How pH sets the amorphous solubility of weakly basic drugs: liquid–liquid phase separation follows Henderson–Hasselbalch

Background and motivation

Many drug candidates are lipophilic and poorly soluble in water, and formulators raise their solution concentration with salts, surfactants, cyclodextrins, cocrystals or amorphous forms (refs 1–7). The paper starts from a distinction drawn by Miller and co-workers (ref 8): approaches that raise the crystalline solubility, for example micellar solubilization, can lower the apparent permeability of a drug, whereas amorphous dispersions raise the solution concentration by creating supersaturation without that penalty C8. That makes the behaviour of supersaturated solutions, rather than the solubility of the crystal, the property to understand.

Supersaturated solutions eventually crystallize, but for slowly crystallizing organic compounds a fast rise to high supersaturation can first produce liquid–liquid phase separation (LLPS): the solution splits into a drug-lean continuous phase and a drug-rich dispersed phase that are in equilibrium with each other but still metastable with respect to the crystal (refs 9–13) C2. In earlier work from the same group, Ilevbare and Taylor (ref 14) showed for eight compounds that the bulk concentration at which LLPS appears is about equal to the predicted amorphous solubility, that the drug-rich phase is amorphous drug with a few percent water, and that a solution can exceed the predicted amorphous solubility only slightly before it separates C9. Almeida e Sousa and co-workers (ref 15) found that the prediction still works when the new phase is a glass rather than a liquid C9. Detecting the LLPS (or glass–liquid phase separation, GLPS) concentration therefore "appears to be a reasonable approach" to measuring the amorphous solubility C10.

LLPS turns up across drug development. In crystallization process work it is called "oiling out" and is unwanted (refs 16, 17); in biochemical screening the drug-rich colloids cause false positives and are known as promiscuous aggregates (refs 18–21); and in formulation it occurs when amorphous solid dispersions dissolve (Alonzo et al., ref 22), where the supersaturated solution can raise bioavailability and the drug-rich phase can act as a reservoir that keeps the supersaturation constant during absorption (refs 23, 24) C11.

The missing element was pH. Nearly 75% of drugs are weak bases (ref 25), and gastrointestinal pH rises from the acidic stomach to the near-neutral intestine (ref 26), so a weak base with a pKa below about 6.5 that dissolves in the stomach can become supersaturated after gastric emptying (ref 27), and salts can disproportionate to the free base (ref 28) C12. In pH-shift experiments, Hsieh and co-workers (ref 29) found that weak bases that precipitated in amorphous form reached the theoretical amorphous solubility and stayed supersaturated for longer than those that crystallized C12. Yet a widely used model of which compounds form drug-rich aggregates (Seidler et al., ref 30) uses lipophilicity, ionizable groups and conjugated bonds, not the degree of ionization C13.

The authors therefore set out to test one hypothesis: the experimental amorphous solubility of a weak base should show a pH profile fixed by the amorphous solubility of the neutral species, the pH and the pKa, like the crystalline solubility, so that the supersaturation ratio (amorphous over crystalline solubility) "should remain constant" wherever the neutral form is present in more than trace amounts C14. They chose three weak bases with pKa below 7.5 from different chemical classes (Figure 1): clotrimazole, an imidazole with pKa 5.89 (from ref 29); nicardipine, a dihydropyridine with pKa 7.2 (from ref 35); and atazanavir, an azapeptide whose pKa of 4.52 they measured M1·M2·M3. Clotrimazole and nicardipine are reported promiscuous aggregators and so were "expected" to undergo LLPS readily C15.

Background concepts

Crystalline and amorphous solubility. The crystalline (equilibrium) solubility is the concentration of drug in equilibrium with the crystal. An amorphous solid has a higher free energy than the crystal, so it can reach a higher concentration before a new phase forms; this ceiling is the amorphous solubility. If the solution concentration rises beyond it and crystallization is slow, the excess drug separates as a drug-rich amorphous phase, a liquid if its glass transition temperature (Tg) is below the experiment temperature (LLPS) and a glass if it is above (GLPS) C2·C38. The paper measures the amorphous solubility as the onset concentration of this separation.

