Stabilization of Ostwald Ripening in Low Molecular Weight Amino

Article pubs.acs.org/molecularpharmaceutics

Stabilization of Ostwald Ripening in Low Molecular Weight Amino Lipid Nanoparticles for Systemic Delivery of siRNA Therapeutics Marian E. Gindy,*,†,‡ Brad Feuston,§,‡ Angela Glass,†,‡ Leticia Arrington,†,‡ R. Matthew Haas,†,‡ Joseph Schariter,†,‡ and Steven M. Stirdivant∥ †

Department of Pharmaceutical Sciences, ‡Department of RNA Therapeutics, §Department of Chemistry Modeling and Informatics, and ∥Department of RNA Biology, Merck Research Laboratories, Merck and Co., Inc., West Point, Pennsylvania 19486, United States S Supporting Information *

ABSTRACT: Lipid nanoparticles (LNPs) represent the most clinically advanced technology for the systemic delivery of therapeutic siRNA in vivo. Toward this end, a novel class of LNPs comprising low molecular weight (MW) ionizable amino lipids having asymmetric architecture was recently reported.1 LNPs of these amino lipids, termed asymmetric LNPs, were shown to be highly efficacious and well tolerated in vivo; advances were enabled by improved endosomal escape, coupled with enhanced amino lipid metabolism and clearance. In this work, we show that, in contrast to their desirable pharmacological performance, asymmetric LNPs present a significant pharmaceutical developability challenge, namely physical instability limiting extended shelf life. Using orthogonal characterization methods, we identify the mechanism of LNP instability as Ostwald ripening and establish it to be driven predominantly by the asymmetric amino lipid component. Through rational optimization of LNP physical and macromolecular properties, we are able to significantly attenuate or entirely eliminate the Ostwald ripening instability. Modulation of LNP size, for example, effectively halts particle growth. Similarly, optimization of LNP macromolecular packing through deliberate selection of structurally matched colipids significantly diminishes the rate of ripening. This later experimental observation is substantiated by molecular dynamics simulations of LNP self-assembly, which establish a quantitative dependence of LNP macromolecular order on colipid structure. In totality, the experimental and molecular dynamics outcomes of this work support the rational design of LNP physical and chemical properties leading to effective Ostwald ripening stabilization and enable the advance of asymmetric LNPs as a clinic-ready platform for siRNA therapeutics. KEYWORDS: lipid nanoparticle, siRNA, Ostwald ripening, molecular dynamics, drug delivery

■

INTRODUCTION

At present, lipid nanoparticles (LNPs) represent a leading technology for the systemic delivery of siRNA in vivo, with recent demonstrations of therapeutic efficacy in clinical trials.3 Lipid nanoparticles are multicomponent systems, typically composed of ionizable amino lipids, phospholipids, cholesterol, and a polyethylene glycol-lipid conjugate (PEG-lipid). The ionizable amino lipid plays a principal role in siRNA transfection, mediating cytosolic delivery of the siRNA through facilitated endosomal escape after LNP endocytosis. Neutral lipids, such as phospholipids and cholesterol, are selected to modulate the fluidity and phase behavior of the LNP, whereas PEG-lipids are utilized to improve particle circulation half-life and systemic exposure.4 Because ionizable amino lipids are a critical functional excipient in the LNP drug product, their optimization based on structure−activity guided design is an active area of

RNA interference (RNAi) is a powerful approach for the sequence-specific silencing of gene expression triggered by short double-stranded RNAs. The foundation underlying the expansive utility of RNAi is that, in principle, RNAi effector molecules, such as small interfering RNA (siRNA), can be designed to target almost any gene of interest. As such, siRNA as a therapeutic modality offers a compelling opportunity for the treatment of many disorders, including cancers, infectious diseases, and metabolic and immune disorders.2 Harnessing the power of siRNA as therapeutics requires the effective and safe delivery of synthetic siRNA molecules into the cytoplasm of target cells, where their incorporation into RNA-induced silencing complexes (RISC) prompts sequence-specific cleavage of complementary mRNA and blocks the production of diseasecausing proteins. However, the physiochemical properties of synthetic siRNA molecules, namely their highly anionic charge and large molecular weight, preclude unaided diffusion across cell membranes, necessitating the use of delivery vehicles to facilitate cytosolic delivery at therapeutically effective concentrations.2 © XXXX American Chemical Society

Received: May 17, 2014 Revised: September 6, 2014 Accepted: September 30, 2014

A

dx.doi.org/10.1021/mp500367k | Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Molecular Pharmaceutics

Article

research.5−8 Toward this end, a new class of highly potent and well-tolerated ionizable amino lipids, termed asymmetric ionizable amino lipids, was recently disclosed.1 The primary distinguishing feature of these novel amino lipids is the unequal lengths of their unsaturated hydrocarbon chains and their corresponding low molecular weight (MW). These design features are exploited to facilitate metabolism of the lipids in vivo, resulting in faster lipid half-life and imparting significant improvements in tolerability. In addition, owing to their molecular architecture, asymmetric amino lipids further favor the adoption of disruptive nonbilayer structures, facilitating enhanced release of LNP-encapsulated siRNA from intracellular endosomal compartments.9 As a consequence, LNPs comprising these novel amino lipids were shown to yield significantly enhanced therapeutic margins in preclinical rodent and nonhuman primate models. For a detailed review of the design and in vivo performance of asymmetric amino lipids representative of this class, the reader is referred to forthcoming publications by Stanton and Koeplinger.10,11 In this work, we study the pharmaceutical developability of LNPs comprising asymmetric amino lipids, termed “asymmetric LNPs”. We show that, in contrast to their improved pharmacological performance, asymmetric LNPs present a significant pharmaceutical developability challenge, namely physical instability limiting extended shelf life. As drug product stability is a key chemistry, manufacturing, and controls consideration because of the potential effects on efficacy, toxicity, and overall quality, addressing drug product instability in development is critical.12 Using a suite of analytical characterization tools, coupled with molecular dynamics modeling, we study the physical and macroscopic properties of asymmetric LNPs and identify the root mechanism of physical instability to be Ostwald ripening. We also apply our mechanistic learnings toward the rational design of optimized LNP formulations, which successfully resolve the stability liability. The present work addresses a key pharmaceutical developability challenge for asymmetric LNPs and facilitates their adoption as a platform for systemic siRNA therapeutics.

