Solubilized or supersaturated? How surfactants, proteins and FaSSIF change the driving force for membrane transport

Background and motivation

Many new drug candidates are poorly soluble in water, and their oral absorption is limited by solubility. Enabling formulations raise the dissolved concentration in the gut by two different routes. Amorphous solid dispersions (ASDs), lipid-based systems after digestion, salts and weakly basic drugs moving from stomach to intestine can produce supersaturated solutions, in which the dissolved drug exceeds its crystalline solubility. Surfactants, cyclodextrins, proteins, co-solvents and the bile-salt micelles of intestinal fluid raise the concentration differently: they solubilize the drug by taking it into micelles or complexes, which raises the equilibrium solubility itself (Introduction, refs 1–7, 11, 14). C7·C8

The two routes look the same if one only measures total concentration, but they are thermodynamically different. In a supersaturated solution the chemical potential, or thermodynamic activity, of the solute is above that of a saturated solution. In a solubilized solution at or below its new equilibrium solubility, the activity is at best that of a saturated solution. Passive diffusion across a membrane is driven by activity, not by concentration (Higuchi 1960, ref 15). Earlier work therefore found that supersaturation stabilised by small amounts of polymer increases membrane transport (Corrigan 1980, ref 8; Davis 1991, ref 9; Pellett 1994, ref 10; Frank 2012, ref 11; Kumprakob 2005, ref 12; Santos 2011, ref 13), whereas solubilizers can leave flux unchanged or lower it, an effect often misread as lower permeability. Surfactants such as dioctyl sodium sulfosuccinate and poloxalene even reduced the absorption of phenolsulfonphthalein in rats (Malik 1975, ref 16). C7·C8

Supersaturation has an upper limit. At very high supersaturation a non-crystalline drug-rich phase forms (refs 17–19); it is often seen when ASDs dissolve (refs 20–26), and it arises by liquid–liquid phase separation (LLPS) once the concentration reaches about the amorphous solubility (Ilevbare and Taylor 2013, ref 21; refs 11, 12, 27). After LLPS the drug-lean continuous phase holds the amorphous solubility, and the drug-rich nanodroplets may act as a reservoir; LLPS has been suggested to be "likely to be beneficial" for oral delivery (refs 17, 27). C9 In the group's previous study with the same diffusion cell (Raina 2014, ref 27), the flux of felodipine and nifedipine rose linearly with concentration and levelled off at the LLPS onset: once a second phase exists, the solute chemical potential is the same in both phases and cannot rise further, so adding drug only adds drug-rich phase. That study defined a maximum achievable flux in buffer. C10·R14

Real formulations mix both routes: a surfactant may be included in an ASD, and a lipid formulation may become supersaturated after digestion. Polymers at low concentration generally do not raise crystalline solubility but inhibit nucleation and crystal growth (refs 5, 28–36), while surfactants and complexing agents typically do raise solubility. C11 The authors state that the effect of solubilizing additives on LLPS and on the maximum flux had not been investigated. They therefore set out to examine how crystalline solubility, thermodynamic activity, supersaturation and passive diffusion interact when solubilizers are present, using felodipine and nifedipine as model drugs, four surfactants, two complexing agents and the biorelevant medium FaSSIF (Introduction, PDF p.3).

Background concepts

Flux is set by activity. The paper describes transport across the membrane of the diffusion cell with Eq. 3 (refs 15, 42):

Here $J$ is the flux, the mass $M$ of drug crossing the membrane per unit time $t$ (reported in μg/min); $D$ is the diffusion coefficient, $S$ the membrane area (7.065 cm² in this cell), $a$ the solute activity in the donor, ${\gamma }_m$ the activity coefficient of the drug in the membrane and $h$ the membrane thickness. In plain terms: with the cell and membrane fixed, the flux is directly proportional to the activity of the drug in the donor solution. E3·C14·P7 The activity itself is given by Eq. 4:

where $C$ is the drug concentration and $\gamma$ its activity coefficient in the donor solution. In plain terms: two solutions with the same concentration need not have the same activity, because anything that binds the drug changes $\gamma$. E4 After Eq. 4 the text lists "D, S, γ and h" as the constants; from Eq. 3 and the preceding sentence the constant meant is ${\gamma }_m$, since $\gamma$ in the donor is exactly what the additives change. X8

