When the drug-rich phase is a glass: the supersaturation ceiling of telaprevir

Background and motivation

Many marketed drugs, and more development compounds, are poorly soluble in water, which can limit their bioavailability (Williams et al., ref 1). Making the drug amorphous raises both the dissolution rate and the highest concentration it can reach, but the amorphous form has a high free energy and can crystallize (Otsuka and Kaneniwa, ref 2). Amorphous solid dispersions (ASDs), in which the drug is blended with a polymer that inhibits crystallization, are therefore used to slow crystallization and to let the dosage form generate a supersaturated solution, that is, a solution above the crystal solubility. Supersaturated solutions raise the rate of passive absorption (refs 6, 7), so their properties matter for formulation. C2

A second line of work explains what happens when supersaturation is pushed far. Colloidal aggregates of drug-like molecules are well known from high-throughput enzyme screens, where they cause false hits ("promiscuous aggregation"; refs 8–10). Ilevbare and Taylor (ref 11) proposed that these aggregates form by liquid–liquid phase separation (LLPS): above a certain concentration, the single supersaturated phase splits off a second, disordered, drug-rich phase. For compounds that melt far above room temperature, this concentration coincides with the "amorphous solubility", which can be estimated from the crystal solubility and the free energy difference between crystal and supercooled liquid. The aggregates thus form only in supersaturated solutions and are a precursor to crystallization. C3

The drug-rich phase may help absorption (Frenkel et al., ref 12) and may act as a reservoir that keeps supersaturation constant. Raina et al. (ref 13) found that passive flux across a membrane rises with concentration only up to the LLPS concentration and then plateaus. Two implications follow: the free drug concentration has a maximum, and so does the achievable supersaturation; adding drug beyond that point only adds drug-rich phase. C4

Almost all drugs examined so far had a low glass transition temperature (Tg). Their drug-rich phase, which holds a little water, is then a supercooled liquid with reasonably well-defined thermodynamic properties. For drugs with a high Tg, the drug-rich phase would be a glass, and their phase behaviour "has not been explored to date". C5 The authors chose telaprevir, a hepatitis C protease inhibitor approved in 2011 and marketed as an ASD because the crystalline form had poor bioavailability (Kwong et al., ref 14). The literature gives a melting point of 246 °C, an aqueous solubility of 4.7 μg/mL and a Tg of 105 °C. C6·M1 Telaprevir is predominantly un-ionized at pH 6.8 (acid pKa 11.8, basic pKa 0.31; ref 15), so pH effects on its solubility can be set aside in this buffer. C7·M1

The goal was to characterize supersaturated aqueous solutions of this high-Tg drug, made by solvent exchange, with NMR, fluorescence and UV spectroscopy and dynamic light scattering (DLS), and to measure diffusive flux against concentration to see how supersaturation affects transport across a membrane.

Background concepts

Amorphous solubility and how to estimate it. The amorphous solubility is the highest dissolved concentration in equilibrium with the amorphous drug. Because the amorphous drug in contact with water takes up some water, it is the water-saturated amorphous form that sets this limit. The paper estimates it with eq 1 (Murdande et al., ref 16):

Here $C_{\mathrm{e}\mathrm{q}}$ is the crystal solubility, $I(a_2)$ is a term for the activity of the amorphous solute saturated with water (obtained from its moisture sorption profile), $\Delta G_{a\to c}$ is the free energy difference between the amorphous and crystalline forms, $R$ is the gas constant and $T$ the temperature. In plain terms: the amorphous form is more soluble than the crystal by the Boltzmann factor of its extra free energy, and this advantage is trimmed by the water it absorbs, which lowers its activity. For telaprevir, $\exp (-I(a_2))$ is 0.30. E1·M1

The free energy difference is the hard part. The Hoffman equation (eq 2, ref 17) is the usual shortcut:

