All-Atom Molecular Dynamics Study of a Spherical Micelle Composed

Oct 26, 2009 - An all-atom molecular dynamics simulation of a spherical micelle composed of amphiphilic N-acetylated poly(ethylene glycol)-poly(γ-ben...
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J. Phys. Chem. B 2009, 113, 15181–15188

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All-Atom Molecular Dynamics Study of a Spherical Micelle Composed of N-Acetylated Poly(ethylene glycol)-Poly(γ-benzyl L-glutamate) Block Copolymers: A Potential Carrier of Drug Delivery Systems for Cancer Hiroshi Kuramochi,*,† Yoshimichi Andoh,‡ Noriyuki Yoshii,§ and Susumu Okazaki‡ Pharmaceutical Research Laboratories, Nippon Kayaku Co., Ltd., Tokyo 115-8588, Japan, Department of Applied Chemistry, Graduate School of Engineering, Nagoya UniVersity, Nagoya 464-8603, Japan, and Department of Pharmacy, Himeji Dokkyo UniVersity, Himeji 670-8524, Japan ReceiVed: June 30, 2009; ReVised Manuscript ReceiVed: September 29, 2009

An all-atom molecular dynamics simulation of a spherical micelle composed of amphiphilic N-acetylated poly(ethylene glycol)-poly(γ-benzyl L-glutamate) (PEG-PBLG-Ac) block copolymers was performed in aqueous solution at 298.15 K and 1 atm. Such copolymers have received considerable attention as carriers in drug delivery systems. In this study, we used copolymers consisting of 11 EG units and 9 BLG units as models. Starting from the copolymers arranged spherically, the calculation predicted an equilibrium state consisting of a slightly elliptical micelle structure with a hydrophobic PBLG inner core and a hydrophilic PEG outer shell. The micelle structure was dynamically stable during the simulation, with the PEG blocks showing a compact helical conformation and the PBLG blocks an R-helix form. Multiple hydrogen bonds with solvent water molecules stabilized the helical conformation of the PEG blocks, leading to their hydration as shown by longer residence times of water molecules near the PEG ether oxygen atoms compared with that of bulk water. Some water molecules have also been found distributed within the hydrophobic core; they showed continuous exchange with bulk water during the simulation. Those molecules existed mostly as a cluster in spaces between the copolymers, forming hydrogen bonds among themselves as well as with the hydrophobic core through hydrophilic groups such as esters and amides. The water molecules forming hydrogen bonds with the micelle may play an important role in the stabilization of the micelle structure. Introduction Amphiphilic copolymers are known to assemble into nanosized polymeric micelles in aqueous solution.1-4 These copolymers provide physical, chemical, and biological functions that make them well suited for various applications. In particular, their use for biomedical applications such as drug delivery has grown rapidly in recent years.5,6 The multifunctional nature of polymeric micelles appears to fulfill several requirements for an ideal carrier to be used in drug delivery systems (DDS): they function to solubilize drugs, transport the drugs to a target tissue, and then release them. Kataoka et al. have shown that the amphiphilic block copolymers composed of a hydrophilic poly(ethylene glycol) block and a hydrophobic poly(L-amino acid) block (PEG-PLAA) are useful as DDS carriers for anticancer drugs.7,8 These block copolymers may self-assemble in aqueous solution to form nanosized micelles with a hydrophobic inner core of PLAA blocks and a hydrophilic outer shell of PEG blocks. Because most solid tumors possess unique pathophysiological characteristics such as extensive angiogenesis, defective vascular architecture, and an impaired lymphatic drainage/recovery system, these nanosized micelles are expected to accumulate in tumor tissues. This characteristic is known as the enhanced permeability and retention effect (EPR effect).9 There are free functional groups such as carboxyl and amine on a PLAA block, providing sites for the attachment of drugs and for hydrophobic moieties that enhance hydrophobic proper* Corresponding author. E-mail: [email protected]. † Nippon Kayaku Co., Ltd. ‡ Nagoya University. § Himeji Dokkyo University.

ties. Thus, PEG-PLAA micelles can encapsulate drugs in the inner core with relatively high stability by chemical conjugation or by physical entrapment.10-14 Block copolymers with poly(aspartic acid) or poly(glutamic acid) as the PLAA block of the PEG-PLAA copolymer have been reported where hydrophobic compounds such as benzyl alcohol15,16 and 4-phenyl-1butanol17 or drugs such as doxorubicin,11,18 7-ethyl-10-hydroxycamptothecin,19 and cisplatin20 are conjugated to the carboxylic acid of Asp or Glu. The polymeric micelles composed of these block copolymers that encapsulate anticancer drugs have been found to have significant anticancer activity; some of them are now under clinical evaluation.21 Polymeric micelles are advantageous as drug carriers compared with low molecular weight surfactants that are well-known to form micelles that solubilize hydrophobic drugs. To understand how the polymeric micelles hold drugs, transport them in blood, and release them in target tissues, it is very important to clarify the structure of the micelles. Most of the PEG-PLAA micelles designed and used for drug delivery, as observed by atomic force microscopy, dynamic light scattering, scanning electron microscopy, and transmission electron microscopy, are reported to be spherical and usually have sizes in the range of several tens of nanometers.13,22-24 There are, however, few experimental investigations on a more detailed characterization of the structure of such micelles using techniques such as smallangle X-ray scattering (SAXS) and small-angle neutron scattering (SANS). Recently, computer simulation has emerged as a powerful tool for investigating the static and dynamic structure of micelles. Molecular dynamics (MD) simulation has been widely

