Anal. Chem. 2005, 77, 6047-6054
Determination of Homopolypeptide Conformational Changes by the Modeling of Electrophoretic Mobilities Raphae 1 l Plasson† and Herve´ Cottet*
Laboratoire Organisation Mole´ culaire, EÄ volution et Mate´ riaux Fluore´ s, UMR 5073, CC017, Universite´ de Montpellier 2, Place Euge` ne Bataillon, 34095 Montpellier Cedex 5, France
This work deals with the modeling of electrophoretic mobilities of end-charged homopolypeptides. The ionic mobilities of six families of homopolypeptides (polyglycines, poly-L-alanines, poly-L-valines, poly-L-leucines, poly-L-isoleucines, and poly-L-phenylalanines), with polymerization degrees up to 11, have been carefully determined. The electrophoretic frictional coefficients derived from the ionic mobility values were modeled by the hydrodynamic frictional coefficient of an equivalent cylinder. The hydrodynamic modeling allowed the determination of the molecular dimensions of the homopolypeptides in the electrolyte. The results were in good accordance with the expected geometry of the molecules. This approach allows monitoring the change in peptide conformations as a function of the experimental conditions (temperature, nature of the solvent) through the determination of geometrical molecular parameters (total peptide length, lateral radius of the equivalent cylinder, and folding angle). The influence of the bulkiness of the homopolypeptide lateral chain on the conformation is also discussed. Capillary zone electrophoresis (CZE) is a widely used analytical tool for the separation of biomolecules such as peptides1-3 or proteins.4 The modeling of the electrophoretic mobility is a fundamental issue for optimizing the separation conditions and for determining the physicochemical characteristics of the solutes (charge, pKa values, molecular mass, etc.). A major interest is the correlation between peptide conformations and the electrophoretic mobility.5-7 Most of the models that were developed aimed at modeling the effective electrophoretic mobility as a function of * Corresponding author. Phone: +33-4-6714-3427. Fax: +33-4-6763-1046. E-mail:
[email protected]. † Present address: Department of Applied Chemistry, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohamashi, 2238522 Japan. Phone: +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) Hearn, M. T. W.; Keah, H. H.; Boysen, R. I.; Messana, I.; Misiti, F.; Rossetti, D. V.; Giardina, B.; Castagnola, M. Anal. Chem. 2000, 72, 1964-1972. 10.1021/ac050783c CCC: $30.25 Published on Web 08/16/2005
© 2005 American Chemical Society
the charge and the molecular mass of the solutes.8-12 For more details on these empirical models, the reader can refer to specific reviews dealing with the electrophoretic behavior of peptides.13-15 Other classical theoretical models are based on the prediction of ionic electrophoretic mobilities µ0,∞ as a function of the hydrodynamic coefficient γh.9 The most commonly used expression is the Hu¨ckel equation, which is related to the StokesEinstein diffusion model,
µ0,∞ )
q q ) γh 6πηr
(1)
where η is the viscosity of the electrolyte, q is the charge of the analyte, and r is the hydrodynamic radius of the solute. The ionic mobility is defined as the value of actual mobility, µ0 (related to fully ionized solute), that would be measured at infinite dilution. Thus, the determination of ionic mobility requires a relationship between ionic and actual mobilities. For that, Li et al.16 used the Pitts equation17 to account for the effect of ionic size on the ionic strength dependence of actual mobilities in CZE. An extension to the Hu¨ckel equation comes from the concept of dielectric friction, which was first introduced by Born18 and further developed by Hubbard-Onsager.19 More recently, Roy and Lucy applied this concept for the modeling of mobility of organic ions in mixed hydro-organic medium, such as methanol-water mixtures.20 This model assumes that the overall electrophoretic frictional coefficient, γe, has two independent contributions, one pertaining to (6) De Lorenzi, E.; Grossi, S.; Massolini, G.; Giogetti, S.; Mangione, P.; Andreola, A.; Chiti, F.; Bellotti, V.; Caccialanza, G. Electrophoresis 2002, 23, 918925. (7) Verzola, B.; Perduca, M.; Mezo, G.; Hudecz, F.; Righetti, P. G. Electrophoresis 2003, 24, 794-800. (8) Offord, R. E. Nature 1966, 211, 591-593. (9) Grossman, P. D.; Colburn, J. C.; Lauer, H. H. Anal. Biochem. 1989, 179, 28-33. (10) Rickard, E. C.; Strohl, M. M.; Nielsen, R. G. Anal. Biochem. 1991, 1971, 197-201. (11) Compton, B. J. Chromatogr. 1991, 559, 357-366. (12) Cifuentes, A.; Poppe, H. J. Chromatogr., A 1994, 680, 321-340. (13) Adamson, N. J.; Reynolds, E. C. J. Chromatogr., B 1997, 133-147. (14) Cifuentes, A.; Poppe, H. Electrophoresis 1997, 18, 2362-2376. (15) Kasicka, V. Electrophoresis 1999, 20, 3084-3105. (16) Li, D.; Fu, S.; Lucy, C. A. Anal. Chem. 1999, 71, 687-699. (17) Pitts, E. Proc. R. Soc. 1953, A217, 43-70. (18) Born, M. Z. Phys. 1920, 221, 1. (19) Hubbard, J.; Onsager, L. J. Chem. Phys. 1977, 67, 4850-4857. (20) Roy, K. I.; Lucy, C. A. Anal. Chem. 2001, 73, 3854-3861.
