Anal. Chem. 2006, 78, 5394-5402
Determination and Modeling of Peptide pKa by Capillary Zone Electrophoresis Raphae 1 l Plasson† and Herve´ Cottet*
Laboratoire Organisation Mole´ culaire, EÄ volution et Mate´ riaux Fluore´ s, Equipe Dynamique des Syste` mes Biomole´ culaires Complexes, UMR CNRS 5073, CC017, Universite´ de Montpellier 2, Place Euge` ne Bataillon, 34095 Montpellier Cedex, France
In this work, pKa values of polyglycines, poly(L-alanines), and poly(L-valines) with a number of residues up to 10 were determined in different conditions of ionic strength (10 and 100 mM) and temperature (from 15 to 60 °C) by capillary electrophoresis. For each peptide family, the pKa values were modeled as a function of the number of residues, the temperature, and the ionic strength. Next, using this set of experimental data, a semiempirical model was developed in order to predict pKa values for any oligopeptide having neutral lateral chains. This model only needs, as input parameters, the number of residues and the pKa of terminal amino acids in their free form. It can predict the peptide pKa values at a given ionic strength and temperature. Comparisons with experimental data from the literature demonstrated that the prediction was possible with a standard deviation of ∼0.1 pH unit. Capillary zone electrophoresis is a widely used analytical tool for the separation of biomolecules such as peptides1-3 or proteins.4 Physicochemical characteristics of the solutes (charge, pKa values, ionic mobilities, frictional coefficient) can be derived from the determination of the electrophoretic mobility as a function of the experimental parameters (pH, temperature, ionic strength, nature of the solvent).5,6 The determination of pKa by CE is based on the study of the variation of effective electrophoretic mobilities as a function of the pH for given conditions of temperature and ionic strength.7-9 This method has been extensively used for the * Corresponding author. Tel: +33-4-6714-3427. Fax: +33-4-6763-1046. Email:
[email protected]. † Present address: Department of Applied Chemistry, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohamashi, 2238522 Japan. Tel: +81-90-6523-9022. Fax: +81-45-566-1560. (1) McLaughlin, G. M.; Anderson, K. W. In High Performance Capillary Electrophoresis: Theory, Techniques and Applications; Khaledi, M. G., Ed.; John Wiley: New York, 1998; pp 637-681. (2) Messana, I.; Rosseti, D. V.; Cassiano, L.; Misiti, F.; Giardina, B.; Castagnola, M. J. Chromatogr.. B 1997, 699, 149-171. (3) Kasicka, V. Electrophoresis 2003, 24, 4013-4046. (4) Hutterer, K.; Dolnik, V. Electrophoresis 2003, 24, 3998-4012. (5) Righetti, P. G. In High Performance Capillary Electrophoresis: Theory, Techniques and Applications; Khaledi, M. G., Ed.; John Wiley: New York, 1998; pp 973-998. (6) Castagnola, M.; Cassiano, L.; Messana, I.; Nocca, G.; Rabino, R.; Rosseti, D. V.; Giardina, B. J. Chromatogr., B 1994, 656, 87-97. (7) Gluck, S. J.; Cleveland, J. A. J. Chromatogr., A 1994, 680, 43-48. (8) Gluck, S. J.; Cleveland, J. A. J. Chromatogr., A 1994, 680, 49-56. (9) Beckers, J. L.; Everaerts, F. M.; Ackermans, M. T. J. Chromatogr. 1991, 537, 407-428.
5394 Analytical Chemistry, Vol. 78, No. 15, August 1, 2006
determination of dissociation constant of different analytes such as pharmaceutical compounds (see, for example, ref 10), amino acids,11 and peptides.3 Sanz-Nebot et al. determined the pKa of seven peptides in both aqueous13 and hydroorganic14,15 conditions by CE. Psurek and Scriba studied the dissociation constants of peptides (diastereoisomeric aspartyl peptide derivatives and neuropeptides) in nonaqueous or hydroorganic electrolytes.16 Physicochemical behavior of phosphinic pseudopeptides was investigated by Koval et al. in highly acidic background electrolytes.17 To decrease the time required for the pKa determination, pressure-assisted capillary electrophoresis was developed. This method allows a reduction of the migration times, especially at intermediate pH values where solute ionization or/and electroosmotic mobility are relatively low.18-20 More recently, to reduce the total time for pKa determination, Geiser et al.21 used noncovalent coatings leading to a constant and strong electroosmotic flow on the whole pH range. In the literature, data regarding pKa values of peptides are only available for specific experimental conditions (temperature and ionic strength) and generally for short peptides.22,23 For this reason, it is often very difficult to get the pKa values of a peptide in a given set of experimental conditions. pKa