10.1021/jp906155z CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009

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utilized to characterize the micellar structure of ionic and nonionic surfactants such as sodium dodecyl sulfate and poly(ethylene glycol) alkyl ether, where atomistic models with explicit water molecules have been employed.25-32 These are the most sophisticated models available. On the other hand, for micelles composed of block copolymers, coarse-grained and dissipative particle dynamics models have been used to simulate the self-assembly behavior because of the large system size required.33-38 In these models, several atoms or sections of chained radicals are represented by a single computational particle; therefore, it is impossible to clarify the interactions among the copolymers and water at the atomic level. Because there is a significant difference in the way surfactant micelles and polymeric micelles function as drug carriers, sophisticated MD simulations based upon an all-atom model are necessary for the characterization of a polymeric micelle to provide a valid comparison. However, to our knowledge, no all-atom explicit solvent MD simulation has been reported for a polymeric micelle composed of amphiphilic block copolymers. In the present study, we have carried out an MD simulation for the N-acetylated poly(ethylene glycol)-poly(γ-benzyl Lglutamate) (PEG-PBLG-Ac) block copolymer, which was selected as a model polymer or prototype of PEG-PLAA copolymers that were developed by Kataoka et al.7,8 Similar copolymers are known to be useful as drug carriers. In the model copolymer, the PBLG block consists of nine monomer units with which the copolymer has been confirmed to form a micelle. Due to limited computer resources, the PEG block was truncated to 11 monomer units (MW ) 0.5K), from the number of units in the actual carrier (MW ) 5K or 12K). Because the aggregation number of the spherical micelles had not been determined experimentally, we adopted 20 as the aggregation number, which had been estimated from a preliminary SECMALLS analysis for the same type of copolymers. Our purpose is to acquire fundamental information about the micelle structure formed by PEG-PBLG-Ac polymers, i.e., the shape, the interaction between the polymers and in particular between the hydrophobic blocks, the hydration of the hydrophilic blocks, and water penetration into the hydrophobic core. Calculations We adopted an all-atom model throughout this work. For PBLG-Ac, we used the CHARMM22 all-hydrogen parameters.39,40 The PBLG block was formed by connecting γ-benzyl Lglutamate (BLG) residues through peptide bonds. The force constants and charges of BLG residues were determined as follows: The BLG residue was constructed from a backbone unit containing β-carbon (BB), methylacetate (MAS), and benzene (BENZ). The atom types and charges of BB are common to all the amino acids in CHARMM22. MAS and BENZ are model compounds that are used in the development of the CHARMM22 protein all-hydrogen parameters, and therefore, their atom types and charges have already been assigned. This information is included in the CHARMM22 parameter files. BB, MAS, and BENZ were linked by deleting extra hydrogen atoms to build a BLG residue. The atom types of the BLG residue were transferred from BB, MAS, and BENZ. The force field parameters were determined using these atom types. The charges of BLG residues were also transferred from BB, MAS, and BENZ with the charge adjustment of the linking atoms according to MacKerell et al.39 In CHARMM22, most of the amino acid residues are constructed from BB and one model compound corresponding to the side chain structure. For amino acid residues with large side chains, such as ARG and

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Figure 1. Structure of PEG-PBLG-Ac copolymer.