Analytical Chemistry, Vol. 77, No. 18, September 15, 2005 6047
the hydrodynamic frictional coefficient and the other pertaining to the dielectric friction,
µ0,∞ )
q q ) γe γh + γd
(2)
where γd is the dielectric frictional coefficient. For small monocharged analytes in water or water-methanol mixtures, the dielectric term can be neglected,20 so that the electrophoretic frictional coefficient is equivalent to the hydrodynamic frictional coefficient. In that case, the frictional coefficient derived from the ionic mobility (γe ) γh ) e/µ0,∞) is directly related to geometrical parameters of the molecule using hydrodynamic equation.21 Our work intends to investigate the relationship between electrophoretic mobilities and geometrical parameters in the case of end-charged homopolypeptides. Polyglycines, poly-L-alanines, poly-L-valines, poly-L-leucines, poly-L-isoleucines, and poly-L-phenylalanines with degrees of polymerization n up to 11, were taken as model compounds. A careful determination of the ionic mobilities of these homopolypeptides as a function of several experimental parameters (temperature, addition of organic solvent) was performed. Next, the molecular geometrical parameters were derived using hydrodynamic modeling of the frictional coefficient. THEORY Influence of the Ionic Strength on Actual Mobility. The ionic mobility of a solute can be derived from the determination of the actual mobility at several ionic strengths using the DebyeHu¨ckel-Onsager equation,16
xI µ0 ) µ0,∞ - (A1 + A2µ0,∞) 1 + BrixI
(3)
where µ0 is the actual mobility, µ0,∞ is the ionic mobility, ri is the ionic radius, and I is the ionic strength. A1, A2, and B are the Pitts parameters, defined for fully dissociated 1:1 electrolytes (all numerical values are in the international units system),
A1 ) A2 ) B)
4.125 10-4 FηxrT 8.201 105 (rT)3/2 5.03 1011
xrT
(4)
where F is the Faraday constant, T is the temperature in K, and r is the relative dielectric constant. The numerical values of these parameters are given in Table 1 for water-based and (75/25 v/v) methanol/water-based electrolytes at different temperatures from 15 to 60 °C. From eqs 3 and 4, the values of the ionic mobility and ionic radius can be determined by nonlinear curve-fitting of experimental actual mobilities using a classical LevenbergMarquardt algorithm.22 (21) Tirado, M. M.; De La Torre, J. G. J. Chem. Phys. 1979, 71, 2581-2587.
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Analytical Chemistry, Vol. 77, No. 18, September 15, 2005
Table 1. Physicochemical Parameters in Water and in Methanol/Water Mixturea ηb cP
A2c Bc A1c 10-8 m2 V-1 s-1 M-1/2 M-1/2 Å-1 M-1/2
τdb ps
T °C
rb
15 25 38 50 60
82.09 78.54 73.84 69.53 65.94
1.137 10.9 0.890 8.29 0.678 6.19 0.546 4.84 0.466 3.96
15 25 38 50 60
45.52 43.12 40.01 37.13 34.74
1.439 1.127 0.858 0.692 0.590
Water 2.445 3.140 4.161 5.220 6.188
0.2254 0.2290 0.2355 0.2435 0.2519
0.3270 0.3288 0.3318 0.3356 0.3394
Methanol/Water 0.439 0.444 0.451 0.459 0.468
2.593 3.346 4.465 5.643 6.735
0.5459 0.5626 0.5904 0.6240 0.6587
Θd 0.0269 0.0235 0.0189 0.0159 0.0147
aRatio 75/25 v/v. b , η and τ values are derived from ref 23 (in r d water) and from ref 29 (in methanol/water mixture). c Pitts parameters (A1, A2, B) were determined from eq 4. d Θ values were determined from eq 15.29
Modeling of the Hydrodynamic Frictional Coefficient of Peptides. A polypeptide is a polymer of amino acids linked by planar and rigid peptide bonds. These bonds act as hinges between the asymmetric carbons supporting the lateral chain. For a limited number, n, of residues (in this paper, n e 11), the peptide chain can be represented as a cylindrical object (see Figure 1a). The total length, L, of the cylinder is proportional to n, with an incremental step per residue, rstp, and a constant residual parameter, rend. The radius of the cylinder, rlat, depends on the length of the lateral chain, rchain, and on the size of the backbone, rcent (see Figure 1a). Any variation in the peptide conformation will induce a change of these parameters, depending on the average angle θ (see Figure 1a and b) between two successive amino acid residues. From the representation given in Figure 1, these geometrical parameters are related by the two following equations (values in Å),
rlat ) rchain + 1.9 sin(θ + 15°)
(5)
L ) rend + 3.64n cos θ
(6)
where rend corresponds to the total length of terminal ends of the peptide chain and was fixed to 2Å (H- and -OH ends of the oligopeptides). For fully stretched conformations of the lateral chain, rchain can be evaluated on the basis of average values of chemical bonds (see Figure 1c).24 The hydrodynamic frictional coefficient γh of a cylinder can be determined using eq 7 on the basis of the geometrical parameters rlat and L.21