data are, however, of great interest for different purposes including kinetic studies,24 (10) Ornskov, E.; Linusson, A.; Folestad, S. J. Pharm. Biomed. Anal. 2003, 33, 379-391. (11) Yang, L.; Yuan, Z. Electrophoresis 1999, 20, 2877-2883. (12) Vcelakova, K.; Zuskova, I.; Kenndler, E.; Gas, B. Electrophoresis 2004, 25, 309-317. (13) Sanz-Nebot, V.; Benavente, F.; Toro, I.; Barbosa, J. Electrophoresis 2001, 22, 4333-4340. (14) Sanz-Nebot, V.; Toro, I.; Benavente, F.; Barbosa, J. J. Chromatogr., A 2002, 942, 145-156. (15) Sanz-Nebot, V.; Benavente, F.; Toro, I.; Barbosa, J. J. Chromatogr., A 2001, 921, 69-79. (16) Psurek, A.; Scriba, G. E. Electrophoresis 2003, 24, 765-773. (17) Koval, D.; Kasicka, V.; Jiracek, J.; Collinsova, M. Electrophoresis 2003, 24, 774-781. (18) Jia, Z.; Ramstad, T.; Zhong, M. Electrophoresis 2001, 22, 1112-1118. (19) Ishihama, Y.; Nakamura, M.; Miwa, T.; Kajima, T.; Asakawa, N. J. Pharm. Sci. 2002, 91, 933-942. (20) Wan, H.; Holmen, A.; Nagard, M.; Lindberg, W. J. Chromatogr., A 2002, 979, 369-377. (21) Geiser, L.; Henchoz, Y.; Galland, A.; Carrupt, P.-A.; Veuthey, J.-L. J. Sep. Sci. 2005, 28, 2374-2380. (22) Perrin, D.; Dissociation constant of organic bases in aqueous solution; Butterworths: London, 1965. (23) Robinson, R. A.; Stokes, R. H. Electrolyte solutions; Butterworths: London, 1959. 10.1021/ac060406f CCC: $33.50
© 2006 American Chemical Society Published on Web 06/29/2006
Table 1. Physicochemical Parameters of the Electrolytesa type
I (mM)
pHtheo
pHexp (25 °C)
pHexp (0 °C)
Θ (10-3 K-1)
cp1 (mM)
P P P P P P P P P P P G G G G P P P P P P P P P P P P B B B B B B B B B B B B P P P P P
100 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 100 10 10 100 10 100 100
1.8 2.0 2.0 2.3 2.3 2.6 2.6 2.8 2.8 3.0 3.0 3.5 3.5 4.1 4.1 6.0 6.0 6.5 6.5 7.0 7.0 7.3 7.3 7.6 7.6 7.9 7.9 8.3 8.3 8.7 8.7 9.2 9.2 9.5 9.5 9.7 9.7 10.0 10.0 10.5 10.5 11.5 11.5 12.0
1.80 1.99 2.05 2.31 2.36 2.63 2.67 2.83 2.90 2.98 3.08 3.52 3.68 4.06 4.19 5.98 6.02 6.46 6.53 7.01 7.02 7.33 7.29 7.61 7.50 7.89 7.87 8.08 8.23 8.64 8.69 9.19 9.21 9.38 9.47 9.66 9.62 9.84 9.81 10.8 10.75 11.3 11.3 12.2
1.690 1.847 1.949 2.179 2.245 2.483 2.542 2.681 2.783 2.840 2.950 3.481 3.652 4.021 4.161 6.011 6.001 6.491 6.505 7.038 7.002 7.364 7.297 7.641 7.495 7.906 7.883 8.175 8.352 8.784 8.842 9.382 9.386 9.541 9.649 9.850 9.808 10.038 10.019 11.237 11.471 11.872 12.063 13.024
5.820 5.862 3.981 5.161 4.604 5.778 5.138 5.812 4.623 5.471 5.097 1.737 1.286 1.654 1.330 -1.212 0.945 -1.119 0.839 -1.268 0.701 -1.227 -0.213 -1.342 0.1450 -0.7170 -0.6784 -3.786 -4.821 -5.684 -5.963 -7.428 -7.139 -6.634 -7.171 -7.619 -7.700 -8.066 -8.482 -18.10 -29.07 -21.40 -29.88 -32.41
262 202 22.6 151 16 126 13 116 11.9 110 11.2
cp52 (mM)
cp3 (mM)
cs (mM)
30 1 30 1 30 1 30 1 30 1 30 1 3.20 32.5 2.07 27.2 21.1
84.0 90.0 0 95.0 5.0 97.5 7.5 98.4 8.4 99.0 9.0 12.4 10 36.0 10 9.45 0.68 18.5 1.49 26.6 2.40 29.6 2.79 31.3 3.03 32.3 3.18 10 7 10 7 10 7 10 7 10 7 10 7 0.351 1.04 3.37 8.23 18.9
87.6 64.0 81.1 8.64 63.0 7.02 46.8 5.21 40.8 4.43 37.3 3.93 35.4 3.65
cg (mM)
cb (mM)
100 71.7 100 25.5
89.4 62.6 41.6 29.1 20.0 14.0 15.0 10.5 13.1 9.21 11.6 8.10
a pH theo is the theoretical value expected for the pH of the electrolytes at 25 °C, on the basis of its composition. pHexp are the experimental values of the pH at 0 and 25 °C. Θ is the value of the slope of the variation of the pH as a function of temperature. cp1, cp2, cp3, cs, cg, and cb, are respectively the concentrations in phosphoric acid, dihydrogenophosphate, hydrogenophosphate, sodium hydroxide, glutamic acid, and boric acid, introduced for the preparation of the buffer.
chemical reactivity understanding, and effective electrophoretic mobility modeling. Recently, using a set of different end-charged homopolypeptides synthesized by ring-opening polymerization of N-carboxyanhydride (NCA), the correlation between the electrophoretic mobility and the peptide conformation was studied.25 Using these families of synthetic homopolypeptides, the first goal of this work was to determine the pKa values of polyglycines, poly(L-alanines), and poly(L-valines) in different conditions of ionic strength and temperature. Using this set of experimental data, a second objective of this work was to model the oligopeptide pKa values as a function of experimental conditions on the basis of the knowledge of a limited number of parameters concerning the (24) Plasson, R.; Biron J.-P.; Cottet H.; Commeyras A.; Taillades J. J. Chromatogr., A 2002, 952, 239-248. (25) Plasson, R.; Cottet, H. Anal. Chem. 2005, 77, 6047-6054.