LYS, two model compounds are used to construct these side chains. This is the same procedure used for the construction of the BLG residue in the present study. For PEG, we used the same force field as Tasaki, initially parametrized for a single PEG chain in water.41 We used the SPC model of water for consistency with the Tasaki study. MD simulations were performed in the NPT ensemble at P ) 1 atm and T ) 298.15 K using the algorithm proposed by Martyna et al.42,43 One spherical micelle formed by 20 PEG-PBLG-Ac copolymers and 47 885 water molecules was contained in a cubic cell in a periodic boundary condition such that the number of atoms in the total system was 150 715. The SHAKE/ROLL and RATTLE/ROLL algorithms were used to impose constraints on the bond length with respect to hydrogen atoms.42 The particle mesh Ewald (PME) method was used for calculation of electrostatic interactions.44 Nonbonded LennardJones and real space electrostatic interactions were truncated at rc ) 12 Å. The PME parameters were chosen to maintain the relative error in electrostatic interactions smaller than 10-5. For this purpose, we used a convergence parameter R ) 0.32 Å-1 and a 150-point grid in each Cartesian direction to account for the PME charge interpolation. The MD integration time step was 1 fs, which ensured a relative fluctuation of the total energy smaller than 10-4. We constructed an initial intramolecular conformation of PEG-PBLG-Ac as follows. PBLG-Ac, consisting of nine γ-benzyl L-glutamate residues with an acetylated N-terminal, was modeled in an R-helix conformation and coupled to a random-coiled PEG (11 units of EG) through a -CH2CH2NHlinking group, resulting in a copolymer having the structure shown in Figure 1. Because it is well-known that PBLG tends to adopt an R-helix conformation,34,45 the conformation of PEG in the copolymer was searched by a simulated annealing method with PBLG fixed. We heated the system consisting of one copolymer and 3011 water molecules to T ) 1000 K. Then, we chose one conformation to be quenched to T ) 1.0 K for the initial configuration. The preparation and the equilibration procedure of the spherical micelle were as follows: the PEG-PBLG-Ac copolymers with the conformation obtained by simulated annealing were used for the construction of the spherical micelle. The aggregation number was 20, which was estimated from a preliminary SEC-MALLS analysis for the same type of copolymers. Twenty copolymers were arranged spherically such that they did not collide with each other, with the Ac-terminal of each copolymer pointing toward the center. As a result, a hollow region approximately 30 Å in diameter was generated in the center. Subsequently, the system was inserted in a 120 Å cubic box filled with 47 885 water molecules, where no water molecules were placed within the PBLG-Ac and the hollow regions. After minimization of the system by the steepest descent method, the temperature was increased from 0 to 298.15 K, with the carbon atom of the innermost terminal acetyl group harmonically bound to the geometrical center. Following this step, the harmonic binding potential was released, and the system was equilibrated for 3 ns. The simulation was continued for

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Figure 2. Change in a 0.2 ns block average of the potential energy of the system during the simulation. Figure 5. Density distribution with respect to the center of mass of the micelle.

Figure 3. Change in the ratio between the principal moments of inertia during the simulation.

Figure 4. Initial and final structures of the micelle in the 7 ns simulation. PEG blocks are shown in pink, and individual PBLG-Ac blocks are distinguished by color. Water molecules are not shown.

another 4 ns to extract statistical data. A symmetric multiple processing (SMP) computer (HITACHI SR-11000) was used with parallel computing techniques for this MD simulation. Results and Discussion We performed MD simulation for the system including 20 PEG-PBLG-Ac polymers and 47 885 water molecules in an all-atom model; the total number of atoms was 150 715. The time required for the potential energy of the system to become almost constant was 3 ns (Figure 2). During this equilibration process, the initial spherical micelle changed to one with a slightly elliptical shape with the average ratios of the principal moments of inertia, I1/I3, I2/I3, and I1/I2, of 1.23 ( 0.05, 1.09 ( 0.03, and 1.13 ( 0.05, respectively (Figure 3). The hollow region in the center was filled with the hydrophobic blocks (PBLG-Ac) of copolymers and disappeared (Figure 4). The hydrophilic blocks (PEG) folded further, becoming shorter. After 3 ns, no large change was observed either in the potential energy

or in the micelle structure. Thus, we collected the simulation data for the analysis over a period of 3-7 ns. Density Distribution of the Micelle Group. We then analyzed the micelle structure in terms of the density of selected groups as a function of the distance from the center of mass. The system was separated into four groups: hydrophobic (PBLG-Ac), linker (-NHCH2CH2-), hydrophilic (PEG), and water. The hydrophobic region formed a core in the interior of the micelle with a density of 1.0-1.5 g/cm3, and its density decreased between 20 and 30 Å (Figure 5). The densities of the linker and the hydrophilic region were nonzero in the range of 18-29 and 21-41 Å, respectively, indicating that each copolymer moved inside or outside to avoid collisions between the copolymers and together formed an aggregate with a hydrophobic inner core and a hydrophilic outer shell. The water density increased sharply from 14 to 30 Å and gradually thereafter; however, it also had a small but nonzero value between 3 and 14 Å, indicating that water molecules had penetrated somewhat into the hydrophobic region. Figure 5 also shows the density of the benzyl group in the hydrophobic region. The group tended to concentrate near the center of the micelle, which agrees with the concept that this group is a key component in the hydrophobic interaction. Hydrophilic Region. The PEG chain maintained a helical conformation during the present calculation. The probability distributions of the dihedral angles of the PEG chain in the micelle are plotted in Figure 6. Only dihedral angles internal to the chain were considered, i.e., 8 C-C and 17 C-O dihedral angles per chain. The average total gauche (gauche+ and gauche-) populations for the C-C and the C-O bonds were 1.0 (g+ ) 0.37 and g- ) 0.63) and 0.06 (g+ ) 0.03 and g- ) 0.03), respectively. This result is in good agreement with both the NMR study (0.9 and 0.1, respectively) and the MD simulation study (1.0 and 0.06, respectively) for a PEG chain in water. This indicates that the conformation of the PEG chain is not affected either by the PBLG block of the block copolymer or by the adjacent PEG chain separated by water molecules in the micelle structure. A direct visualization of the micelle during the MD simulation showed that the PEG chains were distributed inhomogeneously in the micelle structure but were not entangled. The pair distribution functions (PDFs) for the PEG ether oxygen atom and the nearby water oxygen atoms were calculated separately for the ether oxygen of each EG unit (hereinafter, E1 refers to the innermost EG unit, E2-E10 to the central units, and E11 to the outermost EG unit). The PDFs obtained showed almost the same pattern for all EG units, with the first peak at 2.68-2.73 Å and the second peak at 4.68-4.78

