q vs n for the peptide Gly-His-Ile-Asp-Arg-Lys (qi = +4 and qj = ᎑2) in the range from the first (lowest) pK value to the sixth (highest) pK value. This graph also applies for any other peptide that has the same qi and qj values (+4 and ᎑2, respectively). Moreover, for pI determination, it is valid for all other peptides that have the same qi value (+4) and a different qj value.
electrodes (5). In simpler words, as an idealized model, very small particles are fully seen by the electric field; by contrast, macroions are seen only at their surface and not inside (6 ). However, the knowledge of the peptide pI value and the peptide charge value in the pH range from 0 to 14 is of great importance in biology and medicine. Many separation and purification techniques (e.g., ion-exchange chromatography, electrophoresis, isoelectric (differential) precipitation, chromatofocusing, isoelectric focusing) rely upon both pI and charge values of a peptide. Moreover, capillary electrophoresis (7 ), transdermal iontophoretic administration (8), dipeptide– tripeptide transport systems (9), and epitope binding (10) are just some recent examples where the pI value of the peptide as well as its charge plays a crucial role.
2. At a very high value of pH, theoretically pH 14, the negative charge of the peptide q j equals the sum of the ionizable carboxyl groups, the sulfhydryl groups of Cys, and the phenolic groups of Tyr, designated as j.
Rationale As a teacher in biochemistry I (G. D’A.) have always found that students learn how to determine the pI in neutral, diamino, or dicarboxyl amino acids when all pK values are furnished, but find it difficult to ascertain the pI values of di-, tri-, tetra-, penta-, hexa-, or septapeptides. The first problem relates to the presence in peptides of one or more ionizable groups other than those at the N and C termini, and recognizing the analogy between the peptide and the corresponding diamino or dicarboxyl amino acids. The following reminders and rules are helpful. 1. At a very low pH value, theoretically pH 0, the net positive charge of the peptide, qi, is the sum of the number of ionizable amino groups and the number of imidazoyl groups of His residues and the guanidino groups of Arg, designated as i.
3. At the lowest (first) pK value (pKa1) the peptide possesses a net charge of (qi – 0.5) units. At the subsequent (second) pK value (pKa2) the net charge equals (qi – 1.5). At the third lowest pK value (pKa3) the net charge equals (qi – 2.5), and so on. In other words, at the nth pK value (pKan) the peptide has a net charge of [qi – (n – 0.5)]. At the highest (last) pK value the peptide has a net charge of (q j + 0.5) units. 4. The graph of q (the charge of the peptide at any pH value) versus n (the pK values according to positive integers [n]) gives a line that is valid in the range from the first to the last pK value and that is described by the following equation: q = ᎑ n + (qi + 0.5)
(1)
5. When the peptide possesses a zero charge (q = 0), n = (qi + 0.5) = pI. Since the pK values are ordered according to natural integer numbers whereas the pI is always given by qi (real positive integer) plus one-half of a unit, that is, (qi + 0.5), it is more meaningful to mathematically determine the pI value as the mean of two pK values,
(2)
pI = 1/2(pKni + pKni+1) where ni is, in absolute value, equal to qi, and coincides with i.
Then, in eq 2, the number of positive charges that the peptide possesses at a very low pH value, theoretically pH 0
JChemEd.chem.wisc.edu • Vol. 79 No. 8 August 2002 • Journal of Chemical Education
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In the Classroom 4
2
solid line a 3
1
pI =
1 2
(pK2 + pK3) dotted line
2
0
q
q
pI 1
-1 0
-2
-1
-3
solid line b
-2
0
1
2
3
4
5
6
0
1
2
3
4
Ionizable Group n /pK Value Lys carboxyl
1/2.15
Asp β - carboxyl
2/3.71
Gly amino
3/9.58
Tyr phenolic
4/10.10
Lys ε - amino
5/10.67
Figure 3. Plot of q vs n for the peptide Gly-Tyr-Ile-Asp-Lys (qi = +2 and qj = ᎑3) in the range from the first (lowest) pK value to the fifth (highest) pK value. This graph also applies for any other peptide that has the same qi and qj values (+2 and ᎑3, respectively). Moreover, for pI determination, it is valid for all other peptides that have the same qi value (+2) and a different qj value.
