Which polymers slow the growth of ritonavir crystals, and why: hydrophobicity, backbone stiffness and charge across 34 polymers

Background and motivation

Many new drug candidates are hydrophobic and dissolve poorly in water. One way to deliver them is to use the amorphous form, often as an amorphous solid dispersion, which dissolves to give a supersaturated solution: a concentration above the crystalline solubility. Absorption improves only if this high concentration lasts long enough, and the strong driving force for crystallization from a supersaturated solution can end it early. The authors therefore write that the rate of crystallization decides whether such a dosage form succeeds, and that an effective crystal growth inhibitor in solution is desirable to prolong supersaturation (Stegeman 2007; Kwong 2011; Bollag 2010; Warren 2010). C1·C32

Crystallization from solution has two steps, nucleation and growth, and slowing either can keep the solution supersaturated for a physiologically relevant time. Polymers are known to change nucleation rates, growth rates and crystal shape even at very low concentration (Alonzo 2012; Zimmermann 2009; Lechuga-Ballesteros and Rodriguez-Hornedo 1995). Poly(vinylpyrrolidone) (PVP), poly(ethylene glycol) (PEG) and hydroxypropyl methyl cellulose (HPMC) have been tested as inhibitors. The authors point out that most of this work identified polymers that stabilize supersaturated solutions without quantifying their effect on the separate nucleation and growth steps, which is what is needed to understand and predict inhibition. C2

On mechanism, the introduction builds on a general consensus that the additive must adsorb on the crystal surface to inhibit growth (Mullin 2001). Hasegawa et al. concluded that adsorption of carboxymethylethyl cellulose on nifedipine crystals was the most important factor in keeping nifedipine supersaturated; the adsorbed polymer occupies growth sites and acts as a mechanical barrier to incorporation of new molecules (Hasegawa 1988). C3·R19 Adsorption can be physical (van der Waals and electrostatic forces, usually reversible) or chemical (covalent bonds, usually strong and irreversible), and hydrophobicity, electrostatic interaction and hydrogen bonding have all been found to contribute (Somasundaran 1997 and others). C4 Because molecular crystals are anisotropic, adsorption differs from face to face, and a polymer that slows the fast-growing faces can change the crystal habit; HPC and HPMC, for example, changed the morphology of siramesine hydrochloride, each in its own way, with the habit dominated by the faces on which they adsorbed (Zimmermann 2009). C5·R18

The model drug, ritonavir (Figure 1), is a poorly water-soluble compound with a relatively slow crystallization tendency (Baird 2010). C7 The polymer set was built around cellulose. Cellulose derivatives can be modified chemically, are biologically compatible, and some raise the amount of drug solubilized by stabilizing its amorphous form (Posey-Dowty 2007). C8 Cellulose adipates and other ω-carboxyalkanoate esters had been designed for amorphous solid dispersions (Kar 2011): the tetramethylene chain of the adipate and the alkyl parts of the other esters make the polymer more hydrophobic, to raise its affinity for hydrophobic drugs, while the terminal carboxyl group can ionize at small-intestinal pH and release the drug by swelling or dissolving the matrix, and can interact specifically with groups such as amines. C9 The type and degree of substitution of the ester groups strongly change the properties of cellulose esters (Edgar 2001). C10

The objective was therefore to quantify how well a chemically diverse set of polymers inhibits crystal growth from highly supersaturated solution, by adding seed crystals to solutions of known supersaturation with and without predissolved polymer, and to find the polymer properties that matter. The working hypothesis was that only polymers with a certain level of hydrophobicity would be effective for the hydrophobic ritonavir. C6 To test it, 14 new cellulose esters with different hydrophobic substituents were synthesized and compared with commercial cellulose derivatives and a range of synthetic polymers (Tables 1 and 2). A1·M3–M36

Background concepts

Supersaturation. The paper expresses the driving force for crystallization as the supersaturation ratio (Eq. 4):

Here $c$ is the concentration of the supersaturated solution and $c^{*}$ the equilibrium solubility of the crystal at the same temperature. In plain terms: $S$ says how many times more drug is dissolved than the crystal can hold at equilibrium. The crystalline solubility of ritonavir was 1.3 ± 0.1 µg/mL at pH 6.8 and 37 °C, and the growth experiments started at 10 µg/mL, which the paper gives as $S$ = 7.6. E4·R1 Note by the AI writer (not discussed in the paper): 10/1.3 gives 7.7; the printed 7.6 corresponds to an unrounded solubility of about 1.32 µg/mL, inside the stated ± 0.1, so this is a rounding difference. X6

