Interconverting Conformations of Variants of the Human

Capillary electrophoretic separation profiles of cleaved variants of β2-microglobulin reflect the conforma- tional equilibria existing in solutions o...
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Anal. Chem. 2006, 78, 3667-3673

Interconverting Conformations of Variants of the Human Amyloidogenic Protein β2-Microglobulin Quantitatively Characterized by Dynamic Capillary Electrophoresis and Computer Simulation Niels H. H. Heegaard,*,† Thomas J. D. Jørgensen,‡ Lei Cheng,‡ Christian Schou,† Mogens H. Nissen,§ and Oliver Trapp|

Statens Serum Institut, Copenhagen, Denmark, Department of Molecular Biology, University of Southern Denmark, Odense M, Denmark, Institute of Medical Anatomy, University of Copenhagen, Denmark, and Max-Planck-Institut fu¨r Kohlenforschung, Mu¨lheim an der Ruhr, Germany

Capillary electrophoretic separation profiles of cleaved variants of β2-microglobulin (β2m) reflect the conformational equilibria existing in solutions of these proteins. The characterization of these equilibria is of interest since β2m is responsible for amyloid formation in dialysisrelated amyloidosis and thus is able to attain alternative conformations that lead to irreversible aggregation and precipitation. In this study, we quantitate the increased conformational instability of cleaved β2m by extracting rate constants and activation energies by simulating the experimental data using a unified theory for dynamic chromatography and dynamic electrophoresis. The results are correlated with the outcome of independent experiments based on mass spectrometric measurement of H/D exchange. This study illustrates that dynamic capillary electrophoresis is suitable for the investigation of the interconversion of protein conformations of amyloidogenic molecules and is not only restricted to ideal model compounds. While the rules governing protein folding are still not fully understood, it is clear that several clinical conditions arise from pathological deviations from native protein conformations. More than 20 distinct protein conformational diseases such as Alzheimer’s disease, spongiform encephalopathies, senile systemic amyloidosis, dialysis-related amyloidosis and others have now been recognized. They are all characterized by an end-stage with malfolded, irreversibly aggregated, insoluble protein rich in β-sheet structures destroying the organs and tissue in which it is located.1 There is a need to understand and inhibit such processes and therefore for methods to characterize the folding abberations involved. * To whom correspondence should be addressed. Phone: +45 32683378. Fax: +45 32683876. E-mail: [email protected]. † Statens Serum Institut. ‡ University of Southern Denmark. § University of Copenhagen. | Max-Planck-Institut fu ¨ r Kohlenforschung. (1) Merlini, G.; Bellotti, V. N. Engl. J. Med. 2003, 349, 583-96. 10.1021/ac060194m CCC: $33.50 Published on Web 04/28/2006

© 2006 American Chemical Society

In dialysis-related amyloidosis (DRA), the amyloidogenic protein is β2-microglobulin (β2m), a small (12 kDa) molecule that functions as the nonpolymorphic light chain stabilizing the heavy chain of MHC class I complexes on cell surfaces. β2m also circulates as a monomer in plasma.2 The formation of amyloid by β2m in DRA targets osteoarticular tissues and is in some patients associated with the presence of elevated circulating levels3 of a cleaved form of wild-type (wt) β2m that lacks the lysine-58 residue. β2m is in this way transformed from a single-chain molecule with an intrachain disulfide bridge into a molecule consisting of two chains (A and B) held together by an interchain disulfide bridge.4 This variant β2m, ∆K58-β2m, can be generated by an activated complement system, and the generation of the final product is preceded by a cleaved β2m variant, cK58-β2m where lysine-58 is still present C-terminally in the A-chain. The conformation of both variants appears to be considerably more unstable than the seven β-strand globular wt-β2m.5-9 Capillary electrophoresis (CE) and H/D exchange experiments indicate that at physiological pH and temperature the cleaved β2m variants display an equilibrium between folded, native conformations and more unfolded states. Since their solution stability is also decreased and ordered oligomer formation and increase in thioflavin T staining can be observed over time,5 there may be a link between these unfolded conformations and amyloidogenicity. It is therefore of interest to characterize the conformational interconversion reactions of still soluble, monomeric β2m variants. Because of its minimal sample consumption, native, yet highly efficient, separation capabilities, (2) Chatani, E.; Goto, Y. Biochim. Biophys. Acta 2005, 1753, 64-75. (3) Corlin, D. B.; Sen, J. W.; Ladefoged, S.; Lund, G. B.; Nissen, M. H.; Heegaard, N. H. Clin. Chem. 2005, 51, 1177-84. (4) Nissen, M. H.; Thim, L.; Christensen, M. Eur. J Biochem. 1987, 163, 218. (5) Heegaard, N. H. H.; Jørgensen, T. J. D.; Rozlosnik, N.; Corlin, D. B.; Pedersen, J. S.; Tempesta, A. G.; Roepstorff, P.; Bauer, R.; Nissen, M. H. Biochemistry 2005, 44, 4397-407. (6) Heegaard, N. H. H.; Rovatti, L.; Nissen, M. H.; Hamdan, M. J. Chromatogr., A 2003, 1004, 51-9. (7) Heegaard, N. H.; Roepstorff, P.; Melberg, S. G.; Nissen, M. H. J. Biol. Chem. 2002, 277, 11184-9. (8) Heegaard, N. H.; Sen, J. W.; Kaarsholm, N. C.; Nissen, M. H. J. Biol. Chem. 2001, 276, 32657-62. (9) Heegaard, N. H. H.; Sen, J. W.; Nissen, M. H. J. Chromatogr., A 2000, 894, 319-27.

