When two supersaturated drugs meet: a shared drug-rich phase lowers the free concentration of both

Background and motivation

A large share of drug candidates are poorly soluble in water, and in the laboratory they are usually brought into aqueous assays by dilution from an organic solvent such as dimethyl sulfoxide. Under these conditions a non-crystalline, drug-rich colloidal phase can form. In drug discovery this has been called "promiscuous aggregation"; such aggregates are thought to be behind many false results in enzyme screens and have been reported to reduce the cytotoxicity of anticancer drugs (Coan and Shoichet 2008, ref 2; Owen 2012, ref 3). C1 In oral delivery the same colloids may be welcome: anti-HIV compounds that formed aggregates of 100 nm or less showed higher than expected bioavailability (Frenkel 2005, ref 4), and amorphous dosage forms release colloidal species that could improve bioavailability (Friesen 2008, ref 5). C2

Earlier work from the Taylor group had pinned down what these colloids are. A supersaturated drug solution stays a single phase only up to the drug's "amorphous solubility", typically 5–50 times its crystalline solubility; above it the solution undergoes liquid–liquid phase separation (LLPS) into a bulk aqueous phase and a drug-rich phase of initially colloidal size, which is a water-saturated supercooled liquid or a glass and can later crystallize (Ilevbare and Taylor 2013, ref 7; Almeida e Sousa 2015, ref 8; Mosquera-Giraldo 2015, ref 9). C3·R18 The authors therefore prefer the term "drug-rich phase" to "drug aggregates". C3 The amorphous solubility can be estimated from the crystalline solubility and the free energy difference between crystal and supercooled liquid, with excellent agreement with the observed onset of LLPS (ref 8). C4

The drug-rich phase matters for thermodynamics. Once it is present, the free drug concentration in the bulk phase is at its maximum: adding more drug only makes more drug-rich phase, because the chemical potential of the drug is constant in an equilibrated two-phase system. Transport across a semipermeable membrane therefore peaks where the drug-rich phase first forms (Raina 2014, ref 13). C5 The drug-rich phase can also take up other molecules: environment-sensitive fluorescence probes report a more hydrophobic environment when it is present, read as the probe mixing into it (ref 7), and enzymes may adsorb to it (ref 14). C6

This raises a practical question. Two drugs are often in solution together: in combination products such as Kaletra, which contains ritonavir and lopinavir as an amorphous solid dispersion (ASD); when separate products are dosed at the same time; and in metabolic assays that combine a probe substrate with a test compound. C7 Ritonavir is a particularly relevant partner because it is co-dosed to inhibit cytochrome P450 CYP3A4 and boost the bioavailability of a second drug (Zeldin 2004, ref 15), and because it readily forms a drug-rich phase. C8 If one drug forms a drug-rich phase, a second drug "might" mix into it and lose free concentration, which "may" change its biological activity. C7 The authors state their hypothesis plainly: the free drug concentration of a compound will be reduced in the presence of a second compound that readily undergoes LLPS. C7 Before this study, the effect of additional solutes on the maximum thermodynamic activity reachable in a supersaturated solution was "not well understood". C33

Background concepts

Supersaturation, amorphous solubility and LLPS. A solution is supersaturated when it holds more drug than the crystalline solubility. For a poorly soluble drug this can be reached by solvent shift, pH shift or dissolving an amorphous form. As long as no crystals form, the concentration can rise until it meets the solubility of the amorphous (supercooled liquid) drug. Beyond that point the solution splits into two liquid phases: a water-rich bulk phase at the amorphous solubility and a drug-rich phase. The authors treat the LLPS concentration and the amorphous solubility as the same quantity (ref 7). C10·C36 The difference between crystalline and amorphous solubility follows from the difference in chemical potential between the two solid forms (Eq. 1):