γh )
3πηL rlat2 rlat L ln + 0.312 + 1.13 + 0.4 2 2rlat L L
(7)
Substituting rlat and L in eq 7, the hydrodynamic frictional coefficient γh of the end-charged polypeptide can be expressed (22) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-441. (23) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworth: London, 1959.
Figure 1. Geometrical representation of oligopolypeptides. (a) Relationship between the parameters of the equivalent cylinder and the molecular parameters. (b) Geometrical parameters of a single residue as a function of the angle θ with the peptide main axis. (c) Evaluation of the length of the lateral chain in a fully stretched conformation.
as a function of n, θ, rchain, and rend. Next, a curve-fitting of the plot giving µ0,∞ ) q/γh as a function of n using eqs 5, 6 and 7 allows the determination of θ and rchain values. EXPERIMENTAL SECTION Apparatus. Electrophoresis experiments were performed using an automated capillary electrophoresis system (Beckman P/ACE MDQ, Fullerton, CA). Fused-silica capillaries, 50-µm i.d., were used. New capillaries were initially conditioned with sodium hydroxide (1 M for 10 min and 0.1 M for 15 min under a pressure (24) Atkins, P. W. Physical Chemistry, 4th ed.; Oxford University Press: Oxford, 1992.
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 to remove potentially adsorbed compounds. The capillary was thermostated at different temperatures from 15 to 60 °C. Samples were introduced hydrodynamically (0.5 psi for 5 s). Chemicals. The homopolypeptide samples were prepared by polymerization of 0.1 mmol of freshly prepared N-carboxyanhydrides (NCAs) in 5 mL of borate buffer (pH 9.2, 10 mM ionic strength), corresponding to homopolypeptide samples containing the equivalent of 20 mM in monomers. NCAs were synthesized by reaction of gaseous NO/O2 mixture with a suspension of carbamoyl amino acids in acetonitrile.25 Carbamoyl amino acids were beforehand synthesized from carbamoylation of amino acids by KNCO.26 Homopolypeptide samples were filtered off on PTFE filters (0.45-µm pores) to remove insoluble peptides. Amino acids were obtained from Acros (Geel, Belgium); phenyltrimethylammonium chloride (PTMA) was from Avocado (Heysham, Lancashire, England). The homopolypeptide samples were characterized by NMR. The homopolypetide distributions were checked by capillary electrophoresis using pure commercial samples for peak assignment. Pure homopolypeptides (diglycine, triglycine, tetraglycine, pentaglycine, hexaglycine, dialanine, trialanine, and divaline) were purchased from Bachem (Bubendorf, Switzerland). Since not all the peptides were commercially available, peaks were assigned assuming a regular distribution of the peptides starting from the dipeptide. Purified water delivered by a Milli-Q system (Millipore, Molsheim, France) was used in all experiments. Methanol and triethylamine were purchased from Carlo Erba (Val de Reuil, France); 1 M sodium hydroxide and 1 M hydrochloric acid solutions were from Prolabo (Paris, France). Determination of Actual Mobilities. The actual mobilities of the end-charged homopolypeptides were measured in buffers that allow the full ionization of the solutes. Triethylamine/ triethylammonium chloride buffers, pH 11.5, where prepared at different ionic strengths (10, 20, 50, 75, and 100 mM) by diluting pure triethylamine and 1 M HCl in water. In the water-based electrolytes, a positive voltage of 10-15 kV was applied, depending on the dissipated power and the temperature. The detection was performed by UV absorbance at 200 nm. The actual mobilities of polyglycines in methanol-water mixtures were determined according to the method described by Williams and Vigh27 to decrease the analysis time. The separations were performed in methanol/water mixtures (75/25 v/v) containing 5 mM NaOH. The ionic strength (5, 10, 20, 50, 75, or 100 mM) was adjusted to the required value by addition of NaCl. The polyglycine sample in the presence of 0.2% DMF (neutral marker) was hydrodynamically injected in the capillary, and further transferred by the application of a 1 psi pressure during 7 min. The separation was then performed using a 10 kV positive voltage for 10 min at 25 °C. A second neutral marker was then injected, and the capillary was finally flushed by the application of a 1 psi (25) Collet, H.; Bied C.; Mion, L.; Taillades, J.; Commeyras, A. Tetrahedron Lett. 1996, 37, 9043-9046. (26) Taillades, J.; Boiteau, L.; Beuzelin, I.; Lagrille, O.; Biron, J.-P.; Vayaboury, W.; Vandenabeele-Trambouze, O.; Giani, O.; Commeyras, A J. Chem. Soc., Perkin Trans. 2 2001, 7, 8910-8913. (27) Williams, B. A.; Vigh, G. Anal. Chem. 1996, 68, 1174-1180.
