The dominant folding route minimizes backbone distortion in SH3

Abstract

Energetic frustration in protein folding is minimized by evolution to create a smooth and robust energy landscape. As a result the geometry of the native structure provides key constraints that shape protein folding mechanisms. Chain connectivity in particular has been identified as an essential component for realistic behavior of protein folding models. We study the quantitative balance of energetic and geometrical influences on the folding of SH3 in a structure-based model with minimal energetic frustration. A decomposition of the two-dimensional free energy landscape for the folding reaction into relevant energy and entropy contributions reveals that the entropy of the chain is not responsible for the folding mechanism. Instead the preferred folding route through the transition state arises from a cooperative energetic effect. Off-pathway structures are penalized by excess distortion in local backbone configurations and contact pair distances. This energy cost is a new ingredient in the malleable balance of interactions that controls the choice of routes during protein folding.

Figure 1. The SH3 domain folds through a polarized transition state.

The structure of the domain is shown in A. In the contact map B all native contacts are shown colored according to their average degree of formation in the transition state, observed during folding simulations using a coarse-grained structure-based model. Native-like local structures are made preferentially in the central beta sheet formed by strands , and , while the terminal strands and remain mostly unstructured. Specific packing contacts that are relevant for further folding progress are also present, notably between the RT-loop and . Green and red lines define groups of early- and late-forming hairpin contacts that are chosen to characterise the pattern of formed contacts in individual transition state structures for further analysis.

Figure 2. Contributions to the free energy landscape.

A: Free energy. B: Energy contribution . C: Entropy contribution . Two dimensional energy landscapes are plotted as a function of the total number of formed contacts and of , which quantifies the pattern of contact formation. is defined such that positive values correspond to a pattern of contact formation in agreement with the dominant folding route, and negative values mean the inverse preference. White triangles in each plot trace the average folding path that corresponds to the WT-dominant mechanism with its polarized transition state structure. The free energy landscape, shown in panel A, has a saddle point between the unfolded and folded basins, located at positive . Off-pathway transitions (negative ) are blocked by a spur of high free energy. The separated energy and entropy contributions are shown in panels B and C. In gray the full free energy landscape is repeated in the background. The energy contribution , plotted in panel B, shows a peak of high energies at low in the transition region, which corresponds to the spur blocking off-pathway transitions in . In contrast the entropy contribution , plotted in panel C, does not show any feature that would favor a polarized transition state structure.

Figure 3. Cross section through the transition region of the free energy landscape.

The free energy and the contributions and in the transition region at are plotted as a function of the coordinate , along the dashed line in Fig. 2. Positive values of correspond to a native-like pattern of contact formation, negative values signal off-pathway structures with a reversed pattern. The white triangle indicates the position of the average WT reaction path. The bias in the free energy that is favoring WT-dominant transition states is determined by the consistent slope of the energy contribution . The entropy contribution shows a weaker opposite slope towards that would penalize the WT-dominant pattern of contact formation.

Figure 4. Interactions contributing to the energy bias towards WT-dominant transition states.

The potential energy in dependence on , in the transition state region at , is decomposed into the contributions from each term in the structure-based potential. Data are shifted for visibility. From bottom to top the terms shown are: bonds, repulsion, angles, contacts, dihedrals and the total potential energy. The numerically largest parts of the bias towards a WT-dominant pattern of contact formation in the transition state are provided by dihedral angles and contact potentials, followed by angles. The contibution from repulsive interactions is small but significant. Bond stretching interactions are constant along .

Figure 5. Free energy landscape decompositions , and for systems with modified interactions.

