Results and discussion

Structural stability, mismatch, tumbling and lipid-channel interaction The structural stability of the gA-HD and MDg was checked by monitoring the time evolution of the root mean squared displacement (RMSD), shown in Fig. 3.3.

The RMSD was computed with respect to all the backbone atoms after trans-lational and rotational fitting to their starting structure. After a quick initial increase, the RMSD oscillates around their mean value, corresponding to the av-eraged structure generated by the force field. Both gA-HD and MDg structures are stable during the simulation time. The gA-HD conformation shows larger fluctuations than the MDg, presumably caused by the extra structural stability in MDg due to the succinyl linker. The average force field structures have an effective pore radius of 0.14 nm for gA-HD and 0.15 nm for MDg.

For gA-HD, both the N-terminal and C-terminal capping groups (formyl and ethanolamine, respectively) frequently deviate from their original positions. The

3.2. Results and discussion

Figure 3.3: RMSD of the back-bone atoms for the four stud-ied channels, two gA-HD and two MDg, with respect to their initial structure as function of the sim-ulation time.

ethanolamine groups tend to leave their peptidic carbonyl hydrogen bond partner in favor of interactions with water molecules at the lipid/bulk interface, which occasionally blocks the channel. This effect was also seen in the midigramicidin system. Likewise, the formyl groups were observed (∼10% of the simulation time) to bend towards the channel lumen, establishing hydrogen bonds with water molecules from the bulk/lipid interface. Although such disturbances do not completely block the channels, they interfere with permeating water molecules.

Since midigramicidin is linked at the N-terminus, the formyl group is not present and therefore this behavior is not possible.

The pure DMPC bilayer simulated has an average thickness of ∼4 nm, com-puted as the average distance between the center of mass of the head groups under the simulated conditions. This thickness is much larger than the length of the embedded channels (∼2.4 nm for gA-HD, ∼2.2 nm for MDg). However, the hydrophobic lipid chains are shorter,∼ 2.2 nm and therefore are about the right length to match the peptides. The amphiphilic tryptophan residues of gA-HD and MDg peptides tend to remain at the interface between the lipid tails and the solvated lipid head groups. The closest distance between the tryptophan residues located at the extremes of the channel is 1.2 nm in gA-HD, and 1 nm in MDg. Therefore, in order to allow the tryptophan to position in the polar-ity interface, either to establish hydrogen bonds between the NH of the indole group and interfacial water molecules [45, 138–140] or the glycerol oxygens of the DMPC, the membrane has to locally deform [141–143]. This driving force affects the dynamics of the peptides and the lipid bilayer: the membrane thickness is

3. Gramicidin channels: a starting point 3. Gramicidin channels: a starting point

locally altered with respect to a pure bilayer, and the peptides tilt with respect to the bilayer normal. Both effects were observed during our molecular dynamics simulations.

Figure 3.4.: Mass density of the DMPC lipids and the peptidic channels along the membrane normal averaged over the length of the simulation. a) Comparison between the mass density profile for gA-HD - DMPC, MDg - DMPC and pure DMPC systems. b) gA-HD - DMPC and b) MDg - DMPC mass density decomposed in contributions from the lipids (black), the lipid head groups(orange), the lipid tails (blue), the peptides (red) and the tryptophan residues of the peptides (green). The drawing on the side show snapshots of the simulated system displaying one of the two bilayers in the systems. The peptides are drawn as red balls, with the tryptophan residues highlighted in green. The lipid head groups are represented by dark gray balls, and the lipid tails by gray sticks. The water molecules are displayed as white and red sticks. The hydration layers are, in fact, larger than shown due to the periodic boundaries.

Figure 3.4 shows the averaged mass density of the DMPC bilayer and of the peptidic channels as function of the axis normal to the lipid bilayer, for both gA-HD and MDg systems. The densities were decomposed into contributions from the tryptophan groups, the lipid tails and the lipid head groups. The density profiles show that, on average, the channels remain centered in the bilayer, such that the tryptophan residues are located at the interface between the lipid tails and the head groups. The longer peptide, gA-HD, causes the membrane to thicken by about 0.25 nm, depleting the density at the middle of the bilayer.

MDg shows a smaller reduction of the density at the center of the bilayer, and almost no average thickening of the membrane. Since the densities are averaged over slices parallel to the membrane plane, the profiles depend on the molecular ratio between peptide and lipid molecules, in our case 1:120. Larger amounts of excess lipids would have averaged out the effect of the peptide.

3.2. Results and discussion

To further characterize the effect of the peptides on the lipidic membrane, we analyzed the local deformation of the membrane around the embedded channels.

We used the distance between the central carbon atoms of the glycerol residues of opposing DMPC layers to monitor the change of the thickness of the bilayer.

In a pure DMPC bilayer, the mean value of the thickness computed with these criteria is ∼3 nm.

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Distance between glycerol residues of opposite DMPC leaflets (nm) -3

Distance from the channel center of mass (nm)

2.8

Distance from the channel center of mass (nm)

MDg gA−HD

Figure 3.5.: Membrane thickness as function of the distance from the embedded peptide.

The thickness is here defined by the average distance between the central carbon of the lipid glycerol moiety of opposing DMPC leaflets, selected from a circular segment of 0.05 nm centered at a distancedfrom the peptide. The pictures on the side illustrate the effect of the peptides (gA-HD on the left, MDg on the right) on the DMPC bilayer. The central carbon of the glycerol residue is highlighted as a gray ball.

