Khaoula Boukaria, Sébastien Balmeb, Jean-Marc Janotb, and Fabien Picauda,*

Supplementary informations: Towards new insights in the sterol/amphotericin nanochannels formation: a molecular dynamic simulation study

Khaoula Boukaria, Sébastien Balmeb, Jean-Marc Janotb, and Fabien Picauda,*

a Laboratoire de Nanomédecine, Imagerie et Thérapeutique, Université Franche-Comté, Centre Hospitalier Universitaire de Besançon, UFR ST, 16 route de Gray, 25030 Besançon cedex, France

b Institut Européen des Membranes, UMR5635 CNRS-UM2-ENSCM, Place Eugène Bataillon, 34095 Montpellier cedex 5, France

*corresponding author:

S1.Force Field Parameters

To determine the force field parameters we first optimized the initial geometry molecule (Fig SI1, left) inside water solvent with DFT method using the B3LYP hybrid functional at the 6-31++G medium-sized basis set. Then, partial charges and Hessian matrix were extracted according to the Force Field Toolkit Procedure (Fig SI1, middle). The stability of the molecule and the structure was then performed in water using molecular dynamic simulation (Fig SI1, right).

Fig SI 1 Comparison between the initial AmB structure (left panel), the optimized structure using DFT calculations in water solvent (middle panel) and the structure obtained after 2 ns of molecular dynamic simulations in water (right panel).

The large set of parameters obtained for this molecule is difficult to summarize precisely. To obtain the details of it, please feel free to contact the corresponding author that will send it you back. All atoms were considered as different in the force field building. This leads to the parametrization of 140 bonds, 252 angles, and 389 dihedrals for the bonded interaction while 138 charges and van der Waals values were attributed for the non-bonded interaction.

S2.Comparative study at short MD time (t=250 ps)

Baginski et al.(Baginski, Resatb & Borowski, 2002) studied the AmB-ERG and AmB-CHL complexes stabilities embedded inside DMPC membrane using short MD simulations of duration equal to 250 ps. To compare we analyze our simulations at short MD time (t=250 ps) and before letting all the systems evolve until stabilization.

Fig. SI 2 shows the geometry adopted by the different couples inside the membrane at t=250ps. We can already observe in these snapshots that the three couples of molecules do not behave identically during this small MD duration while the initial geometries of the simulation were about the same.

Fig SI 2 Snapshots of the simulation at t=250ps. a) For AmB-ERG, b) For AmB-CHL, c) For AmB-LAN. Yellow, cyan, green and red van der Waals spheres are for amphotericin, ergosterol, cholesterol and lanosterol molecules respectively. Water, ions and lipid molecules are not shown for clarity.

According to literature(Baginski et al., 2002), both intramolecular and intermolecular properties play an important role for these two systems. We have calculated the number of intramolecular hydrogen bonds formed inside each AmB molecules for all the systems (Fig. SI 3a). To carry out this calculation, we have considered the distance between donor and acceptor not longer than 3.3 Å and the planar acceptor-hydrogen-donor angle not bigger than 90°. The distribution of the total number of AmB intramolecular hydrogen bonds showed that 16 hydrogen bonds were formed while in our calculations, two peaks appear centered on12 and 20 hydrogen bonds for the AmB-ERG complex. In the case of AmB-CHL complex, these intramolecular hydrogen bonds presented a similar distribution compared to the AmB-ERG channel (centered on 16 hydrogen bonds) in the literature. Here we found a distribution of hydrogen bonds with a double peak conformation whose average was around 24 hydrogen bonds. Therefore, we found in these simulations that AmB-CHL channel presented more intramolecular hydrogen bonds compared to AmB-ERG one. The small differences observed with literature could be due to the initial starting point of the geometrical molecular arrangement that could lead to a deformation of the AmB molecule in the presence of cholesterol compared to ergosterol. For AmB-LAN complex, a well peaked distribution was obtained centered on the same number of hydrogen bonds than that observed in the AmB-ERG (18 measured hydrogen bonds) (see Fig. S2a).

Fig. SI 3 a) Total number of AmB-AmB intramolecular hydrogen bonds for AmB-ERG, AmB-CHL and AmB-LAN channels. b) Total number of AmB-Sterol intermolecular hydrogen bonds for AmB-ERG, AmB-CHL and AmB-LAN channels

Then, the intermolecular properties of AmB-ERG, AmB-CHL channels and AmB-LAN were investigated. The number of hydrogen bonds formed between molecules were calculated and compared to literature. In this study, we found 9 hydrogen bonds for AmB-ERG complex compared to 10 in reference(Baginski et al., 2002). If we look at the AmB-CHL complex, our results show that AmB molecules formed 12 hydrogen bonds compared to 14 hydrogen bonds in reference(Baginski et al., 2002). For AmB-LAN, only 7 hydrogen bonds were obtained. While small differences were observed between these two studies, we can argue that statistically, MD simulations gave the same behavior. Indeed, the strong instability of the system in terms of energy and structure at this short time (during equilibration phase) canmodify rapidly the properties of the system from one simulation to another. Moreover, since the inside of these complexes is hydrophilic, this will allow water molecules and ions to pass through it (especially for AmB-ERG complex). We have calculated the evolution of the formation of hydrogen bonds between water molecules and AmB molecules inside the pore. In the case of AmB-ERG complex, we found 27 formed hydrogen bonds (compared to 23 in reference(Baginski et al., 2002)). For the AmB-CHL complex, the water molecules form 24 hydrogen bonds with the AmB ones (22 hydrogen bonds in Ref.(Baginski et al., 2002)). We have finally evaluated the number of water molecules confined inside the nanopore at 250 ps. For AmB-ERG complex, 364 water molecules were found while in the case of AmB-CHL system, 322 water molecules were localized inside the nanopore. The number of water molecules and hydrogen bonds are more important for the AmB-ERG channel due to its wider pore diameter. As awaiting the nanopore offering the most number of water molecules allowed the formation of the most important number of hydrogen bonds between them and AmB molecules. This reasoning is verified since, for AmB-LAN complex, we found around 30 hydrogen bonds between the 432 water molecules in the pore and the polyenes (see Fig. SI 4).