Seeded growth and the effectiveness ratio. In a seeded desupersaturation experiment, crystals of the stable form are already present, so there is no need to wait for nucleation: the dissolved drug deposits on the seeds, and the fall in solution concentration measures how fast they grow. The authors took the slope of concentration versus time over the first 2 min as the initial (bulk) crystal growth rate. C12·P12 They compare polymers through the ratio of the growth rate without polymer, $R_{g_0}$, to the growth rate with polymer, $R_{g_p}$:

In plain terms: a ratio of 1 means the polymer has no effect, a ratio of 3 means growth is three times slower. The paper defines this ratio in words, as the y-axis of Figure 6, and considers polymers with a ratio above 1 effective. E5·C15

Solubility parameter as a hydrophobicity scale. To rank the hydrophobicity of the new cellulose esters, the authors calculated their solubility parameter (SP, symbol $\delta$) by the group-contribution method of Fedors (Eq. 1):

Here $\Delta e_i$ and $\Delta v_i$ are tabulated contributions of each atom or group to the energy of vaporization and to the molar volume, and $\Delta E_v$ and $V$ are their sums. In plain terms: the solubility parameter is the square root of the energy needed to pull the molecules apart per unit volume; a high value means strong, polar cohesion (water is 49.01 MPa^1/2), a low value a nonpolar material. The higher the SP of a polymer, the more hydrophilic the authors take it to be. E1·C13·M42 Because the group contributions describe liquids at 25 °C, Fedors adds a correction to the molar volume of glassy polymers (Tg above 25 °C), which the paper applies (Eqs. 2 and 3):

Here $n$ is the number of main-chain atoms in the smallest repeating unit. In plain terms: a small extra volume is added for each backbone atom, to account for the looser packing of a glassy polymer. E2·E3 The SP values of the 14 new esters span 19.62 to 23.28 MPa^1/2 (Table 3). M23–M36 The paper does not print SP values for the 20 commercial polymers, although the discussion uses them. X11

Degree of substitution. Each anhydroglucose unit of cellulose carries three hydroxyl groups, so the degree of substitution (DS) of an ester group can range from 0 to 3. The new esters carry ordinary esters (acetate, propionate, butyrate) and one carboxyl-ended ester (adipate, suberate or sebacate); the DS of the carboxyl-ended ester is written DS (CO2H) and ranges from 0.19 to 0.85, and the total DS from 2.16 to 2.98 (Table 3). The substituents are randomly placed on the 2-, 3- and 6-hydroxyls; the esters are not regioselectively substituted (Figure 2, Scheme 1). M23–M36·P8 The authors note that the adipate carboxyl has a pKa of about 4.43, so these groups are nearly fully (about 100%) ionized at pH 6.8. R15

Polymers at a surface. An adsorbed chain is described by three kinds of segments: trains, which lie on the surface; loops, which leave the surface between two trains; and tails, the free chain ends. The balance of the three sets the properties of the adsorbed layer (Fleer 1993). Molecular dynamics simulations by Kramarenko et al. found that stiffer chains adsorb more easily and that the length of the adsorbed trains depends strongly on chain stiffness and adsorption energy. C39·R16 A related idea, used in the discussion of charged polymers, is the coil-to-globule transition: Roiter and Minko saw extended poly(2-vinylpyridine) chains at a solid–liquid interface collapse into globules as their degree of protonation decreased. R17

Predicted crystal habit (BFDH). The Bravais–Friedel–Donnay–Harker (BFDH) method predicts a crystal shape from the crystal structure alone. For ritonavir form II (orthorhombic, space group P2₁2₁2₁, CSD code YIGPIO01) it gives a rod elongated along the a-axis, bounded at its ends by four fast-growing faces, (−10−1), (−1−10), (−101) and (−110) (Figure 4e). R5·P7

OPLS-DA. Orthogonal projections to latent structures discriminant analysis is a regression method that separates predefined classes of samples. It places the variation that separates the classes in one predictive component and the variation within classes in orthogonal components, which makes the model easier to interpret. Its loadings show which input variables push a sample toward one class. R2Y measures how well the model fits the class membership, Q2Y how well it predicts it under cross-validation, and R2X how much of the input variation it uses. C14

Methods in detail

The study has four parts: a polymer library with measured or calculated descriptors; a seeded growth test, with a solubility control, run on every polymer; an analysis of the growth data against the descriptors, by simple ranking and by OPLS-DA; and a look at crystal shape after growth with the best inhibitor. The flow below summarizes them.

Part 1: a polymer library in which hydrophobicity and carboxyl content vary

Problem. To find which polymer property matters, the polymers must differ in that property, ideally within one chemical family. Commercial polymers differ in many ways at once.

