How the bile salts of the human gut change the thermodynamics of a supersaturated drug solution: telaprevir as a test case

Background and motivation

Oral absorption of a drug depends on its solubility in the gastrointestinal fluid and its permeability across the gut wall, and an increasing share of drug candidates are poorly soluble (Amidon 1995, ref 1; refs 2, 3). Formulators raise solubility with salts, cosolvents, lipids and surfactants, nanocrystals and amorphous solid dispersions (ASDs). Not all of these gains are equal. Solubilizing additives such as surfactants can raise the apparent solubility while lowering membrane transport, because the drug they hold in micelles has a lower thermodynamic activity (Raina et al. 2015, ref 4). Supersaturation, as generated by an ASD, raises the apparent solubility without that penalty (Miller et al. 2012, ref 5). C4

The "spring and parachute" picture describes how supersaturation is used (Guzman et al. 2007, ref 6; Brouwers et al. 2009, ref 8): a formulation generates a supersaturated solution (the spring), and an inhibitor holds back crystallization so that the supersaturation lasts long enough to drive absorption (the parachute). If crystallization is slow, the highest supersaturation reachable is set by the amorphous solubility of the drug. Above it, the solution separates into a drug-lean continuous phase and dispersed, disordered drug-rich droplets (Ilevbare and Taylor 2013, ref 7). C5 Polymers based on poly(vinylpyrrolidone) and cellulose derivatives are the usual crystallization inhibitors, and their effect has been linked to their hydrophobicity and their interactions with the drug (Ilevbare et al. 2013, refs 9, 10). Surfactants act less predictably: they can promote or inhibit nucleation and crystal growth and change polymorphic outcomes (refs 11–14). A further complication is that with solubilizing additives present, the usual concentration-based supersaturation ratio need not match the drug's activity, which is the real driving force for crystallization (ref 4). C6

Bile salts are the body's own surfactants. Chen et al. (2015, ref 11) found that sodium taurocholate (STC) inhibited the crystallization of supersaturated celecoxib. R24 In the gut, bile salts form mixed micelles with lecithin and cholesterol. Human intestinal fluid contains at least six bile salts: STC, sodium taurodeoxycholate (STDC), sodium taurochenodeoxycholate (STCDC), sodium glycocholate (SGC), sodium glycodeoxycholate (SGDC) and sodium glycochenodeoxycholate (SGCDC), and SGC, STCDC and SGCDC are more abundant than STC (Riethorst et al. 2015, ref 15). Yet STC is the only bile salt in the commercial fasted- and fed-state simulated intestinal fluids (FaSSIF, FeSSIF). R22 Bile salts also aggregate differently from ordinary surfactants: their rigid steroid scaffold carries hydroxyl groups on one face (facial polarity), aggregation is stepwise and spread over a wide concentration range, the critical micelle concentration (CMC) depends on the functional groups and is "expected" to change solubilizing power, and reported CMCs of the biologically relevant bile salts lie between 2 and 12 mM (refs 16–20). C7

The authors therefore ask two questions (manuscript p.5). First, how does a bile salt, below and above its CMC, change the thermodynamic properties of a supersaturated solution of a poorly water-soluble drug, and how do solubilization and membrane transport interact? Second, is STC a good surrogate for the other bile salts? Their model drug is telaprevir (Figure 1), a poorly soluble hepatitis C protease inhibitor with a high glass transition temperature and a large reported supersaturation window, which undergoes glass–liquid phase separation (GLPS) rather than rapid crystallization (Mosquera-Giraldo and Taylor 2015, ref 21). C8·A1·A2

Background concepts

Supersaturation as an activity ratio. The driving force for crystallization is the difference in chemical potential between the dissolved drug and the crystal. The paper writes it as (Eq. 3) E3:

Here $\mu$ is the chemical potential of the solute, $R$ the gas constant, $T$ the temperature, $a$ the solute activity, and the superscript ${}^{\circ }$ marks the standard state chosen in this paper: a solution in equilibrium with crystalline drug. In plain terms: the fundamental supersaturation $\delta$ is how many times the drug's activity exceeds its activity in a solution saturated with crystal; $\delta =1$ at the crystalline solubility. Activity is concentration times an activity coefficient (Eq. 2) E2:

In plain terms: the same concentration $C$ can mean different activities if something in the solution (here a bile salt) changes the activity coefficient $\gamma$. A drug held in micelles counts toward the measured concentration but contributes little to the activity, so $\gamma$ falls.

