Article pubs.acs.org/Langmuir

Understanding Miltefosine−Membrane Interactions Using Molecular Dynamics Simulations Matheus Malta de Sá,†,‡ Vishnu Sresht,† Carlota Oliveira Rangel-Yagui,*,‡ and Daniel Blankschtein*,† †

Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, United States School of Pharmaceutical Sciences, Department of Pharmacy, University of São Paulo, São Paulo, SP Brazil

‡

S Supporting Information *

ABSTRACT: Coarse-grained molecular dynamics simulations are used to calculate the free energies of transfer of miltefosine, an alkylphosphocholine anticancer agent, from water to lipid bilayers to study its mechanism of interaction with biological membranes. We consider bilayers containing lipids with different degrees of unsaturation: dipalmitoylphosphatidylcholine (DPPC, saturated, containing 0%, 10%, and 30% cholesterol), dioleoylphosphatidylcholine (DOPC, diunsaturated), palmitoyloleoylphosphatidylcholine (POPC, monounsaturated), diarachidonoylphosphatidylcholine (DAPC, polyunsaturated), and dilinoleylphosphatidylcholine (DUPC, polyunsaturated). These free energies, calculated using umbrella sampling, were used to compute the partition coefficients (K) of miltefosine between water and the lipid bilayers. The K values for the bilayers relative to that of pure DPPC were found to be 5.3 (DOPC), 7.0 (POPC), 1.0 (DAPC), 2.2 (DUPC), 14.9 (10% cholesterol), and 76.2 (30% cholesterol). Additionally, we calculated the free energy of formation of miltefosine− cholesterol complexes by pulling the surfactant laterally in the DPPC + 30% cholesterol system. The free energy profile that we obtained provides further evidence that miltefosine tends to associate with cholesterol and has a propensity to partition into lipid rafts. We also quantified the kinetics of the transport of miltefosine through the various bilayers by computing permeance values. The highest permeance was observed in DUPC bilayers (2.28 × 10−2 m/s) and the lowest permeance in the DPPC bilayer with 30% cholesterol (1.10 × 10−7 m/s). Our simulation results show that miltefosine does indeed interact with lipid rafts, has a higher permeability in polyunsaturated, loosely organized bilayers, and has higher flip-flop rates in specific regions of cellular membranes.

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INTRODUCTION

Evidence for the disruptive effect of APCs on cell membranes comes from studies suggesting that miltefosine’s apoptotic effects are due to its accumulation in lipid raftsregions rich in cholesterol and sphingolipids. Jiménez-Lopez et al.5 hypothesized that miltefosine interferes with nonvesicular cholesterol transport to the endoplasmatic reticulum (ER), leading to a depletion of free cholesterol in the ER and, consequently, to the deregulation of cholesterol homeostasis. Gomide et al.6 showed that the ALP 10-(octyloxy)decyl-2-(trimethylammonium)ethyl phosphate (ODPC), perifosine, and possibly other compounds such as miltefosine induce raft disruption by promoting lipid mixing, which may cause the selective (dis)association of essential proteins within rafts, eventually leading to cell apoptosis. Evidence against the significant disruption of phospholipid membranes by APCs comes from Castro et al.,7 who concluded that, at pharmacologically relevant concentrations, miltefosine and edelfosine do not affect the biophysical properties of lipid rafts. These authors suggested that the mechanism of action is

Alkylphosphocholines (APCs) are a subclass of alkylphospholipids (ALPs) with promising anticancer activity.1 Miltefosine is the prototype of this class and contains the minimal structural requirements for antitumor activity: a long alkyl chain and a phosphocholine moiety (Figure 1a).2 The anticancer effect of APCs has been studied against various tumor cells, including soft tissue sarcomas, metastatic colorectal cancer, head and neck squamous cell carcinoma, hematological malignancies, and brain tumors.3 In contrast to DNA-targeting anticancer agents, APCs are hypothesized to act primarily on the cell membrane. Evidence suggests that this class of drugs interferes with phospholipid metabolism, cholesterol transport and homeostasis, biochemical survival pathways (such as the Akt-mTOR), and proteins involved in signal transduction such as protein kinase C, phospholipase C, and phospholipase D.3,4 Two fundamental questions regarding the anticancer activity of APCs remain unanswered: (1) Does the presence of APCs at pharmacologically relevant concentrations have a significant disruptive effect on the biophysical properties of the cell membrane? (2) If so, which components of the cell membrane do APCs primarily interact with? © 2015 American Chemical Society

Received: January 17, 2015 Revised: March 20, 2015 Published: March 27, 2015 4503

