Is the amorphous solubility the ceiling for every supersaturating solid form? Salts, a co-crystal, a glass and an ASD of one weak base

Background and motivation

More than 60% of newly discovered drug molecules are estimated to have suboptimal aqueous solubility, and the authors frame two broad answers R23. Solubilization (cosolvents, surfactants, cyclodextrins, lipids) raises the amount of drug carried in water but "sometimes" lowers the free drug and with it the flux across membranes (Poelma 1991) C1. Supersaturating systems instead raise the free-drug concentration above the crystalline solubility without that penalty, but the solution is metastable and falls back by crystallization unless an inhibitor is present C1. Two conditions are needed to make and hold supersaturation: the solid must have a higher "apparent" or kinetic solubility than the stable crystal, and it must dissolve faster than the less soluble form precipitates or crystallizes C2. Metastable polymorphs, salts, co-crystals, amorphous drugs and amorphous solid dispersions (ASDs) all qualify in principle.

The introduction then reviews what each class achieves. Polymorphs give only moderate gains: in a survey of 55 compounds, solubility ratios between polymorphs were typically 2–3 and below 5 for all but one compound (Pudipeddi and Serajuddin 2005) R20·C3. Amorphous forms give much larger gains. Because there is a defined free-energy difference between a pure amorphous form and its crystal, their "apparent" solubility can be estimated from the crystalline solubility, that free-energy difference and a correction for the water the amorphous solid absorbs (Ilevbare and Taylor 2013; Almeida e Sousa et al. 2015) C4·E1. ASDs add a polymer that usually raises the glass transition temperature, slows crystallization and speeds dissolution (Shamblin et al. 1998 and others) C5. Earlier work from the same group showed that ASD dissolution has a ceiling: free drug reaches the amorphous solubility, and beyond it a submicron, amorphous drug-rich phase forms. This is liquid–liquid phase separation (LLPS), or glass–liquid phase separation (GLPS) when the new phase is a glass (Alonzo et al. 2011; Ilevbare et al. 2013; Mosquera-Giraldo and Taylor 2015) C6.

Co-crystals and salts are crystalline yet can supersaturate. Carbamazepine co-crystals have given up to about 150-fold solubility gains, linked to the solubility of the coformer (Good and Rodríguez-Hornedo 2009, 2010) R21·C7. Co-crystals tend to dissociate in solution and convert to a less soluble crystal, which excipients "may" retard C7. Salts dissolve fast because the pH in the diffusion layer differs from the bulk, they generate supersaturation near pHmax, and predissolved polymers have maintained the supersaturation, with an amorphous precipitate in the cases where it persisted (Serajuddin and Jarowski 1985; Terebetski and Michniak-Kohn 2014) C8. pH-shift experiments on slowly crystallizing weak bases related the concentration in apparent equilibrium with an amorphous precipitate to the estimated amorphous solubility (Hsieh et al. 2012) C9. Together with the ASD results, the authors write that these observations "suggest" that the highest free-drug concentration reachable from a salt is also the amorphous solubility of the free drug C9.

What was missing was a direct comparison of the different solid forms of one compound. Most work on solubility-enhancing forms had focused on dissolution kinetics, and little compared the degree of supersaturation reached by different solid forms of the same drug. The authors therefore chose CRH1, a corticotropin releasing hormone receptor 1 antagonist from Lilly that is poorly soluble, is a weak base with a measured pKa of about 4.6, exists as several salts and a co-crystal, and crystallizes readily from supersaturated solution in preliminary studies C11·R13·M1. Their hypothesis was that the amorphous solubility is the upper limit of supersaturation achievable by dissolving any solid form (salts, ASDs and others) C10.

Background concepts

Supersaturation and its ceiling. A solution is supersaturated when its concentration exceeds the crystalline solubility, $C_{\mathrm{e}\mathrm{q}}$. The "amorphous solubility" is the highest free-drug concentration in equilibrium with the amorphous form of the drug. It is not a true equilibrium solubility, because the amorphous form itself is metastable, but it is well defined. When a solution is pushed past it, the extra drug does not stay dissolved: it separates as a second, drug-rich liquid (or glassy) phase of submicron droplets. The drug-lean aqueous phase stays at the amorphous solubility C6·C43. This is why the authors call the amorphous solubility the upper limit of supersaturation: more drug can be put into the vessel, but not more free drug into the water.