The ceiling: amorphous solubility. In the absence of crystallization, adding drug beyond the amorphous solubility produces an amorphous, drug-rich disperse phase; for a liquid drug-rich phase this is liquid–liquid phase separation (LLPS), and for a glassy drug-rich phase such as telaprevir's, glass–liquid phase separation (GLPS). The highest supersaturation is therefore (Eq. 4) E4:

In plain terms: the ceiling is the activity of the drug at the amorphous solubility divided by its activity at the crystalline solubility. In a simple dilute solution the activity coefficient is the same at both concentrations, and the ceiling becomes a ratio of concentrations (Eq. 5) E5·C34:

In plain terms: in plain buffer the maximum supersaturation is the amorphous solubility over the crystalline solubility. For telaprevir in this paper's buffer that is about 148/5.2, or about 28 (a check by the card, which matches the boundary drawn in Figure 11). E5·R1·R2·R18 With bile salts that interact with the drug, the activity coefficient can differ between the two concentrations, and "it may no longer be accurate to use concentration ratios to determine the supersaturation" (ref 4). C35

Flux as a measure of activity. The key technique is a side-by-side diffusion cell: a donor and a receiver chamber separated by a membrane. The mass flow rate of drug across the membrane is (Eq. 1) E1:

Here $F$ is the mass flow rate (µg/min), $M$ the mass transferred, $t$ time, $D$ the diffusion coefficient, $S$ the membrane cross-sectional area, $h$ the membrane thickness and ${\gamma }_m$ the activity coefficient of the drug in the membrane. In plain terms: the flux is driven by the drug's activity in the donor, not by its concentration; if $D$, $S$, $h$ and ${\gamma }_m$ do not change, flux is simply proportional to activity. Dividing by the flux $F^{\circ }$ of a solution saturated with crystal gives $\delta$ directly (Eq. 6, where the membrane area is written $S_m$) E6:

In plain terms: the ratio of two fluxes is the ratio of two activities, so flux measured at any concentration, in any medium, can be placed on the same supersaturation scale. Below the phase-separation limit, the slope of flux against concentration also reports the activity coefficient (Eq. 7) E7:

In plain terms: if a bile salt halves the slope, it has halved telaprevir's activity coefficient. Above the amorphous solubility, adding drug only adds drug-rich droplets and the activity no longer rises, so the flux plateaus; the plateau marks the GLPS onset.

Binodal and spinodal. When a drug-rich phase separates, the drug concentration left in the continuous phase is the binodal (coexistence) concentration. A solution can stay one-phase a little beyond it until it reaches the spinodal, where it separates spontaneously. Methods that pellet the drug-rich phase and measure what remains report the binodal; a method that adds drug continuously and watches for turbidity might overshoot toward the spinodal (Taylor and Zhang 2016, ref 24). C15·C16

The six bile salts. All six share one steroid scaffold with a hydroxyl at R1 (Table 1). The cholates, STC and SGC, carry hydroxyls at R1, R3 and R4 (trihydroxy). The deoxycholates, STDC and SGDC, lack the hydroxyl at R3; the chenodeoxycholates, STCDC and SGCDC, lack it at R4 (dihydroxy). At R5 each comes as a taurine conjugate (NHCH₂CH₂SO₃⁻) or a glycine conjugate (NHCH₂COO⁻). The trihydroxy bile salts are less hydrophobic and have higher CMCs than the dihydroxy ones (Madenci and Egelhaaf 2010, ref 34). M3–M8 The authors use 1.86 mM (about 0.1 w/w %) as a "monomer level" and 12 mM as a "micellar level", assuming that telaprevir does not shift the CMCs of 2–12 mM. P1·C42

Methods in detail

All experiments used 50 mM pH 6.5 sodium phosphate buffer at 37 °C, without bile salt or with one bile salt at 1.86 or 12 mM, giving 13 media. M10·A1·A2 Three thermodynamic quantities were measured in each: the crystalline solubility, the GLPS onset (the amorphous solubility) and the flux of telaprevir across a membrane as a function of its concentration. The flux data were then turned into activities and drawn, together with the two solubilities, as phase-boundary diagrams on a concentration scale and an activity scale.

