Effect of Multiple Prolyl Isomerization Reactions on the Stability and Folding Kinetics of the Notch Ankyrin Domain: Experiment and Theory

doi:10.1016/j.jmb.2005.06.041

J. Mol. Biol. (2005) 352, 253–265

Effect of Multiple Prolyl Isomerization Reactions on the Stability and Folding Kinetics of the Notch Ankyrin Domain: Experiment and Theory Christina Marchetti Bradley and Doug Barrick* T. C. Jenkins Department of Biophysics, Johns Hopkins University, 3400 N. Charles St. Baltimore, MD 21218, USA

Studies on the folding kinetics of the Notch ankyrin domain have demonstrated that the major refolding phase is slow, the minor refolding phase is limited by the isomerization of prolyl peptide bonds, and that unfolding is multiexponential. Here, we explore the relationship between prolyl isomerization and folding heterogeneity using a combination of experiment and simulation. Proline residues were replaced with alanine, both singly and in various combinations. These destabilizing substitutions combine to eliminate the minor refolding phase, although unfolding heterogeneity persists even when all seven proline residues are replaced. To test whether prolyl isomerization influences the major refolding phase, we modeled folding and prolyl isomerization as a system of sequential reactions. Simulations that use rate constants of the major folding phase of the Notch ankyrin domain to represent intrinsic folding indicate that even with seven prolyl isomerization reactions, only two significant phases should be observed, and that the fast observed phase provides a good approximation of the intrinsic folding in the absence of prolyl isomerization. These results indicate that the major refolding phase of the Notch ankyrin domain reflects an intrinsically slow folding transition, rather than coupling of fast folding events with slow prolyl isomerization steps. This is consistent with the observation that the single observed refolding phase of a construct in which all proline residues are replaced remains slow. Finally, the simulation fails to produce a second unfolding phase at high urea concentrations, indicating that prolyl isomerization does not play a role in the three-state mechanism that leads to this heterogeneity. q 2005 Elsevier Ltd. All rights reserved.

*Corresponding author

Keywords: protein folding; kinetic simulation; prolyl isomerization; Notch ankyrin domain

Introduction Many repeat-proteins contain a large number of proline residues, in part because they are comprised of repetitive sequence elements. For example, Present address: C. M. Bradley, Laboratory of Molecular Biology, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892, USA. Abbreviations used: Nank1-7*, residues 1901–2148 of the Drosophila Notch receptor; Nank1-7D, residues 1903– 2140 of the Drosophila Notch receptor; PA, proline-toalanine substitution; rmsd, root-mean-square deviation. E-mail address of the corresponding author: [email protected]

proline residues are part of the consensus sequences of ankyrin repeats,1 ribonuclease-inhibitor-type leucine-rich repeats,2 heat repeats,3 and pumilio repeats.4 Isomerization of prolyl peptide bonds can result in considerable kinetic complexity during refolding both in globular proteins5–12 and repeatproteins.13–16 Whereas the effects of isomerization of a single prolyl peptide bond on protein folding are relatively simple and well characterized, the effects of isomerization of multiple prolyl peptide bonds on refolding can be quite complex.17,18 Isomerization of multiple peptide bonds may lead to multiple kinetic phases and, under some circumstances, affect the kinetics of all observed folding phases, complicating (if not preventing) determination of the intrinsic refolding rate.

0022-2836/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

254 Therefore, a better understanding of the effect of multiple prolyl isomerization reactions on folding kinetics is important for our studies of the Notch ankyrin domain, and for studies of other repeat proteins containing large numbers of proline residues. The impact of prolyl isomerization on refolding and unfolding can be modeled most simply as a sequential set of independent isomerization reactions in the denatured state that precede an intrinsic refolding step†. This type of model has been used by Kiefhaber & Schmid to examine the effects of one or two proline residues on refolding kinetics, and has provided considerable insight into the relationship between experimentally observed kinetic phases and the underlying kinetic steps.18 Kiefhaber & Schmid found that for proteins with one or two proline residues, the separation of intrinsic folding and prolyl isomerization into distinct observed phases depends on the relative magnitudes of the intrinsic refolding and isomerization rates.17,18 Only if intrinsic folding is significantly faster than prolyl isomerization does the fast observed phase in refolding correspond to intrinsic folding.18 In the presence of a large number of proline residues, it is not clear to what extent the fast refolding phase corresponds to intrinsic folding and, the difference in folding and isomerization rates that are necessary to maintain this correspondence. The refolding kinetics of the Notch ankyrin domain is biphasic, with a major fast phase and a minor slow phase at a low concentration of urea.43 Several lines of evidence suggest that the slow refolding phase is limited by prolyl isomerization. The slow phase is sensitive to peptidyl-prolyl isomerase, it increases in amplitude with unfolding time in an interrupted unfolding double-jump experiment, and has a rate and activation enthalpy similar to prolyl isomerization in unstructured peptides.43 Although the fast phase in refolding shows no evidence of being limited by prolyl isomerization, the observed rate constant for the fast phase of folding of the Notch ankyrin domain is much slower than that predicted from the low relative contact order of the Notch ankyrin domain.43 Given that there are five and seven proline residues in the two Notch ankyrin domain constructs, it is possible that prolyl isomerization also limits the fast refolding phase but has escaped detection. The kinetics of unfolding of the Notch ankyrin domain is also biphasic, with a minor fast phase and a major slow phase.43 This unfolding heterogeneity appears to result from an on-pathway intermediate. The structural features that make this intermediate

† We use the term "intrinsic folding rate" to refer to the rate of the major conformational transition from the denatured to the native state in the absence of prolyl isomerization. This step corresponds to the last step in a sequential isomerization refolding model.