Here ${\mu }_1^{\circ }$ is the chemical potential of the pure amorphous drug, treated as a supercooled liquid, ${\mu }_{1c}^{\circ }$ that of the crystal, $R$ the gas constant, $T$ the temperature, and $S_a$ and $S_c$ the amorphous and crystalline solubility. E1 In plain terms: the higher free energy of the amorphous form shows up directly as a higher solubility, and the ratio of the two solubilities grows exponentially with the chemical potential difference. In this paper Eq. 1 is used only to explain why every amorphous solubility in Table 1 is far above the crystalline one. C36·R1

Free drug concentration, thermodynamic activity and flux. Membrane permeation is driven by the thermodynamic activity of the dissolved drug, which in dilute solution is set by the free (molecularly dissolved) concentration, not by the total amount of drug in the vessel. C33 In a solution with a drug-rich phase, the free concentration is the concentration in the continuous aqueous phase; the authors measure it in two ways: as the drug left in the supernatant after the drug-rich phase is spun down at high speed, which they regard as one binodal point (ref 13), and from the flux across a dialysis membrane. C10·C27

Mixing in the drug-rich phase. Because amorphous drugs have a liquid-like structure, they can mix with other compounds. If two drugs mix ideally in the drug-rich phase, the chemical potential of each is lowered according to its mole fraction there (Eqs. 2 and 3):

Here ${\mu }_1$ and ${\mu }_2$ are the chemical potentials of drugs 1 and 2 in the mixed amorphous phase, ${\mu }_1^{\circ }$ and ${\mu }_2^{\circ }$ those of the pure supercooled liquids, and $x_1$ the mole fraction of drug 1 in the drug-rich phase. E2·E3 In plain terms: diluting a drug in an ideal amorphous mixture lowers its escaping tendency by $RT\ln x$, a purely entropic effect, and ideal components are miscible in all proportions. C37

The amorphous solubility of a mixture. A lower chemical potential in the drug-rich phase means a lower concentration in the water phase that is in equilibrium with it. For ideal mixing the paper gives (Eq. 4):

Here $S_a(x_1)$ is the amorphous solubility of drug 1 when its mole fraction in the drug-rich phase is $x_1$, and $S_a^{\circ }$ is the amorphous solubility of the pure drug. E4 In plain terms: each drug's ceiling is its own single-drug amorphous solubility multiplied by its share of the molecules in the drug-rich phase; the partner follows the same form with $(1-x_1)$. This is a Raoult's-law-type relation, and the authors note that a similar equation predicted the water solubility of mixtures of structurally related hydrophobic organic liquids (Banerjee 1984, ref 28). C39 To apply it they assume (1) that the activity coefficients in the aqueous phase do not change over the concentration range, (2) that the drug-rich droplets, about 350 nm, are too large to raise solubility appreciably ("a reasonable assumption", ref 29), (3) that the water content of the drug-rich phase is the same in single and binary systems, and (4) that the single-drug amorphous solubility of Table 1 can be used as $S_a^{\circ }$. C38

Detecting the onset of LLPS. Three signals mark the appearance of a drug-rich phase. In UV extinction, scattering at 350 nm rises sharply. P4·C10 With pyrene, a polarity-sensitive probe, the ratio of the emission peaks at 383 nm (I3) and 373 nm (I1) rises when the probe enters a less polar environment, from about 0.51 to about 0.61 according to the methods. P3·R3 Felodipine is itself fluorescent and interferes with pyrene, so for felodipine the rise of its own emission baseline at 430 nm is used instead (ref 18). C11 In the flux experiment, the onset appears as the break between a rising and a flat region of flux versus concentration. R1·R2

Methods in detail

All experiments used 100 mM phosphate buffer at pH 6.8, and all drugs were introduced from methanolic stock solutions, usually at 10 mg/mL; the crystalline solubility, ultracentrifuge, extinction and diffusion experiments were run at 25 °C. M8·M10·P1·P2·P4·P6 Ritonavir, lopinavir, felodipine and paclitaxel came from Attix Pharmaceuticals, diclofenac from Spectrum Chemicals and hydroxypropyl methylcellulose (HPMC) from Shin-Etsu; paclitaxel "appeared to be" a non-stoichiometric hydrate with about 3.6% moisture. M1·M2·M3·M4·M5·M6 HPMC at 10 µg/mL was added to the ultracentrifuge and diffusion media to prevent crystallization during the experiments. C9 Drug concentrations were measured by HPLC (C-18 column, 60:40 acetonitrile–water, detection at 205 nm), except in the diclofenac–ritonavir mixtures, which were measured by UV at 275 and 252 nm. P5·P10 The study combines five kinds of work, shown in the flow below.