Contribution 1: locating the amorphous solubility three ways, with and without bile salts

① Problem. The GLPS onset sets the ceiling of supersaturation. Earlier work measured it for telaprevir in 100 mM pH 6.8 phosphate buffer (ref 21), but not in the presence of bile salts, which may solubilize the drug or interact with its drug-rich phase. R19·C8

② How. The authors used three independent methods. In the UV extinction method a syringe pump added a 12 mg/mL methanol stock of telaprevir at 0.05 mL/min to 15 mL of stirred medium (300 rpm, 37 °C); the drug-rich droplets that form at the onset scatter light, which shows as a rise in extinction at 370 nm, a wavelength where telaprevir does not absorb (n = 3). P2 In the ultracentrifugation method, enough stock (12 or 20 mg/mL) was added to make the solution turbid, the drug-rich phase was pelleted at 35000 rpm for 40 min at 37 °C, and the drug concentration left in the supernatant was measured by UV at 270 nm after 2-fold dilution with methanol. P3 In the flux method the onset is the donor concentration at which flux stops rising (described below). P4·C18 The crystalline solubility was measured by adding excess crystalline telaprevir to 15 mL of medium, stirring for 48 h at 37 °C, ultracentrifuging for 30 min and measuring by UV at 270 nm. P1

③ Why it works. Ultracentrifugation and flux "likely" give a concentration close to the coexistence (binodal) concentration of the continuous phase, because they measure the solution that remains next to the drug-rich phase; the UV method, with its continual addition, "might" approach the spinodal instead. If the three agree, the solution does not stay supersaturated far beyond the onset. C15·C16

④ What is new. The same three methods were applied in 13 media, so that solubilization (a rise in the onset concentration) and other interactions can be separated from method artefacts. A side check compared buffers, because the onset found here in 50 mM pH 6.5 buffer was about 1.5 times the value reported in 100 mM pH 6.8 buffer. C19·P7

Contribution 2: membrane flux as a calibrated read-out of activity

① Problem. Concentration-based supersaturation can mislead in solubilizing media, so a direct measure of activity is needed to know whether a bile salt changes crystallization by changing the driving force or by other effects. C33·C35

② How. In a side-by-side diffusion cell (Figure 2) the donor and receiver chambers, each holding 32 mL of buffer with 5 µg/mL HPMCAS-MF to prevent crystallization, were separated by a regenerated cellulose membrane with a molecular weight cut-off of 6–8 kDa and a 30 mm orifice, stirred at 300 rpm and kept at 37 °C. P4·M2·M9 The same bile salt concentration was put in both chambers, so that the bile salt itself had no driving force to diffuse. C10 Telaprevir stock was added to the donor, and the receiver concentration was followed by a UV dip probe at 270 nm for 60 minutes (Figure S1); the slope of receiver concentration against time gave the mass flow rate. P4·R7 Donor concentrations ran from 5 to 170 µg/mL in buffer and up to 360 µg/mL with bile salts. P4 Control runs without HPMCAS-MF gave consistent flux, so the polymer was taken not to affect solution thermodynamics at 5 µg/mL. R8·C9

Turning flux into activity rests on stated assumptions: constant membrane area and thickness, constant diffusion coefficient and membrane activity coefficient, sink conditions in the receiver (justified because the receiver never exceeded half the crystalline solubility), and an unchanged membrane permeability in all media, "hence the change in solute mass flow is assumed to be due to the change in solute activity". C11·R25 The authors checked one consequence: $F^{\circ }$, the flux extrapolated to the crystalline solubility of each medium (from Table 2), should be the same with and without bile salt, and they report the values to be "comparable within experimental error" (the values are not shown). C36·R15 The buffer series then serves as the calibration: there, $\delta =F/F^{\circ }$ agrees with $C/C^{\circ }$ (Figure 9), and any measured flux in a bile salt medium can be placed on the same $\delta$ scale. C37·R16

③ Why it works. Only the free drug's activity drives transport across the membrane, whatever the drug's concentration in micelles or complexes, so flux measures the quantity that also drives crystallization. The plateau at the onset is a further check: above the amorphous solubility the activity cannot rise, so neither can the flux. C18·E1·E6

④ Difference from earlier work. The approach extends the authors' group's use of flux to separate solubilization from supersaturation with synthetic surfactants (Raina et al. 2015, ref 4) to the bile salts of the gut, and uses the plateau as an extra GLPS method. C4·C18

