Structural Effects and Translocation of Doxorubicin in a DPPC/Chol Bilayer: The Role of Cholesterol

Abstract

We use molecular dynamics simulations to characterize the influence of cholesterol (Chol) on the interaction between the anticancer drug doxorubicin (DOX) and a dipalmitoyl phosphatidylcholine/Chol lipid bilayer. We calculate the potential of mean force, which gives us an estimate of the free energy barrier for DOX translocation across the membrane. We find free energy barriers of 23.1 ± 3.1 k_BT, 36.8 ± 5.1 k_BT, and 54.5 ± 4.7 k_BT for systems composed of 0%, 15%, and 30% Chol, respectively. Our predictions agree with Arrhenius activation energies from experiments using phospholipid membranes, including 20 k_BT for 0% Chol and 37.2 k_BT for 20% Chol. The location of the free energy barrier for translocation across the bilayer is dependent on composition. As Chol concentration increases, this barrier changes from the release of DOX into the water to flip-flop over the membrane center. The drug greatly affects local membrane structure by attracting dipalmitoyl phosphatidylcholine headgroups, curving the membrane, and allowing water penetration. Despite its hydrophobicity, DOX facilitates water transport via its polar groups.

Introduction

Growing interest in liposomal drug delivery presents the problem of finding optimal liposome compositions (1–4). Finding the correct balance between efficacy and toxicity—one of the major obstacles in drug delivery—is dependent on accurate drug release profiles. A systematic knowledge of the effect of composition on release rate will provide greater control and help develop carriers optimized for particular drugs. Optimization of these liposomes requires a thorough understanding of basic molecular interactions within the liposomal membrane. Moreover, understanding the mechanism of drug translocation through lipid layers may shed light on transport processes across biological membranes. To pursue this goal, we study here the role of cholesterol on drug-bilayer interaction, including drug translocation and structural effects on the membrane. The dependence of transport on liposome composition has been studied experimentally for decades (5,6), however there remains a wealth of knowledge to uncover. Both theoretical and experimental efforts will be required to achieve a comprehensive understanding of drug-bilayer interaction. This work can help in the broader understanding of molecular transport in biological membranes, unmediated by proteins.

Doxorubicin (DOX) is an anticancer drug that has been studied for several decades (7,8) and is used clinically to treat a variety of cancers, including various types of carcinoma and sarcoma. Fig. 1 displays the structure of DOX, which consists of a hydrophobic anthracycline backbone, along with several active sites, including an amine group, ketone groups, and hydroxyl groups (9). It is thus largely hydrophobic with the ability for electrostatic interaction. The accepted mechanism of action for DOX is intercalation in the double helix of DNA, which prevents transcription. Because this mechanism is not specific to tumor cells, side effects such as the hand-foot syndrome have prevented more widespread use of the drug. To increase circulation time and decrease side effects through specificity, DOX has been formulated in liposomal drug carriers (2,10,11). The membrane of one these formulations, DOXIL, is composed of hydrogenated soy phosphatidylcholine (HSPC) and cholesterol (Chol).

Figure 1.

Chemical representation of neutral doxorubicin.

The membrane modeled in this study is a binary mixture of dipalmitoyl phosphatidylcholine (DPPC) and Chol, which we consider to represent the membrane of a liposomal drug carrier. DPPC contains two 16-carbon (palmitoyl) chains, as compared to 16-carbon and 18-carbon found in HSPC. DPPC is chosen for modeling because it is a common phospholipid, well studied both by simulation and experiment. The zwitterionic DPPC molecule contains a positively charged choline group and a negatively charged phosphate group. These headgroups are connected to the two saturated palmitoyl 16-carbon chains via a glycerol backbone. Cholesterol is short and rigid, essentially filling in the gaps between DPPC molecules. It has the power to decrease the membrane area per lipid, condense the membrane, and bring order to DPPC acyl chains at various temperatures (12,13). Additionally, the smooth α-face of cholesterol encourages the saturated chains of DPPC to straighten, further ordering and rigidifying the bilayer (14). Cholesterol is therefore included in liposomal drug carrier formulations to provide the rigidity necessary to prevent rapid drug leakage.