Here $\Delta H_f$ is the enthalpy of fusion and $T_m$ the melting temperature. In plain terms: the free energy difference grows with the enthalpy of fusion and with the distance below the melting point. The equation was derived for temperatures reasonably close to $T_m$, and the authors warn that it "may not be appropriate for large undercoolings", as with telaprevir, which melts more than 200 °C above the 37 °C of the experiments. E2·C24·M1 For such compounds they use eq 3, which adds the heat capacity difference $\Delta C_p$ between crystal and amorphous form:

In plain terms: the first term is the free energy difference at $T$ if the two forms had the same heat capacity; the two integrals correct the enthalpy and entropy differences for the different heat capacities of the two forms between $T_m$ and $T$. Which $\Delta C_p$ is used matters: that of the glass (below Tg) or that of the supercooled liquid (extrapolated down to 37 °C). The paper evaluates both. E3·P6

Glass or liquid: why Tg matters here. Below its Tg an amorphous material is a glass, with very slow molecular motion; above it, a supercooled liquid. Water is a strong plasticizer: the paper cites the rule that Tg falls by about 10 °C for each 1% of sorbed water (refs 11, 19, 20). R3 A drug-rich phase that separates from water is saturated with water, so its Tg is lower than that of the dry drug. For low-Tg drugs this pushes the phase well into the liquid state at 37 °C; for a drug whose dry Tg is about 103 °C, a few percent water may still leave it glassy. M1·C13

An environment-sensitive fluorescent probe. The dye 4-Di-2-ASP emits at a wavelength that depends on the polarity around it. After excitation, polar solvent molecules reorganize around the excited dye and lower its energy; the more polar the medium, the larger this Stokes shift and the longer the emission wavelength. If a disordered telaprevir phase forms, the hydrophobic dye is expected to partition into it, the Stokes shift shrinks, and the emission maximum moves to shorter wavelengths (a blue, or hypsochromic, shift). C15

Why NMR does not see the drug-rich phase. Solution NMR detects molecules that tumble fast. The intensity of a peak depends on the spin–spin relaxation time $T_2$, which is inversely related to the correlation time ${\tau }_c$ (eq 6), and ${\tau }_c$ grows with particle size and viscosity (eq 7, a Stokes–Einstein–Debye relation, ref 26):

Here $\eta$ is the viscosity of the medium, $r$ the particle radius and $k$ the Boltzmann constant. In plain terms: large, viscous particles turn slowly, relax fast, and give peaks so broad that they vanish into the baseline. Eq 6 is printed as an equality; dimensionally it can only be a proportionality, which is how the text describes it ("an inverse relationship"). E6·E7·X9 Telaprevir molecules in glassy aggregates of about 300 nm are expected to be invisible, so above the phase boundary the NMR signal should report only the dissolved drug. C18·R5

Flux and activity. Across a membrane, the flux $J$ of a dissolved drug follows Fick's first law (eqs 4 and 5):

Here $M$ is the mass transported in time $t$, $D$ the diffusion coefficient, $S$ the membrane area, $h$ its thickness, ${\gamma }_m$ the activity coefficient of the drug in the membrane, and $a$ the thermodynamic activity of the drug in the donor, equal to concentration $C$ times activity coefficient $\gamma$. In plain terms: with the same membrane and drug, flux is proportional to the activity of the drug in the donor. The paper uses flux in this way, as a measure of the "free" drug concentration (abstract). E4·E5·C10·C19

Methods in detail

The study has four parts: locate the phase boundary with three independent signals; identify the separated phase; test whether dissolved drug and flux stop rising at the boundary; and check which thermodynamic estimate predicts the boundary. All experiments used 100 mM sodium phosphate buffer at pH 6.8; supersaturated solutions were made by solvent exchange, adding a methanol stock of telaprevir (6.7 mg/mL for UV, 7 mg/mL otherwise) to the buffer. M5·M6·P7·P9·P10·P11 The figure below shows the workflow.