Prolyl Isomerization in Notch Ankyrin Domain Folding

kinetically distinct from the native state are not clear. Given the large number of proline residues in the Notch ankyrin domain, it is possible that this intermediate may result from a prolyl isomerization reaction within the native state ensemble.19,20 Here, we examine the extent to which the kinetic heterogeneity in refolding and unfolding of the Notch ankyrin domain results from prolyl isomerization, using a combination of experiments and kinetic modeling. We have replaced the seven proline residues of Nank1-7* with alanine, both individually and in various combinations, and have determined the effect of these substitutions on stability, and on refolding and unfolding kinetics. We have extended the simulations described by Kiefhaber & Schmid to explore the effects of up to seven proline residues on refolding and unfolding kinetics, assuming a sequential isomerization model and a range of intrinsic refolding rates. We compare the calculated eigenvalues with intrinsic folding and unfolding rate constants to evaluate the complexity of progress curves that result from a sequential isomerization model with a large number of proline residues, and to determine the conditions under which the intrinsic folding corresponds directly to an observable phase.

Results Proline replacement studies Previous studies suggest that the slow phase in refolding of the Notch ankyrin domain results from isomerization of prolyl peptide bonds in the denatured state.43 To test directly whether the kinetic heterogeneity seen in the refolding and unfolding results from isomerization about prolylpeptide bonds, we have replaced each of the proline residues of the Notch ankyrin domain with alanine, both as single and as multiple substitutions. Alanine was chosen because it is the most common non-proline residue at the proline consensus position in ankyrin repeats.1,21 Substitutions were made in the Nank1-7* background so that the role of the two non-consensus C-terminal proline residues, which are missing from Nank1-7D, could be examined. Equilibrium unfolding experiments indicate that, with the exception of the proline residue in the partially disordered first repeat, substitution of each proline residue with alanine is destabilizing. For the four consensus proline residues that are ordered in the crystal structure (repeats 3, 4, 6, and 7), similar decreases in unfolding free energy are produced (1.1 kcal molK1, with an rmsd of 0.4 kcal molK1; Table 1). This similarity is consistent with the uniform structural environment of each of these proline residues. In contrast, simultaneous substitution of the two non-consensus C-terminal proline residues has less of an effect, producing a combined decrease in unfolding free energy of 0.7 kcal molK1. In general, substitution of proline with alanine

255

Prolyl Isomerization in Notch Ankyrin Domain Folding

Table 1. Effect of proline substitutions on the unfolding free energy of the Notch ankyrin domain DG8u;H2 O (kcal molK1)a Variantb Nank1-7* PA1 PA3 PA4 PA6 PA7 PA7C2 PA134 PA67 PA13467 PA13467C2

m-value (kcal molK1 MK1)a

CD

Fluorescence

CD

Fluorescence

7.74G0.07 7.53G0.03 6.75G0.05 6.81G0.01 6.1G0.1 5.88G0.09 6.87G0.01 6.1G0.1 4.41G0.08 2.93G0.09 2.58G0.07

7.64G0.08 7.9G0.2 6.8G0.1 6.52G0.08 6.3G0.1 5.88G0.03 6.8G0.1 6.07G0.01 4.67G0.05 3.24G0.02 2.58G0.05

2.89G0.04 2.84G0.01 2.90G0.01 2.68G0.02 2.63G0.05 2.68G0.05 2.73G0.01 2.71G0.03 2.24G0.03 1.89G0.03 1.72G0.06

2.86G0.02 2.97G0.07 2.90G0.01 2.57G0.03 2.71G0.06 2.65G0.01 2.72G0.05 2.72G0.01 2.35G0.03 2.15G0.01 1.85G0.01

a

DG8u;H2 O and m-values were determined from urea-induced unfolding transitions using equations (2) and (3). Reported parameters are mean values from two or more independent unfolding transitions. Uncertainties are standard errors on the mean. Conditions: 25 mM Tris–HCl (pH 8.0), 150 mM NaCl, 20 8C. b Proline-to-alanine variants are named with numbers corresponding to the ankyrin sequence repeats in which consensus proline substitutions are made. For example, PA134 has proline residues substituted with alanine residues in the consensus positions of the first, third, and fourth sequence repeats, and PA13467C2 has additional alanine substitutions at proline consensus positions of the sixth and seventh sequence repeat, and two further substitutions at non-conserved positions in the C-terminal tail. This second construct contains no proline residue.

decreases kinetic refolding heterogeneity as evidenced by more randomly distributed residuals (Figure 1, compare (a) with (b) and (c)) and a smaller value of c2r for the single-exponential fit, compared to Nank1-7* (Table 2). A decrease in refolding heterogeneity is reflected also in a progressive decrease in the fitted amplitude of the slow phase of refolding (A2, Table 2). These effects are most pronounced when proline residues in repeats 1, 3, and 4 are substituted (compare Nank1-7*

with PA134, and PA67 with PA13467). However, the conserved proline residues in repeats 1, 3, and 4 do not account for all of the observed heterogeneity, as further replacement of proline in repeats 6 and 7 decreases the amplitude of the minor refolding phase significantly (compare A2 for PA134 and PA13467; Table 2). Complete elimination of heterogeneity in Nank1-7* requires substitution of all seven proline residues (PA13467C2; Figure 1(d); Table 2).

Figure 1. The effect of proline substitutions on the heterogeneity of refolding of the Notch ankyrin domain. Fluorescence-detected refolding curves, initiated by rapid dilution from 2.8 M to 3.2 M urea (denaturing conditions) to 0.8 M (native conditions), for Notch ankyrin variants in which multiple proline residues are substituted with alanine residues. (a) PA134; (b) PA67; (c) PA13467; and (d) PA13467C2 (see the footnote to Table 1 for a description of the nomenclature). Continuous lines result from fitting a singleexponential and a double-exponential model (black and red, respectively) to the progress curves. The upper panels show residuals from the single-exponential and the double-exponential fits; note that different scales are used for each panel to highlight the differences between the singleexponential and the double-exponential fit. Conditions: 25 mM Tris– HCl (pH 8.0), 150 mM NaCl, 20 8C.

