Journal of Biotechnology 115 (2005) 279–290

Effects of redox buffer properties on the folding of a disulfide-containing protein: dependence upon pH, thiol pKa, and thiol concentration Jonathan D. Gougha , Watson J. Leesb,∗ b

a Department of Chemistry, Syracuse University, Syracuse, NY 13244, USA Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA

Received 12 April 2004; received in revised form 20 September 2004; accepted 27 September 2004

Abstract Aliphatic thiols are effective as redox buffers for folding non-native disulfide-containing proteins into their native state at high pH values (8.0–8.5) but not at neutral pH values (6–7.5). In developing more efficient and flexible redox buffers, a series of aromatic thiols was analyzed for its ability to fold scrambled ribonuclease A (sRNase A). At equivalent pH values, the aromatic thiols folded sRNase A 10–23 times faster at pH 6.0, 7–12 times faster at pH 7.0, and 5–8 times faster at pH 7.7 than the standard aliphatic thiol glutathione. Similar correlations between thiol pKa values and folding rates at each pH value suggest that the apparent folding rate constants (kapp ) are a function of the redox buffer properties (pH, thiol pKa and [RSH]). Fitting the observed data to a three-variable model (log kapp = −4.216(± 0.030) + 0.5816(± 0.0036)pH − 0.233(± 0.004)pKa + log(1 − e−0.98 (±0.02)[RSH]) ) gave good statistics: r2 = 0.915, s = 0.10. © 2004 Elsevier B.V. All rights reserved. Keywords: Protein folding; RNase A; Aromatic thiol; Redox buffer; pH

1. Introduction Disulfide bonds provide stability to the tertiary structure of many extracellular proteins and almost all protein-based pharmaceuticals. Typically, native disulfide bonds are required for native structure and activ∗ Corresponding author. Tel.: +1 305 348 3993; fax: +1 305 348 3772. E-mail address: [email protected] (W.J. Lees).

0168-1656/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jbiotec.2004.09.005

ity. The production of disulfide-containing proteins is undertaken using several different strategies including recombinant and synthetic methods (Lilie et al., 1998). The overexpression of recombinant disulfidecontaining proteins often results in the formation of protein aggregates known as inclusion bodies (Guise et al., 1996; De Bernardez Clark, 1998). To obtain native protein, inclusion bodies need to be resolublized before undergoing in vitro protein folding to form native protein (De Bernardez Clark, 2001). For many

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synthetic preparations of disulfide-containing proteins, the penultimate step is the deprotection of the cysteine residues, and the final step is the in vitro protein folding to obtain native structure (Moroder et al., 1996). Commonly, the slow step in the in vitro folding of disulfide-containing proteins is the formation of native disulfide bonds (Creighton et al., 1995). Disulfide bonds rearrange into their native state via thiol–disulfide interchange reactions (Creighton et al., 1995). Statistically, proteins with more than one disulfide bond have many possible combinations of disulfide bonds, only one of which corresponds to native protein. The breaking of non-native disulfide bonds and the subsequent formation of native disulfide bonds are typically the rate-determining steps in protein folding. In vitro, the formation of native disulfide bonds is typically facilitated by the addition of a small molecule thiol and small molecule disulfide, which is also called a redox buffer (Woycechowsky et al., 1999, 2003; Woycechowsky and Raines, 2003; Annis et al., 1998; Winter et al., 2002; Wedemeyer et al., 2000; Konishi et al., 1981; Gough et al., 2002, 2003). In some cases, in vivo catalysts, such as protein disulfide isomerase (PDI) (Kersteen and Raines, 2003; Winter et al., 2002; Robinson et al., 1994), are added to the redox buffer to improve the in vitro folding (Gilbert, 1997; Puig and Gilbert, 1994). However, PDI is not typically used due to its high cost and low catalytic activity. A limited number of small molecule thiols have been investigated for their ability to fold disulfidecontaining proteins. Traditionally, aliphatic thiols such as glutathione, ␤-mercaptoethanol, or dithiothreitol (DTT) have been used for folding disulfide-containing proteins (Konishi and Scheraga, 1980a; Rothwarf and Scheraga, 1993b). More recently, new aliphatic thiol redox buffers have been developed for increasing the overall yield of active protein, but they do not significantly increase the rate of protein folding (Woycechowsky et al., 1999, 2003; Woycechowsky and Raines, 2003; Annis et al., 1998). Aromatic thiols have been shown to significantly increase the folding rate of disulfide-containing proteins over those obtained using glutathione (Gough et al., 2002, 2003). Previously, thiols 1–5 (Scheme 1) were analyzed for their ability to fold scrambled RNase A at pH 6.0 (Gough et al., 2003). The redox buffer pH was chosen so that the effect of thiol pKa on the apparent folding rate could be analyzed; two of the thiols had pKa values