Estimating the amorphous solubility. The authors use the thermodynamic relation of their earlier work (Eq. 1) E1:

Here $C_{\mathrm{e}\mathrm{q}}$ is the crystalline solubility, $\Delta G_{c\to a}$ is the free-energy difference between crystal and amorphous form, $R$ is the gas constant and $T$ the temperature. The factor $e^{-I(a_2)}$ is the activity of the amorphous drug saturated with water; it is below 1 because the amorphous solid takes up water, which lowers its chemical potential. In plain terms: the amorphous form dissolves to the crystalline solubility multiplied by the exponential of its free-energy excess over the crystal, reduced a little by the water it absorbs. The water term was measured from a moisture-sorption isotherm of amorphous CRH1 by integrating the Gibbs–Duhem equation (the method of Murdande et al. 2010); for CRH1 it is 0.755 P8·E4·M1.

The free-energy difference was obtained in two ways. The Hoffman equation (Eq. 2) needs only the melting point $T_m$ and the enthalpy of fusion ${\Delta }_{\mathrm{f}\mathrm{u}\mathrm{s}}H$ E2:

In plain terms: the free-energy gap between crystal and liquid is zero at the melting point and grows roughly in proportion to how far below $T_m$ one works, scaled by the heat of fusion. The second route, the heat-capacity ("Cp") method of the authors' earlier paper, uses the measured heat capacities of crystal and amorphous form as functions of temperature together with the melting data. The authors call it more accurate, and it gives the free-energy difference both to the supercooled liquid and to the glass E5·C14. The paper names this method but does not print its expressions or the fitted heat-capacity parameters; they are in the earlier paper.

Ionization of a weak base. CRH1 is a base with pKa 4.6 M1. At pH 6.8 it is fully un-ionized; at pH 4.6, equal to the pKa, the ionized and un-ionized concentrations are equal at equilibrium, so the total dissolved drug is about twice the un-ionized amount C13. All concentrations in the paper are given as un-ionized drug, obtained at pH 4.6 with the Henderson–Hasselbalch equation, so that the two media can be compared on the same basis E3·R2. The amorphous-solubility ceiling refers to the un-ionized species, the one that forms the drug-rich phase.

Detecting LLPS. Two solution readouts were used. UV extinction at a non-absorbing wavelength (450 nm) measures light scattered by particles; it rises sharply when a new phase appears P3·C12. The fluorescent probe pyrene reports the polarity of its surroundings through the ratio of its third to its first vibronic emission peak, $I_3/I_1$. In water the ratio is low; if a liquid-like, hydrophobic drug-rich phase forms, pyrene partitions into it and the ratio rises. Crystals offer no such environment, so crystallization from solution leaves the ratio unchanged, which is what makes the probe selective for LLPS P4·C12. For the heminapadisylate (hemi-NAP) salt, whose counterion fluoresces in the pyrene range, the counterion's own fluorescence was used instead: it is strongest in water and weaker in less polar solvents, so it drops when the counterion partitions into a drug-rich phase R16·C49.

Salt disproportionation and pHmax. A salt of a weak base is the stable solid only below a certain pH, pHmax, where the salt and the free base have equal solubility. Above it, the salt in contact with solution tends to convert to the free base, a process called disproportionation. A more soluble salt has a lower pHmax and so a larger driving force to convert at a given pH C36·R22. Co-crystals behave similarly: they can dissociate into the free drug and the coformer C7·C35.

Methods in detail

The study has three parts: fix the ceiling for CRH1 in the two media, dissolve all seven forms without and with a crystallization inhibitor, and tell LLPS from crystallization during dissolution while checking the true solution concentration. All experiments ran at 25 °C where a temperature is stated P3·P5·P11.

