13172
2008, 112, 13172–13176 Published on Web 09/26/2008
The Intrinsic Stiffness of Polyglutamine Peptides Vijay R. Singh and Lisa J. Lapidus* Department of Physics and Astronomy, Michigan State UniVersity, East Lansing, Michigan 48824 ReceiVed: June 26, 2008; ReVised Manuscript ReceiVed: September 04, 2008
We have used the method of Trp/Cys contact quenching to measure the rate of contact formation in polyglutamine and find it to be a very stiff peptide. Separation of observed rates into reaction-limited and diffusion-limited rates show that the reaction-limited rates increase (rather than decrease) slightly with length between 4 and 16 amino acids. Using Szabo, Schulten, and Schulten theory, we have modeled the results with a wormlike chain with excluded volume and find the persistence length to be about 13.0 Å, much longer than has been observed for other random peptides and unfolded proteins. The preferred extended conformation of polyglutamine could account for a propensity for expanded glutamine stretches to unfold the Huntington’s protein and the high propensity to aggregate from a disordered monomer. The polyglutamine amino acid motif is associated with several neurodegenerative diseases, all of which exhibit aggregation in vivo.1 A significant hallmark of many of these diseases, including Huntington’s, is that the age of onset correlates with the length of the repeat, suggesting that long stretches (30-40) of glutamines significantly destabilize the protein,2 reduce the cooperativity of folding,3 or somehow change the unfolded conformational ensemble.4 Nagai et al. have shown that monomeric thio-polyQ fusion protein converts to a β-rich conformation before aggregating and that this conformation is cytotoxic.5 Recent in vitro biophysical studies of polyglutamine peptides have shown that the peptide is generally unstructured6,7 and that the monomer is the critical nucleus of aggregation,4 but there is little consensus as whether the peptide preferentially adopts extended or compact conformations.8-10 In this study we have used the technique of Trp/Cys contact quenching11 to measure intramolecular diffusion and probability of contact formation in short polyglutamine peptides. Modeling the length dependence of contact rates with a wormlike chain reveals an extremely stiff polymer with a persistence length of ∼13.0 Å, which stands in stark contrast to earlier measurements on other sequences and denatured proteins,12-14 all of which appear to be much more flexible. The extended conformation preferred by polyglutamine can explain both the decrease in stability of the host protein and the propensity to form amyloids once unfolded. Materials and Methods Five peptides were made using solid-phase synthesis with the sequence, KKCQnWKK, with n ) 4, 7, 10, 13, and 16. Lengths 4-13 were made by SynBioSci (Livermore, CA). Q16 was a kind gift from Regina Murphy of the University of Wisconsin. Each lyophilized sample was dissolved using the method of Wetzel.15 These samples were diluted 10-fold into buffer and a certain concentration of sucrose that had been * To whom correspondence
[email protected].
should
be
addressed.
E-mail:
10.1021/jp805636p CCC: $40.75
deoxygenated and saturated with N2O, which acts as a good quencher of solvated electrons, and measured within 30 min. The final solution conditions were 100 mM potassium phosphate at pH 3 with 1 mM TCEP to prevent disulfide formation. The typical peptide concentration was 30 µM, determined by optical absorption at 280 nm; at this concentration, bimolecular quenching contributes less than 4% to the observed decay rate. The instrument to measure tryptophan triplet lifetimes has been described elsewhere.11,14 Briefly, the tryptophan triplet is populated simultaneously with the singlet state within a 10 ns pulse of light at 289 nm. The triplet population is monitored by absorption at 442 nm. In aqueous conditions, the triplet lives for 40 µs in the absence of quenching, but can be observed to decay in as little as 100 ns for a short peptide with Trp and Cys at the ends.11 The decay in optical absorption was detected by a silicon detector and observed on two oscilloscopes to cover a time range between 10 ns and 100 ms. The data was logarithmically binned and fit to a single exponential over the range of 100 ns to 100 µs. Each peptide was measured at five temperatures and four concentrations of sucrose (10, 20, 30, 40% by weight). The Wetzel dilution protocol has been shown to produce monomeric solutions which aggregate very slowly at pH 3. All samples were used within 30 min after thawing so aggregation is unlikely. However, if aggregation did occur, the kinetics of the tryptophan triplet would exhibit two decays: one for the monomeric species that can undergo contact quenching (∼3 µs), and one for the aggregated species that cannot undergo contact quenching (∼40 µs). This longer decay was never detected. Wormlike chains were generated using a Monte Carlo algorithm described previously.14 Briefly, each chain is generated with 10 links per amino acid; the polar angle between two links is randomly chosen from a Gaussian distribution specified by the persistence length, lp. Every 10 links, the chain is checked for nonlocal clashes within the excluded volume diameter, dR; if a clash is found the chain is truncated 3 persistence lengths before the clash and regenerated. To simulate fluctuating β structure within the wormlike chain, individual amino acids (10 2008 American Chemical Society
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Figure 1. Scheme for measuring rate of contact formation within a peptide. A pulse of UV light excites the tryptophan (W) to the lowest triplet state, which can then contact the cysteine (C) with rate kD+. After entering the encounter complex, the excited triplet may diffuse away with rate kD- or be quenched with rate q. Equation 1 is derived assuming the encounter complex is in a quasi-steady state.