Scheme 1.

lower than redox buffer pH, two higher than, and one equal to the redox buffer pH. The results demonstrated that the concentration of protonated thiol (thiol in the SH form) was more important for optimizing the folding reactions than the total concentration of aromatic thiol (protonated thiol (SH) plus thiolate (S− )). The optimal total thiol concentration for aromatic thiols 1–5 varied considerably, 2.5–11 mM, but the optimal concentration of protonated thiol varied minimally, 1.8–2.6 mM. Since RNase A folds by initially forming a pre-equilibrium mixture which then forms native protein via rate-determining steps (Narayan et al., 2000), it was proposed that the concentration of protonated thiol affects the composition of the pre-equilibrium mixture through an equilibrium process. The rate of the rate-determining steps then may be affected by the concentration of thiolate. For each aromatic thiol, the concentration of thiolate and protonated thiol are linked by a single thiol pKa value; however, within the series of aromatic thiols, the thiol pKa values vary thus allowing a distinction between protonated thiol and thiolate. To fully depict and quantify the nature of folding RNase A with aromatic thiol based redox buffers, it is necessary to examine the impact that solution pH has upon folding rates; the consequences of changing the solution pH of the redox buffer has not been thoroughly investigated for any redox buffer. To ascertain the processes that pH influences, it was necessary to determine if the conclusions reached at pH 6.0 were valid over a wide range of pH values, including those most relevant for protein folding. Practically, it was important to establish an empirical understanding of the effect that aromatic thiols have on protein folding so that this technology could be applied to other disulfide-containing proteins. Herein, the effect of redox buffer pH on the folding of RNase A using aromatic thiols is evaluated. A group of aromatic thiols with different thiol pKa values was analyzed for their ability to fold RNase A at pH 7.0 and 7.7. Based upon these results, a general equation for the folding of RNase A is proposed.

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2. Materials and methods 2.1. General information Compounds 1 (Toronto Research Corporation), 2 (DeCollo and Lees, 2001), 3 (DeCollo and Lees, 2001), 4 (Kawai et al., 1991) and 5 (Gough et al., 2003) were synthesized or purchased. Scrambled RNase A (0.27 mM) (Hawkins et al., 1991; Hillson et al., 1984) was stored at −5 ◦ C in an aqueous solution (0.6% AcOH, 1 mM EDTA). All buffers were prepared by the addition of base (pH 6.0 bis-tris, pH 7.0 bis-trispropane, pH 7.7 tris) to a 0.6% solution of AcOH. Solutions were deoxygenated prior to use by bubbling Ar through them for 30 min. 2.2. Folding reaction The folding reactions were performed on a 500 ␮L scale and run at 25 ◦ C, pH 6.0 (bis-tris/AcOH buffer), 7.0 (bis-tris-propane/AcOH buffer), or 7.7 (tris/AcOH buffer). All folding reactions contained 25 ␮M sRNase A, 1 mM EDTA, 0.2 mM glutathione disulfide (GSSG), and a variable amount of glutathione or aromatic thiol (Gough et al., 2003). 2.3. Enzymatic assay The recovery of protein activity was monitored using the discontinuous assay developed by Konishi and Scheraga (Crook et al., 1960; Konishi and Scheraga, 1980a) and modified as previously described. (Gough et al., 2002, 2003) Aliquots were removed from the folding mixture at prescribed times, quenched in a pH 5.0 buffer (bis-tris/AcOH buffer, bistris-propane/AcOH buffer, or tris/AcOH), and immediately assayed for RNase A activity by following the hydrolysis of 2 ,3 -cyclic CMP (cCMP) at 292 nm. The enzymatic activity, measured by the discontinuous assay for each individual folding reaction, was plotted as a function of time. The function y = A(1 − e−kt ) was fit to the data points, where k is the apparent rate constant, kapp , and A is the maximum % folded. 2.4. Calculation of components of folding redox buffer The rapidly established equilibria between the aromatic thiol and GSSG in the protein-folding mixture