Part 1: Fixing the ceiling for CRH1

Problem. To test whether any form exceeds the amorphous solubility, that value has to be known in the dissolution medium, and an amorphous solid of a fast-crystallizing drug cannot simply be dissolved to find it. The authors therefore approached it from two sides: an experimental LLPS onset and a thermodynamic estimate C10·C32.

What they did. For the LLPS onset they used solvent shift. A methanol solution of CRH1 was pumped by syringe pump into stirred buffer faster than the drug could crystallize: 1 mg/mL at 80 µL/min into pH 6.8 phosphate buffer (50 mM, ionic strength 155 mM), and 2 mg/mL at 60 µL/min into pH 4.6 citrate buffer (50 mM, ionic strength 98 mM) containing 20 µg/mL HPMC, the dissolution medium. The flask was held at 25 °C and stirred at 300 rpm, and extinction at 450 nm was followed with a 10 mm fiber-optic dip probe; the onset was taken where scattering rose sharply, in triplicate P3·M16·M17. In parallel, measured volumes of the stock were added to 10 mL of each buffer containing 2 µM pyrene, and the emission spectrum was recorded after excitation at 332 nm to give $I_3/I_1$ P4. As a third check, a solution with 36 µg/mL total CRH1 was made by solvent shift at pH 4.6 with HPMC (ionic strength raised to 155 mM with NaCl), the drug-rich phase was removed by ultracentrifugation, and the drug left in the aqueous phase was assayed by HPLC P7·M18.

For the thermodynamic estimate, the crystalline solubility of the free base was measured by a 48 h shake flask at 25 °C in both media, with ultracentrifugation (35 000 rpm, 20 min) and HPLC at 285 nm, in triplicate P5·P6. DSC gave the melting point (141.7 °C) and heat of fusion (28.12 kJ/mol) of the crystal and the Tg of the melt-quenched glass (48.0 °C); modulated DSC gave the heat capacities for the Cp method P9·M1. A water-sorption isotherm of about 10 mg of amorphous CRH1 at 25 °C, from 0 to 95% RH, gave the activity term 0.755 P8·M1. The free-energy difference was 5.68 kJ/mol by Hoffman, 5.85 kJ/mol to the supercooled liquid and 5.95 kJ/mol to the glass by the Cp method M1.

Why it works. The two sides are independent: the LLPS onset is measured in solution with no thermodynamic model, while the estimate uses only solid-state and crystalline-solubility data. Agreement between them fixes the ceiling more firmly than either alone, and the ultracentrifuged supernatant checks directly that the bulk phase in a two-phase solution sits near that value C17·C19. Note by the AI writer (not discussed in the paper): with the printed inputs, Eq. 1 at 298.15 K reproduces all six estimates of Table 2 (for example 1.20 × 0.755 × exp(5.68/(0.0083145 × 298.15)) = 8.96 against the printed 9.0 µg/mL), and Eq. 2 reproduces the Hoffman value (5.685 against 5.68 kJ/mol) E1·E2.

Part 2: Dissolving seven forms, without and with a crystallization inhibitor

Problem. To compare forms, the medium has to let each form supersaturate quickly. For a weak base the salts dissolve best where much of the drug is ionized, but the free base then converts back. The authors chose pH 4.6, equal to the pKa, so that the salts could dissolve rapidly to high supersaturation before converting to the free base; the other forms were run in the same medium for comparison C13.