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Figure 6. Population distributions for the dihedral angles of the PEG blocks.

TABLE 1: Peak Positions Obtained from Pair Distribution Functions for PEG Oxygen-Water Oxygen and PEG Oxygen-Water Hydrogen OPEG-Owater PDF

OPEG-Hwater PDF

first second water molecules first second third unit peak, Å peak, Å within 3.25 Å peak, Å peak, Å peak, Å E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11

2.68 2.73 2.73 2.73 2.73 2.73 2.73 2.73 2.73 2.73 2.68

4.78 4.78 4.78 4.68 4.73 4.68 4.73 4.73 4.73 4.73 4.73

1.68 1.86 2.15 2.10 1.89 2.01 1.94 1.94 1.99 1.90 1.97

1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.73 1.68

2.53 2.48 2.38 2.38 2.53 -

Figure 7. Representative pair distribution functions for (a) PEG oxygen-water oxygen and (b) PEG oxygen-water hydrogen.

3.13 3.23 3.23 3.23 3.33 3.23 3.33 3.18 3.28 3.18 3.18

Å (Table 1 and Figure 7a), although the peak height of the E1 unit was lower than those of the other units. The number of water molecules associated with each EG unit, which was obtained by integrating the distribution curve to the first minimum at 3.25 Å, was approximately 2 (1.86-2.15) for E2-E11 units and 1.68 for the E1 unit. The first number, 2, corresponds to the number of lone pairs of the ether oxygen, indicating that a network of hydrogen bonds was formed around the PEG ether oxygen atoms. The number for the PDF of the E1 unit is lower than that for the others, which is consistent with the decrease in water density near the hydrophobic region. On the other hand, the PDFs for the PEG ether oxygen atom and the nearby water hydrogen atoms indicate that there is a significant difference in the hydrogen bonding of each ether oxygen (Table 1 and Figure 7b). The PDFs for E3, E4, E6, E8, and E10 have a peak at 2.38-2.53 Å in addition to the peaks at 1.73 and 3.18-3.23 Å that are also seen in the other PDFs, indicating that there are at least two types of hydrogen bonds. Previous studies have shown that the gauche effect on the C-C bond dihedral angles of the PEG chains is closely related to the presence of hydrogen bond bridges between ether oxygen groups.41 In a single long PEG chain in aqueous solution, two

Figure 8. Hydrogen bond network in the hydrophilic PEG region of the micelle. Hydrogen bonds are indicated by dotted blue lines and the distances between PEG oxygen and water hydrogen in black lines.

different bridges were observed: (a) bridges formed by a single water molecule connecting an ether oxygen atom to one of its second neighbors along the backbone and (b) bridges formed by two water molecules connecting ether oxygen atoms two units apart. We observed essentially the same types of bridges in the micelle structure, but we also found a more complex hydrogen bond network (Figure 8). Two types of water molecules interacted with the PEG oxygen atom: for one type (W1 and W4), only one hydrogen atom formed a hydrogen bond with a PEG oxygen atom, and for the other (W2 and W5), both hydrogen atoms formed hydrogen bonds to bridge two PEG oxygen atoms separated by two EG units (bridge a). The other hydrogen atom of the former type can form a hydrogen bond with the oxygen atom of the latter type, resulting in bridge b (W4). Furthermore, there is a third type of water molecule (W3)

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Figure 9. Time dependence of the average number of water molecules near the PEG ether oxygen of E1, E5, E6, and E11 units.