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results in the formation of three additional species: aromatic disulfide, mixed aromatic-glutathione disulfide, and glutathione. Furthermore, both thiol species exist in the protonated form (RSH) and also the deprotonated (thiolate, RS− ) form. The concentrations of the five species were calculated as described previously (Gough et al., 2003). The calculated concentrations of the individual species, with the exception of the aromatic thiolate, will be the same for all five thiols as a function of the concentration of protonated aromatic thiol. Six equations were set up to solve for the concentration of the five compounds (glutathione, GSH; glutathione disulfide, GSSG; aromatic thiol, ArSH; aromatic disulfide, ArSSAr and aromatic-glutathione mixed disulfide, ArSSG) and the four general species (aromatic species, ArSX; glutathione species, GSX; disulfide species, RSSR and thiol species, RSH). Two involved the mass balance of the glutathione and the aromatic groups (Eqs. (1) and (2)), two involved the chemical balance of disulfide and thiol (Eqs. (3) and (4)), and two involved chemical equilibria (Eqs. (5) and (6)). The [GSH] and [ArSH] terms are the sum of the protonated and deprotonated forms (RSH + RS− ). The two equilibria were the formation of aromatic disulfide and GSH from aromatic thiol and GSSG (Eq. (5)), and the formation of mixed disulfide and GSH from aromatic thiol and GSSG (Eq. (6)). The equilibrium constants at pH 6 were calculated from the pKa of the thiol and the equilibrium constant at lower pH, where the aromatic thiol was almost fully protonated. From the initial concentration of the five species and the six equations, the final concentration of the five species was determined numerically using the solver subroutine of Microsoft Excel. The equilibrium constant for the formation of aromatic disulfide and glutathione from glutathione disulfide and aromatic thiol (Eq. (5)) at low pH was assumed to be 1. For example, equilibrium constants for aromatic thiols 1 and 4 are 1.0 and 0.67, respectively (Gough et al., 2003). The equilibrium constant for the formation of mixed disulfide and glutathione from glutathione disulfide and aromatic thiol (Eq. (6)) at low pH was assumed to be 2, due to statistical factors. [GSX] = (2 × [GSSG]) + [ArSSG] + [GSH]

(1)

[ArSX] = (2 × [ArSSAr]) + [ArSSG] + [ArSH] (2)

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[RSSR] = [GSSG] + [ArSSG] + [ArSSAr]

(3)

[RSH] = [GSH] + [ArSH]

(4)

Keq1 = Keq2 =

[GSH]2 [ArSSAr] [ArSH]2 [GSSG] [GSH][ArSSG] [GSSG][ArSH]

(5) (6)

2.5. Calculation of the model for the folding of sRNase A The 99 data points used to determine the optimal thiol concentration at pH 6.0, 7.0, and 7.7 were used in the calculation of the constants A, B, C, and D in Eq. (7). The thiol pKa value, solution pH and concentration of total protonated thiol, [RSH], for each of the points were placed into the equation. The optimal values of the constants were determined numerically by minimizing the sum of the square error between calculated and observed log kapp , for all data points, using the solver subroutine of Microsoft Excel. log kapp = A + B pH + C pKa + log(1 − e−D[RSH] ) (7)

3. Results Thiols 1–5 were used to fold the disulfidecontaining protein scrambled RNase A (sRNase A) at pH 6.0, 7.0 and 7.7. The three different pH values were chosen because they encompass the range of pH values typically used for protein folding, and they allow a comparison with previously collected data. Traditionally, either fully reduced RNase A or sRNase A is used for protein-folding experiments; sRNase A is fully oxidized RNase A with a relatively random distribution of disulfide bonds (Gough et al., 2002). Previously, we and others have obtained similar folding rates starting from either reduced or sRNase A (Gough et al., 2002, 2003; Lyles and Gilbert, 1991a,b; Konishi et al., 1981; Woycechowsky et al., 1999). In our hands, sRNase A had greater stability after prolonged storage than reduced RNase A, therefore, we chose to use sRNase A. In general, redox buffers for folding disulfidecontaining proteins require the presence of a thiol and a

Fig. 1. Ak vs. varying concentrations of aromatic thiols, (RSH + RS− ), 1–5: 1 (circles), 2 (squares), 3 (diamonds), 4 (point up triangles), and 5 (point down triangles, pH 6.0 and 7.0 only). (a) pH 6.0 (b) pH 7.0 (c) pH 7.7.