Ionization of a weak base. A weak base B takes up a proton to form BH⁺. The Henderson–Hasselbalch (HH) equation relates the two forms to pH (Equation 1):

In plain terms: at a pH equal to the pKa, half of the drug is neutral and half is protonated; two pH units above the pKa the base is almost fully neutral, and two units below it is almost fully ionized E1·C16. This is why the crystalline solubility was measured within about ±2 pH units of each pKa P3.

The pH–solubility profile. Only the neutral species is in equilibrium with the crystalline free base, and its concentration is fixed by the crystal; the ionized species adds to it. The total solubility $C_T$ then follows Equation 8:

In plain terms: $C_B$, the solubility of the crystalline free base, is the floor; each pH unit below the pKa multiplies the ionized contribution by ten E8. The authors explain this with Equation 7, which splits the free-base solubility into a crystal-lattice term and a solute–solvent term:

Here $\Delta G$ is the free-energy difference between the supercooled liquid and the crystal at the temperature of interest, $R$ the gas constant, $T$ the temperature and $\gamma$ the activity coefficient of the dissolved drug. In plain terms: lowering the pH does not change the lattice term, but the ionized molecules interact more favourably with water, so the total solubility rises while the neutral concentration stays equal to $C_B$ E7·C42. Rearranged, the HH relation gives the concentration of the un-ionized form, $C_U$, from any measured total concentration (Equation 6):

In plain terms: $X/(1+X)$ is the neutral fraction at that pH; if the HH picture holds, $C_U$ is the same at every pH E6. The paper applies this to the crystalline solubility and, replacing $C_T$ by the LLPS onset concentration, to the amorphous form (Figure 4) R9.

Predicting the amorphous solubility. The amorphous form lacks a lattice, so its solubility depends only on how readily the supercooled liquid mixes with water. Assuming that the activity-coefficient term of Equation 7 is the same over the crystalline and the amorphous concentration ranges, the ratio of the two solubilities follows from the free-energy difference between the forms (Hancock and Parks, ref 36) and from the water the amorphous form takes up (Murdande et al., ref 37) C43·C17. The paper prints this as Equation 2:

Here $C_A$ is the amorphous solubility, $C_T$ the crystalline solubility at the same pH, $T$ = 310 K, and $\exp [-I(a)]$ is a factor below 1 that accounts for the lower activity of the amorphous form once it has absorbed water, estimated from its moisture sorption isotherm E2. $\Delta G$ is estimated with the Hoffman equation (Equation 3) from the heat of fusion $\Delta H_f$ and the melting temperature $T_m$ of the crystal:

In plain terms: the further the experiment temperature lies below the melting point, and the larger the heat of fusion, the larger the free-energy advantage of the amorphous form E3. Note by the AI writer (not discussed in the paper): with $\Delta G$ from Equation 3, which is positive, the minus sign printed in Equation 2 would make the amorphous solubility smaller than the crystalline one. The ratios the paper reports (~9.2 for clotrimazole and 62 for atazanavir) are reproduced only with $\exp [+\Delta G/RT]$, using the paper's Tm, ΔHf and exp[−I(a)] values and standard molar masses that the paper does not print; the printed sign is most likely a convention slip X1·R3.

Reading the onset optically. A solution below the amorphous solubility is clear. When drug-rich droplets of a few hundred nanometres form, the solution scatters light, so the extinction at a wavelength where the drug does not absorb (400 nm) starts to rise C18·C25. Environment-sensitive fluorescent probes give a second read-out: pyrene changes the ratio of its first and third emission peaks (I1/I3) and 4-Di-2-ASP shifts its emission maximum when they move from water into a hydrophobic environment, which the drug-rich droplets provide C28. Dynamic light scattering (DLS) reports the polydispersity index (PDI), which is close to 1 when no defined particle population exists and falls when uniform droplets appear C34. Nanoparticle tracking analysis (NTA) counts individual particles and, with a fluorescence filter, only those that carry a dye P12.

