Posaconazole in simulated gut fluids: how pH, bile-salt micelles and supersaturation set its solubility limits and its crystallization rate

Background and motivation

Most new drug candidates are poorly soluble in water, and formulators use salts, cocrystals, amorphous solid dispersions (ASDs) and solubilizing excipients to get more drug into solution. For drugs whose absorption is limited by solubility, the aim is not only to dissolve faster but to create a supersaturated solution: where the intestinal membrane is the main barrier, the flux across it rises linearly with the degree of saturation of the solution in contact with it (Brouwers 2009, ref 3; refs 4–9). C1 Weak bases are the simplest supersaturating systems. About 75% of drugs are weak bases; with a pKa between 2 and 7.5 they dissolve as cations in the acidic stomach and lose that solubility when they reach the near-neutral small intestine, so gastric emptying itself can create supersaturation (Di 2008, ref 17; Indulkar 2015, ref 15). C2

A supersaturated solution is metastable. The expected end point is crystallization, which removes dissolved drug, but if the concentration exceeds the drug's amorphous solubility and crystallization is slow enough, the solution first undergoes liquid–liquid phase separation (LLPS) into a drug-poor phase and a drug-rich colloidal phase (Ilevbare and Taylor 2013, ref 18). C3 Because membrane flux follows the free drug concentration (Higuchi 1960, ref 20), what matters for absorption is which of these transitions happens and when. C4 Physiologically based pharmacokinetic (PBPK) models include crystallization but not LLPS, even though many poorly soluble drugs pass through an amorphous, often colloidal, state before they crystallize; and if the precipitate stays amorphous the solution remains supersaturated (Taylor and Zhang 2016, ref 21; Raina 2014, ref 23). C5 Formulation polymers and endogenous bile salts are known to change the precipitation outcome (Chen 2015, ref 26), but such effects are rarely built into predictions. C5

The authors chose posaconazole (PCZ, Figure 1), a triazole antifungal and BCS class II weak base, as the model. The literature gives two basic pKa values, 3.6 (piperazine nitrogen) and 4.6 (triazole nitrogen), and a crystalline solubility below 1 μg/mL; the drug is dosed at 200–300 mg two or three times a day, as a suspension or as an ASD tablet with an enteric polymer. M1 In healthy volunteers, the gastric concentration set by the administration medium changed the extent of intestinal supersaturation, precipitation and exposure (Hens 2016, ref 31). C6 The paper's stated aim is to "evaluate the landscape of precipitation outcomes and kinetics" for this base in a range of biorelevant media: first define its phase diagrams, then measure phase behaviour and nucleation kinetics at different supersaturations. A1·A2·A3·A4

Background concepts

Two solubility limits. The crystalline solubility is the equilibrium concentration over the stable crystal (here form I). The amorphous solubility is the highest concentration of molecularly dissolved drug a solution can hold; above it, LLPS forms drug-rich droplets, which the paper detects as the onset of light scattering when drug is added gradually from a DMSO stock. P3·P6 The two limits split the concentration axis into three zones: below the crystalline solubility nothing can precipitate; between the two limits only crystallization can occur; above the amorphous solubility LLPS can occur, followed, sooner or later, by crystallization. C18

pH dependence of a weak base. For a monoprotic base the introduction gives the modified Henderson–Hasselbalch equation (eq 1):

Here $C_T$ is the total solubility and $C_B$ the solubility of the crystalline free base. In plain terms: at a pH below the pKa most of the drug is protonated, and the ionized fraction adds to the fixed solubility of the neutral form, so the total rises tenfold for each pH unit below the pKa. E1 Posaconazole has two basic groups, so the authors fitted their data with the diprotic form (eq 4):

Here $C$ is the solubility, $C_o$ the intrinsic solubility of the fully unionized drug, and $p{K}_{a1}$, $p{K}_{a2}$ the two acid dissociation constants. In plain terms: the solubility is the intrinsic solubility multiplied by one plus the singly and the doubly protonated fractions. E4 A consequence matters for the whole paper: if both the crystalline and the amorphous solubility follow this equation with the same pKa values, the ionization factor cancels in their ratio, and the ratio is the same at every pH. C19