256

Prolyl Isomerization in Notch Ankyrin Domain Folding

Table 2. The effect of multiple proline substitutions on the refolding kinetics of the Notch ankyrin domain Single-exponential Variant Nank1-7* PA67 PA134 PA13467 PA13467C2

Double-exponential

k1 (sK1)

c2r

0.197G0.001 0.144G0.003 0.1762G0.0004 0.179G0.001 0.1473G0.0002

2.5!10 4.7!10K4 3.6!10K5 1.3!10K4 3.4!10K6 K4

k1 (sK1)

A1

k2 (sK1)

A2

c2r

0.224G0.001 0.220G0.003 0.194G0.0008 0.172G0.002 0.150G0.004

0.84G0.006 0.81G0.02 0.87G0.07 0.96G0.2 0.9G0.6

0.036G0.003 0.028G0.002 0.04G0.04 12G3 5G5

0.16G0.006 0.19G0.02 0.13G0.07 0.04G0.2 0.1G0.6

1.8!10K6 3.1!10K6 3.1!10K6 6.2!10K5 2.5!10K6

Refolding was to a final concentration of urea of 0.8 M, and was monitored by tryptophan fluorescence. k1 and k2 refer to the major and minor phases (largest and smallest relative amplitudes, A1 and A2), respectively. A1 and A2 are calculated relative to the difference between the denatured (starting) and native (equilibrium) signals. Errors on rate constants and amplitudes are standard errors on the mean from three or more separately fitted progress curves. Conditions: 25 mM Tris–HCl (pH 8.0), 150 mM NaCl, 20 8C.

In contrast to refolding, substitution of proline with alanine has no effect on the kinetic heterogeneity of unfolding. Levels of heterogeneity in unfolding of PA13467C2 (in which no proline remains) are comparable to that for the wild-type

Figure 2. The effect of proline substitutions on the heterogeneity of unfolding of the Notch ankyrin domain. Fluorescence-detected unfolding curve of PA13467C2, initiated by a rapid increase in the concentration of urea from 0 M to 4.0 M. Continuous lines result from fitting a single-exponential and a double-exponential model (black and red, respectively) to the progress curves. Conditions: 25 mM Tris–HCl (pH 8.0), 150 mM NaCl, 20 8C.

Notch ankyrin domain (Figure 2; Table 3). This observation suggests that the rearrangement from the native to the intermediate during unfolding does not involve prolyl isomerization. Unlike the refolding rate constants, which show only marginal sensitivity to proline replacement, both the major and minor unfolding rate constants increase significantly upon proline substitution, especially in repeats 6 and 7, and in the C terminus (Table 3). Analysis of the urea-dependence of the rate constants and unfolding amplitudes of PA13467C2 using the sequential three-state model43 support this kinetic partitioning: kNI and kID increase by 15-fold and 30-fold, respectively, under unfolding conditions (4.2 M urea), whereas kDI decreases by only twofold under folding conditions (0.8 M urea; not shown). These changes suggest that the stabilization provided by the substituted trans proline, relative to alanine, develops progressively as structure accumulates. The observation that replacing proline residues eliminates refolding heterogeneity is consistent with previous studies that indicate that prolyl isomerization limits the slow refolding phase.43 In contrast, the fast phase in refolding is rather insensitive to proline substitution (Table 2). Although this insensitivity is consistent with the fast phase being independent of prolyl isomerization, the decrease in stability produced by the substitutions (by as much as 5 kcal molK1 for PA13467C2) might be expected to decrease the intrinsic rate of folding. Thus, it is possible that the fast phase in refolding of the Notch ankyrin domain is limited by prolyl isomerization, but that

Table 3. The effect of multiple proline substitutions on the unfolding kinetics of the Notch ankyrin domain Single-exponential Variant Nank1-7* PA67 PA134 PA13467 PA13467C2

kK1 (s

K1

)

0.0627G0.0002 0.337G0.002 0.0996G0.0002 0.721G0.001 2.21G0.01

c2r 2.4!10K5 2.8!10K4 9.9!10K7 1.4!10K4 1.4!10K4

Double-exponential kK1 (s

)

K1

0.0654G0.0002 0.437G0.001 0.0997G0.0003 0.801G0.002 2.58G0.02

AK1

kK2 (sK1)

AK2

c2r

1.092G0.0008 1.68G0.03 1.007G0.003 1.248G0.002 1.249G0.009

0.725G0.010 0.946G0.006 0.5G0.15 3.71G0.08 7.8G0.5

K0.092G0.0009 K0.68G0.03 K0.007G0.003 K0.248G0.002 K0.249G0.009

1.2!10K6 1.5!10K6 9.5!10K7 4.2!10K6 7.2!10K6

Unfolding was to a final urea concentration of 4.0 M, and was monitored by tryptophan fluorescence. k1 and k2 refer to the major and minor unfolding phases (largest and smallest relative amplitudes, A1 and A2), respectively. A1 and A2 are calculated relative to the difference between the native (starting) and denatured (equilibrium) signals. Errors on rate constants and amplitudes are standard errors on the mean from three or more separately fitted progress curves. Conditions: 25 mM Tris–HCl, 150 mM NaCl, pH 8.0, 20 8C.

257

Prolyl Isomerization in Notch Ankyrin Domain Folding

in PA13467C 2 , the increase in refolding rate resulting from the loss of prolyl isomerization is offset by the stability decrease. To investigate this possibility, we simulated folding rates to determine whether the fast refolding phase of the Notch ankyrin domain corresponds to intrinsic, nonproline limited folding, or if this phase is a combination of a faster intrinsic refolding process and slower prolyl isomerization steps. Equilibrium distribution of unfolded conformations The presence of proline residues complicates protein folding kinetics by introducing heterogeneity in the denatured state. In one limiting model for the effect of prolyl isomerization on folding kinetics, only unfolded conformations with all prolyl peptide bonds in the native-like isomeric states (all-trans for the consensus proline residues of the Notch ankyrin domain) are folding-competent.12 Thus, refolding should be influenced by the relative populations of different prolyl isomeric states. To examine the effect of the number of proline residues on the population of various denatured species, we computed populations according to the binomial distribution for proteins with one to seven proline residues, setting Ktc equal to 0.111 (see Materials and Methods) for each individual proline residue (Figure 3). As expected, the two isomeric denatured states of a protein containing a single proline residue matches that given by the equilibrium constant (10% cis). The population of the all-trans species decreases as the number of proline residues increases, although

