Liposome transport of hydrophobic drugs: Gel phase lipid bilayer permeability and partitioning of the lactone form of a hydrophobic camptothecin, DB-67

Authors

  • Vijay Joguparthi,

    1. Department of Pharmaceutical Sciences, College of Pharmacy, A323A ASTeCC Bldg., University of Kentucky, Lexington, Kentucky 40506
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  • Tian-Xiang Xiang,

    1. Department of Pharmaceutical Sciences, College of Pharmacy, A323A ASTeCC Bldg., University of Kentucky, Lexington, Kentucky 40506
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  • Bradley D. Anderson

    Corresponding author
    1. Department of Pharmaceutical Sciences, College of Pharmacy, A323A ASTeCC Bldg., University of Kentucky, Lexington, Kentucky 40506
    • Department of Pharmaceutical Sciences, College of Pharmacy, A323A ASTeCC Bldg., University of Kentucky, Lexington, Kentucky 40506. Telephone: 859 218 6536, Ext 235; Fax: 859 257 2489.
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Abstract

The design of liposomal delivery systems for hydrophobic drug molecules having improved encapsulation efficiency and enhanced drug retention would be highly desirable. Unfortunately, the poor aqueous solubility and high membrane binding affinity of hydrophobic drugs necessitates extensive validation of experimental methods to determine both liposome loading and permeability and thus the development of a quantitative understanding of the factors governing the encapsulation and retention/release of such compounds has been slow. This report describes an efflux transport method using dynamic dialysis to study the liposomal membrane permeability of hydrophobic compounds. A mathematical model has been developed to calculate liposomal membrane permeability coefficients of hydrophobic compounds from dynamic dialysis experiments and partitioning experiments using equilibrium dialysis. Also reported is a simple method to study the release kinetics of liposome encapsulated camptothecin lactone in plasma by comparing the hydrolysis kinetics of liposome entrapped versus free drug. DB-67, a novel hydrophobic camptothecin analogue has been used as a model permeant to validate these methods. Theoretical estimates of DB-67 permeability obtained from the bulk solubility diffusion model and the “barrier-domain” solubility diffusion model are compared to the experimentally observed value. The use of dynamic dialysis in drug release studies of liposome and other nanoparticle formulations is further discussed and experimental artifacts that can arise without adequate validation are illustrated through simulations. © 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 97:400–420, 2008

INTRODUCTION

Silatecan 7-t-butyldimethylsilyl-10-hydroxycamptothecin (DB-67, Scheme 1) is a novel anti-cancer agent with superior blood stability and potent anti-cancer activity compared to other camptothecin analogues.1, 2 It has been recently approved by the FDA for phase I clinical studies.3 The biologically active lactone forms of camptothecins undergo pH dependent hydrolysis in solution to the inactive ring opened carboxylate forms.4–6 The carboxylate form is the favored species at equilibrium at physiological pH.6 In human blood this equilibrium may be further shifted towards the carboxylate due to its preferential binding to serum albumin.7–11 Efforts to synthesize camptothecins that remain in their active lactone form in blood resulted in the development of potent, highly lipophilic analogues with improved blood stability but poor water solubility.12 DB-67, along with other camptothecin analogues such as karenitecin and gimatecan, represent this new generation of blood stable but water insoluble camptothecins.13, 14 Novel formulation strategies are required to enable the delivery of these highly potent anti-cancer agents. Carriers that improve delivery of these agents to tumor tissue are also needed to diminish their toxic side effects.

Scheme 1.

Equilibrium between DB-67 lactone (left) and DB-67 carboxylate (right). Rate constants ko and kc are the lactone ring opening and closing rate constants.

Liposome technology has significant potential to improve formulation (e.g., solubility and stability) and tumor delivery-related issues that hinder the clinical advancement of these novel camptothecins. Lipid bilayer association has been previously found to improve solubility and stability of camptothecins.15–17 Liposomes are known to preferentially accumulate in tumor tissue after an i.v. injection and thus liposomal encapsulation offers the potential for improved antitumor specificity.18 Therefore, liposomal formulations are currently being investigated for various camptothecin analogues, several of which are in preclinical or clinical trials.19–23

One current strategy for liposomal encapsulation of camptothecins exploits the pH dependent lipid bilayer association of those compounds having an ionizable amine on the A or B-ring.21, 23–25 The ring-closed lactone has a greater membrane binding constant than the ring-opened carboxylate and therefore a low intraliposomal pH stabilizes the biologically active lactone form in lipid bilayers.15, 21, 23–25 A variety of loading techniques (e.g., pH, ammonium sulfate or ion gradient loading, metal ion complexation, etc.) developed to improve encapsulation efficiency of amphiphilic amines are applicable to amine-containing analogs or prodrugs of camptothecins.21, 23, 26–29 However, these techniques do not improve the loading efficiency of the lactone forms that lack an ionizable amine group such as DB-67 and camptothecin itself.

Another important consequence of the lack of an ionizable cationic functional group is the poor liposomal retention of the neutral analogs. For example, 28% of the amine-containing camptothecin, lurtotecan, was retained in liposomes 4 h after an i.v. injection20 while only 1% of the neutral camptothecin, SN-38, remained in the circulation 4 h after administration of a liposomal formulation.22 Premature leakage of the encapsulated drug fails to take advantage of the passive tumor targeting of liposomes and increases the potential for side-effects to healthy tissue.

To overcome such delivery-related issues with DB-67, efforts are underway in our laboratories to develop novel cationic and anionic prodrug strategies to improve liposomal encapsulation efficiency during formulation and drug retention in liposomes in vivo. A prerequisite to understanding the factors governing liposomal encapsulation, retention and release in vitro and in vivo is the knowledge of bilayer permeability of the biologically active and presumably bilayer permeating camptothecin lactone. To our knowledge, systematic studies of the lipid bilayer permeability of camptothecins including DB-67 have not been previously reported.

The objective of the current work was to understand the gel phase lipid bilayer permeability of the lactone form of DB-67 in vitro both in aqueous buffer and plasma since pegylated liposomes with a rigid gel phase bilayer have better retention of encapsulated drug in vivo.18 Previously, gel filtration and ultrafiltration methods have been used in these laboratories to study the bilayer permeability of various compounds.30–32 However the high lipophilicity (clog P = 5.4 ± 1.3) (calculated from Advanced Chemistry Development (ACD) Labs software) of DB-67 precluded the use of these methods due to ultrafilter membrane binding and the difficulty of maintaining good sink conditions in transport experiments. Therefore, a dynamic dialysis method to study membrane permeability of hydrophobic solutes has been developed and validated. A mathematical model has also been developed to calculate the bilayer permeability coefficients for hydrophobic solutes using dynamic dialysis and simulations were performed to identify situations where the method is suitable for quantifying liposome release kinetics of hydrophobic compounds. A theoretical estimate of the permeability coefficient for gel phase bilayer permeation of DB-67 was obtained using the bulk solubility-diffusion model and the recently developed “barrier-domain” solubility-diffusion model33 and compared to the experimental value. The kinetics of drug release from liposomes in vivo may be influenced by alteration of the bilayer barrier properties by serum proteins that adsorb to membranes34 and by the presence of trans-bilayer pH gradients. The hydrolysis kinetics of liposome entrapped versus free DB-67 lactone in rat plasma were monitored in the studies described herein to estimate the rate constant for drug release from liposomes in the presence of plasma proteins.

