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Department of Biochemistry, Kansas State University, Manhattan, Kansas 66506-3702
Correspondence: Address reprint requests to Paul E. Smith, Dept. of Biochemistry, 36 Willard Hall, Kansas State University, Manhattan, KS 66506-3702. Tel.: 785-532-5109; Fax: 785-532-7278; E-mail: pesmith{at}ksu.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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1 dihedral for g+ states, which appeared to be incompatible with formation of a stable cluster. The results suggest that one should consider the nature of the unfolded state when attempting to fully explain the effects of mutations on hairpin stability. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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; Brooks, 2002). One such element is the ß-hairpin, a proposed precursor in ß-sheet formation. Nuclear magnetic resonance (NMR) studies of hairpins and their mutants have demonstrated that side-chain contacts (Ramirez-Alvarado et al., 1996; Syud et al., 2001), side-chain packing (de Alba et al., 1997b), side-chain hydrogen bonding (de Alba et al., 1997a), turn sequence preference (de Alba et al., 1997a, 1999; Santiveri et al., 2000; Munoz et al., 1997), and salt bridge formation (Ramirez-Alvarado et al., 2001; Zerella et al., 2000) may all be important for hairpin formation. Computer simulations of hairpin folding and unfolding have also been used to help elucidate the atomic level interactions responsible for hairpin stability (Daura et al., 2001; Ma and Nussinov, 2000; Zhou et al., 2001; Klimov et al., 2002; Schaefer et al., 1998; Ferrara et al., 2002). However, in attempting to explain the formation and stability of different hairpins, the vast majority of the experimental and theoretical studies have focused almost exclusively on changes in the interactions within the native state conformation.
A good example of a small hairpin forming peptide has been described by de Alba et al. They designed a 10-residue peptide (P5: YITNSDGTWT), derived from fragment 15–23 of tendamistat, which has been characterized as having a high propensity for a single 3:5 ß-hairpin structure (de Alba et al., 1997b). Residues 1–4 and 8–10 form the strand residues, whereas residues 5–7 constitute the turn (see Fig. 1). The peptide folds to form a single 3:5 ß-hairpin structure with an 80% population in water at 275 K, as estimated from nuclear Overhauser enhancement (NOE) signals. A T3S mutant of P5 was also studied and shown to adopt the same 3:5 ß-hairpin in solution, but with a lower population of 20%. Considering a simple two-state equilibrium between folded and unfolded peptide, the above populations correspond to folding free energies of -3.5 kJ/mol for the wild-type (WT) and 3.5 kJ/mol for the T3S mutant, a difference of -7 kJ/mol in favor of the unfolded form of the T3S mutant. This represents a sizeable change in stability in comparison with the relatively small difference in amino acid structure of just one methyl group.
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). Using a microscopic surface tension value of 10 kJ/mol/nm2 (Creighton, 1984), the above surface-area changes for mutation of Thr3 to Ser predict that the native state is stabilized by -1.0 kJ/mol and the unfolded state by -2.5 kJ/mol. The overall change of -1.5 kJ/mol in favor of the unfolded state for the T3S mutant is considerably less than the experimental estimate of -7 kJ/mol (de Alba et al., 1997b). Consideration of the differences in the intrinsic free energy for sheet formation between Thr and Ser suggests these contributions are also too small (-1.9 kJ/mol) (Stapley and Doig, 1997) to explain the observed changes.