obtained from Sigma-Aldrich (St. Louis, MO), SYBR gold was obtained from Molecular Probes (Eugene, OR). Dulbecco’s phosphate buffered saline solution (PBS) was obtained from HyClone laboratories (Logan, UT). All other buffers used in the study were prepared from the acid or sodium salt form of the components. 1.2. Lipid Nanoparticle (LNP) Preparation. LNPs were prepared according to the rapid precipitation process,12 with tailored modifications for assembly of asymmetric LNPs as described herein. Specifically, LNPs were assembled by micromixing of an organic solution of lipids with an aqueous solution containing siRNA duplexes. The lipids solution was prepared by dissolving amino lipid, cholesterol, phospholipid and PEG2000DMG, in a molar ratio of 58:30:10:2, in ethanol. siRNA duplexes were prepared in an aqueous sodium citrate buffer (20 mM, pH 5) at a concentration targeting a N:P ratio of 6. Reagent solutions were preheated to 30−40 °C and delivered at nearly equal volumetric flow rates to the inlet of a confined volume T-mixer device (ID 0.5 mm) using syringe pumps (Harvard Apparatus PHD 2000, Holliston, MA). The ethanol and aqueous citrate solutions were delivered to the inlet of the T-mixer with a total flow rate from 100 to 150 mL/min. The mixed LNP solution was diluted into an equal volume of citrate buffer (20 mM citrate, 300 mM NaCl, pH 6) preheated to 30−40 °C. The resulting LNP suspension was further mixed with a phosphate buffered saline (PBS) at pH of 7.5 at a ratio of 1:1 vol:vol. Following dilutions, LNPs were incubated for 0.5−1 h at 30−40 °C and subsequently purified for removal of free siRNA via anion exchange chromatography using a “Mustang Q” membrane (Pall Corp., Port Washington, NY). The residual ethanol was removed and the external buffer exchanged into PBS via tangential flow diafiltration a hollow fiber PES membrane (Spectrum Laboratories, Rancho Dominguez, CA). The resulting LNPs were concentrated to target concentration of 2−30 mg/mL total lipids, sterilized via filtration through 0.45 and 0.2 μm sterile filters (Pall Corp.), and dispensed into sterile vials under aseptic conditions. LNPs were held for storage at 4, 25, or 40 °C as indicated. 1.3. LNP In Vivo Studies. LNPs utilizing amino Lipids 1−7 in the composition described above and, encapsulating siRNA targeting the mRNA transcript for the ApoB gene, were evaluated for in vivo efficacy and tolerability in Sprague−Dawley female rats (Charles River Laboratories). Rats (n = 4 per dosing group) were tail vein injected with 1−1.5 mL LNPs at a doses of 0.025, 0.1, or 3 mg/kg (mpk) as indicated, in phosphate buffered saline (PBS) vehicle. Infusion rate was approximately 3 mL/min. Six hours post dose, food was removed from cages. At 24 h postLNP dose, rats were sacrificed and liver tissue samples were immediately preserved in NALater (Ambion). Preserved liver tissue was homogenized and total RNA isolated using a Qiagen bead mill and the Qiagen miRNA-Easy RNA isolation kit following the manufacturer’s instructions. Liver ApoB mRNA levels were determined by quantitative reverse transcription polymerase chain reaction (RT-PCR). Message was amplified from purified RNA utilizing primers against the mouse ApoB mRNA (Applied Biosystems Cat. No. Mm01545156_m1). The PCR reaction was run on an ABI 7500 instrument with a 96-well Fast Block. The ApoB mRNA level was normalized to the housekeeping PPIB mRNA and GAPDH. PPIB and GAPDH mRNA levels were determined by RT-PCR using a commercial probe set (Applied Biosytems Cat. No. Mm00478295_m1 and Mm4352339E_m1). Results are expressed as a ratio of ApoB mRNA/PPIB/GAPDH mRNA. All mRNA data is expressed

1. MATERIALS AND METHODS 1.1. Materials. Asymmetric ionizable amino lipids (Lipids 1− 5) and amino lipids DLin-DMA, DLin-KC2-DMA, and DLinMC3-DMA were synthesized at Merck (West Point, PA) according to published methods.1,6,13,14 Distearoylphosphatidylcholine (DSPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), dilauroylphosphatidylcholine (DLPC), and cholesterol were obtained from Sigma-Aldrich (St. Louis, MO). Poly(ethylene glycol)2000-dimyristoylglycerol (PEG2000-DMG) was manufactured by NOF Corporation (White Plains, NY). Chemically modified siRNAs, targeting the apolipoprotein B (ApoB) mRNA transcript (Accession # NM 019287) were synthesized at Merck (Rahway, NJ). The sequence of siRNA is as follows: 5′‐iB‐CUUUAACAA UUCCUGAAA UTsT‐iB‐3′

3′‐UsUGAAA UUGUUAAGGACUsUsUsA‐5′

siRNA sequences contained the following chemical modifications added to the 2′ position of the ribose sugar when indicated: 2′ fluoro (UC), phophorothioate linkage (UsA). Modification abbreviations are given immediately preceding the base to which they were applied. Passenger strands are blocked with an inverted abasic nucleotide on the 5′ and 3′ ends (iB). Ethanol was B



Article

Figure 1. LNP components, composition, in vivo silencing activity, and tolerability: (a) chemical structures of asymmetric amino Lipids 1−5; (b) lipid components and ratios (mole %) for LNPs A-E comprising Lipids 1−5, as indicated in (a); (c) in vivo silencing activities of LNPs A−E encapsulating siRNA targeting the mRNA transcript for the ApoB gene (ApoB siRNA). LNPs were administered intravenously in rat (n = 4 per group) at a dose of 0.1 mg/kg siRNA. Silencing activity, expressed as percentage of liver ApoB mRNA knock-down (KD) relative to vehicle (PBS) control animals, is measured 24 h after LNP administration. (d) Chemical structures of DLin-KC2-DMA and DLin-MC3-DMA. Their corresponding LNPs, LNP F and LNP G, respectively, are generated with composition as defined in (b). (e) In vivo silencing activities and lethality of LNPs D−G encapsulating ApoB siRNA. LNPs were administered in rat at doses of 0.025, 0.1, or 3 mg/kg, and ApoB mRNA KD measured as earlier described. The fraction of rat legalities occurring for 3 mg/kg dose groups is as indicated in (e). Data in (e) are as reported in WO 2012/0401841 and reproduced herein by permission.