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possibilities for temperature control, and reproducibility, CE has previously been used to characterize conformational equilibria in proteins and peptides.10-16 CE is also able to separate conformational states of wt-β2m and the cleaved β2m variants.7,8 We here use CE peak data in combination with newly developed equations17,18 that simulate elution profiles of interconverting molecules, for the estimation of rate constants and kinetic activation parameters. The conformational interconversion of β2m variants may serve as a paradigm for the early misfolding pathways of other proteins that form amyloid and constitutes a convenient model system for testing, for example, small-molecule approaches to inhibit misfolding and the damaging propagation of intermolecular interactions between misfolded molecules. EXPERIMENTAL PROCEDURES Materials. Wt-β2m, cK58-β2m, and ∆K58-β2m were purified from nephropathy patient urine as described.4,7,19,20 The preparations of wt-β2m and ∆K58-β2m were pure by capillary electrophoresis, reversed-phase HPLC, and mass spectrometry except for 10-20% methionine-99-oxidized species.9 By mass spectrometry, the molecular masses of the purified proteins were in agreement with the theoretical masses of 11729.2 (wt-β2m), 11747.2 (cK58-β2m), and 11619.0 Da (∆K58-β2m). The purified proteins (1-20 mg/mL) in phosphate-buffered saline (PBS; 137 mM NaCl, 2.7 mM KCl, 1.5 mM KH2PO4, and 6.5 mM Na2HPO4, pH 7.4) were kept at -20 °C until used. For some experiments, PBS was exchanged for plain or four times diluted capillary electrophoresis running buffer (0.1 M phosphate, pH 7.4, cf. below) by dialysis overnight at 4 °C in a molecular weight cutoff 3500 dialysis cassette (Pierce, Rockford, IL). Amide Hydrogen (1H/2H) Exchange Monitored by Mass Spectrometry. Amide hydrogen-deuterium exchange (H/D exchange) was monitored by mass spectrometry as detailed previously5 with the exception of using diluted deuterated PBS buffer for the isotopic exchange in some of the experiments. Capillary Electrophoresis. Beckman P/ACE 2050 and 5010 instruments equipped with liquid sample cooling and UV detection were used. Electrophoresis buffer was 0.1 M phosphate (0.081 M Na2HPO4 + 0.019 M NaH2PO4), pH 7.4. Detection took place at 200 nm, and the separation tube was a 50-µm-inner diameter uncoated fused-silica capillary (Polymicro Technologies or Beckman Coulter) of 47- or 57-cm total length with 40 or 50 cm to the detector window. Samples (10-20 µL) were protected against evaporation by overlaid light mineral oil (Sigma M-3516).9 A (10) Rochu, D.; Ducret, G.; Ribes, F.; Vanin, S.; Masson, P. Electrophoresis 1999, 20, 1586-94. (11) Moore, A. W., Jr.; Jorgenson, J. W. Anal.Chem. 1995, 67, 3464-75. (12) Rochu, D.; Ducret, G.; Masson, P. J. Chromatogr., A 1999, 838, 157-65. (13) Ma, S.; Kalman, F.; Kalman, A.; Thunecke, F.; Horvath, C. J. Chromatogr., A 1995, 716, 167-82. (14) Thunecke, F.; Fischer, G. Electrophoresis 1998, 19, 288-94. (15) Verzola, B.; Chiti, F.; Manao, G.; Righetti, P. G. Anal. Biochem. 2000, 282, 239-44. (16) Hilser, V. J.; Freire, E. Anal. Biochem. 1995, 224, 465-85. (17) Trapp, O. Anal. Chem. 2006, 78, 189-98. (18) Trapp, O. Electrophoresis 2006, 27, 534-41. (19) Nissen, M. H.; Johansen, B.; Bjerrum, O. J. J. Immunol. Methods 1997, 205, 29-33. (20) Nissen, M. H.; Roepstorff, P.; Thim, L.; Dunbar, B.; Fothergill, J. E. Eur. J. Biochem. 1990, 189, 423-9. (21) Deleted in proof.