peptides (number of residues and pKa of terminal amino acids in their free form). EXPERIMENTAL SECTION Apparatus and Capillaries. Electrophoresis experiments were performed using an automated capillary electrophoresis system (Beckman P/ACE MDQ, Fullerton, CA). Fused-silica capillariess50 µm i.d. × 60 (50 cm to the detector)swere used. New capillaries were initially conditioned with sodium hydroxide (1 M for 10 min and 0.1 M for 15 min, under a pressure of 20 psi). Prior to analysis, the capillary was washed with 0.1 M sodium hydroxide (20 psi for 2 min) and background electrolyte (20 psi for 3 min). Furthermore, each four runs, the capillary was flushed with 0.1 M sodium hydroxide for 10 min under a pressure of 20 psi in order to remove potentially adsorbed compounds. The capillary was thermostated at different temperatures from 15 to Analytical Chemistry, Vol. 78, No. 15, August 1, 2006
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60 °C. Samples were introduced hydrodynamically (5 psi for 5 s). The pH meter (HI 9017, Hanna Instruments, Tanneries, France) was daily calibrated with three aqueous buffers (4.01, 7.00, and 10.01). Chemicals. Oligopeptides were prepared by polymerization of 0.1 mmol of freshly prepared N-carboxyanhydride of amino acid (NCA) in 5 mL of borate buffer (pH 9.2, 10 mM ionic strength). NCAs were synthesized by reaction of gaseous NO/O2 mixture with a suspension of carbamoyl amino acid in acetonitrile.26 Carbamoyl amino acids were beforehand synthesized from carbamoylation of amino acid by KNCO.27 Oligopeptide samples were filtered off on PTFE filters (0.45-µm pores) to remove insoluble peptides. Pure commercial oligopeptide samples were available up to hexaglycine (Gly6), trialanine (Ala3), and divaline (Val2) for the identification of peaks. Amino acids and oligopeptides were obtained from Acros (Geel, Belgium). Purified water delivered by a Milli-Q system (Millipore, Molsheim, France) was used in all experiments. The 1 M sodium hydroxide and 1 M hydrochloric acid solutions were from Prolabo (Paris, France). Phosphoric acid, sodium dihydrogenophosphate, and disodium hydrogenophosphate were from Aldrich (Saint-Quentin Fallavier, France). Boric acid was from Avocado (La Tour du Pin, France). Determination of the Homopolypeptide Effective Mobilities. The homopolypeptide effective mobilities were determined by capillary electrophoresis in different conditions of temperature, pH, and ionic strength. Temperatures of 15, 25, 38, 50, and 60 °C were studied. A total of 44 different buffers of given ionic strengths (10 and 100 mM) were prepared at different pH values from 2 to 12. The exact chemical composition of all buffers is given in Table 1. Phosphate buffers were used for pH ∼2, ∼7, and ∼11. Glutamate buffers were used at pH ∼4. Borate buffers were used pH ∼9. Some phosphate was also added in these two latter buffers, as it allowed stabilizing the electric current. Applied voltages from 10 to 30 kV were used. The exact pH of these buffers depends on the temperature. The variation of the pH of the buffers was thus monitored as a function of the temperature between 0 and 80 °C. A linear variation following eq 1 was always observed:
pH ) pHexp(0 °C) + Θ(T - 273.15)
(1)
The experimental slope Θ and pHexp(0 °C) are given in Table 1, so that the exact value of the pH can be known for each temperature. THEORETICAL SECTIONS Correlation between Electrophoretic Mobilities of EndCharged Homopolypeptides, pH, and pKa Values. Homopolypeptides with neutral lateral chains (or end-charged homopolypetides) have three different ionization states. They can be positively charged (cationic form, H3N+-Xn-COOH), neutral (zwitterionic form, H3N+-Xn-COO-) or negatively charged (anionic form H2N-Xn-COO-). The acido-basic equilibrium equations related to this peptide are (A- standing for H2N-Xn-COO-): (26) Collet, H.; Bied, C.; Mion, L.; Taillades, J.; Commeyras, A. Tetrahedron Lett. 1996, 37, 9043-9046. (27) Taillades, J.; Boiteau, L.; Beuzelin, I.; Lagrille, O.; Biron, J.-P.; Vayaboury, W.; Vandenabeele-Trambouze, O.; Giani, O.; Commeyras, A. J. Chem. Soc., Perkins. Trans. 2 2001, 7, 8910-8913.