based fluctuation in the light scattering intensity, quantified by a second order correlation function. 1.5. Lipids and siRNA Analyses. The concentrations of the lipid components of the LNP (amino lipid, phospholipid, cholesterol, and PEG2000-DMG) were determined by gradient reverse-phase ultrahigh-performance liquid chromatography methods (Section 1.7 for method details). The total siRNA concentration was determined by a strong anion-exchange (SAX) method using a Dionex DNAPac PA200 (4 × 50 mm) (Thermo Scientific, Sunnyvale CA.) guard column with a rapid gradient of 25 mM sodium perchlorate in 10 mM TRIS in 80% water/20% ethanol and 250 mM 10 mM TRIS in 80% water/

relative to the vehicle control. All animal procedures were practiced in conformity with Public Health Service policy and the guidelines of the Institutional Animal Care and Use Committee of Merck. 1.4. Dynamic Light Scattering of LNPs. LNP size distributions were determined by dynamic light scattering (DLS) using a DynaPro particle sizer (Wyatt Technology, Santa Barbara, CA) and ZetaPALS particle size and zeta potential analyzer (Brookhaven Instruments, Holtsville, NY). DLS analyses were conducted on LNPs in PBS (pH 7.4) and results reported as the average of triplicate measurements along with standard deviations. LNP diameter was calculated from the time C



Article

model system, the membrane and water were heated to 310 K in several temperature increments over 2.7 ns, that is, 900 K steps with a time step of 0.003 ps. The system was then allowed to evolve under constant temperature and pressure for an additional 90 ns. Each of the three models using the different phospholipids DSPC, DMPC, and DLPC were created, minimized, and simulated in an identical manner. Analysis of the equilibrated system was performed over the final 30 ns. Both deuterium order parameters and a distribution of atoms with respect to the membrane surface were calculated.

20% ethanol. The efficiency of siRNA encapsulation in LNPs was determined by SYBR gold fluorimetric method and was greater than 90% for all preparations. 1.6. Cryogenic Transmission Electron Microscopy. Cryo-Transmission Electron Microscopy (Cryo-TEM) was conducted on a FEI Tecnai Spirit BioTWIN (Hillsboro, OR) equipped with a Gatan ultrascan 1000 CCD camera. Undiluted samples of LNP solution were suspended on a plasma-treated Quantifoil holey carbon film supported on a 300 mesh copper grid (Quantifoil Micro Tools GmbH, Germany). Samples were vitrified using an FEI Vitrobot Mark IV operating at 4 °C and 95% relative humidity and then subjected to imaging at 30 000× (0.35 nm/pixel) magnification. 1.7. Analytical Size Exclusion Chromatography. Analytical Size Exclusion Chromatography (SEC) of LNP formulations was performed using Dionex Ultimate 3000 UHPLC (Thermo Scientific, Sunnyvale CA.) liquid chromatography system.15 SEC separation was carried out at room temperature using an isocratic gradient (PBS pH 7.4 as eluent) with a flow rate of 0.16 mL/min on a TSK-GEL G6000 PWxl-CP 7.8 × 300 mm column (Tosoh Biosciences, Montgomeryville PA). The separation properties of this column are as follows: 13 μm particle size, exclusion limit of 20 000 000 Da and total column volume of 14.3 mL. Signal detection was monitored at 210 nm using a photodiode array detector (PDA) and the elution time of the lipid nanoparticles was approximately 40−60 min. Multiple fractions were collected across the total peak and reinjected for chemical analysis by HPLC methods for lipid concentration. The concentration of amino lipid in LNP fractions was determined by gradientreverse-phase ultrahighperformance liquid chromatography methods using an Agilent Zorbax Eclipse Plus C8 RRHD (2.1 × 50 mm, 1.8 μm particle size) column with temperature set at 80 °C. Diluted fractions were automatically reinjected for lipid concentration showed good recovery and required no sample preparation. A gradient method from 30% A (0.1% trifluoroacetic acid (TFA) in water) to 100% B (0.1% TFA in methanol) and a flow rate of 1 mL/min was used for separation. A corona charged aerosol detector ultra (ultraCAD) (ESA Biosciences, Inc., Chelmsford, MA) was used for the lipid detection. The lipid concentration was determined from the area count of the elution peak and calculated from external lipid standard curves with a quadratic fit. 1.8. Coarse Grained Molecular Dynamics Simulations. The GROMACS potentials and tools were used for all the simulations.16−18 The edit conf command was used to create a 16 × 16 component leaflet with makeup of 58.2%, 30%, 9.8%, and 2% asymmetric ionizable amino lipid, phospholipid, PEG-lipid, and cholesterol, respectively. Although the positions in the leaflet were randomly chosen, the same pattern was used for all three phospholipid DLPC, DMPC, and DSPC models to help reduce uncontrollable variables in the comparison of these phospholipids on the average membrane structure. Two leaflets were appropriately aligned to form a model membrane and a 4 nm layer of water was placed on top to complete the initial model. Water molecules within 2 Å of any membrane component, especially with PEG units were removed from the model. Periodic boundary conditions were applied in all three dimensions. The molecular dynamics simulations were carried out using GROMACS force fields and programs for iterating the equations of motions. The initial system as described above was first minimized using steepest descents and then heated to 10 K to allow the system to slowly anneal. After sufficient relaxation the

2. RESULTS AND DISCUSSION 2.1. Asymmetric Ionizable Amino Lipids and In Vivo Silencing Activity of Their LNPs. The chemical structures of representative asymmetric ionizable amino lipids are shown in Figure 1a. As exemplified by Lipids 1−5, the hydrocarbon backbone is readily truncated to generate lipids of variable molecular weight, asymmetry, and chemical structure. In all instances, lipids were designed to have pKa values between 6 and 8,1 enabling charge-neutrality at physiological pH and amino ionization under acidic conditions. Each of the asymmetric Lipids 1−5 was formulated with cholesterol, phospholipid (DSPC), and a poly(ethylene glycol)−lipid conjugate (PEG2000-DMG) in a molar ratio of 58:30:10:2 (Figure 1b) to generate asymmetric LNPs, designated as LNPs A−E in Figure 1a. LNPs encapsulated a siRNA targeting the mRNA transcript for the ApoB gene (ApoB siRNA) and were tested in vivo using a rat model for gene silencing. LNPs were administered intravenously at a single dose of 0.1 mg/kg ApoB siRNA. Silencing activity, expressed as percentage of liver ApoB mRNA knockdown (KD) relative to vehicle control animals, was determined 24 h after LNP administration and measured by quantitative RT-PCR. As seen in Figure 1c, LNPs A−E are highly potent effectors of ApoB gene silencing in rat liver, with LNPs B−E exhibiting >50% silencing of ApoB mRNA. The robust in vivo potency of asymmetric LNPs is consistent with their biophysical performance in vitro, which identified an enhanced propensity to generate nonbilayer structures facilitating siRNA release in models of endosomal membranes.9 The in vivo tolerability of asymmetric LNPs is also significantly improved relative to LNPs comprising symmetric ionizable lipids. LNPs of the highly potent DLin-KC2-DMA14 and DLin-MC3-DMA 6 amino lipids (Figure 1d), best representative of the symmetric class, were generated, and their in vivo silencing activity similarly evaluated. All LNP formulations tested were of equivalent compositions excepting the amino lipid component. When administered to rats at 0.025, 0.1, and 3 mg/kg ApoB siRNA, LNPs E and F, comprising asymmetric Lipids 5 and 6, were shown to be of comparable or better potency than LNPs G and H, comprising DLin-KC2DMA and DLin-MC3-DMA, respectively (Figure 1e). Moreover, the tolerability of LNPs, grossly assessed as the fraction of rat lethality (n = 4 per group) occurring for 3 mg/kg ApoB siRNA dose groups, was significantly improved for the asymmetric LNPs relative to symmetric amino lipid-based LNPs tested. As shown, no lethality was observed for LNP E or LNP F, whereas 3/4 and 2/4 deaths were observed for LNPs comprising DLin-KC2-DMA and DLin-MC3-DMA, respectively. For a view of rat in vivo data in its entirety, the reader is referred to patent publication WO 2012/040184 by Budzik et al.1 2.2. LNPs Containing Asymmetric Amino Lipids Exhibit Colloidal Instability. Encouraged by the potent in vivo silencing activity and tolerability of asymmetric LNPs, we next investigated pharmaceutical properties relevant to their developD