that formed hydrogen bonds with two water molecules of the latter type, resulting in a hydrogen bond network consisting of three water molecules and four PEG oxygen atoms, which may contribute to the stability of the compact helical conformation of the PEG chains. In the case of bridge a, both hydrogen atoms of the water molecule (forming hydrogen bonds with the two PEG oxygen atoms one EG unit apart) were oriented toward the PEG oxygen atom in the middle of the three EG units. The distance between the hydrogen atoms and the PEG oxygen atom was about 2.5 Å, which corresponds to the second peak of PDFs for E3, E4, E6, E8, and E10 (Table 1 and Figure 7b). Therefore, the water molecule may interact with three PEG oxygen atoms in three successive units, supporting the helical conformation of the PEG chain. The average residence time of water molecules in proximity to the PEG oxygen was evaluated by following the time variation of the distance between the two oxygen atoms, i.e., a water oxygen atom and a PEG oxygen atom. When the distance was less than 3.5 Å, the water molecule was considered to be near the PEG oxygen, such that a hydrogen bond could be formed. The average number of water molecules near the PEG oxygen at both times 0 and t was computed for each PEG oxygen atom and was plotted as a function of t. In Figure 9, the plots for PEG oxygen atoms at E1, E5, E6, and E11 units in PEG chains are shown as representative cases. Eleven plots were fitted with a linear combination of exponential functions. All eleven curves are well fitted by a linear combination of just two exponential functions. The residence times of the first decay (τ1) and the second decay (τ2) range from 25 to 69 ps and 131 to 452 ps, respectively (Table 2). Even the first decay was much slower than that of the hydrogen bonds in bulk water (τ ∼ 3 ps) (as calculated from a bulk water simulation), indicating preferential hydration of the PEG chain. Both τ1 and τ2 for the external units (E10 and E11) were shorter than those for the other units, indicating that the water molecules hydrogen bonded to E10 and E11 units dissociate rapidly into bulk water, as expected. The τ2 for the innermost unit (E1) was also short, which can be related to the lower probability of hydrogen bond formation caused by the adjacent hydrophobic region. It should be noted that τ2 had a maximum at the E3 unit and decreased as the unit moves outside, indicating that the water molecules near the internal EG units may be maintained around the PEG chain during a time interval on the order of nanoseconds. Interestingly, there is a regular variation in the ratio of n1 to n2 and the presence of the second peak in the PDF for PEG oxygen atoms and water hydrogen atoms. Because the second peak appeared for only E3, E4, E6, E8, and E10, the bridge with a water molecule was mainly formed between E2 and E4,

unit

n1

τ1 (ps)

n2

τ2 (ps)

E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11

0.98 0.74 0.59 0.55 0.28 0.92 0.39 0.92 0.72 0.86 1.30

43.1 44.6 34.7 30.8 53.7 38.8 69.4 41.6 44.2 25.2 25.7

0.68 1.20 1.59 1.56 1.65 1.07 1.55 0.99 1.27 1.09 0.64

281.3 376.6 452.1 448.8 397.0 329.8 362.2 305.3 267.9 131.4 150.1

a Computed by fitting the time dependence of the average number of water molecules near each PEG ether oxygen with two exponential functions, n1 exp(-t/τ1) + n2 exp(-t/τ2).

E3 and E5, E5 and E7, E7 and E9, and E9 and E11. Thus, the hydrogen bond pattern for E6, E8, and E10 is expected to be different from those of the others, particularly E5, E7, and E9, leading to the differences in dynamical behavior among them. Hydrophobic Region. The hydrophobic block is a polypeptide consisting of γ-benzyl L-glutamate residues, where the N-terminal end is acetylated. The backbone of polypeptides can adopt different conformations (R-helix, β-sheet, and random coil) depending on the number and kind of amino acid residues. Because the PBLG block tends to adopt an R-helix conformation35,45 and the polypeptides in a hydrophobic environment, such as membrane proteins, form an R-helix structure, we selected an R-helix as the initial conformation of the PBLG block. The Ramachandran plot and ribbon diagram of the PBLG block after a 7 ns simulation are shown in Figure 10. Most of the PBLG block had an R-helix conformation at that time, indicating that its conformation was not affected in the aggregation process from the initial structure that had a hollow region approximately 30 Å in diameter. Hydrogen bonds were formed not only with the backbone of the polypeptide but also between the NH group of the backbone and the carbonyl group of the benzyl ester, resulting in the formation of six to eight hydrogen bonds in the same hydrophobic chain. Thus, in the micelle structure, the hydrophobic core may be considered as being constructed of rigid, instead of flexible, rods. The side chains of the polypeptide, particularly the benzyl groups, covered the surface of the hydrophobic region and were in contact with those of the neighboring chains, resulting in a van der Waals or π-π interaction between the phenyl rings in the neighboring chains. In addition, hydrogen bonds were found between the NH group of one chain and the carbonyl group of the benzyl ester of the other chains. These interactions, as well as the so-called hydrophobic effect, are assumed to contribute to the stability of the micelle structure. The density profile for water demonstrates that a small amount of water was present within the hydrophobic region, which constantly redistributed in the region during the simulation. These water molecules existed mostly as a cluster in the space between the PBLG blocks. The clusters consisted of several water molecules that form a hydrogen bond network among them. The water molecules also formed hydrogen bonds with the hydrophobic core through hydrophilic groups such as esters and amides in the core (Figure 11). We evaluated the average residence time of the water molecules in contact with the hydrophobic region, following the time evolution of the distance between the oxygen atom of water and any atom of the hydrophobic region. When the distance was less than 3.5 Å,

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Figure 10. Ramachandran plot (left) and ribbon diagram (right) of PBLG block after the 7 ns simulation.