The radially averaged thickness as function of the distance to the center of mass of the peptidic channels is displayed in Fig. 3.5. Both peptides show re-markable effect on the surrounding lipidic environment. Presumably due to its smaller length, which sets the positions of the tryptophan groups deeper in the membrane, the local bending of the membrane around MDg is more pronounced than around gA-HD. For the MDg, a clear local thinning of the membrane oc-curs around the peptides. At further distances, beyond 2 nm, the membrane thickens. The combination of the thinning and thickening of the membrane re-sults in an average membrane thickness similar to the one of pure DMPC, as seen in Fig. 3.4 panel a. The gA-HD peptide induces a smaller curvature to its surrounding lipids, but the membrane is on average thicker than in pure DMPC bilayer: the match between hydrophobic and amphiphilic regions of the gA-HD - DMPC interface causes a global thickening of the DMPC bilayer normal to the membrane surface, that is propagated through the membrane. Due to the

rela-3. Gramicidin channels: a starting point 3. Gramicidin channels: a starting point

tively small patch of lipids, or the high effective concentration of peptides, the membrane thickness does not decay to the value of pure DMPC at the largest distance from the embedded peptides.

The angle between the main axes of the peptides and the bilayer normal (il-lustrated in Fig. 3.6 panel b) is displayed as function of the simulation time in Fig. 3.6 panel a. Both gA-HD and MDg are found to be tilted with respect to the bilayer normal, the shorter channel being more influenced: the averaged angle for gA-HD is 14.3^◦±0.1^◦, and 20.4^◦±0.1^◦ for MDg.

lipid atoms covering pore entrance

gA-HD (pore A)

Pore axis - bilayer normal angle (degrees)

gA-HD (pore A)

z axis (membrane normal) Channel main axis

Figure 3.6.: a) Angle between the pore main axis and the bilayer normal (illustrated in panel b) as a function of the simulation time for the four studied channels. c) Time dependence of the number of lipid atoms covering the entrance of the peptidic channels. d) Snapshots of gA-HD (orange sticks) simulations in a DMPC bilayer (gray) showing the presence of a lipid molecule (displayed as balls) in the channel entrance. The head group of the lipid molecules disturbs the permeation of water molecules (white and red balls, only the water molecules in the channel are shown) For clarity, a running average using a 500 ps time window was performed on the data for a) and c).

Due to the channel tilt and the membrane curvature around the channel, both the gA-HD and MDg channel entrances are disturbed by the lipid head groups. This interference causes a reduction of the available area for the water molecules to enter the channel. A snapshot of a representative configuration where the lipid head groups block the channel mouth is displayed in Fig. 3.6 panel d. To quantify this effect, we computed the number of lipid atoms lying above the channel entrance as function of the simulation time. We restricted

3.2. Results and discussion

the analysis to those lipid atoms that are within a cylinder with radius equal to the pore radius, defined by the peptidic backbone. To account for the channel tilting, the cylinder was aligned along the main axis of the channel. The time dependence of the number of lipid atoms covering the pore is displayed in Fig. 3.6 panel a. The mean value for gA-HD is 5.89±0.1 atoms/channel, and 14.56±0.2 atoms/channel for MDg. The disturbances of the channel entrance are therefore in agreement with the induced curvature in the lipid bilayer and the average tilt-angle: larger curvatures and tilt-angles allow more lipid head groups to approach the channel entrance.

Permeability coefficients Table 3.1 shows the water permeability coefficients, their ratio minus one (see equation 2.25) and water occupancy results for gA-HD and MDg. For comparison, experimental values for both gramicidin derivatives are also presented.

p_f (10⁻¹⁴cm³/s) p_d (10⁻¹⁴cm³/s) p_f/p_d−1 Pore occ.

gA-HD Pore A 2.85±0.4 0.39±0.1 6.3±2.1 6.7±0.1 Pore B 2.62±0.3 0.28±0.05 8.3±1.9 7.1±0.1

Exp. [144] 1.6 - -

-MDg Pore A 4.10±0.4 0.59±0.1 5.9±1.35 6.0±0.1 Pore B 4.20±0.5 0.55±0.1 6.3±1.65 6.1±0.1

Exp. [64] 5.6 - -

-Table 3.1.: Permeability coefficients, ratio of permeability coefficients and pore occupancy for the studied peptidic channels. For comparison, experimental values for the osmotic perme-ability are also listed.

The computed osmotic permeability coefficients are close to the experimental value, reproducing their tendency: MDg displays a faster permeability than gA-HD. The ratio of osmotic permeability coefficients yields relatively good agree-ment with the occupancy via equation 2.25. Later on in this thesis, the validity of this equation will be discussed. To interpret the permeability results we have to take into account the pore characteristics and external factors that can af-fect the water permeation: accessibility, structural stability, length, radius, pore polarity, etc. The establishment of a clear structure-permeability relationship is problematic due to these multiple and coupled contributions. Although MDg tilts more frequently and it is on average more disturbed by the lipid head groups

3. Gramicidin channels: a starting point 3. Gramicidin channels: a starting point

than gA-HD, the water permeability is nevertheless higher than gA-HD. Factors that could explain the faster transport of water molecules through MDg are its larger structural stability, the absence of pore blockage due to the missing formyl groups, a slightly larger radius (0.1 nm wider that gA-HD) and its shorter length (there is one water molecule less fitting in the pore than in gA-HD).

As we have seen, several factors are presumably involved in determining the permeability properties of a peptidic channel. A gradual approach is therefore required to understand the effects of channel architecture and permeability prop-erties. In the rest of this thesis, we will therefore systematically investigate the individual effect of the channel length, the radius and the pore polarity on the water permeability of narrow pores.