What they did. The library has 34 polymers (Tables 1 and 2). Fifteen are synthetic: PVP (K 29/32), poly(vinylpyrrolidone vinyl acetate) (PVPVA, K 28), poly(allylamine) (PAlAmn), poly(N-methylvinylamine) (Pn-MVAmn), poly(ethylenimine) (PEE), poly(N,N-dimethyl acrylamide) (Pnn-DMAAmd), poly(vinylacetate) (PVAc), 99.7% hydrolyzed poly(vinyl alcohol) (PVAh), poly(4-vinylpyridine) (PVPd), poly(acrylamide) (PAcAmd), poly(N-isopropylacrylamide) (Pn-IPAAmd), poly(acrylic acid) (PAA), poly(4-vinylphenol) (PVPh), poly(4-vinylpyridine N-oxide) (PVPdn-O) and Eudragit L100 (EUD L100). M3–M17 Five are commercial cellulose-based polymers: hydroxypropyl cellulose (HPC), cellulose acetate phthalate (CAPh), HPMC (606 grade), HPMC acetate succinate (HPMCAS, AS-MF grade) and carboxymethyl cellulose acetate butyrate (CMCAB). M18–M22 The remaining 14 are new cellulose esters: cellulose acetate (CA), propionate (CP), acetate propionate (CAP) or acetate butyrate (CAB) carrying adipate (Adp), suberate (Sub) or sebacate (Seb) groups (Figure 2). They were made by attaching the monobenzyl ester of the diacid as its acid chloride and then removing the benzyl group by hydrogenolysis (Scheme 1). M23–M36

For the new esters, DS was measured by ¹H NMR from the ratio of acyl to backbone proton integrals, Mn by size-exclusion chromatography in THF against polystyrene standards, Tg by DSC (second heating at 20 °C/min), and SP was calculated by Eqs. 1–3. P8·P9·P10·P11 Table 3 lists DS and SP; Table 4 lists Mn and Tg.

Table A. The 14 new cellulose esters, in order of decreasing SP (least to most hydrophobic), from Tables 3 and 4 of the paper. Ac acetate, Pr propionate, Bu butyrate; Mn in polystyrene equivalents. M23–M36

Two entries in these tables do not add up, and the reader should know about them. The text gives the Tg range as 82–134 °C, with CAB Adp 0.81 the lowest, but Table 4 lists CAP Seb 0.67 at 74 °C. X1 For CAB Adp 0.81 the listed DS values add to 2.94, not the printed total of 2.84; every other row adds up. X2 The DS (CO2H) ranks in Table 3 also handle ties inconsistently (0.19 is ranked both 10 and 11). X3

Why it works. In Table 3, a longer carboxyl-ended chain goes with a lower SP (CAB Adp 0.25, CAB Sub and CAB Seb: 20.05, 19.84 and 19.62 MPa^1/2), as does a butyrate instead of a propionate ester (CAP Sub 20.19 against CAB Sub 19.84), while more carboxyl groups go with a higher SP. The series therefore runs from SP 23.28 (CP Adp) to 19.62 MPa^1/2 (CAB Seb) within one chemical family. M23–M36 Note by the AI writer (not discussed in the paper): the same structural change usually moves both factors, because carboxyl groups are polar. Within a backbone, the ester with more carboxyl groups always has the higher SP (CAP Adp 0.85 at 21.27 against CAP Adp 0.33 at 20.56; CAB Adp 0.81 at 20.86 against CAB Adp 0.25 at 20.05). Only two esters separate the two factors: CA 398-30 Adp (SP 20.91 but DS (CO2H) 0.21) and CAP Seb 0.67 (DS (CO2H) 0.67 but SP 20.41). X10

Part 2: the seeded growth test and its controls

Problem. A polymer could appear to slow growth for reasons that have nothing to do with the crystal surface: by raising the solubility (and so lowering the supersaturation) or by thickening the solution (and so slowing transport of drug to the crystals).

What they did. The seeds were ritonavir as received, sieved below 250 µm. PXRD showed the form II peaks at 9.51, 9.88 and 22.2° 2θ and none of the form I combination peaks, and DSC gave a melting point of 121.0 °C and a Tg of 50.4 °C for the cooled melt, both consistent with literature values for form II and glassy ritonavir (Law 2001). Polarized light microscopy showed needlelike crystals, the habit of form II. R2·R3·M1·C17 Note by the AI writer: one of the two form I peaks cited, at 3.32° 2θ, lies below the scanned range of 5–35° 2θ, so only its partner at 6.75° could have been checked. X13