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synthetic peptide of the sequence acetyl-Pro-Ser-Lys-Asp-OH was used as an internal marker. Separations were carried out at 80100-µA constant current corresponding to field strengths of 200400 V/cm or as indicated. In some cases, current settings were varied stepwise. The capillary liquid cooling was thermostated at the indicated temperatures. Experiments below thermostat settings of 15 °C were performed in an instrument placed in a 4 °C cold room. In some experiments, sample temperature was controlled by an external circulating water bath, and in this case, the exact temperature at the sample was measured in a sample vial containing water and placed adjacent to the sample position. Injected sample volumes were between 2.2 and 8.8 nL (2-8-s pressure injections), and capillaries were rinsed between runs with 0.1 M NaOH for 1 min and water for 1 min before being equilibrated with electrophoresis buffer for 2 min. Data were acquired and processed by the System Gold software. Data were imported as ASCII files into Excel work sheets or into the Grams/ AI v. 7.01 evaluation software (Thermo Galactic, Salem, NH) and converted for simulations (cf. below) or into GraphPadPrism v. 3.0 (San Diego, CA) for presentation as graphs. Computer Simulation. Computer simulation of elution profiles featured by a plateau formation was performed with the software ChromWin17,18,22-25 (version 7.0 2005) and DCXplorer (Trapp, O. ChromWin is available from O.T. as an executable program, running under Microsoft Windows 98/Me/NT/2000 or XP upon request: [email protected]) to obtain rate constants of the protein folding processes during the time-scale separation. The software algorithm is based on the theoretical plate model, originally derived to describe gas chromatographic interconversion processes, and the stochastic model. As previously shown, both models can be applied to chromatographic and electrophoretic experiments. For the evaluation of the interconversion rate constants and interconversion barriers, the total migration times of the individual protein conformers tR, the plateau height hplateau, the peak widths at half-height of the individual conformers wh, and the peak ratio of the conformers were used. Peak form analysis was performed with the modified stochastic model (SM+) and the advanced method “Find Isomerization Barrier II” using an improved Newton algorithm in order to find the best agreement of the simulated and experimental elution profiles in only a few simulation steps. The method Find Isomerization Barrier II also adjusts the plate numbers to improve the agreement between experimental and simulated elution profile. The principle of microscopic reversibility was neglected because no selector was used in the experiments. ChromWin yielded the forward and backward rate constants kffs and ksff of the protein folding process between the two conformers (first eluted conformer f (fast) and second eluted conformer s (slow). Calculation of Activation Parameters ∆Hq and ∆Sq. The Gibbs free activation energy ∆Gq(T) was calculated according to the Eyring eq 1 with kB as the Boltzmann constant (kB ) 1.380662 × 10-23 J‚K-1), T as the experimental temperature (K), h as Planck’s constant (h ) 6.62617 × 10-34 J‚s), and R as the gas (22) Trapp, O.; Schurig, V. J. Am. Chem. Soc. 2000, 122, 1424-30. (23) Trapp, O.; Schurig, V. Comput. Chem. 2001, 25, 187-95. (24) Trapp, O.; Shellie, R.; Marriott, P.; Schurig, V. Anal. Chem. 2003, 75, 445261. (25) Trapp, O. J. Chem. Inf. Comput. Sci. 2004, 44, 1671-9.