MATERIALS AND METHODS

Materials

1,2-Distearoyl-sn-glycero-3-phosphatidylcholine (DSPC, >99% purity) and 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethyleneglycol)-2000] (m-PEG DSPE, MW = 2806, >99% purity) were purchased as powders from Avanti Polar Lipids (Alabaster, AL) while DB-67 was obtained from Novartis Pharmaceuticals Corporation (East Hanover, NJ). Dialysis tubes (Float-A-Lyzer®, MWCO: 100000) and pre-cut dialysis membrane discs (MWCO: 12000–14000) were purchased from Spectrum Laboratories (Rancho Dominguez, CA). Sephadex™ G-25 M pre-packed size exclusion columns were obtained from GE Healthcare Bio-sciences Corporation (Piscataway, NJ). 1, 9 decadiene was obtained from Sigma–Aldrich Fine Chemicals (St. Louis, MO). All other reagents were purchased from Fisher Scientific (Florence, KY).

Preparation of Liposomes

Pre-weighed lipids, DSPC and m-PEG DSPE (95:5 mol%), were dissolved in chloroform and distributed into test tubes. Chloroform was subsequently evaporated under a stream of nitrogen gas and the residue was vacuum-dried (40°C, 6 h). The dried lipid film was hydrated with acetate (85 mM, pH = 4–4.2) or citrate (100 mM, pH = 4.5) buffer in a 60°C water bath with vigorous shaking to obtain a 16 mg/mL (w/v) lipid suspension. The lipid suspension was extruded (10×, 60°C) through two stacked 200 nm polycarbonate membranes (Nuclepore, Pleasanton, CA) using an extrusion device (Liposofast®, Avestin, Canada) to obtain unilamellar vesicles. Liposomes prepared with acetate buffer were used in partitioning and release experiments in aqueous buffers and liposomes prepared with citrate buffer were used for release kinetics in rat plasma. DB-67 was loaded into liposomes by adding 2–5 µL of a stock solution of DB-67 (1–100 µM) in DMSO to 0.2–1 mL of blank liposome suspension and incubating at 60°C for 2 h. Following their preparation, both blank and drug-loaded liposomes were allowed to cool to room temperature for 3 h and stored at 5°C until the beginning of transport experiments. All vesicle preparations were used within a week. Particle size by dynamic light scattering (DLS, Malvern Zetasizer-3000, Malvern Instruments Ltd, Malvern, UK) and pH were monitored both after preparation and prior to use.

Sampling Procedures

Previous studies in these laboratories demonstrated that DB-67 adsorbs to various surfaces including glassware, pipette tips, pH electrodes, etc.35 A single methanol wash was found to recover most of the adsorbed drug.35 Therefore, all pipette tips used for sampling in partitioning and permeability studies were subjected to a methanol wash and the washings were transferred to the same vial as the sample.

Determination of 1, 9-Decadiene and Lipid Bilayer/Water Partition Coefficients

The 1, 9-decadiene/water partition coefficient for DB-67 was determined by adding a 1 µL stock solution of DB-67 in DMSO to 0.999 mL of 1,9-decadiene pre-washed with 0.04 N HCl to obtain a 50–100 nM concentration. Acetate buffer (1 mL, pH = 4) was mixed with 1 mL of the decadiene containing DB-67 and vigorously vortexed (2 h at 37°C. The mixture was allowed to phase separate overnight at 37°C and the aqueous phase was analyzed for DB-67 concentration. A sample was also collected from the initial decadiene phase prior to addition of the acetate buffer. Samples were diluted in methanol before HPLC analysis.

The liposome membrane/water partition coefficient of DB-67 lactone was determined by equilibrium dialysis (1 mL Teflon® cells, Equilibrium Dialyzer, Spectrum Laboratories). Blank liposome suspension (1 mL, 0.08–0.32 mg lipid/mL) was loaded into the donor compartment and dialyzed at 37°C against 1 mL of DB-67 (5–20 nM) in acetate buffer in the receiver compartment. At equilibrium (24–48 h), 100 µL of liposome suspension and drug solution from the donor and receiver compartments, respectively, were withdrawn and transferred to an HPLC vial followed by a syringe wash (200 µL of acidified methanol) to recover adsorbed drug. Samples were stored at −25°C until HPLC analysis for DB-67.

At equilibrium, the total concentration in the donor compartment containing liposomes can be related to concentration in the bilayer membrane and aqueous phase as follows:

equation image(1a)

where Cd is the total drug concentration in the donor compartment, Cw and Cm are the molar solute concentrations in the aqueous phase and membrane, respectively, and Vd, Vw and Vm are the respective volumes. The volume partition coefficient, Kp can be obtained from dialysis measurements by combining Eq. (1a) with the definition of Kp:

equation image(1b)

where Cr is the drug concentration in the receiver compartment. The volume of the membrane phase was estimated from the lipid concentration and volume occupied per lipid molecule (estimated from bilayer thickness and area per head group).36, 37 The aqueous volume entrapped in each liposome was estimated from the particle size and bilayer thickness.

Determination of Liposome Release Kinetics in Buffers

Liposome entrapped drug was separated from free drug by passing through a Sephadex® G-25 column pre-equilibrated to a required pH (4–4.2) by washing with 50 mL of the acetate buffer. To validate the separation of liposome entrapped from free DB-67, 0.5 mL of drug loaded liposomes were loaded onto a Sephadex® column followed by 35 mL buffer. Eluent fractions (0.2 or 0.5 mL) were analyzed for DB-67 concentration by HPLC and relative lipid concentration by DLS (light scattering intensity of unilamellar vesicles was found to be linearly proportional to lipid concentration over a range of 0.1–1 mM).

DB-67 release kinetics experiments were initiated by passing 75 µL of drug loaded liposome suspension through a Sephadex® column followed by 5 mL of acetate buffer loaded in 1 mL increments. A 5 mL portion of eluent was collected (containing liposome suspension), further diluted to 7.5 mL, and immediately transferred to a dialysis tube preconditioned in deionized water for 15 min and in acetate buffer for 30 min and dialyzed against 1 L of the same buffer at 37°C. At various time points 100 µL of liposome suspension was withdrawn from inside the dialysis tube using a precision pipettor and transferred to a polypropylene vial. The pipette tip was washed with 100 µL acidified methanol and the wash solution was transferred to the same vial. Samples were stored at −25°C until HPLC analysis for DB-67 concentration. Blank liposome suspensions at a lipid concentration similar to that in transport experiments were spiked with DB-67, immediately placed in a dialysis tube, and dialyzed against 1 L acetate buffer in order to determine the influence of the dialysis membrane transport step on the apparent rate of DB-67 efflux from liposomes. Samples were collected at various time points and processed similarly to DB-67 loaded liposome samples.

Determination of Kinetics of DB-67 Release from Liposomes and Rat Plasma Hydrolysis

DB-67 efflux from liposomes was also investigated in rat plasma using an indirect method in which the hydrolysis kinetics of DB-67 were monitored in the presence or absence of liposome encapsulation. Kinetic studies of the hydrolysis of the lactone in plasma were initiated by adding a 1–2 µL stock solution of DB-67 in DMSO to 4 mL of rat plasma in pH 7.4 phosphate buffered saline (PBS) to obtain a concentration of 75–90 nM. Samples were incubated at 37°C and 50 µL of plasma was withdrawn at various times and added to 150 µL of cold (−25°C) methanol:acetonitrile (2:1; (v/v)) in a microcentrifuge tube. The mixture was immediately centrifuged at (−9°C, 14000 rpm, 3 min) and the supernatant was stored at −25°C until HPLC analysis. All samples were kept on dry ice during sample dilutions and transfers from freezer to HPLC sample chamber. Validations of the DB-67 extraction efficiency and quenching of the hydrolysis reaction were performed by spiking blank rat plasma with either DB-67 lactone or carboxylate extractant solution (in cold methanol–acetonitrile) and processing spiked plasma similar to that of the reaction samples. Studies of the hydrolysis kinetics of DB-67 in plasma when added in liposomally entrapped suspensions were initiated after separating liposome entrapped from free drug by size-exclusion chromatography (Sephadex® columns equilibrated with pH 7.4 PBS). A 100–400 µL aliquot of the eluent containing drug-loaded liposomes was added to 4 mL of rat plasma and incubated at 37°C. Samples were collected at various times and processed similarly to those generated in studies of free DB-67 hydrolysis (vide supra).