A–C D50: 50% softer dihedral potentials. D–F: D0: no dihedral potential. G–I V25: bead size 25% of normal. As in Fig. 2, landscapes are shown as a function of the total number of formed contacts and of the coordinate that quantifies the pattern of contact formation. Positive values correspond to the pattern in the WT-dominant transition state, negative values mean a reversed pattern. Average folding paths are marked by white triangles. The system D50 retains the WT-dominant pattern of contact formation in its transition state, indicated by positive values of . Both energy and entropy contributions to the landscape follow the same qualitative picture as in the full model. Again, the bias in towards WT-dominant transition states with positive arises from a peak in the energy contribution at negative , while the entropy contribution provides no such bias. In the system D0 the biasing peak in the energy contribution is lost. The entropy again provides no bias either. The resulting free energy landscape has a very low broad barrier and leads to an unspecific mechanism. A very similar free energy landscape with low barrier also results for the system V25, which also folds with an unspecific mechanism. Here the biasing feature in the energy contribution to the landscape is clearly present, but the entropy contribution is now modified to counteract it.

Figure 6. Loss of folding mechanism.

The route measure, which quantifies the specificity of the folding pathway, is plotted as a function of folding progress for the full structure-based model and for the systems D50 and D0 with softer dihedral potentials and V25 with reduced bead size. The peak near for the WT model reflects the specific transition state. In the system D50 with softer dihedral potentials, the transition state is preserved, although with lowered specificity. In the absence of any dihedral potential in the system D0 only very little specificity remains in the transition state. In the system V25 with reduced bead size, the specificity of the transition state is also completely lost and folding takes place on a variety of routes.

Figure 7. Properties of on- and off-pathway transition states.

Transition state configurations obtained at were classified as reversed, neutral or on-pathway according to their mechanistic coordinates of , or , respectively. Averaged structures are shown in panels A–C. Residues with a high average fraction of formed contacts are colored green, regions with strongly distorted dihedral angles are marked in orange. Translucent spheroids give the standard deviations from the average position for residues whose locations vary strongly between configurations. Strong repulsive interactions are marked in red. The underlying data are plotted in the graphs below each structure; with standard deviations of positions in panels D–F, dihedral energies in panels G–I, and the fraction of formed contacts in panels K–M. Horizontal bars indicate the highlighting thresholds. (Figure prepared with VMD .).

Figure 8. WT-dominant transition states are favored over off-pathway structures by dihedral- and contact energies.

Average contact energies and dihedral energies for each residue are shown ordered from lowest to highest in panels A and B, for on-pathway transition states and for both neutral and reversed off-pathway structures. Both the lowest and the highest residue energies occur in WT-dominant transition state structures. Residues that are stabilized in native transition structures have lower energies than the most stabilized residues in either reversed or neutral off-pathway states, and the most destabilized residues in WT-dominant transition state structures have higher energies than any destabilized residues in any off-pathway structures. The pattern of dihedral energies is very similar in neutral and in reversed off-pathway structures, which both lack the very stable and also the highly unstable residues found in WT-dominant transition states. For contacts, the spread from lowest to highest energies is lowest in neutral structures, larger in reversed states, and largest again for the WT-dominant transition structures. The cumulative differences shown in panels C and D confirm that in the balance the low energies from the majority of better-stabilized residues in WT-dominant transition states outweigh the higher energies from the few strongly destabilized ones.

Figure 9. Cooperative stabilization of highly formed structures.

The average energy contribution from each contact is plotted against the fraction of structures with the contact formed in panel A, for on-pathway transition states and for both reversed and neutral off-pathway structures. Similarly the average energy from each dihedral is plotted in panel B against the fraction of structures with the dihedral in its native-like rotamer state, again for on-pathway transition states and for reversed and neutral off-pathway structures. Both contact and dihedral energies naturally decrease with the fraction of native-like local structures. Due to remaining distortions the average stabilization is generally smaller than it would be expected from perfectly native configurations. For frequently formed contacts and dihedrals the downward curvatures of the plots however indicate an added gain in stabilization beyond their increase in frequency. While more rarely formed contacts and dihedrals also remain relatively more distorted even in native-like structures, dihedrals and contacts that are frequently native-like also come closer to their native configuration when they are formed. This relationship appears equally in on-pathway transition states and in off-pathway structures. Histograms of and shown in panels C and D reveal that on-pathway transition states benefit most from this additional stabilization of frequently native-like contacts and dihedrals, thanks to broadened or even bimodal distributions that maximize the fraction of such very frequently formed contacts and dihedrals.