Recent experimental and theoretical data has indicated that the denatured or unfolded state of peptides and proteins may not be as random as originally thought (Dill and Shortle, 1991; Shortle 1993; O'Connell et al., 1999; Hammack et al., 2001). If so, it becomes just as important to understand the effects of mutations on any favorable or unfavorable interactions present in the unfolded state. Many studies are beginning to probe the properties of unfolded peptide chains (Wilson et al., 1996; Hennig et al., 1999; Fersht and Daggett, 2002; Daura et al., 2002). However, these studies have provided very little atomic level detail of real unfolded structures, especially hairpins, and therefore it is still not clear exactly when one has to consider possible changes in the unfolded state. Consequently, it is important to identify and characterize any possible residual structure present in the denatured or unfolded states of peptides and proteins. In this study we use computer simulations to investigate the differences between the WT and T3S peptides, and quantify these differences using thermodynamic integration (TI) calculations. The results suggest that changes in the unfolded state are more significant (larger) than changes in the native state, and that a detailed knowledge of the unfolded state is therefore essential for a complete understanding of the behavior of the T3S mutant and the thermodynamics of folding.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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). The SPC water model (Berendsen et al., 1981) and a truncated octahedron were used for the simulations. The time-step was 2 fs and SHAKE (Ryckaert et al., 1977) was used to constrain all bond lengths with a tolerance of 10-4 nm. A twin range cut-off of 0.8 nm/1.4 nm was employed and the nonbonded pair list was updated every 10 steps. Long-range electrostatics were treated using a reaction field approach (Tironi et al., 1995) with a reaction field permittivity for SPC water of 54 (Smith and van Gunsteren, 1994). The simulations were performed under conditions of constant temperature (300 K) and constant pressure (1 atm) using the weak coupling approach (van Gunsteren and Berendsen, 1990). The WT (YITNSNGTWT) and T3S (YISNSNGTWT) peptides were simulated in a box of 1016 water molecules. The starting structure for the T3S simulation was the folded structure formed after 20 ns of the WT simulation described previously (unpublished results). In both the WT and the T3S mutant, the only charged side-chain residue (Asp6) was mutated to Asn to make the peptides neutral. This is a very conservative mutation as both residues are similar in size and shape, and NG and DG display the highest two turn propensities among all XG turns in known protein structures (Griffiths-Jones et al., 1999). The Thr and Ser dipeptide simulations were performed using 450 water molecules for a total of 10 ns each. Errors (±1 
) in populations were estimated from four 2.5-ns averages.
The potential of mean force (pmf) between the 
and 
atoms was determined by umbrella sampling (McCammon and Harvey, 1988) using a harmonic distance restraining potential with a force constant of 10,000 kJ/mol/nm2. A series of runs were performed differing only in the position of the reference distance, which varied from 0.35 nm to 1.00 nm in increments of 0.05 nm. Probability distributions corresponding to the carbon to carbon distance were then obtained from 250 ps of simulation performed in each window. After correcting the data for the presence of the biasing function, the resulting set of histograms were combined to generate the final pmf using the weighted histogram analysis method (WHAM) approach (Kumar et al., 1992).
Thermodynamic integration calculations were used to determine the change in free energy on mutation of Thr into Ser and vice versa (Kollman, 1993). Mutation of Thr to Ser involved conversion of the neutral united atom methyl group into a dummy atom with the same mass without changing any of the bond, angle, or dihedral energy terms. TI calculations were performed using 11 equally spaced 
values between 0 and 1 with 200 ps of sampling at each point after 10 ps of equilibration. The Hamiltonians for the initial and final states were coupled using the soft core approach to avoid possible singularity problems (Beutler et al., 1994) with an 
value of 0.5 nm2 for the van der Waals term. A plot of the free-energy derivatives against was subsequently splined to generate 1000 points, and then integrated using a simple trapezoidal integration scheme. Errors (±1 ) were estimated from two or three subaverages.
Additional TI calculations were performed to determine the free-energy change associated with the mutation of Thr to Ser, while maintaining the same 
and 1 rotational states. This was achieved by performing constrained TI calculations using a harmonic dihedral potential (k = 0.005 kJ/mol/degree2) to restrain the main-chain and side-chain dihedrals to the appropriate region of dihedral space (0 = 120° and 01 = -180°, -60°, or +60°). A weak constraining potential was chosen which only affected the free-energy surface for large deviations (60°) from the corresponding minimum (Straatsma and McCammon, 1989). The small differences in free energy (±0.3 kJ/mol) associated with the addition of a constraining potential to the Thr and Ser dipeptide Hamiltonians were accounted for by applying statistical mechanical perturbation theory (Zwanzig, 1954) using reference configurations from the unconstrained dipeptide simulations, and the constraining potential as the perturbation.
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RESULTS |
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10, 102, and 48), a hydrogen bond network mediated by the side chain of Asn4 (64, 74, and 410), and a set of three cross-strand side-chain contacts (residues 1–9, 2–10, and 3–9). The time histories for the nine interactions are displayed in Fig. 2 for both the WT and T3S trajectories. Clearly, although the contacts were maintained (or fluctuated slightly) for the WT simulation, they were lost during the simulation of the T3S mutant. The major unfolding event occurred after 7 ns at which point all three main-chain hydrogen bonds were simultaneously lost. Hence, the GROMOS force field is capable of discriminating between the WT and mutant peptides. This observation, and the previously observed successful folding of the WT peptide, provides some degree of confidence in the simulation results.
