When a surfactant speeds up drug crystallization: SDS monomers, micelles and polymer inhibitors in supersaturated atazanavir solutions

Background and motivation

Many drug candidates dissolve poorly in water, and formulators raise the amount of dissolved drug in two broad ways (Introduction). One is to solubilize the crystalline drug, for example in surfactant micelles or cyclodextrins. The other is to supersaturate: an amorphous solid dispersion (ASD) can produce a solution well above the crystalline solubility. The group had shown that, at the same total concentration up to the amorphous solubility, a supersaturated solution drives a higher flux across a membrane than a micellar or complexed solution (Raina et al. 2015), and that drug-rich nanodroplets formed above the amorphous solubility keep that flux high for longer (Indulkar et al. 2016). C1·C2·C3

The catch is that a supersaturated solution is metastable. There is always a thermodynamic driving force towards crystallization, and once the drug crystallizes the solubility advantage is lost. C4 Formulation additives change how quickly this happens. Adsorbed on a crystal, an additive can lower the interfacial energy or pin growth steps (thermodynamic effects) or block attachment sites (kinetic effects). C5 The common ASD polymers PVPVA, HPMC and HPMCAS are known to slow both nucleation and growth; their effectiveness is "thought to depend" on how they interact with the drug aggregates that form a nucleus and how well they adsorb on the growing crystal. C6

Surfactants are added to ASDs for wetting, dissolution and processing, and bile salts and phospholipids are present in intestinal fluid. Bile salts have consistently inhibited crystallization in earlier work, but formulation surfactants have been seen both to induce and to inhibit it, by adsorbing at the crystal-water interface. C8 Acceleration "is believed" to come from a lower crystal-solution interfacial energy. C9 The literature also distinguishes the form in which the surfactant acts: monomers "are thought to" adsorb on the growing nucleus, whereas a molecule in a micelle acts only if it first leaves the micelle, which requires adsorption to be more favourable than micellization. C10 Finally, a surfactant can meet a polymer in solution. For an inhibiting polymer and an accelerating surfactant the authors envisage three outcomes: the polymer keeps the surfactant off the crystal; the surfactant counteracts the polymer; or the surfactant binds the polymer in solution and stops it adsorbing (Ilevbare et al. 2012). C11

The paper takes atazanavir (ATZ) and SDS, a system the group had characterized before (Indulkar et al. 2017): the critical micelle concentration (CMC) of SDS in 50 mM pH 6.8 phosphate buffer is 0.5 mg/mL, and in micellar media supersaturation has to be judged by activity, not concentration. M2·C12 The aims were to measure the induction time of ATZ at one supersaturation while SDS is varied from well below to well above the CMC, so as to separate monomeric from micellar SDS; to probe the mechanism with pyrene fluorescence on ATZ crystal slurries; and to test whether SDS changes the inhibition by PVPVA, HPMC-606 and HPMCAS-MF at concentrations meant to resemble ASD dissolution. A2·A3·A5·C17

Background concepts

Supersaturation measured as activity. The driving force for crystallization is the supersaturation ratio (SR), defined through the activity of the dissolved drug (Methods, Eq. 1):

In plain terms: SR compares the activity $a$ of the drug in the solution with its activity $a^{*}$ in a reference state, here the crystal, so $a^{*}$ is the activity at the crystalline solubility. E1 In plain buffer, activity tracks concentration, and SR can be taken as the concentration divided by the crystalline solubility. In a micellar solution part of the drug sits in micelles, so a concentration ratio can mislead; the authors cite their 2017 work for this. C12 They measure activity through membrane flux (Eq. 2):

In plain terms: the flux $J$ of drug across a membrane is proportional to its activity $a$ in the donor solution, with the diffusion coefficient $D$, the membrane thickness $h$ and the activity coefficient of the drug in the membrane ${\gamma }_m$ as constants for a given drug and membrane. E2·C13 Dividing Eq. 2 at two concentrations gives Eq. 3:

In plain terms: the supersaturation ratio is the flux measured from the solution of interest divided by the flux $J^{*}$ measured from a solution at the crystalline solubility. E3 The flux itself is the slope of transferred mass $m$ per membrane area $A$ against time $t$ (Eq. 4):

In plain terms: the flux is the mass of drug crossing a unit area of membrane per unit time. E4 The paper applies this at the amorphous solubility of each medium and calls the result SR_amorph. R2

Nucleation induction time. The nucleation induction time (NIT) is the time from creating the supersaturated solution until crystals are first detected, here as a rise in light extinction at a wavelength the drug does not absorb (Eq. 5):

In plain terms: the measured time is the time for the first stable nuclei to form plus the time for them to grow large enough to scatter light, so an additive can lengthen or shorten it by acting on either step. E5·C15·C29

Micelles, hemimicelles and the critical concentrations. SDS is an anionic surfactant with a twelve-carbon tail and a sulfate head group (Figure 1). Below the CMC it is dissolved as single molecules (monomers); above it, the extra SDS forms micelles in solution. M2·C16 On a solid surface, surfactants can adsorb below the CMC as hemimicelles or admicelles, small aggregates attached to the surface; the concentration at which these first form is the critical hemimicelle (or admicelle) concentration (CHMC), and the adsorbed amount generally rises with concentration up to the CMC and no further. C34 In a polymer solution, surfactant molecules can instead gather on the polymer chain, the necklace or bead-on-a-string picture; this begins at a critical aggregation concentration (CAC) below the CMC. C41

Pyrene as a probe. Pyrene is a small hydrophobic fluorescent molecule with five vibronic emission peaks. The ratio of the first to the third (I1/I3) is high in a polar, watery environment (about 1.85 in this paper's buffer) and falls when pyrene sits in a hydrophobic environment such as a micelle core. When two pyrene molecules are within a few ångströms, an excited pair (an excimer) forms and emits a broad band between 450 and 550 nm. Both signals are standard ways of finding a CMC. P8·R6·R7

Methods in detail

All work was done at 37 °C in 50 mM pH 6.8 phosphate buffer with ATZ from Chemshuttle, SDS and pyrene from Sigma-Aldrich, PVPVA from BASF, and HPMC-606 and HPMCAS-MF from Shin-Etsu (Materials). M1·M2·M3·M4·M5·M6·M8 Supersaturated solutions were made by adding a 30 mg/mL methanolic ATZ stock; methanol was held at about 4.5% v/v in every solution experiment. M7·P4 The study has four parts.

Contribution 1: a surfactant series at constant supersaturation

The problem. If one simply adds the same amount of drug to media with more and more SDS, the micelles solubilize part of it and the supersaturation falls as SDS rises; any change in induction time would then mix a surfactant effect with a driving-force effect.

What they did. First they measured both solubilities in each medium. Crystalline solubility came from excess crystalline ATZ equilibrated for 48 h, ultracentrifuged at 35000 rpm (209490 g) and assayed by HPLC (C18 column, UV 210 nm, calibration 0.05–10 μg/mL). P1 Amorphous solubility was the ATZ concentration at which a fibre-optic probe first saw light scattering while the methanolic stock was infused into the stirred medium by syringe pump, each run finishing within 10 minutes. P2 Each induction-time run then received ATZ at the amorphous solubility of its own medium: 20 mL at 300 rpm, extinction read every minute at a non-absorbing wavelength, and the induction time taken as the first rise above baseline noise. P4 Thirteen SDS levels were run, from 0.01 to 3.6 mg/mL, plus buffer alone. A2·P4 To show that this kept the driving force constant, they measured the flux of ATZ at the amorphous and at the crystalline solubility in a side-by-side diffusion cell (7.07 cm² regenerated cellulose membrane, 6–8 kD cut-off, 34 mL on each side, receiver sampled by HPLC) and took the ratio (Eq. 3). P3

Why it works. The paper states that dosing at the amorphous solubility maintained an equivalent SR in all media, and supports it with the flux ratio. C14·R2 (Explanation by the AI writer, not spelled out in the paper: the amorphous solubility corresponds to the activity of the pure amorphous drug, which does not depend on the medium, so dosing each medium there fixes the activity whatever share of the drug sits in micelles.)

