Probing the folding free energy landscape of the src-SH3 protein domain

Abstract

The mechanism and thermodynamics of folding of the Src homology 3 (SH3) protein domain are characterized at an atomic level through molecular dynamics with importance sampling. This methodology enables the construction of the folding free energy landscape of the protein as a function of representative reaction coordinates. We observe that folding proceeds in a downhill manner under native conditions, with early compaction and structure formation in the hydrophobic sheet consisting of the three central β strands of the protein. This state bears considerable resemblance to the experimentally determined transition state for folding. Folding proceeds further with the formation of the second hydrophobic sheet consisting of the terminal strands and the RT loop. The final stages of folding appear to involve the formation of the hydrophobic core through the expulsion of water molecules bridging the two hydrophobic sheets. This work sheds new light on the complementary roles of sequence and topology in governing the folding mechanism of small proteins and provides further support for the role of water in facilitating the late stages in folding.

Energy landscape theory provides a framework for the description of the kinetic and thermodynamic mechanisms of protein folding (1–4). Within this framework, folding is envisioned to proceed along a moderately rough funnel-shaped energy landscape (5–7). The overall shape of the surface arises from a strong energetic driving force to the native global minimum (8, 9). This energetic bias is necessary to overcome the conformational search problem associated with finding the native state of the protein within a biologically reasonable time frame. The roughness of the surface corresponds to local free energy minima arising from geometric (topological) and energetic traps (10, 11). The degree of trapping (or “frustration”) modulates both the thermodynamic and kinetic aspects (12–14) of folding. Geometric or topological traps are associated with the chain connectivity and the shape of the native fold and occur when correct contacts form prematurely (10, 15, 16). Energetic traps, on the other hand, are sequence-related traps and arise when non-native but stabilizing contacts form as the chain folds (1, 11, 17). Although certain folds may be easier to reach than others, topological frustration is an intrinsic property of the polymer chain that is practically impossible to remove (10, 13, 18). Even at sufficiently small energetic frustration, residual geometric frustration remains. Energetic traps, on the other hand, can be controlled through sequence design (17). Naturally occurring proteins appear to be “minimally frustrated” from an energetic perspective, with a sequence optimized to reduce formation of unfavorable contacts. But how “minimally frustrated” are real proteins? How much of the folding mechanism and kinetics is governed solely by the “topology” of the protein?

A significant effort, from both a theoretical and experimental standpoint, has been invested in the last few years into answering these questions, i.e., determining the relative extents of topological and energetic frustration in proteins (10, 11, 17, 19–27). The use of mutagenic Fersht φ values (28) enabled a characterization of the transition state for folding of several homologous proteins (same fold, different sequences). The similarity (or lack thereof) of the transition states has allowed one to make a qualitative assessment of the importance of topology in folding. The observed relationship between protein contact orders and folding rates was particularly instrumental in highlighting the importance of chain connectivity in folding (21). From a theoretical standpoint, simulations using Gō-type models (10, 11, 19) enabled the study of idealized systems with no energetic frustration, revealing the extent of topological trapping in folding. Gō-models (29) allow only attractive interactions between native contacts, hence eliminating energetic traps.

These works seem to reveal a “surprisingly” simple picture in which protein folding is governed mainly by chain topology, rather than by the details of the sequence. Subsequent work, however, suggests that this picture may be an oversimplification (30–32). Although the folding mechanism and transition state of some proteins [chymotrypsin inhibitor 2 (CI 2), for instance] (19, 33) can be predicted from simple models based solely on protein topology, this appears not to be a general rule for all small fast-folding proteins. Proteins L and G, for instance, are two topologically very similar proteins, with a fold consisting of two β hairpins and a helix. The transition states of these proteins, however, are not identical, involving structure in different hairpins in each case (30). Clearly the choice of which hairpin is formed first is determined by the sequence (30, 34). Other examples of homologous proteins in which the transition states consist of different parts of the protein are U1A, S6, and Ada2h (35, 36).