to turn over at n ∼ 13. This length dependence cannot be explained with a simple freely jointed chain model. Therefore these peptides were modeled as a wormlike chain with excluded volume. Using Szabo, Schulten, and Schulten (SSS) theory, which models intramolecular diffusion as diffusion on a onedimensional potential of mean force,16 the reaction-limited and diffusion-limited rates are given by13
kR )
∫r∞ q(r)P(r)dr
(5)
where r is the distance between the tryptophan and cysteine links) were randomly assigned a polar angle of 0°. For a given set of wormlike chain parameters, 10 million chains were generated for the entire peptide length (including the N and C-terminal lysines) and the distance between the Cys and Trp calculated for each to create a histogram, P(r), used in eqs 5 and 6. Results Using a simple two-step model of contact quenching given in Figure 1, the observed rate of tryptophan triplet decay (the * species) is given by
kobs )
kD+q q + kD-
(1)
if q . kD-, kobs ) kD+. Since previous studies on the Trp-Cys quenching system have shown that diffusion and quenching rates are comparable,11 kobs can be rewritten as
1 1 1 1 1 ) ) + + kobs qK kD+ kR(T) kD+(η)
(2)
where K ≡ kD+/kD- is the equilibrium constant for forming the Trp-Cys encounter complex and kR ≡ qK. We assume that the reaction-limited rate, kR, depends exponentially on temperature and the diffusion-limited rate, kD+, depends inversely on viscosity. Therefore, a plot of 1/kobs versus viscosity (η) at a constant temperature is a line with the intercept equal to 1/kR and the slope equal to 1/ηkD+ (see Figure 2). Note that in previous work kD+ also had a temperature dependence,13 but empirically we do not observe such a dependence on the slopes in this work. A data set of kobs at five temperatures and four concentrations of sucrose is simultaneously modeled as
(
kR(T) ) kR0 exp
E0(T - T0) RTT0
)
(3)
kD+0 η
kD+
)
1 kR2D
l dr { ∫a (q(x) - kR)P(x)dx}2 ∫al P(r) c
c
(6)
and P(r) is the probability density of finding the polypeptide at that distance. D is the effective intramolecular diffusion coefficient, a is the distance of closest approach (defined to be 4 Å), lc is the contour length of the peptide and q(r) is the distance dependent quenching rate. The distance-dependent quenching rate for the Trp-Cys system has been determined experimentally17 and drops off exponentially beyond 4 Å, so the reactionlimited rate is mostly determined by the probability of the shortest distances. Thus the only free parameters in the equations above are D and P(r). We endeavored to find wormlike chain parameters, lp and dR that simultaneously fit the reaction-limited rates of all five lengths of polyglutamine. Figure 4 shows the sum of squares of difference between measured and predicted kR for all five lengths for various values of lp and dR. The best fit was for lp ) 13.0 Å and dR ) 4.0 Å; the predicted kR for these parameters are plotted in Figure 3 (blue line). The curve of least-squares is not uniform in all directions and the axis of shallow descent is not along either parameter axis. Therefore, it is difficult to assign an uncorrelated error to either of these parameters. Nevertheless, changing either of these parameters by 10% results in increase of sum of squares of at least a factor of 5 so we chose 0.4 Å as the error for dR and 1.3 Å as the error for lp. Although kR increases with length and begins to turn over at the longest length, kD+ decreases monotonically with length and can be reasonably fit with a power law dependence kD+ ∼ n-3/2, as would be expected for a flexible peptide. This is somewhat surprising because from eq 6, kD+ depends on kR and would be expected to have a similar length dependence if the diffusion coefficient was the same for all lengths. Using P(r) calculated for each peptide with lp ) 13.0 Å and dR ) 4.0 Å and the measured value of kD+, we calculate D using eq 6 for each length. These values are shown in Table 2. Discussion