Supersaturation, defined properly and approximately. The supersaturation ratio $S$ is defined in the Discussion by chemical potentials (Eq. 5, ref 44):

Here $\mu$ is the solute chemical potential, $R$ the gas constant, $T$ the temperature, $c$ the concentration and the asterisk marks the property of a solution saturated with the crystal. In plain terms: supersaturation is the activity of the drug relative to its activity in a saturated solution. For dilute solutions one may assume $\gamma /{\gamma }^{*}\approx 1$, which gives the familiar concentration ratio (Eq. 6): E5·C32

In plain terms: supersaturation is estimated as the dissolved concentration divided by the crystalline solubility measured in the same medium. This is the common practice in the pharmaceutical literature, including in micellar media such as FaSSIF, and it is the assumption the paper puts to the test. Because flux is proportional to activity, flux is also proportional to the true supersaturation, so a plot of flux against c/c* should be a single straight line if Eq. 6 holds. E6·C32·C35

Amorphous solubility and LLPS. The highest supersaturation a solution can sustain before LLPS corresponds to the amorphous solubility ${\sigma }_a$. The paper estimates it from the crystalline solubility ${\sigma }_c$ with the Hoffman approximation for the free energy difference between the supercooled liquid and the crystal (Eq. 1):

where $\Delta G$ is the free energy difference between amorphous and crystalline drug, $\Delta H_f$ the enthalpy of fusion, $T_m$ the melting point, $T$ the temperature of interest and $\Delta T=T_m-T$. Because the amorphous drug takes up water, which lowers its activity, the estimate is corrected with the approach of Murdande and co-workers (ref 41), giving Eq. 2:

In plain terms: the amorphous solubility advantage is the exponential of the free energy gap between amorphous and crystalline drug, reduced by a term $-I(a_2)$ for absorbed water. No ionization term is needed because both drugs have pKa below 2. The melting data and sorption data that feed these equations are not printed. E1·E2·C12·M1·M2 Experimentally, the paper takes the LLPS onset measured by UV extinction as the amorphous solubility, and the ratio σa/σc as the LLPS onset divided by the crystalline solubility measured in the same medium. E8·C13

Micelles and complexes. Surfactants form micelles above their critical micelle concentration (CMC); drug that enters micelles raises the total concentration but not the free, molecularly dissolved drug. Complexing agents such as BSA and β-cyclodextrin bind drug. For BSA the paper uses a single-site binding relation (Eq. 7), valid when the drug is in molar excess over the protein (the 0.1% BSA case):

Here $f$ is the fraction of protein that carries drug, $K_d$ the dissociation constant of the complex and [API] the molar drug concentration. In plain terms: as the drug concentration rises, the protein fills up; once it is nearly saturated, further drug stays free. No value of $K_d$ is given. E7·C40

Methods in detail

The study combines three measurements made in matching media at 37 °C in 50 mM phosphate buffer, pH 6.8 (ionic strength 0.155 M): the equilibrium crystalline solubility, the LLPS onset and the flux across a membrane. HPMC (Pharmacoat 606) was dissolved in every medium to slow crystallization, at 100 μg/mL with felodipine and 1 mg/mL with nifedipine. M3·M4·A1

Model drugs and additives

Felodipine (MW 384 g/mol, log P 4.81) and nifedipine (MW 346 g/mol, log P 2.91) are dihydropyridines with pKa below 2, so they are un-ionized at pH 6.8 (Figure 1; values cited from refs 37–39). M1·M2 The additives were four non-ionic surfactants, Cremophor RH40, Cremophor EL, Vit E TPGS (all Kolliphor grades from BASF) and Tween 20, and two complexing agents, BSA and β-cyclodextrin (Sigma-Aldrich). FaSSIF was made from ready-to-use SIF powder in pH 6.8 buffer; its composition and amount are not printed. M5·M6·M7·M8·M9·M10·M11 Each additive was used at three levels, C1, C2 and C3 (Table I). For the surfactants C1 lay below the CMC and C2, C3 above it: Cremophor EL CMC 0.01% (levels 0.001, 0.02, 0.1%), Cremophor RH40 0.03% (0.01, 0.05, 0.1%), Tween 20 0.009% (0.001, 0.02, 0.1%), Vit E TPGS 0.02% (0.004, 0.04, 0.1%). BSA and β-cyclodextrin were used at 0.001, 0.1 and 1%, chosen so that C1 gave little solubility change and C2, C3 a clear one. The source of the CMC values is not stated. A2