In this study, we characterize membrane structure and permeability at different Chol concentrations in the presence of DOX. Permeability is characterized by the free energy barrier necessary for the translocation of DOX across the membrane. This is found from the potential of mean force (PMF) of the drug calculated at many different positions throughout the membrane. The PMF tells us the amount of work needed for DOX to penetrate from the bulk water to a given depth in the membrane. We perform molecular dynamics (MD) simulations to calculate the potential of mean force, and to study changes in membrane structure as a function of both Chol concentration and DOX location. Simulations provide atomistic detail of bilayer structure, readily allowing the calculation of order parameters, radial distribution functions, density distributions, etc. Numerous MD simulations have been performed concerning molecular transport in membranes (15–23) including relatively large molecules such as drugs (24–30). Additionally, the dependence of DPPC flip-flop rate on cholesterol concentration has been investigated (31). In this study, we will use MD to predict translocation energy barriers and gain insight into the interaction between DOX, water, and a model membrane.

Methods

Molecular dynamics details

We used MD to study the interaction between DOX and a DPPC/Chol membrane. Lennard-Jones forces were calculated with a cutoff of 1.6 nm. Electrostatic forces were found using the particle mesh Ewald summation (32) with a real-space cutoff of 1 nm. We used GROMACS 4.0.5 (33) as the computational tool to perform MD. The GROMOS-based force field of choice is referred to as 43A1-S3 (34). Force field parameters (partial charges, bonding and nonbonding information) and structures for Chol and DPPC have previously been optimized for this force field by Chiu et al. (34). The structure of doxorubicin was taken from DrugBank (35). To maintain consistency, bonding and nonbonding parameters for all atoms on DOX were taken from the same force field as Chol and DPPC. Partial charges on DOX were found using the Hartree-Fock method and a 6-31G^∗ basis set, solved with the program Gaussian (36) (see Table S1, Fig. S1 in the Supporting Material for DOX partial charge specifications). All moieties containing oxygen, nitrogen, or phosphorous are represented in full atomistic detail. The 43A1-S3 force field applies the united atom model to all CH₂ and CH₃ groups. Water is explicitly represented by the simple point charge model (37).

All simulations were run in the isobaric-isothermal NPT ensemble, using a Berendsen thermostat with a relaxation time of 4 ps, and an anisotropic Berendsen barostat set to 1 atm and a relaxation time of 8 ps. The thermostat couples the system to a heat bath of 323 K, well above the phase transition temperature of the model DPPC at all relevant cholesterol concentrations. Anisotropic pressure coupling allows for membrane contraction and expansion independently in all dimensions.

Three systems were created with nearly identical numbers of lipids to measure the effect of DOX on the properties of compatible bilayers. Each system contained 1 DOX and ∼6500 waters. The pure DPPC system contains 128 DPPC molecules, the second system contains 110 DPPCs and 20 Chol molecules, and the third contains 94 DPPCs and 40 Chols. These systems therefore have mole fractions of 0% Chol, 15.4% Chol, and 29.9% Chol, which for convenience will be referred to as 0% Chol, 15% Chol, and 30% Chol, respectively. The size of the systems is ∼6 × 6 × 10 nm. Because of periodic boundary conditions, there are periodic images of DOX separated from one another in the xy plane by 6 nm. The long-range interaction cutoff of 1.6 nm ensures that DOX effectively will not see its periodic images. It has been shown experimentally that for DOX in particular, permeability is independent of drug concentration (38).

Initial configurations were created from a preconstructed bilayer composed of DPPC and Chol (39). To insert the drug, we decreased the density of the bilayer by manually stretching it in the xy plane. The drug was subsequently placed inside the stretched bilayer, which was then shrunk to its original dimensions. Incremental equilibration was performed with the steepest descent method, ranging from 1000 to 10,000 steps, and MD simulation ranging from 200 ps to 1 ns, which allowed for stability during expansion and shrinkage. Because the drug was not pulled, this procedure was repeated for each individual simulation. Data were collected after a minimum of 20 ns of further MD equilibration. The starting orientation for the drug was such that the anthracycline backbone was perpendicular to the bilayer normal. DOX cannot sample all configurations on the time scale of nanoseconds, thus an equilibrium state is not obvious, and the system may settle into a local free energy minimum.