Part 1: Locating the phase boundary

① Problem. A drug-rich phase that forms at high supersaturation is colloidal: the solutions turn turbid "with no obvious particles", and without a polymer the telaprevir solutions developed birefringent crystals within about 15 min. R1 The boundary must therefore be detected quickly, by signals that respond to the new phase itself, and crystallization must be held off long enough to study it.

② How. Three methods were used, each run in triplicate for Table 2. R13 UV extinction: the stock was pumped at about 0.050 mL/min into 10 mL of buffer at 37 °C, stirred at 300 rpm, while an in situ probe recorded the signal at 370 nm, a wavelength telaprevir does not absorb, so any rise is light scattering. P7·C9 DLS (flow-through cuvette, 20 min per concentration, a reading every 2 min) followed count rate and particle size. P8 Fluorescence: 4-Di-2-ASP (3 μg/mL) in buffer containing 5 μg/mL HPMCAS-MF; telaprevir was raised stepwise from 20 to 160 μg/mL, excited at 488 nm, and the emission maximum and intensity recorded. Three controls followed: dilution to 70 μg/mL after the phase had formed; adding the probe only after the phase had formed, to rule out dye trapped inside the glassy particles; and crystalline telaprevir with the probe. P9 NMR: 4 mL buffer with 5 μg/mL HPMCAS-MF plus 1 mL D2O and stock to 40–200 μg/mL, measured at 37 °C on a Bruker AVANCE DRX500 spectrometer with an inverse proton cryoprobe (128 scans, interscan delay 5 s, 16 min per sample, triplicate); three telaprevir peaks at 9.13, 8.81 and 8.74 ppm were integrated against water. P10

③ Why it works. Each method responds to a different property of the new phase: its size (scattering), its polarity (probe) and its slow molecular motion (NMR). If all three change at the same concentration, the change marks a phase boundary rather than an artefact of one technique. HPMCAS at 5 μg/mL was added "where necessary" to inhibit crystallization over the time of the experiment; the turbid solution then lasted several hours. M2·R1

④ Difference from earlier work. The UV, fluorescence and flux approach follows the group's earlier work on low-Tg drugs (refs 11, 13). The new element is the system: a drug whose separated phase would be a glass, which raises the questions of whether the probe can still enter it and whether NMR still sees it as a separate population. The probe-added-afterwards control addresses the first point directly. C5·R9

Part 2: Identifying the separated phase

① Problem. A turbid solution could hold crystals, an amorphous liquid, or an amorphous glass. The answer decides whether the system is in a (metastable) equilibrium with a well-defined amorphous phase or simply crystallizing.

② How. Telaprevir was added at high concentration from the methanol stock to buffer, the turbid solution was ultracentrifuged, and the pellet was scanned by DSC at 10 °C/min. P4 For comparison, DSC gave the onset melting point (238 °C) and enthalpy of fusion (55.8 kJ/mol) of the crystal and the onset Tg (103 °C) of melt-quenched amorphous telaprevir; gravimetric sorption of the melt-quenched glass gave 4.31% water at 95% RH (Table 1) and an estimated water content of about 4.6% at 100% RH. P2·P5·M1 The reversibility of the phase was tested by dilution in the fluorescence experiment. R8

③ Why it works. A Tg event identifies an amorphous phase; its value, set against the dry Tg and the water uptake, tells how much water the phase holds and whether it is glassy at 37 °C. Rapid redissolution on dilution shows that the phase is in contact with, and close to equilibrium with, the surrounding solution, as expected for an amorphous phase and not for crystals. C13·C16

Part 3: Dissolved drug and flux against concentration

① Problem. If the solution splits into a drug-lean and a drug-rich phase at equilibrium, the concentration of dissolved drug should stop rising once the boundary is passed. Total concentration cannot show this; a measurement is needed that sees only dissolved drug. C4