Methods in detail

The study has three parts: a reference curve and a prediction built from the crystal; three independent measurements of the LLPS onset as a function of pH; and a characterization of what separates, together with a test from the other direction, dissolving amorphous drug. All experiments ran at 37 °C unless stated, in 0.1 M citrate (pH 3–6), phosphate (pH 6.5–8) or carbonate (pH 9) buffers M10.

Contribution 1: a crystalline reference curve and a predicted amorphous curve

Problem. To test whether the amorphous solubility follows HH, the authors needed a reference: the crystalline solubility at the same pH values, and a prediction of what the amorphous solubility should be if only the free energy of the solid changes.

What they did. Nicardipine and atazanavir were bought as salts; the free bases were precipitated with sodium hydroxide (both first came out amorphous) and then crystallized from methanol or water/ethanol P1. The pKa of atazanavir was measured by UV-metric acid–base titration on a Sirius inForm in 0.15 M NaCl at 37 °C, giving 4.52 P2·M2. Excess crystalline free base of clotrimazole and atazanavir was equilibrated in the buffers at 37 °C for 48 h, separated by ultracentrifugation at 40 000 rpm and analysed by HPLC at 210 nm (n = 3) P3. Nicardipine could not be included: under crossed polarizers, crystals placed in water at room temperature lost almost all birefringence within 120 min (Figure 2), so no equilibrium between crystal and water was possible R1·C22. For the prediction, DSC gave Tm 144.4 °C, ΔHf 94.9 J/g and Tg 28 °C for clotrimazole and Tm 207.8 °C, ΔHf 90.1 J/g and Tg 104 °C for atazanavir; vapour sorption of melt-quenched amorphous drug at 37 °C (5–95% RH) gave 1.4% and 5.2% water uptake and exp[−I(a)] of 0.82 and 0.22 P6·P7·M1·M2. Nicardipine has a Tm of about 70 °C and a Tg of 15 °C M3.

Why it works. With these inputs Equations 2 and 3 give one amorphous-to-crystalline ratio per drug, ~9.2 for clotrimazole and 62 for atazanavir; multiplying this ratio by the crystalline solubility measured at each pH gives a predicted amorphous solubility at that pH R3·P5. Note by the AI writer (not discussed in the paper): because the predicted curve is the measured crystalline curve scaled by one constant, its shape across pH is inherited from the crystal; the independent test of HH behaviour for the amorphous form is the un-ionized concentration calculated from the measured onsets (Figure 4), not the overlap of curves in Figure 3 X14.

Contribution 2: three routes to the LLPS onset

Problem. A single method can be biased: antisolvent addition introduces organic solvent, optical methods can see artifacts, and a fixed-pH experiment does not mimic a pH transition.

What they did, route 1 (UV extinction). A concentrated drug stock, in methanol for nicardipine and atazanavir and in DMSO for clotrimazole, was pumped by syringe into 15 mL of stirred buffer (300 rpm, 37 °C), with stock concentration and pump rate chosen for each pH (Table 1; for example 30 mg/mL at 80 μL/min for atazanavir at pH 3 and 5 mg/mL at 10 μL/min for clotrimazole at pH 8) P8. The organic solvent reached 1.5–15 μL/mL for nicardipine and clotrimazole and 7–90 μL/mL for atazanavir P8. A fibre-optic dip probe recorded the extinction at 400 nm, and the concentration at which it began to rise was taken as the LLPS concentration, the experimental amorphous solubility (Figure 5) C18·R11.

Route 2 (fluorescence). Pyrene (for clotrimazole and atazanavir) or 4-Di-2-ASP (for nicardipine) was added to 10 mL of buffer at 0.4 μg/mL, drug stock was added in aliquots to concentrations below and above the onset, and emission spectra were recorded after excitation at 332 or 488 nm P9.