For the growth test, the seeds were placed in 100 mM sodium phosphate buffer at pH 6.8 containing the predissolved polymer at 5 µg/mL, equilibrated at 37 °C and stirred at 400 rpm with an overhead stirrer. A small volume of ritonavir dissolved in methanol was then added to give 10 µg/mL. A fibre-optic UV probe (5 mm path) recorded spectra from 200 to 450 nm every 5 s; second derivatives of the spectra were used for calibration and samples to reduce scattering by the crystals. The slope of concentration versus time over the first 2 min was taken as the initial growth rate, and every run was done in triplicate. P12·C11·C12 The seed amount, the solution volume, the ritonavir stock concentration and the methanol fraction are not given. X16

The solubility control used excess crystalline ritonavir in pH 6.8 phosphate buffer at 37 °C for 48 h, with or without eight of the polymers at 5 µg/mL; the solution was separated by ultracentrifugation at 40000 rpm (274,356 × g) and assayed by HPLC with UV detection at 240 nm. P1·P2 The authors further assume that at 5 µg/mL the polymer solutions have essentially the viscosity of water ("it is reasonable to assume"), so that bulk mass transport is unchanged. C33

Why it works. If neither the solubility nor the transport changes, any change in growth rate must come from the polymer acting at the crystal surface, and the growth data can be compared with polymer properties directly. C33 Measuring the initial rate on seeds of the stable form also isolates growth from nucleation. C12

Part 3: relating inhibition to polymer properties

What they did. First, the growth ratios of the 14 new esters were simply ordered by SP (Figure 7) and by DS (CO2H) (Figure 8). R10·R11 Second, an OPLS-DA model was built for the 19 cellulose-based polymers, with seven descriptors as X variables: SP, degree of polymerization (DP, estimated as $M_n$ divided by the molecular weight of the repeating unit), Mn, monomer molecular weight, number of hydrogen bond acceptors (HBA) and donors (HBD) per monomer, and Tg. P14·E6 Monomer Mw, HBA and HBD were calculated from the structure of the repeating unit; Mn of the commercial polymers came from the manufacturers; Tg of the commercial polymers came partly from the literature and partly from DSC. P14 The polymers were assigned to two classes by their ratio, "effective" for 1.32–3.25 and "ineffective" for 0.85–1.01, the variables were centred and scaled to unit variance, and components were validated by cross-validation. P14 Note by the AI writer: the class ranges as printed do not match the cellulose data; 3.25 is the ratio of Pn-IPAAmd, a synthetic polymer outside the model, and CAB Sub (0.83) and CAB Seb (0.84) lie below 0.85. The colours of Figure 9a show 10 effective and 9 ineffective polymers. X8

Part 4: crystal shape after growth

What they did. After growth without polymer and with Pn-IPAAmd, the crystals were recovered, rinsed with water to remove phosphate, and examined by SEM (length and width of 50 crystals per sample, measured in ImageJ) and by PXRD. The predicted shape of form II was obtained with the BFDH tool. P13·P4·P7 The aspect ratio was estimated as average length divided by average width. E7

Why it works. If a polymer adsorbs mainly on the fast-growing end faces of a needle, growth along the needle axis slows more than growth in width, and the crystals become shorter and wider. In a powder pattern of needles, a change of habit also changes the relative intensity of reflections from particular planes, which the authors use through the (200) reflection near 17.7° 2θ. C18·C20

Experimental analysis

The control holds: the polymers do not change the solubility. Without polymer, crystalline ritonavir dissolved to 1.3 ± 0.1 µg/mL at pH 6.8 and 37 °C. With 5 µg/mL polymer the values were 1.2 ± 0.05 (PVP), 1.3 ± 0.03 (PVPVA), 1.5 ± 0.02 (HPMC), 1.4 ± 0.09 (HPMCAS), 1.3 ± 0.02 (CAP Adp 0.85), 1.3 ± 0.01 (CAB Adp 0.81), 1.6 ± 0.01 (CMCAB) and 1.3 ± 0.01 µg/mL (Pn-IPAAmd) (Table 5). The authors call the effect negligible, so the supersaturation in the growth test is the same with every polymer. R1·C16 The authors note that ritonavir, with a log P of 5.98 and a melting point of 121 °C, is un-ionized at this pH. M1·C7

Result 1: three new esters show the range of effects. Figure 5 shows the desupersaturation curves without polymer and with three new esters. Without polymer, the dissolved ritonavir fell from about 10.0 to about 6.9 µg/mL within 2 min of seeding. With CAP Adp 0.85 it fell only to about 9.25 µg/mL, with CAP Adp 0.33 to about 8.0, and with CAB Adp 0.25 to about 6.15 µg/mL (all read from Figure 5, approximate; standard deviations about 0.4–0.5 µg/mL at 2 min). R7 The authors report that CAP Adp 0.33 and CAP Adp 0.85 reduced the growth rate by factors of 1.6 and 3.0, and that with CAB Adp 0.25 desupersaturation was similar to, or even slightly faster than, that without polymer. R8·C21 The two CAP adipates share a backbone and differ in carboxyl content (DS (CO2H) 0.33 and 0.85); CAB Adp 0.25 is both less substituted and more hydrophobic (SP 20.05). M25·M28·M33

Result 2: the 34 polymers span no effect to a threefold slowdown. Figure 6 shows the ratio for all 34 polymers. Table B lists them by group.

