Measuring supersaturation in bile-salt media and human intestinal fluid: concentration ratios versus membrane flux

Background and motivation

Many new drug candidates are poorly soluble in water, and formulations that create supersaturated solutions, such as amorphous solid dispersions or weak bases that leave the acidic stomach, are widely used to improve their absorption (Introduction). A solution is supersaturated when the thermodynamic activity of the dissolved drug, or equivalently its chemical potential, is higher than that of drug in equilibrium with its most stable crystal (Mullin 2001, ref 5). C2 In practice, supersaturation is almost always reported as a concentration ratio: the dissolved concentration divided by the crystalline solubility measured in exactly the same medium, with the same pH, buffer, ionic strength and micellar species (Equation 1). C2·E1

Earlier work from the Taylor group and others had shown why supersaturation matters. Diffusive flux across a membrane rises linearly with supersaturation, but only up to a limit: once the concentration passes the amorphous solubility, the solution undergoes liquid–liquid phase separation (LLPS) and forms a colloidal drug-rich phase, the free drug concentration can rise no further, and the flux levels off (Raina 2014, ref 10; Ilevbare 2013, ref 12). C3 The drug-rich colloids have been "hypothesized" to help absorption by acting as a reservoir that replaces absorbed drug, and particle drifting into the unstirred water layer, which is often the rate-limiting barrier for lipophilic drugs, has also been "suggested" (refs 10, 14–19). C4 All of this holds only while crystallization is prevented. C4

The complication addressed here is that the gut is not water. Intestinal fluid contains bile salts and phospholipids that form micelles and solubilize lipophilic drugs. A characterization of human intestinal fluid had identified six bile salts, sodium taurocholate (STC), taurodeoxycholate (STDC), taurochenodeoxycholate (STCDC), glycocholate (SGC), glycodeoxycholate (SGDC) and glycochenodeoxycholate (SGCDC), which together make up about 98.4% of its biological surfactant (Riethorst 2016, ref 20). R15 Bile salts self-associate stepwise, so their critical micelle concentration (CMC) is not sharply defined; the hydroxyl pattern and taurine or glycine conjugation change the CMC range and the solubilizing capacity, and lecithin lowers the CMC and forms mixed micelles with them (refs 21–29). C5 Commercial fasted-state simulated intestinal fluids (FaSSIF) contain only STC: the first version (FaSSIF-V1) has a phosphate buffer, 3 mM STC and 0.75 mM lecithin, and the second version (FaSSIF-V2, 2008) a maleate buffer, 3 mM STC and 0.2 mM lecithin, both at pH 6.5. P1·C6 The group had already shown that bile salts are not interchangeable in their effect on solution thermodynamics (Lu 2017, ref 32) and on crystallization (refs 33, 34), and little was known about supersaturated solutions in aspirated human fluid. C6

This raises a measurement problem. If a medium solubilizes the drug differently at the crystalline solubility than in a supersaturated solution, the concentration ratio no longer tracks the activity. The authors write that such differences "may impact the perceived supersaturation" (Raina 2015, ref 35; Indulkar 2018, ref 36) and that this matters both for human aspirates collected after dosing and for simulated media used to predict them. C7 They therefore set out to test three linked hypotheses: that the maximum achievable supersaturation is set by the drug's activity at its amorphous solubility; that this activity, with an amorphous precipitate present, is "expected to be largely independent" of the medium; and that using total dissolved concentration in Equation 1 "will lead to incorrect conclusions" about the driving force for membrane transport and crystallization. C8 The test assumes that membrane transport is driven by the gradient of solute activity (Higuchi 1960, ref 37). C9

Two model drugs were chosen: atazanavir (log P 4.5, pKa 4.52) and posaconazole (log P 4.6, pKa 3.6 and 4.6), both weak bases that are "likely" to become supersaturated when they move from the stomach into the small intestine (Figure 1). M1·M2·C10 They were studied in six media: two blank buffers, two commercial FaSSIFs, a composite-FaSSIF made with the six human bile salts, and pooled fasted-state human intestinal fluid (FaHIF). A2