Route 3 (pH shift). On the Sirius inForm, drug was dissolved at pH 2.0 in 60 mL of 0.15 M NaCl, where all three bases are ionized and soluble, and titrated upward with 0.5 M NaOH P10. Before precipitation the titration curve follows the HH form of Equation 4:

Here $\Delta {\mathrm{v}\mathrm{o}\mathrm{l}}_1$ is the titrant used so far (sample minus blank), $\Delta {\mathrm{v}\mathrm{o}\mathrm{l}}_2$ the titrant needed for the whole sample and $[\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}]$ the sample concentration. In plain terms: the fraction of the sample already titrated equals the neutral fraction, and the remainder is still protonated E4. After precipitation the neutral concentration is pinned at its solubility, ${\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_0$, and the curve follows Equation 5:

In plain terms: once the neutral form has reached its limit, only the ionized part can still change, so the pH climbs more steeply E5. LLPS occurs at the pH where the neutral concentration reaches the amorphous solubility of the neutral species, and repeating the run with different amounts of sample moves that pH C19. Note by the AI writer: as printed, the denominator subtracts a concentration from 1; the text's description matches $(1-\Delta {\mathrm{v}\mathrm{o}\mathrm{l}}_1/\Delta {\mathrm{v}\mathrm{o}\mathrm{l}}_2)\times [\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}]$ X18.

Why three routes. The UV and fluorescence routes vary the concentration at constant pH; the titration varies the pH at constant amount and uses no organic solvent, so agreement between them tests both the solvent and the route C33. The onset is then converted to the neutral concentration with Equation 6 E6.

Contribution 3: what separates, and the view from dissolution

What they did. DLS (Zetasizer Nano-ZS, backscatter at 173°) recorded the Z-average size and PDI at each concentration, and the size was taken where the PDI stayed roughly constant P11. NTA (Nanosight LM10, 532 nm laser) counted particles below and above the onset at two pH values, and with a fluorescence filter compared buffer containing Nile red, a dye that fluoresces only in a lipophilic environment, with dye-free buffer P12. Precipitates made at the two pH values of the dissolution study were examined by XRPD and polarized light microscopy, and those of clotrimazole and atazanavir by DSC from −30 °C P14·P15·P16. Nicardipine separated as a supercooled liquid that could only be collected after 4 h at 2 °C made it more viscous R23. For dissolution, amorphous drug films cast by rotary evaporation in 20 mL vials were dissolved in 15 mL buffer under non-sink conditions at 37 °C and 300 rpm, with UV spectra every minute, at one pH where the drug is mostly ionized and one where it is mostly neutral P13.

Why it matters. These experiments test whether the separated phase is really amorphous droplets rather than crystals or artifacts, and whether an amorphous solid dissolving "from below" reaches the same ceiling that a solution reaches "from above" C45·C49.

Experimental analysis

Main result 1: the onset climbs steeply below each pKa. Figure 3 is the paper's central figure. For each drug the LLPS onset is almost flat at high pH and rises steeply once the pH falls below the pKa. Clotrimazole separated at 7.7 μg/mL at pH 8 but at 490.2 μg/mL at pH 4, with intermediate values of about 145, 65, 28 and 14 μg/mL at pH 4.5, 5, 5.5 and 6 R18·R5. Atazanavir separated at 65.1 μg/mL at pH 9 and at about 1970 μg/mL at pH 3; nicardipine at 5.5 μg/mL at pH 9 and at about 355 μg/mL at pH 5.5 R2·R6·R7. Over the range tested the total onset concentration changed about 30-fold for atazanavir and about 65-fold for clotrimazole and nicardipine. The crystalline solubility followed the same shape at a lower level: un-ionized clotrimazole dissolved to 0.55 μg/mL and atazanavir to 1.04 μg/mL, and near the pKa (clotrimazole at pH 6, atazanavir at pH 4.5) the crystalline solubility was 1.08 and 2.12 μg/mL, close to twice the neutral value, "as predicted" R2·R4·C23. The text places the clotrimazole value of 0.55 μg/mL at pH 9, whereas Table 2 gives pH 8 phosphate buffer and clotrimazole was not tested at pH 9 (Table 1); the table value is the consistent one X2.