Contribution 2: looking for SDS aggregates on the crystals

The problem. If SDS acts below the CMC, the question is whether it acts as free monomers or as aggregates on the crystal surface, which ordinary solution measurements cannot tell apart.

What they did. ATZ was crystallized almost to completion from its amorphous solubility in SDS solutions below the CMC (0, 0.025, 0.05, 0.1, 0.2 and 0.3 mg/mL), with the same 4.5% methanol. Pyrene was then added to 0.4 μg/mL and its emission recorded (excitation 332 nm): the I1/I3 ratio and any excimer emission between 450 and 550 nm. P8·A5 The idea is that SDS below its CMC should leave pyrene in a watery environment unless something else makes SDS aggregate, such as a crystal surface.

How it differs from earlier work. Pyrene is a standard probe for micelle formation in solution; here it is used in a crystal suspension to detect surface aggregates below the CMC. P8

Contribution 3: polymer plus surfactant

What they did. Induction times were measured with 1 mg/mL PVPVA, HPMC-606 or HPMCAS-MF, with and without 100 μg/mL SDS, chosen as typical of the concentrations an ASD gives on dissolution. P5·C17 Separately, without any ATZ, the CAC of SDS in each 1 mg/mL polymer solution was found by the same pyrene method, scanning SDS from 0.01 to 0.5 mg/mL and taking the concentration above which I1/I3 falls steadily. P9·A6

Supporting experiments: crystal size and a real ASD

Crystals formed at each SDS level were sized by polarized light microscopy below 75 μg/mL SDS and by nanoparticle tracking analysis (NTA; Nanosight LM10, 532 nm laser, size from Brownian motion through the Stokes-Einstein equation) above it. P10 To check the solution experiments against a formulation, a dispersion of 6% ATZ, 85.5% PVPVA and 8.5% SDS was made by rotary evaporation from methanol, milled and sieved to 150–250 μm, and 23.5 mg was dissolved in 20 mL of buffer, giving on complete dissolution 70 μg/mL ATZ, 1 mg/mL PVPVA and 100 μg/mL SDS, the same concentrations as in Contribution 3 but without any methanol. P6·P7 (Check by the AI writer: 6% of 23.5 mg in 20 mL is 70.5 μg/mL ATZ, 85.5% gives 1.00 mg/mL PVPVA and 8.5% gives 0.100 mg/mL SDS, consistent with the stated values.)

Experimental analysis

Solubility: flat up to the CMC, then rising

Without SDS, ATZ had a crystalline solubility of 1.1 μg/mL and an amorphous solubility of 70 μg/mL (Figure 2). Neither changed noticeably up to 0.3 mg/mL SDS; at 0.5 mg/mL the amorphous value was about 115 μg/mL, and above the CMC both rose with SDS, which the authors attribute to micellar solubilization. At 3.6 mg/mL SDS the crystalline solubility was about 46 μg/mL and the amorphous solubility about 1480 μg/mL (plot readings). R1·C18 The flux-based SR_amorph was about 65 in buffer and in buffer with SDS, so the induction times below were all measured at the same supersaturation. R2

Note by the AI writer (not discussed in the paper): the paper gives neither the flux values nor the SDS levels at which they were measured. Concentration ratios read from Figure 2 are about 64 without SDS (70/1.1) but about 35–38 above the CMC (for example about 1180/33.6 at 3 mg/mL). The authors' own earlier work warns that concentration ratios are unreliable in micellar media, so this is not a contradiction, but equal supersaturation across the series is stated rather than shown. X6 Figure 2, like Figures 3, 5A and 7, also uses a categorical x-axis, so distances between points on the plot do not follow concentration. X14

Induction time: three regions

This is the central result (Figure 3). In buffer the induction time was about 200 min. It stayed at that level up to 0.05 mg/mL SDS (region I), fell steadily from 0.075 to 0.3 mg/mL (region II), and from 0.5 mg/mL up stayed at roughly 50–70 min although SDS rose sevenfold (region III). R3·C19·C20·C21 Table A gives the values read from the figure.

