Two miscible drugs, one drug-rich phase: why multidrug amorphous formulations lower each drug's free concentration and membrane flux

Background and motivation

Fixed-dose combinations, products that contain two or more active pharmaceutical ingredients (APIs), make up a growing share of new medicines (Keith 2005, Cottarel 2007, Kanzer 2010; refs 1–3). They are used where therapy needs several drugs at once, as in cancer, infectious diseases, diabetes and cardiovascular disease, and they also serve life-cycle management (Hiremath 2011, ref 4). Many drugs that enter such combinations are poorly water soluble, so the combined product inherits the solubility problem of each component. The paper asks what happens to that problem when the drugs dissolve together rather than alone.

Two strategies for formulating drugs together had been proposed. The first is the drug–drug cocrystal, in which two drugs share one crystal lattice (refs 5–8). Models predicted large solubility gains for cocrystals with a highly soluble coformer (Bethune 2009; Alhalaweh 2012), but in practice the native drug crystal often precipitates quickly and the expected concentration is not reached (Alhalaweh 2014). The second is the coamorphous blend: a miscible amorphous mixture of two drugs, usually without polymer (Hancock and Zografi 1997; Allesø 2009; Löbmann 2011). Single-phase coamorphous materials were reported to resist crystallization better than either drug alone and to dissolve faster (Allesø 2009; Löbmann 2011, 2012). The authors later call this "the current paradigm of formulating drugs together".

What these studies had not examined, the authors argue, is the solution side: the dissolution behaviour, supersaturation potential and phase behaviour of the solutions that form when such products dissolve (Nguyen and Van den Mooter 2014, ref 16), although these properties decide whether a product performs predictably (Simon 2006, ref 17). One warning sign already existed: a coamorphous system of ritonavir with darunavir had given a lower than expected dissolution rate and extent of supersaturation (ref 16), without a thermodynamic explanation.

For single drugs, the Taylor group had built a framework for that solution side. The highest concentration of molecularly dissolved (free) drug is set by the amorphous solubility; above it, if the drug does not crystallize, the solution undergoes liquid–liquid phase separation (LLPS) (Ilevbare and Taylor 2013; Mosquera-Giraldo and Taylor 2015). The drug-poor phase after LLPS sits at the predicted amorphous solubility (Almeida e Sousa 2014), and membrane flux rises linearly with free drug and levels off at the amorphous solubility (Raina 2014, 2015). A model in which each component's chemical potential is reduced by mixing in a shared amorphous phase had also been described (Lindfors 2006; Trasi and Taylor 2015, ref 27). But, as Section 1.1 puts it, these aspects "have been not widely studied" for multicomponent systems.

The paper therefore measures how high each drug's free concentration can go when a multidrug amorphous formulation dissolves under non-sink conditions, and explains the result through LLPS. The model pair is ritonavir (RTV) and atazanavir (ATV), two HIV protease inhibitors given together once daily as 100 mg RTV with 300 mg ATV; RTV inhibits cytochrome P450 3A (CYP3A) and so slows the metabolism of ATV. The authors compare single-drug and two-drug dispersions in polyvinylpyrrolidone (PVP), a physical mixture (PM) of two single-drug dispersions that stands in for taking two products together, and a three-drug dispersion that adds lopinavir (LPV). They then ask whether a lower free concentration lowers transport across Caco-2 cell monolayers, and whether an ideal-mixing model predicts the size of the effect.

Background concepts

Free drug, amorphous solubility and LLPS. "Free drug" means drug molecularly dissolved in the bulk water. Here it is measured in the supernatant after ultracentrifugation, which removes the colloidal drug-rich phase; the supernatant is also called the drug-poor phase. The amorphous solubility is the highest free concentration that can be reached: adding more drug does not raise it but creates more drug-rich phase, which Scheme 1 draws as droplets in equilibrium with the dissolved drug. In the energy picture of Scheme 2, a solution beyond the spinodal (unstable) or the binodal (metastable) separates until a drug-poor and a water-saturated drug-rich phase coexist, and this state persists until crystals nucleate (Asherie 1996, ref 21). The ratio of amorphous to crystalline solubility is the maximum achievable supersaturation. The amorphous solubility can be measured without making the amorphous solid: a methanol solution of drug is pumped slowly into buffer while light extinction at a non-absorbing wavelength (450 nm) is followed, and the concentration at which extinction rises sharply marks the onset of LLPS (Section 2.9).