A note on references. This is the Just Accepted version of the manuscript. Its printed reference list is shifted against the citation numbers in the text from about reference 15 onward (the list has 71 entries, the text cites up to 76). The reference numbers in this article are those printed in the text, and the authors named are those whose list entry matches the cited content. X1

Background concepts

Concentration-based supersaturation. The usual definition is

In plain terms: the supersaturation ratio $S{R}_{conc}$ is the dissolved drug concentration $C$ divided by the crystalline (equilibrium) solubility $C_{eq}$ in the same medium. When $C$ is the amorphous solubility $C_{amph}$, the ratio is the concentration-based maximum supersaturation, $S{R}_{max}$. E1

Activity-based supersaturation. The thermodynamic definition uses activities:

In plain terms: supersaturation is the ratio of the solute activity $a$ in the solution to its activity $a_{eq}$ at the crystalline solubility; each activity is an activity coefficient $\gamma$ times a concentration. Equation 1 equals Equation 2 only when $\gamma /{\gamma }_{eq}=1$. In a micellar medium, part of the dissolved drug sits in micelles, so the total concentration $C$ is larger than the "free" concentration; $\gamma$ then absorbs that difference. If the micelle-held fraction is the same at both concentrations, $\gamma /{\gamma }_{eq}=1$ and the concentration ratio is correct; if it changes with concentration, it is not. E2·C28

Amorphous solubility and LLPS. The amorphous solubility is the highest concentration a supersaturated solution can reach before a drug-rich amorphous phase separates. At that point the activity of the dissolved drug equals that of the amorphous drug, which is its maximum; adding more drug only adds more drug-rich phase, seen as nanodroplets or colloids. C3 Two techniques detect this here. Both drugs fluoresce, and their emission depends on the polarity around them: when drug-rich colloids form, the intensity rises and, in some cases, the emission maximum moves to shorter wavelength (a blue or hypsochromic shift). Scanning electron microscopy (SEM) shows the shape of the pelleted drug-rich phase. P7·P8

Solubilization versus supersaturation. The authors stress that these two phenomena both raise the measured concentration but have opposite consequences for transport. Supersaturation raises the free drug concentration and so the activity and the flux. Solubilization puts drug into micelles, by binding to the surfactant or into the micellar core, so that two populations coexist, micelle-held and free; the total solubility rises, but the activity is still set by the crystal, so the free concentration does not rise. C26 Only free, un-ionized drug partitions into a membrane and crosses it (refs 35, 55–59). C27

Flux as a measure of activity. In a diffusion cell, the flux $J$ across a membrane is

In plain terms: the amount of drug crossing unit membrane area per unit time is proportional to the activity $a$ of the drug in the donor, with $D$ the diffusion coefficient of the solute, $h$ the membrane thickness and ${\gamma }_m$ the activity coefficient of the solute in the membrane. The authors take $D$, $h$ and ${\gamma }_m$ as constant for a given drug and medium. E3·C12 If the donor holds a second phase, crystals or amorphous drug, the activity of the dissolved drug equals that of this phase, so the flux measures a well-defined activity. The ratio of the fluxes measured at the two solubilities is then the activity-based maximum supersaturation: C12

In plain terms: divide the flux from a solution at the amorphous solubility, $J_{amph}$, by the flux from a crystalline suspension, $J_{eq}$, in the same medium; the membrane constants cancel and what is left is the ratio of activities. E4

Fick's first law and apparent permeability. The familiar relation

In plain terms: flux $J$ equals the membrane permeability $P$ times the drug concentration $C$. Read with total concentration, it implies that any increase in dissolved drug above the crystalline solubility increases transport, in the absence of efflux or first-pass metabolism; the authors use it to show why total concentration misleads when part of the drug is in micelles. In the SI, the apparent permeability $P_{app}$ is calculated as the normalized flux divided by the donor concentration. E5·C3

Micellar partition coefficient. To describe how strongly a medium solubilizes a drug, the paper uses