Table A. Induction time of ATZ at SR_amorph ~65 versus SDS concentration, 37 °C (read from Figure 3, approximate; the number of replicates and the meaning of the error bars are not stated). R3·X9

The authors summarise region I as SDS that "does not seem to impact" the onset of crystallization, region II as SDS that promotes crystallization while it exists as monomers, and region III as no further change "even though the SDS concentration is greatly increased". C19·C20·C21 In the discussion they put the threshold at "a minimum SDS concentration of 0.075 mg/mL", compare it with Michaels and Tausch's finding that extensive surfactant adsorption is needed before adipic acid growth changes, and conclude that because micelles add nothing, "crystallization appears to be induced by monomeric SDS molecules", as Shor found for potassium nitrate nucleation up to the CMC. C30·C31

Two reading notes. First, the threshold is stated in mixed ways across the paper: 0.05 mg/mL is the last level with an unchanged induction time and 0.075 mg/mL the first with a shorter one; the CHMC is placed "around 0.05 mg/mL", while the minimum needed is given as 0.075 mg/mL. X1 Second, the text speaks of 3 mg/mL as the top concentration, but Figure 3 ends at 3.6 mg/mL and has no 3 mg/mL point. X2 Neither changes the pattern. The region I error bars are wide (Table A), so the small rise from about 200 to about 216 min is not resolved. X9

Pyrene in the crystal slurries

In slurries of ATZ crystals grown in buffer or in up to 0.05 mg/mL SDS, pyrene I1/I3 was about 1.85, which the authors report as similar to buffer without ATZ and SDS (the value is not shown). From 0.1 mg/mL it fell, to about 1.68 at 0.3 mg/mL (Figure 5A; Table B). R6 The excimer region showed no peak up to 0.05 mg/mL, a "subtle" rise at 0.1 mg/mL and a broad band with a maximum near 465–475 nm at 0.2 and 0.3 mg/mL, whose spectra nearly overlap (Figure 5B). R7

Table B. Pyrene emission in ATZ crystal suspensions below the CMC (I1/I3 read from Figure 5A, approximate; excimer from Figure 5B and the text). R6·R7

The authors read the falling I1/I3 as a "more hydrophobic environment" around pyrene, "indicating formation of aggregated structures below the CMC", and the excimer as pyrene molecules close to each other. C27·C28 Because the SDS concentrations are below the CMC, they argue, the change "cannot be attributed" to micelles in buffer, and the hydrophobic, crowded environment is "as would be expected" in a hemimicelle on the crystal. C36 The drawn lines in Figure 5A meet near "~0.075 mg/mL", the same place as the induction-time threshold; that point is an intersection on a categorical axis, not a measured sample. R6·X14

Crystal size

At SDS levels of region I the crystals were agglomerates of 25–100 μm (Figure 6A, 0.025 mg/mL). From 0.075 mg/mL, NTA saw sub-micron particles that the authors describe as needle-shaped and scattering anisotropically (Figure 6B, 0.3 mg/mL). R9·R10 Their NTA sizes are given in Table C.