Supersaturation and membrane flux. The paper links free drug to absorption through Fick's first law for passive transport (Eq. 1, citing Hubatsch 2007):

Here $J$ is the flux, $dM/dt$ the mass of drug crossing per unit time, $A$ the membrane area, $D$ the diffusion coefficient of the solute, $a$ the thermodynamic activity of the solute in the donor, ${\gamma }_m$ the activity coefficient of the solute in the membrane and $h$ the membrane thickness. In plain terms: flux is driven by the drug's activity on the donor side, not by its total amount; with area, diffusion coefficient, membrane affinity and thickness fixed, flux is proportional to activity. Activity is defined by Eq. 2:

where $C$ is the drug concentration and $\gamma$ its activity coefficient. In plain terms: activity is an effective concentration, corrected for how comfortable the molecule is in its surroundings. Because all donor solutions are handled the same way, the authors argue that the only difference between them is the free drug (Section 2.15). Once LLPS occurs, free drug and activity stop rising, so flux reaches a plateau at the amorphous solubility (Raina 2014, 2015).

Crystal and solvation terms. Section 3.1 splits the free energy of dissolving a crystal into two parts (Eq. 3):

In plain terms: dissolving a crystal costs energy to take the molecule out of the lattice plus energy to place it in water; making the solid amorphous, in the authors' words, "reduces the barrier to only the solvation contribution". The two terms are estimated from Eq. 4 (citing Miyako 2008):

Here $\chi$ is the measured aqueous solubility under non-ionizing conditions, $X_{\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}}$ the ideal solubility and $\gamma$ the activity coefficient of the solute in water. In plain terms: the measured solubility is the ideal solubility lowered by the solute's dislike of water; a large $\log \gamma$ marks a strongly hydrophobic solute. The ideal solubility comes from the melting properties (Eq. 5):

where $\Delta H_m$ is the melting enthalpy, $T_m$ the melting temperature, $R$ the gas constant and $T$ the experimental temperature, 310 K. In plain terms: the higher the melting point and enthalpy, the lower the solubility of the crystal; the equation assumes no heat capacity change on melting and an enthalpy of solution equal to $\Delta H_m$. Both drugs are weak bases (pKa 2.8 for RTV, 4.3 for ATV), so at pH 6.8 they are almost entirely un-ionized (AI writer's inference from the pKa values).Card check: Eq. 5 recomputed from Table 1 gives log X_ideal −2.59 (RTV) and −4.53 (ATV), whereas Fig. 2 plots about −1.07 and −1.97. The Fig. 2 bar totals equal the log of the molar crystalline solubilities (−5.49, −5.80), not of mole fractions (−7.24, −7.54), so the plotted log γ mixes concentration scales. The order of the terms survives (recomputed log γ 4.65 RTV vs 3.01 ATV) (story notes X1, X2).

Testing whether two drugs mix. In melting point depression, a second compound that mixes into the melt of a crystalline drug lowers the drug's chemical potential in the melt, so the crystal melts at a lower temperature (Marsac 2006, ref 31). A blend that forms a single amorphous phase shows one glass transition temperature ($T_g$) between those of the components, estimated by the Fox equation (Eq. 6):

Here $T_g$ is the glass transition temperature of the mixture, $T_{g(\mathrm{R}\mathrm{T}\mathrm{V})}$ and $T_{g(\mathrm{A}\mathrm{T}\mathrm{V})}$ those of the pure drugs (in K), and $x_1$ and $x_2$ the weight fractions of RTV and ATV. In plain terms: the reciprocal of the blend's $T_g$ is the weight-averaged reciprocal of the component values, as expected for a simple mixture.

Mole fraction and ideal mixing. The mole fraction $X$ of a drug in the drug-rich phase is its share of all drug molecules in that phase (water is not counted). Ideal mixing means the drugs mix there with no net attraction or repulsion, so each drug's activity in that phase equals its mole fraction. Non-sink conditions mean that more drug is added than can dissolve.

Methods in detail

The work splits into three contributions. The first characterizes each drug alone and the RTV–ATV pair: crystalline and amorphous solubility, the origin of the difference between the two drugs, and whether they mix in the amorphous state. The second measures each drug's highest free concentration when the drugs dissolve together, from one dispersion, from a physical mixture of two dispersions and from polymer-free solutions. The third explains the results with an ideal-mixing model for a shared drug-rich phase and tests two of its predictions: a halved Caco-2 flux and a one-third ceiling for a three-drug dispersion.