HPLC Analyses

Samples from liposome partitioning and release experiments were analyzed for DB-67 concentration by HPLC.16 A Waters Alliance 2690 separation system coupled to a Waters fluorescence detector (M474) was employed with excitation and emission wavelengths at 380 and 560 nm, respectively. A Waters Symmetry® C18 (5 µm) column (3.9 × 150 mm) and guard column (3.9 × 20 mm) were used with a mobile phase (48% acetonitrile:52% (v/v) of 2% (pH = 5.5) triethylamine acetate buffer) flow rate of 1 mL/min. Sample compartment temperature was maintained at 4°C and the column was maintained at ambient temperature. DB-67 carboxylate and lactone standards were prepared in 10 mM sodium carbonate buffer (pH = 10.3) and methanol, respectively. The retention times were 1.6 and 5.2 min for DB-67 carboxylate and lactone, respectively.

Lipid analyses were performed using HPLC coupled to an evaporative light scattering detector (ELSD, Sedere, Inc., Lawrenceville, NJ). Separations employed an Allsphere (Alltech Associates, Inc., Deerfield, IL) silica column (5 µm, 4 × 150 mm) without a guard column and a linear gradient, starting with 100% (v/v) mobile phase A (80% chloroform:19.5% methanol:0.5%(v/v) NH4OH) changing to 80% mobile phase A:20% mobile phase B (80% methanol:19.5% water:0.5% (v/v) NH4OH) at 3 min. The gradient was maintained at 80% A:20% B till 7 min and changed back to 100% A by 14 min. The total run time was 15 min at 1 mL/min. ELSD settings included a gain of 10, temperature of 40°C and a pressure of 2.2 lb. Sample compartment temperature was maintained at 4°C and the column was maintained at ambient temperature. The retention time for DSPC was approximately 7.5 min (Fig. 1). Response factor of the standards (prepared in mobile phase A in the range of 0.08–0.32 mg/mL) was calculated using log concentration and log peak area.

Figure 1.

Representative chromatogram obtained during analysis of DSPC by HPLC with ELSD detection.

Samples collected for lipid analysis during partitioning or release experiments were immediately transferred to test tubes, dried under nitrogen, and the resulting lipid film was stored at −25°C until analysis. The lipid films were reconstituted in 75–100 µL of mobile phase A for analysis.

DATA ANALYSIS

Mathematical Model for Drug Efflux from Liposomes in Aqueous Buffer

The permeability coefficient for DB-67 transport across the DSPC lipid bilayer at 37°C was obtained from dynamic dialysis of liposome suspensions containing entrapped DB-67 versus blank liposomes spiked with DB-67 (Scheme 2). Samples taken from inside the dialysis tube at various times were analyzed for total drug remaining. The total mass of DB-67 (Md) in the dialysis tube at any given time is:

equation image(2a)

where Mi and Mo are masses of DB-67 inside and outside the liposomes. The total volume of liposome suspension in the dialysis tube, Vd, is:

equation image(2b)

where Vi is the total liposomally entrapped aqueous volume plus the lipid volume in the inner bilayer leaflet of vesicles in the suspension and Vo is the extravesicular aqueous volume along with the volume of lipid located in the outer leaflet of suspended liposomes in the dialysis tube. For a total number of vesicles, n, Vi and Vo can be expressed as:

equation image(2c)
equation image(2d)

where equation image and equation image are the volumes of the inner aqueous compartment and inner monolayer in each vesicle, respectively, equation image is the volume of the outer monolayer in each vesicle and equation image is the extravesicular aqueous volume in the dialysis tube.

Scheme 2.

Schematic depicting liposome loaded (Panel A) versus liposome spiked (Panel B) experiments used in DB-67 (represented by D) permeability studies. Rate constants km and kd are the rate constants for permeation across the bilayer membrane and dialysis tube membrane respectively.

Converting masses in Eq. (2a) to corresponding concentrations,

equation image(2e)
equation image(2f)
equation image(2g)

where, L is the total suspension concentration of DB-67 in the dialysis tube, Li and Lo are internal and external system concentrations of DB-67, and x is the ratio of the volume outside and inside the vesicles, where, again, the volume of the inner bilayer leaflet is included as a component of the internal volume while the outer bilayer leaflet contributes to the external volume.

The total internal mass of DB-67, Mi, can be related to the masses of drug in the liposome aqueous core (equation image) and bound to the inner monolayer (equation image) which provides the following expression after dividing by Vi:

equation image(3a)

Eq. (3a) can also be expressed as:

equation image(3b)

where a and b are the ratios of total internal volume of the vesicles to the total entrapped aqueous core volume and total volume of lipid in the inner leaflets. Defining Kp, the volume-based partition coefficient, as:

equation image(3c)

The concentration of drug in each intravesicular compartment can be described:

equation image(3d)
equation image(3e)

where equation image and equation image are concentrations of drug in the liposome aqueous core and inner monolayer, respectively, and αi and βi are factors to convert the total internal system concentration (Li) to the respective drug concentrations in the aqueous and membrane phases. The fractions of free and membrane bound drug inside the vesicles are αi/α and βi/b, respectively. The parameters a and b are dependent on vesicle size and bilayer thickness but independent of the lipid concentration. The value of a approaches one (b → ∞) with increasing vesicle size since the thickness of the membrane becomes negligible compared to the total diameter.

Similar to the above treatment, the concentrations of drug in the external aqueous compartment within the dialysis tube (equation image) and in the outer monolayer (equation image) are:

equation image(4a)
equation image(4b)

where c and d are the ratios of total external volume to that of the external aqueous volume and the outer monolayer volume, respectively, and αo and βo are multiplying factors to obtain the respective drug concentrations in the external aqueous and membrane phases from the total external concentration within the dialysis tube. The fractions of free and membrane bound drug in the external compartment are αo/c and βo/d, respectively. The parameters c and d are dependent on vesicle size, bilayer thickness, and the lipid concentration in the suspension. The value of c approaches one (d → ∞) in dilute liposome suspensions since the entrapped volume becomes negligible compared to the total suspension volume.