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[AH][H+] ; [AH2+]
Ka,1 )
Ka,2 )
[A-][H+] [AH]
(2)
The total concentration c of the peptide A whatever its ionization state is given by
(
c ) [AH2+] + [AH] + [A-] ) [AH] 1 +
Ka,2 [H+] + + Ka,1 [H ]
)
(3) The electrophoretic mobility of the peptide A at a given pH is given by
µ)
[AH2+] [AH] [A-] µAH2+ + µAH + µ Ac c c
(4)
Since the zwitterion has no mobility, and stating that the mobilities of both cationic and anionic forms are equal in absolute value to µ0, it leads to
µ)
(
µ ) µ0
[H+] Ka,1
[AH2+] - [A-] µ0 c
(5)
)
Ka,2 1 1 - + Ka,2 Ka,2 [H ] [H ] [H+] 1+ + + 1+ + + Ka,1 Ka,1 [H ] [H ]
(
+
µ ) µ0
1+
1 Ka,1 + Ka,2 [H+]
1
1 + [H+]
(
)
)
1 1 + Ka,1 Ka,2
(6) (7)
As there are ∼5 units of pH of difference between the values of pKa,1 and pKa,2, Ka,2 can be neglected compared to Ka,1, and 1/Ka,1 can be neglected compared to 1/Ka,2. The final expression of the electrophoretic mobility thus becomes
(
µ ) µ0
)
1 1 pH-pKa,1 1 + 10 1 + 10pKa,2-pH
(8)
Thermodynamic and Apparent pKa. In the case of a couple AHz/Az-1, z being the number of charge of the acid form, the pKa is defined by
pKa )
( )
aAz-1 aAz-1aH+ ) pH - log aAHz aAHz
(9)
The activity of a species X having a number of charge zX can be estimated by the extended law of Debye-Hu¨ckel:7 2xI)/(1+1.6405xI)
aX ) [X] × 10(-0.5085zx
The expression of the pKa then becomes
(10)
pKa ) pH - log
(
[Az-1] AHz
xI)/(1+1.6405xI[(z-1)2-z2])
10(-0.5085
)
(11) The pKa is a thermodynamic constant that only depends on the temperature. However, the apparent value pK′asexperimentally determined on the basis of the concentrations of the compounds rather than their activitiessdepends also on the ionic strength. The relationship between the thermodynamic pKa and the apparent pK′a is
pKa ) pK′a +
0.5085xI (1 - 2z) 1 + 1.6405xI
(12)
with
pK′a ) pH - log
[Az-1] [AHz]
(13)
To get the thermodynamic pKa value, the experimental measurement (pK′a) has to be corrected from the actual ionic strength according to eq 12. RESULTS AND DISCUSSION Determination of Oligoglycine pKa. The effective electrophoretic mobilities of oligoglycines were determined in the different buffers described in the Experimental Section. Effective mobilities are positive in acidic conditions (cationic form) and negative in basic conditions (anionic form). Zero values were obtained in neutral conditions (zwitterionic form). Two inflection points can be observed around pH 3 and pH 8, corresponding to the values of the two pKa. An example of this electrophoretic mobility variation is given in Figure 1 (T ) 38 °C, ionic strength I ) 10 mM) for a number n of residues up to 10. Measurements were also performed at 100 mM ionic strength and for different temperatures at both ionic strengths. The current was found to be more stable at 100 mM ionic strength, and the peaks were more symmetrical. However, high power dissipation was generally observed in such conductive buffers. The average value of the ratio of the dissipated power against the capillary length P/Lt ranged from 2 to 5 W‚m-1 for 100 mM buffers (while it was only 0.3-0.5 for 10 mM buffers). During electrophoresis, radial temperature profiles are formed due to generated Joule heat and its dissipation through the capillary wall. The effect of the electrolyte concentration on the generated Joule heat was studied by Cross and Cao.28 Semiempirical laws to evaluate the corresponding elevation of the mean temperature in the capillary were previously described,25 and leaded to the following equation:
δT )
0.037 P θ Lt
(14)
with
θ)
-1 dη η(P)0) dT
( )
T(P)0)
(15)
Figure 1. Variation of the effective electrophoretic mobility of oligoglycines Gn as a function of pH. Electrophoretic conditions: fused-silica capillaries, 50 µm i.d. × 30 cm (20 cm to the detector); electrolytes, phosphate, glutamate/phosphate, or phosphate/borate buffers, I ) 10 mM (see Table 1 for details); applied voltage, 15 kV; temperature, 38 °C; UV detection at 214 nm. The lines were obtained by curve fitting of the data using eq 8.
δT is the temperature elevation induced by the dissipated power. θ is a parameter depending only of the physical property of the solvent, and it can be determined directly from the variation of the viscosity as a function of temperature. η(P)0) is the viscosity of the solvent when no temperature elevation occurs. As a consequence, a temperature elevation by Joule effect of ∼8 °C should be expected in the 100 mM ionic strength buffers (comparing to a temperature elevation of ∼1 °C for 10 mM buffers) according to eq 14.25 In addition to the increase of the equilibrium temperature, the effective mobility curve obtained at 100 mM appeared to be slightly translated of ∼ -10-9 m2‚V-1‚s-1. Mobilities of ∼ -10-9 m2‚V-1‚s-1 rather than zero were observed around the pI of the peptide, and a difference of ∼2 × 10-9 m2‚V-1‚s-1 existed between the absolute values of the ionic mobilities of cationic and anionic forms. This was due to high concentrations of phosphates in the buffer. Indeed, linear variations of the electrophoretic mobilities as a function of the total concentration of phosphate could be observed in a series of experiments performed at pH 2.5, 6.5, and 9.5, keeping constant the ionic strength (100 mM). This was explained by the existence of an interaction between the peptides and the phosphate ions. However, the respective influence of each phosphate species was difficult to interpret in this set of experiments, and this study was not pursued further. Similar phosphate side effects on the electrophoretic mobilities have been previously observed by Survay et al.29 but were also not investigated further. It is worth noting that these variations were totally negligible at 10 mM ionic strength. For all these reasons, the determination of pKa at low ionic strength should be preferred, and only the data obtained at 10 mM ionic strength were used in the subsequent calculations. Nevertheless, it should be noted that the pKa differences between the two sets of experiments were not really significant. Figure 2 shows the differences between the pKa values obtained at 10 and 100 mM after ionic strength corrections according to eq 12. No (28) Cross, R. F., Cao, J. J. Chromatogr., A 1998, 809, 159-171. (29) Survay, M. A.; Goodall, D. M.; Wren, S. A. C.; Rowe, R. C. J. Chromatogr., A 1996, 741, 99-113.