Solubility and estimated amorphous solubility

Excess crystalline drug was shaken for 48 h at 37 °C in 20 mL vials in buffer, in buffer with HPMC (100 μg/mL and 1 mg/mL), in buffer with HPMC plus each additive at C1–C3 and, for felodipine, in FaSSIF. Solids were removed by ultracentrifugation (40,000 rpm, 274,356 × g, 15 min), and the supernatant was diluted 2-fold and assayed by HPLC (Synergi Polar-RP column, acetonitrile:water with 0.1% TFA 70:30, 1 mL/min, 40 °C, 360 nm, standards 0.1–50 μg/mL with R² > 0.998); n = 3. P1·P2 Melting point and enthalpy of fusion were measured by DSC (TA Q2000, 10 °C/min), and the water sorption of the amorphous drugs by a gravimetric analyser from 5 to 95% RH; with these, Eqs. 1 and 2 gave the estimated amorphous solubility. For FaSSIF the authors assumed that its components do not change σa/σc. P3·P4·P5·C17

LLPS onset by UV extinction

A 20 mg/mL methanol stock was pumped into a stirred 20 mL vial of medium at 37 °C, at 20 μL/min (felodipine) or 40 μL/min (nifedipine), and the extinction at 455 nm, where neither drug nor FaSSIF absorbs, was recorded every 10 s. A sharp rise in extinction marks a new scattering phase, taken as the LLPS onset and hence as the amorphous solubility. HPMC was 100 μg/mL (felodipine) or 1 mg/mL (nifedipine) in buffer, and 1 mg/mL in the presence of surfactants or FaSSIF. Stirring was 120–300 rpm; nifedipine crystallized at the higher rates, so slower stirring was used for it. P6·C13·R15 The amorphous-to-crystalline solubility ratio was then calculated as the LLPS onset divided by the crystalline solubility in the same medium. E8 The methods and results write this ratio as σc/σa, while Table V and the calculation use σa/σc; the latter is meant. X3

Flux in the side-by-side diffusion cell

The diffusion cell (PermeGear; Figure 2) has a donor and a receiver of 30 mL each, separated by a regenerated cellulose membrane (MWCO 6–8 kDa) over an orifice of 30 mm diameter (7.065 cm²), held at 37 °C and stirred at about 300 rpm. HPMC and any additive were pre-dissolved in the donor, and drug was added as a methanol stock of 10, 20 or 30 mg/mL, with less than 300 μL methanol per 30 mL. Aliquots of 200 μL were taken from both compartments and assayed by HPLC; the receiver was kept below one-third of the crystalline solubility (sink conditions). The flux is the slope of the linear part of the amount transported versus time. P7·M13 For suspensions, about 500 mg crystalline felodipine was equilibrated overnight with 30 mL buffer (16.7 mg/mL), with or without Vit E TPGS, and the whole suspension was placed in the donor. P8 The paper does not state how many replicate flux runs were made or what the error bars show. X12

How the data were analysed

Three comparisons carry the argument. First, flux at a fixed drug concentration (felodipine 50 μg/mL, nifedipine 100 μg/mL, both above their LLPS onsets in buffer) across additive levels, set against the solubility at the same levels. R7·R8·R2·R3 Second, flux against total felodipine concentration in buffer, 0.04% Vit E TPGS and FaSSIF, set against the LLPS onset measured in each medium. R9·R10·R11 Third, flux against c/c* (Eq. 6) for the same three media, and, for BSA, the supersaturation from Eq. 6 against the supersaturation implied by the flux. R12·R13·E9 The logic of the third comparison is simple: if c/c* measured the true supersaturation, all solutions with the same c/c* would give the same flux, whatever the medium. C35

Experimental analysis

1. A suspension shows that flux follows activity, not concentration

The cleanest experiment of the paper uses crystalline suspensions (Figure 3). In a suspension the dissolved drug is in equilibrium with the crystal, so its activity equals that of the crystal whatever the medium, and $S=C/C^{*}=1$. C20 A felodipine suspension in buffer held about 1 μg/mL dissolved drug; the same suspension with 0.04% Vit E TPGS held about 40 μg/mL. Yet both gave a flux of only about 0.009 and about 0.006 μg/min, the same as a saturated 1 μg/mL solution (about 0.006 μg/min). A 100 μg/mL felodipine solution, above the LLPS point, gave about 0.14 μg/min (all read from Figure 3, approximate). R4 The authors read the fluxes as equal "within experimental error", which they note is large at these low concentrations, and conclude that these experiments "clearly show" that flux is controlled by solute activity rather than concentration. C21·C22·C23 The error bars of the three low fluxes are about ±0.01 μg/min, as large as the values themselves, so this comparison establishes equality only within a wide band. X12