Article

Figure 2. Size growth for a prototypical asymmetric LNP (LNP C) as a function of LNP storage time in solution. (a) Intensity-averaged particle radius and (b) particle size distribution, measured by DLS, determined as a function of LNP storage time (days) in PBS at 4 °C.

Figure 3. Evolution of particle morphology and size-growth for LNP C during storage. Cryogenic-TEM images of LNP C in PBS stored at (a) 4 °C for times as indicated and (b) at 25 and 40 °C for a 2 week period. (c) Number-averaged particle size distributions for samples as in (a).

ment as therapeutic drug products, namely physical and chemical stability attributes critical to definition of product shelf life.12 Initial assessments of asymmetric LNPs indicated that, on the whole, these formulations were highly prone to physical instability. Their chemical stability profile was nonlimiting and will be disclosed in a forthcoming publication. Accordingly, we

aimed to understand the origin of the physical instability observed for asymmetric LNPs of this work. LNP C (Figure 1a), a highly unstable formulation, was selected as a prototypical representative of this class and studied in detail. The particle size growth profile of LNP C is shown in Figure 2a. The intensity-averaged LNP diameter, measured by DLS, was E



Article

primary mechanisms for particle size growth of LNP C stored as a cold (4 °C) liquid dispersion. These data are consistent with physiochemical properties of the LNP lending to protection against aggregation, namely PEG-based steric stabilization. 2.3. Ostwald Ripening as Mechanism of Asymmetric LNP Instability. We, thus, postulated that physical instability in asymmetric LNPs was instead driven by a molecular rather than particle-based destabilization mechanism. For colloidal particles of nanometer scale, molecular instability can also occur through the process of Ostwald ripening; a dissolution−precipitation based process for particle growth in solution. The growth of one particle comes at the expense of a smaller particle and is driven by the difference in the chemical potential of surface atoms arising from the difference in radius of curvature of particles. As smaller particles dissolve and free molecules redeposit onto larger particles, the overall effect is an increase in the average radius of the particles with time. For diffusion-limited Ostwald ripening, the change in average particle size is proportional to the cube root of time. Thus, if LNP C growth occurs via Ostwald ripening, a plot of the cube of the LNP radius as a function of storage time should yield a linear relationship. Light scattering data for LNP C stored at 4 °C are shown in Figure 4. A linear fit to the data yielded a regression coefficient (R2) of 0.994, confirming the cube-root of time growth dependence indicative of Ostwald ripening.

shown to rapidly increase as a function of storage time in PBS at 4 °C. Particles with an initial radius of 42 nm grew to a radius of 70 nm following 60 days of storage as a liquid dispersion. LNP radius is defined as the DLS-measured diameter divided by 2 for the purpose of subsequent discussion. The corresponding LNP size distributions are shown in Figure 2b. The intensity-averaged size polydispersity was similarly shown to increase, from a value of 0.07 at time of initial LNP manufacture (week 1) to a value of 0.14 following 60 day storage (week 8). In contrast, LNPs comprising the symmetric amino lipid DLin-DMA,13 and having all other lipid components and composition as per LNP C, were physically stable as a liquid dispersion following 17 weeks of storage at 4 °C (Supporting Information Figure S1). The light scattering data thus provide evidence for differentiated physical stability characteristics of asymmetric LNPs relative to comparable symmetric LNP counterparts. The most common modes of physical instability in lipid nanoparticles are aggregation (flocculation) and fusion (coalescence). In aggregation, lipid nanoparticles grow in size through a particle combination process, whereby individual particles that comprise the aggregate retain their physical integrity. Conversely, particle growth by coalescence is mediated by the formation of new colloidal structures. Thus, we evaluated the behavior of asymmetric LNPs in context of these colloidal instability mechanisms. Figure 3a displays the structural evolution of LNP C, stored in PBS at 4 °C, over the course of an 8-week period as studied by cryo-TEM. At the time of manufacture and initial analysis (week 1), LNPs appeared as well separated particles, were of a consistently spherical morphology, and were of a distribution skewed toward a population of smallersized particles (based on image analysis of ∼500 particles). The morphology and aggregation state of the LNPs remained unchanged during the monitored storage period, with the majority of particles continuing to present as individual spherical entities. However, a distinct shift in particle size distribution was detected over time. Nanoparticles imaged following 8 weeks of storage exhibited a greater proportion of large-sized particles relative to LNPs imaged at initial manufacture. The increased fraction of larger-sized particles detected by cryo-TEM is consistent with the number-averaged particle size distributions determined via DLS. As shown in Figure 3c, light scattering measurements demonstrated an increase in the number-averaged mean radius of LNPs over time, from a value of 28 nm at initial analysis to 43 nm at the terminal time point evaluated. In addition, complementary analysis via static light scattering confirmed the lack of detectable micron-sized fractions in the LNP population at any of the time points evaluated (data not shown). When the storage temperature was increased, LNPs were shown to undergo temperature-dependent changes in morphology and aggregation. Figure 3b depicts cryo-TEM micrographs of LNP C stored for a period of 2 weeks at 25 or 40 °C. When LNPs were stored at 25 °C, their morphology, structure, and aggregation-state were similar to LNPs stored at 4 °C over an equivalent time period (Figure 3a). However, particles stored at 40 °C showed evidence of structural changes suggestive of particle−particle fusion interactions. As demonstrated by the cryo-TEM micrographs of Figure 3c, LNPs initially presenting with uniform electron-dense structures are transformed into subpopulations of unilamellar vesicles and structures that appear as fusion intermediates between dense particles and unilamellar vesicles. The combined cryo-TEM and light scattering data, thus, indicate that aggregation and fusion are unlikely to be the

Figure 4. Rate of Ostwald ripening for asymmetric LNP C. Particle size growth data for LNP C plotted as the cube of LNP radius (r3) versus time (h) of storage at 4 °C. Symbols indicate experimentally determined LNP radii, with line as linear regression fit to data (R2 > 0.99). The rate of Ostwald ripening (nm3/h) is determined from the slope of the regression line.