In plain terms: $K_{m/w}$ is the drug concentration associated with the surfactant, $C_m$, divided by the free drug concentration, $C_w$. The authors take $C_w$ as the solubility in the blank buffer (where only free drug exists) and $C_m$ as the excess concentration in the micellar medium over the buffer, assuming the bile salts and lecithin do not mix into the crystalline or amorphous drug phase. They call the model "likely oversimplified" for bile acid–lecithin systems but use it to show how solubilization changes with concentration. E6·C31

Methods in detail

The study measures the same quantity, the maximum supersaturation of each drug in each medium, in two independent ways, and then asks why they disagree. The workflow is shown below. A1·A2·A3

The six media

Buffer-V1 and buffer-V2 are the blank buffers of FaSSIF-V1 (sodium phosphate) and FaSSIF-V2 (maleic acid), without bile salt or lecithin. FaSSIF-V1 was made by adding commercial FaSSIF/FeSSIF/FaSSGF powder to buffer-V1, and FaSSIF-V2 by adding FaSSIF-V2 powder to buffer-V2. P1·M5·M6 Composite-FaSSIF was prepared in buffer-V1 with the six human bile salts in the proportions of the Riethorst characterization, 3 mM in total, plus 0.2 mM lecithin: the bile salts were stirred into the buffer, lecithin was dissolved in dichloromethane (less than 1% of the volume) and titrated in, and the dichloromethane was evaporated by stirring at 500 rpm and 50 °C for 30 min. P1·M17 All five were adjusted to pH 6.5. P1 Table 1 gives the compositions. P1

Table A. Bile salt and lecithin composition of the three micellar simulated media (from Table 1), all at pH 6.5. P1

FaHIF came from a previous study at University Hospitals Leuven: duodenal fluid was aspirated near the ligament of Treitz from 20 healthy volunteers every 10 minutes for 90 minutes after an overnight fast and 250 mL of water, the fractions were pooled per volunteer, and a mixed pool of 16 volunteer pools was made for this work and stored at −80 °C. P2·M14 The pH of the pool was 7.3; no adjustment to 6.5 is described, so FaHIF differs from the other media in pH as well as in composition. M14·X5

Crystalline and amorphous solubility

Crystalline solubility was measured by stirring excess crystals in 1 mL of medium for 48 h at 37 °C, separating the solid by ultracentrifugation (50,000 rpm, 135,700 g, 30 min, at 37 °C) and analysing the supernatant by HPLC, with UV detection at 247 nm for atazanavir and fluorescence detection (excitation 240 nm, emission 385 nm) for posaconazole; n = 3. P3·P4·P5 Amorphous solubility was measured by the solvent-shift method: small aliquots of an atazanavir stock in DMSO (50 mg/mL) or a posaconazole stock in methanol (10 mg/mL) were added to 1 mL of stirred medium at 37 °C until the total exceeded the expected amorphous solubility. P6 To keep the supersaturated solutions from crystallizing, HPMC-AS was predissolved at 10 µg/mL for atazanavir and 100 µg/mL for posaconazole. P6·M3 The drug-rich phase was pelleted by the same ultracentrifugation, and the supernatant concentration was taken as the amorphous solubility; n = 3. P6

Confirming the drug-rich phase

Fluorescence emission spectra (220–450 nm) were recorded for solutions below and above the amorphous solubility in FaSSIF-V1, composite-FaSSIF and FaHIF, prepared by solvent shift with HPMC-AS present, at 37 °C; the excitation wavelength was 250 nm for atazanavir and 240 nm for posaconazole. P7 For SEM, highly supersaturated solutions of each drug in FaHIF (posaconazole again with 100 µg/mL HPMC-AS) were centrifuged at 14,800 rpm for 10 min, and part of the pellet was fixed on a stub, sputter-coated with platinum and imaged at 5 kV. P8

Flux and the two supersaturation ratios

Flux was measured in a side-by-side diffusion cell with 1 mL of medium on each side of a regenerated cellulose membrane (molecular-weight cut-off 6–8 kDa, 9 mm orifice), stirred at about 600 rpm to keep the unstirred water layer thin, at 37 °C. P9·M4 For J_amph, drug was added to the donor from the stock solution at the amorphous solubility of that medium, with HPMC-AS (10 or 100 µg/mL) on both sides; for J_eq, a crystalline suspension equilibrated for 48 h in the medium was placed in the donor. P9 Receiver samples of 15 µL were analysed by HPLC; the slope of receiver concentration against time, divided by the membrane area, gave the flux; n = 3. P9·R7 A control without HPMC-AS (atazanavir in buffer-V1) showed that the polymer did not change the mass flow rate. R10·C11