Table B. Rg0/Rgp at 5 µg/mL polymer, 10 µg/mL ritonavir, 37 °C (triplicates). Values for the new esters as printed above the bars of Figures 7 and 8; Pn-IPAAmd from the text; the others read from Figure 6 (approximate). R9

The authors state that some commercial polymers were effective but most polymers were not: of the 20 commercial polymers only five were effective, in the order Pn-IPAAmd > HPMCAS > HPMC > CAPh > CMCAB, with Pn-IPAAmd the most effective at 3.25. Five of the 14 new esters were effective, and two of them, CAP Adp 0.85 and CAB Adp 0.81, were more effective than any commercial cellulose derivative. C22·C23 They summarize that, in general, the synthetic polymers other than Pn-IPAAmd and the very hydrophobic new esters were ineffective, whereas the moderately hydrophobic cellulose-based polymers, commercial and new, were effective. C24 Note by the AI writer: the stated criterion for "effective" is a ratio above 1, but several polymers with mean ratios between 1.0 and 1.4 are grouped as ineffective (PVPVA about 1.42, PVPh about 1.28, PVP and PAA about 1.20; PAA is called "completely ineffective"), and HPC (about 1.32) is not among the five effective commercial polymers although it falls in the "effective" class of the OPLS-DA. No statistical test against 1 is reported. In practice the named effective polymers start near 1.6. X7 The Figure 6 bar labelled "CAB Adp 0.85" is CAB Adp 0.81 (Figures 7 and 8 label it correctly). X5

Result 3: among the new esters, only the less hydrophobic ones inhibit. Figure 7 orders the 14 new esters from least to most hydrophobic. The six esters with SP from 23.28 down to 20.56 MPa^1/2 gave CP Adp 1.68, CA 320S Adp 1.83, CAP Adp 0.85 2.98, CA 398-30 Adp 0.95, CAB Adp 0.81 2.70 and CAP Adp 0.33 1.64; the eight more hydrophobic esters (SP 20.41 to 19.62) gave 0.83–1.01. R10·R9 The authors describe "a notable trend": polymers with SP 20.56–23.28 MPa^1/2 inhibited growth and those below 20.56 did not, with CA 398-30 Adp (SP 20.91, ratio 0.95) the one exception. C25 Inside the window the best two esters, CAP Adp 0.85 and CAB Adp 0.81, sit in its middle (SP 21.27 and 20.86), and the least hydrophobic, CP Adp, gave 1.68. R10

Result 4: more carboxyl groups, better inhibition, with one exception. Figure 8 orders the same esters by DS (CO2H). Of the six esters with DS (CO2H) 0.33–0.85, five gave 1.64–2.98: CAP Adp 0.85 (0.85) 2.98, CAB Adp 0.81 (0.81) 2.70, CA 320S Adp (0.67) 1.83, CP Adp (0.48) 1.68 and CAP Adp 0.33 (0.33) 1.64. The exception is CAP Seb 0.67 (DS (CO2H) 0.67, ratio 0.85). All eight esters with DS (CO2H) 0.19–0.26 gave 0.83–1.01. R11 The authors read this as a trend in which a higher DS (CO2H) gives better inhibition, with CAP Seb 0.67 the exception. C27 Within each adipate pair that shares a backbone, the higher DS (CO2H) gave the higher ratio: 2.98 against 1.64 for CAP Adp 0.85 and 0.33, and 2.70 against 0.99 for CAB Adp 0.81 and 0.25. R11·M25·M27·M28·M33 Two printing problems affect Figure 8: its caption and the discussion name the outlier "CAB Seb 0.67", a polymer that does not exist in Table 2 (the yellow bar is CAP Seb 0.67); and CA 398-30 Adp (DS (CO2H) 0.21) is placed before five esters with DS (CO2H) 0.22–0.26, so the order is not strictly decreasing. X4·X3