To further investigate Ostwald ripening as the mechanism of instability, we next characterized the physical and compositional properties of LNP C subfractions as a function of storage time. A batch of LNP C was fractionated by size exclusion chromatography (SEC), and the subfractions were analyzed by DLS and by ultrahigh-performance liquid chromatography (UPLC) for particle size and amino lipid content, respectively. Figure 5 depicts results of physiochemical characterization of LNP C subfractions. Data for subfractions 2−7, which account for 70− 80% of LNP C population by mass, are plotted as a function of storage time (1, 4, and 8 weeks) at 4 °C. As can be seen from Figure 5a, at time of initial manufacture (week 1) LNP C is comprised of a heterogeneous population of particles, with mean intensity-averaged particle radii ranging from 63 to 23 nm. When LNP C is fractioned following 4 weeks of storage, the mean particle radius of each subfraction is seen to change in accordance with an Ostwald ripening driven mechanism. LNP C subfractions F



Article

Figure 5. Particle size and composition distributions of LNP C subfractions as a function of storage time. LNP C (a) intensity-averaged radius (nm) and (b) Lipid 3 composition (mole %) of individual LNP fractions collected after size exclusion chromatography (SEC). SEC fractionation was performed on LNP C samples stored at 4 °C for 1, 4, and 8 weeks, as indicated.

Figure 6. Modulation of Ostwald ripening via particle size tuning. Data for LNP C compositional variants, prepared via substitution of PEG-DMG (2 mol %) by PEG-cholesterol (2 mol % or 3 mol %) or PEG-ceramide (3 mol %). (a) Particle size growth plotted as the cube of LNP radius (r3) versus time (h) of storage at 4 °C. Symbols indicate experimentally determined LNP radii, with lines representing linear regression fits to data. (b) Intensityaveraged particle size distributions of LNP C PEG-ceramide (3 mol %) variant at weeks 1 and 3 of storage at 4 °C.

dispersion is by tuning (e.g., narrowing) the particle size distribution of LNPs at initial time of manufacture. This follows from the theoretical description of Ostwald ripening in nanoparticles as described by Lifshitz−Slyozof−Wagner (LSW), who defined the rate of ripening using a modified version of the Kelvin equation as follows:19

with initially small radii exhibited greater growth than subfractions of larger particles. The relative growth in mean particle radius ranged from 0.5 to 1.5% for subfraction 2 and 3, up to 78% for subfraction 8. Overall, the effect is an increase in the average radius of LNP C and a narrowing in the size distribution among fractions, which ranged from 63 to 40 nm at end of study. The physical stability of LNP C and its subfractions is thus corroborative of Ostwald ripening as the mode of particle instability. Finally, we postulated that LNP Ostwald ripening was driven by the enhanced solubility of the asymmetric amino lipid component owing to its low molecular weight. Consequently, we next characterized the amino lipid composition of LNP C subfractions as a function of storage time in solution. As shown in Figures 5b, LNP C subfractions with smaller particle sizes at the time of manufacture (week 1) exhibited the greatest change in amino lipid (Lipid 3) content with extended storage (week 8), supporting the proposed amino lipid-mediated instability for these asymmetric LNPs. 2.4. Particle Size Optimization Stabilizes LNP Ostwald Ripening. If instability of asymmetric LNPs occurs via Ostwald ripening as suggested, then one possibility of stabilizing the LNP

⎡ 2γM w ⎤ c(r ) = C∞exp⎢ ⎥ = C∞exp[α /r ] ⎣ ρRTr ⎦

(1)

where r is the particle radius, C∞ is the bulk solubility of the asymmetric amino lipid, γ is the interfacial tension, Mw is the molecular weight of the lipid with density ρ, R is the gas constant, and T is the absolute temperature. The quantity in brackets, α, is the capillary length and defines the length scale below which curvature-induced solubility is significant. Presumably, LNPs with a particle size above the critical radius, where particle dissolution and growth are in balance, should not exhibit a driving force for Ostwald ripening. To test this premise, we compared the kinetics of ripening for LNPs comprising asymmetric amino Lipid 3, but having variable initial particle size. LNP size was modulated through targeted selection of the PEG-lipid stabilizer. We previously showed PEGG



Article

lipid plays an active role in LNP assembly, governing the kinetic arrest of particle growth during self-assembly.12,20 Tuning the kinetics of PEG-lipid adsorption during LNP assembly, by way of altering the hydrophobic lipid anchor on the PEG-lipid conjugate, enabled the modulation of LNP size. Lipid nanoparticles composed of Lipid 3, DSPC, cholesterol and PEG2000ceramide (57:30:10:3 mol:mol) or Lipid 3, DSPC, cholesterol, and PEG2000-cholesterol (57:30:10:2 mol:mol) were prepared and their respective ripening kinetics compared to that of the parent LNP, LNP C. In Figure 6a, the cube of LNP radius for the three formulations is plotted as a function of LNP storage time at 4 °C. As seen, substituting the PEG2000-DMG (2 mol %) of LNP C with either PEG2000-ceramide or PEG2000-cholesterol resulted in the formation of particles with larger initial radii of 105 nm (diamonds) and 70 nm (triangles), respectively, compared to LNP C (43 nm; circles). The storage stability of both PEG2000ceramide and PEG2000-cholesterol containing LNPs was also significantly improved over the monitored storage period. This is in distinct contrast to the growth observed for LNP C. To confirm that the LNP stability for formulations comprising PEG2000-ceramide or PEG2000-cholesterol was not a consequence of altered steric stabilization due to change in the PEG-lipid, we generated LNPs instead comprising 3 mol % PEG2000-cholesterol and compared their behavior to their 2 mol % PEG2000cholesterol LNP counterparts. As shown in Figure 6a, increasing the PEG2000-cholesterol content by only 1 mol % had the effect of reducing the initial particle radius from 70 nm (triangles) to 50 nm (squares) and effectively recaptured the ripening kinetics of the parent LNP C formulation. Ripening rates, calculated from the slope of linear regressions of data in Figure 6a, indicated equivalent ripening rates for LNP C and the comparator LNP comprising 3 mol % PEG2000-cholesterol (162 ± 6.2 nm3/h and 169 ± 1.5 nm3/h, respectively). Finally, in Figure 6b the initial intensity-averaged particle size distribution of a stable asymmetric LNP (LNP C with 3% PEG2000-ceramide) was shown to be minimally changed over the duration of the monitored storage period (3 weeks), in contrast to the behavior of LNP C as is shown in Figure 3b. 2.5. Improving LNP Bilayer Packing Mitigates Ostwald Ripening. Although modulation of particle size was shown to effectively halt Ostwald ripening instability of asymmetric LNPs, generating particles of increasingly larger size may not be always be desirable for therapeutic bioperformance. As shown in Figure 7, LNP C formulations were shown to demonstrate distinct particle size-dependent silencing activity in vivo, with particles having a diameter beyond ∼100 nm yielding very low activity.