Contribution 1: Each drug's own ceiling, measured four ways

Problem. Every later comparison needs a reliable single-drug amorphous solubility, and each detection method has its own weakness. What they did. The crystalline solubility of ritonavir, lopinavir and paclitaxel was measured by shaking excess crystals in 15 mL buffer for 2 days at 25 °C and analysing the ultracentrifuged supernatant. P1 The LLPS concentration was then measured three ways. In the ultracentrifuge method, 150 µL of a 10 mg/mL methanolic solution was added to 15 mL buffer containing 10 µg/mL HPMC at 25 °C, the drug-rich phase was pelleted at 40,000 rpm (274,355×g) in a swinging-bucket rotor, and the supernatant was assayed. P2 In the fluorescence method, small aliquots of drug solution were added to 1 µM pyrene in buffer and the I3/I1 ratio was followed. P3 In the extinction method, a concentrated methanolic solution was pumped continuously into 10 mL stirred buffer (360 rpm, 25 °C) while scattering at 350 nm was recorded. P4 A fourth estimate came from the diffusion cell: two PermeGear chambers of 30 mL each, separated by a regenerated cellulose membrane (6–8 kDa cut-off, 30 mm diameter) at 25 °C, with flux taken as the slope of receiver concentration against time and the break point found by intersecting linear fits to the rising and flat regions. P6·R2 The materials list gives the cut-off as "6000–8000 kDa", most likely a unit misprint. X1 Felodipine values were taken from the literature. R1 Why it matters. Agreement across four physically different read-outs (scattering, probe polarity, phase removal and transport) makes the single-drug ceilings a firm baseline. C12

Contribution 2: Detecting earlier phase separation in mixtures

Problem. If a second drug lowers the amorphous solubility of the first, the drug-rich phase should appear at lower concentrations of either drug. What they did. Lopinavir, paclitaxel or felodipine was dissolved in 1 µM pyrene solution, and ritonavir was added stepwise while the pyrene I3/I1 ratio, or for felodipine its 430 nm emission, was recorded. P7 The partner was used at 10 µM in Figure 4a and at 5–20 µM in Figure 4b; because the authors consider the depression of the LLPS concentration "likely a colligative effect", they compared partners at equal molar concentration. P7·C19 The methods section gives the partner solutions as 4 µg/mL, which is not 10 µM for lopinavir or paclitaxel by the paper's own molar conversions; the figure and results values are used here. X3 In parallel, increasing amounts of lopinavir (5–30 µg/mL) were added to 5, 10, 15 and 30 µg/mL ritonavir, the mixtures were ultracentrifuged, and both drugs were measured in the supernatant; if no drug-rich phase forms, the supernatant holds everything that was added, and any shortfall marks drug that went into the pellet. P8 Some pellets were dried, dissolved in methanol and assayed, and their drug ratio matched the ratio obtained by subtraction, which closes the mass balance. R6

Contribution 3: Partitioning into an existing drug-rich phase, and an ionized control

Problem. If a drug-rich phase is already present, does a second drug added afterwards partition into it? What they did. A ritonavir drug-rich phase was formed by adding 45 µg/mL ritonavir to buffer, well above its amorphous solubility; lopinavir (4–16 µg/mL) was then added and both drugs were measured in the bulk after centrifugation. P9 To vary the amount of drug-rich phase, ritonavir was raised to 65 and 85 µg/mL with 16 µg/mL lopinavir. P9 As a negative control, diclofenac (pKa 4.2, ionized at pH 6.8) was added at 4–20 µg/mL to a 45 µg/mL ritonavir solution; because diclofenac absorbs near ritonavir's UV maximum, ritonavir was quantified against a calibration made in diclofenac solutions at the measured diclofenac concentration. M5·P9·P10 Diclofenac was also chosen because it is used as a substrate in metabolic assays, where it is ionized. C8