The concentration-based SR_max is the ratio of Table 3 to Table 2 in each medium, and the activity-based SR_max the ratio of the two fluxes; each medium was compared with FaSSIF-V1 by a two-tailed t-test. P10 Two details are not fully specified. The results text says the fluxes were measured on systems "containing a suspension of either crystalline or amorphous drug", but the methods describe the amorphous donor as drug added at a concentration equal to the amorphous solubility, so whether excess drug-rich phase was present is not stated; and whether HPMC-AS was also present in the crystalline-suspension experiments is not stated. X6

Micellar partition coefficient and permeability

Using Equation 6, the authors estimated $K_{m/w}$ for both drugs at the crystalline and at the amorphous solubility in FaSSIF-V1, composite-FaSSIF and FaHIF, with the buffer solubility as the free concentration. P11 In the SI they also calculated an apparent permeability from flux over total donor concentration (Table S2) and corrected it for solubilization (Table S3) with

In plain terms: the apparent permeability calculated with total concentration is multiplied by the ratio of total solubility in the medium, $D_{total}$, to solubility in the corresponding buffer, $D_{free}$, so that it refers to free drug only (buffer-V1 is the reference for composite-FaSSIF and FaHIF; in the buffers the ratio is 1). The correction is adapted from Katneni et al. E7·P12

Experimental analysis

Micelles raise the crystalline solubility more than the amorphous solubility

Table B collects both solubilities. In the two blank buffers each drug had the same solubility within error: atazanavir 1.4 and 1.5 µg/mL (crystalline) and 79 and 82 µg/mL (amorphous); posaconazole 0.23 and 0.22 µg/mL and 8.1 and 8.2 µg/mL. R1.a·R1.b·R2.a·R2.b The micellar media changed the picture differently for the two drugs. R1·R2

Table B. Crystalline (Table 2) and amorphous (Table 3) solubility in µg/mL at 37 °C, mean ± SD, n = 3; amorphous values measured with HPMC-AS present. R1·R2

Atazanavir. Its crystalline solubility rose to 2.6–3.1 µg/mL in the simulated micellar media, which the authors describe as "slightly higher", and to 7.1 µg/mL in FaHIF, about five times the buffer value. R1·C13·X4 Its amorphous solubility rose by about 1.25 times, to a nearly identical 99–102 µg/mL in all four micellar media, "suggesting" that the make-up of the bile salt–lecithin mixture had minimal effect on its solubilization in a supersaturated solution. R2·C15

Posaconazole. Its crystalline solubility rose 7–14 fold in the micellar media, to 3.2 µg/mL in FaSSIF-V1, 1.6 in FaSSIF-V2, 1.7 in composite-FaSSIF and 2.6 in FaHIF; the authors read this as more effective solubilization of posaconazole by mixed micelles ("This suggests"), and note that the highest value occurred with the most lecithin. R1·C14 Its amorphous solubility followed the same order: 43.3 µg/mL in FaSSIF-V1, 20.8 in FaSSIF-V2, and lower in composite-FaSSIF (15.5) and FaHIF (13.2), a difference between commercial and composite media that the group had also seen for ritonavir, tacrolimus and cilnidipine. R2·C16

The key pattern is the proportion. For posaconazole in FaSSIF-V1 the crystalline solubility is about 14 times the buffer-V1 value, the amorphous solubility only about 5 times; the authors state that for both compounds the crystalline solubility "showed a proportionally greater increase" than the amorphous solubility. C35·R1.c·R2.c Because the concentration-based SR_max is the ratio of the two, it must fall in micellar media.