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Figure 1. (a) Chemical structures of MIL, the lipids used to build the lipid bilayers, and CHOL. The spheres represent the CG MARTINI mapping scheme, encompassing approximately four heavy atoms. C-type beads (green spheres) represent saturated groups; D-type beads (pink spheres) represent unsaturated groups; GL-type beads (gray spheres) represent the glycerol moiety; PO4 beads (orange spheres) represent phosphate moiety; NC3 beads (blue spheres) represent N,N,N-trimethylammonio moiety; R1, R3, R4, and R5 beads (green spheres) are saturated the portions of cholesterol; R2 bead (brown sphere) is the unsaturated part of and ROH bead (red sphere) is the hydroxyl moiety of cholesterol. (b) Representation of a simulation system where MIL was placed above the lipid bilayer and pulled in the z direction until it completely crosses the bilayer. Blue spheres represent the cationic moiety, orange spheres represent phosphate groups, green spheres represent hydrophobic groups (CH2), and water molecules are represented as small, light blue spheres. In this figure, most of the water molecules were deleted for clarity.

intercellular membranes of the stratum corneum in the presence of miltefosine.9 This uncertainty regarding the interactions of APCs with membranes is compounded by the lack of clarity about which specific lipid components are responsible for APCs selectively targeting tumor cell membranes while sparing normal cells.10 These two outstanding questions concerning the efficacy of APCs may be settled by quantifying the strength of their interactions with various membrane-forming phospholipids. In this respect, molecular dynamics (MD) simulations can be successfully used to model the interactions of APCs and phospholipid (hereafter referred to as lipid) bilayers.11−13 Here,

unlikely to be related to specific biophysical effects on mammalian plasma membranes and/or rafts and is, instead, possibly associated with lipid metabolism and transport deregulation. This suggestion is supported by data from Moreira and co-workers,8 who observed that miltefosine increased erythrocyte membrane fluidity and protein mobility, with no substantial changes in vesicles with raft-forming components. On the contrary, Alonso et al.9 observed no significant changes in the fluidity of dipalmitoylphosphatidylcholine (DPPC) model lipid bilayers in the presence of a 25−35% molar ratio of miltefosine. However, the same authors did observe a large increase in the fluidity of 4504

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conditions, namely, with eight coarse-grained (CG) water beads per lipid.11,19 Because miltefosine (abbreviated hereafter as MIL) is not part of the original MARTINI force field, we parametrized this molecule using dodecylphosphocholine (a standard component of the MARTINI force field) as the template and, as suggested by Marrink and coworkers,11 utilized angle and dihedral distributions obtained from allatom (AA) and CG simulations to validate the chosen parameters (details are provided in the Supporting Information). A summary of the simulations carried out in this work is provided in Table S2 of the Supporting Information. Umbrella Sampling and Potential of Mean Force. Umbrella sampling was used to calculate the PMF of a MIL molecule at different depths in the bilayer. In this method, an artificial biasing potential was added to force the MIL molecule to sample regions that would be poorly visited if the molecule were left to diffuse freely.20 Starting with the self-assembled bilayers described above, the initial simulation boxes were expanded along the z-axis to be at least 14 nm long and contain more water molecules, so as to satisfy the minimum image convention and prevent lipids from interacting with their periodic image during the simulation (Figure 1b). Following steepest descent minimization and equilibration in an isochoric−isothermal (NVT) ensemble, followed by an isobaric−isothermal (NPT) ensemble, the MIL initial position relative to the bilayer surface was 2.5 times greater than the Lennard-Jones cutoff value (1.2 nm), in order to ensure that no long-range forces would act on the molecule.21 MIL’s center of mass (COM) was then pulled along the bilayer normal, i.e., along the z-axis, with a spring constant k = 500 kJ mol−1 nm−2 and pulling rate v = 0.0005 nm ps−1 (0.005 Å ps−1), for about 6.5 nm until it completely crossed the bilayer. Throughout this paper, the values of k and v were chosen after we tested many combinations to find an optimal pair of numbers that did not cause instabilities in the system. In this respect, we opted for a value of k that produced overlapped bins, and a value of v that allowed MIL to be pulled along the bilayer without disrupting its structure (creating pores or disrupting the two-dimensional lamellar structure, for example). Pulling simulations were performed for 40 ns for the single-component bilayers, and for 60 ns for bilayers containing cholesterol in the isochoric−isothermal (NVT) ensemble, which proved to be more computationally efficient in terms of simulation time. From the resulting trajectories, snapshots were taken to generate the initial configurations for the umbrella sampling windows, with the interwindow spacing equal to 0.1 nm. Additional windows were generated when necessary to improve sampling. Before running the umbrella MD simulations, each window was briefly equilibrated in the NPT ensemble for 10 ns. Each equilibrated window was then simulated for 200 ns for systems without cholesterol, and for at least 420 ns for bilayers with cholesterol, with a spring constant of 1000 kJ mol−1 nm−2. To reduce roughness in the PMF profile corresponding to the bilayer containing 30% of cholesterol, we ran each umbrella window for 600 ns for MIL inside the bilayer. The PMF profile was constructed using the weighted histogram analysis method (WHAM),22 with error bars estimated by bootstrapping.23 Additionally, MIL was laterally pulled for about 3.5 nm in the bilayer containing 30% of cholesterol to calculate the PMF associated with MIL−CHOL interaction, with a spring constant of 250 kJ mol−1 nm−2 and pull rate of 0.0005 nm ps−1. In this system, all the MIL− CHOL interactions were turned off, except for the interactions with a single target CHOL molecule. All the MIL−water, CHOL−water, DPPC−water, MIL−DPPC, CHOL−DPPC, DPPC−DPPC, and CHOL−CHOL interactions were kept on. By doing this, we were able to compute the PMF of MIL interacting with a single cholesterol molecule without being affected by other molecules during the pulling simulation. We also ensured that this simulation was carried out in a highly ordered DPPC bilayer, since the ordering effect of cholesterol on DPPC was not altered. As a result, the PMF also accounted for energy landscape of the condensed phase of the DPPC bilayer into which the MIL molecule is inserted. Each umbrella window was equilibrated in the NPT ensemble for 10 ns and then simulated for 600 ns, with a spring constant of 750 kJ mol−1 nm−2. WHAM was used

