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1321 Studies of a benzoporphyrin derivative with Pluronics N. Hioka, R.K. Chowdhary, N. Chansarkar, D. Delmarre, E. Sternberg, and D. Dolphin Abstract: The synthetic route for the benzoporphyrin derivatives produces two regioisomers in equimolar quantities (ring A and B isomers). A derivative of the A-ring product, BPD-MA (benzoporphyrin-derivative monoacid ring A, verteporfin), has recently been approved in North America and Europe for the treatment of age-related macular degeneration. The B-ring isomers, contrary to the A-ring isomers, exhibit high aggregation in many formulations, which results in inadequate drug delivery for clinical uses. To avoid aggregation, a non-ionic surfactant polymer such as a Pluronic — poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) — may be used as a formulation excipient. The triblock polymer investigated here is designated P123 (or poloxamer 403). When used to formulate a monoacid benzoporphyrin B-ring derivative (2), a critical micelle concentration of P123 in water occurred at approximately 0.015 to 0.03%. The apparent pKa of compound 2 was dependent on its concentration in P123, and decreased as the molar ratio (P123:2) increased. High concentrations of P123 and neutral pH were found to be the best conditions to maintain the drug in its monomeric form. Kinetic studies suggest that the aggregate of 2 contains several molecules, and is formed by a catalyzed self-assembly process. Samples with 1 mg mL–1 of drug, at pH = 7.4, and 4.8% of Pluronic showed satisfactory capacity to load and keep monomers stable. This formulation has potential PDT applications. Key words: Pluronic, poloxamers, block copolymers, photosensitizing drug, photodynamic therapy (PDT), formulation, micelles. Résumé : La voie de synthèse des dérivés de la benzoporphyrine conduit à deux régioisomères en quantités équimolaires (isomères des cycles A et B). Un dérivé du produit du cycle A, BPD-MA, (le dérivé monoacide du cycle A de la benzoporphyrine, la vertéporfine) a récemment été approuvé en Amérique du Nord et en Europe pour le traitement de la dégénérescence maculaire associée à l’âge. Les isomères du cycle B, contrairement aux isomères du cycle A, présentent des niveaux d’agrégation élevés dans plusieurs formulations qui les rendent impropres à la dissémination du médicament pour les utilisations cliniques. On peut d’éviter l’agrégation en utilisant comme additif de formulation un agent de surface polymère, non ionique, tel qu’un Pluronique — poly(oxyde d’éthylène)-poly(oxyde de propylène)-poly(oxyde d’éthylène). Le polymère à trois blocs étudié ici est désigné P123 (ou poloxamère 403). Lorsqu’on l’utilise dans la formulation d’un dérivé monoacide du cycle B de la benzoporphyrine (2), on observe une concentration micellaire critique de P123 dans l’eau aux environs de 0,015 à 0,03%. Le pKa apparent du composé 2 dépend de sa concentration dans P123 et il diminue avec une augmentation du rapport molaire (P123:2). On a trouvé que des concentrations élevées de P123 et un pH neutre correspondent aux conditions optimales pour maintenir le médicament dans sa forme monomère. Des études cinétiques suggèrent que l’agrégat de 2 contient plusieurs molécules et qu’il se forme par un processus d’autoassemblage autocatalysé. Des échantillons de 1 mg mL–1 de médicament, à un pH = 7,4 et une concentration de 4,8% de pluronique présentent une capacité satisfaisante à dissoudre et à maintenir les monomères stables. Cette formulation a du potentiel dans les applications de thérapie photodynamique (TPD). Mots clés: Pluronique, poloxamères, copolymères à blocs, médicament photosensibilisant, thérapie photodynamique (TPD), formulation, micelles. [Traduit par la Rédaction] Introduction Photodynamic therapy (PDT) is an approved treatment against cancer and age related macular degeneration, and has been shown to be efficient against psoriasis, arthritis and other diseases (1, 2). The first officially approved drug for PDT was Photofrin®, which exhibited some side effects such as prolonged skin photosensitivity, a long waiting time be- Received 26 June 2002. Published on the NRC Research Press Web site at http://canjchem.nrc.ca on 17 October 2002. N. Hioka. Departamento de Quimica, Universidade Estadual de Maringa, Brazil. R.K. Chowdhary, N. Chansarkar, D. Delmarre, E. Sternberg, and D. Dolphin.1 Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC V6T 1Z1, Canada. 