Contribution 1: Single-drug ceilings and RTV–ATV miscibility

① Problem. To show that combining drugs lowers each drug's ceiling, the single-drug ceiling must be known, and the drugs must be shown to mix. If RTV and ATV did not mix, each could form its own drug-rich phase, and there would be no reason for one to lower the other's free concentration. ATV was also supplied as the sulfate salt, while the work needed the free base in amorphous and crystalline forms.

② What they did. ATV sulfate (1 g) in 50 mL methanol was titrated with 0.1 M sodium hydroxide until a precipitate formed, which was washed, vacuum-dried for 24 h and found amorphous by powder X-ray diffraction (PXRD) and differential scanning calorimetry (DSC); slurrying 250 mg in 1:1 water:methanol for 96 h gave crystalline ATV (Section 2.5). Crystalline solubility: 10 mg of drug (20 mg of a 1:1 w/w crystalline RTV:ATV mixture) in 15 mL of 50 mM sodium phosphate buffer pH 6.8, shaken 48 h at 37 °C, ultracentrifuged 30 min and analysed by HPLC; the residual solid was unchanged by DSC (at least three measurements). Amorphous solubility: a methanol solution of about 10 mg/mL infused at 10 µL/min into 15 mL buffer at 37 °C, at least four runs, less than 1% final methanol. Miscibility: crystalline RTV mixed with amorphous ATV at 0–60 mol% ATV, RTV melting onset by DSC at 1 °C/min; blends melted at 134 °C, quenched to −20 °C and reheated at 20 °C/min to find the $T_g$, compared with Eq. 6. Dispersions: 1 g of 90% w/w PVP K29/32 and 10% w/w drug in 5 mL methanol, rotary evaporation (55 °C bath) and 24 h under vacuum, RTV:ATV from 0 to 100% ATV in 10 mol% steps plus a 1:1:1 molar RTV:ATV:LPV dispersion, in duplicate, amorphous by PXRD and DSC.

③ Why it works. The antisolvent method creates the amorphous drug-rich phase in situ, which the group had shown gives values in agreement with theory (Almeida e Sousa 2014), without the risk that a prepared amorphous solid crystallizes. The two miscibility tests are independent: melting point depression probes mixing in the melt, and a single $T_g$ probes mixing in the glass. If both say the drugs mix, it is reasonable to expect them to mix in the drug-rich phase too; the authors state that miscibility "is expected to influence the solution thermodynamics" (Section 3.2).

④ How it differs from earlier work. Coamorphous studies used miscibility as an argument for solid-state stability (refs 13–15). Here it is read as a warning: drugs that mix in the solid will also mix in the drug-rich phase that forms on dissolution, and that mixing limits how much of each can be dissolved.

Contribution 2: Each drug's ceiling when the drugs dissolve together

① Problem. Does a second drug lower the highest free concentration of the first? Answering this requires conditions in which each drug alone would exceed its amorphous solubility, a way to separate free drug from droplets, and controls that tell a drug–drug effect apart from a polymer effect or a lack of drug. Co-dosing needed its own test: does keeping the drugs in separate particles avoid the problem?

② What they did. For non-sink dissolution (Section 2.11), about 150 mg of powder was added to 15 mL of pH 6.8 buffer at 37 °C, stirred at 300 rpm. Samples at 5, 15, 30, 60 and 120 min were ultracentrifuged (210 053 g, 45 min) and the supernatant analysed by HPLC, with three independent experiments per time point. The arms were PVP-ATV and PVP-RTV (10% w/w drug), the 1:1 molar binary dispersion PVP-ATV-RTV, a 1:1 PM of the two single-drug dispersions, and the 1:1:1 ternary dispersion. A control used 300 mg of a powder with 5% w/w of each drug, sampled at 60 min. For the composition series, each binary dispersion was dissolved for 30 min (Section 2.12). To remove the polymer from the question, mixed drug-rich phases were also made by antisolvent addition: RTV in methanol, in the amount that gives its amorphous solubility, was added to buffer containing different amounts of ATV, and the reverse; the mole fraction of each drug in the drug-rich phase was calculated by mass balance. Nanoparticle tracking analysis (NTA; NanoSight LM20, 37 °C, triplicate) counted particles in antisolvent solutions of RTV, ATV and a mixture of both.

③ Why it works. With enough powder to exceed each amorphous solubility, a drug unaffected by its partner would reach its single-drug ceiling, so any shortfall comes from the combination; doubling the powder tests the alternative that the binary dispersion supplied too little drug. Ultracentrifugation removes the droplets, so the supernatant measures free drug, the quantity that drives flux. The antisolvent route contains no PVP, so if it gives the same composition dependence, the effect lies in the drug-rich phase, not in the polymer. Note by the AI writer (not discussed in the paper): the x-axis of Fig. 5 is the mole fraction in the formulation, not in the drug-rich phase. The two stay close because about 150 mg of a 10% dispersion in 15 mL supplies roughly 1 mg/mL of drug, around ten times the highest free ATV concentration and around thirty times that of RTV, so most of the drug ends up in the drug-rich phase or undissolved.