Table C. ATZ crystal size by NTA (read from Figure 7, approximate; Stokes-Einstein equivalent sizes). R11

The text gives the sizes as at most 350 nm from 0.075 mg/mL; the 0.075 mg/mL bar in Figure 7 is about 367 nm, so the bound holds from 0.1 mg/mL. X3 The authors attribute the small crystals to adsorbed SDS whose "charged head group" prevents agglomeration. C40 No surface charge or electron microscopy is reported. X11

Polymers with and without SDS

At 1 mg/mL each polymer alone kept ATZ from crystallizing for at least 1000 min (Figure 4). With 0.1 mg/mL SDS, which alone shortened the induction time to 130 min, PVPVA held for 350 min while HPMC-606 and HPMCAS-MF still held for more than 1000 min (Table D). R4·C23

Table D. Induction time of ATZ at SR_amorph with polymers, and the critical aggregation concentration of SDS in each polymer solution without ATZ (Figure 4 and text p.12-13; the CAC titration curves are not shown). R4·R8·M2

The authors describe PVPVA's loss with three strengths: "lost some of its inhibitory effect" (abstract), "decreased to some extent" (results) and "substantially reduced (from 1000 to 350 min)" (discussion); the cellulosics were unaffected "at least for the experimental duration studied". C22 The CAC data show that all three polymers bring SDS aggregation below its CMC, and PVPVA does so at the lowest concentration, "suggesting" a stronger PVPVA-SDS interaction. R8·C42 Because the polymer-only runs and the cellulosic runs were stopped above 1000 min, the drop for PVPVA is at least 650 min and any smaller SDS effect on the cellulosics would not be seen. X8

The ASD reproduces the solution result

Dissolving the 6:85.5:8.5 ATZ:PVPVA:SDS dispersion to the same concentrations gave an induction time of about 300 min, which the authors call "in line with" the 350 min from the methanolic stock. They conclude that solid ASD particles did not seed heterogeneous nucleation, "possibly" because the ASD dissolves faster than ATZ crystallizes and/or because the polymer inhibits heterogeneous nucleation. R5·R4·C24·C25 This run also had no methanol, unlike every other run. X10

Discussion

The authors' mechanism

The authors join the results into one chain (Discussion and Figure 8). An SDS molecule has a hydrophobic chain that favours micellization and a charged head group that opposes it. At low concentration SDS is dissolved as monomers and leaves the induction time and the pyrene signal unchanged. C19·C26·C32 As SDS rises, monomers adsorb on ATZ nuclei and small crystals with the tail on the surface; based on Figure 5 the adsorption "appears to become significant" above 0.075 mg/mL, and the adsorbed molecules organize as hemimicelles. C32·C33 Hemimicelles can lower the interfacial energy at the crystal-solution interface, "thereby potentially promoting nucleation and/or growth"; "this mechanism is hypothesized to play a role in the ATZ-SDS systems". C33 Above the CMC the extra SDS forms micelles, which with their "hydrophilic charged surface" cannot adsorb on the hydrophobic nucleus, so the induction time stops falling, and since micelles do not enhance nucleation "it can be safely concluded" that crystallization does not take place inside them. C37·C38

For the polymers, the authors draw on the necklace model: surfactant aggregates form on polymer chains below the CMC, which lowers the free energy of the strained SDS molecules in water and gives a CAC. C41 All three polymers interact with SDS, but PVPVA more strongly. They "can speculate" that the cellulosic polymers adsorb strongly enough on the drug to keep SDS off the emerging crystal, whereas for PVPVA the "highly favorable" interaction with SDS in solution "may reduce" the polymer available to adsorb on the crystal; in the conclusions this becomes "most likely". C42·C43·C44 This is the third of the three scenarios set out in the introduction, the surfactant disarming the polymer in solution. C11 The conclusions add that the extent of surfactant-polymer interaction "was found to correlate" with the change in induction time. C50

What it suggests for formulation

The authors' practical message is twofold. Surfactants chosen to speed dissolution "can induce crystallization" of the supersaturated drug, so a product "can be formulated" with the surfactant minimized to a level that helps dissolution without promoting crystallization. C45·C46 And a polymer that normally inhibits crystallization "may or may not be effective" with a surfactant, depending on the balance between the surfactant's affinity for the polymer and the polymer's affinity for the crystal; testing each polymer with and without the surfactant "can aid" the choice. C47·C48 Both surfactant concentration and the surfactant-polymer pair "can impact" the stability of supersaturating formulations. C51