Table A. Solubility of the un-ionized forms at 37 °C, mean (SD), n = 3 (from Table 2), with the amorphous-to-crystalline ratios stated in the text R2·R3·R10·M1·M2·M3.

Main result 2: the neutral concentration at the onset is flat. Figure 4 converts each point into its un-ionized part with Equation 6. The LLPS-derived neutral concentration of clotrimazole lies at about 7.4–8.4 μg/mL from pH 5 to 8 and about 6.2 and 5.6 μg/mL at pH 4 and 4.5; that of atazanavir rises gently from about 57.5 μg/mL at pH 3 to about 70 μg/mL near pH 6 and is about 65 μg/mL at pH 9; that of nicardipine scatters between about 4.5 and 6.8 μg/mL from pH 5.5 to 9.2 R9. The neutral crystalline solubility is flat too, at about 0.5–0.8 μg/mL for clotrimazole and 0.85–1.2 μg/mL for atazanavir R9. The authors conclude that the un-ionized concentration stays constant "within experimental error" and that the experimental amorphous solubility is ~13 (clotrimazole) and ~63 (atazanavir) times the equilibrium solubility "at all the pH conditions" C27·C26·R10.

Table B. Constancy of the neutral concentration (read from Figure 4, approximate) against the change in the total onset (Tables 2 and 3, Figure 3) R9·R2·R18·R6·R7.

Note by the AI writer (not discussed in the paper): dividing the amorphous by the crystalline neutral values of Figure 4 gives a clotrimazole ratio of about 8 at pH 4 and 4.5 but about 12–17 from pH 5 to 8, and an atazanavir ratio of about 48–75. The ratio is roughly constant for atazanavir and for clotrimazole above pH 5, but not "at all the pH conditions"; at pH 4 the clotrimazole onset (490.2 μg/mL) also lies below the predicted value of about 565 μg/mL X5. The authors note that the constant ratio is expected only where the solution is in equilibrium with the neutral form rather than the salt C46; whether the lowest-pH clotrimazole points approach that limit was not examined.

Main result 3: the prediction from the crystal. For the neutral form, the predicted amorphous solubility was 64.9 μg/mL for atazanavir against 65.1 measured, and 4.9 μg/mL for clotrimazole against 7.7 measured (Table A) R2. Across pH, atazanavir's onsets stay within about 15% of the prediction from pH 3.5 to 9, but at pH 3 the measured value (about 1970 μg/mL) is about 27% below the predicted one (about 2700 μg/mL) R6·X6. The authors describe the agreement as "excellent" C4. The atazanavir ratio is larger than the clotrimazole ratio, which the authors say "can be attributed" to atazanavir's much higher melting point: making a high-melting crystal amorphous gives a larger gain in solubility C44. Note by the AI writer: the agreement is close for atazanavir, while for clotrimazole the measured amorphous solubility of the neutral form is about 1.6 times the prediction, so "excellent" holds for one of the two compounds that could be predicted X6.

Main result 4: three routes, one onset. For clotrimazole at pH 8, extinction at 400 nm stayed near zero up to about 6.6 μg/mL and then rose steadily, to about 0.125 at 13.6 μg/mL; the onset was set at 7.7 μg/mL (Figure 5) R11. The DLS PDI was close to 1 in buffer and below the onset, fell to about 0.27 at about 6.65 μg/mL and to about 0.21 above it R11. The text reports a further drop to 0.186, which is not visible in the figure, and the PDI drop sits about 1 μg/mL below the extinction onset X10. Fluorescence gave the same thresholds: the emission maximum of 4-Di-2-ASP stayed near 593 nm up to 50 μg/mL nicardipine at pH 6.3 and moved to about 580 nm at 65 μg/mL, beginning at 55 μg/mL, the UV onset at that pH (Figure 6A); the pyrene I1/I3 ratio fell slowly from about 1.87 to 1.79 up to 7 μg/mL clotrimazole at pH 8 and then steeply, to about 1.49 at 15 μg/mL (Figure 6B) R12·R13. The authors call the UV–fluorescence agreement "excellent" and argue that the second phase is noncrystalline, because dyes cannot partition into a crystal ("it is apparent") C30·C29. The pH-shift titration fell on the same curves over most of the range, for example about 285 μg/mL for atazanavir at pH 3.97 R8·C31. It departed at the lowest pH tested: about 320 μg/mL for clotrimazole at pH 4, against 490.2 by UV and about 537 by fluorescence, and about 163 μg/mL for nicardipine near pH 5.85, against about 107 by UV R8·R5·R7·X7. Because the titration uses no organic solvent, the authors infer that the solvent in the other methods "did not influence the outcome" C33. The nicardipine onset at pH 7, 15 μg/mL, is in "good agreement" with the concentration at which Coan and Shoichet observed a nicardipine drug-rich phase in aggregation studies (ref 34) R24·C50.