Contribution 3: phase boundaries on two scales

Combining the crystalline solubility, the GLPS onset and the flux calibration, the authors drew, for each bile salt class, a bar with two vertical axes (Figure 11): fundamental supersaturation $\delta$ on the left, telaprevir concentration on the right. The lower dashed line is crystalline saturation ($\delta =1$), the upper one the GLPS onset; between them lies the one-phase supersaturated region. R18·C49 Because the flux calibration fixes how concentration maps onto $\delta$ in each medium, the concentration axes differ in scale between panels (for example up to 480 µg/mL for micellar STDC and SGDC against 200–240 µg/mL without bile salt). R18 The figure is a schematic built from the measured boundaries, and in some panels one bar stands for two bile salts or two concentrations. R18·X12

Experimental analysis

Main result 1: only micellar dihydroxy bile salts solubilize crystalline telaprevir. Table A reproduces Table 2. In buffer, crystalline telaprevir dissolved to 5.2 ± 0.1 µg/mL at 37 °C. R1.g At 1.86 mM, no bile salt raised it beyond 6.9 µg/mL, and at 12 mM the trihydroxy STC and SGC gave only 6.7 and 6.2 µg/mL; the authors call these changes "no significant solubilization", without naming a test. R1·C12·X4 At 12 mM the four dihydroxy bile salts raised the solubility to 9.6–12.4 µg/mL, which the authors summarize as "about 2-fold"; the ratios to buffer span 1.8 (SGCDC) to 2.4 (SGDC). R1·C12·X9 Compared with surfactants used in commercial products, which readily give more than ten-fold enhancement, these bile salts are "not strong solubilizers of telaprevir at the concentrations employed, even when these concentrations are above their CMC". C13

Table A. Crystalline solubility of telaprevir (µg/mL) at 37 °C in 50 mM pH 6.5 phosphate buffer, from Table 2; the ± statistic and n are not stated. The last column was calculated by the AI writer from the printed values. R1·X4

Main result 2: the amorphous solubility moves in three different ways. Table B reproduces Figure 3. In buffer the three methods gave 146, 149 and 148 µg/mL; Figure 4 shows the UV trace, flat to about 140 µg/mL and rising above the onset of 146 µg/mL. R2.a·R3 The authors read the agreement as showing that telaprevir does not supersaturate substantially with respect to GLPS. C14·C15 Their overall value, "about 150 µg/mL", is about 1.5 times the value reported in 100 mM pH 6.8 buffer. C19·R19

Table B. GLPS onset of telaprevir (µg/mL) at 37 °C, values as printed on Figure 3 (n = 3, error bars standard deviation; the flux bars carry no error bars). R2·X4

The trihydroxy bile salts raised the onset slightly, to 147–182 µg/mL, with no clear difference between the two concentrations ("does not appear to significantly affect"). R2.b–e·C21 Micellar STDC and SGDC raised it to 311–360 µg/mL, which the authors call "a factor of 2" (2.1–2.4 times buffer) and read as a stronger interaction of micellar dihydroxy bile salts with telaprevir, consistent with the solubility data; at 1.86 mM the same bile salts left it at 146–168 µg/mL. R2.f–i·C22·X9 The chenodeoxycholates behaved differently. With SGCDC (and STCDC) the extinction rose at once when the stock was added, though the solution looked clear until much higher concentrations and no crystals or aggregates were visible under crossed polarizers; the authors "suspect complex formation between drug and bile salt" and report only ultracentrifugation and flux values. R4·C23 Monomeric STCDC lowered the onset slightly (133 and 110 µg/mL), micellar STCDC raised it to 290 and 238 µg/mL ("approximately doubled"), and SGCDC raised it a little at both levels (169 and 177 µg/mL). R2.j–m·C24

Main result 3: in buffer, flux is proportional to concentration up to the onset. In buffer, receiver concentration rose linearly over 60 minutes at every donor concentration, reaching about 0.13 µg/mL (5 µg/mL donor) to about 2.4 µg/mL (150–170 µg/mL donors) (Figure 5a), which the authors take as confirming the constant-parameter assumption. R5·C17 Flux rose in proportion to donor concentration (fit y = 0.009x, R² = 0.9932): about 0.07 µg/min at 5 µg/mL and about 1.24 µg/min at 140 µg/mL, reaching about 1.32 µg/min at 150 µg/mL and then staying near 1.25–1.27 µg/min at 160–170 µg/mL, where the donor was turbid (Figure 5b). R6·C18 The fit gives $F^{\circ }=0.009\times 5.2\approx 0.047$ µg/min in buffer, and $\delta =F/F^{\circ }$ then matches $C/C^{\circ }$: Figure 9 shows a slope of 1.011 (R² = 0.9928) over $C/C^{\circ }$ from about 1.0 to 26.9. E6·R16·C37