The Src homology 3 (SH3) protein family is particularly well suited to decipher the degree to which sequence matters in folding. There are >400 homologues of these small fast-folding, mostly β-sheet, proteins. Experimental investigations by Baker and coworkers on src-SH3 (21, 37, 38) and by Serrano and coworkers on α spectrin SH3 (39, 40) have revealed a strikingly polarized folding transition state, in which a three-stranded nonspatially local part of the protein is formed. More recent experiments by Serrano and Guerois on Sso7d, a protein with the same fold as src-SH3, but in which the C-terminal β-sheet is replaced by an α-helix, however, reveal a significantly different transition state from src and α spectrin SH3. Rather than involving the β hairpin and a third-strand distance in space, the Sso7d transition state involves a β hairpin and part of the helix. The transition states of SH3 and Sso7d are symmetric, implying that topology imposes a general shape for the transition state, but that the sequence modulates its details (31). The importance of energetics in determining the folding pathway of SH3 explains the observed deviations from Gō-type models in predicting the folding transition state and mechanism of folding of SH3 (20, 32, 33). For example, they do not account for the differences between src-SH3 and its structural analog Sso7d, illustrating that energetic frustration cannot be ignored in some cases when determining the folding mechanisms.

In this paper, we present a fully atomic investigation of the folding thermodynamics of src-SH3. The free energy profile of the protein is constructed under native conditions by using importance sampling molecular dynamics (41, 42). This level of description, which includes both energetic and topological effects, allows for a complete characterization of the folding mechanism. Our method differs from the standard nonequilibrium unfolding simulations (43, 44) by seeking to characterize the equilibrium thermodynamics under natively folding conditions.

By comparing the results of our simulation to those obtained from Gō-type models of SH3 (20, 32, 45), we are able to assess the relative extent to which energetics and topology affect the folding of src-SH3. We also compare our refolding simulations to the recent fully atomic unfolding simulations of Baker and coworkers (22) and Caflisch and Gsponer (24) to determine whether unfolding and refolding pathways differ significantly for this protein.

Model and Method.

The src-SH3 protein is a small fast-folding protein, with a barrel fold formed by five β strands and a short 3–10 helix (Fig. 1a). This protein does not show any stable intermediates and behaves thermodynamically and kinetically as a two-state folder (23, 37). Mutagenic φ value studies indicate a very polarized transition state involving structure in the β strands in the distal hairpin and near the diverging turn (23, 38).

Fig 1.

(a) Ribbon diagram of src-SH3 (Protein Data Bank ID code ) and native contact probability map. A native contact between non-neighboring residues was considered to be formed if the centers of geometry of the side chains were within 6.5 Å of each other. (b) Contact probability map for ρ = 0.2 (above diagonal line) and ρ = 0.4 (below diagonal line). At ρ = 0.2, early secondary structure appears in and between strands β2 and β3. By ρ = 0.4, the central three-stranded sheet consisting of strands β2, β3, and β4 has formed (with probabilities near 1 between strands β2 and β3, and greater than 0.6 between strands β3 and β4). The rest of the protein is mostly unstructured. (c) Contact probability map for ρ = 0.6 (above diagonal line) and ρ = 0.8 (below diagonal line). By ρ = 0.6, the protein is nearly as compact as in the native state, and the central three-stranded β2-β3-β4 sheet has fully consolidated. Structure has begun to form in the second hydrophobic sheet consisting of a portion of the RT loop and the two terminal strands. The two hydrophobic sheets do not make native contacts with each other. By ρ = 0.8, the protein is nearly native, with both hydrophobic sheets formed and mostly packed.

In the present simulations, the protein is represented in atomic detail by using the charmm toph19/param19 force field (46, 47). The structure, with Protein Data Bank ID code (48), was used as a starting point for all simulations. The solvent was explicitly included as TIP3P water molecules (49). The native state of the protein was characterized through two 2-ns constant temperature, constant volume simulations at 298 K. A native contact between non-neighboring residues was considered to be formed if the centers of geometry of the side chains were within 6.5 Å of each other (Fig. 1a). The native contacts are given in Table 1, which is published as supporting information on the PNAS web site, www.pnas.org. A native hydrogen bond was defined for backbone hydrogen–oxygen distances of <2.5 Å. Fifty-seven native contacts and 10 native hydrogen bonds were defined and characterized as descriptors of the native state.