1 Corresponding author (e-mail address: [email protected]). Can. J. Chem. 80: 1321–1326 (2002) DOI: 10.1139/V02-167 © 2002 NRC Canada 1322 tween intravenous injection and photo activation (2 days), and limited light penetration through tissue (1) of the 630 nm light used to activate it. The photoactive component of the liposomal formulated verteporfin (recently approved for the treatment of age-related macular degeneration) is a benzoporphyrin derivative monoacid ring A (BPD-MA, 1). The synthetic route to this type of molecule provides, in equimolar quantities, two reduced porphyrin rings (A and B, which are ring regioisomers). Both sets of regioisomers show similar ability to accumulate selectively and be retained by abnormal or hyperproliferative cells, such as cancerous tissue (3–5). Both classes exhibit a tendency to form aggregates (6, 7), following the typical behavior of many porphyrin and chlorin compounds (8). The A-ring compounds exhibit less tendency to aggregate, however, and can be used in liposomal formulations (5, 9). In contrast, the B-ring derivatives exhibit high aggregation behavior, resulting in nonhomogeneous solutions and diminution of singlet oxygen formation (6), which is suggested as one of the most significant species involved in cell death (1, 10). To avoid aggregation and to improve drug concentration in target tissues, the formulation of the drug is especially important. We have investigated the use of Pluronic (poloxamers), water-soluble triblock copolymers containing ethylene oxide units (PEO = the hydrophilic regions) at the extremities and propylene oxide units (PPO = the hydrophobic section) in the middle (often denoted PEO-PPO-PEO or (EO)m(PO)n(EO)m). Because of their synthetic versatility, a number of copolymers are commercially available for distinct uses in different areas, which include drug solubilization and controlled release (11–13). Many of them are believed to form micelles with the terminal PEO sections hydrated at the surface and the PPO section in the hydrophobic core (12, 14). The basis of this work was the investigation of drug formulations for PDT using Pluronic P123 and a benzoporphyrin B-ring derivative (2). P123 (or poloxamer number 403) has a molecular weight of 5750 with 30% of hydrophile PEO (m = 21 and n = 67). Materials and methods Reagents Pluronic P123 (paste) was supplied by BASF, U.S.A. The photosensitizing drugs (BPD-MA 1 and 2) were synthesized using standard procedures (15). 1,6-Diphenyl-1,3,5-hexatriene (DPH, Sigma) was used as received. The ionic strength was maintained by adding KCl (0.1 mol L–1). Can. J. Chem. Vol. 80, 2002 Buffers (0.01 mol L–1) were potassium phosphate (pH range 6.2–8.5) and potassium phthalate (pH range 3.9–6.1). All solvents were analytical grade. Procedures The aggregation process was monitored by UV–vis spectroscopy (Hewlett-Packard 8452 A and Cary-50). The spectra of 2 were obtained using cells with path length 0.01 cm (cylindrical-shaped) for concentrated solutions (approximately 1 × 10–3 mol L–1) and 1.0 cm for dilute solutions (approximately 1 × 10–5 mol L–1). The term molar ratio refers to the ratio [P123]:[2] using molar concentrations. For the stock preparation, P123 (paste, 2 g) was dissolved in 100 mL of water and mixed (Mixer Thermolyne, type 16700) for 2 to 3 h. All Pluronic concentrations are presented by percentage of weight of polymer per water volume (w/v). All stock solutions of 2 (prepared in dimethyl sulfoxide (DMSO)) and DPH (prepared in methanol) were protected from light and were refrigerated. Critical micelle concentration (cmc) The cmc determination (duplicate) was performed for Pluronic P123 by a solubilization method (13) using DPH as a probe, and by a method based on dye monomer–aggregate equilibration (16) using 2 as the probe. All Pluronic solutions were kept in a water bath for at least 4 h, to achieve thermal and mechanical equilibrium. A stock solution of DPH was prepared at 1.1 × 10–3 mol L–1, and aliquots of 3.0 mL (microsyringe) were added to each 2.0 mL of Pluronic solution. For 2, 4.0 