Figure 3. Equilibrium distribution of unfolded conformations. From top to bottom, rectangles in each column indicate the relative population of unfolded conformations, from all-trans prolyl peptide bonds (C0, top rectangle), to all-cis prolyl peptide bonds when the number of proline residues in the protein is varied and Ktc is set to 0.111. Relative populations were estimated from equation (5).

the decrement becomes smaller and smaller as each proline residue is added. As a result, even when there are seven proline residues, the all-trans species makes up 50% of the total denatured protein. With only four proline residues, the all-trans species comprises more than 70% of the total denatured protein. Moreover, the distribution among denatured species is highly biased toward proteins that have only one or two non-native isomers. For example, even with seven proline residues, the conformation with six out of seven trans prolyl peptide isomers dominates the denatured species, and conformations with three or more non-native prolyl peptide bonds make up no more than 2% of the total denatured species. In short, even in the presence of a large number of proline residues, there is a bias in the denatured state away from species containing large number of non-native prolyl peptide isomers. This feature of the distribution is expected to reduce the complexity of folding kinetics for the Notch ankyrin domain. Effect of the number of proline residues on eigenvalues and amplitudes To determine the effect of the number of proline residues on the folding kinetics of a protein with an intrinsic folding rate matching the major phase of the Notch ankyrin domain, we calculated eigenvalues and amplitudes from the sequential isomerization model with one, four, and seven prolyl peptide bonds as a function of urea concentration (Figure 4). We set Ktc equal to 0.111. For comparison, we present the intrinsic folding curve (kfCku; black line and filled circles, Figure 4). When a single prolyl peptide bond is included in the model, two kinetic phases are predicted (Figure 4(a)–(c)). The eigenvalue of the fast phase is similar to the intrinsic folding curve at all concentrations of urea (Figure 4(a)). The eigenvalue of the slow phase (blue) is significantly smaller than that of the fast phase at all concentrations of urea, and exhibits a modest sigmoidal urea-dependence, with a small increase near Cmin, the concentration of urea at which the intrinsic folding rate is at a minimum. The fast phase has the largest refolding amplitude at all concentrations of urea below Cmin, at which point the refolding amplitudes of both phases decrease to zero. Below Cmin, the refolding amplitude of the slow phase increases slightly at the expense of the fast phase, with increasing concentration of urea. Thus, as expected, in the presence of one proline residue, refolding kinetics should appear to be biphasic, and the fast observed phase should have rate constants that match the intrinsic folding rate. In contrast to refolding, the slow kinetic phase has an unfolding amplitude close to zero at strongly denaturing concentrations of urea, where all of the unfolding amplitude is associated with the fast unfolding phase. Near Cmin, the unfolding amplitude of the slow phase increases modestly, although the fast phase retains most of the amplitude. Thus,

258

Prolyl Isomerization in Notch Ankyrin Domain Folding

Figure 4. The effect of the number of proline residues on eigenvalues and amplitudes of refolding and unfolding. Colored lines and symbols represent (a), (d) and (g) urea-dependence of eigenvalues, and (b), (e) and (h) amplitudes of refolding and (c), (f) and (i) unfolding calculated with the sequential isomerization model for (a)–(c) one, (d)–(f) four and (g)–(i) seven prolyl peptide bonds, each with Ktc set to 0.111. Blue lines (filled squares) represent the slowest eigenvalue, red lines (filled circles) show the dominant remaining eigenvalue. Eigenvalues with smaller amplitudes are colored. Black lines (filled diamonds) represent the intrinsic folding curve. Open black circles and squares represent rate constants and amplitudes of the fast and slow phases, respectively, fitted from progress curves simulated from the calculated eigenvalues and amplitudes. Minor breaks in values of fitted parameters at 3.5 M urea result from switching from a double-exponential to a single-exponential fitting function.

in the presence of one proline residue, unfolding kinetics should appear to be monophasic (except near Cmin), and the rate constant of the single unfolding phase should be similar to the intrinsic unfolding phase. These results are consistent with the work of Kiefhaber & Schmid.18 When four and seven prolyl peptide bonds are included in the sequential isomerization model, there are five and eight kinetic phases that can potentially contribute to kinetics, respectively (Figure 4(d) and (g)). As was seen with a single proline residue (Figure 4(a)), the slowest eigenvalue shows a modest sigmoidal urea-dependence with a midpoint near Cmin, and is always well separated from the faster eigenvalues. At low and high concentrations of urea, the fastest eigenvalue (which has the largest amplitude) is well resolved from intermediate eigenvalues, and shows a ureadependence that matches the intrinsic folding curve, whereas the intermediate eigenvalues are relatively flat. However, these eigenvalues converge near Cmin, (Figure 4(d) and (g)), complicating the assignment of a unique urea dependence to each

eigenvalue (that is, matching the identities of phases at low concentrations of urea with those near Cmin). Because the goal of these simulations is to understand how multiple prolyl isomerization reactions influence experimental folding curves and derived kinetic constants, we chose to designate the eigenvalue that has the largest amplitude (with the exception of the slowest phase, blue) as the “major fast phase.” Since this phase contains the bulk of the refolding amplitude, it will be contribute the most to experimentally observed refolding curves. The remaining phases, which all have small amplitudes, are identified on the basis of the relative magnitude of the respective eigenvalues. This scheme presents a relatively simple ureadependence for refolding and unfolding: the eigenvalue associated with the major fast phase closely approximates the intrinsic refolding curve (Figure 4(d) and (g)). Although this eigenvalue becomes slower than the urea-insensitive minor eigenvalues near Cmin, these minor eigenvalues have very little amplitude at most concentrations of urea (remaining below 10% total for four and seven