Analytical Chemistry, Vol. 77, No. 18, September 15, 2005
6049
κ(P)0) is similar to the relative variation of mobility (see plain (T ) 25 °C) and dotted (T ) 50 °C) lines, as compared to the dots in Figure 2). For dissipated power lower than 5 W m-1, the experimental mobility can be corrected according to this empirical relation:
µ(P)0) )
Figure 2. Relative variation of the conductivity (κ(P)/κ(P)0)) and of actual electrophoretic mobility of PTMA (µ(P)/µ(P)0)) as a function of the dissipated power per unit of length. Straight line, κ(P)/κ(P)0) at 25 °C; dotted line, κ(P)/κ(P)0) at 50 °C; dots, µ(P)/µ(P)0). Electrophoretic conditions: fused-silica capillaries, 50 µm i.d. × 30 cm (20 cm to the detector); electrolyte, triethylamine buffer, I ) 100 mM, pH ) 11.50; applied voltage, 1-30 kV; temperature, 15-60 °C; UV detection at 200 nm.
κ)
∑(z )Λ c ) F∑(z )µ c i
i i
i
i
i i
(8)
i
where Λi is the molar conductivity of the ionic compound i, ci is the concentration, zi is the number of charges, and F is the Faraday constant. κ can be experimentally determined by
κ)
PLt S iU 2
(9)
for a capillary of total length Lt, internal section Si, and an applied voltage U. The observed relative variation of conductivity κ(P)/ 6050
Analytical Chemistry, Vol. 77, No. 18, September 15, 2005
(10)
P 1 + 0.037 Lt
It should be noted that the fluctuations observed in Figure 2 at 50 °C (dotted line) are artifacts associated with the limitations of the thermoregulation system. Equilibrium Temperature inside the Capillary. The variation in temperature inside the capillary can be estimated as a function of dissipated power. The electrophoretic mobility is inversely proportional to the viscosity.
µ µ(P)0)
pressure for 15 min. The detection was performed by UV absorbance at 214 nm. Correction of the Mobility Values from Joule Heating. During the separation, the electric current in the capillary generates heat by Joule effect. Although the capillary is thermostated, the equilibrium temperature inside the capillary can be higher than the temperature of the cooling liquid. Due to the increase in temperature in the capillary, the solvent viscosity decreases, and thus, the electrophoretic mobilities increase. To evaluate this effectsintrinsically dependent on the thermoregulation characteristics of the apparatussthe actual mobility µ0 of a fully ionized compound (phenyltrimethylammonium, PTMA) was measured in a phosphate buffer (100 mM ionic strength, pH 8.0) for different temperatures from 15 to 60 °C and different voltages from 1 to 30 kV. The relative variation of the mobility, µ(P)0/µ(P)0)0, was determined as a function of the dissipated power per unit of length (dots in Figure 2). The increase of mobility is ∼4% for each watt dissipated per meter of capillary, independent of the temperature of the cooling fluid. At the same time, these measurements were completed by the determination of the variation of the conductivity κ of the electrolyte. The relative variation of conductivity κ(P)/κ(P)0) is directly related to the relative variation of the mobility, as, by definition,
µ
)
η(P)0)
(11)
η
For small variations of the parameters (i.e., µ ) µ(P)0) + δµ; η ) η(P)0) + δη; and T ) T(P)0) + δT), eq 11 leads to
1+
δµ δη =1µ(P)0) η(P)0)
(12)
and thus,
δµ -1 dη ) µ(P)0) η(P)0) dT
( )
T(P)0)
δT
(13)
Combining eqs 10 and 13, the elevation in temperature δT inside the capillary can be estimated using
δT )
0.037 P Θ Lt
(14)
with
Θ)
-1 dη η(P)0) dT
( )
T(P)0)
(15)
Θ is a parameter depending only on the physical property of the solvent and can be determined directly from the variation of the viscosity as a function of temperature24 (see Table 1 for numerical values). For all the experiments of this work, the voltage was kept sufficiently low (below 15 kV) to ensure a good regulation of the capillary temperature. In all experiments, the values of P/Lt were lower than 0.5 W m-1, and the average increase in temperature was estimated using eq 14 from 0.2 °C (measurements at 15 °C) to 0.8 °C (measurements at 60 °C). The increase in temperature estimated by this method is actually only an average value. The gradient in temperature that is established from the capillary wall to the center of the capillary was not considered; however, this nonhomogeneity of the temperature mainly increases the peak width by generating a
Figure 3. Separation of homopolypeptides samples by capillary electrophoresis. Electrophoretic conditions: fused-silica capillaries, 50 µm i.d. × 30 cm (20 cm to the detector); electrolyte, phosphate buffer 50 mM, NaCl 50 mM, pH ) 2.50; applied voltage, 15 kV; temperature, 25 °C; UV detection at 214 nm.