The drug-rich phase forms above the amorphous solubility, also in human fluid

In each of FaSSIF-V1, composite-FaSSIF and FaHIF, the emission intensity of the drug stayed nearly flat at low concentration and rose above a break (Figure 2, insets). R3 Read approximately from the insets, the break lies between 105 and 110 µg/mL for atazanavir in FaSSIF-V1, between 95 and 100 µg/mL in composite-FaSSIF and between 100 and 105 µg/mL in FaHIF; for posaconazole between 38 and 39 µg/mL in FaSSIF-V1, between 14 and 16 µg/mL in composite-FaSSIF and around 12–13 µg/mL in FaHIF. R3 The authors report "good correspondence" with the ultracentrifugation values of Table 3. C17 Most onsets fall within 1–2 µg/mL of the inset spacing, but for posaconazole in FaSSIF-V1 the intensity starts to rise about 10% below the 43.3 µg/mL measured by centrifugation. X8 In several panels the emission maximum also moved to shorter wavelength, for example from about 372 to 365 nm for posaconazole in FaSSIF-V1; this "is attributed to" the lower polarity experienced by drug molecules in the colloids, which raises the quantum yield. R3.d·C18

SEM of pellets from highly supersaturated FaHIF showed densely packed, mostly spherical particles for both drugs, roughly 0.1–0.5 µm across when read against the 1 µm scale bar, with some atazanavir particles joined into elongated shapes; none had the needle shape of atazanavir crystals (Figure 3). R4·C19 The authors present this as the first demonstration that such colloids form in human intestinal fluid above the amorphous solubility, "a significant finding" given their proposed reservoir role in vivo, which was not tested here. C24

Flux follows free drug, not total solubility

Receiver concentrations rose linearly with time in every diffusion experiment (Figures 4 and 5). R5·R6 For atazanavir at the amorphous solubility, the receiver reached about 7.0–7.5 µg/mL after 90 min in buffer-V1, composite-FaSSIF and FaHIF alike, and the three crystalline-suspension runs overlapped, reaching about 0.55 µg/mL after 6 h. R5 For posaconazole at the amorphous solubility, buffer-V1 and composite-FaSSIF reached about 0.85 µg/mL after 60 min and FaHIF about 0.73 µg/mL; the crystalline runs reached about 0.14–0.19 µg/mL after 6 h. R6

Table C. Normalized diffusive flux in µg/(min·cm²), mean values from SI Table S1 (standard deviations omitted). R7

Table C shows the central observation. At the crystalline solubility, the flux of posaconazole was 5.79–6.97 × 10⁻⁴ µg/(min·cm²) in all six media, although its crystalline solubility differed up to 14-fold between them; atazanavir's J_eq was 2.08–2.48 × 10⁻³ while its crystalline solubility ranged from 1.4 to 7.1 µg/mL. R7·R1 The authors call the fluxes "relatively close" between media and note that, as in earlier reports, flux at the crystalline solubility showed no correlation with the gain in solubility from solubilization. C20·C27 At the amorphous solubility the fluxes were also similar: 0.105–0.139 µg/(min·cm²) for atazanavir and 0.0191–0.0239 for posaconazole. R7

The SI makes the same point with permeability. Calculated on total concentration, the apparent permeability dropped in the micellar media and depended on which solubility was used; for posaconazole at the crystalline solubility it fell from 2.60 × 10⁻³ cm/min in buffer-V1 to 2.18 × 10⁻⁴ in FaSSIF-V1. R12 After multiplying by the ratio of total to buffer solubility, it became 1.33–1.77 × 10⁻³ cm/min for atazanavir and 2.36–3.03 × 10⁻³ cm/min for posaconazole in every medium and at both solubilities, values the authors call "considerably similar ... as it would be expected". R13·C48

The flux ratio stays put while the concentration ratio falls

Table D. Maximum supersaturation ratio SR_max, read from Figures 6 and 7 (approximate; n = 3). p values: two-tailed t-test of the activity-based value against FaSSIF-V1; all other activity-based values not significantly different. R8·R9