The 100 μg/mL solution serves as the second reference point. In buffer, felodipine solutions above about 9 μg/mL split into two phases, all with the same activity, and so give the same, maximum flux. C24·R14

2. The additives raise crystalline solubility; HPMC does not

HPMC alone did not solubilize either drug: felodipine 1.2 ± 0.0 μg/mL without and 1.1 ± 0.0 μg/mL with 100 μg/mL HPMC; nifedipine 10.0 ± 0.0 and 10.3 ± 0.0 μg/mL with 1 mg/mL HPMC (Table II). In FaSSIF, felodipine reached 40.8 ± 5.0 μg/mL without and 42.8 ± 7.0 μg/mL with HPMC, an increase the authors describe as "approximately 40-fold". R1·C15·C16 Table A collects the solubilities with the six additives.

Table A. Equilibrium crystalline solubility (μg/mL, mean ± SD, n = 3) in pH 6.8 buffer with HPMC at 37 °C; buffer alone with HPMC gives 1.1 (felodipine) and 10.3 μg/mL (nifedipine) (from Tables II–IV). R1·R2·R3

Three features stand out. At C2 and C3 all six additives raised solubility to similar values: felodipine 35.3–39.3 and 45.2–49.0 μg/mL, nifedipine 53.4–60.9 and 78.8–90.7 μg/mL. The standard deviations are large, up to 13.6 μg/mL for felodipine and 20.5 μg/mL for nifedipine. And the C1 levels behave differently for the two drugs: for felodipine they gave 0.6–0.9 μg/mL, not above buffer, but for nifedipine 16.3–22.0 μg/mL, about 1.6–2.1 times the buffer value, although the table footnote describes C1 as giving minimal change. R2·R3·X6 The authors summarise that higher additive concentrations gave higher solubility overall. C19

3. At a fixed concentration, solubilizing levels cut the flux

Figure 4 shows the raw data for the Vit E TPGS series with felodipine. The donor concentration stayed at about 10 μg/mL (neat 10 μg/mL) and about 49–52 μg/mL (all 50 μg/mL runs) over 40 min. In the receiver, the curves of the neat 10 and 50 μg/mL solutions and of 50 μg/mL with 0.004% Vit E TPGS overlapped, rising from about 0.07–0.08 to about 0.25–0.27 μg/mL; with 0.04% they rose only to about 0.13 μg/mL, and with 0.1% to about 0.08 μg/mL (read from Figure 4, approximate). R5·R6 The 0.004% level is below the CMC of Vit E TPGS (0.02%) and did not raise felodipine solubility; 0.04% and 0.1% are above the CMC and raised it to 39.3 and 48.2 μg/mL. A2·R2·C25 Figure 5 extends this to all six additives (Table B).

Table B. Flux (μg/min) of felodipine at 50 μg/mL and nifedipine at 100 μg/mL in the donor, with each additive at C1–C3, 37 °C; all values about, read from Figure 5. R7·R8

At C1 the flux of both drugs stayed at the buffer level; at C2 and C3 it fell, for felodipine to as little as about 0.010 μg/min (Cremophor EL, C3) and for nifedipine to about 0.15 μg/min (Tween 20, C3). The authors' summary: "In general", additives at levels where the equilibrium solubility is increased "lead to a large reduction in diffusive flux", while at levels with little or no solubility enhancement the flux remains at the maximum of the phase-separated solutions. R7·R8·C26·C1 The data also contain a detail the authors do not discuss: at C2 the six additives gave similar felodipine solubilities (35.3–39.3 μg/mL) but fluxes ranging from about 0.051 to about 0.12 μg/min, with the complexing agents (BSA about 0.096, β-cyclodextrin about 0.12) above the surfactants (about 0.051–0.063). R2·R7 Note by the AI writer (not discussed in the paper): for nifedipine, the C1 levels already raised solubility 1.6–2.1-fold without any loss of flux; with 100 μg/mL in the donor, the solution may still have been above the LLPS onset of these mildly solubilizing media, but the paper does not measure those onsets. X6

4. Adding more drug brings the maximum flux back

The key question is whether the lost flux is lost for good. For felodipine in 0.04% Vit E TPGS and in FaSSIF, the authors raised the donor concentration step by step (Figure 6, Table C).