mL from a stock solution (3 × 10–3 mol L–1 in DMSO) was added to each 2.0 mL of P123 solution, and mixed for 15 s (mixer). The solutions were kept in the dark (1 h for DPH and 30 min for 2), before the visible or fluorescence (Aminco-Bowman Series 2) spectra were recorded. Effect of pH Solutions of 2 (1.14 × 10–5 mol L–1) at different pH and in several fixed concentrations of P123 were investigated ([P123] from 0 to 0.16% w/v). The ionic strength was kept constant (0.1 mol L–1 KCl), and phosphate and phthalate potassium buffers (0.01 mol L–1) were used. P123 solutions (2.25 mL) were previously prepared with KCl and KOH (to set the initial pH to approximately 7.3) and kept at least 4 h at 25°C. 14 mL of 2 (stock, c = 2.05 × 10–3 mol L–1 in DMSO) were added to the sample and mixed (using the mixer for 15 s). After 1 to 2 min, 0.25 mL (micropipette) of the buffer solutions, at the desired pH, were added, and the behaviour of monomer and aggregate equilibrium was monitored with respect to time. For 0, 0.04, and 0.06% P123, experiments were performed in duplicate. To investigate the effect of [2] on the pH dependence of aggregation, 0.06% of P123 was used with different concentrations of 2. Kinetic investigation of the aggregation process The same procedures used to investigate the effect of pH on 2–P123 solutions were used to study the aggregation behaviour with respect to time. Only the kinetics of acid-pH solutions were followed, because at neutral or alkaline pH the aggregation processes were too slow. The monomer and aggregate peaks were monitored simultaneously. © 2002 NRC Canada Hioka et al. Fig. 1. Visible spectra of 2 in DMSO. Monomer and aggregate ([2] = 1.1 × 10–5 mol L–1 in DMSO–water). 1323 Table 1. Sample preparation with [2] = 1.4 × 10–3 mol L–1 (1 mg mL–1), pH = 7.4. Sample 0 1 2 3 4 5 6 7 Micellar size determination using laser light scattering The micelle size was measured by laser light scattering (submicron particle sizer model 370, NICOMP, Santa Barbara, CA). Solutions with 1 mg of 2 and 10% of P123 (pH = 7.4) were analyzed. Solutions at low concentrations of 2 (3.5 × 10–6 mol L–1) and Pluronic (0.06 and 0.2%), with pH = 7.4, were also examined. Formulations Solutions with different P123 concentrations were prepared by a thin film method. Compound 2 and P123 were codissolved in methylene dichloride; after solvent evaporation via rotary evaporation, the thin film produced was hydrated with an aqueous potassium phosphate solution. Samples were lyophilized and rehydrated using 1 mL of pure water, leading to final solutions composed of [buffer] = 0.01 mol L–1, pH 7.4, [2] = 1.4 × 10–3 mol L–1 (1 mg mL–1), and P123 concentrations as presented in Table 1. After the solution was well mixed, visible spectra were obtained with respect to time. Aliquots of the solutions prepared as described in Table 1 were frozen immediately after rehydration, and were used to check the stability of the diluted samples. These solutions were defrosted and aliquots of 40 mL were added to 2.0 mL (1:50 dilution) of pure water and buffer solution (pH = 7.4, c = 0.01 mol L–1). The stability of their monomeric species was followed with respect to time. Results and discussion For 2 in DMSO (or other organic solvents), the most intense Q-band appeared at 692 nm (e = 32 000 M–1 cm–1), corresponding to the monomeric species, while the aggregate peak showed a red-shifted band with a more intense peak at 715 to 738 nm (see Fig. 1). The wavelength of the aggregate peak was dependent on solution conditions. Samples exhibiting aggregation peaks usually precipitated with time. For 2 in Pluronic solutions, the monomer peak had a molar absorptivity (e) around 27 000 M–1 cm –1 , while the aggregate peak intensity was higher (approximately 50 000 M–1 cm–1). P123 (mg) 16.9 26.8 47.7 75.6 100.8 125.8 154.3 199.7 [P123] (%, w/v) 1.7 2.7 4.8 7.6 10.1 12.6 15.4 20.0 Molar ratio [P123]:[2] 2 3 6 9 13 16 19 25 Fig. 2. Absorbance at 356 nm as a function of P123 concentration ([DPH] = 1.6 × 10–6 mol L–1, pH = 7.25, [phosphate] = 0.01 mol L–1, 30°C). Critical micelle concentration of P123 DPH in methanol exhibits an absorption peak at 356 nm and an emission peak at 428 nm (excitation at 356 nm). DPH is insoluble in water (or low P123 concentration). As