we have used umbrella-sampling MD simulations to compute potential of mean force (PMF) curves and to calculate the free energy change for the transfer of miltefosine from water to the interior of various lipid bilayers. We have also characterized the kinetics of the transport of miltefosine through these lipid bilayers using permeance values computed indirectly from the umbrella-sampling MD simulations. We found that miltefosine has a propensity to partition into bilayers that are rich in cholesterol, suggesting that miltefosine’s interactions with lipid rafts are important. Moreover, we found that the permeance of miltefosine is higher in polyunsaturated lipid bilayers, indicating that passive transmembrane diffusion of miltefosine is facilitated in loosely organized bilayers. Our study provides a molecular and thermodynamic view of miltefosine interactions with various lipid components found in healthy and malignant cells, thereby shedding light on the mechanism of action of APCs.

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METHODS

Bilayer Self-Assembly and Simulation Details. In our MD simulations, we have used the coarse-grained MARTINI force field, version 2.011 (see the Supporting Information for details) where molecules are represented by particles that correspond to approximately four heavy atoms. Standard MARTINI parameters for lipids, cholesterol, surfactants, and water were used to model the following lipids: dipalmitoylphosphatidylcholine (DPPC) containing 0%, 10%, and 30% of cholesterol (CHOL), dioleoylphosphatidylcholine (DOPC ), p almitoy loleo ylpho spha tid ylcho line ( POPC), diarachidonoylphosphatidylcholine (DAPC), and dilinoleylphosphatidylcholine (DUPC). DPPC is one of the main components of cellular membranes and has been used very widely in the computational biophysics literature as a model for lipid bilayers and liposomes.14 Since mixed DPPC−CHOL systems have also been extensively characterized and studied as models for cellular membranes,15,16 we have also considered the effect of miltefosine on mixed DPPC−CHOL bilayers. We started our simulations with the lipid monomers randomly placed in an equilibrated box containing water molecules and then simulated the system until all the molecules assembled into a bilayer. For the systems containing CHOL, we started with the equilibrated DPPC bilayer and evenly distributed CHOL molecules in both leaflets, removing the overlapping DPPC molecules. As suggested by Marrink and co-workers,11 in all our MD simulations, Lennard-Jones and Coulombic nonbonded interactions were shifted to zero between 0.9 and 1.2 nm and cutoff of 1.2 nm. We used a relative dielectric constant value of εr = 15 for water instead of using the MARTINI polarized water model. This value incorporates the hydration strength of the CG particles in this model and is a balance between the larger value of εr in bulk water and the smaller value of εr in the hydrophobic core of lipid bilayers. In addition, it maintains the accuracy of structural properties (such as the area per lipid) and thermodynamic quantities (such as the free energy).11 Temperature (300 and 323 K; see Table S2 in the Supporting Information for details) and pressure (1 bar, semi-isotropic in the x−y directions) were kept constant using the Berendsen thermostat and barostat,17 with coupling time constants of τT = 0.3 ps and τP = 3.0 ps, respectively. Time steps of 20 and 30 fs were used for single-component and cholesterol containing lipid bilayers, respectively. To confirm that the simulations reached equilibrium, the simulated time evolution of the surface area per lipid was determined for each bilayer and then compared to the appropriate experimental values. All simulations were performed using GROMACS 4.5.5.18 To ensure that the simulated lipid bilayers remained in the liquid crystalline phase, the simulation temperatures were kept above the liquid-gel phase transition temperatures of the various lipids considered (323 K for bilayers with DPPC and CHOL and 300 K for other bilayers). Each lipid bilayer was simulated at fully hydrated 4505