Figure 1. Conformational heterogeneity of wt-β2m in CE at different sample ionic strengths and electrophoresis current conditions. Left panel: wt-β2m diluted from 9.4 mg/mL in PBS to 0.5 mg/mL by water was injected for 4 s. Right panel: same sample but diluted in CE buffer (0.1 M phosphate, pH 7.4) to 0.5 mg/mL. CE was performed using constant current conditions as indicated by the insets. The capillary was liquid thermostated at 18 °C. Under CE conditions with a rapid current ramping after sample injection, β2m separates into two peaks (f, fast and s, slow) representing different conformations.

constant (R ) 8.31441 J‚K-1‚mol-1). The statistical factor κ was set to 1 as the true statistical factors for the conformational change are not experimentally accessible.

(

∆Gq(T) ) - RT ln k1

h κkBT

)

(1)

As the studies were performed at different temperatures, the activation enthalpy ∆Hq for the f-s and s-f interconversion was obtained via the slope and the activation entropy ∆Sq via the intercept of the Eyring plot (T -1 versus ln(kffs/T) and (T -1 versus ln(ksff/T)) for the respective samples. At higher temperatures, peak coalescence occurred in some experiments. Therefore, rate constants could not be determined with sufficient precision, and thus, these experiments were not included for the calculation of activation parameters. RESULTS AND DISCUSSION ∆K58-β2m, the β2m variant cleaved after and devoid of lysine58, is conformationally more unstable than the wild-type parent molecule. This has previously been demonstrated by different approaches including H/D exchange monitored by mass spectrometry and by CE.5,7 In CE, the distribution of conformers was indirectly inferred by the size of two distinct peaks, and the interconversion was reflected by a plateau or intermediary peak formation between these peaks. Such profiles are typical for interconversion processes taking place in the time scale of separation and are amenable to quantitative analysis.16,22,26-30 Conformers in Wild-Type β2m. While wt-β2m under physiological separation conditions exhibits only minor peak profile heterogeneity, substantial heterogeneity can be induced by adding

organic solvent to the protein solution.8,32 This induces a conformer electrophoretic peak pattern consisting of a first (fast, f) peak and a more slowly migrating variant peak (slow, s), presumably corresponding to the native and a partially unfolded species, respectively. We previously observed that the ionic strength of the CE separation buffer influenced the f/s peak ratio of wt-β2m conformers induced by organic solvents.8 We now find (Figure 1) that an increase in the twin-peak pattern is also observed when lowering the sample ionic strength in the absence of any organic solvent. Thus, a wt-β2m sample diluted with water (lower trace, left column, Figure 1) shows an increase in the s-form and in the height of the plateau connecting the two peaks when compared to higher ionic strength sample conditions (lower trace, right column, Figure 1). Whereas this observation might be due to an increased conformational heterogenity of the sample under low ionic strength conditions, H/D exchange monitored by mass spectrometry failed to show any significant difference in the exchange kinetics of wt-β2m in low or high ionic strength buffers (data not shown). At 18 °C, the unfolding kinetics of wt-β2m is very slow, with a T1/2 for unfolding of much more than 2 h (data not shown). In comparison, a rate of 0.9 × 10-2 min-1 (T1/2 ) 77 min) was found for the unfolding at 37 °C.5 Thus, the temperature has a major influence on the unfolding rate. Therefore, the induction of unfolded forms, especially in the samples in dilute (26) Trapp, O.; Schoetz, G.; Schurig, V. Chirality 2001, 13, 403-14. (27) Schoetz, G.; Trapp, O.; Schurig, V. Electrophoresis 2001, 22, 2409-15. (28) Trapp, O.; Schurig, V. Chem. Eur. J. 2001, 7, 1495-502. (29) Trapp, O.; Trapp, G.; Schurig, V. Electrophoresis 2004, 25, 318-23. (30) Trapp, O. Electrophoresis 2005, 26, 487-93. (31) Deleted in proof. (32) Chiti, F.; DeLorenzi, E.; Grossi, S.; Mangione, P.; Giorgetti, S.; Caccialanza, G.; Dobson, C. M.; Merlini, G.; Ramponi, G.; Bellotti, V. J. Biol. Chem. 2001, 276, 46714-21.

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Figure 2. Comparison of the stability and amount of conformers under sample stacking conditions in wt- and ∆K58-β2m (columns A and B, respectively). CE performed as given in the text of Figure 1, but using different separation currents after an initial 3-min phase of 140 µA (see inset current diagram).