Main result 5: amorphous nanodroplets, liquid or glassy. Above the onset the second phase was in the nanometre range at every pH (Figure 7A). DLS Z-averages were about 145–310 nm for clotrimazole, 116–232 nm for atazanavir and 213–387 nm for nicardipine, the largest for nicardipine at pH 7.5 and 8 R14. NTA of clotrimazole at pH 8 found very few particles at 5 μg/mL, below the onset, and a mean size of 167 ± 54 nm at 8 μg/mL (164 nm in the text), against 182 ± 39 nm by DLS R15·C35·X9. Some nanoparticles appeared below the expected onset at pH values where the drug is mostly ionized; the authors consider these "an artifact" of antisolvent addition C36. Under the fluorescence filter, dye-free buffer showed no particles, whereas with Nile red a droplet population of about 100–450 nm appeared above the onset, so the droplets are lipophilic (Figure 7D) R16·C37.

Table C. Physical state of the separated phase (Figure 9 and Figures S1–S5; Tg by DSC; halo positions read from the diffractograms, approximate) R19·R20·R21·R22·R23·M1·M2·M3.

The precipitates of all three drugs were X-ray amorphous and showed no birefringence at both pH values (Table C) C6. Their Tg values lie below the dry Tg, which the authors find "consistent with" the water absorbed by the amorphous forms (1.4% for clotrimazole, about 5% for atazanavir) and with a typical drop of about 10 °C per 1% water (ref 44) C39. At 37 °C clotrimazole therefore separates as a supercooled liquid and atazanavir as a glass, for which the authors prefer the term glass–liquid phase separation; nicardipine, with a dry Tg of 15 °C, is "expected" to separate as a liquid C38·C40. The glassy or liquid nature of the drug-rich phase "does not appear" to change the pH behaviour C51.

Main result 6: dissolving amorphous drug reaches about the onset. Dissolution of amorphous films, approaching the amorphous solubility from below, gave maxima close to the LLPS concentrations (Table D) R18·C5. Atazanavir reached a plateau near 60 μg/mL at pH 9 within about 2 h and about 635 μg/mL at pH 3.5 by 3 h; clotrimazole reached about 485 μg/mL at pH 4 within about 0.6 h, then drifted to about 420 μg/mL by 3 h with widening error bars, and at pH 8 it was still rising at about 6.8 μg/mL when the run ended at 2 h (Figure 8) R17.

Table D. Non-sink dissolution of amorphous films at 37 °C (from Table 3) R18.

Three details of Table D deserve care. The atazanavir onset at pH 9 is 65.8 μg/mL here but 65.1 μg/mL in Table 2 and the text X3. The nicardipine pH 9 entry of 0.9% ionized does not follow from its pKa of 7.2, which gives about 1.6%; the other entries reproduce within rounding X4. And several SDs are printed as ± 0.0 X17. Across the six conditions the maxima are 69–110% of the onset, with nicardipine at pH 9 the lowest (3.8 against 5.5 μg/mL) R18·X8. The authors read the agreement as "very close" and conclude that dissolving an amorphous solid reaches the amorphous solubility when crystallization is slower than dissolution C5·C45.