6
Figure 4. Plot of q vs n for the peptide Gly-His-Val-Ile-Asp-Lys (as in Fig. 1). The dotted line is as shown in Fig. 1. The solid line a, the dotted line, and the solid line b allow the determination of the charge at any pH value, and vice versa. This complete graph also applies for any other peptide that has the same qi and qj values (+3 and ᎑2, respectively).
to n = 6). In fact, since line a obeys the equation q = ᎑ 0.5n + qi
(i.e., qi), dictates the relationship to the peptide pI value. Surprisingly, neither qj nor j is directly involved in determining the pI value, although the parameter n can be linked in a certain way to both i and j. To mention some examples, for the hexapeptide GlyHis-Val-Ile-Asp-Lys where qi = +3 (Gly amino group, His imidazoyl group, Lys ε-amino group) and i = 3, it follows from eq 2 that pI = 1⁄2 (pK3 + pK4), where pK3 corresponds to the pK value of the His imidazoyl group (6.04) and pK4 corresponds to the pK value of the Gly amino group (9.58). Then, pI = 1⁄2 (6.04 + 9.58) = 7.81, as observed in Figure 1. For the peptide Gly-His-Ile-Asp-Arg-Lys where qi = +4 (imidazoyl group of His, amino group of Gly, ε-amino group of Lys, and guanidino group of Arg) and i = 4, the pI = 1⁄ (pK + pK ), where pK = 9.58 (amino group of Gly) and 4 5 4 2 pK5 = 10.67 (ε-amino group of Lys). Then, pI = 1⁄2 (9.58 + 10.67) = 10.125 (Fig. 2). Finally, in the case of Gly-Tyr-Ile-Asp-Lys where qi = +2 (Gly amino group, Lys ε-amino group), and i = 2, the pI is given by the mean of the second and third pK values (βcarboxyl group of Asp and amino group of Gly, respectively); that is, pI = 1⁄2 (pK2 + pK3), where pK2 corresponds to 3.71 and pK3 corresponds to 9.58. Then, pI = 1⁄2 (3.71 + 9.58) = 6.645 (Fig. 3). By assuming that pH = 0 for n = 0 and pH = 14 for (nh + 1), (where nh indicates the nth pK with the highest value), some graphical extensions of the above observations allow determination of the peptide charge in the region from pH 0 to the first (lowest) pK value (Fig. 4, solid line a; in the region from n = 0 to n = 1) and in the region from the last (highest) pK value to pH 14 (Fig. 4, solid line b, in the region from n = 5
(3)
and line b is given by the relationship q = ᎑ 0.5n + [qj + 0.5(nh + 1)]
974
5
n
n
(4)
it possible in these two peculiar regions to graphically determine the charge of a peptide at any pH value, and vice versa. It should be stressed that eqs 1, 3, and 4 are valid only in their specific range: that is, from the lowest to the highest pK value, from pH 0 to the lowest pK value, and from the highest pK value to pH 14, respectively. Interestingly, peptides that have the same qi and qj values will show the same four linear equations reported above, although the actual pI value determined analytically could be different. Moreover, peptides that have the same qi value but a different qj value will all show the same graphical value of pI (n intercept). However, since n values are reported in a series of integer positive numbers, their correspondence with the real pK values is not linear and one should keep this aspect in mind to better determine graphically, on a case-by-case basis, the relationship between peptide charge and pH value. A better understanding of this crucial point based on the data corresponding to the peptide reported in Figure 1 is observed in Figure 5, which shows a graph of q versus pK, and in this case the x intercept directly gives the real value of pI. For completeness, it should be underscored that eqs 1 and 2 both can be expressed also as a function of nh, qj, and nj (where nj = nh + qj), instead of n, qi, and ni (or i ). Now, what happens if the peptide, theoretically, has two or more ionizable groups with identical assigned pK values? In this peculiar case the pK values are considered as coming from only one amino acid residue. Thus, in the theoretical hypothesis that all the His, Tyr, or Asp residues have the same pK value, the peptide Gly-His-Tyr-Ile-Asp-Lys will analytically give the same pI value as the following one: Gly-His(n)Tyr(n)-Ile-Asp(n)-Lys. Of course, owing to the different electrostatic interactions and the sequence position caution
Journal of Chemical Education • Vol. 79 No. 8 August 2002 • JChemEd.chem.wisc.edu
In the Classroom 4 1 2 1 2
pI =
3 2
(pK3 + pK4) = (6.04 + 9.58) =
q
7.81 1 0 -1 -2 0
2
4
6
8
10
12
14
pK Ionizable Group n /pK Value Lys carboxyl
1/2.15
Asp β - carboxyl
2/3.71
His imadazoyl
3/6.04
Gly amino
4/9.58
Lys ε - amino
5/10.67
Figure 5. Plot of q vs pK for the peptide Gly-His-Val-Ile-Asp-Lys (as in Fig. 1) in the pH range from 0 to 14. The trend of this graph applies only for this peptide; other peptides that have the same qi and qj values (+3 and ᎑2, respectively), but a different pK value, will show a different trend.