disulfide. Using an aromatic disulfide does not convey any measurable rate enhancement over using GSSG (Gough et al., 2002, 2003). GSSG was thus added as the disulfide, as it is commercially available, unlike the aromatic disulfides. GSSG is also the disulfide, traditionally used in the folding of disulfide-containing proteins (Rudolph and Lilie, 1996; De Bernardez Clark, 1998). The concentration of thiol was varied to elucidate the optimal folding conditions (Fig. 1). Optimal conditions are defined as the concentration of a thiol at which the initial rate of protein folding is at a maximum. The initial rate of protein folding corresponds to

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Table 1 Folding of scrambled RNase A at pH 6.0, 7.0, and 7.7a Additive

pH

Initial [ArSH] (mM)

Thiol at equilibrium (mM) Calculated

Protonated

[ArSH]

[GSH]

k app × 103 (min−1 )b

A (%)b

Relative rate at each pH value

1 2 3 4 5

6.0

2.6 2.9 4.2 5.7 13.5

1.8 1.8 1.8 1.8 1.8

0.34 0.34 0.34 0.34 0.34

88 83 91 98 86

± ± ± ± ±

12 10 9 9 10

5.2 7.5 8.0 9.1 12.4

± ± ± ± ±

0.4 0.4 0.6 0.8 0.8

0.42 0.60 0.65 0.73 1.000

1 2 3 4

7.0

4.0 5.3 13 22

1.0 1.0 1.0 1.0

0.31 0.31 0.31 0.31

115 109 92 105

± ± ± ±

2 9 17 10

16 22 26 27

± ± ± ±

4 3 5 2

0.59 0.81 0.96 1.000

1 2 3 4

7.7

2.6 4.2 11.5 20.2

0.2 0.2 0.2 0.2

0.19 0.19 0.19 0.19

91 89 94 84

± ± ± ±

4 6 8 9

16 21 25 20

± ± ± ±

5 5 6 3

0.64 0.84 1.000 0.80

a

The data at pH 6.0 and 7.0 are collected at optimal conditions; data at pH 7.7 are collected at less than the optimal conditions. The error corresponds to the 95% confidence interval, ts/N0.5 , where N is the number of data points, s the standard deviation, and t is from the t-test table. The error was determined from four side-by-side runs comparing all five thiols. b

Ak, where A is the maximum % folded and k is the apparent rate constant of protein folding kapp . The optimal folding concentration for each of the thiols increases as thiol pKa decreases (Fig. 1). At a given pH and at optimal conditions, the concentration of total protonated thiol is found to be nearly equal for all thiols after taking thiol pKa and the equilibrium with glutathione species into account (Fig. 2). It should be noted that the concentration of total thiol (Fig. 1) at optimal conditions varied considerably for a given pH value (pH 6.0, 2–11 mM; pH 7.0, 4–16 mM; pH 7.7, 4–30 mM). Optimal folding conditions for the five thiols at pH 6.0 were found to be at 1.8 mM protonated aromatic thiol (ArSH) or 2.1 ± 0.5 mM total protonated thiol (ArSH + GSH). Thiols 1–5 were evaluated side by side at 2.1 mM total protonated thiol (Table 1). Optimal folding conditions for the four thiols at pH 7.0 were found to be at 1.0 mM protonated aromatic thiol or 1.3 ± 0.5 mM total protonated thiol. Thiols 1–4 were measured side by side at 1.3 mM total protonated thiol (Table 1). At pH 7.7, optimal conditions were found to be at 0.4 mM protonated aromatic thiol or 0.6 ± 0.1 mM total protonated thiol for thiols 1, 2 and 4. To compare thiols 1–4 at pH 7.7, folding activity was measured side by side at 0.38 mM total protonated thiol (Table 1); values were determined at less than optimal concentration

to minimize background absorbance. With the exception of aromatic thiol 4, at high concentrations of total aromatic thiol, >17 mM, the background absorbance of the aromatic species at the assay wavelength of 292 nm, negatively affected the results. To compensate for this, the side-by-side comparisons of the aromatic thiols at pH 7.7 were performed at a fixed concentration of protonated thiol but under non-optimal conditions, which involved lower concentrations of aromatic thiol. In addition, aromatic thiol 5 was not included in the data at pH 7 or 7.7 as its corresponding concentration would have been approximately 60 mM.

4. Discussion 4.1. Protein folding Of all disulfide-containing proteins, the folding of RNase A is one of the best-understood systems (Wedemeyer et al., 2000; Narayan et al., 2000; Creighton et al., 1995, 1996; Gilbert, 1997). However, only a limited number of small molecule thiols have been used as redox buffers. No studies have compared and contrasted the effects of several redox buffers over a range of pH values.