Supersaturation in simple and in micellar media. The degree of supersaturation $S$ is strictly the activity of the drug in the solution divided by its activity at the crystalline solubility in the same medium. C30·E11 In plain buffer the ratio of concentrations is a good stand-in. In biorelevant media it is not: bile salt and lecithin micelles take up drug, and the fraction taken up depends on the drug concentration, so a ratio of total concentrations misstates the driving force (Indulkar 2017, ref 40; Elkhabaz 2019, ref 41). C8 The paper quantifies micellar uptake with the micelle–water partition coefficient (eq 5):

Here $V_m$ is the volume fraction of the micellar phase, taken as the mass fraction of bile acids and lipids added to the medium. In plain terms: $K_{m/w}$ is the number of drug molecules held in micelles per free molecule, normalized to how much micellar material there is. The free drug is taken as the solubility in the surfactant-free buffer, and the drug in micelles as the total solubility in the medium minus that free drug. E5·C46

Induction time and classical nucleation theory. Measuring how many nuclei form per unit volume and time is hard for a drug this insoluble, so the authors measure the induction time $t_{ind}$: the time from creating a supersaturated solution until the dissolved concentration starts to fall while turbidity rises. P7 It includes both the time to form a critical nucleus and the time to grow it to a detectable size. C35 Classical nucleation theory (CNT) gives the nucleation rate $J$ (eq 6):

Here $A$ is the pre-exponential factor, $k$ the Boltzmann constant, $T$ the temperature, $\nu$ the molecular volume and $\gamma$ the interfacial free energy between nucleus and solution. In plain terms: nucleation speeds up very steeply as $S$ rises and slows steeply as $\gamma$ rises, because $\gamma$ enters cubed in the exponent. E6·C48 Taking logarithms gives a straight line (eq 7):

In plain terms: plotted against $1/{\ln }^{2}S$, $\ln (J/S)$ falls on a line whose intercept gives $A$ and whose slope gives $B$, and so $\gamma$. E7 The same parameters give the height of the nucleation barrier and the size of the smallest stable nucleus (eqs 8 and 9):

In plain terms: both the barrier $\Delta G^{*}$ and the critical radius $r^{*}$ shrink as supersaturation rises, which is why concentrated solutions crystallize faster. E8·E9 Nucleation in the bulk solution is called homogeneous; nucleation on foreign surfaces such as dust or the vessel wall is heterogeneous and has a lower barrier, so it tends to dominate at low supersaturation; nucleation on crystals already present is secondary nucleation. C28·C35 The paper reads the pre-exponential factor $A$, following the literature, as the number of sub-critical molecular clusters formed per cubic metre of solution per second. C53

Methods in detail

The work has three parts, run on one drug: map the two solubility limits against pH, measure how biorelevant media shift them, and time crystallization over a range of supersaturation, without and with seed crystals. All experiments were at 37 °C. A1·A2·A3·A4

Part 1: the two solubility limits as a function of pH

Problem. The solubility of a weak base depends on buffer composition and ionic strength as well as pH, and literature pKa values may not apply at body temperature. To build a phase diagram that can be compared across pH, the authors needed both limits measured in the same buffers under the same conditions. C10

What they did. Phosphate buffers from pH 1.0 to 7.0 in steps of 0.5 were made with low salt content and a common ionic strength of about 0.14 M, a biorelevant value (SI Table S1). P2 For the crystalline solubility, excess PCZ form I was equilibrated in each buffer at 37.0 ± 0.5 °C for 48 h in triplicate; the solution was separated by ultracentrifugation at 35,000 rpm and analysed by HPLC with fluorescence detection (excitation 240 nm, emission 385 nm), and the remaining solid was confirmed by powder X-ray diffraction to be form I. P3·P4·R5 For the amorphous solubility, a concentrated DMSO stock of PCZ was pumped at a known rate into 50 mL of buffer stirred at 350 rpm, so that the LLPS concentration was reached within 2–4 min, before crystals could form; the extinction at 350 nm, where the drug does not absorb, was followed with a fiber-optic UV probe, and the amorphous solubility was the added concentration at which it began to rise (triplicate). P6 DMSO was kept below 1%, normally at most 0.5%, of the medium volume, except at pH 1.0, where the amorphous solubility of about 8000 μg/mL and a stock limited to about 100 mg/mL required up to 8%. P6·M1 The pH rose by only 0.02–0.05 units during these additions. R4·C15