What they did. The forms were the crystalline free base, a glass made fresh by melting the free base on aluminum foil and quench-cooling it in liquid nitrogen (no degradation by HPLC), the adipic acid co-crystal, the HCl, HBr and hemi-NAP salts supplied by Lilly, and a 20:80 CRH1:HPMC ASD made by rotary evaporation from methanol/dichloromethane at 45 °C and dried for 24 h M1–M8·P1·P2·R14. XRPD showed five distinct crystalline patterns (Figure 2) R1. Each form was added to 50 mL of pH 4.6 buffer at 25 °C, stirred at 200 rpm in a foil-wrapped flask: about 10 mg of the free base, glass and HCl and HBr salts, 15 mg of co-crystal to compensate for the adipic acid, and only 5 mg of the hemi-NAP salt and 10 mg of ASD (2 mg of drug), because more saturated the UV detector P11. Concentration was read in situ by a UV dip probe against calibrations made in each medium, in triplicate P11. The runs were repeated with 20 µg/mL HPMC predissolved in the medium. HPMC was chosen after screening a vinylpyrrolidone–vinyl acetate copolymer and several HPMC acetate succinate grades, for its delay of crystallization and its solubility at pH 4.6; above 20 µg/mL it gave no further improvement R10·P17.

Why it works, and its limits. In plain buffer, crystallization competes freely with dissolution. With the inhibitor in the medium, the competition is shifted toward dissolution, so forms that would otherwise crystallize first get a chance to approach the ceiling C26·C27. The authors stress that the UV values are apparent concentrations: once LLPS starts, nanometer-sized droplets absorb light much like dissolved drug, so the probe reads the true concentration only up to the amorphous solubility (Van Eerdenbrugh et al. 2011) C20. Note by the AI writer (not discussed in the paper): the drug amounts differ between forms by up to about five-fold. The ASD supplies 40 µg/mL total CRH1, about 20 µg/mL un-ionized at pH 4.6 if fully dissolved, against about 200 µg/mL total for 10 mg of free base or glass. Maxima and plateaus are therefore comparable across forms, dissolution rates less so X9.

Part 3: Telling LLPS from crystallization, and measuring the true concentration

Problem. A UV maximum at or above the ceiling could be dissolved drug, drug-rich droplets, or for the hemi-NAP salt the counterion. A falling UV curve could be crystallization. The authors needed a readout of the drug-rich phase and a measurement free of these artefacts C15·C20.

What they did. Pyrene (2 µM) was predissolved in the dissolution medium and sampled at intervals; an $I_3/I_1$ above 0.586, the average ratio at the LLPS onset in the pH 4.6 medium (Figure 3b), was read as LLPS P13·C38. For the hemi-NAP salt, the counterion (1,5-naphthalenedisulfonic acid, NAP) absorbs in the same UV region as CRH1 and fluoresces near pyrene (Figure S1) R15. The authors first showed that NAP fluorescence at 40 µg/mL is strongest in water and weakest in DMF (Figure S2), then that, in solvent shift of the hemi-NAP salt into the pH 4.6 HPMC medium, the NAP peak at 320 nm (excitation 270 nm) falls beyond about 10 µg/mL of un-ionized drug (Figure S3); they used this drop to detect LLPS during dissolution (Figure S4) R16·R17·R18·C50. Finally, immediately after each UV maximum, a sample was taken, centrifuged and its supernatant assayed by HPLC P12.

Why it works. Pyrene responds to a liquid-like hydrophobic environment and not to crystals, so a rise in $I_3/I_1$ separates LLPS from crystallization C12. Centrifugation removes the drug-rich phase and any particles, and HPLC then measures dissolved drug only, free of scattering and counterion absorbance C15. Note by the AI writer (not discussed in the paper): the methods call this step "centrifuged" and the results "ultracentrifugation", and neither gives the speed or time for these dissolution samples; the authors themselves suspect incomplete separation even at 35 000 rpm for the solvent-shift sample X11·C18.

Experimental analysis

The ceiling: LLPS onset and amorphous solubility agree

In both media, UV extinction stayed near zero as drug was added and then rose steeply, and the pyrene ratio rose over the same range (Figure 3) R3·R4. The solutions first turned turbid with no particles visible to the eye and later cleared as numerous visible particles appeared, which the authors find "consistent with" LLPS followed by crystallization R5·C16. Table A collects the values.

Table A. The ceiling for CRH1 at 25 °C, from Table 2, the insets of Figure 3 and the text R2·R3·R4·R6.