Generation of the Free Energy Surfaces.

The free energy surfaces of the protein as a function of a number of reaction coordinates were generated by using a combination of denaturing simulations and native condition importance sampling (41, 42, 50). Three unfolding simulations were performed at temperatures ranging from 400 to 500 K to generate conformations spanning the folded to the unfolded state. The structures from the native state and unfolding runs were clustered according to the number of native contacts, the number of hydrogen bonds, and the surface energy. Seventy-five cluster centers were identified in this manner and were used as starting points for biased molecular dynamics sampling in the ρ coordinate at 298 K. The biasing potential was quadratic in ρ, a continuous analog of the number of a native contacts (42, 50), with a force constant between 1,000 and 2,000 kcal/mol. The cluster center structures were solvated with a constant number of water molecules in a truncated octahedron box. The sampling involved 100 ps of constant pressure, constant temperature equilibration followed by 400–600 ps of constant volume, constant temperature production runs. Long-range interactions were treated by using the particle mesh Ewald method (51). The data were combined and unbiased by using the Weighted Histogram Analysis Method (52), which provides an optimal estimate of the density of states. The resulting data were combined to produce the free energy surface of src-SH3 at 298 K. A total of 45 ns of simulations was used to generate the free energy profile. We note that each initial condition simulation is independent, and hence several production runs can be performed at the same time, greatly enhancing parallelization and significantly reducing overall time to solution. All runs were performed on the Pittsburgh Supercomputing Center's T3E.

Results and Discussion

Potential of Mean Force (pmf) and Folding Mechanism.

The pmfs for SH3 are given as a function of the reaction coordinate, ρ, in Fig. 2a and as a function of both the radius of gyration R_g and ρ in Fig. 2b. At this temperature, the profiles are downhill in free energy, with no apparent barriers. Experimentally, the folding of src-SH3 appears to be single exponential, suggesting the presence of a barrier in the free energy surface. Although no barrier is apparent in the pmf, folding can be described as a progressive organization of an ensemble of partially folded structures, and the structural nature of this time-dependent ensemble is in good agreement with experimental observation. The small free energy barriers observed in protein folding arise from the near cancellation of the large energetic and entropic contributions to folding. Small errors in both the calculated energetic and entropic terms can lead to the disappearance of the barrier. Experimentally, the estimated barrier is only of the order of a few k_BT. Additionally, it is possible that our force field overly stabilizes the protein at the temperature studied. At temperatures below the folding temperature, the folding can become downhill in free energy. There is experimental evidence that small changes in the environment can cause the appearance or disappearance of folding barriers (53, 54). Minor fluctuations (of the order of k_BT) can be sufficient to shift the folding route from one pathway to another. Although the presence of barriers is extremely sensitive to the fine tuning of the energetics, the mechanism of folding is a robust feature of the landscape and will remain largely unaffected either by temperature changes or small energetic or entropic errors.

Fig 2.

(a) pmf at 298 K as a function of ρ. The free energy surface is downhill with a native basin at r ≥ 0.8. The stability of the native state is ≈3 kcal/mol. (b) pmf at 298 K as a function of ρ and radius of gyration, R_g (in angstroms). Contours are drawn every 1 kcal/mol. (c) pmf at 298 K as a function of ρ and the number of water molecules in the core. Contours are drawn every 0.6 kcal/mol. (d) Three high-temperature unfolding runs (T = 400 K) superimposed onto the free energy surface at 298 K.