An independent estimate. The amorphous solubility at pH 7.0 was also estimated thermodynamically, from the free-energy difference between amorphous and crystalline drug (eq 2), with that difference from the Hoffman approximation (eq 3):

Here $C_A$ is the amorphous solubility, $C_T$ the crystalline solubility, $R$ the gas constant, $T$ = 310 K, $\Delta H_f$ the enthalpy of fusion and $T_m$ the melting temperature; the factor $\exp (-I_a)$ corrects for the lower activity of the amorphous solid after it absorbs water. In plain terms: the amorphous form is more soluble than the crystal by a factor set by how much higher its free energy is, reduced somewhat by the water it takes up. E2·E3 The inputs were measured: a melting point of 169.1 °C and an enthalpy of fusion of 76.95 J/g by DSC, and 4.6% water uptake by melt-quenched amorphous PCZ at 37 °C, giving $\exp (-I_a)$ = 0.33. M1·P5·P10

pKa at the test conditions. The crystalline solubility data were first fitted with the literature pKa values; the predicted solubilities came out well above the data, especially at low pH. The authors refitted the pKa values with pDISOL-X and obtained 3.53 ± 0.03 and 1.24 ± 0.05. R2·P13

Part 2: the limits in biorelevant media

Problem. Intestinal fluid contains bile salts and phospholipids that form micelles, and their amounts differ between the fasted and fed states and between generations of simulated media. Whether a given dose reaches LLPS depends on how the medium moves both limits. C47

What they did. Both solubilities were measured in five commercial media and in surfactant-free buffers of the same pH (Table 3). R8 Table A gives the composition of the media.

Table A. Composition of the biorelevant media (from Table 1; sodium chloride and sodium hydroxide omitted). P1

From the solubilities, eq 5 gave $K_{m/w}$ at the crystalline and at the amorphous solubility for the four intestinal media. P14·R14 To compare kinetics on a fair scale, the authors converted concentration ratios in the media to thermodynamic supersaturation: they assumed the free drug concentrations at both limits equal those in buffer, as shown earlier for PCZ in FaSSIF, and that $K_{m/w}$ falls linearly with drug concentration between its two measured values (SI Section S1). P8·C9

Part 3: crystallization kinetics

Problem. Between the two limits, the only question is how long the supersaturation lasts. That time depends steeply on supersaturation and possibly on the medium, and it cannot be predicted from first principles. C4

What they did. Single-phase supersaturated solutions were made by adding a DMSO stock (below 1% of volume) to 50 mL of stirred PBS pH 6.5 or of one of the four intestinal media, a volume within the range reported for the upper intestine. P7·C7 UV spectra from 200 to 450 nm were recorded every 5–60 s; the induction time was the moment the 252 nm concentration began to fall while the 350 nm extinction rose, and microscopy showed that crystals had formed. P7·R5 PBS pH 6.5 served as the reference for all media because both solubility limits are almost the same at every pH from 5.0 to 7.0. C30 For the CNT analysis the high-supersaturation points of each medium were plotted as $\ln (J/S)$ against $1/(T^3{\ln }^{2}S)$ (Figure S2), with $\nu$ = 920 ų calculated from the density and molecular weight of PCZ and $T$ = 310 K, and $\gamma$ and $A$ were taken from slope and intercept (Table 4); $\Delta G^{*}$ and $r^{*}$ followed from eqs 8 and 9 (Figure 10). P15·R15·R16·R17 The paper does not state how the nucleation rate $J$ was derived from the induction times. X10