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Langmuir to reconstruct the PMF curve, with errors estimated by bootstrapping new trajectories based on the umbrella histograms.23 Permeance Calculations. The time scales associated with the penetration of MIL through, and the flip flop of MIL between, the leaflets of a lipid bilayer are too long to observe a statistically significant number of such transitions using our simulations. Consequently, we utilized the techniques developed by Marrink and Berendsen24 to characterize the rates of these processes in terms of the permeance25 of MIL for each umbrella sampling MD simulation. The theory26,27 underlying these permeance calculations is outlined in the Supporting Information. Two different permeance values P1(i) and P2(i) were calculated for each bilayer i. P1(i) was defined as the MIL permeance between the exterior of the lipid bilayer (i.e., bulk water) and the equilibrium position in one of the bilayer leaflets. P1(i) is therefore a quantitative measure of the rate at which MIL enters lipid bilayer i from bulk water. On the other hand, P2(i) corresponds to the MIL permeance from its equilibrium positions in one of the two leaflets of bilayer i to its equilibrium position in the other leaflet. P2(i) is therefore a quantitative measure of the rate at which MIL flip-flops between the two bilayer leaflets.

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RESULTS AND DISCUSSION Bilayer Stabilization. In order to verify bilayer stabilization, we calculated the temporal evolution of the surface area/ lipid for all the lipid bilayer systems considered (see Table 2 and Figure S3 in the Supporting Information for details). In general, our results are in excellent agreement with the available experimental data.28,29 We find that bilayers containing 10% and 30% of CHOL have lower surface areas/lipid relative to CHOL-free bilayers (Table S2). This is consistent with the general consensus in the literature that CHOL exerts a condensing effect on lipid bilayers and smoothens them from a gel-like phase toward a liquid-crystalline phase transition through a variety of plausible mechanisms.30−33 This condensing effect of CHOL34 is also reflected in the observed decrease in the cross-sectional area of the phospholipids, in an increase in the bilayer thickness, and in both intra- and intermolecular motion restrictions (Table S2). On the other hand, as the cholesterol content in the lipid bilayer decreases, or as the unsaturated lipid content increases, the lipid packing becomes looser and the mean surface area/lipid increases,35 as observed for DAPC and DUPC (Table S2). Potential of Mean Force and Free Energy Calculations, and Effects on Lipid Order Parameters. Calculating the free energy (ΔG) values associated with pulling MIL through a bilayer using umbrella sampling resulted in significantly different PMF curves for the different bilayers considered in this study (Figure 2). Error bars are larger in DPPC and DPPC + CHOL bilayers (Figure 2a) than in the mono- and polyunsaturated bilayers (Figure 2b,c), and this can be accounted for by slow transitions that take place with an increase in the bilayer’s rigidity, making sampling more difficult.36 Larger error bars (thicker shades around solid lines) are also observed when MIL is around z = 0.0 nm, indicating that the slowest transitions are located at this position. The nonlinear variation in the free energy barrier in DPPC bilayers with increasing CHOL content (Figure 2a) is consistent with experimental37 and simulation38 studies reported in the literature that postulate the formation of condensation complexes between DPPC and CHOL. The peaks and valleys on the left of Figure 3 correspond to specific and distinct chemical environments in the DPPC bilayer illustrated on the right of the figure. At the equilibrium

Figure 2. Potential of mean force (PMF) profiles for the systems considered. (a) Schematic representation of the ΔG values: Gmin is the free energy difference associated with transferring one MIL molecule from bulk water to its equilibrium position (zeq) in a bilayer; ΔGflip is the free energy difference associated with transferring one MIL molecule from zeq to the metastable free energy minimum at the center of the bilayer; ΔGbarr is the free energy barrier that the MIL molecule must overcome before reaching the center of the bilayer. The shade around the solid lines represents the 1 standard deviation error in the PMF estimated by bootstrapping. (b) Increasing the cholesterol content in a DPPC bilayer decreases Gmin. (c) PMF profiles for the unsaturated bilayers.

point, zeq ≈ 1−1.5 nm, the MIL polar head (NC3 and PO4 beads) has a higher probability to be aligned with the DPPC polar head (NC3 and PO4 beads), while the first carbon of the MIL alkyl tail (C-type beads) resides in the bilayer hydrophobic core. This propensity of certain moieties of MIL to preferentially reside near similar moieties in the lipid bilayer in order to maximize like−like interactions can also be observed in the manner in which the nature of the bilayer affects the equilibrium position of the MIL molecule in DOPC and DAPC bilayers as seen in Figure 4. Away from zeq, the PMF experienced by the MIL molecule sharply increases (as seen in Figures 2 and 4). In all PMF curves, there is a shift to a plateau when MIL loses contact with the bilayer and is solvated in water (right and left ends of Figure 4506

