Energy landscape underlying spontaneous insertion and folding of an alpha-helical transmembrane protein into a bilayer

Abstract

Membrane protein folding mechanisms and rates are notoriously hard to determine. A recent force spectroscopy study of the folding of an α-helical membrane protein, GlpG, showed that the folded state has a very high kinetic stability and a relatively low thermodynamic stability. Here, we simulate the spontaneous insertion and folding of GlpG into a bilayer. An energy landscape analysis of the simulations suggests that GlpG folds via sequential insertion of helical hairpins. The rate-limiting step involves simultaneous insertion and folding of the final helical hairpin. The striking features of GlpG's experimentally measured landscape can therefore be explained by a partially inserted metastable state, which leads us to a reinterpretation of the rates measured by force spectroscopy. Our results are consistent with the helical hairpin hypothesis but call into question the two-stage model of membrane protein folding as a general description of folding mechanisms in the presence of bilayers.

Fig. 1

Free energy landscape underlying GlpG’s folding and insertion into a bilayer under low-applied force (Top) Two-dimensional free energy landscape at low-applied force as a function of Z, the average of the z-coordinates of the C_α atoms, and D, the distance between the N-terminus and C-terminus of GlpG. Relative free energies are indicated with colors in units of kT, where blue indicates a low free energy and red indicates a high-free energy. A folding path is shown as a purple line drawn from a highly extended state (Z ≈ −10 Å, D ≈ 250 Å) to the folded state (Z ≈ −3 Å, D ≈ 37 Å). Two metastable (I1 and I2) states are present at intermediate values of D and values of Z that are more negative than the average Z of the folded state. (Bottom) One-dimensional free energy profile along the path shown in the top panel as a function of D. A red double-headed arrow that is 50 Å in length is shown between N and I1. This distance corresponds to the end-to-end distance change during the rate-limiting step of refolding at low force. The first metastable state, I1, is about 6.5 kT less stable than the folded state. I2 is about 9 kT less stable than the folded state. Three locations (α, β, and γ) on the path near the transition state (TS) are also indicated. Representative structures from I1, α, β, and γ are shown in Fig. 2. Representative structures for I2 are shown in Fig. 4

Fig. 2

Structural mechanism of the rate-limiting step of refolding at low force. Progression of folding is shown from top to bottom. The structure labels (I1, α, β, γ, and TS) are the same as those used in Fig. 1. The structure of GlpG is colored according to sequence index from red (N-terminal, TM1) to blue (C-terminal, TM6). TM1 is red, TM2 is yellow, TM3 is yellow-green, TM4 is green, TM5 is light blue, and TM6 is dark blue. For each state, several representative structures are aligned and overlayed. Translucent panels are shown to indicate the locations of the upper and lower bilayer interfaces. In I1, TM5–6 are on the bilayer interface. As folding proceeds, TM5 and then TM6 are pulled into the bilayer and fold onto TM1–4

Fig. 3

Free-energy landscape underlying GlpG’s unfolding and extraction from a bilayer under high applied force (Top) Two-dimensional free energy landscape at high applied force as a function of Z, the average of the z-coordinates of the C_α atoms, and D, the distance between the N-terminus and C-terminus of GlpG. Relative free energies are indicated with colors in units of kT, where blue indicates a low-free energy and red indicates a high-free energy. An unfolding path is shown as a purple line drawn from the folded state, N, (Z ≈ −3 Å, D ≈ 37 Å) to the unfolded state, U (Z ≈ −17 Å, D ≈ 270 Å). (Bottom) One-dimensional free energy profile along the path shown in the top panel as a function of the end-to-end distance, D. Representative structures from TS and I1 are shown in Fig. 2. Representative structures from I2, U1, and U2 are shown in Fig. 4. Under these high force conditions, the folded state is metastable and is separated by a large barrier from the first intermediate state, I1. The barriers separating the intermediate states I1, I2, and U are significantly smaller than the barrier between N and I1. At this particular value of the applied force, the completely extended state U2 is slightly higher in free energy than U1, which has TM1–2 inserted in the membrane but unfolded (see Fig. 4). At larger values of the applied force, U2 becomes the global free energy minimum

Fig. 4

Representative structures of GlpG at high values of D, the end-to-end distance. The structure labels (I2, U1, and U2) are the same as those used in Fig. 3. The structure of GlpG is colored according to sequence index from red (N-terminal, TM1) to blue (C-terminal, TM6). TM1 is red, TM2 is yellow, TM3 is yellow-green, TM4 is green, TM5 is light blue, and TM6 is dark blue. The helices are also labeled with text. For each state, several representative structures are aligned and overlayed. Translucent panels are shown to indicate the locations of the upper and lower bilayer interfaces. In I2, TM3–6 are on the bilayer interface and TM1–2 are inserted and folded. In U1, TM1-2 are unfolded but still inserted in the bilayer. In U2, none of the helices are fully inserted into the bilayer. For clarity, all of the structures have been aligned, but only a single location of the upper and lower bilayer interfaces are shown. Therefore, particularly for structures that are difficult to align such as those in U2, the locations of the bilayer interfaces relative to the structures should be considered approximate

Fig. 5

Functional form of f(r_ij) given in Eq. (18). The orange line is a spline fit to the data obtained from ref. for two 5 Å inclusions embedded in a DMPC bilayer