The stability of the native state was calculated from the potential of mean surfaces as −k_BT⋅ln(K_eq), where K_eq is the equilibrium constant. By using a cutoff of ρ > 0.8, the stability was found to be 3.1 kcal/mol, in reasonable accord with the experimental result of 3.7 kcal/mol under similar conditions (37). If one defines the native state as all configurations with ρ ≥ 0.8, the mechanism for folding can be reconstructed from the free energy profiles. Contact probability maps at ρ = 0.2, 0.4, 0.6, and 0.8 are given in Fig. 1 b and c. Completely unfolded conformations (ρ = 0) span a radius of gyration from 12.9 to 20 Å. The protein compacts as it forms native contacts, reaching a radius between 12.8 and 15.8 Å by ρ = 0.2. Early secondary structure is observed in strands β2 and β3 and occasionally in strand β1. The rest of the protein is still unstructured. As folding proceeds (ρ = 0.2–0.5), the protein compacts further, with radii of gyration spanning 14 to near-native 10 Å. The β2, β3, and β4 strands are mostly formed as are the contacts between β2 and β3 and in the distal hairpin (β3 and β4). A folding nucleus ensemble comprising the above strands emerges. The contact map at ρ = 0.4 reveals the beginning of a polarized folding mechanism. Contacts between strands β2 and β3 have near-unit probability of formation (in particular, Leu-24–Ala-37, Leu-24–Ser-39, and Ile-26–Ala-37), and those in the distal hairpin (β3 and β4) have formation probabilities greater than 0.6 (in particular Leu-36–Thr-45 and His-38–Thr-45). (The i, i + 3 and greater native contact probabilities for ρ = 0.4 are listed in Table 2, which is published as supporting information on the PNAS web site). This folding nucleus is reminiscent of the experimentally determined transition state, in which high φ values are observed in the β2-β3-β4 region (which forms the first of the two hydrophobic sheets of the protein) and low φ values throughout the rest of the protein (20). Indeed, in our simulations, the first hydrophobic sheet is structured, whereas the second hydrophobic sheet, comprising the terminal strands and the RT loop, is mostly unstructured. The lowest contact probabilities lie between the RT loop and strands β2, β3, and β4. The remaining contacts have intermediate contact probabilities, and a variety of different conformations are observed. We note that, whereas the conformations are consistently structured in the central β stranded region, they can show different secondary structural elements in the other parts of the protein. For instance, the β1 strand is formed in certain conformations, whereas in others, the opposite terminus (near the 3–10 helix) is formed. This observation implies that the terminal strands do not play a critical stabilizing role and points to the possibility of multiple pathways for folding after the nucleus has been formed. This nucleus persists and stabilizes as folding proceeds. By ρ = 0.6, the protein is nearly as compact as in the native state, and the β2-β3-β4 region is completely formed. Additional secondary structure elements in the N and C termini are also more developed. Low contact probabilities remain between the RT loop and nucleus. The structure resembles an “open form” of the native structure, in which the two hydrophobic sheets consisting of the terminal strands and the RT loop (sheet 1) and the nucleus (sheet 2) are mostly formed but do not fully interact to complete the hydrophobic core. By ρ = 0.8, the protein is as compact as in the native state, and contacts have begun to form between the two hydrophobic sheets. The last elements for folding involve the final contacts between the hydrophobic sheets and the terminal strands.

Role of Water Late in Folding.

The role of water in the final stages of folding was investigated by calculating the pmf as a function of ρ and the number of waters in the core (50, 55). The hydrophobic core of the protein is comprised of two hydrophobic sheets, the first sheet consisting of the three-strand complex β2, β3, and β4, and the second sheet consisting of the RT loop and the two terminal strands. The core water molecules were defined as those lying within an 8-Å radius of the center of geometry of the protein core. The pmf at 298 K as a function of ρ, and the number of water molecules is given in Fig. 2c. The profile is downhill in free energy, with the number of core water molecules decreasing rapidly as the protein folds. At ρ = 0.95, less than five water molecules reside in the core, whereas at ρ = 0.7, more than 15 are present. A barrier is present in the pmf around ρ = 0.8. This barrier is associated with the final stages of folding, which involve the association of the two hydrophobic sheets to form the hydrophobic core. This association is accompanied by the expulsion of water molecules bridging the hydrophobic sheets. The water molecules hence act as “lubricants” (as was postulated by Sheinerman and Brooks; ref. 50), crucial to the final folding process. Two types of water molecules are present before the desolvation barrier, those serving as bridges between the sheets as well as core waters residing within the hydrophobic sheets. This barrier does not correspond to the transition-state barrier for the folding of src-SH3 (as defined by the mutagenic studies of Baker and coworkers; refs. 20, 23). Rather, this barrier, which occurs late in the folding process, after the formation of the transition state, may be a generic feature of proteins that form their hydrophobic core through desolvation.