difference in mobility according to the radial position of the analyte in the capillary. Thus, the average mobility given by eq 10 is related to the average equilibrium temperature inside the capillary. Moreover, the dissipated power was kept as low as possible to limit the fluctuations of the temperature inside the capillary. RESULTS AND DISCUSSION The electrophoretic behavior of six families of homopolypeptides, namely, polyglycines, poly-L-alanines, poly-L-valines, poly-Lleucines, poly-L-isoleucines, and poly-L-phenylalanines, was studied. The electropherograms of the six families of polypeptides obtained in a pH 2.5 phosphate buffer are given in Figure 3. As shown in Figure 3, the mixtures of homopolypeptides were composed of Gly2 to Gly11, Ala2 to Ala7, Val2 to Val6, Leu2 to Leu5, Ile2 to Ile4, and Phe2 to Phe5, respectively. The actual mobility, µ0, was determined at different ionic strengths and was corrected from the joule effect according to eq 9. Ionic mobilities, µ0,∞, and ionic radii, ri, were then determined from these values using the Pitts equation, eq 3. The resulting values are given in Table 2. For polyglycines (n e11), µ0,∞ was determined at different temperatures from 15 to 60 °C and in electrolytes based on two different solvents (aqueous triethylamine buffers or methanol/water (75/ 25 v/v)-based electrolytes). For the five other homopolypeptide families, the ionic mobilities, µ0,∞, were determined at 50 °C in the aqueous triethylamine buffers. Triethylamine buffers were used to ensure a complete ionization of the peptides. Figure 4 displays the experimental µ0 values as a function of the ionic strength for polyglycines at 15 °C. The plain lines represent the nonlinear curve-fitting using the Pitts equation (eq 3). As expected, ionic mobility values decrease with n in correla-
tion with the increase of the ionic radius. The experimental µ0,∞ values obtained for polyglycines were in very good agreement with available literature data28 (see Table 3 for comparison). The relative differences between experimental values and data from the literature at 25 °C are below 2.5% (except for diglycine, 5%). The higher difference observed for diglycine was explained by a lower accuracy on the determination of the actual mobilities of this dipeptide below 38 °C due to higher peak asymmetry. Thus, the two µ0,∞ values for diglycine at 15 and 25 °C were not considered in further calculations. It is worth noting that the values of ionic radii obtained from the Pitts equation should be considered with caution, especially for large values of ri (i.e., for all compounds except polyglycine or polyalanine). Indeed, the variation of actual mobility of the end-charged oligopeptides with the ionic strength was moderate, and all the more moderate as the ionic radius is large. Thus, the radii values derived from the curvefitting were not as accurate, as compared to the determination of ionic mobilities. Conformation of Oligoglycines. Figure 5a displays the variation of oligoglycine ionic mobilities, µ0,∞, as a function of the degree of polymerization n (n e11) at different temperatures, from 15 up to 60 °C. The geometric parameters θ and rchain were determined by curve-fitting of the ionic mobilities (µ0,∞ ) q/γh) as a function of n using eqs 5, 6, and 7. For oligoglycines, rlat was set to 1.0 Å, since there is no degree of freedom associated with such a small lateral