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Figure 3. Probabilities of a moiety being found at depth (in this case, the z-axis) into a DPPC bilayer, p(z) (on the left), is juxtaposed against a crosssectional view of the DPPC bilayer with 30% CHOL (gray and green beads) content (on the right). Blue spheres represent the nitrogen-rich moieties, orange spheres represent phosphate groups, green beads and chains represent hydrophobic groups (with dark green beads representing the aromatic groups in cholesterol), gray beads and chains represent oxygen-rich moieties, and the water surrounding the bilayer is shown in light blue. The MIL tail is shown in a lighter shade of green.

that when the number of double bonds of the acyl chain increases, the flip-flop rate also increases. The PMF profiles support these findings by showing that penetration of MIL beyond zeq, and thus a flip-flop, is energetically more favorable in polyunsaturated-rich regions of the membrane, in particular in regions with PUFAs with multiple double bonds, such as arachidonic and lynolenic acids. In contrast, we observe a higher ΔGbarr for the DOPC system (as seen in Figure 4a). This lipid has 18 carbons (5 beads) in each chain, versus 16 carbons in the DPPC chain (4 beads), resulting in a thicker bilayer (Table S2), which implies that the MIL headgroup stays in contact with the apolar medium for a longer time. The same tendency is observed in the POPC system. The high ΔGbarr observed in the 30% CHOL DPPC bilayer reflects a greater difficulty for MIL to penetrate this bilayer. To understand this, we allowed MIL to freely diffuse in this bilayer for 3600 ns and compared the probability distribution, p(θt), of the angles θt adopted by the MIL tail relative to the bilayer normal with the distribution of angles θt adopted when the MIL molecule is pulled through the bilayer. We observed (Figure 5a) that an increase in CHOL content drives the bilayer tails to adopt conformations parallel to the bilayer normal (i.e, θt = 0 is more strongly favored). This observation is consistent with the fact that cholesterol increases the ordering of bilayers. The more ordered the bilayer, the larger the free energy penalty incurred when a MIL molecule disrupts this ordering by adopting an oblique tail conformation. As evident from Figure 5b, at its equilibrium position in a bilayer (i.e., at z ≈ ±1.2 nm

2). The free energy change of transferring MIL from water to the bilayer can be directly obtained by measuring the difference between this plateau and the free energy, Gmin, at zeq. Further penetration of MIL past z ≈ 0.0 nm, a process known as “flipflop” (i.e., the transferral of a molecule from one leaflet to another), is prevented by an energy barrier (Figure 2). Therefore, a flip-flop is not generally a spontaneous event, and APC translocation through the bilayer is possible only by means of specific energy-dependent mechanisms, such as the flippase ATP-dependent complexes and the endocytosis-based internalization via lipid rafts.39,40 The flip-flop energy (ΔGflip) can be calculated as the energy difference between MIL at z = 0.0 nm and zeq (Gmin) (Figure 2). MIL monomers interact preferentially with the bilayer hydrophobic core (as seen in Figure 4), with a valley in energy when MIL is fully solvated and a second smaller valley when the molecule is fully inserted (z = 0.0 nm). A difference can be seen in the DAPC profile (Figure 4b) whose flip-flop barrier (defined here as ΔGbarr, and calculated as the difference between the peak of energy just before z = 0.0 nm) is absent, indicating a spontaneous event. The ΔGbarr observed in DUPC is also significantly smaller. These two systems have polyunsaturated fatty acid (PUFA) chains that change the fluidity and permeability of plasma membranes.41 Armstrong et al.42 showed that membranes rich in the PUFA docosahexaenoate (DHA, six double bonds) promote faster flip-flop and permeability rates than other membranes containing less amounts of unsaturated lipids. Ogushi and colleagues43 showed 4507

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Figure 4. Inside a lipid bilayer, MIL moves to an equilibrium position where its moieties can optimally interact with corresponding moieties in the lipid molecules. Nitrogen-rich groups are colored in blue, and phosphate-rich groups are colored in orange. The MIL tail prefers to interact with the saturated hydrophobic zone (indicated by the groups colored in green) of the lipid bilayer. (a) When placed in a (monosaturated) DOPC bilayer, the MIL molecule resides in one of the two leaflets, while (b) when placed in a (polyunsaturated) DAPC bilayer, the MIL molecule resides at the center of the bilayer. We consider the MIL molecule to be fully solvated when it reaches the first free energy minimum in the PMF curve and to be fully inserted when it reaches the center of the bilayer.