④ How it differs from earlier work. Earlier coamorphous work judged combinations by solid-state stability and dissolution rate (refs 13–15). This paper measures, separately for each drug, the free-drug ceiling under non-sink conditions, and adds a co-dosing arm and a polymer-free arm, so the result can be traced to the drugs themselves and to the way they are dosed.

Contribution 3: An ideal-mixing model for a shared drug-rich phase, tested on flux and on three drugs

① Problem. A measured drop needs an explanation that predicts its size for other ratios and numbers of drugs, and it matters for a product only if it lowers absorption. The paper therefore needed a model and a transport measurement in a biologically relevant system.

② What they did. The model (Section 4) takes Scheme 3 as its picture: when two miscible drugs dissolve from one ASD, or are pushed above their solubility by antisolvent addition, each dissolved drug is in metastable equilibrium with one drug-rich phase that holds both. "If mixing in the drug-rich phase is ideal", the free concentration of drug 1 follows Eq. 7 (citing Trasi and Taylor 2015):

Here $S_1$ is the amorphous solubility of component 1 in the bulk aqueous phase when a drug-rich phase containing a second component is present, $S_{A1}$ the amorphous solubility of component 1 alone, and $X_1$ the mole fraction of component 1 in the drug-rich phase. In plain terms: a drug that makes up half of the drug-rich phase can reach only half of its own amorphous solubility. If maximum flux is obtained at the amorphous solubility, flux scales the same way (Eq. 8):

where $J_1$ is the flux of component 1 at its reduced amorphous solubility and $J_{A1}$ its flux alone at its amorphous solubility. In plain terms: a drug whose free concentration is halved crosses the membrane at half the rate. For more than two drugs, the mole fraction counts all of them (Eq. 9):

where $n_1,n_2,n_3$ are the amounts (in moles) of each drug. In plain terms: each further miscible drug dilutes the others, so three drugs at equal moles each reach about one third of their own ceiling.

For transport, Caco-2 cells were grown on polycarbonate inserts (12 mm, 0.4 µm pores) for 21–30 days. Donors were made by adding 30 µL of a 10 mg/mL methanol stock of each drug to 3 mL of Hank's balanced salt solution (HBSS) with HEPES at pH 6.5 (20 µL into 2 mL in the second run), with the same amount of each drug in the single and 1:1 molar donors, always above the amorphous solubility; solutions at the crystalline solubility were also tested. The receiver was at pH 7.4; inserts were kept at 37 °C and stirred at 500 rpm, and receiver samples were taken at 15, 30 and 60 min (n = 3, run twice except the crystalline-solubility solutions). Monolayer integrity was checked with [¹⁴C]-mannitol. The authors' chain of reasoning can be drawn as follows.

③ Why it works. A dissolved drug molecule must have the same chemical potential as the same drug in the drug-rich phase. In a pure drug-rich phase this is the chemical potential of the amorphous drug, matched by a free concentration equal to the amorphous solubility. A second drug dilutes the drug-rich phase and lowers the first drug's chemical potential there; with ideal mixing its activity equals its mole fraction, and the matching free concentration falls in the same proportion, which is Eq. 7. Because the two mole fractions add up to one, Eq. 7 for both drugs becomes a straight line in a plot of free ATV against free RTV (Fig. 7): each drug's free concentration divided by its own amorphous solubility, summed over the two drugs, equals one. Flux follows from Eqs. 1 and 2, since it tracks the activity of free drug in the donor.

④ How it differs from earlier work. The model itself comes from Lindfors 2006 and Trasi and Taylor 2015 (refs 26, 27). What is new is its application to solutions generated by dissolving ASDs, to co-dosed dispersions, to three drugs and to a cell-based flux test. The authors also separate the effect from salting out and cocrystallization, where the components precipitate as a new crystal of fixed stoichiometry (Higuchi and Zuck 1953; Kostenbauder and Higuchi 1956). With LLPS, "a wide range of supersaturations" can arise, because the drug-rich phase composition, and so each drug's ceiling, follows the dose ratio continuously (Section 4).