chain. Consequently, in this case, θ was the single independent parameter. The curve-fittings lead to very good correlation coefficients. The experimental values of θ and rchain are gathered in Table 4. A dramatic drop of θ from 60 to 35° was observed when the temperature was increased from 15 to 60 °C. This drop corresponds to a stretching of the peptide chain with increasing temperature. This behavior can be easily explained in terms of variations of inter- and intramolecular hydrogen bonds. At low temperature, intramolecular interactions (i.e., hydrogen bonds between functional groups of the same molecule) are favored to the detriment of intermolecular interactions (i.e., hydrogen bonds between oligoglycines and water molecules). When temperature was increased, intramolecular interactions were destabilized in favor of intermolecular interactions, leading to more elongated conformations (low θ values). To demonstrate that the variations of ionic mobility with the temperature are not due to the changes in electrolyte viscosity, ηµ0,∞ was plotted as a function of n (see Figure 5b). Important variations of ηµ0,∞ (∼15%) with the temperature prove that viscosity variation cannot be the unique source of ionic mobility variations. Next, we checked that these variations were not related to fluctuations of the dielectric frictional coefficient γd (see eq 2). γd can be evaluated using the following equation,18
γd )
2 17 τdq 280 r 3 i r
( )
(16)
where τd is the dielectric relaxation time (see Table 1). Taking the experimental values for ri (see Table 2), γd was found to decrease with the temperature. Thus, the dielectric contribution (28) Survay, M. A.; Goodall, D. M.; Wren S. A. C.; Rowe S. C. J. Chromatogr., A 1996, 741, 99-113.
Analytical Chemistry, Vol. 77, No. 18, September 15, 2005
6051
Table 2. Ionic Mobilities (µ0,∞) and Ionic Radii (ri) of Homopolypeptides at Different Temperaturesa,b T °C Gc
n
108 µ0,∞ m2 V-1 s-1
ri Å
T °C
n
108 µ0,∞ m2 V-1 s-1
ri Å
R
Go
15 15
5 6
1.714 1.493
2.69 3.67
0.999 0.997
Go Go Go Go Go
25 25 25 25 25
2 3 4 5 6
3.298 2.732 2.455 2.070 2.002
1.17 1.86 1.85 3.91 2.78
0.999 0.999 0.999 0.999 0.995
Go Go Go Go Go
38 38 38 38 38
2 3 4 5 6
4.134 3.721 3.206 2.831 2.650
1.67 1.08 1.40 2.46 2.64
0.999 0.999 0.999 0.999 0.998
Go Go Go Go Go
50 50 50 50 50
2 3 4 5 6
4.730 4.037 3.768 3.307 3.055
3.49 4.29 3.13 3.45 3.71
0.997 0.999 0.992 0.997 0.999
Go Go Go Go Go
60 60 60 60 60
2 3 4 5 6
5.545 4.921 4.602 4.041 3.751
3.64 3.28 2.17 2.79 3.13
0.997 0.999 0.985 0.998 0.993
A A A A A A
50 50 50 50 50 50
2 3 4 5 6 7
3.383 3.455 3.070 2.775 2.577 2.403
14.95 6.31 5.65 7.85 8.21 11.10
0.973 0.992 0.999 0.993 0.976 1.000
V V V V V
50 50 50 50 50
2 3 4 5 6
3.640 2.869 2.494 2.311 2.117
16.52 30.96 29.41 26.11 25.30
0.982 0.941 0.969 0.999 0.987
L L L L
50 50 50 50
2 3 4 5
3.383 2.620 2.313 2.027
14.95 38.62 33.10 43.01
0.973 0.907 0.932 1.000
I I I
50 50 50
2 3 4
3.536 2.876 2.437
10.28 17.58 29.21
0.986 0.995 0.978
F F F F F
50 50 50 50 50
1 2 3 4 5
3.979 3.064 2.436 2.170 1.898
7.77 39.98 57.78 37.73 54.37
0.997 0.507 0.689 0.758 1.000
R
G G G G G G G G G
15 15 15 15 15 15 15 15 15 15
2 3 4 5 6 7 8 9 10 11
2.467 2.179 1.952 1.764 1.623 1.507 1.423 1.342 1.269 1.196
7.65 4.70 4.59 5.37 5.91 6.55 6.77 7.38 8.10 9.34
0.992 0.998 0.998 0.998 0.997 0.996 0.997 0.995 0.993 0.993
G G G G G G G G G G
25 25 25 25 25 25 25 25 25 25
2 3 4 5 6 7 8 9 10 11