Table C. Felodipine flux (μg/min) versus donor concentration at 37 °C; all values about, read from Figure 6 (the same points appear in Figure 7a). The reference band, ±1 SD of neat felodipine at 50 μg/mL in buffer, runs from about 0.109 to about 0.154 μg/min. R9

With Vit E TPGS, flux rose slightly from 50 to 100 μg/mL, stayed just below the buffer band at 150 μg/mL and entered it at 175 μg/mL; between 175 and 350 μg/mL it "appears to have reached a plateau". The authors stress that the same maximum flux as in buffer was observed, "but only at higher felodipine concentrations where LLPS had occurred". R9·C27 In FaSSIF the recovery was slower: some recovery at 100 μg/mL, more at higher concentrations, and from 250 μg/mL a flux that approaches a constant comparable to the buffer maximum. In buffer, 50 and 100 μg/mL felodipine gave the same flux (about 0.143 and 0.150 μg/min, Figure 7a), both being above the LLPS point. R9·R10·C28 The authors generalise this: the maximum membrane transport rate "can still be achieved" with solubilizing additives once the total concentration exceeds the LLPS concentration. This was shown for felodipine in two media; the other additives and nifedipine were tested at one donor concentration only. C2·X10

5. Solubilizers raise the LLPS onset, but less than the solubility

The plateau should start where LLPS starts in each medium. Independent UV extinction measurements gave the LLPS onsets in Table D.

Table D. Felodipine solubility, estimated amorphous solubility and measured LLPS onset at 37 °C, all with HPMC (from Tables II and V; n = 3, ± one SD). Nifedipine in buffer: crystalline solubility 10.3 ± 0.0, estimate 72.9 ± 6.0, LLPS onset 71.2 ± 6.0 μg/mL. R1·R11

The LLPS onsets of 177 and 215 μg/mL are, in the authors' words, "in good agreement with the concentrations where the flux approaches a plateau". C42·R9·R11 In buffer the measured onsets matched the estimates from Eqs. 1 and 2 for both drugs (felodipine 10.4 against 8.7, nifedipine 71.2 against 72.9 μg/mL), but in FaSSIF the measured onset of 214.6 μg/mL was "substantially lower" than the estimate of 308.0 μg/mL, which had assumed the buffer ratio. R1·C17·C18 So the amorphous-to-crystalline ratio did not stay constant: although the crystalline solubility rose almost 40-fold, σa/σc fell from 9.2 in buffer to 4.5 with 0.04% Vit E TPGS and 5.0 in FaSSIF. R11·C29 Two inconsistencies in the paper concern the buffer value. The text gives the buffer LLPS onset as 8.7 μg/mL in one place (the estimated value) and as about 9 μg/mL in others, while both tables print 10.4; and 10.4/1.1 gives 9.45, not the printed 9.2, which would require an unrounded crystalline solubility of about 1.13 μg/mL. Neither changes the halving of the ratio. X1·X2

6. The concentration ratio c/c* does not predict the flux

Figure 7b replots the flux of the three felodipine series against c/c*. If Eq. 6 were valid, all points would lie on one line. They do not. At c/c* of about 4.1–4.5, neat felodipine gave about 0.052 μg/min, FaSSIF solutions about 0.085 μg/min and Vit E TPGS solutions about 0.138 μg/min; neat felodipine reached about 0.127 μg/min only at c/c* about 8.3 (read from Figure 7b, approximate). R12 The authors conclude that this "points to a breakdown in the validity of the assumption inherent to Eq. 6" and indicates that c/c* is not S. C36 The c* values behind Figure 7b are not stated; the point positions correspond to 1.2, 39.3 and 40.8 μg/mL, partly the values without HPMC, which shifts the points by less than 10% and does not change the picture. X4