presence of MIL, as there is no correlation between the total order parameter and the distance from MIL. The Voronoi tessellation maps confirm that one MIL molecule does not change the biophysical state of lipid bilayers because lipid clusters were not observed. These results are in agreement with experimental data that show that MIL by itself does not form an ordered domain in the fluid membrane, but rather stabilizes the DPPC/sphingomyelin/cholesterol-rich domains against temperature induced melting.44 Details and figures pertaining to the S2 calculations are provided in Supporting Information (Figures S5−S7). Permeance of Miltefosine in Lipid Bilayers. The diffusion coefficient for MIL in bulk water, calculated using our simulations, is 3.4 × 10−10 m2/s, comparable to the value of 11.2 × 10−10 m2/s obtained for SDS monomers in water.45 The two permeance values for each of the bilayers, P1 and P2, are reported in Table S3 of the Supporting Information. The values we have obtained are consistent with the P1 values estimated by Sun et al.46 for fullerene (C60) using the MARTINI force field and a similar approach to calculate the permeance. These permeance calculations were based on the computed variation of the diffusion coefficients for MIL in the various lipid bilayers

from the bilayer center), when MIL keeps its tail parallel to the bilayer normal, it can maximize contact with the hydrophobic moieties around it without disrupting the ordering of the lipids around it. However, when MIL approaches the center of the bilayer (z = 0.0 nm), its tail prefers to maintain contact with the hydrophobic moieties in the bilayer leaflet and, therefore, is forced to disrupt the ordering of the lipids around it and adopt a larger angle relative to the bilayer normal (with θt sometimes greater than 90°, as shown in Figure 5c). The increased lipid ordering that accompanies higher cholesterol content makes these oblique tail conformations increasingly unfavorable, leading to an increase in the height of the free energy barrier at the bilayer center. Table 1 summarizes the ΔG values of the transferral of MIL from the solvent to the interior of the lipid bilayers considered (ΔGtrans) as well as of ΔGflip, ΔGbarr, and the position of Gmin. We also investigated whether MIL can form local lipid clusters in the l0 phase by calculating the order parameter S2 of the lipid tails in the upper leaflet (with MIL) and in the lower leaflet (without MIL). MIL has a very small effect on the local order parameter (for definition and results, see Supporting Information), and the overall S2 seems to be unaffected by the 4508

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We can see that the DAPC bilayer system and the DPPC bilayer system containing 30% cholesterol have higher P1 values, indicating that MIL has a preference for penetrating the cell membrane in regions rich in cholesterol and/or in polyunsaturated lipids. Regions rich in DPPC and monounsaturated lipids may exert a protective effect on the cell, preventing the penetration of MIL. Once inserted into the lipid bilayer, MIL has an increased flip-flop rate in polyunsaturated, loosely packed bilayers such as DUPC. On the other hand, the flip-flop rates are smaller in the lipid systems containing cholesterol. A small flip-flop rate is also observed in the DOPC bilayer, probably because this lipid has the longest alkyl chain, and therefore, MIL needs to traverse a longer path to reach the second equilibrium point. This result indicates that polyunsaturated regions in the lipid bilayer are the preferred gateways used by MIL to reach the interior of a cell. During cancer progression and transformation, the content of unsaturated lipids in the cell membrane increases, rendering it more fluid and thereby allowing cancer cells to migrate and metastasize.47 Therefore, MIL preference for polyunsaturated regions may explain the drug’s selectivity toward cancer cells. Our results are also consistent with the observation that MIL has an antitumoral effect in strains of leukemia cells,48 which are reported to have membranes that are rich in unsaturated fatty acids.49,50 Partition Coefficients of Miltefosine into Lipid Bilayers. The partition coefficient K of MIL between water and the lipid bilayer interior can be estimated using the simulated PMF curve as follows:

K = e−ΔGmin / kBT

where ΔGmin corresponds to the minimum in the PMF curve, kB is the Boltzmann constant, and T is the temperature in kelvin. Analysis of the partition coefficients of the bilayers studied here relative to the pure DPPC bilayer (Table 2) shows that

Figure 5. Cholesterol has a significant effect on the interaction between MIL and DPPC bilayers. (a) Probability distribution p(θt) of the angle θt between the MIL tail and the bilayer normal. (b) Crosssectional view of a DPPC + 30% cholesterol bilayer when MIL is in equilibrium within a leaflet (and θt ≈ 0°). (c) Most favored orientation of MIL when it is pulled to an unstable position at the center of a DPPC + 30% cholesterol bilayer (θt ≈ 80°).