Seed crystals. To mimic a crystalline dose (for example a suspension) whose undissolved part reaches the intestine, Noxafil oral suspension (200 mg/5 mL; crystals 160 ± 60 nm by dynamic light scattering) was diluted 10,000 times in pH 6.5 buffer and equilibrated so that a defined amount of crystals stayed undissolved, at 0.04, 0.1, 0.2, 0.4, 2 or 20 μg/mL; supersaturation was then created at the amorphous solubility, S 33.6. P9·M2·C34 The authors cite a report that up to 30% of a 40 mg PCZ dose can remain undissolved in the stomach. R20

Experimental analysis

The two limits move together with pH

Both solubilities rise steeply as the pH falls below 3 (Figures 2–4). The crystalline solubility is 0.27 ± 0.01 μg/mL from pH 5.5 to 7.0, where the drug is almost fully unionized, and reaches 347.03 ± 8.05 μg/mL at pH 1.0; the amorphous solubility rises in parallel from about 9 μg/mL to 7761.96 ± 944.86 μg/mL (Table S2). R1·C12 Table B shows the values at selected pH together with their ratio.

Table B. Crystalline and amorphous solubility of PCZ in phosphate buffer at 37 °C (from Table S2, mean ± SD, triplicate). The ratio column was computed by the AI writer from these values; the paper states the ratio in words. R1·X5

The authors conclude that the unionized concentration at each limit does not change with pH, so the ratio is constant: "ca. 33.6" across pH 1.0–7.0 in the results, about 34 across pH 2.5–7.0 in the discussion, and about 34 across the tested range in the conclusions. C19 Table B supports a ratio of 32–37 from pH 2.0 to 7.0; at pH 1.0 and 1.5 it is 22.4 and 27.5, and Table 3 gives 28.3 for the pH 1.6 buffer. X5·R8 The authors explain the excess of the measured values over the calculated ones below pH 2.5 by self-complexation or self-aggregation of the highly ionized drug, "probably", and for the amorphous solubility also by the large DMSO volume needed at pH 1.0, which "may result in a higher apparent amorphous solubility". C13·C16 The amorphous precipitate was short-lived and converted rapidly to crystalline form I. R5

At pH 7.0 the measured amorphous solubility is given as 9.08 ± 0.07 μg/mL in the text and Table 2, 33.6 times the crystalline solubility, while Table S2 lists 8.92 ± 0.07 μg/mL for pH 7.0 and 9.10 ± 0.11 μg/mL for pH 6.5; Table 3 gives 9.08 ± 0.11 μg/mL for buffer pH 6.5. R6·R1·R8·X1 The difference is small, but it means the 33.6 ratio is best read as "33 to 34". The thermodynamic estimate, a ratio of 37.9 and an amorphous solubility of 10.22 ± 0.37 μg/mL, is in what the authors call "reasonable agreement" with the measurement. R7·C17 Note by the AI writer (not discussed in the paper): eq 2 is printed with $-\Delta G/RT$ in the exponent, which with a positive $\Delta G$ from eq 3 would make the amorphous form less soluble than the crystal; and with the molar mass of PCZ (about 700.8 g/mol, from the structure in Figure 1; not printed in the paper) the printed inputs give a ratio of about 26.5 rather than 37.9. The estimate should therefore be treated as not reproducible from the printed numbers. X2

A second point concerns the fitted curves. The text reports good agreement between the data and eq 4 from pH 2.5 to 7.0. C14 The "Fitting" points actually drawn in Figures 2 and 3, however, read about 0.6 μg/mL (crystalline) and about 10 μg/mL (amorphous) at pH 2.5, against measured values of 3.52 and 120.59 μg/mL; on the linear axes these gaps are invisible. R3·R1 Note by the AI writer: the plotted points match eq 4 when 3.53 is placed only in the doubly protonated term, whereas placing 3.53 in the singly protonated term reproduces the data closely from pH 2.5 upward, as the text describes; which assignment the authors used is not printed. Figure 4 also shows the crystalline point at pH 1.0 at about 155 μg/mL, the fitted value, rather than the measured 347 μg/mL. X3·X4