The solute flux across a homogeneous membrane derived from Fick's first law is:

equation image(5a)

where Dm is the diffusion coefficient within the membrane, Km/w is the membrane/water partition coefficient, and A and hm are the membrane area and thickness, respectively. (Although lipid bilayer heterogeneity implies that a more complex treatment than that in Eq. (5a) is necessary, the “barrier-domain” solubility-diffusion model for lipid bilayer permeability attempts to circumvent this complication by assuming that the barrier properties of lipid bilayers reflect a nearly homogeneous sub-domain (e.g., the ordered hydrocarbon chain region; vide infra). Under these conditions, the diffusion coefficient, partition coefficient and membrane thickness in Eq. (5a) refer to properties of the barrier domain.) Eq. (5a) can also be expressed in terms of the permeability coefficient, equation image:

equation image(5b)

Mass flux can be converted to the corresponding change in internal liposomal drug concentration:

equation image(5c)
equation image(5d)

where km, the first-order rate constant for efflux, can be used to calculate Pm.

equation image(5e)

Similarly, the rates of change of external drug concentration (Lo) within the dialysis tube and drug concentration (Lb) in the reservoir in which the dialysis tube is immersed having a volume Vbulk are:

equation image(6a)
equation image(6b)
equation image(6c)

where kd is the first-order rate constant for drug permeation across the dialysis membrane. Eqs. (6a–6c) assume sink conditions in the reservoir (i.e., drug concentration in the reservoir is negligible in comparison to the external drug concentration within the dialysis tube (equation image)) such that back flux of drug into the dialysis tube can be ignored.

Eqs. (5d) and (6b) can be solved using Laplace transforms to obtain the following general solutions:

equation image(7a)
equation image(7b)
equation image(7c)
equation image(7d)
equation image(7e)

In the present experiments, the total drug concentration versus time profiles inside the dialysis tube [L(t)] initially containing either drug-loaded liposomes or blank liposomes with drug spiked into the external aqueous compartment were fit to Eq. (7e) subject to the revelant initial conditions for drug-loaded (At t = 0, Li = Li(0); Lo = 0) or spiked (At t = 0, Li = 0; Lo = Lo(0)) liposome suspensions by non-linear least squares regression analysis (Scientist®, Micromath Scientific Software, St. Louis, MO). The volume ratios (a, b, c, d) used to calculate the fractions of drug bound inside and outside the vesicles were obtained from the lipid concentration and the particle size of the liposomes (after calculation of liposome entrapped and free volume, see Eqs. 3b and 4a). Since literature studies employing dynamic dialysis to monitor drug release from liposomes or nanoparticles often assume a simple first-order rate constant for drug efflux from the dialysis tube or drug appearance in the reservoir, it is of interest to explore the experimental conditions or parameter values under which the above solutions reduce to simple first-order behavior. At steady-state equation image, the ratio of the external drug concentration within the dialysis tube to that inside the vesicles can be expressed as:

equation image(8a)

Substituting Eq. (8a) into Eq. (5d) and simplifying gives:

equation image(8b)

If the rate constant for drug transport across the dialysis membrane is much faster than back flux into the liposomes (equation image), Eq. (8b) can be further simplified:

equation image(8c)
equation image(8d)

Under these conditions, the apparent permeability coefficient (Papp) generated from the apparent first-order rate constant (kapp) can be used to calculate the true permeability coefficient (Pm):

equation image(8e)

Thus, under the appropriate conditions (i.e.,equation image), an accurate liposomal membrane permeability coefficient can be obtained from the apparent rate constant for drug efflux from the dialysis tube after correction for drug binding to the inner monolayer. The conditions under which Eq. (8d) could be employed were explored quantitatively by generating drug concentration-time profiles in the dialysis tube using Eq. (7e) then applying Eqs. (8d) and (8e) to obtain a value for Pm that could be compared to the original value used in the simulations.

Obtaining a reliable value for Pm by dynamic dialysis requires that the rate of drug disappearance from the dialysis tube be governed by the apparent rate constant for release from the vesicles (kapp < kd). This condition inherently puts an upper limit on the maximum apparent permeability coefficient that can be obtained by this method as equation image, where Rv is the radius of the vesicle. At steady-state and when back flux of drug into the liposomes can be ignored (i.e.,equation image), the maximum membrane permeability coefficient that can be determined using the dynamic dialysis method is:

equation image(8f)

Upon substitution of the relevant volume terms for αi, and simplifying, this upper Pm value can be expressed as a function of vesicle radius, permeant partition coefficient, bilayer thickness and the rate constant for dialysis tube permeation:

equation image(8g)

Mathematical Model for DB-67 Efflux from Liposomes and Hydrolysis in Plasma

Since the volume of liposomes added to plasma was small compared to the total volume of plasma and both DB-67 lactone and carboxylate bind to plasma proteins with high affinity,7, 8, 10, 11 sink conditions were assumed for drug released from liposomes into plasma. Due to the low pH inside the liposomes (pH = 4) and the ability of citrate buffer to maintain the trans-membrane pH gradient in plasma (pH = 7.4) for the time period of this study, all of the entrapped DB-67 was assumed to exist in lactone form. Carboxylate was assumed to form only from DB-67 lactone after its release into plasma. Rate equations for the liposomal and plasma lactone and carboxylate concentrations are then:

equation image(9a)
equation image(9b)
equation image(9c)

where equation image is the first-order rate constant for transport of the lactone from liposomes into plasma, Li and Lo are the concentrations of lactone inside liposomes and in plasma, respectively, Co is the concentration of carboxylate in plasma, and ko and kc are the rate constants for lactone ring-opening and closing in plasma, respectively.

The kinetics of hydrolysis of drug added directly to plasma could also be described by Eq. (9b) (excluding the liposome transport term) and (9c). Data from the hydrolysis kinetics of liposomally entrapped DB-67 and nonliposomal DB-67 were fit simultaneously to Eqs. (9a–9c) to obtain estimates of equation image, ko, and kc by nonlinear least-squares regression analysis. The liposomal permeability of DB-67 in plasma could then be obtained from equation image using Eq. (5e).

RESULTS

Validation of Analytical Methods and Characterization of Liposomes

DB-67 samples from size exclusion chromatography, partitioning studies and dynamic dialysis studies were analyzed by HPLC with fluorescence detection. Initial DB-67 concentrations were in the range of 50–2700 and 20–200 nM in the dynamic dialysis experiments and bilayer/water partition coefficient determinations, respectively. The HPLC response was found to be linear from 5 to 30 nM for DB-67 lactone so all samples were diluted in acidified methanol to a lactone concentration within this range. Coefficients of variation in the response factors were ±5% intraday and ±6% interday.

The initial concentrations of DB-67 in plasma hydrolysis experiments ranged from 50 to 300 nM. The HPLC response factor for DB-67 carboxylate was linear over the range 10–100 nM. Plasma extracts were directly analyzed by HPLC or further diluted with cold methanol–acetonitrile where necessary to be within this range. Precision of DB-67 carboxylate response factors was ±3% intraday (±5% interday). The extraction efficiency of DB-67 in spiked plasma samples using DB-67 concentrations of 10–1000 nM was >95% and the lactone–carboxylate interconversion quenching efficiency was 100% (Fig. 2).

Figure 2.

Extraction of DB-67 from plasma at varying DB-67 concentration (Panel A) and the quenching efficiency of the reaction between DB-67 lactone and carboxylate (Panel B) starting from either lactone or carboxylate as the initial reactant.

Liposomes prepared for these studies exhibited particle diameters of 190 ± 55 nm obtained by DLS. Particle diameter and pH of vesicle suspensions were constant after preparation and during storage. For both dynamic dialysis and plasma hydrolysis experiments, liposome loaded drug was separated from free drug by size exclusion chromatography while monitoring light scattering intensity (kilocounts/s (Kcts)) of eluent fractions. Representative elution profiles for DB-67 and drug-loaded liposomes are shown in Figure 3. Liposomes eluted between 2.5–5 mL and were well separated from the free drug.

Figure 3.

Elution profiles of free (▵) or liposome loaded DB-67 (▴) as determined by HPLC (nM) and liposomes (□) as determined by light scattering intensity (kilocounts/s (Kcts)).

