3.1. SNX-482 Partitions into Partially Anionic Membranes in a Conserved Manner
To investigate in detail membrane partition, we carried out molecular dynamic simulation in CG and AT resolutions of SNX-482 in the presence of lipid bilayer with different ratios of neutral (POPC) and anionic lipids (POPG). Mixtures of POPG/POPC have been used for experimental measurements of GMTx/membrane partitioning [
12,
15]. Only neutralizing ions were added, keeping the ionic strength to a minimum and preventing surface charge screening from reducing the impact of membrane charges [
15]. We considered two parameters to evaluate membrane insertion: (1) the fraction of simulation in which at least one insertion event was observed and (2) the insertion score detailed in the method section.
Table 1 summarizes the results of four simulations in each condition, i.e., lipid composition, and for each resolution level, i.e., CG or AT. For CG simulations, we did not observe insertion events in any of the four simulations carried out with neutral membrane (POPC). Insertion events were observed in all other conditions. More notably, when considering only simulation with insertion events, IS values fall within the error margins for all anionic membranes, from POPC: POPG (3:1) to full POPG. This observation would lead us to conclude that anionic lipids are necessary for the toxin insertion process. However, only in one of the four AT MD simulations with a neutral membrane did we observe a successful membrane insertion. Thus, membrane binding, although disfavored, is still possible without anionic lipids.
We also observed a significant preference toward partially charged membranes in AT simulations, particularly for the 3:1 condition, and that fully charged membrane also disfavors membrane insertion. Overall, IS appears more sensitive to the membrane composition in AT simulation than CG. A partial explanation may be that COM values for each residue are closer to the protein backbone in CG, and thus, a fraction of the shallower insertion event counted in AT is missing in CG. In AT simulations, IS appears very sensitive to the ratio of neutral to anionic lipids, reaching an optimum with a 3:1 ratio, about three-fold higher than the other mixed membranes. In contrast, pure POPC or POPG seems equally unfavorable to membrane partition. A preference for a partially charged membrane over neutral ones has been observed experimentally with Protox II using plasmon resonance and all-atom simulation [
14].
To explore the differences between the CG and AT descriptions in more detail, we computed the average Ip for each residue for all simulations in which there was a successful insertion event, regardless of the membrane composition (
Figure 2a). Overlaying color-coded Ip values over a surface representation of SNX-482 allows us to visualize the global binding pose (
Figure 2b). These results show that membrane partitioning residues are conserved regardless of membrane composition or resolution in all trajectories with at least one insertion event. We observe a bimodal distribution encompassing similar segments of the amino acid sequence in both cases. The first segment would span from residues 9 to 12 having an Ip > 0.2. Following a similar criterion, the second segment spans 29 to 39. The insertion process was investigated in more detail on simulations with the membrane composition that reported the most significant proportion of insertion events. These correspond to POPC: POPG ratios of 1:1 and 3:1 for CG and AT. The time evolution, average Ip for each residue, and binding pose are shown for these two cases:
Figure 3 corresponds to CG simulation and
Figure 4 to AT MD. Results for the other membrane compositions are reported in
Supplementary Figures S2–S12. In both systems, the toxin comes into close contact with the membrane and reaches a plateau (below 0.5 nm) that remains stable for the final 200 ns of the simulation (
Figure 3a and
Figure 4a). Note that the system’s volume is larger for CG, and SNX-482 start 12.5 nm away from the membrane in CG in contrast to the 2.5 nm for AT. Consequently, it takes more than 800 ns for the toxin to contact the membrane in CG. During this time, SNX-482 is expected to explore all orientations before insertion, thus not being influenced by the initial pose. Nevertheless, we set different initial poses in each of the four CG simulations. In AT, the time to the first toxin-membrane contact was about 300 ns, more likely influenced by the initial pose. However, the gray area depicted in AT simulation trajectory suggests that even at such a short distance, the initial pose was not a relevant factor in the final configuration of the toxin-membrane complex.