The BSA data make the same point with numbers in the text. With 0.1% and 1% BSA, felodipine solubility rose by factors of around 35 and about 42. For a 50 μg/mL solution, Eq. 6 then gives S of about 1.3 and 1.1, which would predict a flux close to that of a saturated solution. R13·E6 The measured fluxes (about 0.096 and 0.055 μg/min, Figure 5) were reduced but "considerably higher" than that of a saturated solution, and correspond to S of 7.3 and 4.2 when referred to the flux data of felodipine in buffer. The authors conclude that the true supersaturation, determined from flux, is "again much higher" than Eq. 6 predicts. R7·R13·C39 The paper does not say how the reference was applied. With the saturated-solution flux of Figure 3 (about 0.006 μg/min) the ratios would be about 16 and 9; the printed values match a reference of about 0.013 μg/min per unit of S, close to the slope of neat felodipine flux against c/c* in Figure 7b. Either way, the flux-based S is far above the Eq. 6 values. X5 The authors extend the conclusion to β-cyclodextrin ("suggests"), for which only solubility and flux are given, not computed S values. C41·X13

Discussion

The authors' chain of reasoning

The Discussion ties the results together with one thermodynamic picture. The amount of free drug, which corresponds to the solute activity, rather than the total concentration drives flux (Eq. 3); drug inside micelles raises the solubility and the achievable concentration but not the free drug available to partition into the membrane. C30·C14 A solution saturated with the crystal has its activity fixed by the crystal, so its activity stays at unity however much a solubilizer raises its concentration. C20·C46 From there the outcome depends on where the total drug concentration sits relative to the LLPS onset of the medium:

In the authors' words, a solubilizing excipient reduces the supersaturation "by a factor that depends on the magnitude of the solubilizing effect", so the supersaturation is "consumed" and the total concentration must be raised to reach the same flux. C33 By substantially increasing the drug concentration, "the supersaturation is restored to a maximum value". C42 They draw the practical consequence that this "clearly needs to be taken into account when designing formulations". C34

Why the concentration ratio fails

For Eq. 6 to be right, the relative speciation must be the same in the supersaturated and in the saturated solution: if half the drug sits in micelles at saturation, half should sit in micelles at supersaturation too. C35 The data of Figure 7b say otherwise, and the authors offer two explanations, both hedged and neither measured. For surfactants, the micelles "most likely" have a variable capacity that depends on how many drug molecules they already hold: at a fixed micelle fraction they solubilize a smaller fraction of drug as the drug concentration rises, so the free fraction grows faster than c/c* implies. In a two-phase model of micellar solubilization this would appear as a surfactant:water partition coefficient that falls with drug concentration. C37 For BSA, Eq. 7 says that the protein fills up as drug is added; once its finite binding sites are nearly saturated, further drug stays free, so estimating S with Eq. 6 is "clearly a gross oversimplification". C40·E7 Both mechanisms predict that c/c* under-estimates the true supersaturation, which is what the flux shows. C41·C43 No free fraction, micelle partition coefficient or binding constant was measured, so these remain explanations of the data rather than results. C37·C40

The phase picture of Figure 8

Figure 8 summarises the thermodynamics for a hypothetical drug with a crystalline solubility of 1 μg/mL and an amorphous solubility of 10 μg/mL in buffer. In buffer (Figure 8a) the region between the two is a single supersaturated phase, and above the amorphous solubility LLPS or crystallization follows; for slowly crystallizing systems, as here where the polymer impedes crystallization, LLPS is typically seen. C47 With a solubilizer (Figure 8b) the crystalline solubility rises, here 50-fold, yet a saturated solution still has unit activity; LLPS occurs at a much higher concentration but at the same activity as in buffer, a statement that "holds if the additives do not mix with the drug-rich phase". The amorphous-to-crystalline concentration ratio then need not equal its value in buffer. C46 A third case (Figure 8c) is possible: an additive that partitions into the drug-rich phase "may reduce the activity" of the drug, so that LLPS would occur at a lower supersaturation; the authors "did not see evidence of this". C48 One detail of the figure is inconsistent: panel b is labelled with an amorphous-to-crystalline ratio of 10, whereas its concentration axis places the two boundaries at 50 and 150 μg/mL (a ratio of 3); the 10 is the activity ratio of the right axis, which fits the text. X9

From the diffusion cell to the gut

Figure 9 places these findings in the gastrointestinal tract, where ionized and un-ionized free drug coexist with drug in micelles, complexes and lipid vesicles, and with crystals or an LLPS phase. The total concentration sums all these species, but only the un-ionized, molecularly dissolved free drug drives passive transport (the pH-partition idea, ref 47, "is thought" to hold; dissolution kinetics are set aside). C49 Flux measurements are therefore offered as "an extremely useful approach" to evaluate the free drug concentration in complex formulations, and the conclusion calls them "an excellent approach" to separate solubilization from supersaturation. C50 The authors add that ignoring the solubilizing components of biorelevant dissolution media "may explain" difficulties with in vitro–in vivo correlation. C44