The lipid concentration in liposome suspensions was 0.16 mg/mL during dynamic dialysis studies (after Sephadex® elution and dilution) and 0.032 mg/mL during plasma hydrolysis experiments. Lipid concentration was analyzed during bilayer/water partition studies and bilayer transport studies by gradient HPLC with ELSD detection. The response factor (RF) was non-linear within the fourfold concentration range of the standards employed. Therefore a log concentration versus log peak area was used to calculate the response factor. Precision of the assay was ±6% intraday and ±<8% interday. Since DSPC composition was 95% of the total lipid in the vesicles and given the similar chain length of both DSPC and DSPE, the vesicles were assumed to be 100% DSPC for estimation of volume parameters. Previously reported36 values for bilayer and head group thickness of DSPC vesicles were used to calculate volume ratio parameters (a, b, c, d, x) for the estimation of permeability coefficients.

1, 9-Decadiene and Lipid Bilayer/Water Partition Coefficients

A 1, 9 decadiene/water partition coefficient for DB-67 of 1.08 ± 0.11 (n = 4) was found. The concentration dependence of this value was not explored due to the low solubility of DB-67 both in decadiene and pH 4 acetate buffer.16

Figure 4 shows the partition coefficient of DB-67 determined by equilibrium dialysis as a function of lipid concentration. The drug concentration could not be varied over a wide range in the partition experiments here due the low intrinsic solubility of DB-67.16 Within the concentration range used (20–200 nM), the partition coefficient was found to be 2443 ± 230 and independent of drug and lipid concentration. Equilibrium was attained within 24 h and lipid analysis indicated that the concentration of DSPC remained constant over this period.

Figure 4.

Membrane (DSPC with 5mol% m-PEG DSPE) partition coefficient of DB-67 (Mean ± SD) as a function of varying lipid concentration.

Efflux of DB-67 from Liposomes in Aqueous Buffer

Initial studies of DB-67 permeability were conducted using a previously developed ultrafiltration technique.30–32 However this method was found to be unsuitable due to significant adsorption of DB-67 lactone to ultrafilter membranes (data not shown) and the inability to maintain sink conditions in a reasonable extravesicular volume.

The dynamic dialysis method developed involves monitoring the liposome suspension concentration of DB-67 within the dialysis tube as a function of time while dialyzing the suspension against a large reservoir of buffer to maintain sink conditions and ensure complete release of entrapped drug. Initially, the reservoir solution was magnetically stirred during the transport experiments but significant increases in lipid concentration within the dialysis tube were observed, reflecting an apparent reduction in fluid volume presumably due to an increase in fluid pressure on the dialysis tube during stirring. A decrease in stirring rate did not completely ameliorate fluctuations in lipid concentration. In the absence of stirring, the lipid concentration in the dialysis tube remained constant during the transport experiments (Fig. 5).

Figure 5.

Concentration of DSPC (□) in the dialysis tube during transport experiments. DSPC was analyzed by a gradient HPLC method with ELSD detection.

Figure 6 shows the fractions of initial DB-67 lactone (mean ± SD) remaining in the liposomal suspension within the dialysis tube at various times after introducing liposomes containing varying concentration of entrapped DB-67 or spiking blank liposome suspensions with DB-67. The apparent half-life for loss of liposomally entrapped DB-67 lactone (based on the decline in drug concentration inside the dialysis tube) was 3.33 ± 0.24 h compared to 0.50 ± 0.04 h for DB-67 added to blank liposomes. This ∼6-fold difference did not appear to be sufficiently large to justify the steady-state assumption. Therefore, the complete transport model developed previously (Eq. 7e and supporting equations) was used to simultaneously fit the two concentration-time profiles. Table 1 lists the estimated phase volume ratios and other constants that were used in the regression analyses.

Figure 6.

Fractions of initial amount of DB-67 lactone (mean ± SD, n = 4) remaining inside the dialysis tube in liposomes spiked with drug (●) or liposomes entrapped with drug (▪). The solid line is a fit of the data generated using Eqs. (7a–7e). The initial DB-67 concentration (entrapped) of the liposome suspension ranged from 50 to 2700 nM.

Table 1. Estimated Phase Volume Ratios and other parameters for the Lipid Concentration used in the Transport Experiments in Buffers and Plasma
ParameterBufferPlasma
  1. Parameters a and b are the ratios of the total intravesicular volume to that of the aqueous core and inner lipid monolayer volumes, respectively. Parameters b and c are the ratios of the total extravesicular volume in the dialysis tube to that of the aqueous and outer lipid monolayer volumes, respectively. n is the number of vesicles, Kp is the volume partition coefficient and x is the ratio of total unentrapped to entrapped volume.

n2.4 × 10114.3 × 1010
a1.071.07
b15.6715.67
c11
d1932896700
x12896447
Kp2443 ± 2302443 ± 230
Suspension lipid concentration0.16 mg/mL0.032 mg/mL

The solid lines shown in Figure 6 represent the fitted profiles for the fraction of DB-67 lactone remaining in the dialysis tube from which values for km and kd, the first-order rate constants for DB-67 transport across the liposome and dialysis membranes, respectively, were generated. At the lipid concentration employed (0.16 mg/mL), greater than 99% of the entrapped drug is bound to the inner bilayer leaflet. Using the fitted value for km, the membrane permeability coefficient for DB-67 lactone was found to be 3.5 ± 1.0 × 10−8 cm/s.

Based on the experimentally measured value for Kp, about 13% of the drug released from liposomes but remaining within the dialysis tube is bound to the outer monolayer. This was considered in the mathematical model used to fit the data in Figure 6. Using the value for km, the half-life for liposomal release of DB-67 under sink conditions (conditions in which drug binding to the outer monolayer of liposomes is negligible) can be estimated to be 2.75 ± 0.29 h. Similarly, the half-life for release of DB-67 from the dialysis tube under sink conditions and in the absence of perturbing effects from liposomes in the dialysis tube can be estimated from kd to be 0.44 ± 0.02 h.

Table 2 displays the calculated values of km, the corresponding liposomal membrane permeability coefficient of DB-67, and kd as a function of drug concentration over a concentration range of 50–2700 nM. Within this concentration range, the transport parameters were observed to be independent of drug concentration. Due to the low solubility of DB-67 lactone,16 formulation of liposomes at higher encapsulated drug concentrations was not feasible.

Table 2. Estimated Rate Constants for Lipid Bilayer and Dialysis Membrane Transport (± 95% CI) of DB-67 in Dynamic Dialysis Experiments and the Intrinsic Permeability Coefficients for Bilayer Membrane Transport of DB-67 Obtained from Application of the Model Described in Eqs. (7a–7e) at Varying Concentrations of DB-67
Initial DB-67 Concentration in Liposome Suspension (nM)km (h−1)kd (h−1)Pm (×108) cm/s
5543.5 ± 3.81.27 ± 0.113.8 ± 1.2
18043.3 ± 4.71.60 ± 0.153.8 ± 1.2
82037.6 ± 2.91.73 ± 0.163.3 ± 1.0
267040.0 ± 4.31.47 ± 0.143.5 ± 1.1

Kinetics of DB-67 Lactone Release from Liposomes and Hydrolysis in Rat Plasma

The kinetics of DB-67 release from liposomes were also evaluated by comparing the hydrolysis kinetics of free versus liposome encapsulated DB-67 in rat plasma. Figure 7 shows the observed lactone and carboxylate concentration (mean ± SD) versus time profiles generated after a liposome suspension containing entrapped DB-67 or free DB-67 lactone were added to plasma. The data in Figure 7 were fit simultaneously (Eqs. 9a–9c) assuming that hydrolysis of DB-67 lactone to DB-67 carboxylate occurs after lactone release from liposomes. The assumption that the liposomally entrapped species is the lactone form over the 12 h period during which hydrolysis was monitored is supported by the fact that citrate buffer has been shown to maintain a low pH inside liposomes for more than 24 h in vivo.38

Figure 7.