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Fig. 3. Protein-folding pathway of RNase A, as proposed by Scheraga et al.

(R), one disulfide (1S), two disulfide (2S), three disulfide (3S), and four disulfide (4S) species of RNase A (Fig. 3). Only a limited number of species within the pre-equilibrium mixture will be protein substrates for the rate-determining steps. These substrates will then be converted via the rate-determining steps to a limited number of intermediary species (3S* species). These 3S* species are rapidly converted to native protein. 4.2. Equilibrium effects, concentration of protonated thiol

Fig. 2. For each compound at each pH value, the maximum Ak value was normalized to 1, Akrel . Akrel vs. concentration of total protonated thiol: 1 (circles), 2 (squares), 3 (diamonds), 4 (point up triangles), and 5 (point down triangles). (a) pH 6.0 (b) pH 7.0 (c) pH 7.7.

To understand the issues associated with the folding of RNase A, it is important to consider its folding pathway. Scheraga et al. has thoroughly investigated the folding pathway of RNase A and its intermediates (Konishi and Scheraga, 1980a,b; Konishi et al., 1981, 1982a,b; Rothwarf and Scheraga, 1993a,b,c,d; Narayan et al., 2000). Non-native RNase A in the presence of a redox buffer is expected to rapidly form a pre-equilibrium mixture (a quasi-steady state condition) which is subsequently converted to native protein (N) via rate-determining steps. The contents of the pre-equilibrium mixture consist of fully reduced

The protein-folding rate depends on the concentration of protein substrates for the rate-determining steps and thus is related to the concentration of the small molecule thiol and disulfide in the protein-folding mixture. The concentration of protein substrates in the preequilibrium mixture will vary with the concentrations of the small molecule thiol and disulfide in the redox buffer, since they are in equilibrium with each other. For instance, if the redox buffer contains a high concentration of the small molecule disulfide and little or no small molecule thiol, then the pre-equilibrium mixture will contain a high fraction of proteins with no free thiols. The equilibrium between the small molecule thiol and the protein disulfide can be expressed most simply in terms of the small molecule thiol in the protonated thiol form, [RSH]; the protein disulfide, [PSSP]; the small molecule disulfide [RSSR], and the protein thiol in the protonated thiol form [PSH], Scheme 2. The concentration of small molecule thiol in the protonated form

Scheme 2.

J.D. Gough, W.J. Lees / Journal of Biotechnology 115 (2005) 279–290

Scheme 3.

can be calculated from the total thiol concentration, [RSH]tot , the thiol pKa values and the pH of the solution, Eq. (8). 
1 [RSH] = [RSH]tot (8) 1 + Ka /[H+ ] Based on Schemes 2 and 3, at a given pH and small molecule disulfide concentration the optimal concentration of protonated thiol for protein folding should be similar for a range of small molecule monothiols. At low pH, where almost all the thiol groups are protonated, the equilibrium constant between one monothiol (RSH) and the disulfide of another monothiol (R SSR ) is almost always close to 1, Scheme 3. For thiols 1 and 4, at low pH, the equilibrium constants with glutathione disulfide are 1.0 and 0.67, respectively (Gough et al., 2003). Barring any specific interactions with the protein, the Keq value in Scheme 2 will be directly proportional to the K value in Scheme 3. Thus, the Keq value in Scheme 2 will be the same for glutathione and compound 1 and only slightly different for compound 4. If the Keq value is the same and the concentration of small molecule disulfide is the same, then the contents of the pre-equilibrium mixture, PSH and PSSP, will vary only with the concentration of the small molecule thiol in the protonated form, Scheme 2. Therefore, at a given concentration of small molecule disulfide and protonated thiol, approximately the same optimal preequilibrium mixture should be obtained, irrespective of the small molecule monothiol. The concentration of protonated thiol is related to the reduction potential and thus optimal folding conditions occur at approximately the same reduction potential as well. Since the thiol pKa values of monothiols differ considerably, the concentration of total thiol may vary dramatically for a given concentration of protonated monothiol. Experimentally, we find that the optimum folding conditions for the aromatic thiols occur at similar concentrations of protonated thiol but not total thiol. At pH 6, the optimum total protonated thiol concentration varied from 1.8 to 2.6 mM (thiols 1–5), Fig. 2, and the optimum total thiol concentration varied from 2.5 to