Figure 11. Hydrogen bond network in the hydrophobic core of the micelle.

Figure 12. Time dependence of the average number of water molecules that are in contact with the hydrophobic region.

the water molecule was considered to be in contact with the hydrophobic region. The average number of water molecules in contact with the hydrophobic region at both times 0 and t was computed and was plotted as a function of t (Figure 12). The plot was well fitted with a linear combination of three exponential functions, and the water residence times obtained were 28, 230, and 1810 ps for the first, second, and third decay, respectively. The number of water molecules associated with each decay was 271, 273, and 119, respectively. Although the process of dissociation of water molecules from the hydrophobic region appears to not be so simple as implied by the use of

three exponential functions, these parameters may be used as a guide for understanding the process. By a direct visualization of the water molecules of interest, we found that the first and second decay may be related to the water molecules on the exposed surface of the hydrophobic core, whereas the third slow decay may be related to the water molecules within the hydrophobic core that form a hydrogen bond network with other water molecules and the hydrophilic groups in the hydrophobic core. It is noteworthy that the water molecules within the hydrophobic core can be replaced with bulk water molecules on a nanosecond time scale, meaning that water molecules penetrate dynamically from bulk water into the hydrophobic core. Note that the ester bond in the γ-benzyl L-glutamate residues of the hydrophobic blocks may be activated for hydrolysis by water molecules and the NH groups of the backbone that are hydrogen bonded to the carbonyl group; the ester is hydrolyzed by water molecules that have been retained in the hydrophobic core. In this case, however, the hydrolysis is expected to be very slow because of the stability of the alkyl ester. Interestingly, it has been reported that the SN-38-conjugated poly(ethylene glycol)-poly(glutamate) block copolymer, where SN-38 is attached to the glutamate residue through an ester bond with the phenol group on SN-38, forms a micellar particle. The latter gradually releases SN-38 in phosphate-buffered saline at 37 °C.19 The water molecules in the hydrophobic core may play an essential role in controlled release of drugs in drug-conjugated PEG-poly(glutamate) block copolymer micelles. Polymeric micelles have been proved to be useful as a carrier for drugs, particularly anticancer drugs.7,8 Among them, PEG-PLAA possesses a singular advantage over other micelleforming block copolymers, i.e., a potential for attachment of drugs and hydrophobic moieties in the micellar core through a free functional group (e.g., amine or carboxylic acid) of the amino acid chain and a desirable biodegradability. Each drug delivery process, such as circulation in the blood, passive targeting to tumor tissues, and drug release, is significantly dependent on the size, shape, and stability of drug-loaded polymeric micelles. In the present study, we have shown that a spherical micelle composed of PEG and PBLG block copolymers may exist stably with a core-shell structure, i.e., a hydrophilic PEG outer shell and a hydrophobic PBLG inner core, in aqueous solution, and that there can be water molecules in the inner core that may be involved in the hydrolysis of drug-polymer conjugates, resulting in drug release. These

Micelle Composed of PEG-PBLG-Ac Block Copolymers results give us some insight into the pharmacokinetic character of drug-loaded polymeric micelles. Relationship with Actual Polymeric Micelles. In this study, the hydrophilic PEG block was truncated to 11 monomer units (MW ) 0.5K) due to limited computer resources, although the MW of the PEG block in the actual carrier is 5K or 12K. The effect of the PEG block length on the micellar structure is as of yet unknown because no experimental data are available. We may, however, consider the effect based on this study, from which the following results have been obtained: (1) hydrophilic PEG blocks in the micelle form a helical conformation, which is in good agreement with both NMR and MD simulation studies for a PEG chain in water; and (2) the PEG blocks in the micelle are surrounded with an extensive water-hydrated outer shell, extending into the water phase. These results suggest that each PEG block extends further into the water phase as the chain becomes longer, while keeping a helical conformation but not entangled with other chains. Thus, it may be considered that the PEG conformational structure near the PBLG block and the hydration state will be little influenced even if the MW of the PEG blocks increases up to 5K or 12K. This environment will allow the PBLG-Ac blocks to form the hydrophobic core as in the present simulation. Further, the mechanism of the dynamic process of water penetration into the hydrophobic core, that is, water penetration through the hydrophilic groups in the PBLG blocks and the exchange with the water molecules in the core, is reasonable, and the PEG segments far from the core will be virtually unaffected. Although the micellar structure may change with the length of the PEG block and the aggregation number, we believe that the fundamental behavior predicted by this study such as the hydrophobic core formation, hydration of the hydrophilic block, and water penetration must be exhibited in the actual micelle. Conclusions In the present study, we conducted an all-atom MD simulation of a spherical micelle composed of an amphiphilic block copolymer, PEG-PBLG-Ac, in aqueous solution at constant temperature and pressure. After a 3 ns equilibration process, we obtained a micelle structure with a slightly elliptical shape (I1/I3 ) 1.23), which was stable during another 4 ns simulation. The central region of the micelle was filled with hydrophobic blocks (PBLG-Ac), leading to the formation of a hydrophobic core. Hydrophilic blocks (PEG), which extend into the water phase, form a helical conformation where almost all the C-C bond dihedral angles are in a gauche form. This conformational behavior is in good agreement with both NMR and MD simulation studies for a PEG chain in water. The conformation of PBLG-Ac maintains its R-helix form during the 7 ns simulation, which was modeled as the initial conformation. It should be noted that the formation of the micelle structure has little influence on the conformation of both the PEG and PBLGAc blocks. Further, the density profile analysis shows that the resulting micelle remains as a core-shell structure during the simulation. We analyzed the hydration structure of the hydrophilic region in the micelle and obtained the following results: (1) One PEG oxygen atom forms hydrogen bonds with about two water molecules. (2) There are a few types of water molecules that form hydrogen bonds with PEG oxygen, differing in the number and pattern of the hydrogen bonds. (3) The dissociation of water molecules from PEG oxygen is fitted well by two exponential functions, resulting in average residence times of 25-69 and 131-452 ps, which are significantly longer than that of bulk