Contribution 4: Free concentration and flux in mixtures

Problem. Lower supernatant concentrations should mean lower thermodynamic activity, and so lower flux. What they did. The donor chamber received 30 µg/mL of each drug, as ritonavir with paclitaxel or ritonavir with lopinavir, and each drug's appearance in the receiver was followed by HPLC and compared with single-drug donors at the same concentration (Figure 8). P6·R12 The flux of each drug in the mixture was converted to a free concentration by reading it against that drug's single-drug flux curve (Figure 2), and solutions of the same composition were also ultracentrifuged to measure the free concentration directly (Table 2, n = 3). R13 A control with ritonavir and lopinavir below the LLPS concentration checked whether the drugs interact in the bulk solution. R14

Contribution 5: A prediction with no fitted parameter

Problem. If the effect is the thermodynamics of mixing, its size should be predictable from single-drug data alone. What they did. For ritonavir–lopinavir mixtures, the ritonavir mole fraction in the drug-rich phase was obtained by mass balance (amount added minus amount in the supernatant, for each drug), and the bulk concentrations of both drugs were plotted against it together with the Eq. 4 predictions built only from the single-drug amorphous solubilities (Figure 9). P12·R16 Which Table 1 column serves as the single-drug value is not stated; the plotted lines correspond to about 26 µg/mL ritonavir and about 17 µg/mL lopinavir, the ultracentrifuge values. X14·E4 As an independent check of miscibility, the melting point depression of crystalline ritonavir by lopinavir was compared with the Schröder–van Laar prediction (data not shown). P13·R17

Experimental analysis

Single drugs: a ceiling far above the crystal solubility

All drugs underwent LLPS once a certain concentration was exceeded, and the four estimates agreed within experimental error (Table A). C12·R1 Ritonavir separated at 26–28 µg/mL against a crystalline solubility of 1.7 µg/mL, lopinavir at 16–17.3 µg/mL against 2.7 µg/mL, and paclitaxel at 27.2–30.1 µg/mL against 0.32 µg/mL for its hydrate. R1 Felodipine, from the literature, separates at 5.1–6 µg/mL. R1 Table 1 attributes the felodipine values to ref 16, the Pharmaceutical Codex that the paper also cites for the diclofenac pKa, while the text cites earlier felodipine flux data to ref 13, so the source of these values is uncertain. X2

Table A. Crystalline and amorphous solubility (µg/mL; mean of three, SD in parentheses), from Table 1 of the paper. R1

The flux experiments show the ceiling as a transport limit (Figure 2). Flux rose linearly with donor concentration above the crystalline solubility and then stayed flat: about 0.21–0.22 µg/min for ritonavir from 30 µg/mL, about 0.13–0.14 µg/min for lopinavir from 20 µg/mL and about 0.25–0.27 µg/min for paclitaxel from 30 µg/mL (read from Figure 2). R2 The break points, 27.3, 16.1 and 30.1 µg/mL, fall on the LLPS concentrations. R1·C13 The authors read the linear part as rising thermodynamic activity and the plateau as constant activity once the drug-rich phase forms ("indicates"); in the discussion they say the diffusion data "clearly illustrate" that the maximum flux is limited by the amorphous solubility. C14·C34 Without HPMC, paclitaxel crystallized during the ultracentrifuge measurement, while ritonavir and lopinavir gave unchanged values, so the reported values refer to solutions with a small amount of polymer. R4·C9

Note by the AI writer (not discussed in the paper). The ratio of amorphous to crystalline solubility from Table 1 is about 15–16 for ritonavir, 6–6.4 for lopinavir and 7–8 for felodipine, but about 85–94 for paclitaxel, whose crystal solubility is that of a hydrate; paclitaxel thus falls outside the 5–50-fold range cited in the introduction. X12·R18 Supersaturation ratios are therefore not a common yardstick across these drugs; the amorphous solubility is.