285

11 mM, Fig. 1. At pH 7, protonated thiol varies from 1.0 to 2.3 mM (thiols 1–4) and the total thiol from 4 to 16 mM. At pH 7.7, protonated thiol varies from 0.5 to 0.7 mM (thiols 1, 2 and 4) and the total thiol from 4 to 30 mM. 4.3. Relative rates, thiol pKa value The following section will provide a theoretical basis for the relative rates of protein folding within a series of monothiols. In summary, at a given concentration of small molecule disulfide and small molecule thiol in the protonated form the relative abundance of protein species in the pre-equilibrium mixture, PSH and PSSP, should be very similar, Section 4.2, irrespective of the monothiol. At a given concentration of protonated thiol and disulfide, the rate of conversion of the protein species in the pre-equilibrium mixture to folded protein will depend on the nature of the rate-determining steps and the specific properties of the monothiol. If the monothiol is a nucleophile in the important ratedetermining steps, then the rate of protein folding will be affected by the concentration of the small molecule thiolate, the reactive species, and the inherent reactivity of the small molecule thiolate, Scheme 4. Increasing the total thiol concentration (RSH + RS− ) and thus the concentration of small molecule thiolate, however, may not increase the folding rate as it may negatively alter the relative abundance of protein species within the pre-equilibrium mixture by also increasing the concentration of protonated thiol. For a single compound, the effects of protonated thiol and thiolate concentration are difficult to disentangle, as they are linked by a single thiol pKa value but this is not the case for a series of compounds with different pKa values. At a given pH, the optimal concentration of protonated thiol for protein folding varies only slightly with the properties of the monothiol. At optimal conditions, the absolute rate of protein folding, however, changes with the properties of the small molecule thiol in a predictable manner. In the rate-determining steps the small molecule thiol could act as a nucleophile or as a leaving group, Scheme 4. In addition, it could also be involved as the center half of the disulfide, which is attacked by the nucleophile. In general, aromatic thiols with lower thiol pKa values are better leaving groups and worse nucleophiles. Model systems using non-protein thiols and disulfides have demonstrated how a change in the

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Scheme 4.

thiol pKa value can alter the rate constant of the reaction (DeCollo and Lees, 2001; Szajewski and Whitesides, 1980). If the thiol acts as a leaving group, a one-unit increase in the thiol pKa value decreases the log of the rate constant by between 0.5 and 1. If the thiol acts as a nucleophile, a one-unit increase in the thiol pKa value increases the log of the rate constant by between 0.5 and 1. The rate constant of the reaction is obtained by dividing the reaction rate by the concentration of the nucleophilic thiolate and the concentration of the disulfide, Scheme 4. The thiolate is the reactive species in thiol–disulfide interchange reactions. During protein folding, if the small molecule thiol is acting primarily as the nucleophile and the protein as the disulfide in the important rate-determining steps, then Scheme 5 will apply. The rate constant, k, will be proportional to the rate constant of protein folding kapp , divided by the concentration of small molecule thiolate, [RS− ], and the concentration of protein disulfide substrate used in the rate-determining steps, [PSSP]. Based on the arguments in Section 4.2, at a given protonated thiol concentration, the concentration of PSSP should be approximately the same irrespective of the small molecule thiol used. Therefore, the rate constant for the rate-determining steps, which involves the small molecule thiolate reacting with the protein disulfide, will be proportional to kapp /[RS− ]. Plots of log(kapp /[RS− ]) versus thiol pKa at a fixed concentra-

Scheme 5.

tion of protonated thiol have a slope of between 0.7 and 0.9, very consistent with the results obtained in model systems, 0.5–1.0, Fig. 4 (DeCollo and Lees, 2001; Szajewski and Whitesides, 1980). At pH 6, the slope is 0.77. During protein folding, if the small molecule thiol is acting primarily as a leaving group and the protein as the nucleophile in the important rate-determining steps, then Scheme 6 will apply. The rate constant, k, will be proportional to the rate constant of protein folding, kapp , divided by the concentration of protein substrate [RSSPS− ] used in the rate-determining steps. Again at optimal protonated thiol concentration, the concentra-

Fig. 4. (a) log(kapp /[RS− ]) at 1.3 mM total protonated thiol vs. the thiol pKa value at pH 7.0 and (b) log(kapp /[RS− ]) at 0.39 mM total protonated thiol vs. the thiol pKa value at pH 7.7.