The estimates (9.0–12.5 µg/mL) and the measured onsets (11–14 µg/mL) overlap closely. The authors see "a strong correlation" between them and call the small differences "not surprising" given the uncertainty of prediction methods C19. They summarise the LLPS concentration as about 12 µg/mL in both media, roughly ten times the crystalline solubility R24·C17. The drug-lean phase of the ultracentrifuged two-phase solution held 15 µg/mL, a little above the other values; the authors suggest the difference "may be related" to inefficient separation of the drug-rich phase R6·C18. Note by the AI writer (not discussed in the paper): that sample had its ionic strength raised to 155 mM, while the pH 4.6 buffer used everywhere else has 98 mM, and no replicates are given X2. Figure 4 summarises the values as bars; its crystalline-solubility bar (about 1.2 µg/mL) is the pH 6.8 value, while all other bars are pH 4.6 values, and the caption calls the measured LLPS concentrations "predicted" R7·X1.

Without polymer, crystallization wins

Figure 5 shows the seven forms dissolving in plain pH 4.6 buffer R8. The free base dissolved slowly to a plateau of about 1.4 µg/mL, which the authors match with the crystalline solubility (about 1.5 µg/mL by HPLC) R8.b·C21. The co-crystal, glass and HCl and HBr salts dissolved much faster and supersaturated almost at once, but they peaked within 30 min (about 2.9, 3.3, 3.9 and 5.4 µg/mL, read from Figure 5) and then fell to about 2 µg/mL by 3.5 h as drug crystallized R8.a·R8.c–e·C21. None reached the estimated amorphous solubility, so the rapid crystallization "effectively prevents" the hypothesis from being tested in this medium C26.

The ASD was the exception. It rose to about 12.9 µg/mL within half an hour, stayed near the band of estimates for about 1.5 h and then declined to about 7.5 µg/mL by about 3.1 h, with a wide spread between runs R8.g. Since the glass, which is also amorphous, never exceeded 4 µg/mL, the amorphous state alone does not explain the ASD; the authors conclude that "Clearly" the HPMC in the ASD is important, helping dissolution and delaying crystallization from the solution "and/or" from the dissolving matrix, which gave a higher maximum and a larger area under the curve C24·C25. The hemi-NAP salt read about 15.8 µg/mL and stayed near 13 µg/mL after crystallizing, about 30 min after addition according to the SI; the authors trace this to the counterion, which absorbs in the CRH1 region and stays in solution as drug crystallizes, so the 2:1 salt calibration no longer applies ("can be explained") R8.f·R19·R15·C22·C23.

With HPMC in the medium, the salts climb to the ceiling

With 20 µg/mL HPMC predissolved (Figure 6), every form except the free base reached a higher maximum and crystallized later R9·C28. The co-crystal, glass and two halide salts started at a similar rate but peaked at different heights and times: co-crystal about 6.2 µg/mL at about 0.6–0.75 h, glass about 7.9 µg/mL at about 1.2–1.4 h, HCl salt about 10.7 µg/mL at about 1.2 h, HBr salt about 12.1 µg/mL at about 2.0–2.3 h R9.a·R9.c–e. Run-to-run differences in induction time made the error bars widen after each maximum R9·C28. The authors divide the forms into two groups. The ASD and all three salts generated supersaturation at or above the estimated amorphous solubility, the ASD and HBr salt "exactly in the gray region" and the HCl salt "near the lower limit"; the free base, glass and co-crystal did not C29. The ASD curve shown in Figure 6 is, by its caption, the run without polymer in the medium, added for comparison R9.g·X5. The hemi-NAP salt read about 19 µg/mL by UV R9.f.

For the glass and co-crystal, the authors are careful: "we cannot conclude" that these forms are unable to reach the ceiling; the only conclusion they draw is that, under these conditions, crystallization was faster than dissolution C31. They note that dissolving amorphous solids to measure the amorphous solubility often fails because the solid itself crystallizes on contact with water, with a few slowly crystallizing exceptions (Alonzo et al. 2010; Indulkar et al. 2015) C32.