where T is the absolute temperature, T0 ) 273 K, η is the
kD+(η) )
1
(4)
solution viscosity, and kR0, kD+0, and E0 are fitting parameters. The results of the fits for different length peptides are shown in Table 1 and the fitted kR and kD+ at T ) 293 K and η ) 1 cP are plotted in Figure 3. These rates are quite low compared to previous measurements on AGQ peptides, and surprisingly the reaction-limited rates increase slightly with length and appear
Because the polyglutamine motif has been implicated in number of aggregation-based diseases, a large number of structural studies have been undertaken to understand what makes this particular sequence different from others. A number of computational and structural studies have suggested that polyglutamine tends to form an extended polymer. The crystal structure of a Q10 inserted in CI2 shows domain swapping within a dimer with the glutamine stretch extended between the two domains, but the structure of the stretch itself could not be determined, indicating it had much conformational flexibility.3,18 Simulation of this system suggests an extended random coil, rather than R helix, β-sheet, or PPII structure, best fits the
13174 J. Phys. Chem. B, Vol. 112, No. 42, 2008
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Figure 2. Viscosity versus observed tryptophan triplet lifetimes at various temperatures for KKCQnWKK where (a) n ) 4 and (b) n ) 10. The lines are the fits to equatons 3 and 4 with the parameters given in Table 1.
TABLE 1: Fit Parameters from Equations 3 and 4 n
kR0 (s-1)
4 7 10 13 16a
1.79 × 10 2.61 × 105 2.42 × 105 2.77 × 105 3.13 × 105 5
kD+0 (s-1)
∆E
4.11 × 2.45 × 106 8.04 × 105 1.36 × 106 2.31 × 105
1.38 2.19 4.81 1.23 0
106
a Q16 was constrained to have ∆E ) 0 for good convergence of the fit.
Figure 3. Number of peptide bonds between the Trp and Cys (n + 1) versus reaction-limited (blue) and diffusion-limited (red) rates for polyglutamine peptides (circles). The triangles are rates for Ala-GlyGln peptides reported in ref 12 (water at pH 7). The blue line plots the rates predicted by eq 5 using the wormlike chain parameters lp ) 13 Å and dR ) 4 Å (solid), lp ) 12 Å and dR ) 4 Å (long dash), and lp ) 14 Å and dR ) 4 Å (short dash). The red line is power law fit to k ∼ (n + 1)-3/2.
measured thermodynamics with a Flory characteristic ratio of ∼3.2.8 On the other hand, Pappu and workers have simulated polyglutamine peptides with molecular dynamics simulations and concluded that the peptide favors collapsed conformations, though the conformational distribution is very heterogeneous,9,19,20 and measurements of the translational diffusion coefficient of single molecules of polyglutamine indicate the average hydration
Figure 4. (a) Sum of squared difference between the measured kR and the calculated kR from eq 5 for all 5 peptides. P(r) was calculated from ensembles of wormlike chains for various values of lp and dR. (b) Normalized probability distributions for the wormlike chain parameters lp ) 13.0 Å and dR ) 4.0 Å for all five peptide lengths.