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Scheme 6.

tion of RSSPS− should be approximately the same irrespective of the small molecule thiol used. Therefore, at optimal conditions, the rate constant for the ratedetermining steps, which involves the protein thiolate reacting with a mixed protein disulfide and the small molecule thiolate acting as the leaving group, will be proportional to kapp . Plots of log kapp versus thiol pKa at optimal conditions have a slope of between −0.1 and −0.3, inconsistent with the results obtained in model systems where the small molecule thiol acts as the leaving group, −0.5 to −1.0 (DeCollo and Lees, 2001; Szajewski and Whitesides, 1980). A slope of −0.1 to −0.3 is, however, consistent with the small molecule thiol acting as the center thiol based on similar arguments. Thus, we conclude that the small molecule thiol is acting not as a leaving group but as the nucleophile and/or center thiol in the important rate-determining steps. The conclusion is valid over the range of pH values. 4.4. Description of sRNase A folding using aromatic thiols The folding rate of RNase A with a series of aromatic thiols can be described with three parameters, the solution pH, the pKa value of the aromatic thiol, and the concentration of protonated thiol in solution ([glutathione in the protonated form] + [aromatic thiol in the protonated form]). At each pH value and at similar concentrations of protonated thiol, the relationship between the log of the folding rate and the thiol pKa value is approximately linear, based on the results in Fig. 4. The best single variable function we found for fitting the log of the folding rate constant versus protonated thiol concentration, Fig. 2, was log(1 − e−D[RSH] ), where D is a variable (residual sum of the differences between calculated and observed

287

values squared = 0.95). Polynomial functions and log polynomials were also tried but required at least three variables to improve upon the single variable equation above (residual = 0.85). The best three-variable equation we found was log(D + E[RSH] − e−F[RSH] ), where D, E, and F are variables (residuals = 0.72). For simplicity, we chose the best one-variable equation but we also present the best three-variable equation. The relationship between the log of the folding rate and the pH was also expressed in linear terms. Using the 99 values of kapp obtained in the concentration studies and the experimental conditions (pH, pKa , and [RSH]) (Fig. 1), the constants A, B, C and D were optimized numerically, using a least squares method (Eqs. (9) and (10); error is at the 95% confidence level). The resulting equation can be regarded as a model of the folding of sRNase A in the presence of an aromatic thiol. In applying the model, the concentration of GSH in the protonated form can be ignored as long as the concentration of protonated aromatic thiol is greater than 1 mM. Using two additional variables to fit the concentration of protonated thiol, the best equation becomes Eq. (11). log kapp = A + B pH + C pKa + log(1 − e−D[RSH] ) (9) log kapp = −4.216(±0.030) + 0.5816(±0.0036) pH +(−0.233)(±0.0043) pKa + log(1 − e−0.98(±0.021)[RSH] )

(10)

log kapp = −3.957 + 0.597 pH − 0.245 pKa + log(0.974−0.120[RSH] − e−0.683[RSH] ) (11) The model describes the folding of sRNase A in terms of pH, thiol pKa , and total protonated thiol. Statistical analysis of the model gives the regression statistics r2 = 0.915 and s = 0.10 (Fig. 5a). Using the “leave-oneout method”, where each point is predicted based on the model from all data excluding that point, the cross2 = 0.904 and s validation statistics were rpres pres = 0.10. Only three data points (of 99) have residuals greater than two standard deviations; these data points were either at a very low (≤1.0 mM) or a very high concentration of total thiol (≥10.0 mM). It is observed that

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Fig. 5. (a) log kcalc as determined from Eq. (10) vs. log kapp obtained empirically and (b) kcalc as determined from Eq. (10) for the values of the validation set vs. log kapp obtained empirically.

when pH increases (pH 6.0–7.7) the optimal concentration of total protonated thiol decreases (2.1–0.63 mM). Adding mathematical factors to account for this trend does not significantly enhance the model; they were therefore not included. However, the regression statistics of the model and results from the predictive leave-