Potential of mean force

Because DOX translocation is on the order of minutes (40), and MD simulations generally run on the order of 10–100 ns, we must force translocation in our simulations. We fixed the center of mass of DOX at 1 Å intervals from the center of mass of the bilayer (z = 0 nm) to the bulk water (z = – 3.7 nm), leading to 38 independently created simulations per Chol concentration. Because this constraint is only on the center of mass of the drug in the z direction, DOX can freely rotate and translate in the xy plane. The constraint is imposed by a very stiff spring having a tolerance of 2 × 10⁻⁶ nm, allowing a calculation of the force on the spring.

The PMF at each position z′ along the drug's path is represented here as ΔG(z′). Because the constraint between the drug and the membrane is only in the z direction, we can write the PMF (41) as

$$\Delta G\left(z^{\prime }\right)=\Delta G\left(z_0\right)-{\int }_{z_0}^{z^{\prime }}\langle F\left(z\right)\rangle dz.$$ (1)

The negative sign ensures that a positive, attractive force between DOX and the bilayer results in a decrease in the PMF. The mean force is denoted < F(z) >, and is calculated with the final 4 ns of constraint force data (4 × 10⁶ data points for a time step of 1 fs). A plot of the mean force of 0% Chol simulations can be found in Fig. S2. Errors on the mean force are the standard deviation of the mean forces of four 1 ns blocks making up the total 4 ns block (each corresponding to 10⁶ data points). We chose the bulk water as the arbitrary initial position z₀, because it is independent of composition, allowing us to easily compare the free energy profiles of the three systems. We defined the dimensions of the system with z′ = 0 in the center of the bilayer, and z′ = – 3.7 nm as the maximum distance from the bilayer, in the bulk water. The PMF then simplifies to

$$\Delta G\left(z^{\prime }\right)={\int }_{-3.7\text{nm}}^{z^{\prime }}\langle F\left(z\right)\rangle dz.$$ (2)

The PMF for each position z′ is thus exactly the work necessary to bring the drug from the bulk water to z′. In these calculations DOX is able to freely tilt and reorient. Steric hindrance may, however, bias DOX orientation and affect the calculation of the potential of mean force, meaning that this calculation is an approximate one and the error should be considered a lower bound. The error in PMF was found by propagating the constraint force error in the direction of translocation by summation.

Order parameters

To characterize order in the bilayer we use an average order parameter, <S_Z>, where

$$S_Z=\frac{1}{2}\left(3{\cos }^2{\theta }_i-1\right)$$ (3)

is the order parameter for carbon i. Here, θ_i is the angle between the vector bisecting carbons (i – 1) and (i + 1) and the (vertical) membrane normal, hence the subscript Z. The average order parameter for the carbons of all DPPC tails is given by

$$\langle S_Z\rangle =\frac{1}{2N}\sum _i^N\frac{1}{n}\sum _j^n{\left(S_Z\right)}_{i,j}.$$ (4)

Here, N is the total number of DPPC lipids, n is the number of carbons per acyl chain, excluding the first and last, and (S_Z)_{i, j} is the order parameter for carbon j in chain i. The factor of two is due to the two tails of DPPC. Perfect vertical orientation of the representative vector results in S_Z = 1, whereas perfect horizontal orientation results in S_Z = – 1/2, for a random distribution of angles <S_Z> = 0.