Pyrene shows a drug-rich phase only for the salts and the ASD

Figure 7 plots the apparent concentration and the pyrene ratio for six forms in the HPMC medium (Table B, last column) R11. For the free base, glass and co-crystal the ratio stayed at about 0.52–0.57, below the 0.586 ± 0.009 threshold throughout, and the authors write that the "Fluorescence data confirmed" no LLPS R11.a–c·C39. For the ASD the ratio passed 0.586 within about 5 min and peaked at about 0.709 (the text gives 0.71) at about 80 min; for the HCl salt it stayed above the threshold from about 30 to about 150 min (maximum about 0.644), and for the HBr salt from about 60 to about 195 min (maximum about 0.631) R11.d–f. The authors read these as "suggesting" LLPS, and the highest ratio, for the ASD, as a sign that "more of the drug-rich phase" formed there C40·C41. For the hemi-NAP salt, NAP fluorescence fell within minutes of addition while the apparent concentration rose to about 20 µg/mL, and rose again from about 3 h as the concentration started to fall; the authors take this as LLPS "almost immediately" and crystallization after about 3 hours R18·C51.

Table B. Maxima of apparent un-ionized concentration (µg/mL) and highest pyrene ratio for each form, read from Figures 5–8 (approximate). Figures 5 and 6 are means of three runs; Figure 7 shows single runs; Figure 8 gives single values. The estimated amorphous solubility in this medium is 11.2–12.5 µg/mL R8·R9·R11·R12·R2.

Note by the AI writer (not discussed in the paper): two features of Figure 7 sit uneasily with the ceiling. First, the caption and dotted lines show that in both salt runs the pyrene ratio crossed 0.586 once the apparent concentration passed about 9 µg/mL (about 9.3 for the HCl salt, about 9.0 for the HBr salt). That is below the lowest estimate (11.2 µg/mL) and below the solvent-shift onsets in the same medium (12.49 and 13.73 µg/mL) R11.d–e·R4·X3. Second, the single runs differ from the Figure 6 means: the HBr salt peaks at about 9.9 µg/mL in Figure 7e against about 12.1 µg/mL in Figure 6, and the ASD in Figure 7f falls to about 2.9 µg/mL by about 3 h against about 7.5 µg/mL in Figure 6 R11·R9·X4. The NAP-fluorescence onset of the hemi-NAP salt in solvent shift (about 10 µg/mL) is also lower than the pyrene and UV onsets R17·X13. The paper does not discuss these offsets.

The true solution concentration stays at the ceiling

Figure 8 compares the UV maximum of each form with the HPLC value of the centrifuged sample taken at that moment (Table B) R12. For six forms the two agree within about 1.3 µg/mL: the free base at about 1.4, the co-crystal at about 6.2, the glass at about 9.8, the HCl salt at about 11.1, the HBr salt at about 12.4 and the ASD at about 13.2 µg/mL by HPLC R12. The hemi-NAP salt is the exception: about 19.1 µg/mL by UV but only about 11.4 µg/mL by HPLC, in the region of the estimate R12.e·C42. The authors explain the UV excess as drug-rich droplets absorbing like dissolved drug, which they call "highly probable" C30. They conclude that the free base, glass and co-crystal did not reach the estimate while all salts and the ASD generated supersaturated solutions around it C42. From these data they draw the paper's central statement: "These data provide strong support for the conjecture" that, whatever the solid form, the upper limit of supersaturation is governed by the amorphous solubility, and that dissolution beyond it gives LLPS and a two-phase solution whose bulk concentration equals the amorphous solubility C43.

Note by the AI writer (not discussed in the paper): the HCl salt reached about 10.7 µg/mL by UV and about 11.1 µg/mL by HPLC, at or just below the lowest estimate of 11.2 µg/mL. The abstract nevertheless places the salts among the forms that dissolved "above" the amorphous solubility. The glass, classed as failing, reached about 9.8 µg/mL by HPLC, about 1.3 µg/mL below the HCl salt, so the HCl salt's place in the successful group rests mainly on its pyrene signal X6. The free-base plateau by UV (about 1.2–1.4 µg/mL) is also somewhat below its shake-flask solubility in the same medium (1.50 ± 0.02 µg/mL), although the text calls them similar X14.