one-out method support the statistical relevance of the model. To validate the efficacy of the model, the apparent rate constants at optimal activity were predicted. The data points in Table 1 were not used in the creation of the model, and were used as a validation set. The buffer pH, thiol pKa , and [RSH] were used to predict the values of the apparent rate constant, kapp (Table 2). The validation set has regression statistics of r2 validation = 0.87 and svalidation = 0.031 for predicting kapp (Fig. 5b) and r2 validation = 0.94 and svalidation = 0.083 for predicting log k. In predicting kapp , only two points (of 13) have residuals greater than one standard deviation. Analysis of the error in predicting the apparent rate constants reveals that the average error in the validation set corresponds to the experimental error (15%). The regression statistics of the validation set as well as its relative predictive accuracy corroborate the efficacy of the model. The equation indicates the significant rate enhancement in the folding of RNase A that can be achieved by increasing the pH of the reaction mixture. For a given thiol, the rate enhancement is between 3 and 4 for a one-unit increase in pH. However, the equation also points out that by judiciously choosing the aromatic thiol, the change in folding rate with pH can be minimized. This point can be illustrated by comparing two aromatic thiols with pKa values approximately 0.8 units lower than the solution pH value. At pH 6, the folding rate of aromatic thiol 5, pKa = 5.2, is only half that of aromatic thiols 2 (pKa = 6.4) or 3 (pKa = 5.95) at pH 7.

Table 2 Values for kapp /[RS− ] and predicted values of kapp and log kapp pH

Thiol

Deprotonated thiol concentration [ArS− ] (mM)

6 6 6 6 6 7 7 7 7 7.7 7.7 7.7 7.7

1 2 3 4 5 1 2 3 4 1 2 3 4

0.44 0.73 2.0 3.6 11.4 3.0 4.0 11.6 20.6 2.4 4 11.3 20

kapp /[RS− ] (mM−1 min−1 ) 12 10 3.9 2.5 1.1 5.5 5.5 2.2 1.3 6.7 5.2 2.2 1.0

Observed log kapp

Predicted log kapp

Observed kapp × 10−3 (min−1 )

Predicted kapp × 10−3 (min−1 )

−2.28 −2.12 −2.10 −2.04 −1.91 −1.80 −1.66 −1.60 −1.57 −1.80 −1.68 −1.60 −1.70

−2.32 −2.27 −2.17 −2.11 −2.00 −1.82 −1.77 −1.67 −1.61 −1.81 −1.75 −1.64 −1.58

5.2 7.5 8.0 9.1 12.4 16 22 25 27 16 21 25 20

4.7 5.3 6.8 7.7 10.1 15.2 16.6 21.5 24.5 15.6 17.9 23.2 26.5

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The general conclusions from this paper should apply to all proteins that fold using a similar mechanism as RNase A, establishment of a pre-equilibrium mixture prior to conversion to native protein via ratedetermining steps. At a given pH and disulfide concentration, optimal folding conditions should occur at approximately the same concentration of protonated thiol in solution, irrespective of the monothiol. The rate of protein folding should increase as the thiol pKa value decreases. This is applicable whether the small molecule thiol acts as the nucleophile, the central part of the disulfide, or as the leaving group in the ratedetermining steps. The total concentration of thiol at optimal conditions should also increase as the thiol pKa value decreases. Ultimately, the best thiol will be the one with the lowest thiol pKa value that is tolerated by the protein at high concentrations. Since the optimal total thiol concentration varies with pH, the best thiol will vary with the pH of the folding mixture. Our expectation is that the best small molecule aromatic thiol will have a thiol pKa value approximately one unit lower than the pH of the solution but clearly, in some cases, protein specific interactions may become important. Consistent with the above observations, RNase A folds faster in the presence of an aromatic thiol based redox buffer than in the presence of an aliphatic thiol based redox buffer. With aromatic thiols, the folding of scrambled RNase A occurs 10–23 times faster than with glutathione at pH 6.0, 7–12 times faster at pH 7.0, and 5–8 times faster at pH 7.7. Aromatic thiol 5 folds RNase A two times faster at pH 6.0, and aromatic thiol 4 folds RNase A four times faster at pH 7.0 than glutathione does at pH 7.7. Therefore, aromatic thiols provide greater versatility than aliphatic thiols for choosing a folding pH, while still retaining a significant folding rate. Some similarities in folding RNase A at each of the pH values examined were noted. For a given pH, the optimum folding condition for each thiol occurred at an equal concentration of total protonated thiol, and not total thiol (protonated plus thiolate). In addition, a change in thiol pKa had the same relative effect on the folding rate at each pH value. The noted similarities enabled generation of a statistically relevant predictive model for the folding rates of RNase A under a range of conditions. The model should allow the appropriate selection of an aromatic thiol redox buffer for the folding of other disulfide-containing proteins under a variety of conditions.

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Acknowledgement This work was supported by the NSF (Grant Number CHE 0342167) to W. J. L. We thank Dr. Lowell L. Hall of Eastern Nazarene College for helpful comments.

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