the P123 concentration increased, the absorbance and fluorescence intensity also increased. A plot of absorbance at 356 nm (or fluorescence intensity at 428 nm) vs. log (%P123) produced two straight lines whose intercept gave the cmc (see Fig. 2 as an example) (13). Cmc determination using 2 (soluble in water at low concentration) as a probe is based upon a monomer aggregation equilibrium (16). Compound 2 in aqueous solutions, at low P123 concentration, exhibited an aggregation band. At higher P123 concentration, this band decreased, while the monomer peak at 692 nm increased. This aggregation behavior of 2 enabled the determination of the P123 cmc. The absorption ratio of the aggregate and monomer peaks as a function of log (%P123) is shown in Fig. 3. The cmc value was obtained from the intercept. Table 2 presents cmc values obtained from experiments with DPH and 2 under different conditions. The cited cmc value for P123 at 25°C (13) is 0.03%, which agrees with our results using both probes (0.028% and 0.029% for DPH and 2, respectively). At 30°C and pH 7.3, the value found with both compounds (0.020%) demonstrated again the agreement between these two methods. The values obtained with 2 at different buffer concentrations (0.01 and 0.1 mol L–1) are in accordance with the literature, which predicts that the cmc decreases with salt © 2002 NRC Canada 1324 Fig. 3. Effect of P123 concentration on monomer–aggregate equilibrium (25°C) ([2] = 6 × 10–6 mol L–1). Can. J. Chem. Vol. 80, 2002 Table 2. Average cmc values of P123 using DPH and 2. Probe Temp (°C) Phosphate (mol L–1) pH cmc DPH DPH 2 2 2 25 30 25 30 30 — 0.01 — 0.01 0.1 — 7.3 — 7.3 7.3 0.028 0.020 0.029 0.020 0.015 Table 3. Apparent pKa for 2 and the maximum wavelength of the aggregate band at different P123 concentrations (25°C). [P123] (%, w/v) Fig. 4. Effect of pH on monomer–aggregate equilibrium ([2] = 1.14 × 10–5 mol L–1, [P123] = 0.04%, [KCl] = 0.1 mol L–1, [buffer] = 0.01 mol L–1) (25°C). Experimental points were obtained at 90 min after buffer addition. 0.0 0.02 0.04 0.05 0.06 0.07 0.08 0.12 0.16 Molar ratio [P123]:[2] 0 3 6 8 9 11 12 18 24 pKa (±0.1) l max (nm) 6.8 6.6 6.4 — 5.8 — 5.8 5.6 5.7 718 728 728 734 734 735 734 736 736 Note: [KCl] = 0.1 mol L–1; [buffer] = 0.01 mol L–1; [2] = 1.14 × 10–5 mol L–1. addition (13, 17). These experiments with 2 clearly demonstrated that the micelles of P123 stabilize it in the monomeric form. Effect of pH on stability Solutions of 2 in P123 at low pH showed a red-shifted peak corresponding to aggregates. All samples were, therefore, initially prepared at neutral pH (without buffer). At low pH, after buffer addition, a decrease of the 692 nm peak and a simultaneous increase in the aggregate band with respect to time was observed. At neutral or higher pH, aggregation was diminished (but not completely avoided), probably resulting from the negative–negative charge repulsion of the carboxylate group on 2. The ratio between the aggregate and monomer peaks at an arbitrarily fixed time was taken as a parameter to estimate the magnitude of the effect. An example is presented in Fig. 4. The extent of the aggregation process with pH (Fig. 4) permits an estimate of the pKa value of 2 at that Pluronic concentration. This method cannot directly measure pKa, however, since protonation is followed by aggregation. The pKa value did not change with time of analysis. For the example presented in Fig. 4, the measured pKa was 6.4. For solutions without Pluronic, 2 exhibits only one peak around 718 nm, which decreases with time at lower pH. To estimate these pKas, absorbance as a function of pH was used. Measurements of these apparent pKa values, obtained using this indirect technique at different P123 concentrations, are shown in Table 3. In Pluronic solutions, the aggregate peak undergoes a red shift as the Pluronic concentration is increased, probably reflecting the different geometry and size of the micelles. The pKa values (Table 3) obtained were higher than those expected for a simple carboxylic acid, and probably reflect the local environment. Increasing the P123 concentration ([P123]:[2]) lead to a decrease in pKa; this effect was caused by a Pluronic micelle forcing molecules of 2 inside the micelle core (away from the