Result 5: the multivariate model puts SP first. The OPLS-DA model of the 19 cellulose-based polymers had one predictive and three orthogonal components, R2Ycum 0.713, Q2Y 0.512 and R2Xcum 0.91; the authors read a Q2Y above 0.5 as good prediction. R12·C28 In the score plot (Figure 9a), the ineffective polymers lie at negative values of the predictive score t[1] and the effective ones at positive values, except CAB Adp 0.81 and CAP Adp 0.33, which lie just below zero. The ineffective polymers vary little along the orthogonal score, except CAB 381-20 Adp and CAP 482-20 Adp. Four effective commercial polymers (HPC, CMCAB, HPMC, HPMCAS) lie at positive orthogonal scores, while CAPh and the effective new esters lie at negative ones; the authors relate this spread to differences in HBD, HBA, SP and Mn. HPC lies outside the 95% confidence ellipse, and the authors say it does not fit any class. R13·C29 In the loadings (Figure 9b), SP had the largest value, about 0.70, followed by HBD (about 0.46), Tg (about 0.39) and monomer Mw (about 0.29); polymer Mn (about 0.01), DP (about −0.17) and HBA (about −0.19) were small, and their error bars cross zero (values read from Figure 9b, approximate). R14 The authors conclude that SP, that is polymer hydrophobicity, was the most important variable and that no significant correlation was found between inhibition and Mn, monomer Mw, DP, HBA or Tg. C30·C31 Note by the AI writer: the error bars of HBD, Tg and monomer Mw stay above zero in Figure 9b, and their meaning is not stated, so the statement of no correlation is clear only for Mn, DP and HBA. X9 Because SP loads positively on the side of the effective class, the model says that, among these cellulose polymers, the less hydrophobic ones tend to be effective, which matches Figure 7. R13·R14·R10

Result 6: Pn-IPAAmd changes the crystal shape. Table C gives the crystal dimensions measured by SEM.

Table C. Mean ± SD of 50 crystals per sample (Figure 4b–d); aspect ratio from the average length and width. R4·E7

Without polymer the crystals grew lengthwise and became more elongated along the a-axis (aspect ratio 7.7 to 8.8). With Pn-IPAAmd they came out less elongated and more rodlike (aspect ratio 4.4), mainly because the width rose from 5.7 to 9.3 µm. R4·C19·C20 BFDH places the fast growth direction along the a-axis, and the seeds appear to grow fastest along a as well, because the (200) reflection near 17.7° 2θ, strong in the predicted pattern, is weak in the experimental seed pattern (Figure S1). R5·R6·C18 After growth with Pn-IPAAmd this reflection was more intense, which the authors take to suggest that growth along the a-axis is inhibited. R6·C20 Read from Figure S1 (approximate): the peak near 17.8° rose from about 150 counts in the seeds, against a maximum of about 600, to about 245 counts, one of the two strongest peaks of the after-growth pattern. R6 Note by the AI writer: the after-growth pattern also differs at other angles (stronger peaks near 28.7° and 31.5–32.3°) and has about half the counts, and sample amount and packing are not discussed, so the PXRD comparison is qualitative. The size spreads in Table C overlap widely, and panels c and d of Figure 4 are at different magnifications. X14·X12

Discussion

The authors' explanation: adsorption needs the right hydrophobicity

The discussion starts from Figure 6: "it is clear that polymer hydrophobicity appears to be a key parameter" for the effect of a polymer on ritonavir growth. C34 The proposed mechanism goes through adsorption. Hydrophobicity "is likely" to control how much polymer adsorbs on the crystal, and adsorbed polymer blocks the sites where new growth units are incorporated, so growth slows and smaller crystals form. C35 A very hydrophilic polymer interacts more favourably with water; a polymer that is too hydrophobic interacts with its own monomer units and forms a condensed globule, which "may not adsorb" or, if it does, covers little surface. A polymer therefore needs an optimal hydrophobicity, a hydrophilic/hydrophobic balance that drives it to the surface, and enough of it must still dissolve. C36 The chain of reasoning, as the authors give it, can be drawn as follows.

The authors find these expectations "in general" supported, particularly for the cellulose derivatives: apart from Pnn-DMAAmd, EUD L100, CA 398-30 Adp and PAlAmn, the moderately hydrophobic polymers in the middle of Figure 6, with SP values of 20.56–25.98 MPa^1/2, were effective to varying extents. C37 For the commercial polymers the SP values behind this range are not printed in the paper, so this part of the argument cannot be checked from the paper itself. X11