② How. NMR gave the dissolved concentration directly (Part 1). For flux, a side-by-side diffusion cell (PermeGear; 34 mL per compartment, 30 mm orifice, jacketed at 37 °C, stirred) held 32 mL of buffer with 5 μg/mL HPMCAS-MF on each side of a regenerated cellulose membrane (molecular weight cutoff 6–8 kDa; Figure 2). The donor was dosed from the crystal solubility to above the amorphous solubility (5–130 μg/mL in Figure 8), and a UV fiber-optic probe in the receiver recorded concentration at 270 nm for 60 min; flux is the slope of receiver concentration against time. Sink conditions were kept: the receiver never exceeded half the crystal solubility. P11·M4·R11 The Results section calls the membrane "cellulose acetate"; the Materials, Methods and Figure 2 all describe regenerated cellulose. X1

③ Why it works. With $D$, $S$, $h$ and ${\gamma }_m$ fixed (eq 4), any change in flux reflects a change in the activity of the drug in the donor. C10 A plateau in flux above a concentration therefore means a plateau in activity, which is what a two-phase equilibrium predicts.

Part 4: Predicting the boundary

① Problem. For low-Tg drugs, eq 1 with the Hoffman free energy "will generally provide a reasonable estimate" of the LLPS concentration (refs 11, 13). C22 Whether this holds for a high-melting, high-Tg drug was open.

② How. Eq 1 was evaluated at 37 °C with the crystal solubility, $\exp (-I(a_2))=0.30$ and three free-energy differences (Table 2): (b) the Hoffman equation; (d) eq 3 with the heat capacity change from crystal to glass; (c) eq 3 with the heat capacity change from crystal to supercooled liquid, the liquid's properties extrapolated down to 37 °C. Heat capacities of crystal, glass and supercooled liquid came from modulated DSC (2 °C/min, the amorphous form made in situ by cooling the melt at 10 °C/min). P6·P3·E1·E2·E3 The heat-capacity values are not printed, so estimates (c) and (d) cannot be recomputed from the paper; the Hoffman estimate can (see Experimental analysis). E3

③ Why the third route. Route (c) assumes that the glass formed by precipitation in water is "highly relaxed" and has thermodynamic properties close to a supercooled liquid at the same temperature, unlike the quench-cooled glass made in the DSC, which is "expected" to hold more excess enthalpy and entropy. C26·C25 This assumption was introduced after routes (b) and (d) overestimated the measured boundary. X11

Experimental analysis

Starting values. The crystal solubility at 37 °C was 4.6 ± 0.1 μg/mL in buffer and 4.7 ± 0.2 μg/mL with 5 μg/mL HPMCAS (n = 3), "in good agreement" with the 4.7 μg/mL of Kwong et al.; HPMCAS at this level barely changes it. R13.a·R13.b·C11 The measured onset melting point (238 °C) and Tg (103 °C) are a few degrees below the literature values quoted in the introduction (246 °C and 105 °C); the paper's calculations use the measured values. M1·X2

Main result 1: one boundary, three methods. Solutions stayed clear until the concentration exceeded about 90 μg/mL and were turbid above. R1·C12 In the UV experiment (Figure 4) the extinction at 370 nm scattered around zero (about −0.006 to 0.002) up to about 93 μg/mL and then rose steeply, to about 0.048 at about 129 μg/mL; the authors place the onset at 92 ± 2 μg/mL. DLS recorded a sudden rise in count rate at about the same concentration, with an initial size of about 300 nm (data not shown). R4·R5·C14 The probe (Figures 5 and 6) kept its emission maximum at about 592–593 nm from 20 to 90 μg/mL; above, the maximum moved to shorter wavelengths and the intensity rose (Table B). R6·R7 NMR (Figure 7) showed dissolved telaprevir rising with added drug up to about 92 μg/mL and then levelling off. R10 Table A collects the boundary values and the estimates.