micelle surface). Consequently, the porphyrin is exposed to a less hydrophilic environment (18). An abrupt change in pKa was observed between 0.04% and 0.06% (6.4 to 5.8). This suggested two different micelle populations. Perhaps, one was a unimolecular micelle (0.04%) and the other one was a multimolecular micelle (in 0.06% or higher) (11, 12). These values are more appropriately called the apparent pKa, because P123 micelles can induce local pH changes (18). Table 4 provides data for the effect of the concentration of 2 on its apparent pKa. The apparent pKa increased as the concentration of 2 increased. This effect resulted from the limited capacity of P123 micelles (at 0.06%) to support high quantities of 2 inside the micelle core (drug loading). As the [P123]:[2] molar ratio decreased, more drug molecules were exposed to the micelle surface or bulk solution where they could be protonated and suffer aggregation. Kinetic investigation of the aggregation process Acidic solutions of 2 and P123 were prepared by buffer (phthalate) addition. Visible absorption vs. time showed a quasi-isosbestic point at approximately 702 nm that was not © 2002 NRC Canada Hioka et al. 1325 Table 4. Apparent pKa values of 2 at different concentrations. [2] (10 0.33 1.14 2.02 –5 –1 mol L ) Molar ratio [P123]:[2] Apparent pKa 32 9 5 5.5 5.8 6.2 Fig. 6. Absorption at monomer peak as a function of time ([2] = 1.4 × 10–3 mol L–1 (1 mg mL–1), (25°C), pH = 7.4, [phosphate] = 0.01 mol L–1). Light pathway cell length (0.01 cm). Sample 0 (!); sample 1 (#); samples 2–7 ( ). > Note: [P123] concentration fixed at 0.06% (25oC); [KCl] = 0.1 mol L–1; [buffer] = 0.01 mol L–1. Fig. 5. Kinetic behaviour of 2–P123 solutions in acidic media ([2] = 1.14 × 10–5 mol L–1, [P123] = 0.04%, [P123]:[2] = 6, [phthalate] = 0.01 mol L–1, pH = 4, [KCl] = 0.1 mol L–1, T = 25°C). The line represents the theoretical fitting. well-defined; the absence of a clear isosbestic point suggests a multiple-step reaction. Moreover, supposing dimeric aggregation, the kinetics data should obey a second-order rate equation (19), which is not shown in the present case. Figure 5 illustrates the monomer and aggregate absorption behavior with respect to time. As shown, there is a lag phase, which is preceded by what has been termed “a sigmoidal progress curve” indicating an autocatalytic-type reaction (20). The initial phase is a nucleation step, after which the nucleus promotes a catalytic process where more molecules are added, forming a polymeric aggregate. The initial nucleus could be a dimer of 2, as is found in the aggregation process in homogeneous solutions (DMSO–water) (21). Figure 5 shows one example of the kinetics of the aggregation process for the drug in Pluronic solution at low pH. The kinetic data has been treated using an approach proposed by Micali et al. (20) and Pasternack et al. (22). The basis of this kinetic treatment derives from chaos theory, which predicts that the rate constants are themselves time-dependent (20). The kinetic equation is shown in eq. [1]: [1] (abs – absi) / (abso – absi) = 1 / (1 + (m–1){kot + (n + 1)–1 (kct)n + 1 }) 1/(m–1) where abs is the absorbance at time t, abso is the absorbance at t = 0, absi is the absorbance at infinite time, and m, n, ko, and kc are kinetic parameters. The theoretical fit with experimental points (600 points) as a function of time was performed using the software Kaleidagraph (Synergy Software v 3.0.9), which resulted in an excellent correlation coefficient (>0.9999) for these absorption profiles at monomer and aggregate peaks. Micelle size determination Laser light scattering experiments showed that a solution of 2 and 10% P123 (pH approximately 7.4) resulted in one population of micelles whose size ranged from 15 to 20 nm. After 1 day, these micelles maintained the same size, and the visible spectra confirmed the presence of the drug in monomeric form. For solutions with low concentrations of P123 (0.06%) and 2 (3.5 × 10–6 mol L–1) at pH 7.4, the experiments showed two micelle populations with sizes approximately 20 nm and 100 nm, although with a high c-square error (cr2 = 5). After 1 day, both micelle populations increased their micelle size (almost double) and the drug started to exhibit the aggregation