Concentration-time profiles (n = 4) for the disappearance of DB-67 lactone (Mean ± SD) when entrapped in liposomes (□) or as free drug (Δ) and the appearance of DB-67 carboxylate (mean ± SD) in liposome entrapped (▪) or free (▴) plasma hydrolysis experiments. The solid lines were generated by fitting the concentration-time data to Eqs. (9a–9c).

The curves in Figure 7 represent the best fits of Eqs. (9a–9c) to the experimental data. From the value for equation image, the liposome permeability coefficient for DB-67 lactone was found to be 3.1 ± 1.0 × 10−8 cm/s in plasma, which is not significantly different from that observed in aqueous buffers. The rate constants for DB-67 lactone ring-opening and ring-closure in plasma (pH ∼ 7.4) were observed to be 1.04 ± 0.11 and 0.24 ± 0.07 h−1, corresponding to a half-life to equilibrium for ring opening of DB-67 of 39.9 ± 4.3 min which is slightly higher than that in PBS (31.8 ± 0.4 min) but much lower than that in whole blood (133 ± 16 min).1 The half-life to equilibrium for DB-67 lactone ring-opening is much greater than that for camptothecin in rat plasma (4.6 min).39 This is consistent with the hypothesis that blood stability of DB-67 lactone is improved compared to camptothecin due to differences in protein binding and partitioning into red blood cell membranes.

DISCUSSION

Liposomal Formulation of Neutral and Weakly Acidic Amphiphiles

The therapeutic class of camptothecins consists both of hydrophobic compounds that are unionized in their lactone form but weakly acidic after lactone ring-opening (DB-67, karenitecin, SN-38, 9-nitro camptothecin etc.) and weakly basic amines (topotecan, irinotecan, lurtotecan, exatecan, etc.). The active form of the drug is the neutral lactone form and it is desirable to deliver the active form of the drug to tumor tissue.

Liposomes are being considered for the formulation of a variety of anticancer agents following the clinical success of liposomal doxorubicin.40–42 Success of liposomal formulations relies on the ability to load drugs at therapeutically relevant concentrations and retain the encapsulated drug in liposomes while in the circulation. Most formulation techniques developed thus far for encapsulation of anti-cancer agents including camptothecins are active loading methods (e.g., pH, ion or ammonium sulfate gradient methods) modeled after methods that were useful for loading doxorubicin, an amphiphilic amine. The successful retention of amphiphilic amines entrapped by these active loading methods has been due to trans-membrane pH gradients that are retained in vivo (low intraliposomal pH) or intraliposomal drug or salt precipitation that results in improved retention.28, 38, 43–47

Liposome loading and retention strategies developed for amphiphilic amines allow for the loading and retention of the active lactone form of cationic (i.e., weakly basic amine-containing) camptothecins but such techniques are not useful for neutral analogues. For example, DB-67 has been previously loaded into DMPC vesicles using a passive encapsulation technique that relies on the binding of the lactone form of the drug to the liposome membrane but the pharmacokinetic profile for DB-67 when administered in DMPC liposomes did not differ significantly from that of the free drug due to the rapid leakage of encapsulated drug (Zamboni et al., Unpublished work).

Two techniques that have been proposed recently for liposomal loading of neutral compounds and weak acids include attempts to entrap drug-cyclodextrin (CD) complexes48–50 and drug loading in the presence of a trans-membrane pH gradient combined with a metal ion (Na+, Ca2+) gradient.51 Both techniques have shown improved drug loading but have failed to prolong liposome retention to the extent that has been possible with amphiphilic amine-containing compounds. The lack of success of the drug-CD entrapment strategy has been attributed to lipid bilayer destabilization by entrapped cyclodextrin.48–50, 52, 53 Thus, in spite of the demonstration of excellent anti-cancer activity by several neutral or weakly acidic hydrophobic compounds, active liposomal loading and retention strategies have not been successful for this group of compounds.

In the present studies in plasma, a prolonged liposomal retention half-life of approximately 3 h (Fig. 7) has been observed by encapsulation of DB-67 in rigid gel phase DSPC bilayers. Given this substantial improvement in retention, it would be of interest to ascertain whether or not this value could have been anticipated and whether or not retention could be prolonged further.

The “Barrier-Domain” Solubility Diffusion Model Estimate of the Permeability Coefficient of DB-67

The success of formulation-based approaches for improving the liposome loading and retention of drug candidates relies to a large extent on altering the rate of bilayer permeation of the encapsulated material (drug plus excipients). Systematic selection and manipulation of variables such pH, buffers, lipid composition and other excipients may enable one to control the retention of neutral and weakly acidic hydrophobic compounds. If the effects of these variables on bilayer permeability could be fully understood it may be possible to predict the permeability of a given compound under various conditions. Previous studies in these and other laboratories have investigated the role of membrane composition and pH on the bilayer permeability of weak acids and predictive relationships have been developed to account for the effect of varying pH and bilayer phase structure on permeability.30–33, 36, 54

Approaches to predict passive permeability across lipid bilayers and biomembranes based solely on the structure of the permeant and compositions of the membrane have been the subject of research in biology for over a century. The simplest model is the bulk-solubility diffusion model which assumes that the membrane is homogenous and isotropic. The permeability coefficient derived from this model is:

equation image(10a)

where Po is the permeability coefficient, PCm/w is the membrane/water partition coefficient, hm is the thickness of the membrane and Dm is the diffusion coefficient.

Taking into account the heterogeneity of the bilayer, Diamond and Katz55 proposed a general expression for the passive permeability of a solute across a membrane:

equation image(10b)

where Pm is the permeability coefficient, K(x) and D(x) are the local partition and diffusion coefficients at a depth x normal to the bilayer and r′ and r″ are interfacial resistances.

Xiang and Anderson further simplified the above model by assuming that permeability across a bilayer may be rate-limited by a distinct region (barrier-domain) within the bilayer.33 The barrier domain was shown to exhibit a chemical selectivity similar to that expected for the hydrocarbon chain region in liquid crystalline bilayers though its properties vary somewhat with the lipid bilayer phase structure.31, 36, 54, 56 Xiang and Anderson31–33, 36, 56, 57 also developed a model to account for the effects of bilayer chain ordering as well as permeant size on the permeability. The permeability coefficient according to the “barrier-domain” solubility diffusion mode is:54

equation image(10c)

where Kbarrier/water is the barrier/water partition coefficient of the solute, hbarrier is the thickness of the bilayer chain region, and Dm is the diffusion coefficient. Pm has been shown to be equal to the product of permeability coefficient, Po from the homogeneous bulk solubility diffusion theory and a scaling factor f, the permeability decrement due to lipid chain ordering. The scaling factor f was shown to be dependent on the two-dimensional packing structure, as characterized by the free surface area per lipid molecule, af, and the solute size parameter, as:56

equation image(10d)

where as is the minimum cross sectional area of the solute and fo and λ are constants independent of permeant size and bilayer packing structure. Depending on the composition of the membrane, the chemical selectivity of the “barrier-domain” has been shown to be mimicked by suitable reference solvents, exemplified by 1,9-decadiene in the case of phosphatidylcholine and egg lecithin bilayers.30, 32, 33, 36, 54 Thus, the “barrier-domain” model described by Eqs. (10c) and (10d) provides a simple framework to predict the passive permeability of a solute through the membrane of interest from parameters that can be either experimentally determined or calculated.