Table D is the paper's main result. In the two buffers the two measures agree. R8.a·R8.b·R9.a·R9.b In every micellar medium the concentration-based value is lower, and it is lowest in FaHIF, so that judged by concentration the maximum achievable supersaturation "appears to decrease" in human fluid; the activity-based values, in contrast, are "approximately the same" across media. C21 For atazanavir the activity-based SR_max averaged ~54, and no medium differed from FaSSIF-V1 (p > 0.05), so the authors conclude that "all media achieved an equivalent maximum supersaturation"; an earlier study by Indulkar et al. had reported an average of 65. R8·C22·R16 Recomputed from the Table S1 means, the atazanavir ratio in buffer-V1 is 1.19 × 10⁻¹ / 2.17 × 10⁻³ = 54.8, matching Figure 6. E4

For posaconazole the authors give ~36 and note a slight but statistically significant decrease in composite-FaSSIF and FaHIF. C23·R9 Note by the AI writer (not discussed in the paper): the ratios of the Table S1 means for the six media are 36.6, 36.6, 34.3, 37.4, 30.4 and 28.9, whose mean is about 34; the figure of ~36 matches the four media other than composite-FaSSIF and FaHIF. X7

In FaHIF the gap is largest: for atazanavir about 53 against about 14, and for posaconazole about 29 against about 5. R8.f·R9.f The authors put it in transport terms: in FaHIF a solution at the amorphous solubility moved posaconazole across the membrane about 30 times faster than a crystalline suspension, "indicating that the amorphous solubility advantage is not lost in FaHIF", although the concentration ratio is only about 5. R9·C30 (The text attributes the value of about 5 to Figure 6, but it is the posaconazole value of Figure 7; atazanavir in FaHIF is about 14. X3)

Solubilization weakens at the amorphous solubility

Table E. Micellar partition coefficient K_m/w as printed in Table 4; in brackets, the value recalculated by the AI writer from Tables 2 and 3 with Equation 6 as the text defines it (excess over buffer-V1 divided by buffer-V1). R11·X2

From Table 4 the authors draw four observations. At the crystalline solubility posaconazole has a higher $K_{m/w}$ than atazanavir, "indicating" that it is more effectively solubilized by the micelles. C32 $K_{m/w}$ is "much lower" at the amorphous than at the crystalline solubility for both drugs, in agreement with the strong concentration dependence that Indulkar et al. reported for atazanavir with sodium dodecyl sulfate. C33 $K_{m/w}$ varies with medium and with drug, and the larger solubilization capacity for posaconazole "explains why" its discrepancy between the two ratios is larger than atazanavir's. C33·C34 Finally, the fall from crystalline to amorphous solubility is largest in FaHIF (5.1 to 1.3 for atazanavir, 11.3 to 1.6 for posaconazole), so the concentration-based ratio "can be expected" to err most in that medium. R11.c·C40

Note by the AI writer (not discussed in the paper): every value printed in Table 4 equals the total solubility in the medium divided by the buffer-V1 solubility (for example 2.7/1.4 = 1.93 for atazanavir in FaSSIF-V1), whereas Equation 6 and the text define $K_{m/w}$ as the micelle-associated concentration, the excess over buffer, divided by the free concentration, which gives values smaller by exactly 1 (the bracketed values in Table E). X2·E6 Figure 8 uses the printed numbers as counts of micelle-held to free molecules. R14 The conclusions drawn from Table 4 do not depend on this: under either reading the coefficient is lower at the amorphous solubility, falls most in FaHIF, and is higher for posaconazole. X2

Comparison with clinical data

Hens et al. had measured posaconazole supersaturation directly in human intestinal aspirates, dividing the measured concentration by the crystalline solubility in each individual sample: the mean maximum supersaturation ratio was about 4 after an acidified or neutral suspension and about 7 after a solid dispersion given in the fasted state. R17 The authors find these values "Remarkably" close to their FaHIF concentration-based value of about 5 at the amorphous solubility, and argue that the in vivo solutions "were likely much more highly supersaturated than they appeared". C29·C30 Note by the AI writer (not discussed in the paper): the in vivo values are mean maxima in individual aspirates after dosing, not values at the amorphous solubility in a pooled fluid, so the agreement compares different quantities. X11

