(Un)Folding mechanisms of the FBP28 WW domain in explicit solvent revealed by multiple rare event simulation methods

Abstract

We report a numerical study of the (un)folding routes of the truncated FBP28 WW domain at ambient conditions using a combination of four advanced rare event molecular simulation techniques. We explore the free energy landscape of the native state, the unfolded state, and possible intermediates, with replica exchange molecular dynamics. Subsequent application of bias-exchange metadynamics yields three tentative unfolding pathways at room temperature. Using these paths to initiate a transition path sampling simulation reveals the existence of two major folding routes, differing in the formation order of the two main hairpins, and in hydrophobic side-chain interactions. Having established that the hairpin strand separation distances can act as reasonable reaction coordinates, we employ metadynamics to compute the unfolding barriers and find that the barrier with the lowest free energy corresponds with the most likely pathway found by transition path sampling. The unfolding barrier at 300 K is approximately 17 k(B)T approximately 42 kJ/mol, in agreement with the experimental unfolding rate constant. This work shows that combining several powerful simulation techniques provides a more complete understanding of the kinetic mechanism of protein folding.

Figure 1

(a) Sequence of FBP28 and FBP28ΔNΔC. Amino acids are numbered according to their position in the sequence of original WW domain. The truncated amino acids are shown in gray font, with the turn regions and the strands β₁ (residues 8–12), β₂ (residues 18–22), and β₃ (residues 27–29) as thick lines. Native H-bonds are plotted as dotted lines. Hairpin-1 comprises strands β₁, β₂, and turn I t1, whereas hairpin-2 comprises strands β₂, β₃, and turn II t2. (b) The structure of the native state N of the WW domain in cartoon representation. The hydrophobic core residues have been shown as licorice, with the upper hydrophobic core in a lighter shade than the lower core. (c) Side view of the structure in panel b.

Figure 2

FE contour maps for the (row 1) REMD-fol and (row 2) REMD-unf simulations of FBP28ΔCΔN in four different planes (a) ($R_{\text{oh}}^{\left(1\right)}$, $R_{\text{oh}}^{\left(2\right)}$); (b) (rmsd_t1, rmsd_t2); (c) (rmsd_t1, $R_{\text{oh}}^{\left(1\right)}$); and (d) (rmsd_t2, $R_{\text{oh}}^{\left(2\right)}$). All distances and RMSDs are in nm. The legend gives the free energy in k_BT units. The native state area in the REMD-unf plots from row 2 is indicated by an ellipse. Note that in the ($R_{\text{oh}}^{\left(2\right)}$, rmsd_t2) plane the native state overlaps with the intermediate I₁.

Figure 3

BE-Meta unfolding trajectories of the truncated FBP28 WW domain, described in the main text as unfolding Scenarios 1, 2, and 3. The protein structures are depicted as in Fig. 1.

Figure 4

Three typical TPS pathways presented in four planes: (Top left) $R_{\text{oh}}^{\left(1\right)}$ – $R_{\text{oh}}^{\left(2\right)}$; (Top right) rmsd_t1 – rmsd_t2; (Bottom left) $R_{\text{oh}}^{\left(1\right)}$ – rmsd_t1; and (Bottom right) $R_{\text{oh}}^{\left(2\right)}$ – rmsd_t2. The whole TPS ensemble is plotted as yellow and the REMD-unf ensemble as gray points. The contours give the FE landscape of the REMD-fol simulation (compare to Fig. 2, row 1), and are separated by 1 k_BT. In panel a, the initial and the final state boundaries are indicated with green and red lines. The blue trajectory represents a typical N → I₂ transition, the cyan trajectory an N → I₁ transition, and the violet depicts a switching pathway.

Figure 5

(g), (d), (e), and (b) FE barriers based on metadynamics simulations for the N → I₁, N → I₂, I₁ →U, and I₂ → U transitions, respectively. The simulations biasing in $R_{\text{oh}}^{\left(1\right)}$ are represented as horizontal and in $R_{\text{oh}}^{\left(2\right)}$ as vertical arrows. One metadynamics simulation was done using R_oh = $R_{\text{oh}}^{\left(1\right)}$ + $R_{\text{oh}}^{\left(2\right)}$, and is depicted with a bent arrow, indicating that these trajectories pass I₂ without relaxing in it. The numbers indicate the approximate FE barriers in k_BT associated with every transition. Protein configurations are depicted as in Fig. 1. Configurations: (a) intermediate state I₂ with unfolded hairpin-2; (c) unfolded state, with a roughly native topology; (f) native state N; and (h) intermediate state I₁ with unfolded hairpin-1.