As such, an alternative approach of stabilizing LNPs against Ostwald ripening is desirable. To this end, we investigated the ability to lessen Ostwald ripening through modulation of particle surface tension, γ, as per eq 1. We postulated that the asymmetric molecular architecture of the amino lipid has the effect of reducing hydrocarbon interactions with colipids of the LNP formulation. This reduced tendency for hydrophobic interactions is proposed to generate patchy lipid packing in LNP bilayers that exposes lipophilic surfaces from the inner bilayer to the aqueous dispersion medium. Exposure of lipophilic surfaces will have the effect of increasing the surface tension, γ, which consequently will impart higher saturation solubility and drive instability of LNPs. This hypothesis is analogous to that proposed by Müller and Peters to explain the differentiated Ostwald ripening kinetics of nanosized drug crystals having different polymorphic forms.21 To impart more favorable lipid packing in LNP bilayers, we proposed a deliberate selection of the phospholipid component based on a criterion of molecular-shape complementarity with the asymmetric amino lipid. As an exemplar of this strategy, LNPs composed of asymmetric Amino Lipid 3, cholesterol, PEG2000-DMG, and the phospholipid moieties DSPC, DMPC, and DLPC were prepared and their size growth evaluated. The phospholipids tested varied only in their hydrocarbon chain lengths; DSPC (C18), DMPC (C14), and DLPC (C12). Particle size growths of DSPC-, DMPC-, and DLPC-containing LNPs, plotted as the cube of LNP radius versus storage time, are shown in Figure 8. As seen, LNPs containing DMPC were significantly

Figure 8. Modulation of Ostwald ripening via interfacial tension tuning. Data for LNP C phospholipid variants, prepared via substitution of DSPC in LNP C by DMPC or DLPC, as indicated. Particle size growth is plotted as the cube of LNP radius (r3) versus time (h) of storage at 4 °C. Symbols indicate experimentally determined LNP radii, with lines representing linear regression fits to data.

more stable compared to DSPC- and DLPC-containing LNPs. Linear regression fit of the experimental data (R2 > 0.99) indicate a nearly 3-fold reduction in ripening rate of DMPC-containing LNPs (56 ± 1.5 nm3/h) relative to either DSPC-containing (162 ± 6.2 nm3/h) or DLPC-containing (205 ± 63 nm3/h) LNPs, which were comparable in ripening. The experimental data thus suggest the existence of an optimal phospholipid hydrocarbon chain length matched to the molecular geometry of the asymmetric Amino Lipid 3 and support a strategy of physical stabilization based solely on LNP composition design. We next evaluated the silencing activity of LNP C phospholipid variants. As per earlier studies, LNPs were administered intravenously to rat at a dose of 0.1 mg/kg

Figure 7. Effect of LNP C diameter on silencing activity in vivo. LNPs were administered intravenously in rat (n = 4 per group) at a dose of 0.1 mg/kg ApoB siRNA. Silencing activity is measured 24 h after LNP administration. H



Article

interactions a cut off of 1.3 nm was applied. Particle-mesh Ewald method was employed for the Fourier space contributions to the forces.29 These molecular dynamics simulations were performed on Merck’s CRAY-XT with the support of the high performance computing (HPC) IT department. Due to the way the initial LNP membrane conformations were constructed, each resembling a lipid gel structure, much care was taken to evolve the system to a physically meaningful structure. The initial system, as described here, was first minimized using steepest descents and then heated to very low temperatures to allow the system to slowly anneal at constant pressure. Anisotropic pressure was applied through the Berendsen barostat with 1 atm applied pressure in each of the three dimensions. After sufficient relaxation of the model system, the bilayer and water were heated to 310 K in several temperature increments over 2.7 ns, that is, 900 K steps with a time step of 3 fs. The system was then allowed to evolve under constant temperature and pressure for an additional 90 ns. Each of the three LNP C compositional variants, using DSPC, DMPC, and DLPC, were created, minimized, and simulated in an identical manner. Analysis of the equilibrated systems was performed over the final 30 ns. Both deuterium order parameters and the distribution of specific atoms with respect to the membrane surface were calculated.30 The analysis supports the conclusion that LNP membrane with DMPC is more ordered than either DSPC- or DLPCcontaining LNP membranes. Although the average surface area per lipid component is somewhat independent of the length of the phospholipid chain, 46.1 Å, 46.1 Å, and 45.8 Å for DSPC, DMPC, and DLPC respectively, the deuterium order parameter for the sn2 chain finds the highest order for DMPC (Figure 10a). The anomalous behavior of DMPC is also clearly shown in the distribution of the nitrogen and carbon positions relative to the membrane surface in the model membrane. Figure 10b indicates those atoms in each of the components contributing to the distributions in Figure 11. The relatively sharp atom positional distributions demonstrate that the DMPC lipid bilayer is better defined, with narrow range of atom positions, especially with respect to the DSPC membrane model. The cholesterol carbon tail and the terminal carbon (+Lipid C2 in Figure 11) of the long chain of the amino lipid define the center of the bilayer. The two terminal carbons on the hydrophobic chains of the phospholipid form a single uniform distribution for DMPC, whereas for DSPC and DLPC these terminal carbons are less ordered. The

siRNA, and their silencing activity measured 24 h after administration. As shown in Figure 9, ApoB mRNA knock-

Figure 9. Effect of LNP C phospholipid composition on silencing activity in vivo. LNPs were administered intravenously in rat (n = 4 per group) at a dose of 0.1 mg/kg ApoB siRNA. Silencing activity is measured 24 h after LNP administration.