band. The presence of drug aggregation probably promotes micelle destabilization, inducing an increase in total particle size. Similar micelle (or colloid) size increase was exhibited in a 0.2% P123 solution. Because of the high c error these results are not accurate, but suggest that a low [P123] results in micelles that cannot adequately sustain monomeric species of the drug. Drug loading and stability Samples formulated at pH 7.4 and compositions described in Table 1 were used to investigated the concentrations of P123 that can support 1 mg mL–1 of drug (in monomeric form) and their stability, with respect to time, for prolonged use. Figure 6 shows the initial capacity of Pluronic solution that is able to solubilize 2 in monomer form, as well as their stability over time after rehydration with 1 mL of water. Samples containing P123 at concentrations of 1.7 and 2.7% (samples 0 and 1) exhibited low capacity to load 2 in its monomeric form (time zero). Their spectra did not exhibit an aggregation peak; however, undissolved material remained in the flask. Taking [2] = 1.4 × 10–3 mol L–1, e = 27 000 M–1 cm–1, and considering the light path of the cell (0.01 cm), the expected absorbance at 692 nm should be approximately 0.378, which is close to the value of 0.36 obtained experimentally for sample 2 (4.8%) and those at higher [P123]. After 48 h, samples 2 (4.8%) to 7 (20.0%) did not exhibit an aggregate peak, and the absorption at 692 nm did not change (Fig. 7). Samples 0 (1.7%) and 1 (2.7%) exhibited a © 2002 NRC Canada 1326 Fig. 7. Ratio of aggregate–monomer absorbances for [P123] solutions at 20 h after dilution (in pure water and in [phosphate] = 0.01 mol L–1, pH = 7.4) ([2] = 2.8 × 10–5 mol L–1, 25°C). Can. J. Chem. Vol. 80, 2002 Samples with a Pluronic concentration of 4.8% (molar ratio = 6) or higher showed high drug loading and capacity to support the drug in monomeric form. After dilution (1:50) in buffer solution at pH 7.4, these samples still demonstrated high stability. Acknowledgements We express our gratitude to the Brazilian granting agency CNPq for the support of Noboru Hioka. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). References new band at 734–736 nm (not shown), which increased with time, while the monomer peak decreased. Thus, for drug loading and stability, samples formulated with P123 at concentrations below 4.8% are not useful for clinical use. After 20 days (sample solutions were maintained at room temperature in the dark) the absorbance at 692 nm exhibited only a small decrease. The absorbance of sample 2 (4.8%) decreased 5.2%, and sample 4 (10.1%) decreased 4.3%. For samples 5 (12.6%) to 7 (20.0%), absorbance decreases were not observed. The pH of all solutions was 7.4, which means that despite the negative charge, 2 still tended to aggregate. It is important to note, however, that this tendency is much reduced when compared with low pH. These results show that dilute buffered solutions (pH = 7.4) were more stable for all samples. This formulation process should, therefore, use buffer solutions at pH » 7.4, rather than pure water. Previous buffer (from the cake) cannot adequately sustain the pH for formulations after dilution (1:50) in pure water. At 20 h, samples diluted in pure water exhibited aggregation at 0.20% (original 10.1%) of P123 (or higher), while for dilution made in the buffer, the solution at 0.10% (original 4.8%) of P123 was still stable. Conclusion Micelles of P123 in water can support 2 in its monomeric form. The monomer aggregate equilibrium of the drug can provide a reasonable estimation of the pKa for 2, and permits cmc determinations for Pluronic. The apparent pKa of 2 decreased as the molar ratio ([P123]:[2]) increased. Mixtures of 2 with low [P123] showed unstable micellar systems, leading to drug aggregation. Acidic solutions of the drug in Pluronic underwent aggregation via a self-catalytic process, where the rate constant, or “rate coefficient” (22), is time dependent, and can be analyzed by chaos theory. Prevention of the nucleation step can slow down the aggregation process. The best conditions for Pluronic micelles to sustain 2 as a monomeric species were high molar ratios and neutral pH. 1. E.D. 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