Discussion

How the authors explain the gap. The argument is a chain from thermodynamics to measurement. C26·C28·C37

In the authors' words, using Equation 1 in solubilizing media assumes that the fraction of drug solubilized at the crystalline solubility is the same as in the supersaturated solution; if solubilization capacity varies with concentration, $\gamma /{\gamma }_{eq}$ differs from 1, and "This appears to be the situation in the biorelevant media tested herein". C28 In simple buffers there is no solubilization, the solution is dilute and close to ideal, and the two measures agree. C42 In micellar media, "We can anticipate" that the micelles have a finite capacity, so that at the amorphous solubility they take up proportionally fewer of the extra drug molecules; $K_{m/w}$ therefore drops, and the total concentration rises far less than the activity. C37 The lower posaconazole amorphous solubility in composite-FaSSIF and FaHIF than in commercial FaSSIF "can be attributed in large part" to this change, because the fluxes, and so the free concentrations, are similar; the concentration ratio thus "drastically underpredicts" the posaconazole flux in micellar media. C36 Figure 8 illustrates the idea: the free drug is drawn as constant (about 1 unit at the crystalline solubility, about 35 at the amorphous solubility) while the micelle-held drug varies with medium and is relatively smaller at the amorphous solubility. R14·C37

Why the two drugs differ. Lecithin-rich micelles take up more posaconazole: its amorphous solubility was 43.3 µg/mL in FaSSIF-V1 (0.75 mM lecithin) against 20.8 µg/mL in FaSSIF-V2 (0.2 mM), and the authors write that mixed micelles with greater lecithin content "clearly improve posaconazole solubilization in supersaturated solutions". R2·P1·C38 Atazanavir's amorphous solubility was largely unaffected by the medium. Since the two drugs have similar log P, the authors turn to Hammad and Muller, who found that solubilization in bile salt–phosphatidylcholine micelles depends on micelle size and on drug size, branching, polarizability and conformation, and conclude that the difference "likely arises from structural differences between these two compounds". C39

A second, smaller effect. The slight but significant fall of posaconazole's activity-based SR_max in composite-FaSSIF and FaHIF came from a lower J_amph (0.0192 and 0.0191 against 0.0212–0.0239 µg/(min·cm²) in the other media). R7·R9 The authors propose that it "could be due to mixing of specific bile salts with the amorphous posaconazole phase", which would lower the free concentration in equilibrium with that phase, as had been reported for telaprevir, whose thermodynamic SR_max fell to about three-fourths in the presence of the dihydroxy bile salts STCDC and SGCDC. C44·R18 Both composite-FaSSIF and FaHIF contain STCDC and SGCDC, whereas FaSSIF-V1 and FaSSIF-V2 do not. P1 The composition of the posaconazole-rich phase was not measured. C44

What the authors conclude for practice. The most important implication, in their words, is that Equation 1 "cannot be used to estimate supersaturation in complex biorelevant media or aspirated human fluids", in particular for compounds that are solubilized: it underestimates supersaturation and makes the amorphous solubility advantage seem to decrease in vivo. C45 The activity-based ratio is "undoubtedly more accurate" in complex media with bile salts, although experimentally more demanding. C41 They also write that the findings matter for modelling the effect of supersaturation on absorption rate and for defining the thermodynamic driving force for crystallization in complex media. C1 On simulated fluids, composite-FaSSIF mimics human bile composition more closely than single-bile-salt FaSSIF and "comes closer" to FaHIF in solubilization and supersaturation behaviour, but human fluid varies between and within subjects and contains cholesterol and lipid digestion products that composite-FaSSIF lacks, so "more work needs to be done" to optimize simulated fluids for testing supersaturating formulations. C46

Note by the AI writer (not discussed in the paper): what this means in a formulation laboratory. When a supersaturating formulation is tested in FaSSIF, composite-FaSSIF or human fluid, the drop of the amorphous-to-crystalline concentration ratio relative to buffer can come entirely from solubilization rather than from a loss of driving force: in this paper the flux ratio stayed near 53 for atazanavir and near 29 for posaconazole in FaHIF while the concentration ratios were about 14 and 5. R8·R9 The size of the distortion follows how much more the medium solubilizes the crystal than the supersaturated solution; a simple first indicator is the ratio of crystalline solubility in the medium to that in buffer, which was 1.9–5.1 for atazanavir and 7.4–13.9 for posaconazole here. R11 A second practical point is that the flux from a crystalline suspension barely changed with medium, so a medium that raises crystalline solubility does not by itself raise absorptive flux in this set-up. R7