A second drug lowers ritonavir's onset of phase separation

In the pyrene experiments (Figure 4a), the I3/I1 ratio of ritonavir alone stayed near 0.533–0.536 up to about 24 µg/mL and rose from about 26 µg/mL, the single-drug onset (36 µM). R7 With 10 µM lopinavir present the rise began at about 14 µg/mL ritonavir, with 10 µM paclitaxel at 10 µg/mL, and with 10 µM felodipine (followed by its own 430 nm emission) at 12 µg/mL. R7·C18 The baseline ratio near 0.53 in Figure 4a differs from the value of about 0.51 given in the methods, so the onset rather than the absolute ratio carries the information. X4 Expanding this to other partner concentrations (Figure 4b, Table B) shows the onset falling steadily as more partner is present. R8·C20

Table B. Ritonavir concentration (µg/mL) at the onset of LLPS as a function of the partner's molar concentration, read from Figure 4b (approximate). R8

Per mole, paclitaxel and felodipine lowered the ritonavir onset more than lopinavir did; the authors write that ritonavir with paclitaxel or felodipine "appears" to undergo LLPS most readily. R8·C20 They describe the lowering as "likely a colligative effect" and compare the partners at equal molar concentration for that reason. C19 Note by the AI writer (not discussed in the paper): at equal molar concentration the three partners do not give the same onset (at 10 µM about 14, 12 and 10 µg/mL ritonavir for lopinavir, felodipine and paclitaxel), so partner molarity alone does not set the effect; the paper does not analyse why, and the colligative explanation was not tested. R8·C19

The ultracentrifuge experiments with ritonavir and lopinavir (Figure 3, Table C) show the same effect in a direct concentration measurement. With 5 µg/mL ritonavir, all added lopinavir stayed in solution up to 10 µg/mL; beyond about 15 µg/mL the lopinavir in the supernatant levelled off at about 15 µg/mL, below its single-drug ceiling of 16–17.3 µg/mL, and ritonavir fell from about 5 to about 3.2 µg/mL. R5·C15 As the initial ritonavir rose, less lopinavir was needed before both drugs were depleted; at 30 µg/mL ritonavir both drugs were depleted from the first lopinavir addition. R5·C17 In every case the drug-rich phase formed at lower concentrations than for either drug alone, which the authors read as a single drug-rich phase containing both drugs ("consistent with"). C15·C17

Table C. Supernatant concentrations (µg/mL) of lopinavir (LPV) and ritonavir (RTV) after ultracentrifugation, read from Figure 3 (approximate; no error bars are shown). R5

Lopinavir partitions into a ritonavir drug-rich phase; ionized diclofenac does not

When lopinavir was added to a solution that already contained a ritonavir drug-rich phase (45 µg/mL ritonavir), only about a third stayed in the bulk solution: about 1.4, 2.8, 4.2 and 5.3 µg/mL for 4, 8, 12 and 16 µg/mL added (read from Figure 5). R9·C22 Bulk ritonavir fell at the same time, from about 23.6 to about 19.8 µg/mL. R9 Raising ritonavir to 65 and 85 µg/mL, which makes more drug-rich phase, lowered bulk lopinavir further, to about 4.15 and 3.4 µg/mL of the 16 µg/mL added, while bulk ritonavir rose to about 20.6 and 23.0 µg/mL (Figure 6). R10 The text describes this as a fall "from about 1/3 to 1/4" of the added lopinavir; the plotted values give about 0.33 and 0.21. C23·X13 The authors take this as confirmation that more drug-rich phase takes up a larger share of a second lipophilic solute. C23

Diclofenac behaved differently (Figure 7). Added at 4–20 µg/mL to the same 45 µg/mL ritonavir solution, it was recovered in full (about 4.5 to 20.2 µg/mL), and bulk ritonavir stayed at about 25.1–25.7 µg/mL. R11·C25 The authors explain this by the ionic charge of the diclofenac anion, which makes mixing with the hydrophobic ritonavir-rich phase energetically unfavourable ("readily explained"). C44