It is interesting to note that a similar barrier could be observed in the recent minimalist simulations of src-SH3 by Cheung et al. (45) when the protein was modeled using a standard Cα-based Gō-model potential augmented with a phenomenological potential mimicking water desolvation. Simulations of the collapse of a hydrophobic polymer in a coarse-grained water model also support our conclusion of the importance of dewetting in protein folding (56). The present work significantly augments these concepts by providing an atomically detailed picture of the water desolvation process.

Folding and Unfolding Pathways.

The folding scheme determined from the folding thermodynamics at room temperature closely resembles the unfolding mechanisms observed in the high-temperature unfolding simulations of Levitt and coworkers (fully atomic with explicit solvent; ref. 22) and Caflisch and Gsponer (fully atomic with implicit solvent; ref. 24). Two high-temperature unfolding simulations are overlaid on the folding pmf in Fig. 2d. The unfolding runs closely follow the folding free energy surface, implying that the folding and unfolding mechanisms are very similar for src-SH3. We note that this is not the case for all proteins. Unfolding trajectories of Protein A (57), for instance, do not fall on its calculated folding free energy surface. Theoretical studies have shown that folding and unfolding do not necessarily occur by the same route when a large perturbation (such as the use of high temperature) is applied to the system (42, 58). Src-SH3 seems to be a special case where folding closely parallels unfolding. This feature can be explained by the polarized nature of the folding mechanism, which involves an early structural formation in strands β2, β3, and β4. This required nucleus ensemble reduces the number of folding pathways and offers very little flexibility for the unfolding and folding mechanism for the protein, in contrast to proteins with more delocalized folding nuclei (such as the helical protein A) (57), which show far more diversity in the unfolding and folding behavior. In such cases, the energy landscape approaches a more “perfect” funnel, and the folded state can be reached via a large number of pathways. In the case of SH3, on the other hand, topological frustration leads to a less ideal funnel and restricts the possible folding pathways. This fact explains the remarkable homogeneity in the unfolding simulations of src-SH3 and the overlap of the unfolding trajectories with the folding pmf. In the unfolding simulations of Caflisch and Gsponer (24), contacts between the hydrophobic core and the terminal sheets precede the unfolding of the central β stranded region for both src and α spectrin SH3. The pathways diverge for the two homologues during the unfolding of the central region. Src-SH3 showed a statistical preference to lose the β4 strand first, whereas α spectrin disassembled from the β2 strand. Consistently, our folding studies reveal more structure between strands β2 and β3 than in the distal hairpin in conformations with ρ = 0.2 (i.e., before formation of the three-stranded nucleus). It is interesting to note that a simulation based on Gō-type models of src-SH3 (32) shows a folding mechanism in which the distal hairpin is formed before the β2-β3 region, opposite to what we find. This difference illustrates the importance of using models that include sequence details to correctly capture the folding mechanism (34). Nonetheless, the similarities in the overall pathways for folding between our fully atomic folding simulations and those of SH3 Gō-models imply that the dominant source of frustration in src-SH3 is topological. The Gō-model simulations of Koga and Takada (32) on a number of SH3 folds all yield a transition state that matches most closely the experimentally determined transition state for src-SH3. It is perhaps fair to conclude that src-SH3 is a prime example of a “minimally frustrated” protein, with one of the most optimized sequences possible for its fold.

Conclusion

We explored the folding thermodynamics of the src-SH3 protein domain by using a fully atomic solvated description of the system. This level of detail allowed an investigation of the role of energetic frustration in folding. Our investigations point out that the energetic frustration of the src-SH3 protein domain is sufficiently small so that the folding mechanism is governed mostly by topology, with the finer details tuned by sequence effects. We observe an initial compaction of the protein associated with early structure formation in the first hydrophobic sheet of the protein consisting of the three strands, β2, β3, and β4. Formation of the second hydrophobic sheet (RT loop and terminal β-sheets) ensues. Our results furthermore support a folding mechanism in which the final stages of folding are mediated by the expulsion of water from the hydrophobic core of the protein.

Abbreviations

• pmf, potential of mean force

• SH3, Src homology 3