To identify residues that contribute to membrane insertion, we computed the average Ip values of the final 150 ns of CG simulation with a 1:1 POPC: POPG membrane (
Figure 3b). We chose the 3:1 POPC:POPG membrane for AT MD as it corresponds to the lipid ratio with the highest IS. In this case, we computed the average Ip for the final 200 ns (
Figure 4b). In CG, Met10, Phe11, Phe30, Ala34, Trp35 dwell below the lipid head more than 50 % of the time (
Figure 3c). This is in close agreement with AT MD, where Tyr9, Met10, Phe11, Leu29, Phe30, Tyr32, Ala34, Trp35 felt below the lipid head more than 60% of the time (
Figure 4c). A surface representation of the toxin colored by average Ip values (
Figure 3d and
Figure 4d) shows that SNX-482 binding converges to the same pose with both CG and AT simulations. To evaluate the long-term stability of the AT binding pose, we took the last snapshot of one of the POPC: POPG 3:1 simulations and ran it for an additional 2 μs in an extended cubic box (see
Section 2.5). IS values computed in 0.5 μs windows exhibit a monotonic increment and reach 21 in the last window while maintaining the binding pose (
Supplementary Figure S14). Residues 23 to 39 kept increasing their Ip values over time (compare
Figure 4 with
Supplementary Figure S14). A rough linear estimation of the IS time-derivative (yields a value near 2 IS units per microsecond (
Supplementary Figure S15). If residues 8 to 14 and 20 to 40 are the only membrane binders that, at equilibrium, reach an Ip value near one, IS maximum would be 26 (see Equation (1)). With an IS time-derivative of two, an additional 3 μs would be necessary to reach a final IS value and, thus, a stable binding pose. Such a slow stabilization of the membrane-toxin complex raises a cautionary note on information derived from short simulations.
The COM-based calculations may underestimate insertions and miss events where only the side chain falls below the membrane plane. Thus, we computed Ip profiles considering COM of the residues’ side chains (
Figure S16) and revealed a slight reduction in Ip for polar and charged residues. IS calculated with this new criterion were virtually identical (
Table S3). These restricted Ip measurements were also carried out for the last 0.5 µs of the extended simulation in the 3:1 system (
Supplementary Figure S17A). We confirmed a reduction in Ip for polar residues, particularly from the first insertion patch encompassing residues 9 to 12. We also carried out Ip calculations employing a stricter criterion: a residue was considered inserted if it laid below C1 carbon of lipids’ fatty acid chain (
Figure S17b). The latter is consistent with polar residues remaining closer to the polar heads while hydrophobic residues will go deeper in the membrane hydrophobic core.
We computed typical membrane descriptors for all compositions with the toxin unbound (first 50 ns simulation) to investigate if anionic phospholipids may influence membrane properties. Specifically, we measured area per lipid and membrane thickness (
Table S2) and found no significant differences between the systems. Furthermore, as discussed below, toxin diffusivity is not affected by the presence of anionic lipids. We also explored whether changes in conformational stability might be relevant. We found that α-carbon RMSD for the bound configuration of the 1:0 and 3:1 systems exhibit similar fluctuations (
Supplementary Figure S19a) and nearly identical inserted poses (
Supplementary Figure S19b). We also corroborated that conformational freedom is significantly reduced upon membrane partitioning (
Supplementary Figure S19c). Overall, the take-home message derived from this analysis is that both CG and AT identify a conserved binding mode towards the membrane surface with a preference over partially anionic composition.
3.2. The Role of Electrostatic Interactions in SNX 482 Membrane Partitioning
It is seemingly contradictory that electrostatic forces favor the binding of negatively charged SNX-482 to membranes containing anionic lipids. However, because the size of the toxin is relevant, the dipole moment is a more appropriate parameter to understand electrostatic forces. Indeed, as shown in
Figure 5, the dipole moment of the bound toxin has a preferred orientation whose angle increases with the ratio of POPG, whose dipole orientation is perpendicular to the membrane plane and points to the interior. Thus, electrostatic forces would help align SNX-482 and POPG dipoles while the optimal orientation for membrane insertion falls around 100–120°.