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; Bartels and Karplus, 1997; Mitsutake et al., 2001). In an effort to characterize the equilibrium between folded and unfolded hairpin states, a pmf calculation was performed. As the NOE intensity between the H atoms of residues Thr3 and Trp9 was used to estimate the hairpin population from the experimental data, the distance between the backbone C atoms of residues 3 and 9 was chosen to investigate the free-energy profile for unfolding. The results for the WT and T3S mutant are presented in Fig. 3. The pmfs displayed a single minimum at the contact distance with no minima at larger distances where all the main-chain hydrogen bonds would have been broken. The differences between the two pmfs appeared to be minor with only a small apparent stabilization of the T3S form between 0.6 and 0.8 nm. As there were no minima at larger distances, it appeared the pmf did not fully capture the differences in stability very well. The reasons for this are unclear but could include incomplete sampling of the unfolded state, and difficulties attempting to project a multidimensional folding surface onto a single coordinate.
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and 1 dihedrals underwent multiple (>10) transitions during the simulations, indicating that their populations should be representative, whereas the 
dihedral remained in the < 0 region for the majority of the trajectory. Both the Thr and Ser dipeptides favored the ß state with free-energy differences of Gß - G = -RT ln (Pß/P) = -4.5 kJ/mol for Thr and -3.6 kJ/mol for Ser. The difference of -0.9 kJ/mol is in agreement with the estimated relative sheet forming abilities (-1.9 kJ/mol) of the two amino acids (Stapley and Doig, 1997), albeit smaller in magnitude. The 1 probability distributions as a function of backbone conformation ( or ß) are displayed in Fig. 4. The Thr dipeptide preferred g+ side-chain conformations with little population of the t state for both and ß backbone arrangements (presumably due to interactions between C
and the backbone N and C atoms). On the other hand, all the Ser 1 minima (g-, g+, and t) were significantly populated. However, the g+ minima for 1 displayed a relatively low population when the backbone was in the highly populated ß state conformation.
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). The free-energy difference for mutating Thr in the g+ state to Ser in the g+ state was 0.7 kJ/mol, compared to -6.0 and -8.4 kJ/mol for the corresponding g- and t transitions, respectively. These values, in combination with the populations presented in Table 1, enabled the construction of the free-energy diagram presented in Fig. 5 for the Thr and Ser dipeptides. In constructing the free-energy diagram the TI results were considered to be the most accurate, followed by the g+/t ratio in the Thr dipeptide and the g-/t ratio in the Ser dipeptide, both of which possessed multiple (>10) transitions during the dipeptide simulations. Hence, although the relative free-energy differences in Fig. 5 do not agree exactly with all the differences presented in Table 1, they are consistent within the estimated errors. The free-energy diagram illustrates several features that will be important for later discussions. The free-energy difference between the g+ states of Thr and Ser was small and favored Thr. In contrast, the difference between the g- and t states was much larger and favored Ser.
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) and is outlined in Fig. 6. The difference in folding free energy between the WT and T3S mutant (
G) can be determined by mutating Thr into Ser (or vice versa) in the folded and unfolded states. However, there is a potential complication in this type of approach. Although the folded state is well defined, the unfolded state is unknown and may be significantly different for the WT and T3S peptides. One approach is to assume an absence of structure in the unfolded state and to perform the corresponding amino acid perturbation for a simple model system (Hu et al., 2003). The simplest model corresponds to a blocked single amino acid residue (dipeptide) which is essentially fully exposed to solvent.
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G of -2.7 ± 0.5 kJ/mol in favor of Ser. Another TI calculation was performed for the blocked three-amino acid sequence ITN, corresponding to the local sequence in the WT peptide. The G obtained for this system was -2.5 ± 0.5 kJ/mol, which is in agreement with the dipeptide result. Hence, the inclusion of local sequence effects did not appear to change the results. Five different initial folded structures were used to determine the free-energy change for the native hairpin. The average of the five calculations resulted in a G of -1.3 ± 0.2 kJ/mol. These numbers follow the pattern expected from the estimated changes in hydrophobic surface area as discussed in the Introduction (-2.5 kJ/mol for the random state and -1.0 kJ/mol for the folded state). Again, they are too small to explain the experimentally estimated difference.