Results

DOX translocation

The potential of mean force is calculated for three systems composed of 0%, 15%, and 30% Chol, for which Chol has been shown (in the absence of DOX) to affect membrane structure and molecular interactions to significantly different degrees (31,42,43). As mentioned above, we calculate the PMF beginning with DOX in the bulk water and ending with DOX in the center of the bilayer (the values from the center of the bilayer to the opposing bulk water are assumed to be identical). Fig. 2 displays the three PMF curves. The general trends in the free energy landscapes are held in common between the three compositions. The drug begins in the isotropic water, experiencing a mean force (and PMF) of close to zero (Figs. 2 and S2). As DOX contacts the interface, the PMF characteristically decreases, indicating overall attraction between DOX and the bilayer. This decrease in free energy is attributed to the transfer of the hydrophobic drug from water to an increasingly hydrophobic environment, as well as the electrostatic attraction of DOX polar groups to charged DPPC headgroups. These attractions pull the drug into the position of the PMF minimum, at which point the mean force goes to zero. From here, movement of DOX in either direction requires energy to overcome the attraction of DOX to DPPC headgroups. Moreover, further penetration into the membrane requires an increase in free energy due to the steric hindrance from DPPC acyl tails and cholesterol. Movement of DOX back toward the bulk water is resisted due to hydrophobic/hydrophilic repulsion. Therefore, the PMF minimum indicates relative equilibrium for DOX along the constrained coordinate, where the instantaneous forces in both directions are, on average, equal. This position can be visualized with Fig. 3, A–C. Here, we see snapshots of DOX at the point of minimal free energy, which from Fig. 2 are ∼19, 25, and 26 Å from the bilayer center for 0%, 15%, and 30% Chol, respectively. Fig. 3 A shows that DOX prefers to partition mainly into the headgroups in a pure DPPC bilayer, whereas in Fig. 3, B and C we see DOX partition on the hydrophilic side of the interface. Fig. 3, D–F show DOX in the center of the bilayer, a region of high free energy. Note the ability of DOX to rotate around its center of mass.

Figure 2.

Potential of mean force, ΔG, as a function of the distance between the centers of mass of DOX and the bilayer (Z_DOX–BIL), for 0% (black line, bottom), 15% (blue line, middle), and 30% (red line, top) Chol systems. From left to right, the drug begins in the bulk water, penetrates into the center of the bilayer, and exits into the water on the opposite side. Calculations were performed on one side of the membrane, and assumed to be identical on the opposite side. The error is a propagation of mean force errors. Error bars omitted on the left side for clarity.

Figure 3.

Snapshots (A–C) show 0%, 15%, and 30% Chol systems with Z_DOX–BIL = −1.9, −2.5, and −2.6 nm, respectively, corresponding to the most likely position of DOX based on the free energy minima in Fig. 2, and (D–F) show the corresponding systems with the drug in the center. Representations include water (blue), DPPC nitrogen (purple), DPPC phosphorous (green), and Chol oxygen (red). DOX is shown in a van der Waals representation, with oxygen (red), hydrogen (white), nitrogen (blue), and carbon (teal). Note the various degrees of water penetration, and the horizontal Chol molecule bound to the drug in snapshot (E). DOX may act as a facilitator of cholesterol flip-flop.

To quantify the translocation process, we define the free energy barrier, or activation energy, as the difference in the PMF from the minimum to the highest maximum. We find free energy barriers of 23.1 ± 3.1 k_BT, 36.8 ± 5.1 k_BT, and 54.5 ± 4.7 k_BT for the 0%, 15%, and 30% Chol compositions, respectively. Based on Chol content, Table 1 compares our results with related experimental measurements. In terms of the dependence of energy barrier on cholesterol, our results are in qualitative agreement with experimental studies (40,44), as well as simulations of DPPC flip-flop (31). The systems in this study and those used by Regev et al. and Frézard et al. both involve phospholipid membranes and are in the liquid (liquid disordered) phase. We extracted the free energy barrier from the work of Regev et al. using the Arrhenius equation on their Arrhenius plot. The barrier found by Regev et al. is within our error margins in the case of 0% Chol, providing a very reassuring result. Additionally, the free energy barrier of 37.2 k_BT for a 20% Chol composition found by Frézard et al. is close to our 15% Chol measurement (44) (Table 1). Our results show self-consistency in the qualitative trend of these free energy barriers with Chol, and remarkable quantitative agreement with experimental results from similar systems. Constraint-biased MD has shown here its utility as a tool for measuring free energy barriers of molecular translocation.