Micelles lift both limits, but not equally

Table C. Solubility of PCZ in biorelevant media and same-pH buffers at 37 °C (from Table 3), with the micelle–water partition coefficients read from Figure 9 (approximate). R8·R14

Every medium raised both limits relative to its buffer (Table C, Figure 5). R8·C25 In FaSSGF the solubility is high because the drug is ionized at pH 1.6 ("suggesting that the extensive ionization at a lower pH is the underlying cause"), although even 0.08 mM taurocholate and 0.02 mM lecithin raised the crystalline solubility from 70.7 to 117.8 μg/mL; the amorphous solubility rose only from 2006 to 2108 μg/mL. C22·C23·R8 In the intestinal media, where PCZ is essentially unionized, the rise "can be attributed" to micellar solubilization of the neutral drug. C21 FaSSIF V1 raised the crystalline and amorphous solubility 8.3- and 5.1-fold over buffer; raising lecithin from 0.2 to 0.75 mM at 3.0 mM taurocholate (FaSSIF V2 to V1) raised solubility 2.3-fold; and five times more taurocholate and lecithin (FaSSIF V1 to FeSSIF V1) raised it, in the text, "approximately 4 times". R9·C23 Table 3 itself gives 3.5-fold for that last step (7.80/2.23 and 160.89/46.18). X15 FeSSIF V2, with less taurocholate and lecithin than FeSSIF V1, gave nearly the same solubilities, which the authors attribute ("likely") to synergistic solubilization by glycerol monooleate and sodium oleate. C24

The ratio of the two limits fell from about 34 in buffer to about 20 in all biorelevant media (17.9–20.7). R8 The authors read this "most likely" as a smaller micelle–water partition coefficient in supersaturated than in saturated solution. C26 Figure 9 bears this out within their framework: $K_{m/w}$ at the amorphous solubility is about 0.44–0.61 of its value at the crystalline solubility in every intestinal medium, which they call "almost a half", "suggesting a decrease in the solubilizing capacity of the surfactant micelles at high drug supersaturation". R14·C45 Because the ratio of $K_{m/w}$ values does not depend on $V_m$, it can be checked from Table 3 alone: for FaSSIF V1 it is 4.086/7.259 = 0.563, matching the bars of Figure 9. E5 Under the assumption that micelles leave the free drug unchanged, the concentration ratio of about 20 at the amorphous solubility corresponds to a thermodynamic supersaturation of about 34, the same as in buffer. C9

Induction time falls steeply with supersaturation

In PBS pH 6.5, the induction time fell from about 54.5 min at S 5 to about 41.3 min at S 10, about 14.2 min at S 20 and about 8.4 min at S 33.6, the amorphous solubility (Figure 6). R10 On a plot of $\log t_{ind}$ against $1/{\log }^{2}S$ the points fall on two straight lines: $\log t_{ind}$ = 1.6703x + 0.2048 (R² = 0.9847) at high supersaturation and $\log t_{ind}$ = 0.1167x + 1.4992 (R² = 0.9986) at low supersaturation, with the break near S 12. R10·E10 The first line reproduces the plotted point at the amorphous solubility: at $x=1/{\log }^{2}33.6$ = 0.429 it gives 8.35 min. E10 Following earlier work, the authors attribute the steep high-S line to homogeneous nucleation and the shallow low-S line to heterogeneous nucleation. C28 The text describes the low-S induction times as "hours"; the longest plotted value is about 54.5 min. C27·X8

Table D. Induction times read from Figure 6 and the left panel of Figure 7 (all values approximate; S is the estimated thermodynamic supersaturation). R10·R11

Against estimated thermodynamic supersaturation, induction times in the four intestinal media were shorter than in PBS at moderate to high S: near S 34 they were about 1.5–3 min against about 8.4 min in buffer (Table D, Figure 7). R11·R10 The authors rank the media above S 11 as PBS > FaSSIF V2 > FaSSIF V1 > FeSSIF V1 > FeSSIF V2, and below S 11 as FeSSIF V1 > FaSSIF V1 > FaSSIF V2 > FeSSIF V2. C31 At the lowest supersaturations FeSSIF V1 (about 112 min at S 4.3) and FaSSIF V1 (about 89 min at S 4.7) were slower than buffer at S 5, while FeSSIF V2 was the fastest medium throughout. R11 Every medium showed the two-slope pattern, with the break at a different supersaturation in each. R12 The authors' summary for the discussion, that crystallization occurs within about 60 min below SR 10 and lasts less than 10 min above SR 20, does not match every plotted point. C43·X8