Table 2. Partition Coefficient K of MIL Relative to Pure DPPC Bilayer

Table 1. ΔG Values for the Transferral of MIL from Water to the Equilibrium Point, zeq, Corresponding to ΔGtrans); from the Equilibrium Point to between the Two Leaflets, Corresponding to ΔGflip; the Partition Coefficient K of MIL between Water and the Bilayer Interior, Relative to DPPC; and the Position of Gmin system DPPC DOPC POPC DAPC DUPC DPPC:CHOL (10%) DPPC:CHOL (30%)

ΔGtrans (kBT)

ΔGflip (kBT)

ΔGbarr (kBT)

position of Gmin (nm)

K (relative to DPPC)

−15.7 −17.4 −17.6 −15.7 −16.5 −18.4

3.2 11.3 5.5 −1.5 0.8 1.8

3.8 11.4 6.1 −1.3 1.5 3.4

1.16 1.45 1.42 1.12 1.06 1.28

1.0 5.3 7.0 1.0 2.2 14.9

−20.0

14.7

14.3

1.36

76.2

(1)

system

K (relative to DPPC)

DPPC DOPC POPC DAPC

1.0 5.3 7.0 1.0

system

K (relative to DPPC)

DUPC DPPC:CHOL (10%) DPPC:CHOL (30%)

2.2 14.9 76.2

MIL partitions more extremely into DOPC and POPC bilayers compared to DPPC bilayers (5.3 and 7.0 times greater K values, respectively). These results are consistent with the experimental data reported by Wnet̨ rzak et al.10 Although the authors did not specify K, they showed that MIL exhibits smaller repulsive deviations from the ideal behavior in a POPC monolayer, indicating stronger interactions with this lipid. The unsaturation in the oleyl fatty acid chain of POPC and DOPC creates a tilt in the phospholipid tail, enabling the MIL tail to better organize inside these bilayers. These findings, along with the P1 values for POPC and DOPC, indicate that although K is higher in POPC and DOPC bilayers, these two bilayers are as impermeable to MIL as the DPPC bilayer. The unsaturation content appears to play an important role in polyunsaturated systems in reducing the MIL lipid bilayer miscibility. DUPC is loosely packed (as reflected in its high

considered as a function of the distance above the bilayer center (Figure S9 in the Supporting Information). 4509

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value (−1.0 kBT) calculated at the minimum of the PMF curve confirms that MIL is likely to form stable complexes with cholesterol in a DPPC bilayer. Note that the right end of the PMF curve in Figure 6 corresponds to MIL in bulk DPPC, with no physical contact with CHOL. We note that the equilibrium distance between MIL and CHOL is located at z ≈ 0.6 nm (minimum in the PMF curve). This value is reasonable considering that we used a σ value of 0.47 nm to represent each CG bead. We also observe, from right to left, several peaks and valleys located between ∼2.0 and ∼1.0 nm. As with a PMF curve between two molecules in any fluid medium, the valleys in Figure 6 represent the positions of successive solvation shells. The positions of the solvation shells, in this DPPC + CHOL system, correspond to the distances between MIL and CHOL, such that the space between them can be comfortably occupied by one or more shells of DPPC molecules. Conversely, the peaks in Figure 6 correspond to MIL− CHOL separations that disrupt and hinder the ordering of DPPC molecules between MIL and CHOL. To better understand the effect of CHOL, we studied the radial distribution functions quantifying the spatial organization of DPPC and CHOL molecules around MIL in DPPC bilayers containing 10% and 30% CHOL (Figure 7). The higher

surface area/lipid value, Table S2), with a K approximately 2 times higher than that for the DPPC bilayer but lower than the K’s for the DOPC and POPC bilayers (Table 2), probably because of the low propensity of MIL to be miscible in a medium with higher polarity. DAPC responds similarly to MIL, with a K value similar to that observed for DPPC (Table 2). However, these findings along with the P1 values in these lipid bilayers shed light on why MIL does not tend to stay in any leaflet (leading to the low K values), but instead penetrates the lipid bilayer and reaches the intracellular environment (leading to the high P1 and P2 values). This suggests that bilayers which are rich in PUFA chains are more permeable to MIL than bilayers which are rich in saturated or monounsaturated fatty acids. The K values are significantly larger in lipid bilayers with CHOL and increase as the CHOL composition increases. K is 15−76 times higher for DPPC systems with 10% and 30% of CHOL, respectively, relative to DPPC alone. This suggests that MIL prefers to interact with cholesterol-enriched bilayer regions, such as lipid rafts. Cancer cells have elevated levels of lipid rafts, which correlates with an increase of apoptosis sensitivity induced by cholesterol-depleting agents.51 Additionally, our results are consistent with experimental results which show that APC interactions with cholesterol-free monolayers are significantly weaker than those with monolayers containing cholesterol.10 Here, it is important to discuss the effect of the temperature on the simulated systems. The MARTINI force field is parametrized to accurately reproduce free energies with reduced degrees of freedom. That means that the entropy of the system is affected and then compensated by reduced enthalpic terms in the model. However, one limitation of this model is that the temperature dependence of properties is not, a priori, correct52 and can be interpreted from a qualitative point of view. In our case, the calculated ΔGmin and K values are consistent with the experimental data reported by Wnet̨ rzak and colleagues10 for the systems simulated at 300 K (DOPC and POPC). For the polyunsaturated bilayers, the behavior of the permeance values is consistent with the experiments done by Ogushi and colleagues.41 We also noticed that even at a higher temperature (323 K) the DPPC systems did not show higher permeance or K values, suggesting that in these models the entropic term is not the driving force. In summary, the good agreement with the experimental data suggests that our simulation results are reliable. In order to evaluate the interaction between MIL and CHOL, we calculated the PMF between these molecules in the 30% cholesterol DPPC system (Figure 6). The negative ΔG