3.000 2.729 2.410 2.176 1.995 1.851 1.755 1.645 1.555 1.481
8.49 4.03 4.66 5.33 6.08 6.75 6.66 7.50 8.19 8.71
0.999 0.995 0.994 0.994 0.992 0.991 0.994 0.991 0.992 0.991
G G G G G G G G G G
38 38 38 38 38 38 38 38 38 38
2 3 4 5 6 7 8 9 10 11
4.022 3.391 2.984 2.688 2.466 2.289 2.205 2.041 1.934 1.842
4.62 5.31 6.26 7.11 7.81 8.51 7.48 8.90 9.51 10.05
0.988 0.995 0.997 0.998 0.998 0.999 0.998 0.998 0.997 0.998
G G G G G G G G G
50 50 50 50 50 50 50 50 50
2 3 4 5 6 7 8 9 10
4.699 3.949 3.506 3.190 2.942 2.729 2.613 2.426 2.276
6.57 7.56 7.72 8.03 8.38 9.30 8.67 10.17 11.24
0.997 0.993 0.999 0.995 0.995 0.996 0.996 0.985 0.985
G G G G G G G G
60 60 60 60 60 60 60 60
2 3 4 5 6 7 8 9
5.338 4.576 4.040 3.661 3.334 3.113 3.014 2.891
7.49 7.21 7.82 8.48 9.70 10.07 8.67 8.34
0.989 0.991 0.996 0.997 0.996 0.997 0.991 0.995
Go Go Go
15 15 15
2 3 4
2.688 2.008 1.904
0.68 3.62 2.05
0.938 0.994 0.999
God
a These values are determined from nonlinear curve-fitting of experimental µ0 data by eq 2 (correlation coefficient R given). b Electrophoretic conditions: see Experimental Section for details. c G: polyglycines in water-based electrolyte. d Go: polyglycines in methanol/water (75/25 v/v). A: poly-L-alanines. V: poly-L-valines. L: poly-L-leucines. I: poly-L-isoleucines. F: poly-L-phenylalanines.
could not explain the decrease of ηµ0,∞ with temperature. Moreover, the γd variations were too low to explain the observed ηµ0,∞ variations. Consequently, variation of the hydrodynamic frictional coefficient, i.e., variation of the peptide conformation, was considered to be the prevailing factor in the variations of ηµ0,∞ with temperature. In the case of polyglycines in methanol-water (75/25 v/v) electrolytes, only a few conformational changes with the temperature were observed (see lines GO in Table 4). A slight decrease 6052 Analytical Chemistry, Vol. 77, No. 18, September 15, 2005
of θ was observed with increasing temperature. However, it is worth noting that the peptide conformation was much more compact in the hydro-organic electrolyte (θ varying from 72.5 to 69°) than in water (θ varying from 60 to 35°). This can be explained by a lower affinity between the solvent and the peptides in hydro-organic electrolyte. As a consequence, intramolecular interactions remained predominant at all temperatures, and the peptide conformation remained very compact for all temperatures from 15 to 60 °C.
Figure 4. Variation of actual mobilities µ0 of polyglycines Gi (2 e n e 11) as a function of ionic strength I, at 15 °C. The symbols represents the experimental µ0 values, and the straight lines, the nonlinear curve-fitting by the Pitts equation, eq 3. Electrophoretic conditions: fused-silica capillaries, 50-µm i.d. × 60 cm (50 cm to the detector); electrolyte, triethylamine buffer, I ) 10-100 mM, pH ) 11.50; applied voltage, 10-15 kV; temperature, 15 °C; UV detection at 200 nm. Table 3. Comparison of Ionic Mobility Values of Oligoglycines in Water at 25 °Ca n
µ0,∞ lit.b 10-8 m2 V-1 s-1
µ0,∞ lit.c 10-8 m2 V-1 s-1
µ0,∞ exptld 10-8 m2 V-1 s-1
2 3 4 5 6
3.18 2.69 2.40 2.17 1.97
3.15 2.67 2.38 2.15 1.95
3.000 2.729 2.410 2.176 1.995
a Values from literature (µ0,∞ lit.)28 or from this work (µ0,∞ exptl; see Table 2). bDetermined in borate buffers. c Average value from experiments in borate buffers, phosphate buffers, and citrate buffers. d Determined in triethylamine buffers. For n > 6, values from the literature were not available.