Their reading, in the order of the paper: the biological surfactants "induce nucleation" ("suggesting"); at high supersaturation taurocholate and/or lecithin work against keeping supersaturation, so richer media nucleate faster; at low supersaturation the same surfactants "appeared to decelerate nucleation"; and glycerol monooleate and/or sodium oleate in FeSSIF V2 "possibly" accelerate nucleation at every supersaturation. C29·C32·C33 The abstract's statement that induction times were "much shorter" in biorelevant media therefore holds above about S 8 on the scale of the left panel of Figure 7, not at the lowest S, which the discussion acknowledges. X7·C55 Note by the AI writer: the two panels of Figure 7 place the media points at different S. The point at 112 min in FeSSIF V1, for example, sits at S 4.3 in the left panel but at $1/{\log }^{2}S$ = 3.85, that is S 3.2, in the right panel, while the PBS points agree in both. The right-panel values match those used in Figure 10 and Figure S2. Comparisons between a medium and buffer at equal S at the low end depend on which panel is right. X6

What classical nucleation theory adds

Table E. Linear fits of $\ln (J/S)$ against $(1/T^3{\ln }^{2}S)\times {10}^6$ for the high-supersaturation points (Figure S2) and the resulting interfacial free energy and pre-exponential factor (Table 4). R15·R16

The fitted interfacial free energy was 3.52 mJ/m² in buffer and 2.61, 2.73 and 3.24 mJ/m² in FaSSIF V1, FaSSIF V2 and FeSSIF V1; the FeSSIF V2 data could not be fitted (Table E). R16 These values are slightly above those reported for naproxen, acetaminophen, tolazamide, lovastatin, cefodizime sodium, prasugrel hydrochloride and spironolactone (0.60–2.80 mJ/m²), "probably due to the more hydrophobic nature of PCZ". R18·C49 The table values can be reproduced from the printed fits: the PBS slope gives $\gamma$ = 3.52 mJ/m² with $\nu$ = 920 ų and $T$ = 310 K, and $A$ is simply $e$ raised to the intercept ($e^{0.8915}$ = 2.44). E7 The barrier and critical radius computed from these values fall as S rises in every medium, from about 5.11 × 10⁻²¹ J and 5.89 × 10⁻¹⁰ m at S 13 to about 2.72 × 10⁻²¹ J and 4.29 × 10⁻¹⁰ m at S 33.6 in buffer (Figure 10), consistent with higher supersaturation favouring nucleation. R17·C50·E8·E9

The authors' key observation is that the induction times do not follow $\gamma$: buffer and FeSSIF V1 have similar $\gamma$ but very different induction times, contrary to an earlier suggestion that surfactant adsorption lowers the interfacial energy (Elkhabaz 2021, ref 74), and the induction times do not follow $\Delta G^{*}$ or $r^{*}$ either. C51 The pre-exponential factor, by contrast, rises in every medium and is largest in FeSSIF V1, and its order matches the induction-time order. C52 Note by the AI writer: $\gamma$ also falls in the induction-time order for buffer, FaSSIF V2 and FaSSIF V1 (3.52 > 2.73 > 2.61 mJ/m²), and in Figure 10 the FaSSIF media have barriers less than half that of buffer at equal S, so a contribution from a lower barrier is not excluded; and the fits rest on 3–9 points with R² between 0.84 and 0.97. X12·X11