A theoretical estimate of the permeability coefficient for DB-67 across a gel phase bilayer was obtained using Eqs. (10a–10d), and compared to the experimentally observed value. Po was estimated using 1, 9-decadiene as a reference solvent. The diffusion coefficient for DB-67 in 1,9 decadiene was estimated to be 1.23 × 10−5 cm2/s using a relation previously developed from experimental diffusivities for a series of alkane homologues in hexadecane:56, 58

equation image(10e)

where η is the viscosity of decadiene (0.755 cp, 25°C) and Vs is the molecular volume of the solute (Å3). The molecular volume of DB-67 (413 Å3) was calculated from the atomic additivity method.59 The thickness of the barrier domain was estimated to be 3.91 × 10−7 cm for a DSPC bilayer.36 From the decadiene/water partition coefficient for DB-67 (=1.08) and estimates of its diffusion coefficient and the membrane thickness, Po was calculated from bulk solubility-diffusion theory (Eq. 10a) to be 33.97 cm/s.

The permeability decrement due to lipid chain-ordering, f, was estimated to be 1.3 × 10−8 from a plot (Fig. 8) of solute cross sectional area (=87 Å2 for DB-67) versus the natural logarithm of f based on previously observed values for the gel phase permeability of a series of monocarboxylic acids at 37°C.56 The membrane permeability coefficient of DB-67, corrected by this permeability decrement due to chain ordering was then estimated (Eq. 10c) to be 4.42 × 10−7 cm/s.

Figure 8.

Effect of solute size (Å2) on permeability decrement (f) for transport across a gel phase bilayer. The extrapolated dashed line is a best fit of the experimental values (▪) obtained previously for a series of carboxylic acids.56 “Barrier-domain” model predicted (▴) and experimentally observed (Δ) values of DB-67 are also shown.

The experimental permeability value of DB-67 (=3.5 ± 1.0 × 10−8 cm/s) is nine orders of magnitude lower than that predicted from the bulk solubility diffusion model but within an order of magnitude of that predicted from the “barrier-domain” solubility diffusion model. The success of the “barrier-domain” model in predicting the permeability of DB-67 appears to be the result of taking into account the effects of chain ordering combined with the large permeant size. The plot in Figure 8 shows the predicted permeability decrement using the “barrier-domain” model and the observed value from experiments. The lower experimentally observed value compared to that predicted from the “barrier-domain” model suggests a slightly greater sensitivity to permeant size due to lipid chain ordering than that predicted by the “barrier-domain” model. The discrepancy between the observed and predicted values in the case of DB-67 may be attributed to two factors. Firstly, the f values for various solutes in Figure 8 used to predict the gel phase permeability of DB-67, were experimental values in dipalmitoylphosphatidylcholine (DPPC) bilayers and not the longer chain DSPC (pegylated) used in the experiments here. Secondly, the size of the permeants in Figure 8 that were used to estimate the permeability value are much smaller than DB-67. The size of the largest permeant in Figure 8 is about fourfold smaller than DB-67. Due to the lack of gel phase permeability data for larger solutes, the values for the series of permeants previously tested in the investigators' laboratories were used here.56 The slope of the plot in Figure 8 is very sensitive to permeant size. A broader range of solute sizes may yield a better estimate of the slope and consequently better estimates of permeability coefficient.

Dynamic Dialysis Method to Study Liposome Release Kinetics of Hydrophobic Drugs—Validation of the Model and Pitfalls in Applying Simpler Models

While liposomal permeability coefficients for slowly transported hydrophilic solutes can be reliably measured by a variety of methods including ultrafiltration, ultracentrifugation, and various dialysis techniques, measuring the release kinetics of hydrophobic solutes such as DB-67 from liposomes or other nanoparticles may be complicated by their poor aqueous solubility, high membrane partitioning, extensive adsorption to other surfaces (e.g., ultrafiltration membranes, glass, etc.) and potentially rapid release rates. Low solubility coupled with extensive adsorption to surfaces may complicate sampling procedures and cause errors in analyses. Hydrophobic drugs having a high affinity for liposomal membranes may cause difficulties in maintaining sink conditions. The lack of sink conditions during release experiments can lead to misleading results and incorrect values for intrinsic permeability coefficients unless an appropriate mathematical model that takes into account the approach to equilibrium is used to fit the data.60

Dialysis methods are popular for obtaining release kinetics of entrapped drug from liposomes and other particulate drug carriers since sink conditions are assumed to be readily established by simply dialyzing against a large volume of dialysate or by the addition of binding/complexing agents (proteins, lipids, etc.) to the dialysate to create a thermodynamic activity gradient. Even when such approaches are used, maintaining sink conditions during dialysis can be particularly difficult for hydrophobic solutes, especially when high lipid concentrations or trans-membrane pH gradients (high extravesicular pH in the case of bases or low extravesicular pH in the case of acids) are employed. Data from such experiments are often shown as a percent of drug retained or released from the donor compartment as a function of time without any further analysis.60–62 It is often implicitly assumed that release from the carrier is first-order and that the dialysis membrane is not influencing the process (kapp < kd, Eqs. 8a–8g) such that the apparent release rate in fact reflects release from the carrier. Several validation experiments are required before the apparent release kinetics of hydrophobic compounds from a donor compartment containing the liposome suspension can be considered as representative of the kinetics of release from the carrier itself. These include selection of appropriate experimental conditions (lipid concentration, dialysate volume), selection of the appropriate sampling compartment and sampling procedures, and verification that steady-state conditions apply.

The utility of the dynamic dialysis method for accurately determining liposome or other nanoparticle release rates requires that release rate from the drug carrier to be the slow step when compared to the rate of transport across the dialysis membrane. Figure 9 (generated using Eq. 8g) shows the upper limit for permeability coefficient that can be measured using the dynamic dialysis method as a function of the bilayer/water partition coefficient of the permeant at three different values for the half-life of drug transport across the dialysis membrane in the absence of drug carrier. If the bilayer/water and 1,9-decadiene partition coefficients are determined for a given hydrophobic solute, then Eq. 8g in conjunction with the “barrier-domain” model can be used to predict if the dynamic dialysis method will produce reliable values for the membrane permeability coefficient and liposome release kinetics of a given permeant.

Figure 9.

Simulation of the maximum permeability coefficient (Pm) that can be measured using the dynamic dialysis method as a function of the bilayer/water partition coefficient (Kp) when the half-life for transport of free drug across the dialysis tube membrane is 15 min (- - -), 30min (…) or 60 (––) min.

High lipid concentrations (>10 mg/mL) are often used during the formulation of liposomal drug delivery systems and may also be employed in release studies using dialysis methods. Figure 10A shows the simulated effect of varying liposome concentration in the dialysis tube on the rate of appearance of DB-67 outside the dialysis tube. It is evident that the apparent rate constant for DB-67 appearance in the bulk volume outside the dialysis tube is dependent on the lipid concentration. The concentration-time profile shown by the solid line in Figure 10A represents the true release profile if sink conditions could be established (i.e., if the dialysis membrane were absent). Only at the lowest lipid concentration shown does the rate of appearance in the external reservoir resemble the true rate of release. This is due to more perfect sink conditions within the extraliposomal volume (inside the dialysis tube) at low lipid concentrations (i.e., Lo → 0). Figure 10B also shows the effect of varying liposome concentration on the build-up of liposomally released drug inside the dialysis tube. Again, only at the lowest lipid concentration is the steady-state approximation reasonable. Figure 11 shows the % error in the estimation of the liposomal release rate constant by use of the steady-state approximation (Eq. 8d) to fit the concentration-time profiles shown in Figure 11. Even when good sink conditions are maintained in the external reservoir, caution must be exercised in using dynamic dialysis to assess liposome release kinetics of hydrophobic drugs due to possible experimental artifacts or incorrect model assumptions.