Table A. Crystal solubility, measured phase boundary and estimated amorphous solubility of telaprevir at 37 °C (from Table 2). R13

The three boundary values agree within 2 μg/mL, although the methods probe different properties and, as far as the methods state, the UV medium did not contain HPMCAS while the fluorescence and NMR media did. R13.f–h·X8 On this basis the authors conclude that "a noncrystalline phase of telaprevir is formed" in aqueous media above around 90 μg/mL, which they call glass–liquid phase separation (GLPS). C21

Main result 2: the drug-rich phase is a glass. The pellet from turbid solutions showed a Tg event at 52 °C. R2 Dry amorphous telaprevir has a Tg of 103 °C; with about 4.6% water at 100% RH and a Tg drop of about 10 °C per 1% water, the 52 °C value is, in the authors' words, "consistent with an amorphous telaprevir phase containing a few percent of water". M1·R3·C13 Since 52 °C lies above 37 °C, the drug-rich phase is a glass, not the supercooled liquid seen with low-Tg drugs; Figure 3 places the experimental temperature, the precipitate Tg, the dry Tg and the melting point on one enthalpy–temperature diagram. C13 The water content of the pellet itself was not measured, and the paper does not say whether its DSC trace showed any melting; the 4.6% at 100% RH is an estimate from the sorption profile, next to a measured 4.31% at 95% RH. X3·X12

Table B. Emission maximum and intensity of 4-Di-2-ASP against telaprevir concentration (read from Figure 6, approximate). R7

Main result 3: the glassy phase behaves like a liquid one. Above 90 μg/mL the probe moved into a less polar environment: the emission maximum fell by about 22 nm between 90 and 160 μg/mL while the intensity rose about 2.5-fold (Table B). R7 Diluting to 70 μg/mL shifted the emission back to its original wavelength within about 2 min, which the authors read as rapid redissolution ("demonstrating that the drug aggregates dissolve rapidly"). R8·C16 When the phase was formed without the probe and the probe added afterwards, the spectrum was identical, so the dye was not simply trapped during formation; crystalline telaprevir gave no blue shift. R9·C17 The authors summarize that the system with a glassy drug-rich phase "appear[s] very similar" to systems whose drug-rich phase is a supercooled liquid: the phase forms at a specific and reproducible concentration, redissolves within 2 min and lets environment-sensitive probes partition into it. C30 They generalize, with "it appears", that high-Tg drugs behave like low-Tg drugs once the amorphous solubility is exceeded and crystallization does not intervene. C29 Crystallization still comes quickly: without a polymeric inhibitor the solutions crystallized within about 15 min, and the authors call the disordered phase "relatively short-lived" and a precursor to crystallization. C31·C36·C37

Table C. Selected points of dissolved telaprevir by NMR (read from Figure 7) and of flux (read from Figure 9), approximate. The two pairs of columns are separate experiments. R10·R12

Main result 4: dissolved drug and flux stop rising at the boundary. NMR concentration rose with added drug and then stayed at about 81–90 μg/mL from about 98 to 200 μg/mL added (Table C). The authors' reading: drug added beyond about 90 μg/mL does not raise the concentration in the aqueous phase but increases the amount of telaprevir-rich phase, which NMR does not detect. R10·C19·C18 Flux rose linearly from about 0.068 μg/min at 5 μg/mL to about 0.97 μg/min at 90 μg/mL and then stayed at about 0.97–1.07 μg/min up to 130 μg/mL (Figure 9). R12·C20 The receiver curves of Figure 8 behind these slopes are straight for the high donor concentrations but bent for the lowest ones, and the receiver never exceeded about 1.95 μg/mL, under half the crystal solubility. R11 The same pattern, a flux maximum at the LLPS concentration, had been seen for felodipine and nifedipine. R16