The authors summarise the partitioning in a schematic (Figure 10): lopinavir added to a pre-existing ritonavir-rich phase mixes preferentially into it rather than staying in water, and, because mixing with lopinavir lowers ritonavir's own amorphous solubility, bulk ritonavir falls too; adding more ritonavir raises its mole fraction in the droplets and lets bulk ritonavir climb back. C42·R10

The authors' reasoning for the two cases (Figures 5, 7 and 10; Eqs. 2–4). C42·C44·C45

Free concentration and flux fall for both drugs

In the diffusion cell, each drug reached the receiver more slowly from a 30 + 30 µg/mL mixture than from its single-drug donor at the same concentration (Figure 8). At 75 min the receiver held about 0.24 µg/mL ritonavir from the ritonavir–paclitaxel mixture against about 0.48 µg/mL from ritonavir alone, and about 0.33 against 0.49 µg/mL for paclitaxel; in the ritonavir–lopinavir system the values were about 0.26 against 0.48 µg/mL for ritonavir and about 0.21 against 0.41 µg/mL for lopinavir (read from Figure 8). R12·C26 The text assigns the two panels of Figure 8 in the opposite order to the caption; the caption is followed here. X5

Table D. Free drug concentration (µg/mL; SD in parentheses, n = 3) in mixtures of 30 µg/mL of each drug, from Table 2; the last column is added from Table 1 for comparison and is not part of Table 2. R13·R1

The two independent estimates of free concentration agree within error (Table D), which the authors take as evidence that the presence of two solutes at drug-rich-phase-forming concentrations reduces the thermodynamic activity of both ("Clearly"). R13·C27·C28 They summarise ritonavir as reduced "to just a third of the added concentration" with paclitaxel and "a little less than half" with lopinavir, and paclitaxel and lopinavir by "a factor of around two". C28 These statements use different reference points: the ritonavir figures are relative to the 30 µg/mL added, whereas the factor of two for lopinavir holds against its own amorphous solubility (8.5 against 16.1–17.3 µg/mL), not against the 30 µg/mL added. X8 Measured against each drug's own single-drug ceiling (an arithmetic comparison by the AI writer, not made in the paper), the drop is about two-fold for paclitaxel, lopinavir and ritonavir with lopinavir, and nearly three-fold for ritonavir with paclitaxel. R13·R1 The paper describes paclitaxel at 30 µg/mL as "close to, but just below" its LLPS concentration, although three of the four Table 1 values are below 30 µg/mL. C26·X7 A control with ritonavir and lopinavir below the LLPS concentration diffused at the single-drug rates (data not shown), which the authors take to exclude interactions in the bulk solution; the methods describe this control as 30 µg/mL ritonavir with 12 µg/mL lopinavir, a composition at which Figure 3 already shows phase separation, so its exact composition is uncertain. R14·C29·X6

Note by the AI writer (not discussed in the paper). The ritonavir curves in the two mixtures of Figure 8 are close to each other (about 0.24 and 0.26 µg/mL at 75 min), whereas Table 2 gives free ritonavir of 9.3 and 13.2 µg/mL from flux. X10 The number of replicates behind Figure 8 is not stated; Table 2, with n = 3, is the better basis for the free concentrations.

Ideal mixing describes the ritonavir–lopinavir data, roughly

Figure 9 plots the bulk concentrations of both drugs against the ritonavir mole fraction in the drug-rich phase, computed by mass balance, together with the Eq. 4 lines from the single-drug amorphous solubilities. R16·E4 The 34 ritonavir and 32 lopinavir points span mole fractions of about 0.06 to 0.70; bulk ritonavir rises from about 3.0 to about 21.4 µg/mL and bulk lopinavir falls from about 15.2–15.6 to about 4.6–4.7 µg/mL (read from Figure 9). R16 The authors find "good agreement" with the predicted values and conclude that ritonavir and lopinavir are miscible as amorphous materials in an aqueous environment and mix "nearly ideally". C40 The melting point depression of crystalline ritonavir by lopinavir, larger than the Schröder–van Laar prediction, is offered as confirmation of their tendency to mix (data not shown). R17·C41 They add that the near-ideal behaviour "can perhaps be anticipated" from the structural similarity of the two drugs, and that other pairs "are likely" to behave more non-ideally, up to immiscibility. C43