down was comparable for all LNPs tested, demonstrating little dependence on the phospholipid excipient. Thus, in contrast to particle size tuning for the stabilization of Ostwald ripening, particle stabilization via modulation of surface tension enables retention of desirable pharmaceutical and pharmacological properties. 2.6. Molecular Dynamics Simulations Confirm Dependence of LNP Bilayer Packing on Phospholipid Identity. Prompted by experimental evidence suggesting stabilization of asymmetric LNPs through deliberate colipid selection, we next aimed to better understand through computational modeling the effect of phospholipid structure on the molecular packing of lipids in LNP bilayers. To study the LNP bilayer, molecular dynamics simulations were carried out using the GROMACS united atom potentials for biomolecular systems as well as its suite of simulation programs.16−18,22 The force field of Hoetje et al. was employed for cholesterol, whereas the lipid/OPLS force field derived from the work of Berger et al. were utilized for all other lipid components.23,24 The SPC/E rigid water model was combined with the SETTLE algorithm to enforce the holonomic constraints for water.25,26 All simulations were performed in the NPT ensemble using periodic velocity rescaling to the target temperature.27,28 For the Lennard-Jones forces and the direct part of the Ewald sum for Coulombic

Figure 10. (a) Deuterium order parameters for the sn2 chain of the phospholipids DSPC, DMPC, and DLPC, and (b) lipid components of LNPs, with atoms of each component contributing to the distributions of Figure 11 as indicated by circles. I



Article

metabolism coupled with an improved propensity for nonbilayer structure formation better facilitating siRNA endosomal escape. These modifications translate into a reduction of lipid-induced toxicities without loss of silencing activity, effectively widening the LNP therapeutic index.1 This significant advance in ionizable amino lipid design nonetheless presents a substantial challenge in the development of asymmetric LNPs as pharmaceutical drug products. Asymmetric LNPs were shown to exhibit physical instability that considerably limited their solution-phase shelf life. Contrary to typically ascribed modes of nanoparticle instability, such as aggregation and fusion, the mechanism of instability for this new class of LNPs was shown to be Ostwald ripening mediated predominantly by the low molecular weight and molecular architecture of asymmetric amino lipid component. Through rational formulation optimization of LNP physical and macromolecular properties we were able to significantly attenuate or entirely eliminate the Ostwald ripening instability. Modulation of LNP size effectively halted particle size growth. Similarly, improving the packing order of LNP bilayers, through matched molecular structures of amino and colipid components, significantly mitigated ripening in a size independent manner. In support of these later experimental results, molecular dynamics simulations revealed a dependence of LNP bilayer packing order on phospholipid architecture. In totality, the experimental and molecular modeling outcomes of this work establish the rational formulation design and development of asymmetric LNPs as competitive siRNA pharmaceutical products.

■

ASSOCIATED CONTENT

S Supporting Information *

Figure S1: Particle size stability of LNP comprising symmetric cationic lipid DLin-DMA. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 215-652-7004. Fax: 215-652-5299. Address: Merck and Co., Inc., P.O. Box 4, West Point, PA 19486, United States. Notes

The authors declare no competing financial interest.

■

Figure 11. Partial density distributions of asymmetric amino lipid (Lipid 3) and phospholipid nitrogen (N) and carbon (C) positions along the direction perpendicular to LNP bilayer surface. Distributions are for LNP C compositional variants comprising (a) DLPC, (b) DMPC, and (c) DSPC as the phospholipid component. All other lipids and lipid composition are fixed, as described in text.

ACKNOWLEDGMENTS The authors acknowledge M. Stanton, L. Sepp-Lorenzino, K. Koeplinger, A. Leone, J. Lebron, and J. Armstrong along with Merck chemistry, biology, and pharmacology colleagues for the design and syntheses of ionizable amino lipids and for support of in vivo studies cited in this work.

■

deuterium order parameters and atom positional distributions thus support the experimental results and suggest that DMPCcontaining LNPs are stabilized against Ostwald ripening through a mechanism of improved bilayer packing order relative to either DSPC- or DLPC-containing LNPs.

REFERENCES

(1) Stanton, M. G.; Budzik, B. W.; Beutner, G. L.; Liao, H. Novel Low Molecular Weight Cationic Lipids for Oligonucleotide Delivery. U.S. Patent Application 20130090372 A1, 2013. (2) Whitehead, K. A.; Langer, R.; Anderson, D. G. Knocking down barriers: advances in siRNA delivery. Nat. Rev. Drug Discovery 2009, 8 (2), 129−138. (3) Davidson, B. L.; McCray, P. B. Current prospects for RNA interference-based therapies. Nat. Rev. Genetics 2011, 12 (5), 329−340. (4) Foged, C. siRNA Delivery with Lipid-based Systems: Promises and Pitfalls. Curr. Top. Med. Chem. 2012, 12 (2), 97−107.

3. CONCLUSIONS Asymmetric LNPs, comprising a new class of ionizable amino lipids characterized by a truncated acyl backbone and low molecular weight, are a highly promising platform for the therapeutic delivery of siRNA. Their differentiated biological performance in vivo is the result of enhanced amino lipid J