259

Prolyl Isomerization in Notch Ankyrin Domain Folding

proline residues, Figure 4(e) and (h)), and should not contribute to observed kinetics. Furthermore, in the narrow range of urea concentrations where the minor eigenvalues show increased amplitudes, they are roughly the same as the major fast eigenvalue, and will simply contribute their amplitude to the major fast phase. Thus, in addition to the slow phase, a single fast refolding phase is predicted, with the fast phase closely approximating the intrinsic refolding rate. Calculated amplitudes for the sequential model with four and seven proline residues are dominated by the major fast (red) and slow (blue) eigenvalues (Figure 4(e) and (h)). In the absence of urea, the major fast eigenvalue contributes around 60% and 50% of the total refolding amplitude, with four and seven proline residues, respectively. As the concentration of urea is increased, the refolding amplitude of the slow phase increases at the expense of the fast phase, crosses the fast phase, and peaks around 1.5 M urea before decreasing to zero. This is reminiscent of the increase in the refolding amplitude of the slow phase with urea in the presence of one proline residue, described above (Figure 4(b)) and elsewhere.18 The results of the refolding simulations are consistent with our experimental characterization of the Notch ankyrin domain, in that refolding appears to be biphasic even in the presence of five conserved proline residues, and for Nank1-7*, two additional C-terminal proline residues.43 Moreover, as with the calculated refolding amplitudes (Figure 4(e) and (h)), the amplitudes of the experimentally determined refolding phases cross at intermediate concentrations of urea, with the slow phase becoming larger than the fast phase. However, for Nank1-7D we measure a fast-phase refolding amplitude of 85% at a low urea concentration (and an even larger amplitude for Nank17*), as opposed to the predicted 50–60%. A possible reason for this difference is that the value for the equilibrium population of cis isomers used in these simulations (10%) may be too large. Alternatively, some of the prolyl peptide bonds may convert from cis to trans after the rate-limiting step, and may be accelerated by partial structure formation. In contrast to refolding, only one eigenvalue has significant amplitude at strongly denaturing concentrations of urea, even in simulations that include four and seven proline residues (Figure 4(f) and (i)). This dominant eigenvalue closely approximates the intrinsic folding curve (Figure 4(d) and (g)). As with refolding, over a narrow range of urea concentrations near Cmin, three phases have unfolding amplitudes above 5% (the slowest overall eigenvalue, and two phases with eigenvalues very similar to the intrinsic folding curve). Thus, the sequential isomerization model predicts that observed unfolding kinetics for a protein with as many as seven proline residues should appear to be biphasic near Cmin, and monophasic at a high concentration of urea. The fastest observed unfold-

ing phase should have an apparent rate constant similar to the intrinsic unfolding rate. Fitting simulated kinetic traces with multiple proline residues Modeling refolding of the Notch ankyrin domain as a set of stepwise prolyl isomerization reactions in the denatured state followed by an intrinsic folding reaction leads to a general solution that has many different kinetic phases. However, as described above, consideration of the amplitudes of each phase suggests that typically only two phases will be detected at a particular concentration of urea, leading to apparent biphasic kinetic behavior, as is seen experimentally. To demonstrate quantitatively that the sequential isomerization model would lead to experimental refolding curves that appear biphasic despite a large number of theoretical eigenvalues, and to demonstrate that a rate constant corresponding to intrinsic refolding can be recovered by fitting data from a sequential isomerization mechanism, we used the entire set of eigenvalues and amplitudes defined by the sequential isomerization model to generate refolding and unfolding kinetic traces (below and above Cmin, respectively) according to: Y Z a0 C

n X

ai eli t

(1)

1

where ai is the amplitude associated with the ith eigenvalue, n is the number of proline residues, and a0 (the amplitude associated with the zero eigenvalue) gives the signal once equilibrium is reached. We introduced 0.2% Gaussian error (approximately that in our stopped-flow fluorescence measurements) into kinetic traces that had been generated using equation (1), and then fitted exponential functions to the curves. The kinetic traces, fits, and residuals for one simulation, modeling seven proline residues with Ktc set to 0.111, are shown in Figure 5. The progress curves generated from the seven proline residue sequential isomerization model are fit significantly better by a double-exponential than a single-exponential function (Figure 5(a)–(c)) for refolding at all concentrations of urea below Cmin and for unfolding under marginally destabilizing conditions (slightly above Cmin). The use of a tripleexponential function does not improve the fits significantly. Thus, as predicted from inspection of the calculated eigenvalues and amplitudes (Figure 4), only two phases can be resolved from the synthetic data at urea concentrations near or below Cmin, despite the use of eight eigenvalues to generate the progress curves. Unfolding curves generated from the seven proline residue model under strongly destabilizing conditions (urea concentration well above Cmin) are fit adequately with a single-exponential function (Figure 5(d)). The use of a double-exponential function does not improve the fit significantly.

260

Prolyl Isomerization in Notch Ankyrin Domain Folding

Figure 5. Least-squares fitting of data simulated using the sequential isomerization model. Calculated eigenvalues and amplitudes for a protein with seven prolyl peptide bonds and Ktc set to 0.111 were used to generate kinetic traces according to equation (1), to which 0.2% Gaussian error was added (circles). Representative curves for refolding in (a) 0 and (b) 2 M urea, and unfolding in (c) 3 and (d) 5 M urea. Continuous lines are singleexponential and double-exponential fits to the simulated data (black and red, respectively); the upper panels show residuals from the single-exponential and the doubleexponential fits. Note that the residuals in (b)–(d) are plotted on a much finer scale than those in (a).