Note by the AI writer (not discussed in the paper). Read point by point, most ritonavir points lie about 2–4 µg/mL above the ideal line (for example about 19.1 µg/mL at a mole fraction of about 0.56, where the line gives about 14.7), and lopinavir points lie below the line at mid-range (about 7.9–8.7 µg/mL at mole fractions of about 0.37–0.47, against about 9.1–10.8). R16·X9 No fit statistic is given. A check with the Table 2 ultracentrifuge values for the 30 + 30 µg/mL mixture, using molar masses implied by the paper's own µM conversions, gives a ritonavir mole fraction of about 0.41 and predicted bulk concentrations of about 10.8 µg/mL ritonavir and 10.1 µg/mL lopinavir, against 13.3 and 9.1 µg/mL measured: the same pattern. X9·R13 Ideal mixing is a useful first approximation for this pair, with ritonavir systematically above it.

Droplet size

Dynamic light scattering of selected solutions gave a drug-rich phase of about 360 nm for 30 µg/mL ritonavir, a similar 370 nm after adding 5 µg/mL lopinavir, and a somewhat smaller size of about 225 nm for 15 µg/mL ritonavir with 9 µg/mL lopinavir, each slightly above half of its single-drug LLPS concentration. R15·C30 This size is within the 50–500 nm initially reported for such phases and underlies the assumption that the droplets are too large to raise the solubility appreciably. R18·C38 The paper gives no instrument or settings for these measurements. P11

Discussion

What the paper establishes. The central result is that the maximum free concentration a poorly soluble drug can reach in water, its amorphous solubility, is not a fixed property of the drug once a second, miscible drug is present. C50 The authors put it strongly in the discussion: they have "clearly demonstrated" that the thermodynamic activity of a drug in a highly supersaturated solution is considerably reduced by a second solute, particularly when that solute is also highly supersaturated, and that a drug-rich phase formed by one component "has the potential to" affect the free concentration of a second solute. C32 They describe the observation that the maximum flux of a compound falls in the presence of a second component as new, and say it "suggests" that the amorphous solubility of that compound is reduced, which conventional thermodynamics explains (refs 26–28). C35 In the conclusions the reduction is said to be "highly dependent" on the drug's mole fraction in the drug-rich phase, and membrane transport is "dramatically reduced". C50 The abstract adds that "a simple thermodynamic model could be used to predict" these changes; in the paper this was tested for the ritonavir–lopinavir pair. C51·R16

Where it applies. The authors place the result in several settings. For fixed-dose combinations and co-amorphous formulations, co-formulating two or more amorphous drugs "would be expected" to reduce the amorphous solubility of each and so the achievable supersaturation and membrane transport; a similar reduction had been reported for a ritonavir–darunavir ASD without an explanation (Nguyen and Van den Mooter 2014, ref 31). C45·C46·R19 They see particular relevance for HIV and hepatitis C antivirals, which are very poorly soluble and often formulated or dosed with other compounds, and write that "more attention needs to be paid to this phenomenon" because of its "potential implications" for bioavailability, precipitation and crystallization. C47 The same applies to drugs given separately at the same time that supersaturate in the gut, from ASDs, weakly basic drugs and their salts, or lipid formulations (refs 19–23). C31 For in vitro metabolic assays, a drug-rich phase of a neutral test compound "would be expected" to lower the free concentration of the test substance and of miscible unionized substrates, "potentially" causing false positives in inhibition assays; ionized substrates such as diclofenac would be spared, as Figure 7 suggests. C48·R11 Finally, they warn of analytical artefacts: drug in nanosized droplets "may" absorb UV light and inflate the apparent dissolved concentration, and turbidity from the drug-rich phase "may be mistaken" for crystallization. C49