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Figure 2. Variation of oligoglycine pKa as a function of the number of residues n. The values were determined at 50 °C for 10 (black dots) or 100 mM (cross) ionic strengths. All pKa values were corrected from the ionic strength effect according to eq 17. White circles represent values from the literature22 obtained at identical temperature. Table 2. pKa Values of Oligoglycines Determined at Different Temperaturesa n
15 °C
20 °C 6 25 °C 14 25 °C 38 °C 50 °C 6 50 °C 60 °C
1 2 3 4 5 6 7 8 9 10
2.177 2.993 3.438 3.390 3.202 3.262 3.281 3.319
2.33 3.19 3.19 3.11 3.10 3.13 2.94
1 10.143 2 8.435 3 8.266 4 8.192 5 8.150 6 8.130 7 8.119 8 8.109 9 8.134 10
9.80 8.23 8.11 8.06 8.02 7.69 7.69
3.12 3.26 3.05 3.05 3.05
8.17 7.91 7.75 7.70 7.60
pKa,1 2.206 3.096 3.176 3.246 3.233 3.256 3.276 3.293 3.309 3.312 pKa,2 9.910 8.236 8.018 7.985 7.926 7.909 7.886 7.887 7.874
2.267 3.169 3.322 3.346 3.364 3.415 3.425 3.439 3.400 3.404
2.32 3.16
9.500 7.897 7.713 7.670 7.646 7.626 7.607 7.599 7.625 7.574
9.19 7.67
2.359 3.286 3.393 3.416 3.425 3.392 3.406 3.423 3.473 3.465
2.455 3.393 3.459 3.475 3.433 3.452 3.475 3.488 3.552 3.559
9.146 7.737 7.448 7.557 7.308 7.530 7.263 7.506 7.239 7.470 7.197 7.442 7.147 7.427 7.106 7.410 7.108 7.367 7.109
a
All pKa values were corrected from ionic strength according to eq 12. Values in italics are data from the literature.
important variations were actually observed between the two sets of experiments. To accurately determine the pKa values, the experimental effective mobility data were fitted by nonlinear curve fitting (Levenberg-Marquardt algorithm30) using eq 8. Good correlations were observed as exemplified by Figure 1 (correlation coefficient R higher than 0.999 in all cases). All the data are given in Table 2. These data are in good accordance with the available data from the literature22,31 (available at 20, 25, and 50 °C for a limited number of residues). Modeling of the Oligoglycine pKa. (a) Variation with the Number of Residues n. Figure 3 represents the oligoglycine
Figure 3. Influence of the number of residues n on oligoglycine pKa at different temperatures. pKa values were corrected from the ionic strength effect. Temperature: 15 (dots), 25 (squares), 38 (diamonds), 50 (up triangles), and 15 °C (left triangles). Data from literature22 at 25 °C, circles. Plain lines were derived from curve fitting of the data using eq 12.
pKa values as a function of the number of residues n and for different temperatures. pKa,1 increases with n, while pKa,2 is a decreasing function of n. The variation of the pKa,i with n can be explained by electrostatic interactions between ammonium and carboxylate of the zwitterion.32,33 The influence of the electrostatic interaction between function j on the function i on the pKa can be modeled by ∞ ∆pKa,i ) pKa,i - pKa,i )
Czj Di,j
(16)
∞ where pKa,i is the pKa that would have the function i in the absence of the function j (or when the electrostatic influence would become negligible). pKa,i is the pKa of the function i in the peptide (influenced by the function j). zj is the number of charge of the function j. Di,j is the distance in angstroms between the charges of the two functions i and j. C is a constant in angstroms, only dependent on the dielectric constant of the solvent. Assuming that the peptide are roughly in a stretched conformation, the pKa can be modeled by
∞ pKa,i ) pKa,i -
Ci 3.64(n - 1) + βi
(17)
The curves giving the variation of the pKa as a function of n were (30) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-441. (31) Greenstein, J. P.; Winitz, M. Chemistry of the Amino Acids; Wiley: New York, 1961; Vol. 1.
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(32) Bjerrum, N. Z. Phys. Chem. 1923, 106, 219-242. (33) Cifuentes, A.; Poppe, H. J. Chromatogr., A 1994, 680, 321-340.
Table 3. pKa Values of Oligo(L-alanines) and Oligo(L-valines) Determined at Different Temperaturesa pKa,2 n
15 °C
25 °C
1 2 3 4 5 6 7 8
10.43 8.56 8.46 8.40 8.37 8.35 8.35 8.31
9.97 8.24 8.13 8.04
1 2 3 4 5
10.05 8.23 8.10 8.07 7.94
9.68 7.97*
pKa,1
25 °C
50 °C
15 °C
Oligo(L-alanines) 10.08 9.50 2.32 8.37 8.03 3.28 8.26 7.66 3.33 8.13 7.71 3.37 8.10 7.72 3.28 8.04 7.70 3.37 8.02 7.67 3.38 7.95 7.63 3.40 Oligo(L-valines) 9.82 9.20 2.33 8.08 7.66 3.41 7.97 7.44 3.52 7.85 7.36 3.55 7.73 7.30 3.65
25 °C
25 °C
50 °C
2.24 3.20 3.29 3.32
2.20 3.21 3.38 3.38 3.45 3.57 3.57 3.56
2.36 3.26 3.23 3.30 3.35 3.40 3.45 3.45
2.30 3.39*
2.35 3.48 3.59 3.68 3.75
2.14 3.31 3.37 3.41 3.44
a All pK values were corrected from ionic strength according to eq a 12. Values in italics are data from the literature (all from Perrin22 except *, from Lyons et al.34).