Discussion

The argument in one chain. The authors' reasoning runs from the crystal to the amorphous form and then to the gut.

The authors' practical conclusion is that "it is essential to consider the impact of pH on the amorphous solubility" when judging whether a compound will form a drug-rich phase or aggregates C48.

From the beaker to the gut. Gastrointestinal pH is about 1–2 in the fasted stomach, 4.4–6.6 in the duodenum and jejunum and 6.8–8 in the ileum (ref 26) R25. A weak base with a pKa between 4 and 8 is therefore mostly ionized and soluble in the stomach; in the intestine its solubility falls and a supersaturated solution "potentially" forms, and if the neutral concentration exceeds the LLPS concentration a colloidal amorphous phase "will result", in particular for slow crystallizers C53. Earlier work showed that membrane flux rises with supersaturation but plateaus once LLPS occurs (Raina et al., ref 48), so the authors consider a colloidal drug-rich phase "likely" favourable during absorption: it gives the maximum flux and can act as a reservoir that replenishes absorbed drug C54·C55. To show what this means for real doses they work through two fasted-state scenarios (Table E).

Table E. The authors' dose calculations (p. 2375); volumes and pH from refs 26 and 49–54. None of these steps was measured R25·R26·R27·C56·C57.

The authors add that the outcome depends on dose, pKa, pH and any solubilizing components, which "have not been considered in this study" C58. From the comparison they conclude that, since small-intestinal pH is around 6.5, basic drugs with pKa below 5 "will have a higher propensity" to undergo LLPS on passing from the stomach to the small intestine C61. Note by the AI writer: two scenario numbers can be checked with the paper's own constants: the crystalline atazanavir solubility at pH 1.5 from Equation 8 is about 1090 μg/mL, matching the stated 1.1 mg/mL, and atazanavir at pH 6 is about 97% un-ionized, close to the stated 96% E8·E1.

The screening context. LLPS is also the mechanism behind promiscuous aggregation in screening assays. Doak and co-workers (ref 31) found that 22 of 33 BCS class II and IV drugs formed aggregates in phosphate buffer at pH 7 but only 6 of them in fed state simulated intestinal fluid (FeSSIF) at pH 5; nicardipine aggregated in the buffer but not in FeSSIF R28. The authors suggest that this "may be due" to nicardipine's conversion to the more soluble ionized form at pH 5, given its pKa of 7.2, and that the argument "may be true" for other compounds in that study C59. Bile salts in FeSSIF "cannot be ignored", but the assay pH and the compound's pKa "need to be considered" when interpreting precipitation in screening C60.

Where the framework applies. The evidence covers three weak bases with pKa 4.52–7.2 in simple 0.1 M buffers at 37 °C, without polymers, surfactants or bile salts A1·M10. The drug-rich phase was a liquid for two drugs and a glass for one, which the authors find makes no difference to the pH behaviour C51. The prediction from crystal properties could only be tested for the two drugs whose crystals are stable in water C22. The framework assumes that the solution is in equilibrium with the neutral form rather than with a salt, which the authors name as the condition for a constant ratio C46.

What it suggests for formulation. Note by the AI writer (not discussed in the paper): for weak bases the paper turns the amorphous solubility into a property of the neutral species. One LLPS measurement at a pH where the drug is neutral, together with the pKa, estimates the onset at any other pH through Equation 8; in this paper the neutral onset stayed within about a quarter of its mean across pH for clotrimazole and closer for atazanavir R9. For a pH-shift (two-stage) dissolution test of an amorphous formulation, the same arithmetic tells in advance whether a drug-rich phase can form after the shift: the nicardipine example shows that a low dose can stay below the onset even for an amorphous product R27. And where the prediction from melting data and water sorption is used instead of a measurement, it was close for atazanavir but about 1.6-fold low for clotrimazole X6.

