Comparative analysis of drug-salt-polymer interactions by experiment and molecular simulation improves biopharmaceutical performance

The propensity of poorly water-soluble drugs to aggregate at supersaturation impedes their bioavailability. Supersaturated amorphous drug-salt-polymer systems provide an emergent approach to this problem. However, the effects of polymers on drug-drug interactions in aqueous phase are largely unexplored and it is unclear how to choose an optimal salt-polymer combination for a particular drug. Here, we describe a comparative experimental and computational characterization of amorphous solid dispersions containing the drug celecoxib, and a polymer, polyvinylpyrrolidone vinyl acetate (PVP-VA) or hydroxypropyl methylcellulose acetate succinate, with or without Na+/K+ salts. Classical models for drug-polymer interactions fail to identify the best drug-salt-polymer combination. In contrast, more stable drug-polymer interaction energies computed from molecular dynamics simulations correlate with prolonged stability of supersaturated amorphous drug-salt-polymer systems, along with better dissolution and pharmacokinetic profiles. The celecoxib-salt-PVP-VA formulations exhibit excellent biopharmaceutical performance, offering the prospect of a low-dosage regimen for this widely used anti-inflammatory, thereby increasing cost-effectiveness, and reducing side-effects.


INTRODUCTION
peak of -S=O asymmetric stretching at 1158 cm -1 which was also observed in both CEL 250 PVP-VA and HPMCAS ASDs. However, the disappearance of this peak in the CEL 251 (Na + /K + ) salts and all the CEL ASSDs confirms electrostatic interactions between the CEL 252 -S=O group and the counterions (Na + /K + ), resulting in salt formation. Furthermore, the -253 NH peak present for crystalline CEL at 1573 cm -1 was of low intensity in amorphous CEL 254 and disappeared in all the formulations, confirming the hydrogen bonding interactions 255 between the -NH group of CEL and the -C=O group of PVP-VA polymer and, -C=O or - 256 OH groups of HPMCAS polymer as observed in FTIR spectra. Thus, the FTIR and micro- 257 Raman spectroscopy both reveal in situ salt formation of CEL with the counterion and 258 CEL hydrogen bonding with the polymer. 259 NMR spectroscopy Chemical shifts in the aliphatic and aromatic regions of CEL as a 260 result of alterations in the proton microenvironments were measured by NMR [32] for CEL 261 and its amorphous formulations (Fig. S6, Fig 2E). The upfield shift in the two doublet 262 peaks of aromatic protons attached to the sulphonamide group of CEL and the 263 disappearance of the -NH2 peak at a chemical shift of 7.52 ppm in ASSDs but not ASDs 264 ( Fig. 2E) confirmed salt formation between CEL and the counterion (Na + /K + ) due to loss 265 of a proton from the -SO2NH2 group, leading to shielding of the neighbouring aromatic 266 protons in CEL. In the -SO2NH2 group, the −NH2 and −SO2 act as proton donor and 267 acceptor, respectively. The −SO2, being a strong electron-withdrawing group, will undergo 268 a -R effect due to conjugation between the lone pairs of electrons of the oxygen atoms and 269 the pi electron of the resonating system. There is a delocalisation of pi electrons towards 270 the oxygen atoms, which further extracts electrons from the N atom of the -NH2 group and 271 leads to formation of the -S=NH bond. This effect will lead to more electron-rich oxygen 272 atoms that can make an ionic interaction with the positively charged counterion (Fig. 1A). 273 Furthermore, the upfield shifts of the aromatic protons in the ASSDs indicate a change in 274 their electron density because of drug-polymer interactions. The doublet peaks of the 275 aromatic protons in CEL at chemical shift values of 7.87 and 7.54 ppm were shifted 276 upfield in the ASSDs, whereas no such alteration in the peaks was observed for the ASD 277 formulations (Fig. 2E). Hydrophilic polymers can interact with drug molecules by forming 278 electrostatic interactions or by hydrogen bonding, thereby inhibiting drug-drug 279 aggregation and maintaining supersaturation for prolonged times [27] . The CEL chemical 280 shifts, along with the enhanced Tg obtained in the DSC studies, further confirm the in situ 281 salt formation between CEL and the counterions (Na + /K + ) and the drug-polymer 282 interactions in the ASSD formulations. 283