Figure 4. Influence of the temperature on oligoglycine pKa,1 (A) and pKa,2 (B) for different numbers of residues n. Gn is the oligoglycine containing n residues. Straight lines represent linear regression of experimental data and dotted lines data from the literature.23
adjusted by nonlinear curve fitting using eq 17. The values obtained for C1, C2, β1, and β2 were roughly identical at all ∞ temperatures, since only pKa,i was dependent on the temperature. As a consequence, the pKa can be described as a sum of ∞ being a function of the temperatwo independent terms: pKa,i ture, and a second term being dependent on the number of residues n. The fitting was thus performed with parameters shared between the pKa data obtained at all temperatures, leading to β1 ) 1.068, C1 ) 1.256, β2 ) 0.880, and C2 ) 1.723. Correlation coefficients between 0.995 and 0.9999 were obtained in all cases. ∞ The values of pKa,i are represented as a function of the temperature in Figure 4 (crosses). (b) Variation with the Temperature. Empirically, the variation of pKa as a function of temperature can be described as23
pKa )
A1 - A2 + A3T T
(18)
where A1, A2, and A3 are contants. The variation between 15 and 60 °C is mostly linear for both data from the literature23 (glycine, G, and diglycine, G2) and experimental data obtained in this work. Moreover, parallel straight lines are obtained for each value of n (see Figure 4). The average value of the slopes of pKa as a function of the temperature is Θ1 ) 0.004 95 K-1 for pKa,1 and Θ2 ) -0.0213 K-1 for pKa,2. Θ2 is in very good accordance with literature. However, a small deviation from the literature is observed for
Θ1: a small slope is observed for pKa,1, while literature data23 give a zero value for Θ1. General Modeling of Oligoglycine pKa. To sum up the results obtained by modeling of the experimental data, it has been observed that the variation of pKa as a function of n is independent of temperature and that the variation of pKa as a function of T is independent of n. It is thus possible to model the oligoglycine pKa by combining the preceding equations. The following general empiric expression of pKa can be derived from these results:
pKa,1 ) 3.266 -
1.26 + 0.00495(T - 273.15) 3.64(n - 1) + 1.07 (19)
pKa,2 ) 8.372 +
1.72 - 0.02130(T - 273.15) 3.64(n - 1) + 0.88 (20)
(with T in K). Generalization of the Modeling to Other Homopolypeptides with Neutral Lateral Chain. (a) General Modeling of Oligo(L-alanines) and Oligo(L-valines) pKa. Similar experiments were performed for oligo(L-alanines) and oligo(L-valines). However, to limit the total number of experiments, the study was limited to 15, 25, and 50 °C, and for 10 mM ionic strength. The results are given in Table 3. Experimental results are in good accordance with literature.22,34 The general modeling was similarly performed as described for oligoglycine, leading to the following equations for oligo(L-alanines):
pKa,1 ) 3.523 -
1.65 -0.0001(T - 273.15) 3.64(n - 1) + 1.33 (21)
(34) Lyons, A. Q.; Pettit, L. D. J. Chem. Soc., Dalton Trans. 1984, 10, 23052308.
Analytical Chemistry, Vol. 78, No. 15, August 1, 2006
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Table 4. Comparison between Literature Valuesa and Modeled Values Using Eqs 30 and 31b calculated
peptide
T (°C)
I (M)
n
term pKN a,2
pKCa,1term
pK∞a,2
pK∞a,2
pKa,1
pKa,2
Ala-Gly Ala-Gly Ala-Gly Ala-Gly-Gly Ala-Leu-Gly* Ala-Pro Asn-Gly Gln-Gly Gln-Gly Gly-Ala Gly-Ala Gly-Ala Gly-Ala Gly-Ala Gly-Ala-Ala Gly-Ala-Ala-Gly Gly-Asn Gly-Asn Gly-Asn Gly-Gln Gly-Gln Gly-Gly Gly-Gly-Ile* Gly-Gly-Phe* Gly-Gly-Val* Gly-Ile Gly-Leu Gly-Leu Gly-Leu Gly-Leu Gly-Phe Gly-Pro Gly-Pro Gly-Pro Gly-Pro Gly-Sar Gly-Sar Gly-Sar Gly-Ser Gly-Ser Gly-Ser Gly-Ser-Gly Gly-Try Gly-Val Gly-Val Gly-Val Leu-Asn Leu-Asn Leu-Gln Leu-Gln Leu-Gly Leu-Gly Leu-Gly Leu-Gly Leu-Gly-Gly Leu-Gly-Gly Leu-Ise Phe-Gly Phe-Gly Phe-Gly Pro-Gly Sar-Gly Sar-Gly Sar-Leu Sar-Sar Ser-Gly Ser-Leu Val-Gly Val-Gly
25.0 25.0 25.0 20.0 25.0 25.0 18.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 18.0 25.0 25.0 18.0 18.0 25.0 25.0 25.0 25.0 25.0 20.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.1 25.0 25.0 25.1 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.1 18.0 20.0 18.0 18.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 0.0 25.0 25.0 25.1 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.1