Figure 3. Sample temperature influence on the electrophoretic distribution of conformers in ∆K58-β2m but no influence of sample ionic strength. Samples were ∼1 mg/mL ∆K58-β2m after dialysis against low ionic strength buffer (four times diluted electrophoresis buffer) or plain electrophoresis buffer. All experiments were performed at a capillary cooling liquid temperature setting of 5 °C to preserve distribution of conformers in the samples that were incubated at the indicated temperatures. Samples were electrophoresed using 90-µA constant current after injection for 2 s. The f- and s-conformer distribution (% f-peak area of total peak area) at low (O) and isotonic (b) ionic strength in samples incubated at different temperatures is shown. Results are expressed as the mean ( the SD of triplicate experiments.

and the electrophoresis buffer. When the conductance in the sample zone is lower than the conductance of the electrophoresis buffer, stacking, i.e., electrical field amplification, in the sample zone will occur. This causes a potentially considerable local increase of temperature. In the present case, theory estimates that the sample zone may experience temperature increases up to 50 °C upon initiation of electrophoresis.33 However, in practice, the assimilation to the electrophoresis buffer conditions probably occurs very quickly. The most important temperature gradient may in fact arise in the portion of the capillary (∼4 cm) from the inlet end to the entry into the cassette where no thermostating is encountered.34 The experiments in the upper panel of Figure 1 confirm that the degree of conformational heterogeneity in wtβ2m is related to the current ramping conditions at the initiation of electrophoresis; i.e., a slower onset of current and thus a lower temperature increase in the sample zone and in the exposed part of the capillary results in a nonheterogeneous β2m peak, even when the final current is higher to get comparable peak appearance times. Thus, the notion that CE performed at various field strengths may be used to examine the reversibility of the unfolding8 fails to take this temperature variability into account. Indeed, experiments using a fast ramp to 140 µA followed by different low current conditions showed the relative stability of

buffer, may be due to temperature pertubations of the sample zone caused by conductance differences between the sample solution

(33) Vinther, A.; So ¨eberg, H. J. Chromatogr. 1991, 559, 27-42. (34) Porras, S. P.; Marziali, E.; Gas, B.; Kenndler, E. Electrophoresis 2003, 24, 1553-64.

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Figure 4. Folding kinetics of cleaved β2m studied on-line by CE. CE analysis at different capillary cooling fluid thermostat settings as indicated. Sample, incubated at same temperature as capillary temperature as indicated on the figure, was ∆K58-β2m (upper panel) or cK58-β2m (lower panel) at 0.95 and 1.50 mg/mL, respectively, in electrophoresis buffer. Samples also contained 0.2 mg/mL marker peptide and were overlaid with mineral oil to prevent evaporation. f and s indicate the β2m conformers while the late peak represents the marker peptide. Samples were injected for 2 s and separated using a constant current of 90 µA in 0.1 M phosphate, pH 7.3.

the two-peak pattern over time (Figure 2). The existence of an interpeak plateau, however, suggests that some intermediary forms may exist.16 Conformers in Lysine-58-Cleaved β2m. In accordance with previous results5,7 (Mimmi et al. 2006, submitted), a conformational heterogeneity is found to be present in β2m cleaved at lysine58 (cK58- and ∆K58-β2m, where the first is cleaved wt-β2m with the K58 residue preserved and the latter has the K58 residue removed (as occurs in vivo20)). This conformational heterogeneity is readily observed as the pronounced s-peak and increased intermediary forms in Figure 2B as compared to the peak profile of wt-β2m obtained under the same stacking conditions (Figure 2A). In contrast to the case for wt-β2m, the cleaved β2m variants display twin peaks in the CE analyses also at sample buffer conductivities similar to the electrophoresis buffer (Figure 3). Thus, a fraction of ∆K58-β2m exists as an alternative conformation at room temperature (20 °C). In the experiments of Figure 3, the very low separation temperature (5 °C) and the relatively low current setting of 90 µA suppress temperature increases even under stacking conditions, and thus, the peak ratios obtained using different ionic strengths of the sample buffers are essentially similar. However, as also suggested by the preponderance of the s-peak under stacking conditions (Figure 2B), the sample temperature influences the peak ratio to a major degree (Figure 3). This is in close agreement with mass spectrometry time course experiments of H/D-exchanged ∆K58-β2m at different temperatures, which showed a pronounced temperature dependency of the unfolding rate of the cleaved and noncleaved β2m-species.5 In Figure 3, the low (5 °C) separation temperature and constant current mode ensure the highest possible conservation of the equilibrium distribution in the sample incubated at different temperatures, and it was found that the f/s-peak area ratio was very dependent on the sample temperature especially above