Table 1.

Free energy barriers from MD simulations and experiments

Source	Composition (mol/mol)	Chol content	Activation energy
Regev et al. (40)	1:0 HSPC/Chol	0% Chol	20 kBT
Present work	1:0 DPPC/Chol	0% Chol	23.1 ± 3.1 kBT
Present work	11:2 DPPC/Chol	15.4% Chol	36.8 ± 5.1 kBT
Frézard et al. (44)	75:5:20 egg PC/PA/Chol	20% Chol	37.2 kBT
Present work	9.4:4 DPPC/Chol	29.9% Chol	54.5 ± 4.7 kBT

Membrane structure

The changes in structure induced by the presence of DOX were analyzed by the systems both visually and by quantifying a variety of properties. As seen in Fig. 3, D–F, DOX has the ability to dramatically distort the membrane interface. Consistent with previous observations of molecules embedded in bilayers, we see DOX attracting headgroups and allowing water penetration to varying degrees (22,31). Additionally, the drug appears to pull cholesterol into the center of the bilayer, perhaps facilitating cholesterol flip-flop (see Fig. 3 E). Despite its relatively large hydrophobic anthracycline backbone, DOX interacts electrostatically with water and DPPC headgroups, through its hydroxyl, ketone, and other polar sites (see Fig. 1). In Fig. 4 A, we see DOX in the hydrophobic core of the bilayer. This simulation contains 30% Chol, with DOX 1 Å from the center. In addition to electrostatics, this distortion is due in large part to the size of DOX, as it is large enough to interact with both leaflets, yet too small to span the bilayer, creating a sort of hydrophobic mismatch. Because of the symmetry of this distortion, the net force on DOX is low and contributes to the plateau in the 30% Chol curve in Fig. 2. Fig. 4 B shows the same snapshot as Fig. 4 A, with everything but DOX and water removed. By watching the trajectory of this simulation, we see water molecules bind to DOX for periods of time estimated on the order ∼1 ps. These waters move from one polar site on DOX to the next, and exit the bilayer into the bulk water in either direction. This observation illustrates the ability of DOX to induce water pores or fingers and facilitate water translocation.

Figure 4.

Snapshot of DOX in 30% Chol, with Z_DOX–BIL = −0.1 nm. (A) DOX causes membrane curvature on both sides of the membrane by attracting DPPC headgroups from both leaflets. (B) Shows (A) with everything removed except the drug and water, showing water translocation. Snapshots are rendered as in Fig. 3, with DOX reduced in thickness to show its structure and interaction with water.

We analyzed this phenomenon graphically with a comparison of species density distributions between the system shown in Fig. 4 A and that of the same bilayer without DOX present. Fig. 5 B shows the density profile for the 30% Chol system without DOX, showing a clear region of bilayer interior free of headgroups and water. With DOX in the center of the bilayer, Fig. 5 A shows a finite density of water throughout the bilayer, and headgroups venturing closer to the bilayer center. The asymmetric water density profile is due to the asymmetric shape and irregular distribution of polar sites of DOX. There is also a general broadening of density distributions for the representative headgroup atoms of DPPC and Chol in the presence of DOX (Fig. 5 A).

Figure 5.

Number density profiles in 30% Chol bilayers with DOX (A), see Fig. 4, and without DOX (B). Colors correspond to Figs. 3 and 4. Representations include water (blue), DPPC nitrogen (purple), DPPC phosphorous (green), Chol oxygen (red), and DOX (black). Note the penetration of water and a general broadening of the head-group atom densities in the presence of DOX.