Figure 5. Variation of µ0,∞ (A) and ηµ0,∞ (B) for oligoglycines as a function of the degree of polymerization n and at different temperatures. The closed symbols represent the experimental data. The open squares represents values from the literature.28 The straight lines represent the nonlinear curve-fittings using eq 7. Same electrophoretic conditions as in Figure 4 with temperatures from 15 to 60 °C. Table 4. Geometrical Parameters of Oligopeptides in Water-Based and Methanol/Water-Based Electrolytesa
G G G G G A V L I F Go Go Go Go Go
T °C
rchainb,c Å
θb
rlatb Å
R
rchaind Å, theoretical
15 25 38 50 60 50 50 50 50 50 15 25 38 50 60
1.00 1.00 1.00 1.00 1.00 1.72 3.19 4.07 3.28 5.12 1.00 1.00 1.00 1.00 1.00
60.1 56.9 50.1 40.6 35.5 34.1 31.7 21.8 27.7 0.1 72.5 71.9 71.0 68.1 69.3
2.83 2.81 2.72 2.57 2.47 3.16 4.57 5.21 4.57 5.61 2.90 2.90 2.90 2.89 2.89
0.9996 0.9998 0.9989 0.9996 0.9978 0.9999 0.9998 0.9989 0.9993 0.9978 0.995 0.991 0.993 0.987 0.974
1.09 1.09 1.09 1.09 1.09 1.91 3.16 3.98 3.98 5.00 1.09 1.09 1.09 1.09 1.09
Conformation of Other Oligopeptides. The ionic mobility of the six families of homopolypeptides is plotted as a function of the degree of polymerization in Figure 6. The geometric parameters θ, rchain, and rlat were determined by curve-fitting of the ionic mobilities (µ0,∞ ) q/γ h) as a function of n using eqs 5, 6 and 7. The hydrodynamic modeling led to very good correlation coefficients (see Table 4), giving even more credits to the hydrodynamic modeling of the molecule using a cylindrical geometry. The experimental values of rchain are very close to the theoretical values corresponding to a fully stretched conformation of the lateral chain (see Figure 1c and column theoretical rchain in Table 4). One exception is the poly-L-isoleucines, whose experimental rchain value is 21% lower than the theoretical one, corresponding to a more compact conformation of the lateral chains. For the five other families of oligopeptides, the lateral chains were mainly in a stretched conformation. The experimental θ values are very different for all oligopeptides. However, these values are always lower than 41°. The corresponding values of rstp are >2.5 Å for all oligopeptide families, indicating that these oligopeptides did not adopt helicoidal structures, at least in the range of degrees of polymerization that was considered in this work (R-helix corre-
sponds to a step of 1.5 Å per residue, and 310-helix corresponds to a step of 2 Å per residue30). This is in accordance with the fact that helix formation generally needs at least six residues to be
(29) Janz, G. J.; Tomkins R. P. T. Nonaqueous Electrolyte Handbook; Academic Press: New York and London, 1972; Vol. 1.
(30) Spach, G.; Freund, L.; Daune, M.; Benoıˆt, H. J. Mol. Biol. 1963, 7, 468482.
a Electrophoretic conditions: see Experimental Section for details. rlat, rchain, and θ were determined by nonlinear curve-fitting (correlation coefficient R given) of ionic mobilities as a function of n, using eqs 5, 6, and 7 for rend)2 Å. c rchain was beforehand set to 1 Å in the case of oligoglycines and was not determined by curve-fitting. d The theoretical values of rchain have been calculated on the basis of a fully stretched conformation as described in Figure 1c.
b
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Figure 6. Variation of ionic mobilities of oligopeptides (G, A, V, L, I, F) as a function of the degree of polymerization, n, at 50 °C and in water-based electrolytes. The symbols represent the experimental data. The straight lines represent the nonlinear curve-fittings using eq 7. Same electrophoretic conditions as in Figure 4 with T ) 50 °C.
stable. Finally, θ was found to decrease when rchain increased. Thus, the stretching of the peptide chain is favored by the bulkiness of the lateral chain. The peptide conformation changed from a compact conformation for oligoglycines (θ ) 40.6°) to a fully stretched conformation for oligo-L-phenylalanines (θ ) 0.1°).
6054 Analytical Chemistry, Vol. 77, No. 18, September 15, 2005
CONCLUSION Good correlations were obtained in the modeling of experimental ionic mobilities of six families of oligopeptides using hydrodynamic equations derived from a cylindrical geometry. This modeling has been demonstrated to be very effective for quantitatively monitoring changes in peptide conformations when changing the temperature, the nature of the solvent, or the bulkiness of lateral chains. Contrary to more empirical modeling based on relationship between the effective mobility and the peptide molar mass, hydrodynamic modeling of the frictional coefficient allows one to directly correlate the ionic mobility with the molecular geometrical parameters, such as the average distance between residues or the average length of the lateral chain. Consequently, this approach allows a direct determination of the geometry acquired by a compound in given conditions (temperature, solvent, etc.). It should also allow a better modeling of separation performances on the basis of the precise knowledge of the geometry of the analytes. Further experimental studies involving multi- or evenly charged polypeptides are being investigated to generalize these results obtained for end-charged homopolypeptides. Received for review May 6, 2005. Accepted July 5, 2005. AC050783C