Main result 4: bile salts change the activity of dissolved telaprevir in three patterns. Table C collects readings from Figures 5b and 7. With STC or SGC at either concentration the flux points lie on the buffer series; the plateaus lie at about 1.30–1.53 µg/min, reached at 180–210 µg/mL, in line with their slightly higher onsets, and 18 mM STC also left flux unchanged (data not shown). R10·R11·C26 With 1.86 mM STDC or SGDC flux again followed buffer. At 12 mM both bile salts lowered the flux at a given concentration by about half (at 90 µg/mL about 0.43 µg/min with STDC against about 0.83 in buffer), and flux kept rising to about 1.34–1.38 µg/min at 330–360 µg/mL, near their onsets. R12·C27 The authors read this, through Eq. 1, as lower telaprevir activity with micellar bile salt, the pattern seen earlier for felodipine with Vitamin E TPGS above but not below its CMC. C27·R20 Monomeric STCDC followed buffer up to 90 µg/mL, micellar STCDC lowered the slope like STDC and SGDC, and SGCDC lowered it at both concentrations equally (about 0.58 µg/min at 90 µg/mL). R13·C29

Table C. Mass flow rate of telaprevir (µg/min) across the 6–8 kDa membrane at 37 °C, read from Figures 5b and 7 (approximate; — = not read). R6·R10·R12·R13

Main result 5: STCDC and SGCDC lower the ceiling. The highest flux with STCDC or SGCDC, at either concentration, was about 1.06–1.11 µg/min against about 1.32 µg/min in buffer; the decrease is "statistically significant (t test, p value<<0.05)", and the authors put the maximum at "about three fourths" of the value without bile salt. R13·R6·C30 Because the highest flux marks the highest activity, this means a lower maximum achievable supersaturation: Figure 11 draws the GLPS boundary at $\delta$ of about 22 with monomeric STCDC, micellar STCDC and SGCDC, against about 28 without bile salt and with the other four bile salts. R18·C30 Note by the AI writer: the plotted maxima correspond to about 0.8–0.9 of buffer, and the Figure 11 boundaries to about 0.79, somewhat above "three fourths". X6 Earlier work showed that a second solute miscible with the drug in the drug-rich phase lowers the maximum supersaturation (Trasi and Taylor 2015, ref 28; Alhalaweh et al. 2016, ref 29); on that basis the reduced maximum flux "suggests mixing" of STCDC and SGCDC into the telaprevir drug-rich phase. C31

Main result 6: concentration and activity give different supersaturations. Figure 10 plots $\delta =a/a^{\circ }$ from flux against $C/C^{\circ }$, with $C^{\circ }$ the crystalline solubility of each medium. Buffer points lie on the 1:1 line. Most bile salt points lie on or above it, for example 12 mM STC at $C/C^{\circ }$ of about 25.4 with $\delta$ of about 29.0, and 1.86 mM SGDC at about 21.7 with about 27.5, while every 1.86 mM SGCDC point lies below it, for example about 28.9 with about 20.2. R17 The authors write that "Figure 10 clearly shows the discrepancy", which varies with bile salt type and aggregation state; at $\delta =5.0$ the concentration-based value ranges from 3.9 to 6.7 across the media. C39 Since nucleation rates depend steeply on supersaturation, they present flux-based $\delta$ as "an improved approach for the estimation of crystallization driving forces". C40

The phase-boundary summary (Figure 11). With trihydroxy bile salts both boundaries stay close to buffer on both scales. With micellar STDC and SGDC the concentrations of both boundaries roughly double, while on the activity scale the boundaries stay at $\delta =1$ and about 28; the authors take this to mean that the bile salts do not change the activity of the crystalline or the amorphous phase, "indicating that the composition of these phases are not altered", and that the concentration–activity difference comes from solubilization of the dissolved drug. R18·C49 With STCDC, at both concentrations, and with SGCDC, the window narrows to about 22, which the authors attribute ("presumably") to the bile salt mixing into the drug-rich phase on GLPS and lowering telaprevir's activity there. R18·C50·C51