Experimental analysis

Setup in brief. Solubility, dissolution, antisolvent and NTA work used 50 mM sodium phosphate buffer pH 6.8 at 37 °C; the Caco-2 donors used HBSS pH 6.5. The dispersions contained 90% w/w PVP K29/32 and 10% w/w total drug. The main read-out is the free concentration of each drug after ultracentrifugation. Table A collects the single-drug baselines.

Table A. Properties of the three drugs (from Table 1, whose caption cites ref 25) and molar solubilities at 37 °C in pH 6.8 buffer (from Table 2; mean ± SD of at least three measurements; LPV values footnoted to ref 27). NA, not applicable; ND, not determined.

Single-drug baselines and miscibility. Amorphous RTV is about 14 times more soluble than crystalline RTV, amorphous ATV about 83 times (the text says "~80 fold"): ATV has the lower crystalline but the higher amorphous solubility. The authors explain this with Fig. 2: ATV has the larger crystal-packing term and the lower $\log \gamma$. They describe RTV as having "a considerably lower melting point and enthalpy of fusion"; Table A shows that the difference lies mainly in the melting point (399 vs 483 K), since the enthalpies differ by only 8%. With both crystals present, RTV's crystalline solubility rose from 3.2 to 4.9 µM, which the paper does not comment on. In mixtures with amorphous ATV, the RTV melting onset fell from about 394.4 K to about 380.1 K at an ATV mole fraction of about 0.52 (Fig. 3a), which the authors read as "indicating" miscibility in the melt. Melt-quenched blends showed one $T_g$ at every ratio, from about 349 K at an RTV weight fraction of about 0.39 to about 323 K for pure RTV (Fig. 3b). The authors call this "well described" by the Fox equation, but the measured values lie about 3–8 K below the Fox line. All PVP dispersions showed a single $T_g$ between 139 and 160 °C.

Table B. Free drug concentration (mg/mL, mean of n = 3) during non-sink dissolution of 90% PVP / 10% drug powders, about 150 mg in 15 mL pH 6.8 buffer, 37 °C, 300 rpm; read from Fig. 4, approximate. Reference lines in Fig. 4: amorphous solubility about 0.093 (ATV) and 0.033 mg/mL (RTV); crystalline solubility about 0.001 and 0.0023 mg/mL.

Main result 1: one dispersion, half the ceiling. The single-drug dispersions dissolved quickly to their amorphous solubility and held it for 120 min (Fig. 4). In the 1:1 binary dispersion both drugs were just as flat, but lower: ATV about 0.046–0.052 mg/mL against about 0.101–0.119 mg/mL alone, RTV about 0.0177–0.0185 against about 0.0318–0.0343 mg/mL. The authors summarise this as "only approximately 50%" of the single-drug values, "despite the fact that sufficient powder was used" to exceed the amorphous solubility, and doubling the powder again gave about 50% at 60 min (data not shown). The flat profiles show a lower plateau, not slower release. The authors call the result "in contradiction with the current paradigm" of co-formulating drugs. One detail needs care: the ATV-alone dispersion reached about 8–28% above the antisolvent amorphous solubility (about 0.093 mg/mL), an overshoot the paper does not discuss. Relative to the dispersion's own plateau the binary ATV values are a little under half; relative to the antisolvent value, a little over half.

Main result 2: co-dosing does not avoid the drop. In the 1:1 PM of the two single-drug dispersions, ATV reached about 0.037 mg/mL at 5 min (with a wide error bar) and about 0.042–0.054 mg/mL thereafter, overlapping the binary dispersion. RTV started at about 0.0258 mg/mL and fell to about 0.0205 mg/mL by 120 min: below the single-drug level, but about 16–45% above the binary dispersion. The authors conclude that it "made no difference" whether the drugs were combined in one amorphous phase or added from two dispersions, and attribute this to a new drug-rich phase containing both drugs ("our data show"); its composition was not measured. The equivalence holds for ATV; for RTV the PM gave clearly higher values. Note by the AI writer (not discussed in the paper): an RTV curve that falls toward the binary level is what one might expect if droplets released from the two kinds of particles take time to reach one shared composition; the paper gives no data to test this.

Table C. Highest free concentration after 30 min of dissolution of binary PVP dispersions (10% total drug), read from Fig. 5, approximate (ranges span the three points per composition). The Eq. 7 columns are the AI writer's arithmetic with the Table 2 amorphous solubilities and the formulation mole fraction; the paper's own dashed lines start at about 143 µM ATV and about 46 µM RTV, and the paper does not state which amorphous solubility it used.