Thus, despite the use of eight eigenvalues to generate strong unfolding curves, only one phase can be resolved from the synthetic data. As was seen with seven proline residues, progress curves generated from the sequential isomerization model with one and four proline residues were best-fit with a double-exponential function below 3.5 M urea, and with a singleexponential function at concentrations of urea above Cmin. Fitted rate constants and amplitudes are plotted over a range of urea concentrations as open symbols in Figure 4, for comparison with the eigenvalues and amplitudes used to generate them. For all simulations, the slow fitted rate constant (squares) closely approximates the slowest eigenvalue, and the fast fitted rate constant (circles) approximates the rate constant for intrinsic folding (and the fast major eigenvalue), with only modest deviations near Cmin (Figure 4). Effect of slow intrinsic folding on the sequential isomerization model The simulations above examine the effect of multiple prolyl isomerization reactions on folding kinetics when intrinsic folding is faster than prolyl isomerization, and show that intrinsic folding and prolyl isomerization are partitioned separately into the fast and slow observed folding phases. Previous studies with one and two proline residues show that as the rates of the intrinsic folding and prolyl isomerization approach each other, each of the two processes influences both observed kinetic phases.18 To examine how the observed refolding

kinetics of destabilized Notch ankyrin variants are influenced by more than two prolyl isomerization reactions, we calculated eigenvalues and amplitudes from the sequential model for which the intrinsic rate of folding is slowed to approximately that of prolyl isomerization, using the kinetic parameters of a slow-folding variant of the Notch ankyrin domain bearing a single-residue substitution (our unpublished results). In the presence of four proline residues and with Ktc set to 0.111, none of the calculated eigenvalues track the input intrinsic folding curve under refolding conditions (Figure 6(a)). Although the two eigenvalues with the largest refolding amplitudes are closest to the intrinsic curve, they deviate significantly, providing upper and lower bounds for the intrinsic curve (Figure 6(a) and (b)). Refolding kinetic traces simulated from calculated eigenvalues and amplitudes at urea concentrations below 1 M were best-fit by a double-exponential function, and produced fitted refolding rate constants similar to the eigenvalues with the largest amplitudes (Figure 6, open symbols). Thus, if intrinsic folding and prolyl isomerization occur at similar rates, the observed kinetic phases appear to provide upper and lower limits for the intrinsic folding rates, but neither can be considered to represent the intrinsic folding rate.

Discussion The linear, modular architecture of repeat proteins provides a simple framework in which to test

Prolyl Isomerization in Notch Ankyrin Domain Folding

Figure 6. Effect of slow intrinsic folding on eigenvalues and amplitudes of refolding and unfolding. Urea dependence of (a) eigenvalues, and amplitudes of (b) refolding and (c) unfolding, for the sequential isomerization model in which the intrinsic folding rate (black filled diamonds) is similar to the rate of prolyl isomerization, with four proline residues and Ktc set to 0.111. Colors and symbols are as given in the legend to Figure 4. Progress curves were fit by a double-exponential function below 1 M urea, and by a single-exponential function above 1 M urea.

protein folding theories developed from studies on globular proteins. For example, Plaxco & Baker have shown that folding rates are correlated with relative contact order,22 suggesting that protein folding is limited by the formation of native contacts between residues that are far away from each other on the polypeptide chain. Thus, repeat proteins, which contain contacts exclusively between residues that are nearby on the poly-

261 peptide chain,22–31 should fold fast. Moreover, since the length of repeat proteins can be varied without changing the overall fold, these proteins can be used to test and refine theories relating chain length to folding rates.32–34 We have shown that the Notch ankyrin domain folds several orders of magnitude slower than predicted from contact order calculations and that there is heterogeneity both in refolding and unfolding. 43 This study seeks to thoroughly investigate the role of prolyl isomerization, a kinetic process known to limit protein folding, in the folding and unfolding of the Notch ankyrin domain, to determine whether prolyl isomerization can account for the slow refolding and heterogeneous unfolding kinetics. The disappearance of kinetic heterogeneity in refolding of the variant of Nank1-7* in which all seven proline residues are replaced with alanine (PA13467C2) provides compelling evidence that refolding heterogeneity (but not unfolding heterogeneity) is caused by prolyl isomerization in the denatured state. The observation that some refolding heterogeneity is retained in variants with subsets of the seven proline residues replaced (Figure 1(a)–(c); Table 2) indicates that more than one proline residue contributes to kinetic heterogeneity. Although the proline substitution studies do not rule out the contribution of proline to the fast observed refolding phase of the wild-type Notch ankyrin domain, since substitutions are destabilizing, the PA13467C2 variant can itself be considered to have a highly local ankyrin topology with an intrinsic folding rate much slower than predicted from topological considerations. To further investigate how isomerization of as many as seven prolyl peptide bonds influences the folding and unfolding of the wild-type Notch ankyrin domain, we examined the behavior of a simple kinetic model in which a series of sequential prolyl isomerization reactions is coupled to a final folding reaction. These modeling studies provide a means to determine whether multiple prolyl isomerization reactions in the denatured state can slow the major phase of refolding, and whether such isomerization can contribute to heterogeneity in unfolding. If the eigenvalues calculated for the sequential prolyl isomerization model deviate from the assumed intrinsic rate of refolding (which we have set equal to the major experimentally determined refolding phase), then the major observed refolding phase of the Notch ankyrin domain is not a direct measure of the intrinsic rate of refolding, but is influenced by prolyl isomerization. In contrast, if a dominant eigenvalue calculated from the prolyl isomerization matches assumed intrinsic refolding rate, then the major observed refolding phase can be taken to represent the intrinsic rate. Our simulations suggest that for the sequential isomerization model with as many as seven prolyl isomerization steps, the faster of the two dominant eigenvalues calculated from the prolyl isomerization model reproduces the intrinsic folding curve,

262 provided the intrinsic curve is set equal to the rate of folding of the Notch ankyrin domain. These results are consistent with work by Kiefhaber & Schmid on folding in the presence of one and two prolyl isomerization reactions.18 In addition, our simulations suggest that the complexity of observed folding kinetics does not increase with the number of prolyl isomerization steps. Rather, simulated progress curves should appear biphasic near Cmin and at a low concentration of urea, and monophasic at a high concentration of urea, even when eight theoretical phases exist. Thus, these calculations indicate that the fast observed phase in refolding of the Notch ankyrin domain represents intrinsic folding, and that its slow rate is not a consequence of prolyl isomerization. However, our simulations suggest that when intrinsic folding rates are slowed to that seen for some destabilizing Notch ankyrin domain variants, neither of the two observed phases provides a direct measure of the intrinsic rate; rather, they provide upper and lower limits for the intrinsic folding rate. This effect must be taken into account when analyzing the kinetics of slowfolding variants of repeat-proteins that contain a large number of proline residues.