Induction times do not follow supersaturation

One might expect the forms that dissolve fastest to the highest supersaturation to crystallize first, as suggested in the literature (Sun and Lee 2013). The authors find this "clearly not the case", within their ability to measure the rate of supersaturation generation C33. The HBr and HCl salts dissolved at a similar rate in the HPMC medium, yet the HCl salt peaked at about 1.2 h and the HBr salt at about 2.0–2.3 h; the co-crystal, the least supersaturated of these, peaked first at about 0.6–0.75 h R9.a·R9.d–e. Their explanation follows in the Discussion.

Discussion

How the authors connect the results. The argument is a race between dissolution and crystallization, with the amorphous solubility as the finish line.

Supersaturation needs a form that dissolves faster than the stable form crystallizes C2. Without an inhibitor, CRH1 crystallizes so readily that only the ASD, which carries its own polymer, reached the ceiling C21·C24·C25. With 20 µg/mL HPMC in the medium, crystallization slows, and the forms that dissolve fast enough (the three salts) reach the amorphous solubility, form a drug-rich phase and hold the bulk at the ceiling C29·C40·C42. The glass and co-crystal still lose the race C31. The authors' general statement is that the observed supersaturation profile depends on "the competition" between the dissolution rate of the form and the crystallization rate to the more stable form, and that both the solid form and the inhibitor can be used to manipulate these rates C47.

Where crystallization starts. For the different induction times the authors offer a chain of hedged explanations. Because the HBr and HCl salts dissolve at a similar rate and the same inhibitor is present, the earlier crystallization of the HCl system "suggests that crystallization may be initiated from undissolved solid phase" rather than from solution; this "could also explain" why the co-crystal had the shortest induction time C34. They consider it "likely" that the undissolved salts and co-crystal convert to a different phase, the free base, because they are not stable solids under these conditions (Babu and Nangia 2011; Shiraki et al. 2008) C35. The HCl salt has been reported to have a lower pHmax than the HBr salt, stemming from its roughly twofold higher solubility (Merritt et al. 2013); being further from the pH below which it is stable, it has a larger driving force to convert to the free base, and this "may explain" its shorter induction time R22·C36. If the undissolved solid converts rapidly to the crystalline free base, any supersaturation is quickly depleted, so the dissolution rate of the form "appears to be a key parameter" when conversion is possible C37. None of this was tested directly: the undissolved solids were not analysed after dissolution, and the pHmax values are cited, not measured C35·C36.

What it suggests for formulation. The authors state that a crystallization inhibitor is "clearly essential" for the salts or co-crystals of CRH1 to give supersaturated solutions, and that combining a salt or co-crystal with a polymer "may provide a formulation strategy" as an alternative to an ASD C44·C45. They expect the work to "aid" solid-form selection and the understanding of how to reach maximal supersaturation in vivo C48. Note by the AI writer (not discussed in the paper): the polymer was only ever predissolved in the medium. The paper does not show that a polymer blended into a salt or co-crystal formulation would act the same way; the ASD, the only system where the polymer travelled with the drug, reached the ceiling even without polymer in the medium R8.g·X8.

Note by the AI writer (not discussed in the paper): for a formulation scientist the practical message is a target and a check. The target is the amorphous solubility, which can be estimated from crystalline solubility, DSC and one water-sorption isotherm, or measured as the LLPS onset by solvent shift; a form that reaches it gains nothing more in free drug, only a drug-rich phase. The check is that an in situ UV signal above that target should not be read as a higher free-drug concentration: here it came from drug-rich droplets and, for the hemi-NAP salt, from a UV-active counterion, and centrifugation with HPLC brought it back to the ceiling R12·C20·C30.