What remains open. None of these settings was tested directly: all solutions were made by adding methanolic stock solutions to buffer, and no co-amorphous or two-drug ASD was dissolved. C52·P2 The authors themselves expect other drug pairs to mix less ideally, up to immiscibility, which would weaken the effect; only an ionized partner was examined as the extreme case. C43·C25 The colligative reading of the lower onset was stated as "likely" but not tested. C19

Note by the AI writer (not discussed in the paper). For a formulator, Eq. 4 turns the result into a simple rule of thumb for two drugs that both supersaturate and mix: each drug's free-concentration ceiling is roughly its own amorphous solubility times its mole fraction in the shared drug-rich phase. E4·R16 The drug present in the smaller molar amount loses most, so the dose ratio of a combination matters as much as the choice of partners. A booster dosed above its own amorphous solubility, as ritonavir is, can act as a sink for a co-dosed lipophilic drug, while a partner that is ionized at the relevant pH is protected. R9·R11 A cheap first screen is whether the two drugs mix in the amorphous state, for example by melting point depression, as the authors did for ritonavir and lopinavir. R17 The drug-rich phase may also act as a reservoir that replenishes free drug as it is absorbed; this paper measured free concentration and flux across a dialysis membrane, not absorption.

Limitations

Limits the authors state. The ideal-mixing analysis rests on four stated assumptions: constant aqueous activity coefficients, no size effect of the roughly 350 nm droplets on solubility ("a reasonable assumption"), equal water content in single and mixed drug-rich phases, and the use of single-drug amorphous solubilities as reference values. C38 The authors note that the ritonavir–lopinavir pair "appears" to form a fairly ideal solution, and that other combinations "are likely" to behave more non-ideally. C43 Their implications for formulations, metabolic assays and bioavailability are framed with "would be expected", "potentially" and "potential implications". C45·C47·C48

The AI writer's own judgement.

• The central measurement is well supported: free concentrations from flux and from ultracentrifugation agree within error (n = 3), and the lowered onset appears in fluorescence and in ultracentrifugation. R13·R7·R5
• The model test is limited to one structurally similar pair, gives no fit statistic, and ritonavir runs systematically above the ideal line. X9·X14
• Most data are read from plots, and replicates are not stated for Figures 2–9; Figure 3 has no error bars. R5·R12
• Some conditions are reported inconsistently: the partner concentration in the fluorescence runs (4 µg/mL in the methods, 10 µM in the results), the composition of the below-LLPS control, the membrane cut-off and the assignment of the Figure 8 panels. X3·X6·X1·X5
• HPMC presence, time from mixing to centrifugation and centrifugation time are not stated for the fluorescence, extinction and binary ultracentrifuge experiments, although Figure 9 treats the supernatants as in equilibrium with the drug-rich phase. X11
• The reductions are stated against different baselines, and paclitaxel at 30 µg/mL sits at, not below, its LLPS concentration. X8·X7
• Only one buffer at pH 6.8 and one temperature (25 °C where stated) were used, without bile salts or other biorelevant components. M8·P6

Conclusion

This paper extends the idea of an amorphous solubility ceiling from one drug to two. Each drug alone has a ceiling that four methods agree on and that caps its membrane flux. R1·R2 A second unionized drug lowers that ceiling: ritonavir separates at about 10–14 µg/mL instead of about 26 µg/mL when 10 µM of a partner is present, lopinavir is drawn into an existing ritonavir drug-rich phase, and in 30 + 30 µg/mL mixtures the free concentration and flux of each drug fall to roughly a third to a half of its single-drug value. R7·R9·R13 An ionized drug, diclofenac, does not mix and is unaffected. R11 For ritonavir and lopinavir, the bulk concentrations follow, approximately, the ideal-mixing relation in which each drug's ceiling is its single-drug amorphous solubility times its mole fraction in the shared drug-rich phase. R16·E4 The authors draw implications for co-amorphous and fixed-dose combination products, co-dosed antivirals and in vitro metabolic assays, which this study did not test. C45·C47·C48·C52