To get further insights into the dynamic behavior of the toxin electric dipole along the binding process, we evaluated how the toxin molecular dipole changes as the partitioning proceeds for the 3:1 and 1:0 systems (for all four AT simulations), corresponding to the ones with the highest and lowest number of binding events, respectively (
Figure 6).
Compared to the 1:0 condition, in the 3:1 system, as the distance to the membrane decreases, allowed orientations (Dip
z) are diminished (
Figure 6c,f). Moreover, for the 3:1 system, the magnitude of the dipole is larger. Thus, dipole-dipole interactions appear relevant to orient and lock the toxin in a configuration that favors binding. We followed the same descriptors for the extended 2 μs simulations of the 3:1 system (
Supplementary Figure S18). Quite interestingly, the orientation is maintained, but the dipole magnitude as time progresses is reduced and reaches even lower values than bulk conditions (see inset of
Supplementary Figure S18A). The presence of anionic lipids appears to have a kinetic effect that facilitates the correct encounter between the membrane and SNX-482. This finding is in agreement with previous studies on a different family of peripheral membrane proteins, proving that the macrodipole of the peptide orientation plays a central role in membrane binding [
35,
36].
We estimated binding energies (ΔE;
Table 2) to check whether the membrane composition also impacts the thermodynamics of membrane binding. To compute the total energetics of the partitioning, bound and unbound states of 3:1 and 1:0 systems were simulated for an additional 200 ns. We placed the toxin 4 nm above the outer membrane leaflet for unbound states and applied a soft-harmonic wall below this threshold only along the z-axis to avoid any approximation toward the membrane and minimize long-range interactions. We decomposed the total potential energy for the unbound and bound states into Van der Waals (VdW), electrostatic (Ele), and bonded (Bond) terms. We also decomposed these total energies for the pairs only involving the toxin (Tox) and the rest (Rest) of the interacting members (membrane, water, and counterions), which were also decomposed into its dispersion and electrostatic components. ΔE
TotPot values reveal that the 3:1 system exhibits favorable binding energy while the 1:0 system essentially shows no preference between the bound and free states; this is in line with the spontaneous binding results shown in
Table 1.
Decomposing ΔE
TotPot into its ΔE
TotVdW and ΔE
TotEle components reveals that ΔE
TotVdW is deeper for the 3:1 system while ΔE
TotEle is positive for both, but four times higher for the 3:1 condition. A closer look at the decomposed interactions of the toxin and the rest of the system (ΔE
ToxVdW, ΔE
ToxEle, ΔE
RestVdW and ΔE
RestEle) reveals that these basically cancel out for the 1:0 system. All interactions involving SNX-482 are not very different between the 1:0 and 3:1 systems. Consequently, the main difference between the binding processes for 3:1 and 1:0 ratios arises for the ΔE
RestEle and ΔE
RestVdW terms, with even a sign change for the latter. Therefore, membrane interactions with itself and water are differentially perturbed upon toxin binding onto the 3:1 and 1:0 systems. On the one hand, desolvating a charged membrane is more costly (thus the increase in ΔE
RestEle), but in the same manner, the water removal and the deeper toxin insertion for the 3:1 condition increment dispersion interaction within the membrane. In the 3:1 system used there is also a larger concentration of ions, 30 to be exact. These are the counterions neutralizing anionic lipids. To check whether there was some preferential ion binding towards the membrane, we computed Na+ densities along the z-axis for the 3:1 system. We found that they concentrate in the membrane boundary with a small asymmetry between the upper and lower leaflet that can be attributed to the initial toxin placement closer to the upper leaflet (
Supplementary Figure S20). Na
+ density near the membrane increases in the toxin-bound system, indicating no counterion removal occurs upon membrane insertion. Comparing pair interactions between the toxin, ions, and water (
Supplementary Table S5), the expected reduction in toxin–water electrostatic interactions upon membrane insertion is compensated by an increase in the interactions between the toxin and surface counterions. There is also a significant loss in VdW interactions with water compensated by the Vdw interactions with the membrane (see
Table 2). Thus, surface counterions essentially cancel out the electrostatic cost of desolvating the toxin. We also observed a gain in interactions with surface ions upon binding for the 1:0 system but with only two ions, equivalent to 3.5 mM, it is insufficient to compensate the electrostatic cost of desolvation. Consequently, the toxin is more solvated when bound to neutral membrane. Thus, indirectly, anionic membrane composition by concentrating cations near the membrane surface reduces the cost of toxin desolvation necessary for binding.