Materials and Methods Mutations to replace proline with alanine residues were introduced by a procedure similar to the QuikChange Multie method (Stratagene; La Jolla, CA). Up to seven mutagenic oligonucleotides corresponding to the sense strand were mixed with an intact plasmid encoding the Notch ankyrin repeat domain (Nank1-7*, encoding seven full ankyrin sequence repeats43), and were subjected to multiple rounds of polymerization using Pfu Turbo polymerase (Stratagene). Taq DNA ligase (New England Biolabs, Beverly, MA) was included during polymerization reaction cycles. Reactions were subsequently digested with DpnI (New England Biolabs), were precipitated in ethanol, and were electroporated into Escherichia coli strain TB1. Mutations were verified by DNA sequencing. All variants of the Notch ankyrin domain containing proline-to-alanine (PA) substitutions were expressed and purified as described in the companion paper. Equilibrium and kinetic folding studies Estimates of free energies of unfolding were obtained from urea-denaturation experiments by tryptophan fluorescence and CD spectroscopy as described.35,36 Unfolding free energies were estimated from ureainduced unfolding transitions by non-linear least-squares (KaleidaGraph, Synergy software) fitting of a two-state model to the transition: !
 8 1 eKDGu =RT Yobs Z YN (2) C YD 8 8 1 C eKDGu =RT 1 C eKDGu =RT where Yobs, YN, and YD are the observed spectroscopic signal, and the signal of the native and denatured ensembles, which were treated as linear functions of the concentration of urea. The unfolding free energy, DG8u , was also treated as a linear function of the concentration

Prolyl Isomerization in Notch Ankyrin Domain Folding

of urea: DG8u Z DG8u;H2 O K m½urea


(3)

where DG8u;H2 O is the free energy of unfolding in the absence of urea, and the m-value is independent of the concentration of urea.37–39 Stopped-flow fluorescence measurements and analysis of kinetic unfolding and refolding data were performed as described.43 Simulation of folding and unfolding with multiple isomerization steps Prolyl isomerization is simulated as n sequential isomerization reactions in the denatured state, followed by an intrinsic folding step:12 nkct

ðnK1Þkct

3kct

2kct

kct

kf

ktc

2ktc

ðnK2Þktc

ðnK1Þktc

nktc

ku

Cn # CnK1 # / # C2 # C1 # T# N

(4)

In this scheme, prolyl isomerization rates at each residue are treated as identical and independent of one another. The rate constants kf and ku are taken as the intrinsic rates folding and unfolding, respectively. The rate constants kct and ktc are used to represent cis-to-trans and trans-to-cis isomerization at each individual prolylpeptide bond. The numbers multiplying these microscopic rate constants represent the number of prolylpeptide bonds for which a particular isomerization step can occur.12 For example, in the first isomerization step in the scheme above there are n different cis proline residues that can react to give the product, whereas in the backreaction there is only a single trans proline residue capable of converting to the all-cis form. As written, equation (4) assumes that all proline residues are in the trans conformation in the native state. Although the four consensus proline residues in repeats 3, 4, 6, and 7 are trans in the crystal structure of the Notch ankyrin domain,44 the conformation of the prolylpeptide bond in the first repeat is not known, because this region is disordered in the crystal structure. Likewise, the conformations of the two prolyl-peptide bonds at the C terminus of Nank1-7* are not known, because these residues were omitted from the polypeptide to improve crystallization. Here we make the assumption that these three proline residues are also trans in the native state. We also make the assumption that individual proline residues do not differ significantly in their isomerization rates or equilibrium constants. This assumption is supported by the similarity of the primary sequence surrounding the five consensus proline residues (four threonine, one leucine). The time-evolution of a system governed by a stepwise reaction such as that proposed for prolyl isomerization (equation (4)) can be obtained by treating the rate equations as a differential matrix equation, and determining the eigenvalues of the square matrix of rate coefficients, which are equivalent to the frequencies with which the system evolves.40,41 Amplitudes are determined by constructing a convenient set of orthogonal eigenvectors, and combining these eigenvectors with starting concentrations of all of the species. Such amplitudes reveal which eigenvalues dominate the kinetics. This approach, which is further detailed in Appendix A, is similar to that used to analyze refolding coupled to one or two proline residues.18 However, unlike these simpler schemes, analytical solution of the differential equation for folding in the presence of a large number of proline residues (see Appendix A, equation (A6)) is

263

Prolyl Isomerization in Notch Ankyrin Domain Folding

impractical at best. Instead, we use the matrix manipulation program Matlab (Mathworks; Natick, MA) to find eigenvalues and eigenvectors numerically by inputting specific values for kct, ktc, kf and ku (see below). We then solve for folding and unfolding amplitudes associated with each eigenvalue by imposing the initial conditions that the native species is fully populated at the start of unfolding, and the denatured species (Cn, CnK1, ., C0) are fully populated at the start of refolding. Initial concentrations of these denatured species are calculated from the binomial distribution: 0 1 n X n! (5) ½Ci
Z Pi PnKi @ ½Cj
A ðn K iÞ!i! t c jZ1 The first term in equation (5) represents the probability, out of all the non-native states, of populating a state with i out of n cis-proline residues, given the probabilities of individual prolyl peptide bonds being trans (Pt) versus cis (PcZ1KPt). The second term gives the total concentration of non-native protein. Solving the differential rate matrix (Appendix A, equation (A6)) by numerical methods requires numerical values for folding, unfolding, and prolyl isomerization rates. We used values of 0.0215 and 0.0024 sK1 for kct and ktc, respectively. These values, which are within the range found for prolyl isomerization in unstructured peptides,18 give an equilibrium constant for cis–trans isomerization (Ktc†) of 0.111, and thus Pc and Pt values of 0.10 and 0.90, respectively. This value of Ktc matches the value expected based on the residues immediately preceding each proline residue in the Notch ankyrin domain, which are the primary determinant of Ktc, kct, and ktc.42 We set kf and ku equal to the fast experimentally observed refolding and major unfolding rate constants of Nank1-7D (k1 and kK1 in the companion paper, respectively). These two rate constants combine to describe the slow folding eigenvalue that is most closely related to the I5D step in the three-state folding model.43 This phase was chosen because it is the slowest of the two intrinsic steps, and thus it is expected to be more sensitive to the effects of prolyl-isomerization. In addition, it best represents the step in which structure is formed from the denatured ensemble, where prolyl isomerization is most likely to occur. Intrinsic folding parameters from Nank1-7D were chosen for simulation over those of the slightly longer Nank1-7* construct, because Nank1-7D shows a greater level of heterogeneity. To simplify calculations, the urea-dependence of intrinsic refolding and unfolding rates was represented using the quadratic chevron in the preceding paper (equation (2)), with fitted parameters from Nank1-7D.43 The rates of prolyl isomerization were assumed to be independent of urea.