To understand the influence of DOX on membrane structure, we analyzed local and global changes in the average DPPC acyl chain order parameter, <S_Z>. Fig. 6 A shows this parameter for local (within a 1.75 nm shell around DOX center of mass) and global (beyond the shell) regions, split into the leaflet containing DOX and the opposing leaflet, for 0% Chol. The order of the system decreases very slightly beyond the local shell, and very significantly within the shell as DOX penetrates to the bilayer center. Additionally, based on the similarity of the linear regressions, both local and global orders are strongly coupled between the leaflets. The local order is higher than the global order for DOX positioned in the outer region of the hydrophobic-hydrophilic interface. Though the extent of local versus global order in Fig. 6 depends slightly on the definition of the local shell, the observations above hold for shell defined up to at least 3 nm (data not shown), and the results are qualitatively identical for the 15% and 30% Chol systems (shown in Fig. S3).

Figure 6.

(A) Average DPPC order parameters, <S_Z>, as a function of DOX-bilayer distance, Z_DOX–BIL. To elucidate structural effects of DOX, the bilayer is split into four regions, as denoted in the legend of (A) and the corresponding colored regions of snapshot (B). Open data points account for DPPC with phosphorous within a 1.75 nm shell of the drug in the xy plane, while solid points are for chains beyond the shell. The simulation shown in (B) thus contributes the four data points at Z_DOX–BIL = −0.9 nm in (A). Lines are regressions as a guide for the eye. Note strong coupling between leaflets, even with DOX far from the center.

As the drug enters further toward the center, it slightly expands the bilayer. Fig. 7 shows the area per lipid of each system as a function of drug depth, with the area being that of the xy plane. The area per lipid of the systems without DOX are shown as dashed lines, with values of 63.9, 53.9, and 46.2 Å²/lipid for the 0%, 15%, and 30% Chol systems, respectively. These values agree with findings of other studies (43), as do deuterium order parameters for the drug-free systems (Fig. S4) (13,42). We see DOX cause changes in the area per lipid on the order of 10% in our 6 × 6 nm systems.

Figure 7.

Area per lipid as a function of the distance between the center of mass of DOX from the center of the bilayer, Z_DOX–BIL. Dashed lines correspond to the area per lipid calculated in DOX-free systems.

Discussion

An interesting implication of Fig. 2 is that the limiting physical barrier of DOX translocation changes with bilayer composition. Experimentally it has been assumed that the rate determining step in translocation is flip-flop from one leaflet to the other (38,40). In other words, this leaflet-leaflet barrier (over the center of the bilayer), has been assumed to be much greater than the leaflet-bulk barrier (release of DOX into the water). Fig. 2 shows that for both 15% and 30% Chol, this is what we predict, as the highest PMF maximum is at the center of the bilayer. In the absence of cholesterol, the highest maximum in the PMF is in the bulk water. Flip-flop is therefore not the rate determining step in our pure DPPC/DOX system, meaning DOX moves from one leaflet to the other frequently compared to its release from the interface. A rough estimate of the ratio of rate constants of DOX flip-flop, k_flip–flop, to DOX release into the bulk water, k_release, can be obtained from the difference in free energy barrier between the two processes. Namely, it is given by

$$\frac{k_{\text{flip}-\text{flop}}}{k_{\text{release}}}=\text{exp}\left[-\left(\Delta G_{\text{flip}-\text{flop}}-\Delta G_{\text{release}}\right)/k_{\text{B}}T\right].$$ (5)

On the basis of the results presented in Fig. 2, DOX flip-flops on the order of 10³ times per release in the absence of Chol. Because Chol alters the physical barrier, DOX flip-flops only once every 10⁹ times it is released to the water in the case of 15%, and once every 10¹⁶ times for 30% Chol.