We carried out an exploratory potential of mean force (PMF) calculations for the 1:0 and 3:1 systems via well-tempered meta-dynamics (wt-MetaDym) to complement the energy calculations. To avoid noise and optimize these demanding calculations, translational (along with the x-y plane) orientational and conformational degrees of freedom were restrained to the bound state. With these restraints, PMFs were calculated as a function of the COM distances between the toxin and the membrane along the z-axis for both systems. Distances up to 4.2 nm were considered (
Figure 7). At this distance, both systems do not exhibit detectable dipole alignment and magnitudes in solution (
Figure 6 and
Supplementary Figure S16). Since the adsorbed states exhibit a conserved binding mode regardless of the membrane composition (see
Figure 2,
Figure 3 and
Figure 4), the main difference in adsorption strength arises from the cost of transferring the restrained toxin from the bound state to the bulk and, therefore, the entropic penalties associated with introducing and removing these restraints (and the standard state correction) should cancel out when determining relative adsorption affinities. For a convergence analysis of the wt-MetaDym calculations, please refer to
Supplementary Figure S20. The energetic calculations of the PMFs shown in
Figure 7 clearly indicate that the 3:1 membrane composition favors toxin binding, while the 1:0 shows essentially a rather flat free-energy profile for the restrained axial transfer. A thermodynamic cycle in which we add the free energy cost of restraining the bound state system will be positive but small, due to low conformational and orientational freedom of the bound toxin while in the unbound state, the difference in free energy will be negative and larger for the more extensive conformational and orientational freedom of the toxin in solution reducing the absolute binding free-energy differences. We did not carry out these calculations as we were mainly interested in the relative difference between both conditions. Considering the conserved binding poses, it is reasonable to assume that these terms will cancel out. According to the energy calculations shown in
Table 2, the potential energy difference of absorption for the 1:0 system is essentially zero. It is expected that the gain in entropy in the unbound state, which can be roughly approximated by removal the aforementioned restraints, will further reduce the affinity of the toxin towards the 1:0 system. We did not carry out these calculations as we were mainly interested in the relative difference between both conditions. Considering the conserved binding poses, it is reasonable to assume that these terms will cancel out. According to the energy calculations shown in
Table 2, the potential energy difference of absorption for the 1:0 system is essentially zero. It is expected that the gain in entropy in the unbound state, which can be roughly approximated by the restraints removal, will further reduce the affinity of the toxin towards the 1:0 system.
From the measured partition coefficient for other toxins, the free energy change of membrane binding is in the order of −7 to −8 Kcal/mol [
12]. Our PMF calculations for the 3:1 system exhibit a (partial) binding free energy in the order of −20 kcal/mol (
Figure 7). However, this value is expected to increase when removing the energetic penalty of the employed restraints, in particular the conformational and orientational ones imposed over the toxin, given that there is a relevant change in the dipole magnitude and orientation between the unbound and bound states (see
Figure 6 and
Supplementary Figure S18). Furthermore, the standard state correction (logarithm of the ratio between the sampled restrained volume and the standard volume) leads to a further increment of around 3 Kcal/mol. The discrepancy with ΔE
TotPot (see
Table 2) can be attributed to a relevant entropic loss expected from the loss in translational, rotational, and configurational degrees of freedom of the toxin upon binding, which is not compensated by interfacial water molecules. The precise nature of the membrane-toxin interaction for the 3:1 condition is reflected by the ΔE
ToxVdW and ΔE
ToxEle shown in
Table 2. Both terms are favorable, reflecting the polar, charged, and hydrophobic nature of the protein insertion within the membrane.
As a whole, these calculations strongly suggest that the partition process is energetically driven, and the anionic membrane composition, specifically the dipole moment, aids the optimal orientation and configuration for membrane insertion.