Main result 3: the ceiling scales with mole fraction. Across the composition series (Fig. 5), free ATV fell from about 138–154 µM without RTV to about 11–14 µM at an RTV mole fraction of 0.9, and free RTV rose from about 5.6 µM at 0.1 to about 43–47.5 µM at 1.0, both close to straight lines. The authors write that the highest free concentration "appears to be directly related" to the drug's mole fraction in the dispersion. Table C shows how close Eq. 7 comes: with the Table 2 values, every measured range lies on or a few µM above the prediction, consistent with the small ATV overshoot. Two prepared compositions (x_RTV 0.3 and 0.7) are not reported, and the text speaks of "nine different ATV:RTV molar ratios" although the methods describe eleven. The Fig. 5 caption says the dashed line comes from Eq. 5; the text says Eq. 7, which is what the line shows.

The same lines without polymer. With drug-rich phases made by antisolvent addition (Fig. 6), free ATV was about 130–134 µM at an RTV fraction of 0 in the drug-rich phase, about 69 µM at about 0.5 and about 5–16 µM at about 0.85–0.98; free RTV was about 20 µM at about 0.5 and about 43.5–47.5 µM at 1. The authors conclude that the free concentration is "directly proportional" to the mole fraction in the drug-rich phase and that Eq. 7 predicts Figs. 5 and 6 "very well". Since PVP is absent here, the polymer cannot be the cause.

A phase diagram for two solutes. Fig. 7 plots free ATV against free RTV for every sample with a drug-rich phase present. Points from dispersions and from antisolvent addition fall along the Eq. 7 line, from about 133 µM ATV at zero RTV to about 45.5 µM RTV at zero ATV; the largest offsets are one dispersion point (about 34 µM RTV, 63 µM ATV) above the line and one antisolvent point (about 6 µM RTV, 96 µM ATV) below it. In Region I, a thin band near the axes, both drugs are below their crystalline solubility (about 1.6 µM ATV, 3.2 µM RTV). In Region II, below the line, both are supersaturated relative to their crystals but no LLPS occurs. In Region III, above the line, a mixed drug-rich phase forms and free concentrations fall back to the line, until "eventually crystallization will occur". The authors state that Fig. 7 "clearly shows" that high free ATV is possible only at low free RTV, and vice versa. The y-axis labels above 8 × 10⁻⁵ M are all printed as "1.E-04", so values there were read assuming regular tick spacing.

Table D. Particle counts by nanoparticle tracking analysis (from Fig. 8, mean of three runs). The middle column is the card's and the AI writer's arithmetic, using amorphous solubilities of about 32.6 µg/mL (RTV) and 93.1 µg/mL (ATV) from Table 2 and the molecular weights in Table 1.

Particle tracking: supportive for single drugs, not for the mixture. For each drug alone, the counts rise steeply above the amorphous solubility: RTV from 1.52 × 10⁷ particles/mL at 20 µg/mL to 5.88 × 10⁸ at 50 µg/mL, ATV from 6.54 × 10⁶ at 55 µg/mL to 2.15 × 10⁸ at 110 µg/mL; particle size also grew (Table S1, not available). The authors read this as "consistent with the concept" that free drug is capped once LLPS occurs. Two values fit less well. The 20 µg/mL RTV solution, below its amorphous solubility, counted about three times the buffer background, although the text states that no scattering species formed below the amorphous solubility. More important, the authors write that the ATV + RTV mixture, each drug below its own limit, formed a scattering phase ("This confirms"). Eq. 7 does predict LLPS for this mixture, but its count, 1.08 × 10⁶ particles/mL, is below that of buffer alone. The evidence for the shifted boundary therefore comes from Figs. 5–7, not from Fig. 8.

Table E. Apical-to-basolateral flux across Caco-2 monolayers (from Table 3, n = 3); donor HBSS pH 6.5, receiver pH 7.4, 37 °C, 500 rpm, 60 min. The ATV Eq. 8 value is checked in the card; the ratios and the RTV Eq. 8 value are the AI writer's arithmetic.

Main result 4: flux halves along with free drug. With the same amount of each drug in the donor, each drug's flux from the 1:1 mixture was about half its flux alone (Table E). The authors call the drop to about 50% "in excellent agreement with the dissolution data" and explain it by the reduced maximum free drug concentration ("can be explained by"). Eq. 8 gives 5.25 × 10⁻⁵ mg/min/cm² for ATV, which the authors call "a good estimate". Donors at the crystalline solubility gave receiver concentrations below the detection limit of 2.7 × 10⁻⁷ mg/mL, so no flux value could be calculated; the authors take this as further confirmation that supersaturated solutions give higher flux. Donor concentrations were analysed but not reported. Note by the AI writer, from the card's arithmetic: 30 µL of a 10 mg/mL stock in 3 mL gives about 0.1 mg/mL of each drug, which for ATV is only about 1.06 times its amorphous solubility in pH 6.8 phosphate buffer, so saturation of the ATV-alone donor in HBSS pH 6.5 was not demonstrated.