J. Phys. Chem. B, Vol. 113, No. 46, 2009 15187 water (∼3 ps). These results show that an extensive waterhydrated outer shell is formed around the hydrophilic region in the micelle. We also elucidated some structural characteristics of the hydrophobic region: (1) The PBLG blocks with an R-helix conformation form the hydrophobic core, which may be considered as being constructed of rigid rods. (2) The benzyl group in the side chain of the PBLG blocks covers the surface of the blocks, and a van der Waals or π-π interaction is observed between the phenyl rings in the neighboring chains. (3) Some water molecules are present within the hydrophobic core, which are constantly redistributed in the core during the simulation. These water molecules exist mostly as a cluster in the space between the PBLG blocks, forming hydrogen bonds among themselves, as well as with hydrophilic groups such as the ester and amide groups in the hydrophobic core. Furthermore, the water molecules exhibited continuous exchange with bulk water during the simulation. These results show that different types of interactions are involved in the dynamic behavior of the hydrophobic core in addition to the so-called hydrophobic effect. The PEG-PBLG-Ac copolymer is considered to be a model polymer or prototype of drug-conjugated PEG-poly(glutamate) block copolymers that have been used as drug carriers and have been reported to form a spherical micellar aggregate in aqueous solution. Thus, we believe that our micelle model is useful as a basic model for realistic micellar structures. Although the present work is a model study of micelle-forming polymeric drug-conjugated copolymers, we anticipate that it will be very useful for understanding the properties of the polymeric micelle in different drug delivery steps such as loading, transporting, and release of drugs. Acknowledgment. This work has been done as a part of Grand Challenges in Next-Generation Integrated Nanoscience, “Development & Application of Advanced High-Performance Supercomputer” Project supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors thank Okazaki Research Center for Computational Science, National Institutes of Natural Sciences, for the use of supercomputers. References and Notes (1) Moffitt, M.; Khougaz, K.; Eisenberg, A. Acc. Chem. Res. 1996, 29, 95. (2) Tuzar, Z.; Kratochvil, P. AdV. Colloid Interface Sci. 1976, 6, 201. (3) Munk, P.; Prochazka, K.; Tuzar, Z.; Webber, S. E. CHEMTECH 1998, 28, 20. (4) Talingting, M. R.; Munk, P.; Webber, S. E.; Tuzar, Z. Macromolecules 1999, 32, 1593. (5) Chiellini, E., Migliaresi, C., Sunamoto, J., Eds. Biomedical Polymers and Polymer Therapeutics; Kluwer Academic: Dordrecht, The Netherlands, 2001. (6) Qui, L. Y.; Bae, Y. H. Pharm. Res. 2006, 23, 1. (7) Yokoyama, M.; Miyauchi, M.; Yamada, N.; Okano, T.; Sakurai, Y.; Kataoka, K.; Inoue, S. Cancer Res. 1990, 50, 1693. (8) Kataoka, K.; Harada, A.; Nagasaki, Y. AdV. Drug DeliVery ReV. 2001, 47, 113. (9) Matsumura, Y.; Maeda, H. Cancer Res. 1986, 46, 6387. (10) Kataoka, K.; Kwon, G. S.; Yokoyama, M.; Okano, T.; Sakurai, Y. J. Controlled Release 1993, 24, 119. (11) Yokoyama, M.; Miyauchi, M.; Yamada, N.; Okano, T.; Sakurai, Y.; Kataoka, K.; Inoue, S. J. Controlled Realease 1990, 11, 269. (12) Kwon, G. K.; Naito, M.; Yokoyama, T.; Okano, T.; Sakurai, Y.; Kataoka, K. J. Controlled Release 1997, 48, 195. (13) Li, Y.; Kwon, G. S. Colloids Surf. B: Biointerfaces 1999, 16, 217. (14) Piskin, E.; Kaitian, X.; Denkbas, E. B.; Kucukyavuz, Z. J. Biomatter Sci. Polym. Ed. 1995, 7, 359. (15) Cammas, S.; Kataoka, K. Macromol. Chem. Phys. 1995, 196, 1899. (16) Hruska, Z.; Riess, G.; Goddard, Polymer 1993, 34, 1333.