Limitations

Limitations stated by the authors. The authors are brief about limits. They state that the tendency of weak bases to supersaturate and form colloids in the small intestine depends on the dose, the pKa, the pH and solubilizing components, "which have not been considered in this study" C58, and that the effect of bile salts in simulated intestinal fluid "cannot be ignored" C60. They note that nanoparticles seen below the onset at ionizing pH are "thought to be" an artifact of antisolvent addition C36, that the constant amorphous/crystalline ratio is expected only where the solution is in equilibrium with the neutral form rather than the salt C46, and that nicardipine's crystalline and predicted amorphous solubility could not be obtained because its crystals turn amorphous in water C22.

The AI writer's own judgement (1): how strong the central claim is. The core observation is solid: for three structurally unrelated weak bases the total onset changed 30- to 65-fold with pH while the neutral concentration at the onset stayed within a narrow band, and UV extinction, two fluorescence probes and a solvent-free titration agree over most of the range R9·R5·R6·R7·R8. Three qualifications apply. First, the claim of a constant amorphous/crystalline ratio "at all the pH conditions" does not hold at the low-pH end for clotrimazole, where the ratio is about 8 instead of about 13 X5. Second, the predicted amorphous curve is the crystalline curve scaled by one constant, so its visual overlap with the onsets in Figure 3 adds little beyond the single-point comparison of Table 2, where the prediction is close for atazanavir but about 1.6-fold low for clotrimazole; Equation 2 is printed with a sign that does not give the stated ratios X14·X6·X1. Third, the routes diverge at the lowest pH, where the titration reads lower for clotrimazole and higher for nicardipine, and where the antisolvent runs carried the most organic solvent (up to 90 μL/mL for atazanavir) X7·X16.

The AI writer's own judgement (2): what the numbers and the gut argument can bear. Several values disagree between text, tables and figures: the buffer pH for the clotrimazole crystalline solubility (pH 9 in the text, pH 8 in Table 2), the atazanavir onset at pH 9 (65.1 or 65.8 μg/mL), the NTA mean size (164 or 167 nm, with a plotted distribution that peaks near 80 nm), the lowest PDI (0.186 in the text, about 0.21 in Figure 5), the % ionized of nicardipine at pH 9, and the separation route for the XRPD samples (filtration in the methods, ultracentrifugation in the Figure 9 caption) X2·X3·X9·X10·X4·X11. Several plotted pH values are not the nominal buffer pH, and replicate numbers are stated only for Table 2 X12·X17. None of these changes the main pattern, but they limit how precisely individual numbers should be reused. The intestinal conclusion is weaker: it rests on two calculated scenarios, and atazanavir and nicardipine differ 20-fold in dose as well as in pKa, so the comparison does not isolate the pKa effect behind the statement about bases with pKa below 5 X15. Droplet size also varies more with pH than "does not impact the size" suggests, with nicardipine droplets about 1.5 times larger at pH 7.5–8 X13.

Conclusion

The paper makes three contributions. First, it measured the LLPS onset of clotrimazole, atazanavir and nicardipine across 4–6 pH units by three routes and showed that the neutral concentration at the onset hardly changes with pH, so the total onset follows HH R9·C3·C27. Second, it compared the onsets with an amorphous solubility predicted from crystalline solubility, melting data and water sorption, with close agreement for atazanavir and a 1.6-fold gap for clotrimazole R2·C4·X6. Third, it showed that the separated phase is made of amorphous nanodroplets of about 100–400 nm, liquid or glassy depending on its Tg, and that dissolving amorphous drug reaches about the same ceiling R14·R19·R22·R18·C5.

For formulation the message is that the supersaturation an amorphous form of a weak base can deliver is a property of its neutral species: the onset of a drug-rich phase scales with pH through the pKa, so whether a weak base forms a drug-rich colloidal phase after gastric emptying depends on its pKa, the intestinal pH and the dose C46·C47·C58. The authors' further step, that bases with pKa below 5 are the most prone to LLPS in the intestine and that the resulting colloidal phase helps absorption, rests on calculation and earlier work rather than on measurements in this paper C61·C55·X15.