A key aspect of the change in maximal free energy barrier is the effect of membrane structure on the most probable position of DOX. Fig. 3 A shows that, in the absence of cholesterol, DOX prefers to partition within the headgroups of DPPC. Fig. 7 shows, as is well known, that the area per lipid depends heavily on Chol concentration. As the area per lipid decreases with added Chol, an increasingly dense bilayer prevents DOX from positioning itself on the inside of the interface (Fig. 3, B and C). This effectively reduces the depth at which the net force between DOX and the bilayer is attractive, thus raising the PMF minimum and decreasing the leaflet-bulk free energy barrier from 0% to 15% Chol and from 15% to 30% Chol (Fig. 2). Likewise, as the area per lipid decreases, the membrane resists entry of DOX into the membrane interior. The steep slope in the 30% Chol PMF curve, rising from the PMF minimum to the bilayer center, corresponds to a highly negative, repulsive force, between the bilayer and DOX. This repulsion increases the leaflet-leaflet free energy barrier with increasing Chol. By condensing the bilayer, cholesterol thus has the ability to induce a transition in the dominant physical barrier, as it causes both a decrease in the leaflet-bulk barrier and an increase in the leaflet-leaflet barrier. We postulate that transitions of this nature will predict the Chol concentration at which abrupt changes in membrane properties are observed. As an example, Rebolj et al. have seen ostreolysin membrane activity jump dramatically at 30% Chol, associated with the creation of a liquid-ordered domain (45).

We observe in our simulations, i.e., Fig. 4, the specific effects of the shape, size, and chemical structure of doxorubicin on membrane structure. Fig. 7 shows that, with respect to the area per lipid without DOX, the drug generally induces a decrease in the total area per lipid on the hydrophilic side of the interface. This observation is accompanied by an increase in local DPPC order (Fig. 6). We explain this finding with Fig. 3, B and C, which show DOX horizontal, above DPPC headgroups. The electrostatic attraction of DOX polar groups to the zwitterionic DPPC headgroups encourages the lipids to aggregate closer than they otherwise would, decreasing the area per lipid and compacting DPPC tails. Fig. 6 shows that even with DOX over 2 nm from the opposing leaflet, DPPC order is virtually paralleled between leaflets, indicating a very strong, short-range interleaflet coupling in lipid order.

It is worth noting the implications of these results on the question of whether DOX is charged during translocation. Several simulation studies have discussed the effect of charge on molecular translocation (25,28,30). Charge has a dramatic effect on the potential free energy barrier in all of these studies, making the question pressing. In general, charging a molecule will change the barrier from leaflet-leaflet to leaflet-bulk or vice versa. Our calculations of the free energy barriers found for the neutral doxorubicin molecule agree well with values found experimentally (40,44). Thus, DOX is most likely neutral as it travels through the membrane, otherwise our results would likely be in dramatic disagreement.

Conclusions

We have analyzed the potential of mean force characterizing the translocation of doxorubicin across a DPPC/Chol membrane. Free energy barriers of 23.1 ± 3.1 k_BT, 36.8 ± 5.1 k_BT, and 54.5 ± 4.7 k_BT have been found for 0%, 15%, and 30% Chol, respectively. However, the effect of cholesterol on DOX translocation is not only quantitative. Beneath these values lies a qualitative transition in the mechanism of translocation. In the cases of 15% to 30% Chol, the maximum in the free energy is in the center of the bilayer, in agreement with the belief in flip-flop-limited translocation. However, in the case of 0% Chol, the free energy maximum is in the bulk water, and the limiting step in translocation is then the release of DOX into the bulk water. Thus, not only does DOX prefer to be inside the bilayer without cholesterol present, it actually flip-flops very rapidly (10³ times faster) compared to its release from the bilayer.

Doxorubicin is a relatively large, complex drug with many polar sites, for which molecular volume is indeed not the only factor in translocation and membrane deformation. This is shown most dramatically in Fig. 4, where the attraction of DOX active sites to DPPC deforms the bilayer and allows water penetration. Based on Fig. 6 we estimate the propagation of DPPC disorder to dissipate 2–4 nm from the drug. Constrained MD provides a thought-provoking and applicable tool in the study of molecular transport across model membranes. It will be interesting to investigate the interactions between various drugs and lipid compositions. By measuring the most optimal drug depth, we can determine the dominant physical barrier, characterize drug hydrophobicity, and ultimately gain insight into the nature of drug-bilayer interaction. Both theoretical and experimental methods will be required to comprehensively understand drug-bilayer interactions in liposomal drug carriers. This study represents one step in the effort to predict drug-release profiles and optimize the composition and design of liposomal drug carriers. Small changes in liposome composition may provide more accurate release profiles for specific drugs.