should be exercised, since the pK values of amino acids differ slightly from the ones reported in standard tables. Furthermore, an additional complexity arises when amino acids are altered by posttranslational modifications (e.g., phosphorylation of Ser or Tyr, or acetylation or methylation of Lys). It should be pointed out that the prediction of the properties in aqueous solutions of a simple ion such as Na+ at more than infinitesimal concentrations is a complex problem that has not yet been satisfactorily solved despite intense efforts by some of the most respected theoretical chemists (11). In fact, using the mechanical rules reported here will not provide a reasonable estimate of the actual pI of a complex polyelectrolyte such as a small peptide, thus the pI must still be determined experimentally. However, as an arithmetic exercise, given the pK values for each ionizable group, all four equations apply. Conclusions In determining the pI of small peptides, students often find some difficulties once they know the pK values of all ionizable groups. In this paper, fundamental reminders and rules are provided, and general equations are given to graphically determine the pI value and the charge of small peptides in the pH range from 0 to 14. A noteworthy aspect of eq 1 is that it is possible to determine the relationship between peptide charge and the pH value in the range from the first (lowest) pK value to the last (highest) pK value. Interestingly, eq 2 shows that the number of positive charges the peptide possesses at a very low pH value, theoretically pH 0 (i.e., qi) dictates the relationship with the peptide pI
value. Conversely, both the negative charge of the peptide at very high value of pH, theoretically pH 14 (qj), and the absolute number of ionizable carboxyl groups of Asp and Glu, sulfhydryl groups of Cys, and phenolic groups of Tyr (j) do not need to be accounted for in eq 1. Moreover, eqs 3 and 4 allow determination of the peptide charge in two peculiar pH regions not covered by eq 1. Calculations are not so strictly correct for known pK values of single amino acids, although for small peptides the differences involved are not remarkable. However, the larger the peptide, the more difficult it is to know the correct pK values corresponding to all specific ionizable groups. Additional difficulties arise when modified amino acids (e.g., phosphorylated Ser or Tyr, or acetylated or methylated Lys) are present in the peptide. Finally, in the present paper an opportunity is given to better assess and determine both the peptide pI and charge value in the pH range from 0 to 14. Acknowledgment This work was supported by MURST (Ministero dell’Università e della Ricerca Scientifica, Rome, Italy). W
Supplemental Material
A program list written in Pascal by which it is possible to determine the peptide pI and its charge in the pH range 0 to 14, once the main peptide parameters are inserted, is available in this issue of JCE Online. As an arithmetic exercise the program can accept up to 20 pK values. All equations included in the program are based upon a graph of q versus pK. Literature Cited 1. Voet, D.; Voet, J. G. Biochemistry, 2nd ed.; Wiley: New York, 1995; p 57. 2. Handbook of Chemistry and Physics, 79th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1998; Section 7, p 1. 3. Wilson, K.; Walker, J. M. Principles and Techniques of Practical Biochemistry, 4th ed.; Cambridge University Press: Cambridge, 1994; p 164. 4. Mc Naught, A. D.; Wilkinson, A. IUPAC Compendium of Chemical Terminology. The Gold Book, 2nd ed.; Blackwell Science: Oxford, 1997. 5. Van Holde, K. E. Physical Biochemistry, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1985; p 139. 6. Dryer, R. L.; Gene, F. L. Experimental Biochemistry, Oxford University Press: Oxford, 1989; pp 112–113. 7. Righetti, P. G.; Ghelfi, C.; Bossi, A.; Olivieri, E.; Castelletti, L.; Vergola, B.; Stoyanov, A. V. Electrophoresis 2000, 21, 4046–4053. 8. Marro, D.; Guy, R. H.; Begona Delgado-Charro, M. J. Controlled Release 2001, 70, 213–217. 9. Sanz, Y.; Lanfermeijer, F. C.; Konings, W. N.; Poolman, B. Biochemistry 2000, 39, 4855–4862. 10. Bendahmane, M.; Koo, M.; Karrer, E.; Beachy, R. N. J. Mol. Biol. 1999, 290, 9–20. 11. Honig, B.; Nichols, A. Science 1995, 268, 1144–1149.
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