Clearly, the changes in stability did not appear to be due to differences between the WT and T3S forms in the folded state. As we have high confidence in the nature of the folded state, this brings into question our model of the unfolded state. A subsequent set of TI calculations was therefore performed using five different initial structures obtained from the unfolded (>10 ns) section of the T3S mutant trajectory. The average G for the three TI calculations was 7.4 ± 0.2 kJ/mol for the Ser to Thr mutation. The resulting G of 6.1 ± 0.3 kJ/mol was in excellent agreement with the difference estimated by NMR (7 kJ/mol). Although the agreement was probably somewhat fortuitous, as both the NMR and simulation data are subject to some error, the results clearly suggest that the major change in hairpin folding thermodynamics was related to significantly larger effects in the unfolded state.
A final set of five TI calculations was then performed using unfolded structures obtained from the early stages of the WT folding simulation. Two of the initial structures displayed very small free-energy differences, similar to that observed for the folded state. However, two of the initial structures generated a large G in favor of Ser, and very similar to the values obtained after using initial structures taken from the T3S unfolded trajectory. Hence, it appeared that the unfolded conformations of the WT peptide may only sample a few of the highly populated conformations corresponding to the T3S mutant, and vice versa. This considerably complicates the determination of free-energy changes using the TI and thermodynamic cycle approach for small peptides, as one requires the relative population of each distinct conformation in both the initial and final states (Straatsma and McCammon, 1989).
Residual structure in the unfolded state
In an attempt to determine the basis for the increased stability of the unfolded state in the T3S mutant the interactions of the Ser side chain with other amino acid residues were investigated. A stable cluster of interactions was observed shortly after unfolding from the native hairpin. The corresponding time histories are presented in Fig. 7, and a representative configuration is displayed in Fig. 8. The interactions were centered on the C-terminal carboxylate group. There appeared to be a strong affinity of both the Ser and Tyr hydroxyl groups for the carboxylate group. This cluster formed after 8 ns, was then lost after 17 ns, but appeared to be reforming toward the end of the simulation. The to distance was 0.6 nm when this cluster was intact, suggesting this may be the reason for the small differences observed in the corresponding region of the pmfs shown in Fig. 3. The initial starting structures for the TI calculations were taken from configurations corresponding to 10, 12.5, 15, 17.5, and 20 ns of the T3S trajectory. Hence, the larger G values presented in Table 2 were observed when this interaction was intact (at 10, 12.5, and 15 ns). Analysis of the final structures obtained at = 1 (WT peptide) for these three starting structures indicated that the interaction with the C-terminus was lost. Consequently, the free-energy differences reflected the loss of this interaction.
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) with a grid size of 0.1 nm. On examination of the solvent density, no significant high probability solvation sites were observed in the vicinity of the Thr or Ser side chain (data not shown). Hence, it was concluded that the change in stability did not appear to be a specific solvation effect.
The Ser dipeptide simulation indicated a high preference for the g- and t arrangements of 1. This was in agreement with the distribution of Ser 1 values observed during the T3S simulation, which are presented as a time history in Fig. 9. Interestingly, during the time that the cluster of hydroxyl and carboxylate groups was stable (8–17 ns) only the g- and t minima of 1 were sampled. Hence, it appeared that the intrinsic side-chain distribution for Thr was incompatible with the formation of the cluster. Introduction of a Thr residue, which prefers the g+ state, would destabilize the cluster causing it to break up with the corresponding loss of free energy associated with cluster formation. Furthermore, the 1 of Thr adopts the g+ conformation in the folded hairpin. Hence, this is incompatible with the preferred side-chain preferences of Ser and could explain the initial instability of the folded structure.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The small free-energy changes associated with the folded state could be related to either the requirement of a g+ arrangement for Thr 1 (see Fig. 5), and/or the loss of a specific side-chain contact in the folded state, which partially offsets the usually favorable (-2.7 kJ/mol) Thr to Ser free-energy difference. The large unfavorable free-energy change observed for the mutation of Ser to Thr in the T3S cluster conformations appeared to be the result of two major effects. One being the difference in the intrinsic free energies of the two residues (2.7 kJ/mol), and the other being the penalty associated with maintaining the Thr 1 dihedral in the g- conformation (4.1 kJ/mol). These penalties make the relative free energy of the cluster conformation comparable to that of the other members of the unfolded WT ensemble. The results suggest that 1), a Thr to Ser mutation may not be as conservative as it first appears; and 2), similar effects may be encountered for other ß-branched amino acids. Furthermore, the results illustrate the problems that can be encountered if one focuses solely on changes in the native state.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Submitted on June 18, 2003; accepted for publication July 25, 2003.
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and H6, 
and 
, and three side-chain contacts (bottom). The center of mass was used to define the positions of the side chains.