Seed crystals remove the waiting time

Started at the amorphous solubility in PBS pH 6.5, an unseeded solution still held about 8.5 μg/mL after 8 min and had an induction time of more than 8 min; with 0.4 μg/mL of seed crystals it was down to about 7.8 μg/mL at 4 min and the induction time was below 4 min; with 2 and 20 μg/mL the concentration fell at once, to about 4.9 μg/mL by 4 min and to about 3.4 μg/mL within about 1 min, respectively (Figure 8). R13·C36 The authors explain this by secondary nucleation on the seeds: the barrier is far lower than for homogeneous nucleation, so forming a critical nucleus becomes negligible. C35 Note by the AI writer: three seed levels (0.04–0.2 μg/mL) are below the crystalline solubility of 0.27 μg/mL, a 10,000-fold dilution of the suspension gives 4 μg/mL rather than 20 μg/mL, and the 20 μg/mL profile levels off at about 3.2 μg/mL, about 12 times the crystalline solubility; the seed levels are best read as nominal. X14

Discussion

The authors assemble the results into a picture of what happens to a dose of posaconazole on its way from the stomach into the small intestine. Typical median pH values are 1.0–2.0 in the fasted stomach, 4.0–8.0 in the duodenum and jejunum, and 6.5–8.0 in the ileum. R19 Because PCZ is 2–3 orders of magnitude more soluble at pH 1–2 than above pH 4, transfer from the stomach can produce intestinal concentrations far above the equilibrium solubility. C38

Above the amorphous solubility. Here LLPS and crystallization compete. Fast crystallizers may crystallize before LLPS is seen, whereas for molecularly complex drugs such as PCZ LLPS is "often" faster, giving drug-rich droplets of about 100–500 nm. C41·R21 Such colloids "are thought to" act as a reservoir that keeps the free drug at the amorphous solubility and the membrane flux at its maximum, so a formulation that undergoes LLPS can absorb better. C39 But because the induction time at high supersaturation in simulated intestinal fluid is short, "typically less than 3 min", the authors expect that without a crystallization inhibitor PCZ "will rapidly crystallize" and any amorphous drug-rich phase will be short-lived. C42

Between the two limits. Here only crystallization is possible, and the lifetime of the supersaturated solution depends on the degree of supersaturation and on the medium. C43 The steep dependence of induction time on supersaturation "suggests" that physiological variation in pH, fluid volume and composition "may lead to large variations in the time frame for crystallization in vivo and hence might contribute to inter-patient absorption variability". C44

How the medium enters. Because micelles raise both limits, the choice of biorelevant medium decides whether a formulation reaches LLPS in a dissolution test, and the authors call the medium's effect on the amorphous solubility "a critical input" for in silico and PBPK modelling. C47 They add that the concentration dependence of $K_{m/w}$ has been "largely overlooked" when free drug in supersaturated solutions is estimated, although it is needed to predict both absorption and nucleation rates. C47 For nucleation itself, they propose that bile salt micelles "may promote the formation of pre-nucleation clusters": many more drug molecules sit in micelles than in water, binding to micelles raises the local drug concentration, and since nucleation is a collision-based process, this "may impact the collision frequency"; alternatively, micelles may act as templates for oriented nucleation. C53·C54 At low supersaturation, where heterogeneous nucleation on dust and vessel walls is more probable, surfactants "could potentially block the heteronucleation pathway" by adsorbing on these surfaces; taurocholate in particular is known to inhibit the nucleation of several drugs. C55

The surfactant summary. Table 5 condenses these readings: taurocholate accelerates or inhibits homogeneous nucleation and inhibits heterogeneous nucleation; lecithin accelerates homogeneous and inhibits heterogeneous nucleation; glycerol monooleate and sodium oleate accelerate both. C56 The authors note that the effect of each surfactant "must be evaluated separately" to test this, and from earlier studies "it can be anticipated" that taurocholate and lecithin act in opposite directions on PCZ nucleation. C57·C58

Use of the results. In the authors' view, Figures 4 and 5 together with the induction times of Figure 7 "can be used to predict the likely phase behavior" for different doses and physiological conditions, and the findings "could be broadly applicable" to other weakly basic compounds once pKa, solubility and molecular structure are taken into account. C40·C59 Note by the AI writer (not discussed in the paper): three practical consequences follow from the data. First, the free-drug ceiling of about 34 times the crystalline solubility applies at every intestinal pH, so aiming above the amorphous solubility gains no free drug. Second, the higher total concentrations measured in FaSSIF or FeSSIF overstate the free-drug gain, by about 34/20 at the amorphous solubility in the authors' framework. Third, residual crystals, such as those from a suspension or an incompletely amorphous product, can remove most of the supersaturation within minutes.