Backbone stiffness: why most synthetic polymers fail

With the exception of Pn-IPAAmd, the synthetic polymers were ineffective even when their SP was similar to that of an effective cellulose derivative; Pnn-DMAAmd, EUD L100 and PAlAmn are named as polymers with SP between 20.56 and 25.98 MPa^1/2 that did not work. C38 The authors write that this "most likely can be attributed to their flexible structures": flexible chains form loops with limited contact with the crystal, while the more rigid cellulose backbone lies flatter and makes more contact, in line with the simulations of Kramarenko et al., in which stiffer chains adsorbed more easily. C39·R16 Chain stiffness and the conformation of the adsorbed chains were not measured. C39

Ionized carboxyl groups: amphiphilicity

The amphiphilic nature of the new cellulose esters "appears to further enhance" their ability to inhibit growth, the polymers with higher DS (CO2H) being more effective (Figure 8). C40 With an adipate pKa of about 4.43, the carboxyl-ended substituents are nearly fully ionized at pH 6.8; the ionized carboxylate is the water-loving part of an amphiphilic polymer and "may influence" the conformation of the adsorbed chain, by analogy with the coil-to-globule transition of poly(2-vinylpyridine) seen by Roiter and Minko. C40·R15·R17 The only exception to the DS (CO2H) trend is the very hydrophobic ester the discussion calls "CAB Seb 0.67" (CAP Seb 0.67 in Tables 2 and 3). PAA, which carries many ionized carboxyl groups, was "completely ineffective", which the authors take as support for "the conjecture that the correct balance of multiple chemical and/or structural features is needed". C41·X4

The authors then explain both outliers with the two factors together. CA 398-30 Adp has the right hydrophobicity (SP 20.91) but few ionizable groups (DS (CO2H) 0.21), so it is less amphiphilic than the effective CAP Adp 0.85 and CAB Adp 0.81. CAP Seb 0.67 is fairly amphiphilic (DS (CO2H) 0.67) but too hydrophobic (SP below 20.56). C43 Hydrophobicity, rigidity and amphiphilicity "appear to be jointly responsible" for the effect of the cellulose polymers and are interrelated. C42 The OPLS-DA is cited as further support for the importance of hydrophobicity, and Mn, monomer Mw, DP, HBA and Tg "do not appear" to be the most important considerations when choosing a polymer for ritonavir. C30·C31

Pn-IPAAmd: a special case

Hydrophobicity alone does not explain why Pn-IPAAmd, a synthetic and moderately hydrophobic polymer, was the best inhibitor. "It is speculated" that it adsorbs to one or more of the fast-growing faces through specific intermolecular interactions. C44 The four fastest-growing BFDH faces, roughly perpendicular to the a-axis, expose carbonyl oxygens and the nitrogen atoms of the thiazole groups of ritonavir, which, "assuming these are also the fast growing faces in the experimental system", "can potentially" interact with the amide group of Pn-IPAAmd. C45 The shorter, wider crystals grown in its presence are read as adsorption on those faces ("suggesting"). C46·R4 The strong inhibition "can likely be attributed" to moderate hydrophobicity combined with "fortuitous" intermolecular hydrogen bonding at the fast-growing faces. C47 The other two amide polymers were "probably" ineffective because they were either too hydrophilic or have no hydrogen bond donor groups; Figure 3 shows that Pnn-DMAAmd has no N–H group, whereas PAcAmd has an NH₂ group. C48 Note by the AI writer (not discussed in the paper): poly(N-isopropylacrylamide) is known in the general polymer literature for a lower critical solution temperature near 32 °C in water. The growth tests ran at 37 °C, so its chains are expected to be collapsed rather than extended; its solution state at 37 °C was not characterized, and its "moderate hydrophobicity" is not tied to temperature in the paper. X15

What it suggests for formulation

The authors' practical message is that polymers differ so widely in their effect on crystal growth that "it is clearly important to consider this factor when choosing a polymer" for a supersaturating dosage form, and that understanding the structural factors helps to design new polymers for this purpose. C51·C52

Note by the AI writer (not stated in the paper): for ritonavir at 5 µg/mL, HPMCAS, HPMC, CAPh and the new CAP Adp 0.85 and CAB Adp 0.81 slowed growth two- to threefold, whereas PVP and PVPVA, which are common amorphous dispersion carriers, gave ratios of only about 1.2–1.4. R9 For a cellulose ester, adding hydrophobic ester groups helps only up to a point, and carboxyl groups that are ionized at intestinal pH seem to help; the new esters were designed with both features in mind for amorphous dispersions, and the data favour the more carboxylated, moderately hydrophobic members of the series. C9·R10·R11 A seeded growth test at a few µg/mL of polymer is a quick and cheap way to rank candidate inhibitors before formulation work, provided the solubility control is included. P12·R1 Whether the ranking holds for nucleation, for other drugs, for other supersaturations and polymer concentrations, and for release from a solid dispersion was not tested.