30 °C. Thus, after an increasing plateau formation (mainly contributed by the f-peak), there was an increase of the s-peak area at the expense of the f-peak area up to an ∼55:45 distribution at sample temperatures around 40-45 °C in contrast to the ∼70: 30 distribution in the 5-25 °C temperature range (Figure 3). This change in peak ratio was reversible; i.e., the relative increase of the s-form reverted when sample temperature was again lowered (data not shown). However, over time, irreversible aggregation occurred in samples that were kept at 40-45 °C. The peak area of both conformers decreased equally. This process was dependent on protein concentration, and irreversible aggregation was more pronounced in ∆K58-β2m than in cK58-β2m.5 Similar observations were made in recent work on NMR measurements of cleaved β2m (Mimmi et al. 2006, submitted). The disappearing material could not be recovered by reverting to lower sample temperatures (data not shown). These data are compatible with an aggregation and precipitation process that is dependent on sufficiently long lifetimes (i.e., temperature dependent) of partially unfolded species as well as on the likelihood of partially unfolded molecules encountering similarly unfolded molecules (i.e., concentration dependent). While the experiments (Figure 3) show a temperaturedependent increase of the rate of formation of partially unfolded ∆K58-β2m, they do not readily allow modeling of the interconversion rates because incubation and separation temperatures are different in these experiments and designed to preserve the equilibrium distribution of conformational species in the sample and not to allow interconversion during electrophoresis. However, given the clear temperature dependency of the unfolding (i.e., population of the s-form), we next examined the separation profiles of the two cleaved β2m variants using identical sample and separation temperatures (and nonstacking conditions) in the Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

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Figure 6. Eyring plots (ln(k1app/T) as a function of 1/T) for the determination of the activation parameters ∆Hq and ∆Sq of the f f s (red curves) and s f f (blue curves) for the interconversion of (A) ∆K58- and (B) cK58-β2m. Data obtained on the basis of the simulations shown in Figure 5. The upper and lower curves represent the error bands of the linear regression with a level of confidence of 95%. (correlation coefficients r and residual standard deviations sy: cK58-β2m f f s r ) 0.9815 sy ) 0.1817, s f f r ) 0.9921 sy ) 0.1123; ∆K58-β2m f f s r ) 0.9971 sy ) 0.0688, s f f r ) 0.9945 sy ) 0.0762).

Figure 5. Simulated elution profiles based on the data from the electropherograms of cleaved β2m shown in Figure 4. Simulation parameters yield rate constants and activation barriers of the interconversion process. Electromigration profile simulation of (A) ∆K58and (B) cK58-β2m separations between 5 and 27 °C as indicated.

5-29 °C temperature range employing constant current conditions (Figure 4). These experiments show changes in the unfolding-refolding rates reflected by the changes of the plateau between the conformer peaks (f and s) with increasing temperature. While separations at 5 °C conserve the equilibrium present in the sample, separations at elevated temperature may allow some interconversion to take place in the time scale of the CE experiment, especially when getting above 20 °C; i.e., unfolded molecules refold and native molecules unfold during electrophoresis. CE affords an analysis of the interconversion kinetics because plateau formation reflects this process.16 One limitation is that only conditions where the two distinct conformer peaks and a plateau height exist can be used. Thus, data from temperatures (in these experiments, ∼30 °C) where peak fusing occurs could not be used. Consequently, a rather narrow temperature range underlies the 3672 Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