Table F. Free drug during 120 min of dissolution of the 1:1:1 molar ATV:RTV:LPV dispersion (90% PVP, 10% drug), read from Fig. 9, approximate.

Main result 5: a third drug cuts each to about a third. In the ternary dispersion, RTV stayed at about 36–38% and LPV at about 28–36% of their amorphous solubility lines over 120 min (Fig. 9). Eq. 9 gives each drug a mole fraction of one third, and the authors write that, "As expected", each drug reached "about one third" of its amorphous solubility; the abstract says the model "well-predicted" the binary and ternary cases. For RTV and LPV the data support this. For ATV they do not settle it: the ATV points of Fig. 9 carry the same values and error bars as the PM series of Fig. 4, which suggests a plotting duplication, and they sit at 40–58% of the line. The LPV line also has unclear provenance: Table 2 footnotes the LPV amorphous solubility to ref 27, while the Fig. 9 caption says it was measured here and agreed with ref 27. The plotted line (about 0.0183 mg/mL) differs from 27.2 µM × 628.8 g/mol = 0.0171 mg/mL; with the Table 2 value the LPV percentages rise by about 7% (relative). No LPV-alone series is shown.

Controls and what they rule out. The doubled-powder control rules out a shortfall of drug supply; the polymer-free antisolvent series rules out PVP as the cause; the physical mixture shows that separate particles do not avoid the effect for ATV, and avoid it only partly for RTV. The residual-solid DSC rules out a form change during crystalline solubility tests, the methanol check rules out a cosolvent effect (data not shown), and the mannitol test rules out monolayer damage. Across systems, the same proportional rule describes two drugs with quite different amorphous advantages (about 14-fold and 83-fold), with and without polymer, for two and three drugs. Because the rule counts moles, the drug with the smaller molar share loses most. At the clinical 100 mg RTV with 300 mg ATV, the RTV mole fraction is 0.246, and Eq. 7 gives free RTV at only about 25% of its amorphous solubility ("it can be expected"); by the same arithmetic ATV would keep about 75% (AI writer's arithmetic). The authors add that free RTV reaches its crystalline solubility at an RTV mole fraction of around 0.1 in the drug-rich phase.

Discussion

Where the result applies. The mechanism requires drugs that are poorly soluble enough to undergo LLPS, miscible in the amorphous state, and dissolving in the same volume of medium; the model adds ideal mixing in the drug-rich phase. Under these conditions the authors expect the effect to be common: many fixed-dose combinations contain structurally similar compounds, so the likelihood of at least partial miscibility is "quite high", and multi-API ASDs are "clearly at risk" of lower supersaturation than single-drug products dosed individually. They extend the argument beyond ASDs: similar mixed drug-rich phases "may form" in vivo when weakly basic drugs that supersaturate on gastric emptying are given together. They also present the work as the thermodynamic basis for the lower than expected dissolution of the ritonavir–darunavir coamorphous system (ref 16).

Unlike salting out or cocrystallization. Those effects form a new crystal of fixed stoichiometry and act at one composition. The shared drug-rich phase acts continuously: its composition follows the dose ratio, and so does each drug's ceiling. The authors add that a component at a low mole fraction "could even" fall below its crystalline solubility, so that the amorphous form gives it no supersaturation at all. This was not shown; in the AI writer's reading, the closest data are the RTV values at a formulation fraction of 0.1 in Fig. 5, which at about 5.6 µM are only somewhat above the crystalline solubility of 3.2 µM.

What remains unresolved. The drug-rich phase composition was calculated by mass balance, not analysed, and activity coefficients in that phase were not measured, so ideal mixing is supported only by the fit of Eq. 7. For pairs with specific interactions or partial miscibility the rule could over- or underestimate the drop, and immiscible pairs were not tested. Crystallization kinetics of the mixed solutions were not studied. Absorption was not measured; the authors expect an effect ("may in turn impact" absorption; "is anticipated to negatively impact bioavailability"). The work used one polymer, one drug loading (10%), phosphate buffer without bile salts and three structurally related protease inhibitors, so biorelevant components that might solubilize or reshape the drug-rich phase remain open.