3.3. Toxin Diffusivity Is Reduced upon Membrane Insertion
To obtain insights on the diffusional effects of membrane partitioning, we computed the diffusion coefficient of the toxin in the aqueous phase (D
AP) and the lateral diffusion coefficients (D
M) when bound to the membrane for the AT POPC: POPG 3:1 system (see
Section 2.5 for more details). Due to finite-size effects, we also extrapolated D
M values to macroscopic scales, D
∞ [
36,
38]. These results are presented in
Table 3,
Table S1 and
Table S2. Bulk diffusion for SNX-482 is one or more than one order of magnitude larger than lateral diffusion within the membrane for the microscopic (D
sim) or macroscopic (D
∞) estimations, respectively. The latter is expected due to the toxin-membrane interactions and the higher viscosity of the membranous phase. Indeed, a comparison between D
M values of SNX-482 and the lipids not regarding their composition reveals that the toxin diffusivity is determined mainly by the membrane, particularly for D
∞ estimations (second column of
Table 3).
The question arises then on the impact of slower membrane diffusion on the preferred path to binding, i.e., directly from the bulk or through lateral diffusion along the membrane. Is RD sufficient to sustain a higher encounter rate for the membrane-bound ligand despite a near ten-fold slower diffusion? The seemingly simpler scenario of a diffusion-limited process in which all toxin-receptor encounters led to binding is not trivial and is the subject of intense debate in the literature, as for 2D (and 1D as well). The main caveat is that binding rates contain time and concentration dependencies [
5,
10,
36,
37]. Fortunately, the more realistic scenario in which toxin-channel binding is a “reaction-limited” process. Axelrod and Wang developed a simple RD theory for reaction-limited receptors either for reversible or irreversible binders [
10]. In detail, it assumes the following: (i) the 2D and 3D processes are indirectly coupled by reversible adsorption on non-occupied regions of the surface; (ii) the receptor binding site is equally available from the bulk or from the surface and randomly distributed; (iii) the binding probability per collisions is low; (iv) receptor single-occupancy, (vi) a spherical geometry and (vii) equilibrium is reached, so the concentrations of ligand and receptor remain constant. With all these conditions satisfied and for the reversible ligand-receptor binding case, the fraction of its rate from the surface with respect to the total binding rate (F
2) is:
where
σ and χ are the Brownian persistence distance (free path between collisions) and the fraction of collisions that lead to binding. For simplicity, we assume that these parameters are the same in bulk (σ
3 and χ
3) and membrane-bound (σ
2 and χ
2). R
a is the capture radius, which is in the order of nanometers. D
2 and D
3 are the toxin’s diffusion constants membrane-bound or free in solution, respectively. K
P is the partition coefficient between the membrane and bulk phases. Axelrod and Wang’s [
10] original formulation was expressed in terms of absorption constant (K
ads), being the quotient between surface (mol/cm
2) and bulk (mol/cm
3) concentration, it has units of cm
−1. Assuming that all toxin remains on the surface in the membrane phase, K
p = (SA:V)K
ads being SA:V the surface area to volume ratio, a parameter that strongly depends on size and geometry. At the microscale and in perfect spherical geometry, SA:V is in the order of 10
6 cm
−1. Inspection of Equation (4) shows that F
2 increases with K
P and D
2.
Figure 8 illustrates how these two variables influence F
2. For the diffusion constants obtained in this work (D
∞ and D
sim), the RD mechanism is clearly the dominant process even for K
P near unity. We also estimated F
2 for diffusion constants of 10
−9 and 10
−10 cm
2/s that displace the curves to the right. In such cases, F
2 approaches one when K
P > 1000. Some final points are worth mentioning: two parameters were defined as equal in the bulk and within the membrane; σ depends on the viscosity of the medium and should be more prominent within the membrane, thus reducing F
2; χ may also increase in 2D given the reduced sampling space for random collisions, thus augmenting F
2. Notwithstanding, it is reasonable to assume that apart from partially canceling each other in Equation (7), these factors will likely not differ by more than an order of magnitude with respect to bulk conditions. Finally, this model assumes that binding occurs with a low probability per collision as when a kinetic barrier for binding exists, as it is often the case in protein-ligand binding phenomena.