calculations. The risk of field-amplified temperatures in the sample zone as seen Figure 1 is minimized in the experiments of Figure 4, because sample and electrophoresis buffer conductivities are similar. Despite the liquid thermostating, the exact temperature during electrophoresis in the electrophoresis buffer is unknown and is higher than in the absence of an electrical field and also, as mentioned above, the very first portion of the capillary separation path is not thermostated. However, phosphate buffers do have a small ionization heat and almost constant pH with rising temperatures.10,12 Additionally, a precise quantitative analysis is complicated by the fact that the viscosity of the sample as well as of the electrophoresis buffer changes with temperature. The lower viscosity at higher temperatures influences peak appearance times as well as the amount of sample injected. Thus, it can be observed that the marker peak increases with higher temperature. With these limitations in mind, the computer-based simulation of the electrophoretic profiles between 5 and 27 °C are shown in Figure 5. The activation enthalpies ∆Hq for the f-s and s-f interconversion were obtained via the slope and the activation entropies ∆Sq via the intercept of the Eyring plots (T -1 versus ln(kffs/T) and (T -1 versus ln(ksff/T)) (Figure 6). Deviations of the activation parameters ∆Hq and ∆Sq have been calculated by error band analysis of the linear regression with a level of confidence of 95% and are listed in Table 1.17,18Activation enthalpies going from the f- to the s-form were consistently higher than the reverse reaction, and within experimental error, these values were comparable for cK58- and ∆K58-β2m while the energy for the reverse interconversion (sff) was highest for the cK58-β2m variant. The ffs interconversion enthalpies of ∼65 kJ/mol found

Table 1. Activation Enthalpy and Entropy for the Conformational Interconversions of Cleaved β2m Obtained from the Simulation Parameters (Figure 6) ∆Hq (kJ/mol)

∆Sq (J/mol K)

f fs s ff

∆K58-β2m 66.2 ( 3.6 49.95 ( 4.1

-76.7 ( 7.8 -128.5 ( 26

f fs s ff

cK58-β2m 66.9 ( 4.6 61.8 ( 4.5

-67.1 ( 8.5 -83.8 ( 12

in the present study are less than the 173 kJ/mol found by H/D exchange studies.3 The discrepancy may be explained by different experimental conditions including the contributions from the time it takes to amide exchange in the mass spectrometric studies and the fact that the H/D exchange studies were performed in PBS and not in the CE buffer. H/D exchange results do suggest that the unfolding is accelerated in CE buffer compared with PBS (data not shown), which is consistent with the lower activation enthalpy found by analysis of the CE experiments. However, the most important factor contributing to the discrepancy is probably the uncertainty regarding the precise temperatures in the CE experiments, which are higher than the thermostat setting values used for calculating the results of Table 1. With a 90-µA current in a 0.1 M phosphate buffer, the induced Joule heat is estimated to contribute with a 2-4 °C increase in buffer temperature.33 With a temperature correction like this, the values derived from the CE experiments will get closer to the activation enthalpy values derived from the mass spectrometric data. However, the exact temperatures in the electrophoresis buffer during a run are not known and the temperature gradients arising from the unshielded capillary ends also contribute to the variability, but the consistency of conformer peak distribution (Figure 3) actually suggests that conformer analysis may be a convenient molecular thermometer to reveal CE buffer temperatures under a given set of conditions. This notion is analogous to the proposed use of interaction (35) Berezovski, M.; Krylov, S. N. Anal. Chem. 2004, 76, 7114-7.

parameters in affinity CE to reflect electrophoresis buffer temperature.35 For improved conformational studies, the correspondence between thermostat temperature settings and actual running temperature may be increased by using thinner capillaries and lower driving currents albeit at the expense of resolution, analysis time, and detection limits. CONCLUSIONS The present study confirms the temperature-dependent instability of the native conformation of β2m and the increased instability of a cleaved form of the molecule. Detailed analysis of the interplay between sample solution conditions, electrical parameters, and peak profiles showed that the temporary temperature increases induced under sample stacking conditions and the variability induced by the nonshielded capillary ends in some cases were enough to perturb the native conformation of β2m. Also, conformational heterogeneity exists in solutions of lysine58-cleaved β2m to a greater extent than in wt-β2m and is also highly influenced by temperature. With the application of molecular dynamics simulation with newly developed unified equations for access to rate constants of first-order reactions, it was possible to use capillary electrophoretic separation peak profiles at different temperatures to extract activation parameters for the conformational interconversions. While the uncertainty about the exact temperature experienced by the analytes during electrophoresis hampers the precision of the determined parameters, the study shows the feasibility of the approach not only for ideal model compound but also for biomolecules. Dynamic CE promises to be useful for further quantitative studies of early events on the pathological folding pathways of protein conformational diseases. ACKNOWLEDGMENT This work was supported by Sygesikringen “danmarks” forskningsfond, The Danish Medical Reseach Council, and CarlsbergFondet. O.T. thanks the Deutsche Forschungsgemeinschaft for an Emmy Noether grant (TR 542/3-1). Received for review January 28, 2006. Accepted March 29, 2006. AC060194M

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