Limitations

Limitations stated by the authors. They acknowledge that without polymer the rapid crystallization of most forms "effectively prevents" the hypothesis from being tested C26. They do not claim that the glass and co-crystal cannot reach the ceiling: "we cannot conclude" that, only that crystallization outran dissolution "at these conditions" C31. They treat UV concentrations as apparent once LLPS has started, because droplets absorb like dissolved drug C20, and they flag the counterion interference of the hemi-NAP salt C22·C23. The slightly high 15 µg/mL value after ultracentrifugation "may be related" to incomplete separation C18, and the finding on induction times holds only "within our ability to determine the rate of supersaturation generation" C33.

The AI writer's own judgement (1): what the data show and how far the claim reaches. The ceiling itself is well founded for CRH1. Two solution readouts in two media and three thermodynamic estimates fall within about 9–14 µg/mL, and Eq. 1 and the Hoffman equation reproduce every tabulated estimate from the printed inputs R2·R3·R4·E1·E2. The statement that the ceiling holds "regardless of the solid form used, salt, ASD, co-crystal, amorphous" goes further than the data: only the three salts and the ASD reached it, the glass and co-crystal never did, and all of it concerns one compound in one medium at 25 °C C43·X12. Within the successful group, the HCl salt sits at or just below the lowest estimate X6. The maxima of Figure 8 are single values without error bars, and the separation conditions for the dissolution samples are not given X11. The "significant" increases in maximum, induction time and area under the curve with HPMC are visual readings of Figures 5 and 6; no areas, induction times or statistics are reported, and the conclusions' "in all cases" excludes the free base, which never supersaturated, and the ASD, which was not shown with HPMC in the medium X7·X8.

The AI writer's own judgement (2): measurement details that affect reading the figures. In the salt runs the pyrene ratio signalled a drug-rich phase at about 9 µg/mL, below the 11.2–12.5 µg/mL ceiling and the 12.5–13.7 µg/mL solvent-shift onset; whether this reflects earlier LLPS during dissolution, a probe effect or run-to-run variation cannot be decided from the paper X3. The single runs of Figure 7 differ noticeably from the means of Figure 6 X4. The medium of the ASD runs in Figures 7 and 8 is unclear: Figure 6 states that the ASD data come from buffer without polymer, while Figures 7 and 8 state that all forms were dissolved with 20 µg/mL HPMC X5. Drug amounts differ between forms by up to about five-fold, which confounds comparisons of dissolution rate X9. The estimated band and the pH 4.6 crystalline solubility were determined with HPMC in the medium, but the band is also drawn on the no-polymer data of Figure 5 X10. Figure 4 places the pH 6.8 crystalline solubility next to pH 4.6 values X1, the ultracentrifuged sample had a higher ionic strength than the buffer X2, and the NAP-fluorescence onset is lower than the pyrene and UV onsets X13. None of these overturns the central observation, but they set the precision with which the ceiling is shown.

Conclusion

The paper makes three contributions. First, for the weak base CRH1 it fixed the ceiling from two sides: LLPS onsets of 11.3–14.2 µg/mL by solvent shift and amorphous-solubility estimates of 9.0–12.5 µg/mL from Eq. 1, which agree R2·R3·R4·C19. Second, it dissolved seven solid forms in the same medium and showed that, without an inhibitor, crystallization caps all of them except the ASD far below this value, while with predissolved HPMC the three salts reach it and the glass and co-crystal do not R8·R9·C29. Third, it combined a pyrene (or counterion) fluorescence readout with centrifugation and HPLC to show that the forms which reached the ceiling formed a drug-rich phase while their true solution concentration stayed near the amorphous solubility, even when the UV probe read much higher R11·R12·C40·C42.

Within these conditions, a single compound at pH 4.6 and 25 °C with the polymer predissolved, the results support the authors' picture of supersaturation as a race between dissolution and crystallization with the amorphous solubility as the finish line C43·C47. Where crystallization starts, on undissolved salt or co-crystal converting to the free base, remains a hedged proposal ("may", "likely") C34·C35·C36. Testing it would need analysis of the undissolved solids, more compounds and a polymer formulated with the salt rather than dissolved in the medium.