Limitations

Limitations the authors state. The authors acknowledge that the predictive power of classical nucleation theory "has been widely debated" and use it as "a convenient means" to understand the role of supersaturation. C48 They note that the amorphous solubility below pH 2.5 may be inflated by the DMSO volume needed. C16 They state that the roles of taurocholate and lecithin are inferred and that each surfactant "must be evaluated separately". C57 The link from in vitro phase behaviour to absorption is phrased with "might" and "may". C44·C60

The AI writer's own judgement (1): the solubility map is solid, its fitted curves are not. The measured solubilities at 13 pH values and in five media, each in triplicate with small standard deviations, are the strongest data in the paper, and the ratio of about 34 from pH 2.0 to 7.0 follows directly from them. R1·R8·X5 The statement that the ratio holds "across the pH range tested" does not hold at pH 1.0–1.6 (22–28). X5 The fitted Henderson–Hasselbalch points drawn in Figures 2–4 do not reproduce the data at pH 2.5–3.0, Figure 4 plots a fitted rather than a measured crystalline value at pH 1.0, the amorphous solubility at pH 7.0 is printed as both 9.08 and 8.92 μg/mL, and the thermodynamic estimate of 37.9 cannot be reproduced from the printed inputs. X3·X4·X1·X2

The AI writer's own judgement (2): the kinetic comparisons rest on an estimated supersaturation scale. The supersaturation in the media is not measured but estimated with the assumption of a linear change in $K_{m/w}$, and the two panels of Figure 7 place the media points at different S, by up to about 1.5-fold at the low end. C9·X6 Some FaSSIF V1 points sit at S 35.7–36.9, above the supersaturation at the amorphous solubility, although the solutions were meant to be single-phase. X13 The number of replicate induction-time runs and the stirring rate are not stated. P7 The abstract's "much shorter" induction times in biorelevant media do not hold at the lowest supersaturations, and the summary durations in the discussion (within about 60 min below SR 10, under 10 min above SR 20) miss several plotted points. X7·X8

The AI writer's own judgement (3): the mechanisms are proposed, not tested. The homogeneous/heterogeneous assignment of the two slopes is taken from earlier work; no filtration, surface or seeding test separates the routes, and the break falls at a different supersaturation in each medium, from about 7 to about 13. C28·X11 The micelle–cluster mechanism rests on CNT fits of 3–9 points with an unstated definition of $J$, and $\gamma$ itself follows the induction-time order for three of the four media. X10·X11·X12 The media differ from each other and from PBS pH 6.5 in pH, buffer species and salt as well as surfactant, so the surfactant roles in Table 5 are inferences from mixtures. X16 The seed levels are nominal, and the excipients carried over from the commercial suspension are not described. X14 No polymer or crystallization inhibitor was included, so the data describe the unprotected drug rather than any formulation.

Conclusion

The paper gives a complete, replicated map of the crystalline and amorphous solubility of posaconazole from pH 1 to 7 and in five simulated gastrointestinal fluids. Its central finding is that the two limits move together with pH, so the largest free-drug supersaturation is about 34-fold from pH 2.0 to 7.0, while micelles raise both limits and reduce the concentration ratio to about 20, which the authors trace to a smaller micelle–water partition coefficient at supersaturation. R1·R8·R14·C19·C26 Crystallization timing depends steeply on supersaturation: in buffer the induction time falls from about 55 to about 8 min between S 5 and 33.6, intestinal media shorten it further at moderate to high supersaturation, and seed crystals remove it altogether. R10·R11·R13 The proposed mechanisms, micelles promoting pre-nucleation clusters at high supersaturation and blocking heterogeneous nucleation at low supersaturation, fit the data but were not tested directly, and the supersaturation scale of the media carries an internal inconsistency. C53·C55·X6