Figure 10.

Simulated concentration-time profiles for the appearance of DB-67 lactone (shown as fraction of initial drug concentration) in the bulk volume outside the dialysis tube (Panel A) and outside the liposomes in the dialysis tube (Panel B) at varying lipid concentrations (Δ-0.15mg/mL; □-1.5mg/mL; ×-5mg/mL and ◊-15mg/mL). Solid line in Panel A represents the concentration outside the liposomes if sink conditions can be established without using a dialysis membrane.

Figure 11.

% Error in estimation of the liposome release rate constant as a function of suspension lipid concentration using either the steady-state approximation (▵, Eq. 8d) or the general model (▴, Eqs. 7a–7e). The lipid concentration for the general model was 0.16 mg/mL. Concentration time-profiles shown in Figure 11 were used for estimation of the rate constants.

The general mathematical model (Eqs. 7a–7e) developed herein takes into account the effects of membrane binding and corrects for the lack of steady-state conditions, if necessary, to determine a reliable rate constant for liposome release. As illustrated in Figure 11, the use of the general mathematical model (Eqs. 7a–7e) provides reliable rate constants for drug release from liposomes even when the steady-state assumption within the dialysis tube is invalid.

As shown in Figure 6, the complete transport model described in Eqs. (7a–7e) was able to simultaneously fit the relative concentrations for DB-67 lactone remaining in the liposomal suspension within the dialysis tube at various times after introducing liposomes containing entrapped DB-67 or spiking blank liposome suspensions with DB-67. The effect of drug concentration on the permeability of DB-67 was explored by varying the drug concentration by two orders-of-magnitude. The permeability coefficient values in Table 2 obtained with varying DB-67 concentration show that the permeability coefficient for DB-67 is independent of drug concentration.

Comparison of the Kinetics of Liposomal Release of DB-67 in Buffer and in Plasma

The dynamic dialysis method was developed and validated to study the membrane permeability and release kinetics of liposome encapsulated DB-67 lactone in aqueous buffers. Given the ultimate intent to use liposomes for in vivo drug delivery, methods to compare the kinetics of drug release from liposomes in both buffer and plasma, with the aim of understanding possible effects of plasma proteins on the gel phase bilayer permeability are of interest. A relatively simple indirect method was therefore developed to study the release of DB-67 lactone in plasma by comparing the kinetics of hydrolysis of free and liposomally entrapped lactone. Evaluating drug release kinetics after intravenous injection of liposomes in vivo requires methods to separate liposome entrapped drug from protein bound and free drug in plasma.63–67 Separation methods such as gel filtration, solid-phase extraction or ultrafiltration may be possible but additional validation would be required. The fraction of liposomally entrapped drug may be altered during the separation process if the method of separation is not relatively fast. This problem can be severe for compounds with a relatively short half-life for liposomal release in plasma. The method employed in this study does not require separation of liposome entrapped and free drug and is much simpler to use.

The similar apparent permeability coefficients obtained both in aqueous buffers and plasma (Fig. 7) suggests that the barrier to DB-67 permeation is not significantly altered in the presence of plasma proteins in vitro. This observation has to be further confirmed in an in vivo animal model.

Correction for Membrane Binding in Determining Permeability of Hydrophobic Solutes such as DB-67

In the present work, a novel mathematical model has been developed to determine intrinsic permeability coefficients (i.e., permeability coefficients of the neutral, unbound species) from release data using the dynamic dialysis method. In keeping with Fick's law, the model (Eqs. 6a and 6b) requires knowledge of the permeant concentration gradient from the aqueous core of the liposome to the external aqueous solution. An important factor that must therefore be accounted for in the model is the binding of the permeant to the lipid bilayer. Similar considerations are applicable to the determination of intrinsic permeability coefficients from liposome release data in plasma using the indirect hydrolysis method, since the driving force for drug release from liposomes is still governed by the free, unbound drug concentration in the aqueous core of the liposomes.

At equilibrium, DB-67 is mostly bound to the inner bilayer leaflet17 with a very small fraction of the permeant in the aqueous phase. Since the concentration of DB-67 in the aqueous compartments inside and outside the vesicles cannot be readily sampled, the experimentally determined membrane/water partition coefficient of DB-67 (=2443 ± 230, Fig. 4) was used in conjunction with estimates for the external and entrapped volumes (from lipid analysis and particle size measurements) to calculate the aqueous concentrations of free drug in the respective compartments. When sink conditions apply in the external reservoir and steady-state conditions apply for the concentration of drug outside the vesicles within the dialysis tube in the dynamic dialysis experiments, the intrinsic membrane permeability coefficient, Pm, can be related to the apparent permeability coefficient (Papp) in the liposome efflux experiments by Eq. (8e), where equation image is the fraction of drug unbound inside the liposomes. Thus, the apparent permeability coefficient has to be corrected for the fraction bound inside the vesicle to obtain the intrinsic permeability coefficient.68 Ignoring this correction can result in an error of several orders-of-magnitude in the permeability coefficient depending on the partition coefficient of the permeant.

Figure 12 illustrates the ratio of apparent permeability coefficient to the true intrinsic permeability coefficient as a function of varying bilayer/water partition coefficients and vesicle diameter. Even when the partition coefficient is relatively small, the binding correction cannot be ignored when using the dynamic dialysis/liposome efflux method. The apparent permeability coefficient of DB-67 is about two orders of magnitude lower than the intrinsic permeability coefficient (equation image).

Figure 12.

Simulation of the effect of varying bilayer/water partition coefficient (Kp) on the ratio of apparent (Papp) to the true permeability coefficient (Pm) in unilamellar vesicles of 50nm (- - -), 100nm (…) and 200nm (––) in diameter.

CONCLUSIONS

We have developed a systematic quantitative approach to obtain the intrinsic permeability coefficients of hydrophobic solutes from partitioning and permeability experiments. A new dynamic dialysis method has been developed and validated to study permeability of hydrophobic solutes and applied to DB-67. A method to analyze DSPC was developed and lipid analysis along with DLS measurements has been used to estimate the relevant phase volumes. The importance of accounting for membrane binding in the estimation of permeability coefficients for hydrophobic compounds has been demonstrated and experimental artifacts or incorrect model assumptions that can result in erroneous conclusions during studies of liposome release kinetics for hydrophobic drugs have been explored. A simple method has also been developed to obtain the release kinetics of hydrophobic camptothecins in plasma by comparing the hydrolysis kinetics of liposome entrapped versus free drug. The liposomal membrane barrier properties as gauged by DB-67 efflux were found to be similar in aqueous buffer and in plasma. A liposome retention half-life of approximately 3 h was obtained by entrapping DB-67 lactone in rigid gel phase liposomes. Further studies appear to be necessary to devise strategies to further improve the loading and liposomal retention of DB-67 in vivo.

Acknowledgements

This work was financially supported by a grant from the NIH (NCI RO1 CA87061). The investigators also thank Dr. Paul Bummer for use of his ELSD instrument.

Ancillary