Figure 7. PMF curve between MIL and CHOL, shown in Figure 6, directly influences the spatial organization arrangement of cholesterol molecules around miltefosine, as shown in (a). (b) Radial distribution functions (RDFs) of DPPC molecules around miltefosine resemble RDF curves typically encountered in conventional solute−solvent systems. (c) Cholesterol-DPPC RDF is much less sensitive to the cholesterol content in the DPPC bilayer. The “C2”, “R3”, and “C2A” beads in the MARTINI representations of MIL, CHOL, and DPPC, respectively (Figure 1a), were used to compute these RDF curves, since they are positioned at the same height above the DPPC bilayer center (see Figure S3 in Supporting Information).

Figure 6. Potential of mean force (PMF) for the MIL−CHOL interaction, simulated for the DPPC + 30% cholesterol system. The shade around the solid line represents the 1 standard deviation error calculated by bootstrapping. 4510

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Langmuir Author Contributions

primary peak in Figure 7a indicates stronger intermolecular attractions between MIL and CHOL than between MIL and DPPC (Figure 7b) or between CHOL and DPPC (Figure 7c). The RDF and PMF characterizing the interactions of CHOL molecules with other CHOL molecules are described in the Supporting Information. Our results show that MIL strongly interacts with CHOL in cholesterol-containing lipid bilayers, and this important finding could potentially form the basis for the drug’s mechanism of action. As a result of MIL−CHOL interactions, CHOL traffic from the plasma membrane to the endoplasmic reticulum is impaired, leading to an imbalance in CHOL esterification and signaling cell apoptosis.5 Accordingly, we hypothesize that MIL’s main mechanism of action is not related to an alteration in the membrane fluidity as previously suggested,8 but instead, it is based on the types of interactions between MIL and CHOL in biomimetic membranes that have recently been described by Alonso et al. and by Castro et al.7,9

M.M. and V.S. contributed equally. Funding

V.S. acknowledges funding from the MIT Energy Initiative Seed Fund Program. M.M. acknowledges funding from PDSECAPES/Science without Borders (Brazil, Process Number 9803-12-2), CNPq (Process Number 140927/210-7), and MIT. C.O.R.Y. acknowledges funding from FAPESP (Project Number 02189-8). Notes

The authors declare no competing financial interest.

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CONCLUSIONS The thermodynamic and kinetic behaviors of MIL in different lipid bilayers that we have observed in our simulations provides fresh insights into this molecule’s interactions with cellular membranes. Since we did not observe a significant change in the S2 order parameter of the alkyl chains of the bilayer-forming lipids considered, we hypothesize that MIL’s main mechanism of action is not related to alteration in the membrane fluidity. The strong interaction of MIL with CHOL, and MIL’s miscibility in cholesterol-containing lipid bilayers, points to the formation of stable complexes that hinder the transport of CHOL from the plasma membrane to the intracellular environment, signaling cell apoptosis. We have also observed that MIL has enhanced penetration into bilayer regions that are rich in polyunsaturated lipids, leading to the conclusion that passive diffusion is preferred, and flip-flop events are favored, in such regions. Our findings suggest a dual mechanism for miltefosine’s anticancer action based on interactions with lipid rafts and alteration in cholesterol traffic and facilitated translocation in loosely packed bilayer regions. Our findings also shed light on the selectivity of the cytotoxic action of MIL based on its strong preference for interacting with malignant cells that are either rich in cholesterol or in PUFAs.

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ASSOCIATED CONTENT

S Supporting Information *

Details regarding the parametrization of miltefosine consistent with the MARTINI framework, additional results describing the effects of miltefosine on bilayer organization, and the theory underlying permeation calculations for this system. This material is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.B.). *E-mail: [email protected] (C.O.R.Y.). Present Address

M.M.: Laboratory of Genetics and Molecular Cardiology Heart Institute (InCor), University of São Paulo Medical School, Avenida Dr Eneas de Carvalho Aguiar, 44, 10th floor, 05403000 São Paulo, SP, Brazil. 4511

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