Implications for formulation. The authors state that awareness of how multidrug combinations change solution thermodynamics is "essential", and that dosing separate formulations together does not solve the problem. Further points are the AI writer's reading, not statements in the paper. A dissolution or flux test of each drug alone overstates what each achieves in a combination; for miscible pairs, a first estimate of each ceiling is the drug's amorphous solubility times its molar share of the total drug. The share is counted in moles, so a drug dosed at a low molar amount, often a pharmacokinetic booster such as RTV, loses most; whether that matters clinically depends on whether its absorption is solubility-limited, which the paper does not address. More powder does not lift the ceiling once a shared drug-rich phase forms. The coamorphous route, chosen for stability and faster dissolution, may trade away supersaturation when both drugs are poorly soluble and miscible. Partners that do not mix in the amorphous state, or release separated in time or place, might avoid the loss, but this paper tested neither.

Limitations

Limitations stated by the authors. The paper has no separate limitations section; its limits are carried by its conditions and hedges. The model is conditional ("If mixing in the drug-rich phase is ideal"), and the conclusion restricts its "good predictive power" to "these miscible systems". The drug-rich phase composition was "calculated from mass balance". The in vivo consequences are expectations: the lower free concentration "may in turn impact the absorption in vivo", reduced activity "is anticipated to negatively impact bioavailability", and the effect "is likely to be of importance" for "some fixed dose combination formulations". The crystalline-solubility transport runs were not repeated and gave values below the detection limit, and the doubled-powder control and the methanol check are "data not shown".

The AI writer's own judgement (1): reporting problems. The card's extractor notes list several problems, most already flagged where the values appear above. The ternary ATV series repeats the physical-mixture series, so the one-third result is shown for RTV and LPV only, not for all three drugs as the abstract states. The Fig. 5 caption names the wrong equation, and the amorphous solubility behind the Fig. 5 ATV line is not stated. The Fig. 2 solubility terms cannot be reproduced from Eq. 5 and Table 1; only their order survives. The blend $T_g$ values lie 3–8 K below the Fox line, so "well described" overstates the fit, although the single $T_g$ still supports miscibility. Table 1 is cited from ref 25 although the methods describe DSC measurements, and the RTV melting onset in Fig. 3a (about 394.4 K) differs by about 5 K from Table 1 (399 K). The ATV form used after conversion from the sulfate is not stated for the later experiments, although the molar ratios depend on it, and the LPV amorphous solubility has two stated sources.

The AI writer's own judgement (2): what the evidence shows. The core result is strong: for RTV and ATV, binary dissolution, the composition series, the polymer-free series and Caco-2 flux agree, with replicates and controls, that a 1:1 combination about halves each drug's ceiling, and the model arithmetic reproduces (0.246 at the clinical ratio, 5.25 × 10⁻⁵ mg/min/cm² for ATV flux, one third for three drugs). Three supporting claims are weaker than their wording. Co-dosing equals co-formulation for ATV, but for RTV the PM gave about 16–45% more. The NTA count of the mixture is below the buffer background, so "This confirms" is not supported by Fig. 8. The flux test was run in HBSS pH 6.5 rather than the pH 6.8 buffer used for solubility, the ATV-alone donor was barely above its pH 6.8 amorphous solubility, donor concentrations were not reported, and the assumption that stirring at 500 rpm removes boundary-layer effects was not tested; the halving is consistent with the model but donor saturation was not demonstrated. There are no in vivo data, so the bioavailability consequence remains an inference.

Conclusion

For three HIV protease inhibitors in PVP dispersions, the paper shows that combining miscible, poorly soluble drugs lowers the highest free concentration each can reach. At a 1:1 molar ratio RTV and ATV each reached about half their single-drug level; a physical mixture of two single-drug dispersions gave a similar drop for ATV and a smaller one for RTV; and a 1:1:1 dispersion with LPV held RTV and LPV near one third. Across compositions, with and without polymer, each drug's ceiling followed its mole fraction in the drug-rich phase, and Caco-2 flux fell by the same factor as free drug. The authors explain this by one shared drug-rich phase in which ideal mixing lowers each drug's activity, $S_1=S_{A1}{X}_1$, and expect, without in vivo data, reduced absorption for some fixed-dose combinations and co-administered drugs.

For formulation, the practical message is that the supersaturation of a combination must be judged per drug and in molar terms, not inferred from single-drug data. The open questions are the composition and non-ideality of real mixed drug-rich phases, partly miscible pairs and biorelevant media, the crystallization kinetics of mixed supersaturated solutions, and whether the in vitro loss carries through to bioavailability.