Acknowledgements We thank Katherine Tripp for providing stability estimates for Nank1-7D, and for measuring the unfolding kinetics of PA134. We thank Cecilia Mello and Katherine Tripp for critical discussion of this material. This work was supported by grants † We define Ktc as Pc/PtZktc/ktc.

GM60001 and GM068462 from the National Institutes of Health.

Appendix A: Matrix Methods to Model Sequential Prolyl Isomerization Here, the matrix methods that are used to analyze and simulate the kinetics of a sequential prolyl isomerization reaction (equation (4) of the main text) are outlined. Although the ideas behind this procedure have been presented elsewhere,18,40 we present these methods to describe how the method is generalized to proteins containing many proline residues. We begin with a simple intrinsic folding reaction, because a compact analytical solution can be obtained easily, and then derive a matrix equation for a scheme involving four proline residues as an example. In the absence of proline residues, protein folding can often be described as a simple, two-state reaction: kf

D# N ku

where kf and ku are the intrinsic folding and unfolding rate constants, respectively, that convert the denatured (D) and native (N) forms of the protein. The differential equations that describe the time evolution of the system can be written as: ! ! Kkf ku D d ð ¼Y ðZ Y ZC (A1) dt N kf Kku The general solution to equation (A1) is a linear combination of specific exponential solutions: ð Z cð1Þ X ð ð1Þ el1 t C c2 X ð ð2Þ el2 t Y 1

(A2)

ðiÞ

ð is the ith eigenvector, li is the ith where X eigenvalue or macroscopic rate constant, and ci are constants determined by the initial conditions of the system (i.e. starting concentrations D0 and N0). ¼ are the The eigenvalues, li, for the rate matrix, C, solutions to the secular equation: ¼ K l¼ jC Ij Z 0

(A3)

where ¼ I is an identity matrix with the same ¼ These eigenvalues represent the dimensions as C. negative of the observed rate constants in an unfolding ðiÞor refolding experiment. The eigenð , of the system are found separately vectors, X for each eigenvalue from the equation: ¼X ¼ Z lX ¼ C

(A4)

The constants, ci, can then be found by evaluating equation (A1) at tZ0: ! Do ¼ ð1Þ C c2 X ¼ ð2Þ (A5) Z c1 X No The experimentally observed amplitude for the

264

Prolyl Isomerization in Notch Ankyrin Domain Folding

ith phase in a refolding or unfolding experiment is simply the product of the ith eigenvector and its associated coefficient, ci. The refolding and unfolding of a protein containing multiple proline residues can be treated with the same formalism as given above, including additional steps to represent prolyl isomerization in the denatured state. This approach assumes that isomerization and folding are mutually exclusive, and that all proline residues are equivalent.12,18 In the presence of four independent and equivalent trans proline residues, protein folding can be described as a series of sequential cis to trans isomerization reactions in the denatured state followed by a final intrinsic folding step:

in protein denaturation reactions is due to cis–trans iso-merism of proline residues. Biochemistry, 14, 4953–4963. Schmid, F. X. & Baldwin, R. L. (1978). Acid catalysis of the formation of the slow-folding species of RNase A: evidence that the reaction is proline isomerization. Proc. Natl Acad. Sci. USA, 75, 4764–4768. Schmid, F. X. & Baldwin, R. L. (1979). The rate of interconversion between the two unfolded forms of ribonuclease A does not depend on guanidinium chloride concentration. J. Mol. Biol. 133, 285–287. Schmid, F. X. (1986). Fast-folding and slow-folding forms of unfolded proteins. Methods Enzymol. 131, 70–82. Schmid, F. X. (1986). Proline isomerization during refolding of ribonuclease A is accelerated by the presence of folding intermediates. FEBS Letters, 198, 217–220. Kiefhaber, T., Quaas, R., Hahn, U. & Schmid, F. X. (1990). Folding of ribonuclease T1. 1. Existence of multiple unfolded states created by proline isomerization. Biochemistry, 29, 3053–3061. Creighton, T. E. (1978). Possible implications of many proline residues for the kinetics of protein unfolding and refolding. J. Mol. Biol. 125, 401–406. Tang, K. S., Guralnick, B. J., Wang, W. K., Fersht, A. R. & Itzhaki, L. S. (1999). Stability and folding of the

4kct

3kct

2kct

kct

kf

ktc

2ktc

3ktc

4ktc

ku

7.

8.

9. 10.

11.

C4 # C3 # C2 # C1 # C0 # N where kct and ktc are the prolyl isomerization rate constants, and Ci is the denatured form of the protein with i out of four cis prolyl isomers (and 4Ki trans isomers). The differential equation that describes the time-evolution of the system is:

12. 13.

d ð ¼Y ð Y ZC dt 0 ktc 0 0 0 K4kct B B 4kct Kktc K 3kct 2ktc 0 0 B B 3kct K2ktc K 2kct 3ktc 0 B 0 ZB B 0 2kct K3ktc K kct 4ktc B 0 B B 0 0 0 kct K4ktc K kf @ 0

0

0

kf

0

This example can be generalized for any number of trans proline residues.

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Edited by F. Schmid (Received 21 November 2004; received in revised form 1 June 2005; accepted 17 June 2005) Available online 5 July 2005