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(17) Hamaguchi, T.; Matsumura, Y.; Suzuki, M.; Shimizu, K.; Goda, R.; Makamura, I.; Nakatomi, I.; Yokoyama, M.; Kataoka, K.; Kakizoe, T. Br. J. Cancer 2005, 92, 1240. (18) Yokoyama, M.; Inoue, S.; Kataoka, K.; Yui, N.; Sakurai, Y. Macromol. Chem. Rapid Commun. 1987, 8, 431. (19) Koizumi, F.; Kitagawa, M.; Negishi, T.; Onda, T.; Matsumoto, S.; Hamaguchi, T.; Matsumura, Y. Cancer Res. 2006, 66, 10048. (20) Nishiyama, N.; Okazaki, S.; Cabral, H.; Miyamoto, M.; Kato, Y.; Sugiyama, Y.; Nishio, K.; Matsumura, Y.; Kataoka, K. Cancer Res. 2003, 63, 8977. (21) Matsumura, Y. AdV. Drug DeliVery ReV. 2008, 60, 899. (22) Li, Y.; Kwon, G. S. Pharm. Res. 2000, 17, 607. (23) Jeong, Y.-I.; Cheon, J.-B.; Kim, S.-H.; Nah, J.-W.; Lee, Y.-M.; Sung, Y.-K.; Akaike, T.; Cho, C.-S. J. Controlled Release 1998, 51, 169. (24) Nakanishi, T.; Fukushima, S.; Okamoto, K.; Suzuki, M.; Matsumura, Y.; Yokoyama, M.; Okano, T.; Sakurai, Y.; Kataoka, K. J. Controlled Release 2001, 74, 295. (25) Yoshii, N.; Okazaki, S. J. Chem. Phys. 2007, 126, 096101. (26) Yoshii, N.; Iwahashi, K.; Okazaki, S. J. Chem. Phys. 2006, 124, 184901. (27) MacKerell, A. D., Jr. J. Phys. Chem. 1995, 99, 1846. (28) Tieleman, D. P.; van der Spoel, D.; Berendsen, H. J. C. J. Phys. Chem. B 2000, 104, 6380. (29) Bruce, C. D.; Senapati, S.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 10902. (30) Rankitin, A. R.; Pack, G. R. J. Phys. Chem. B 2004, 108, 2712. (31) Sterpone, F.; Brignti, G.; Pierleoni, C. Langmuir 2001, 17, 5103. (32) Sterpone, F.; Pierleoni, C.; Briganti, G.; Marchi, M. Langmuir 2004, 20, 4311.

Kuramochi et al. (33) Garde, S.; Yang, L.; Dordick, J. S.; Paulaitis, M. E. Mol. Phys. 2002, 100, 2299. (34) Lin, S.; Numasawa, N.; Nose, T.; Lin, J. Macromolecules 2007, 40, 1684. (35) Diang, W.; Lin, S.; Lin, J.; Zhang, L. J. J. Phys. Chem. B 2008, 112, 776. (36) Cass, M. J.; Heyes, D. M.; English, R. J. Langmuir 2007, 23, 6576. (37) Srinivas, G.; Discher, D. E.; Klein, M. L. Nat. Mater. 2004, 3, 638. (38) Michel, D. J.; Cleaver, D. J. J. Chem. Phys. 2007, 126, 034506. (39) MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr.; Evanseck, J. D.; Field, M. J.; Fisher, S.; Gao, J.; Guo, H.; Ha, S.; JosephMcCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E., III; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiórkiewicz-Kuczera, J.; Yin, D.; Karplus, M. J. Phys. Chem. B 1998, 102, 3586. (40) MacKerell, A. D., Jr.; Feig, M.; Brooks, C. L., III J. Comput. Chem. 2004, 25, 1400. (41) Tasaki, K. J. Am. Chem. Soc. 1996, 118, 8459. (42) Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Mol. Phys. 1996, 87, 1117. (43) Martyna, G. J.; Tobias, D. J.; Klein, M. L. J. Chem. Phys. 1994, 101, 4177. (44) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed.; Academic: New York, 2002. (45) Block, H. Poly (γ-benzyl L-glutamate) and other glutamic acid containing polymers; Gordon and Breach Science Publishers: New York, 1983.

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