Buffer strength and controls. Without bile salt the onset was 149/146 µg/mL (ultracentrifugation/UV) in 50 mM pH 6.5 buffer, 153/148 in 50 mM pH 6.8 buffer and 104/102 in 100 mM pH 6.8 buffer (Figure 6), so the higher salt concentration, not the pH, lowered the onset. R9 The authors explain this as "promoted aggregation of molecules via hydrophobic interactions" at higher ionic strength, as reported for ritonavir and for micelle formation. C20 The controls without HPMCAS-MF and the receiver concentrations below half the crystalline solubility support the flux set-up. R8·R25

Discussion

How the authors connect the results. The argument runs in four steps. Flux reports free-drug activity, so $F/F^{\circ }$ gives $\delta$ in any medium. C11·C36 The bile salts are monomeric at 1.86 mM and partly micellar at 12 mM. C42 What then happens depends on the bile salt:

For the dihydroxy bile salts the authors combine two observations: a higher crystalline solubility and a lower flux at a given concentration. From both, "it is apparent that STDC and SGDC solubilize telaprevir by incorporation of the drug into bile salt micelles". C28 They add a Stokes–Einstein argument: the diffusion coefficient of a particle falls with its radius, so drug carried in larger bile salt aggregates diffuses more slowly, which "suggests" incorporation into aggregates. C46·E8 As "one possible explanation" for why the dihydroxy bile salts interact more strongly, they point to hydrophobicity: trihydroxy bile salts are less hydrophobic and have higher CMCs, so at 12 mM fewer of them are in micelles, in line with an earlier study in which dihydroxy bile salts solubilized various drugs more than trihydroxy ones (Wiedmann and Kamel 2002, ref 37). C45·C47·R23 For STCDC and SGCDC, the lower maximum flux "suggests" that the bile salt mixes into the drug-rich phase on GLPS, which "presumably" lowers telaprevir's activity there. C31·C50·C51 They see no effect of the conjugate at R5 (taurine against glycine). C48

What the paper concludes. At least three types of impact on solution thermodynamics exist among the six bile salts, so STC, the only bile salt in commercial simulated fluids, "is not an adequate surrogate for the entire bile salt family"; since SGC, STCDC and SGCDC are more abundant in vivo, in vitro testing with STC-based FaSSIF "could potentially lead to inaccurate prediction of drug in vivo supersaturation and crystallization rates". C25·C52·C53 Overall, trihydroxy bile salts affect telaprevir solution thermodynamics less than dihydroxy ones, and the activity-based supersaturation "should be determined" before changes in crystallization kinetics are interpreted. C57·C58

Where the approach applies. The data cover one drug, telaprevir, in one buffer (50 mM pH 6.5 phosphate) at 37 °C, single bile salts at two concentrations, and no lecithin, although the introduction notes that bile salts form mixed micelles with lecithin and cholesterol in vivo. A1·A2·M10 The GLPS onset itself depends on the buffer, so values from 100 mM buffers or biorelevant media are not directly comparable. R9·X11 The paper measured thermodynamics only; crystallization kinetics, the motivation for the work, are left to later studies "as a function of the fundamental supersaturation". C59

Note by the AI writer (not discussed in the paper): what it suggests for formulation. For telaprevir, micellar dihydroxy bile salts double the dissolved concentration at the same activity. In a dissolution test with such a medium more drug is in solution, but no more driving force for membrane transport is gained; reading the concentration alone would overrate the benefit. The ceiling for supersaturation, often taken as a fixed property of the drug, moved in both directions here: up in concentration with micellar STDC and SGDC, down in activity with STCDC and SGCDC. An amorphous solubility measured in an STC-only medium is therefore a medium-specific number, and a bile salt that enters the drug-rich phase lowers the highest activity a formulation can reach, much as a second drug does in combination products.