Article

(5) Blagbrough, I. S.; Metwally, A. A.; Ghonaim, H. M. Asymmetrical N4,N9-Diacyl Spermines: SAR Studies of Nonviral Lipopolyamine Vectors for Efficient siRNA Delivery with Silencing of EGFP Reporter Gene. Mol. Pharmaceutics 2012, 9 (7), 1853−1861. (6) Jayaraman, M.; Ansell, S. M.; Mui, B. L.; Tam, Y. K.; Chen, J. X.; Du, X. Y.; Butler, D.; Eltepu, L.; Matsuda, S.; Narayanannair, J. K.; Rajeev, K. G.; Hafez, I. M.; Akinc, A.; Maier, M. A.; Tracy, M. A.; Cullis, P. R.; Madden, T. D.; Manoharan, M.; Hope, M. J. Maximizing the Potency of siRNA Lipid Nanoparticles for Hepatic Gene Silencing In Vivo. Angew. Chem., Int. Ed. 2012, 51 (34), 8529−8533. (7) Metwally, A. A.; Reelfs, O.; Pourzand, C.; Blagbrough, I. S. Efficient Silencing of EGFP Reporter Gene with siRNA Delivered by Asymmetrical N4,N9-Diacyl Spermines. Mol. Pharmaceutics 2011, 9 (7), 1862−1876. (8) Semple, S. C.; Akinc, A.; Chen, J.; Sandhu, A. P.; Mui, B. L.; Cho, C. K.; Sah, D. W. Y.; Stebbing, D.; Crosley, E. J.; Yaworski, E.; Hafez, I. M.; Dorkin, J. R.; Qin, J.; Lam, K.; Rajeev, K. G.; Wong, K. F.; Jeffs, L. B.; Nechev, L.; Eisenhardt, M. L.; Jayaraman, M.; Kazem, M.; Maier, M. A.; Srinivasulu, M.; Weinstein, M. J.; Chen, Q.; Alvarez, R.; Barros, S. A.; De, S.; Klimuk, S. K.; Borland, T.; Kosovrasti, V.; Cantley, W. L.; Tam, Y. K.; Manoharan, M.; Ciufolini, M. A.; Tracy, M. A.; de Fougerolles, A.; MacLachlan, I.; Cullis, P. R.; Madden, T. D.; Hope, M. J. Rational design of cationic lipids for siRNA delivery. Nat. Biotechnol. 2010, 28 (2), 172− U18. (9) Zhang, Y.; Arrington, L.; Boardman, D.; Davis, J.; Xu, Y.; DiFelice, K.; Stirdivant, S.; Wang, W.; Budzik, B.; Bawiec, J.; Deng, J.; Beutner, G.; Seifried, D.; Stanton, M.; Gindy, M.; Leone, A. The development of an in vitro assay to screen lipid based nanoparticles for siRNA delivery. J. Controlled Release 2014, 174, 7−14. (10) Koeplinger, K.; Tracy, R.; Xu, Y.; Kaplanski, C.; Hochman, J.; Ke, V.; Spellman, D.; Diequez, F.; Raab, C.; Clark, S.; Gerhold, D.; Su, M.; Lebron, J.; Thudium, D.; Abrams, M.; Sepp-Lorenzino, L.; Gindy, M. E.; Stanton, M. Correlation of Apolipoprotein Binding Affinity of Lipid Nanoparticles (LNP) with Effective siRNA Delivery in Non-Human Primate; Merck and Co.: White House Station, NJ, 2014; in preparation (11) Stanton, M. G.; Koeplinger, K. A.; Gindy, M. E.; Stirdivant, S. M.; Hochman, J. H.; Lebron, J.; Leone, A.; Cunningham, J. J.; Raab, C.; Mathre, D. J.; Budzik, B.; Seifried, D.; Cameron, M.; Davis, J.; Colletti, S. L.; Sepp-Lorenzino, L.; Burke, P.; Caldwell, J.; Sachs, A. B., Discovery of Novel Low Molecular Weight Lipids for Systemic Delivery of siRNA Therapeutics with Enhanced Therapeutic Index. Merck and Company, Inc: White House Station, NJ, 2014; in preparation. (12) Gindy, M. E.; Leone, A. M.; Cunningham, J. J. Challenges in the pharmaceutical development of lipid-based short interfering ribonucleic acid therapeutics. Expert Opin. Drug Delivery 2012, 9 (2), 171−182. (13) Heyes, J.; Palmer, L.; Bremner, K.; MacLachlan, I. Cationic lipid saturation influences intracellular delivery of encapsulated nucleic acids. J. Controlled Release 2005, 107 (2), 276−287. (14) Semple, S. C.; Akinc, A.; Chen, J. X.; Sandhu, A. P.; Mui, B. L.; Cho, C. K.; Sah, D. W. Y.; Stebbing, D.; Crosley, E. J.; Yaworski, E.; Hafez, I. M.; Dorkin, J. R.; Qin, J.; Lam, K.; Rajeev, K. G.; Wong, K. F.; Jeffs, L. B.; Nechev, L.; Eisenhardt, M. L.; Jayaraman, M.; Kazem, M.; Maier, M. A.; Srinivasulu, M.; Weinstein, M. J.; Chen, Q. M.; Alvarez, R.; Barros, S. A.; De, S.; Klimuk, S. K.; Borland, T.; Kosovrasti, V.; Cantley, W. L.; Tam, Y. K.; Manoharan, M.; Ciufolini, M. A.; Tracy, M. A.; de Fougerolles, A.; MacLachlan, I.; Cullis, P. R.; Madden, T. D.; Hope, M. J. Rational design of cationic lipids for siRNA delivery. Nat. Biotechnol. 2010, 28 (2), 172−U18. (15) Zhang, J.; Haas, R. M.; Leone, A. M. Polydispersity Characterization of Lipid Nanoparticles for siRNA Delivery Using Multiple Detection Size-Exclusion Chromatography. Anal. Chem. 2012, 84 (14), 6088−6096. (16) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4 (3), 435−447. (17) Berendsen, H. J. C.; Vanderspoel, D.; Vandrunen, R. GROMACS: A message-passing parallel molecular dynamics implementation. Comput. Phys. Commun. 1995, 91 (1−3), 43−56.

(18) Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26 (16), 1701−1718. (19) Physical Characterization of Pharmaceutical Solids; Brittain, H. G., Ed.; Marcel Dekker: New York, 1995 (20) Gindy, M. E.; DiFelice, K.; Kumar, V.; Prud’homme, R. K.; Celano, R.; Smith, J. S.; Haas, R. M.; Boardman, D. Mechanism of Macromolecular Structure Evolution in Self-Assembled Lipid Nanoparticles for siRNA Delivery. Langmuir 2014, 30 (16), 4613−4622. (21) Muller, R. H.; Peters, K. Nanosuspensions for the formulation of poorly soluble drugs: I. Preparation by a size-reduction technique. Int. J. Pharm. 1998, 160 (2), 229−237. (22) Lindahl, E.; Hess, B.; van der Spoel, D. GROMACS 3.0: a package for molecular simulation and trajectory analysis. J. Mol. Model. 2001, 7 (8), 306−317. (23) Holtje, M.; Forster, T.; Brandt, B.; Engels, T.; von Rybinski, W.; Holtje, H. D. Molecular dynamics simulations of stratum corneum lipid models: fatty acids and cholesterol. Biochim. Biophys. Acta, Biomembr. 2001, 1511 (1), 156−167. (24) Berger, O.; Edholm, O.; Jahnig, F. Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature. Biophys. J. 1997, 72 (5), 2002−2013. (25) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The missing term in effective pair potentials. J. Phys. Chem. 1987, 91 (24), 6269− 6271. (26) Miyamoto, S.; Kollman, P. A. Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comput. Chem. 1992, 13 (8), 952−962. (27) Hess, B. P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation. J. Chem. Theory Comput. 2008, 4 (1), 116−122. (28) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126 (1), 014101. (29) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103 (19), 8577−8593. (30) Vermeer, L. S.; de Groot, B. L.; Reat, V.; Milon, A.; Czaplicki, J. Acyl chain order parameter profiles in phospholipid bilayers: computation from molecular dynamics simulations and comparison with 2H NMR experiments. European Biophysics Journal 2007, 36 (8), 919−931.

■

NOTE ADDED AFTER ASAP PUBLICATION The version of this paper that was published ASAP October 15, 2014, contained incorrect versions of Figures 5, 6, and 7. The revised version was reposted October 16, 2014.

K


Stabilization of Ostwald Ripening in Low Molecular Weight Amino

Recommend Documents