Lipid bilayer deformation and the free energy of interaction of a Kv channel gating-modifier toxin

Abstract

A number of membrane proteins act via binding at the water/lipid bilayer interface. An important example of such proteins is provided by the gating-modifier toxins that act on voltage-gated potassium (Kv) channels. They are thought to partition to the headgroup region of lipid bilayers, and so provide a good system for probing the nature of interactions of a protein with the water/bilayer interface. We used coarse-grained molecular dynamics simulations to compute the one-dimensional potential of mean force (i.e., free energy) profile that governs the interaction between a Kv channel gating-modifier toxin (VSTx1) and model phospholipid bilayers. The reaction coordinate sampled corresponds to the position of the toxin along the bilayer normal. The course-grained representation of the protein and lipids enabled us to explore extended time periods, revealing aspects of toxin/bilayer dynamics and energetics that would be difficult to observe on the timescales currently afforded by atomistic molecular dynamics simulations. In particular, we show for this model system that the bilayer deforms as it interacts with the toxin, and that such deformations perturb the free energy profile. Bilayer deformation therefore adds an additional layer of complexity to be addressed in investigations of membrane/protein systems. In particular, one should allow for local deformations that may arise due to the spatial array of charged and hydrophobic elements of an interfacially located membrane protein.

FIGURE 1

Experimental setup and validation of approach. (A) Umbrella sampling. The reaction coordinate is along the bilayer normal; 104 independent windows spaced 1 Å apart were used to sample from bulk, across the bilayer, and into bulk again (z = −52 to 52 Å). The bilayer center is at z ∼ 0 Å. An identical initial orientation of the toxin with respect to the bilayer (as shown) was used in all windows. (B) Setup details specific to VSTX-PC-free. The lipids at the edge of the bilayer, which represents a border of thickness 15 Å, had a positional restraint applied on their phosphates in x, y, and z. All other lipids had no restraint applied. (A) The hydrophobic, basic, acidic, and polar residues of the toxin are colored green, blue, red, and white, respectively. (B) All toxin residues are colored green for clarity. The phosphate and choline groups of the lipids (POPC bilayer shown) are colored dark blue and light blue, respectively, in a dotted scheme. In B the phosphate and choline groups of the restrained lipids at the edge of the bilayer are identically colored but in a solid scheme. Other lipid particles, waters, and counterions are omitted for clarity. (C) Angle of hydrophobic moment of the toxin (i.e., a measure of toxin orientation) with respect to the bilayer normal in VSTX-PC-free (first 40 ns per window shown). The thick lines represent the average over windows z = −30 to 2 Å (black) and z = 2 to 30 Å (red). The region between the upper and lower limits of each set is shaded in.

FIGURE 2

PMF profiles. The approximate location of the headgroup and tail region of the bilayer is shown; Asterisks highlight the main differences between VSTX-PC and VSTX-PC-free. The image shows the toxin in a POPC bilayer at the free energy well. The color scheme for the toxin is identical to Fig. 1 A. The phosphate and choline groups of the lipids are colored dark blue and light blue, respectively, in a dotted scheme. All other lipid particles are colored gray. Waters are shown in pink. Counterions are not shown.

FIGURE 3

Bilayer deformation (VSTX-PC-free). (A and B) Dynamics as the toxin approaches the bilayer surface. (C and D) Dynamics as the toxin crosses the bilayer center. Snapshots were taken at (A and B) 40 ns and (C and D) 30 ns. The contour plots show the average displacement along the bilayer normal of the lipid phosphates of either the upper (φ_U) or lower (φ_L) leaflet for the respective window (averaged over 80–240 ns, relative to the phosphates of the restrained lipids at the edge of the bilayer). For convenience of representation, the displacement values of the contour plot of window z = 1 to 2 Å (C) are multiplied by −1. The color scheme for the toxin is identical to Fig. 1 A. The color scheme for the bilayer is identical to Fig. 1 B. Waters and counterions are not shown.

FIGURE 4

Bilayer deformation (VSTX-PC-free). (A) Average distance between lipid phosphates of the upper and lower leaflets (d_pp) as a function of toxin position along the bilayer normal. (B) Average displacement (δ) of lipid phosphates of the upper (δ_U) and lower (δ_L) leaflets as a function of toxin position along the bilayer normal. A cylindrical region of bilayer of radius 20 Å, centered on the initial xy-coordinates of the c.o.m. of VSTx1 is defined (the long axis of the cylinder is along the bilayer normal). δ is with respect to the restrained lipids at the edge of the bilayer (Fig. 1 B). Averages are taken spatially across this region and over the final 160 ns per window. Bars represent ± SD.

FIGURE 5

Solvation structure of VSTx1 when positioned in the hydrophobic core of the bilayer. The color schemes for the toxin and the bilayer are identical to Fig. 3. CG water particles are shown in pink. Counterions are not shown.

FIGURE 6

(A) Equilibrium positions of the residues of VSTx1 (relative to the bilayer) with the toxin located at the free energy well. Distances are measured relative to the center of the bilayer (z ∼ 0 Å). The c.o.m. of VSTx1 is located ∼21 Å away from the bilayer center. The horizontal dotted lines indicate the approximate headgroup region of the bilayer. The color scheme for the toxin is identical to Fig. 1 A. (B) Distributions of side chains of VSTx1 and the VS domain of KvAP along the bilayer normal. The toxin distributions were averaged over 10–40 ns of window z = −21 to −20 Å of VSTX-PC and have been scaled by a factor of 10 to improve clarity. The hydrophobic, basic, acidic, and polar residues of the toxin are shown in green, blue, red, and white, respectively, and are colored in. K4, F5, W7, S22, and W27 of VSTx1, thought to be important for binding the VS of KvAP (26), are shown separately. The VS distributions were averaged over 50–200 ns of a CG bilayer self-assembly simulation in which one molecule of the VS of KvAP was placed in a simulation box with randomly positioned POPC lipids (see main text for details). A bilayer formed with the VS molecule adopting a TM orientation by 20 ns. The VS (scaled by a factor of 10) is shown in white. Residues important for binding VSTx1 (16) (scaled by a factor of 100) are shown separately. The location of the peaks of the lipid headgroup distributions is shown as a horizontal dotted line. Distances are measured relative to the center of the bilayer (z ∼ 0 Å).