Limitations

Limitations stated by the authors. The authors describe the $K_{m/w}$ model as "likely oversimplified" for bile acid–lecithin systems, and it rests on the assumption that the solubilizing components do not mix with the crystalline or amorphous drug phase. C31 Their own explanation for the lower posaconazole flux in composite-FaSSIF and FaHIF, bile salts entering the amorphous phase, would break that assumption, and they offer it only as "could be due to". C44 They note that human intestinal fluid is highly variable between and within subjects and contains components missing from composite-FaSSIF, so their simulated fluid is still an approximation. C46 The activity-based method itself assumes that the diffusion coefficient, membrane thickness and membrane activity coefficient are constant for a drug and medium. C12

The AI writer's own judgement (1): what is measured and what is inferred. The central contrast is well supported. Solubilities and fluxes were measured in triplicate in all six media for both drugs, with standard deviations, and the printed numbers are internally consistent: the flux ratios of Table S1 reproduce Figures 6 and 7, the apparent permeabilities of Tables S2 and S3 reproduce from Table S1 and the solubilities, and the slopes of Figure 4 match Table S1 if the membrane area is the 9 mm orifice (0.636 cm²). R7·R8·R12·R13·E4·E5·E7·X6 Fluorescence and SEM independently confirm that a drug-rich phase forms. R3·R4 The mechanistic layer is weaker. Free drug was never measured directly: $K_{m/w}$ is calculated from solubilities, with the buffer solubility taken as the free concentration, and Table 4 does not follow its own Equation 6 (each printed value is total over buffer, one more than the defined coefficient). C31·X2 The claim about the driving force for crystallization is not tested, because HPMC-AS was present in every supersaturated experiment to prevent crystallization. X9·X10

The AI writer's own judgement (2): comparability and reporting. FaHIF had pH 7.3 while all simulated media were adjusted to pH 6.5, and it was a single pooled sample; differences between FaHIF and the simulated media therefore reflect pH and composition together, and subject-to-subject variation was not tested. X5 HPMC-AS was present in the amorphous solubility measurements but is not stated for the crystalline ones, and the no-effect control covers only atazanavir flux in buffer-V1. X10 How the standard deviations of the ratios were obtained is not stated, and significance was tested only against FaSSIF-V1. X12 Several references in the discussion point to the wrong figure, the stated posaconazole average of ~36 exceeds the six-medium mean of about 34, and the reference list of this Just Accepted manuscript is shifted against the in-text numbers. X3·X7·X1 None of these changes the main result, but readers should take the per-medium values from Table S1 and Figures 6 and 7 rather than the summary numbers in the text. X7

Conclusion

For two un-ionized, lipophilic weak bases, the solubilizing capacity of each medium strongly affected both the crystalline and the amorphous solubility, and it raised the crystalline solubility proportionally more, so the concentration-based maximum supersaturation fell in every bile salt–lecithin medium and most in aspirated human intestinal fluid. C47·C35·R8·R9 Measured by membrane flux, which follows the free drug, the maximum supersaturation was about 50–56 for atazanavir and 29–37 for posaconazole in all six media, with only a slight decrease for posaconazole in the two media that contain the six human bile salts. R8·R9·C23 A drug-rich amorphous phase formed above the amorphous solubility in every medium examined, including human fluid. R3·R4·C24 The authors' explanation, a micellar partition coefficient that is lower at the amorphous than at the crystalline solubility, fits all their data but was calculated rather than measured, and its tabulated values need a correction of 1 to match their own definition. C33·C37·X2 Their practical conclusion is that supersaturation in complex biorelevant media and aspirated human fluids should be judged by activity, for example by flux, and not by Equation 1. C45·C41