radius is compact, although this analysis assumes the average peptide conformation is spherically symmetric.21 This study is the first to attempt to experimentally describe the accessible conformational ensemble of monomeric, unstructured polyglutamine. From measurement of contact formation of the ends of the polyglutamine we have extracted reactionlimited and diffusion-limited rates of contact which can be related to the one-dimensional end-to-end distance probability using SSS theory. Compared to AGQ peptides of the same length, the reaction-limited rates are 10-100 times lower and
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TABLE 2: Diffusion Coefficients from Equation 6 Using Wormlike Chain Models with lp ) 13.0 Å, dr ) 4.0 Å n
D × 10-7 (cm2/s)
4 7 10 13 16
16.6 10.5 4.3 6.6 1.5
for the shortest lengths, the reaction-limited rate increases with length rather than decreases, as would be expected of a flexible polymer. Modeling these peptides as wormlike chains with excluded volume leads to the surprising conclusion that the persistence length for this sequence is ∼13.0 Å, whereas for AGQ, the persistence length was found to be 5.5 Å.12 One reason the contact rates might be so low for this sequence is because the charged lysines, added to the ends for solubility, would repel the ends to prevent contact between the Trp and Cys. Lysines have been used before in this sort of study without any apparent slowing of the contact rate22 and control experiments on the peptides in these studies with 170 mM NaCl showed a similar rate as without salt (data not shown). Therefore, long-range coulomb interactions do not appear to affect the peptide dynamics. Because a Lys is next to both the Cys and Trp, short-range interactions could play a role, but should affect all lengths of polyglutamine the same way and could not explain the observed length dependence of kR, which largely determined the 13.0 Å persistence length. While a single set of wormlike chain parameters were found to fit the reaction-limited rates at all lengths, this was not true for the diffusion coefficient which varied by a factor of 10 over the length range. In contrast, the diffusion coefficients for the AGQ peptides, found to be typically 1.5 × 10-6 cm2 s-1, varied by only 15%. This suggests that the homogeneous wormlike chain is not a perfect model for the dynamics of polyglutamine. Also, all but the shortest lengths of polyglutamine has a significantly lower D than the AGQ peptides, perhaps because fluctuating residual structure influences the conformational population. One alternative model is to add random β-strand structure to a wormlike chain (see Materials and Methods). While the inclusion of β-strand orientation on randomly selected residues does decrease kR in proportion to the relative population of β structure, it cannot produce the observed turnover in length dependence if the underlying wormlike chain has a short (∼4 Å) persistence length. Thus any model that describes the experimental results must have a high intrinsic stiffness. Huang and Nau, using a similar contact quenching technique, measured kD+ ∼7 × 106 s-1 for a Q6 peptide,12 which is in agreement with our results if one accounts for the fact that the previous peptide had no tails beyond the probe and quencher which decreases the contact rate by about a factor of 3.12 Their results showed that most amino acids were more flexible than glutamine. Other groups have found that other repeating peptide motifs have a high level of flexibility,24-28 and recent results on denatured proteins L and G were well modeled by wormlike chains with persistence lengths of ∼4 Å and excluded volumes of 2-4 Å, depending on denaturant concentration.14 Also Fo¨rster resonance energy transfer studies on various sequences, such as Mastroparan X,29 and mechanical unfolding of proteins30 have also yielded persistence lengths of around 3-4 Å. Since the AGQ motif seems to be as flexible as either GS24 or AAAAK12 motifs, the sequence context of glutamine matters very much; glutamine is not an inherently “stiff” amino acid.