Limitations

Limitations stated by the authors. The flux-to-activity conversion rests on assumptions the authors state explicitly: constant diffusion coefficient and membrane activity coefficient, unchanged membrane permeability in all media, and sink conditions in the receiver. C11 They check only one consequence of them, the constancy of $F^{\circ }$, and report it as "comparable within experimental error" without showing the values. C36·R15 The monomer and micelle levels assume that telaprevir does not change the CMC. C42 The nature of the light-scattering species with STCDC and SGCDC is unknown; complex formation is only "suspected". C23 The mechanisms (incorporation into micelles, mixing into the drug-rich phase) are stated with hedges ("it is apparent", "suggests", "presumably"). C28·C31·C50 Crystallization was not measured. C59

The AI writer's own judgement (1): what Figure 10 can and cannot show. The constancy of $F^{\circ }$ is more than a check: it is the condition under which $\delta$ from flux and $C/C^{\circ }$ from solubility are comparable at all. Where flux is proportional to concentration in a medium, the ratio $(a/a^{\circ })/(C/C^{\circ })$ equals $F^{\circ }$ of that medium divided by $F^{\circ }$ of buffer. Part of each offset in Figure 10 therefore reflects how the crystalline solubility measured in a medium (Table 2) compares with its flux slope. For the monomeric bile salts, whose flux matches buffer, the points above the line follow directly from small solubility rises that the authors themselves call not significant (for example 6.9 ± 0.8 µg/mL for 1.86 mM SGDC against 5.2 ± 0.1 in buffer). X7·R1·R17·C12 SGCDC shows the problem sharply: its flux is the same at 1.86 and 12 mM, yet its crystalline solubility is 5.7 and 9.6 µg/mL; equal activity at equal concentration requires equal crystalline solubility, so $F^{\circ }$ cannot match buffer in both media (an extractor estimate puts it at about 0.7 and about 1.2 times buffer). In Figure 10 the 1.86 mM SGCDC points fall below the line and the 12 mM points above it. X7·R13·R14 The paper does not separate this solubility–flux mismatch from genuine concentration-dependent activity coefficients, so the 3.9–6.7 range at $\delta =5.0$ is best read as partly within the uncertainty of Table 2. X7·C39

The AI writer's own judgement (2): the membrane and the mechanisms. The activity reading assumes that only free telaprevir crosses the membrane and that its diffusion coefficient is constant, while the discussion explains the same flux drop with dihydroxy micelles by slower diffusion of drug-loaded aggregates. The paper does not state whether bile salt micelles or drug–bile salt aggregates can pass a 6–8 kDa membrane, and it does not separate lower free-drug activity from slower diffusion; the conversion to $\delta$ in micellar media rests on the membrane excluding the micelles. X8·C11·C46 None of the mechanistic links (micelle loading, aggregate size, composition of the drug-rich phase, the suspected complexes) was measured directly. C28·C31·C23

The AI writer's own judgement (3): smaller points. The statement that the conjugate at R5 has no impact does not hold for the chenodeoxycholates: monomeric STCDC leaves flux at buffer level up to 90 µg/mL while monomeric SGCDC lowers it, and micellar STCDC raises the onset to 238–290 µg/mL against 177 µg/mL for SGCDC; the authors themselves treat them as separate classes. X5·C48 Likewise, "monomeric bile salts have minimal interaction with telaprevir, with the exception of SGCDC" refers to the flux slope below the onset; monomeric STCDC does lower the onset and the maximum supersaturation. X10·C43 Replicate numbers are not given for the solubility and flux data, and the flux-plateau onsets carry no error bars. X4 The rounded factors in the text ("about 2-fold", "a factor of 2", "about three fourths") are approximate summaries of the tabulated and plotted values. X9·X6 Three minor slips in the manuscript: p.14 names SGDC where SGCDC is meant, the text gives 34 mL chambers while Figure 2 labels 32 mL cells, and the captions of Figures 7 and 11 are printed as "Figure 7c" and "Figure 11d". X1·X3·X2

Conclusion

Using membrane flux as a calibrated read-out of activity, this paper measured the crystalline solubility, the amorphous (GLPS) solubility and the activity of supersaturated telaprevir in buffer and with each of the six main human bile salts below and above their CMC. R1·R2·R6·R16 The trihydroxy bile salts STC and SGC changed little; micellar STDC, SGDC and STCDC solubilized telaprevir about 2-fold without changing its activity at the phase boundaries; and STCDC and SGCDC lowered the highest reachable supersaturation from about 28 to about 22, which the authors attribute to mixing of the bile salt into the drug-rich phase. R1·R12·R13·R18·C31·C50 The authors conclude that bile salts are not interchangeable, that STC alone cannot stand for them, and that the activity-based supersaturation should be determined before crystallization in bile salt media is interpreted. C52·C56·C58 The mechanisms remain inferences, and part of the concentration–activity discrepancy may lie within the uncertainty of the solubility data. X7·X8