0.01 0.02 0.1 0.1 0 0.03 0.015 0.03 0.1 0.02 0.0 0.05 0.1 0.1 0.1 0.0 0.015 0.0 0.03 0.015 0.015 0.0 0 0 0 0.02 0.005 0.02 0.0 0.05 0.1 0.01 0.0 0.16 0.16 0.05 0.16 0.16 0.02 0.1 0.15 0.15 0.1 0.0 0.16 0.16 0.015 0.1 0.015 0.015 0.005 0.01 0.02 0.1 0.005 0.2 0.04 0.01 0.01 0.1 0.16 0.01 0.16 0.005 0.005 0.15 0.15 0.16 0.16
2 2 2 3 3 2 2 2 2 2 2 2 2 2 3 4 2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2
9.871 9.871 9.871 9.871 9.871 9.871 8.845 9.135 9.135 9.809 9.809 9.809 9.809 9.809 9.809 9.785 9.809 9.809 9.809 9.785 9.809 9.785 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.809 9.785 9.809 9.809 9.809 9.809 9.749 9.749 9.749 9.749 9.749 9.749 9.749 9.749 9.749 9.749 9.749 9.389 9.389 9.389 10.645 10.205 10.205 10.205 10.205 9.213 9.213 9.724 9.724
2.350 2.350 2.350 2.350 2.350 1.952 2.350 2.350 2.350 2.348 2.348 2.348 2.348 2.348 2.348 2.350 1.922 1.922 1.922 2.064 2.064 2.286 2.318 1.952 2.286 2.318 2.327 2.327 2.327 2.327 2.522 1.952 1.952 1.952 1.952 2.134 2.134 2.134 2.210 2.210 2.210 2.350 2.430 2.286 2.286 2.286 1.922 1.922 2.064 2.064 2.350 2.350 2.350 2.350 2.350 2.350 2.720 2.350 2.350 2.350 2.350 2.350 2.350 2.327 2.134 2.350 2.327 2.350 2.350
8.311 8.311 8.311 8.311 8.311 8.311 7.285 7.575 7.575 8.249 8.249 8.249 8.249 8.249 8.249 8.225 8.249 8.249 8.249 8.225 8.249 8.225 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.249 8.225 8.249 8.249 8.249 8.249 8.189 8.189 8.189 8.189 8.189 8.189 8.189 8.189 8.189 8.189 8.189 7.829 7.829 7.829 9.085 8.645 8.645 8.645 8.645 7.653 7.653 8.164 8.164
3.35 3.35 3.35 3.35 3.35 2.952 3.35 3.35 3.35 3.348 3.348 3.348 3.348 3.348 3.348 3.35 2.922 2.922 2.922 3.064 3.064 3.286 3.318 2.952 3.286 3.318 3.327 3.327 3.327 3.327 3.522 2.952 2.952 2.952 2.952 3.134 3.134 3.134 3.21 3.21 3.21 3.35 3.43 3.286 3.286 3.286 2.922 2.922 3.064 3.064 3.35 3.35 3.35 3.35 3.35 3.35 3.72 3.35 3.35 3.35 3.35 3.35 3.35 3.327 3.134 3.35 3.327 3.35 3.35
3.099 3.114 3.161 3.289 3.183 2.726 3.107 3.124 3.161 3.112 3.053 3.136 3.159 3.159 3.287 3.234 2.679 2.627 2.696 2.821 2.821 2.991 3.151 2.785 3.119 3.082 3.064 3.091 3.032 3.115 3.333 2.701 2.657 2.780 2.780 2.922 2.962 2.962 2.974 3.021 3.036 3.304 3.241 2.991 3.114 3.114 2.679 2.733 2.821 2.821 3.087 3.099 3.114 3.161 3.216 3.315 3.502 3.099 3.099 3.161 3.178 3.099 3.178 3.064 2.871 3.176 3.153 3.178 3.178
8.264 8.249 8.202 8.092 8.103 8.239 7.363 7.503 7.466 8.187 8.246 8.162 8.140 8.140 7.935 7.936 8.327 8.246 8.177 8.303 8.327 8.222 8.041 8.040 8.041 8.187 8.308 8.187 8.246 8.162 8.140 8.202 8.246 8.123 8.121 8.162 8.123 8.121 8.187 8.140 8.125 7.896 8.140 8.246 8.123 8.121 8.267 8.175 8.267 8.267 8.153 8.142 8.127 8.080 7.948 7.849 8.109 8.257 7.782 7.720 8.957 8.598 8.519 8.609 8.609 7.529 7.529 8.038 8.036
a
All data from Perrin22 except *, from Sanz-Nebot et al.13
b
5400 Analytical Chemistry, Vol. 78, No. 15, August 1, 2006
literature pKa,1 3.14 3.17 3.19 3.26 3.04 2.9
∆pKa,1
∆pKa,2
8.25 8.21 8.18 8.15
-0.04
0.01 0.04 0.02 -0.06
8.38 7.25 7.52
3.15 3.15 3.153 3.17 3.34 3.38 3.3 2.82 2.9 2.942 2.88 2.88 3.26 3.07 3.21 3.1 3.18 3.18 3.12 2.81 2.84 2.97 2.76 2.98 2.9802 2.92 3.23 3.17 3.15 3.0 2.83 2.99 2.99 3.25 3.15 3.19 3.28 3.27 3.188 3.11 3.07 3.13 3.19 3.14 3.15 3.15 2.89 3.1 3.08 3.23
calc - lit.
pKa,2
-0.01 0.10 -0.08 -0.31 0.21
-0.14 0.11 -0.02
0.01 8.21 8.25 8.23 8.19 8.1 7.93 8.44 8.3 8.33 8.33 8.252 8.09 8.04 8.12 8.0 8.41 8.17 8.29 8.17 8.65 8.531 8.5 8.48 8.61 8.59 8.57 8.38 8.1 7.99 8.06 8.25 8.22 8.18 8.12 8.23 8.11 8.11 8.28 8.13 8.0 7.97 8.207 8.41 7.74 7.62 8.97 8.66 8.56 8.67 9.18 7.33 7.45 8.02 8.0
-0.10 -0.02 -0.01 -0.18 -0.09 -0.07 -0.14 -0.27 -0.25 -0.06 -0.06 -0.11 -0.29 -0.09 -0.04 -0.15 -0.06 0.21 -0.11 -0.18 -0.19 0.16 -0.02 0.04 0.12 0.07 -0.18 -0.04 -0.32 -0.10 -0.17 -0.17 -0.16 -0.05 -0.03 -0.06 0.04 0.31 -0.01 0.03 0.03 -0.01 -0.04 0.03 -0.09 -0.02 0.08 0.07 -0.05
-0.02 0.00 -0.09 -0.05 -0.17 0.01 -0.11 -0.05 -0.03 0.00 -0.03 -0.05 0.00 -0.08 0.19 -0.10 0.02 -0.04 -0.03 -0.45 -0.29 -0.38 -0.36 -0.45 -0.47 -0.45 -0.19 0.03 -0.09 0.08 0.00 -0.10 -0.06 0.15 -0.05 0.16 0.16 -0.13 0.01 0.13 -0.02 -0.10 -0.15 0.04 0.10 -0.01 -0.06 -0.04 -0.06 -0.57 0.20 0.08 0.02 0.04
Peptides alkylated on the nitrogen of the peptide bond are in boldface type.