Fig SI 4. Total number of AmB-water hydrogen bonds for AmB-ERG , AmB-CHL and AmB-LAN channels

To understand where these small differences came from, we investigated the size of the pore diameter. At 250 ps, we found a mean diameter for the AmB-ERG pore equal to 13.0±0.6 Å (value comparable with reference(Baginski et al., 2002), i.e. around 14 Å). For the AmB-CHL system, we found a pore diameter equal to 12.0 ±0.5 Å in agreement with the calculations of Baginski et al., who obtained a pore diameter ranging between 12 Å and 13 Å. For AmB-LAN, this distance is around 15±2 Å, showing an important increase of the pore diameter depending on the sterols incorporated inside the membrane (see Fig. SI 5). The AmB-ERG pore diameter channel is slightly larger than the AmB-CHL as demonstrated in reference(Baginski et al., 2002). This may explain the difference in the number of hydrogen bonds formed in each channel. The distance between AmB molecules should be shorter in the case of AmB-CHL complex which allow them to form more hydrogen bonds between each other's than in the case of AmB-ERG channel. However, as shown in Fig. SI 5, the short MD durations cannot give any information on the dynamical evolution of the pore since the diameter of each remains constant during 250 ps. It cannot be concluded on the stability of these structures and the necessity to increase the MD duration is here evident.

Fig SI 5. AmB pore diameter for AmB-ERG, AmB-CHL and AmB-LAN channels

Another crucial property should be studied to verify the stability of the systems. The root mean square deviation denoted RMSD, was calculated for the eight AmB molecules and sterols separately as a function of the time simulation (Fig. SI 6). A close inspection of the RMSD reveals the presence of some small increasing fluctuations during 250 ps which indicate that the AmB-ERG couples are moving with each other.

Fig SI 6. a) RMSD for AmB (blue curve) and ERG (green curve). b) RMSD for AmB (blue curve) and CHL (green curve). c) RMSD for AmB (blue curve) and LAN (green curve).

The RMSD for the three complexes showed the same behavior with a concomitant evolution of the polyene geometry and the sterol one. The RMSD fluctuations were however less important for AmB-CHL, which indicated stronger interaction between AmB molecules and this sterol.

Our results show that the type of sterol plays a major role in the formation of the nanopore, especially in the size of the pore diameter. At 250 ps in the case of AmB-CHL channel, pore diameter is smaller than the AmB-ERG one and water forms less hydrogen bonds with AmB molecules (in agreement with Ref.(Baginski et al., 2002)). Therefore, having a larger pore diameter promotes the leakage of water molecules through the nanopore. Moreover, the RMSD calculations show that the three systems have not converged in terms of geometrical stability and further MD simulations are necessary to improve these preliminary conclusions.

S2.Stability at the end of the simulations

We plotted in Figs. SI 7 and SI 8 the RMSD and total energy as a function of simulation time for the whole simulation. As clearly shown, it is necessary to stand for 70 ns to reach structural and energetic stabilities of the system. The constant evolution of the structure during simulations indicates that the sterol plays a major role in the AmB behavior. We stop the simulations for the AmB-LAN system at t=50ns since it behaves comparatively to AmB-ERG one.

Figure SI 7: RMSD of AmB-ERG (blue curve), AmB-CHL( red curve) and AmB-LAN (green curve).

Figure SI 8: Total energy of AmB-ERG (blue curve), AmB-CHL( red curve) and AmB-LAN systems (green curve)

The averages performed between 35/50ns and 55/70ns are a bit different between the two ranges of time especially for the AmB-ERG interactions but the standard deviations increase also. However, considering two equivalent time ranges, LAN and ERG present the same value for this kind of contribution. We could thus hypothesize on the same behavior for the two systems containing different sterols. Concerning the inter polyene interaction, the AmB-ERG system presents a small increase of its energy while AmB-CHL has an inverted behavior between table SI1 and table SI2. This corroborates the expansion of the AmB-ERG system compared to the cohesion of the AmB-CHL one. The system built with LAN presents a higher energy (less stable) than ERG and CHL. This would thus lead to the expansion of the system as for ERG.

System / AmB-ERG / AmB-CHL / AmB-LAN
VdW energies AmB-sterol (Kcal/mol) / -100±5 / -188±8 / -102±9
VdW energies AmB-DMPC (Kcal/mol) / -330±20 / -250±10 / -290±20
VdW energies AmB-AmB (Kcal/mol) / -53±9 / -85±9 / -35±7

Table SI 1 : VdW energies estimated as an average between t=35 and t=50ns

System / AmB-ERG / AmB-CHL / AmB-LAN
VdW energies AmB-sterol (Kcal/mol) / -88±9 / -190±9
VdW energies AmB-DMPC (Kcal/mol) / -320±20 / -260±10
VdW energies AmB-AmB (Kcal/mol) / -49±6 / -90±9

Table SI 2 : VdW energies estimated as an average between t=55 and t=70ns

Baginski, M., Resatb, H., Borowski, E. 2002. Comparative Molecular Dynamics Simulations of Amphotericin B–Cholesterol/Ergosterol Membrane Channels, . Biochimi. Biophys. Acta.1567 63–78.