Limitations

Limitations stated by the authors. The paper is frank that a general mechanism for additive effects on growth is out of reach and that several interrelated features act together (a "conjecture"). C41·C42 It treats two inputs as assumptions: that the polymer solutions have the viscosity of water at 5 µg/mL ("it is reasonable to assume"), and that the fast-growing BFDH faces are also the fast faces of the real crystals ("assuming"). C33·C45 It names its exceptions openly: CA 398-30 Adp in the SP ranking, CAP Seb 0.67 in the DS (CO2H) ranking, Pnn-DMAAmd, EUD L100 and PAlAmn among the moderately hydrophobic polymers, PAA among the carboxylated ones, and HPC, which lies outside the 95% limit of the OPLS-DA model. C25·C27·C37·C41·C29 The explanation for Pn-IPAAmd is labelled as speculation. C44

The AI writer's own judgement (1): what the data show and what they do not. The measured core of the paper is solid: one seeded protocol, run in triplicate on 34 polymers under one controlled condition, with a solubility control that rules out a change in supersaturation. R9·R1 The ranking of the new esters by SP is clean apart from one polymer, and in both backbone-matched adipate pairs the ester with more carboxyl groups wins. R10·R11 Everything beyond the ranking is inference. Adsorption, the conformation of the adsorbed chains, backbone stiffness, the ionization state of the polymers and hydrogen bonding at the crystal surface were not measured, so the three proposed factors are explanations consistent with the data rather than demonstrated causes. C35·C39·C40·C47 In the new esters, hydrophobicity and carboxyl content rise and fall together, and the two single polymers that separate them are explained after the fact, so the data cannot apportion the effect between the two factors. X10 The comparison between synthetic and cellulose polymers of "similar hydrophobicity" rests on SP values that the paper does not print. X11

The AI writer's own judgement (2): the statistics and the cut-off. The OPLS-DA model has 19 observations, seven variables and four components, and a Q2Y of 0.512, just above the authors' threshold of 0.5; its input values for the commercial polymers are not printed, so it cannot be reproduced, and the loadings of HBD and Tg do not support a blanket statement that only SP matters. R12·X9 The "effective" label is defined as a ratio above 1 but applied as roughly 1.6 and above in the text, while the OPLS-DA classes are stated with ranges (1.32–3.25 and 0.85–1.01) that do not match the cellulose data. Comparisons between polymers are safer made with the ratios themselves. X7·X8

The AI writer's own judgement (3): Pn-IPAAmd and reporting details. The face-binding explanation for Pn-IPAAmd rests on means of 50 crystals with wide, overlapping spreads and on relative PXRD intensities; the seed mass and growth time are not given, so it cannot be checked whether the drug available, at most about 8.7 µg/mL above the solubility, could widen the seeds by about 60%. X12·X14 Several printing errors should not be copied: "CAB Adp 0.85" in Figure 6 and the abstract graphic is CAB Adp 0.81; "CAB Seb 0.67" in the Figure 8 caption and the discussion is CAP Seb 0.67; the stated Tg range misses the 74 °C of CAP Seb 0.67; one DS total does not add up; and the absent form I peak at 3.32° 2θ lies outside the scanned range. X5·X4·X1·X2·X13 The seed amount, solution volume and methanol fraction of the growth medium are not reported, so the absolute rates cannot be compared with other studies. X16

Conclusion

The paper makes three contributions. First, it measured, under one seeded protocol with a solubility control, how strongly 34 chemically diverse polymers slow the initial growth of ritonavir crystals: from no effect to 3.25-fold for Pn-IPAAmd, with HPMCAS, HPMC, CAPh and two new cellulose adipates, CAP Adp 0.85 and CAB Adp 0.81, close behind. R9·R1 Second, a family of 14 new cellulose ω-carboxyalkanoate esters showed that, within one chemistry, inhibition appears inside a window of moderate hydrophobicity (SP 20.56–23.28 MPa^1/2) and goes with higher carboxyl content, and an OPLS-DA model of the cellulose polymers gave SP the largest loading. R10·R11·R14 Third, it proposed a picture in which moderate hydrophobicity, a semirigid backbone and ionized carboxyl groups promote adsorption on the crystal, and in which Pn-IPAAmd adds hydrogen bonds to the fast-growing faces. In the authors' words, these factors "are likely to promote adsorption onto ritonavir crystal surfaces". C49·C50·C47

In the AI writer's own judgement, the measured ranking is the firm part, and the mechanism is a well-argued hypothesis that the paper does not test directly. For a formulation scientist, the paper is a reminder that the choice of polymer for a supersaturating dosage form should include a check of crystal growth inhibition, and a template for how to make that check quickly. C51·P12