The authors explain the plateau by equilibrium between the drug-lean and drug-rich phases: added drug only increases the amount of drug-rich phase, so the drug-lean concentration, the supersaturation and the flux stay constant; "a solution of total concentration of 130 μg/mL has the same flux as a solution with a concentration of 90 μg/mL". C35 They state the maximum supersaturation ratio as "approximately 18" for telaprevir at 37 °C, and the plateau flux as approximately 18-fold that of a saturated solution. R14·R15·C34·C40 Note by the AI writer (not discussed in the paper): the ratio of 18 equals 90 μg/mL divided by a crystal solubility rounded to 5 μg/mL; with the measured 4.6–4.7 μg/mL it is about 19–20. Against the lowest measured flux (about 0.068 μg/min at 5 μg/mL) the plateau is about 14–16-fold. And neither plateau is perfectly flat: flux at 130 μg/mL is about 10% higher than at 90 μg/mL, and the NMR plateau drifts from about 82 to about 89 μg/mL. X4·X5·X6

Main result 5: which free energy predicts the boundary. With the Hoffman free energy, eq 1 gave 245 ± 5 μg/mL, 2.7 times the observed value. R13.c·R17·C23 The authors attribute this "most likely" to the large undercooling: the Hoffman equation assumes a temperature close to the melting point, "an assumption that is clearly violated" for telaprevir at 37 °C. C24 Note by the AI writer: the Hoffman estimate can be recomputed from the printed inputs. With $\Delta H_f$ = 55.8 kJ/mol, $T_m$ = 511.15 K and $T$ = 310.15 K, eq 2 gives about 13.3 kJ/mol; eq 1 with 0.30 then gives about 241 μg/mL with $C_{\mathrm{e}\mathrm{q}}$ = 4.6 μg/mL, or 246 μg/mL with 4.7 μg/mL, matching the printed 245 ± 5. E1·E2 Including the heat capacity change from crystal to glass lowered the estimate to 189 ± 16 μg/mL, still 2.1 times too high. The authors' "most likely" reason is that the glass formed in solution differs from the DSC glass, which is "expected" to have a greater excess enthalpy and entropy. R13.e·C23·C25 Using instead the heat capacity of the supercooled liquid, extrapolated to 37 °C, gave 97 ± 8 μg/mL, "in good agreement" with the measured 90–92 μg/mL. R13.d·C27 The authors add that the same approach agreed with experiment for two more high-Tg compounds in their laboratory; these are not named and their data are not shown. C28·X11

Discussion

What the paper establishes. For one high-Tg drug in one buffer, the paper shows that the boundary at which a supersaturated solution splits into two phases is sharp, reproducible and seen by three unrelated signals, and that above it the dissolved drug, as seen by NMR and by flux, no longer rises. R13.f–h·R10·R12 The separated phase is amorphous and, by its Tg, glassy at 37 °C; yet in the properties tested (reproducible onset, fast redissolution, uptake of a hydrophobic probe) it behaves like the liquid drug-rich phases described for low-Tg drugs. R2·C30 The term "glass–liquid phase separation" names this case; thermodynamically, the authors treat it as the same split into a drug-lean and a drug-rich phase, located "in a metastable region of the phase diagram" because the solution remains supersaturated with respect to the crystal (Bonnett et al., ref 31). C36

What it means for formulation, as the authors state it. The authors draw a direct lesson for ASDs, worded with "Our data suggest": if an ASD dissolves in a medium to above the amorphous solubility, precipitation will be seen; it is "not necessarily an indication that crystallization has occurred" but may be liquid–liquid (for telaprevir, glass–liquid) phase separation, and then the solution is maximally supersaturated and the membrane flux is at its maximum. C38 As argued in earlier work (refs 13, 35), the noncrystalline precipitate "will also provide a reservoir" that keeps supersaturation at that maximum. C39 This is relevant for telaprevir because its commercial product is an ASD. C6 Determining the phase behaviour of supersaturated solutions is, in their words, "obviously important" for evaluating ASDs, their crystallization routes and the bioavailability gains they give. C41