pKa,2 ) 8.352 +
2.16 - 0.00193(T - 273.15) 3.64(n - 1) + 1.06 (22)
and the following equations for oligo(L-valines):
pKa,1 ) 4.080 -
1.86 + 0.0055(T - 273.15) 3.64(n - 1) + 1.25 (23)
pKa,2 ) 8.138 +
2.17 - 0.00196(T - 273.15) 3.64(n - 1) + 1.00 (24)
(b) General Modeling on the Basis of Three Homopolypeptide Families. To try to develop a more general model, all the experimental pKa values obtained for the three aforementioned families of oligopeptides were modeled using the following general equation: ∞ pKa,i ) pKa,i
Ci 3.64(n - 1) + βi
+ Θi (T - 273.15) (25)
where the negative sign is valid for pKa,1 and the positive sign for pKa,2. Average values for β1,av, β2,av, Θ1,av, and Θ2,av were directly obtained by the average values from eqs 16-23: β1,av ) β2,av ) 1.1 Å; Θ1,av ) 0 K-1, and Θ2,av ) -0.019 K-1. To check the validity of this general equation, pKa,i - Θi,av (T - 273.15) was plotted as a function of (3.64(n - 1) + 1.1)-1. Parallel straight lines were obtained, as shown in Figure 1S (Supporting Information). Linear regression allowed the determination of the following parameters:
C1 ) 1.4 Å
(26)
C2 ) 2.24 Å
(27)
∞ pKa,1 ) pKa,1Cterm + 1.00
(28)
∞ ) pKa,2Nterm - 1.56 pKa,2
(29)
where pKa,1Cterm and pKa,2Cterm are respectively the pKa of the acid function of the C-terminal amino acid and of the amino function of the N-terminal amino acid, in their free form at 25 °C. Assuming that this model can be extrapolated for any oligopeptide as far as the lateral chains of the residues are neutral, the apparent pKa can thus be determined by the following equations, on the basis of the knowledge of the pKa,1 of the C-terminal residue, the pKa,2 of the N-terminal residue, the temperature T, the ionic strength I and the number of residues:
pK′a,1 ) pKa,1Cterm + 1.00 1.4 0.5085xI (30) + 3.65(n - 1) + 1.1 1 + 1.6405xI pK′a,2 ) pKa,2Nterm - 1.56-0.019(T - 273.15) + 2.24 0.5085xI + (31) 3.65(n - 1) + 1.1 1 + 1.6405xI
Figure 5. Graphical comparison between literature values13,22 and modeled values by eqs 30 and 31 of pKa of several oligopeptides (see Table 4 for details). Dots are pKa,2 values, triangles pKa,1 values, and crosses pKa,2 values of peptides alkylated on the nitrogen of the peptide bond. The difference between modeled and literature date is less than 0.2 unit of pKa for values situated between the dashed lines.
(c) Prediction of Oligopeptide pKa. The pKa values of 37 oligopeptides taken from the literature,13,22 in different conditions of ionic strength and temperature, were compared to the values predicted by the semiempirical eqs 30 and 31 (see Table 4 for comparison). These peptides are composed of up to four residues, but none of them are laterally charged. As can be seen on Figure 5, a good correlation was observed between experimental (literature) and calculated values. The average difference between predicted and literature data is equal to -0.05 with a standard deviation of 0.13 for pKa,1, and to -0.07 with a standard deviation of 0.17 for pKa,2. Differences of less than 0.2 unit of pKa are actually obtained for all peptides, except for three of them (Gly-Pro, Gly-Sar, Sar-Sar). These latter peptides have a difference of ∼0.5 unit for their pKa,2. All these peptides are alkylated on the nitrogen of the peptide bond. Such a deviation from the semiempiric equations may be explain by conformational changes induced by these alkylations, implying modifications of the Di,j parameter in eq 15. When removing their corresponding data to the statistic analysis, the average difference between predicted and literature data for nonalkylated oligopeptides becomes equal to -0.01 with a standard deviation of 0.09 for pKa,2, with no substantial change for pKa,1. CONCLUSION Capillary electrophoresis was fruitfully implemented for the determination of the pKa values of oligoglycines, oligo(L-alanines) and oligo(L-valines) at different temperatures between 15 and 60 °C. On the basis of these experimental data, pKa values of these peptides were modeled by a general equation allowing the estimation of the pKa as a function of experimental conditions (temperature and ionic strength) and as a function of the number of residues. Moreover, a general model derived from these data allowed the prediction of the pKa of short end-charged peptides on the basis of the knowledge of the peptide sequence and the experimental conditions of temperature and ionic strength. Comparisons with experimental data from the literature demonstrated that the prediction was possible with a standard deviation of ∼0.1 unit of pKa. Analytical Chemistry, Vol. 78, No. 15, August 1, 2006
5401
These results are however limited to peptides with no lateral charge. Furthermore, the possibility of the influence of conformational changes on the values of the pKa has been observed in the case of N-alkylated peptides. More general studies of the electrophoretic behavior of oligopeptides should enlighten more precisely the influence of conformations and lateral charges, toward a more precise prediction of pKa and electrophoretic mobilities of peptides.
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SUPPORTING INFORMATION AVAILABLE Addtional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
Received for review March 6, 2006. Accepted May 26, 2006. AC060406F