Note by the AI writer (not discussed in the paper): three practical readings follow from the data. First, for an ASD that contains a surfactant, or one tested in FaSSIF, what matters is whether dissolution reaches the LLPS onset of that medium; dissolved drug held in micelles below that point adds little driving force. Second, a lower σa/σc in a solubilizing medium does not mean a smaller amorphous advantage in flux: the maximum flux was the same, it only needed more dissolved drug. Third, surfactant levels below the CMC did not reduce the flux of felodipine or nifedipine at the concentrations tested, so small amounts used as wetting agents may cost little driving force, although this was tested at one donor concentration per drug. R7·R8·R9·R11

Limitations

Limits the authors state. The suspension comparison carries an experimental error the authors call "quite large" because of the low concentrations detected. C22 The concentration-based ratio "may vary between different additives" relative to buffer, and the third scenario of Figure 8c was not observed. C29·C48 The assumption $\gamma /{\gamma }^{*}\approx 1$ is described only as possibly "reasonable" for dilute solutions, and the Discussion explicitly ignores the kinetic effects of dissolution when moving to the in vivo picture. C32·C49

The AI writer's own judgement. The core measurements are direct and consistent across Figures 3–7, so the claims that flux follows activity and that solubilizing levels cut the flux at a fixed concentration are well supported. The broader claims rest on a narrower base, and several details need care:

• Recovery of the maximum flux, the shifted LLPS onsets and the σa/σc values were measured only for felodipine with 0.04% Vit E TPGS and in FaSSIF; the abstract and conclusion speak of solubilizing additives in general. X10
• The buffer LLPS onset of felodipine appears as 8.7, about 9 and 10.4 μg/mL in different places, the ratio 9.2 does not follow from 10.4/1.1, and the ratio is written as σc/σa in two places. X1·X2·X3
• The reference behind the BSA supersaturations of 7.3 and 4.2 is not stated, and the c* values behind Figure 7b must be inferred; the β-cyclodextrin under-estimate is stated but not calculated. X5·X4·X13
• LLPS onsets with surfactants or FaSSIF were measured with 1 mg/mL HPMC, while the HPMC level in the additive and FaSSIF flux runs is not given; no solid-state or scattering check of the donor during the flux runs is reported, and nifedipine crystallized at higher stirring rates in the infusion tests. X7·X11·R15
• Replicate numbers and error-bar definitions of the flux data are not stated, and the reference band of Figure 6 is wider than the error bar of the corresponding buffer bar in Figure 5a. X12
• At C1, nifedipine solubility was already 1.6–2.1 times the buffer value, contrary to the description of C1 as giving minimal change. X6
• The membrane is regenerated cellulose, not a lipid or cell membrane, and both drugs are un-ionized at pH 6.8; ionizable drugs were not studied. M13·M1·M2

Overall, the AI writer rates the evidence as moderate: strong for the direct flux observations, weaker for the generalisation to all solubilizers and for the proposed mechanisms. X10·X12·C37·C40

Conclusion

This paper separates two ways of raising the dissolved drug concentration that are easily confused. Supersaturation raises the activity of the drug and therefore its flux across a membrane, up to the maximum set by LLPS. Solubilization by surfactants, BSA, β-cyclodextrin or FaSSIF raises the crystalline solubility but not the activity of a saturated solution, so at a fixed total concentration it lowers the flux. C23·C26·C33 For felodipine in 0.04% Vit E TPGS and in FaSSIF, raising the total concentration above the LLPS onset of the medium, 177 and 215 μg/mL instead of about 10 μg/mL in buffer, restored the same maximum flux as in buffer, while the amorphous-to-crystalline ratio fell from 9.2 to 4.5 and 5.0. R9·R11·C2·C42 Because flux did not follow c/c* across media, and because BSA solutions with c/c* close to 1 still showed flux-based supersaturations of 4.2–7.3, the authors conclude that concentration-based ratios under-predict the true supersaturation in solubilizing media and "may lead to erroneous conclusions", and they recommend flux measurements to read the free drug concentration of complex formulations. R12·R13·C38·C50