The implications of these results within the context of Huntington’s and other neurodegenerative diseases are quite significant. Polyglutamine appears to be much stiffer than either most random peptides or unfolded proteins and is therefore likely significantly stiffer than the rest of the host protein in vivo. Small stretches of glutamine may not significantly alter the native conformation, but long stretches could put significant mechanical stress on the folded protein, making it more prone to aggregation from an unfolded state. Furthermore, the intrinsic stiffness of the peptide may explain in vitro observations of aggregation of polyglutamine peptides. Wetzel and others have suggested that the aggregation of polyglutamine follows a nucleation-propagation model in which the monomeric nucleus is in rapid and reversible pre-equilibrium with normal monomeric protein.4 However, recent results by Klein et al. show that monomeric Q22 and Q44 have no difference in structure by NMR even though one is below and one is above the pathogenic threshold.31 This suggests that there is no structural transition that longer lengths undergo before aggregation. The aggregation nucleus may simply be a highly extended conformation which is usually very improbable in a very flexible chain. But an examination of Figure 4b shows that extensions close to the contour length of the peptide are quite probable. Thus a pathogenic protein may be one that is destabilized by an intrinsically stiff sequence and then prone to aggregation through bimolecular contact of extended conformations. References and Notes (1) Zoghbi, H. Y.; Orr, H. T. Ann. ReV. Neurosci. 2000, 23, 217. (2) Tanaka, M.; Morishima, I.; Akagi, T.; Hashikawa, T.; Nukina, N. J. Biol. Chem. 2001, 276, 45470. (3) Barton, S.; Jacak, R.; Khare, S. D.; Ding, F.; Dokholyan, N. V. J. Biol. Chem. 2007, 282, 25487. (4) Chen, S. M.; Ferrone, F. A.; Wetzel, R. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 11884. (5) Nagai, Y.; Inui, T.; Popiel, H. A.; Fujikake, N.; Hasegawa, K.; Urade, Y.; Goto, Y.; Naiki, H.; Toda, T. Nat. Struct. Mol. Biol. 2007, 14, 332. (6) Masino, L.; Kelly, G.; Leonard, K.; Trottier, Y.; Pastore, A. FEBS Lett. 2002, 513, 267. (7) Chen, S.; Berthelier, V.; Yang, W.; Wetzel, R. J. Mol. Biol. 2001, 311, 173. (8) Finke, J. M.; Cheung, M. S.; Onuchic, J. N. Biophys. J. 2004, 87, 1900. (9) Wang, X. L.; Vitalis, A.; Wyczalkowski, M. A.; Pappu, R. V. Proteins: Struct., Funct., Bioinf. 2006, 63, 297. (10) Lee, C. C.; Walters, R. H.; Murphy, R. M. Biochemistry 2007, 46, 12810. (11) Lapidus, L. J.; Eaton, W. A.; Hofrichter, J. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 7220. (12) Buscaglia, M.; Lapidus, L. J.; Eaton, W. A.; Hofrichter, J. Biophys. J. 2006, 91, 276. (13) Lapidus, L. J.; Steinbach, P. J.; Eaton, W. A.; Szabo, A.; Hofrichter, J. J. Phys. Chem. B 2002, 106, 11628. (14) Singh, V. R.; Kopka, M.; Chen, Y.; Wedemeyer, W. J.; Lapidus, L. J. Biochemistry 2007, 46, 10046. (15) Chen, S. M.; Wetzel, R. Protein Sci. 2001, 10, 887. (16) Szabo, A.; Schulten, K.; Schulten, Z. J. Chem. Phys. 1980, 72, 4350. (17) Lapidus, L. J.; Eaton, W. A.; Hofrichter, J. Phys. ReV. Lett. 2001, 87. (18) Chen, Y. W.; Stott, K.; Perutz, M. F. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 1257. (19) Pappu, R. V.; Wang, X.; Vitalis, A.; Crick, S. L. Arch. Biochem. Biophys. 2008, 469, 132. (20) Vitalis, A.; Wang, X. L.; Pappu, R. V. Biophys. J. 2007, 93, 1923. (21) Crick, S. L.; Jayaraman, M.; Frieden, C.; Wetzel, R.; Pappu, R. V. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16764. (22) Lapidus, L. J.; Eaton, W. A.; Hofrichter, J. J. Mol. Biol. 2002, 319, 19. (23) Huang, F.; Nau, W. M. Angew. Chem., Int. Ed. 2003, 42, 2269. (24) Bieri, O.; Wirz, J.; Hellrung, B.; Schutkowski, M.; Drewello, M.; Kiefhaber, T. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 9597. (25) Huang, F.; Hudgins, R. R.; Nau, W. M. J. Am. Chem. Soc. 2004, 126, 16665.
13176 J. Phys. Chem. B, Vol. 112, No. 42, 2008 (26) Hudgins, R. R.; Huang, F.; Gramlich, G.; Nau, W. M. J. Am. Chem. Soc. 2002, 124, 556. (27) Krieger, F.; Moglich, A.; Kiefhaber, T. J. Am. Chem. Soc. 2005, 127, 3346. (28) Neuweiler, H.; Schulz, A.; Bohmer, M.; Enderlein, J.; Sauer, M. J. Am. Chem. Soc. 2003, 125, 5324. (29) Tucker, M. J.; Oyola, R.; Gai, F. J. Phys. Chem. B 2005, 109, 4788.
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