Note by the AI writer (not stated in the paper): two points follow from the numbers. The acceleration began at about a tenth of the CMC, so "stay below the CMC" is not a safe rule for a surfactant level. R3·M2·X1 And the tested ASD, with 8.5% SDS and 6% drug, put 0.1 mg/mL SDS in solution when the drug reached its amorphous solubility, inside the accelerating range; what matters for a dissolving ASD is the surfactant-to-drug ratio and the dose, not the surfactant loading alone. P7·R3

Limitations

Limits the authors state

The authors note that the induction time covers both the formation of critical nuclei and their growth to a detectable size, so effects on both "should be considered". C29 They add that, besides interfacial energy, additives can change the pre-exponential kinetic factor (solute diffusivity) and the solvation or desolvation of the nucleus. C39 They qualify the polymer results "at least for the experimental duration studied" and "at least at the concentration ratios employed". C22 The mechanism itself is offered as "hypothesized". C33

The AI writer's own judgement

The induction-time pattern is clear: thirteen SDS levels at one supersaturation give an unchanged region, a fall from about 200 to about 56 min, and a plateau that holds while the amorphous solubility rises more than tenfold. R3·R1 The polymer contrast is also large. R4 The weaker parts are the explanations.

• No control without crystals. The hemimicelle reading rests on pyrene in crystal slurries, but the paper reports no pyrene run in the same SDS solutions (0.1–0.3 mg/mL, with 4.5% methanol) without crystals, and the CMC is cited from earlier work rather than measured under these conditions. The data do not by themselves place the hydrophobic environment on the crystal surface. X4
• Very different slurries. The crystals in the low-SDS slurries were 25–100 μm agglomerates and those from 0.075 mg/mL were about 130–370 nm, so the solid surface available to SDS and pyrene changed over the same step as the fluorescence. X5
• Induction time is not nucleation rate. The paper speaks of a nucleation rate rising with SDS, but induction time includes growth to detection, and crystal size changed with SDS. X7
• Equal supersaturation stated, not shown. The flux data behind SR_amorph ~65 are not given. X6
• A narrow polymer comparison. The ranking rests on two CAC values and one SDS level, 0.1 mg/mL, which equals the PVPVA CAC and lies below the cellulosic CAC; the polymer runs are censored at 1000 min; polymer adsorption on ATZ was not measured. X8
• Inferences from the plateau. That micelles cannot adsorb and that nucleation does not happen inside micelles both rest only on the flat induction time above the CMC. X12
• Reporting gaps. Replicate numbers, the meaning of the error bars, the extinction wavelength and the basis of the ASD percentages are not stated; the threshold, the top SDS level and the size bound are given inconsistently; the needle shape rests on one NTA frame. X9·X1·X2·X3·X11
• Scope. One drug, one surfactant, three polymers at one concentration, 37 °C, pH 6.8, and about 4.5% methanol in every solution run except the ASD run. X10

One citation slip: the discussion cites "Shor (42)", but Shor is reference 55; reference 42 is a resveratrol ASD paper. X13

Conclusion

The paper separates the roles of monomeric and micellar SDS in atazanavir crystallization by holding the supersaturation fixed. SDS left the induction time unchanged up to 0.05 mg/mL, shortened it from about 200 to about 50–60 min between 0.075 and 0.3 mg/mL, and did nothing more above its CMC of 0.5 mg/mL. R3·M2 Pyrene in crystal slurries changed over the same range, which the authors read as SDS hemimicelles on the crystal lowering the interfacial energy, a mechanism they call "hypothesized". R6·R7·C33 With 0.1 mg/mL SDS, PVPVA's protection fell from more than 1000 to 350 min while HPMC-606 and HPMCAS-MF kept theirs, and PVPVA also bound SDS at the lowest concentration; the authors link the two through SDS taking polymer away from the crystal surface, "most likely". R4·R8·C44 A dissolving ASD reproduced the PVPVA result. R5 The measurements are clear; the surface mechanism and the polymer explanation remain to be tested directly. X4·X8