What remains open. No ASD was dissolved in this study; every solution was made from a methanol stock, and the methanol fraction is not reported (by stock concentration it rises from about 1.3% v/v at 90 μg/mL to about 2–3% at the highest concentrations). X7 Whether an ASD reaches the same ceiling, and whether the glassy phase forms in the same way from a dissolving solid, is therefore an extrapolation. The reservoir role was not tested: no experiment removed dissolved drug and followed whether the drug-rich phase resupplied it. C39 The assumption that the solution-formed glass is relaxed, which carries the successful estimate, was not measured. C26 Note by the AI writer (not discussed in the paper): a glassy drug-rich phase is expected to be far less mobile than a liquid one, which could change how fast crystals form from it; the paper reports crystallization within about 15 min without polymer but does not compare this with low-Tg drugs. R1

Limitations

Limitations stated by the authors. The authors note that the Hoffman approach "may not be appropriate for large undercoolings" and that the glass formed during precipitation "has different thermodynamic properties" from the DSC glass, which is why two of their three estimates fail. C24·C25 They describe the disordered telaprevir phase as "relatively short-lived": without a polymeric inhibitor it crystallizes within about 15 min, and HPMCAS was needed to study it. C37·C31·R1 Their claim for other high-Tg drugs is hedged ("it appears"). C29

The AI writer's own judgement (1): what the measurements support. The boundary at 90–92 μg/mL and the levelling-off of NMR concentration and flux are well supported: three methods with n = 3 agree, and two independent readouts of dissolved drug change slope at the same point. R13.f–h·R10·R12 The glass assignment is thinner: it rests on one Tg event of a pellet, with its water content inferred, not measured, and no statement on whether the pellet contained crystals. R2·X3·X12 Several conditions are not reported: the methanol content, HPMCAS in the UV medium, the DLS medium and temperature, the fluorescence temperature, and the number of replicates behind the flux points; the DLS data are not shown. X7·X8·X13·R5 The text also calls the membrane cellulose acetate in one place and regenerated cellulose in three. X1

The AI writer's own judgement (2): numbers to read with care. The "approximately 18-fold" values are rounded: about 19–20 for concentration with the measured crystal solubility, about 14–16 for flux against the lowest measured donor. X4·X5 The plateaus still rise slightly, so "the same flux" at 90 and 130 μg/mL holds to about 10%. X6 Below the boundary, the NMR concentrations lie under the added concentrations (about 33 μg/mL at about 40 added), and the plateau (about 81–90 μg/mL) under the 92 μg/mL break; the paper does not comment, so the break, not the plateau level, is the safer NMR value. X10 Finally, the successful amorphous-solubility estimate was chosen after the Hoffman and crystal–glass estimates failed, and its support beyond telaprevir is unpublished; the heat capacities needed to check it are not printed. X11·E3

Conclusion

For telaprevir in pH 6.8 phosphate buffer at 37 °C, the paper locates the amorphous solubility at 90–92 μg/mL by UV, NMR and fluorescence, identifies the phase that separates above it as a water-plasticized glass with a Tg of 52 °C, and shows that above this boundary neither the dissolved concentration nor the membrane flux increases further. R13.f–h·R2·R10·R12 In the authors' words, "the maximum achievable supersaturation for aqueous telaprevir solutions is limited by the amorphous solubility", stated as about 18-fold the crystal solubility. C34 The glassy drug-rich phase redissolves within about 2 min and takes up a hydrophobic probe, so it "appear[s] very similar" to the liquid drug-rich phase of low-Tg drugs. C30 For predicting this ceiling, the Hoffman estimate fails by a factor of 2.7; an estimate that treats the solution-formed glass as a relaxed supercooled liquid (97 ± 8 μg/mL) matches. R13.c·R13.d·C27 For formulation, the practical message the authors give is that a cloudy dissolution medium above the amorphous solubility can signal maximal supersaturation rather than crystallization ("Our data suggest"); this was not tested with an ASD here. C38