Supersaturation and precipitation studies
The extent of CEL supersaturation in the ASSDs and ASDs was studied at 37 °C using an 285 ultraviolet (UV) spectrophotometer. CEL and all CEL-polymer formulations were 286 dissolved separately in methanol at 5 mg/mL CEL concentration and poured into 25 mL 287 water. Supersaturation experiments were conducted in water because water can act as a 288 strong plasticizer for amorphous systems and cause them to recrystallize [49] . Initially, a 289 high absorbance was observed for CEL followed by a rapid decline due to precipitation of 290 CEL in water. The CEL-K-PVP-VA ASSD generated maximum supersaturation of CEL 291 for 4 h due to the hydrophilic nature of the PVP-VA polymer, however the CEL-Na-PVP- 292 VA ASSD showed a slower decline in CEL concentration for 40 min and maintained it for 293 4 h (Fig. S7b). This confirmed the greater hindrance of water-induced crystallization of 294 CEL in the CEL-K-PVP-VA ASSD than in the CEL-Na-PVP-VA ASSD. CEL in the 295 binary ASDs with both the polymers showed reduced absorbance compared to the ASSDs 296 due to crystallization from its supersaturated state, which can be attributed to weaker polymer aggregates in aqueous solutions that promote interactions within the polymer [50] . 305 The better behaviour of the systems containing PVP-VA than those containing HPMCAS 306 is contrary to the predictions from the calculation of drug-polymer miscibility parameters 307 (Table 1) but correlates well with the observed melting point depression in DSC 308 thermograms which indicated high CEL-polymer miscibility in the case of PVP-VA (Fig. 309 S1A). Therefore, to investigate the physical mechanisms underlying the supersaturation of 310 CEL, we next performed molecular modelling and simulation. 311 In silico molecular modelling 312 The systems simulated, labelled a-j, are listed in Table 2.

Simulation of CEL aggregation
Simulations were conducted to model the amorphous 320 forms of CEL (both neutral and anionic forms) in the absence of polymer and the presence 321 of ~0.01M NaCl (see Table 2 and Methods). CEL aggregates during simulations in 322 aqueous solution at supersaturated concentration. The neutral form of CEL aggregated 323 within a few hundred ns (Fig. 3). On the other hand, the anionic form of CEL only 324 partially aggregated during one simulation (system e, final snapshot at 916 ns shown in 325 Fig. 3) and remained dissociated during the other simulation (system f simulated for 1042 326 ns). In the aggregates of CEL, no specific non-covalent interactions were found, except 327 that for neutral celecoxib, an intermolecular hydrogen bonding interaction was observed 328 between the sulfonamide -NH2 group of one CEL molecule and the -SO2 group of another 329 molecule (see radial distribution function (RDF) in Fig. 4A (a)). The same interaction was much reduced for the anionic form of CEL ( Fig. 4A (b)). These results support the faster 331 aggregation of CEL in the neutral state than in the ionic state, in the absence of polymer, 332 due to stronger interactions between the CEL molecules.

333
Simulation of CEL-polymer systems Simulations were next performed for CEL in the 334 presence of polymer and ~0.01M NaCl and the aggregation propensity of the 335 CEL:polymer systems was compared with that of the CEL-CEL systems (see Table 2 and 336 Methods). The CEL-polymer interactions modulate the CEL:CEL hydrogen-bonding 337 interactions. We performed two sets of MD simulations per CEL-polymer combination 338 and observed formation of drug-polymer aggregates showing structural convergence after 339 about half the simulation length (see Fig. S8). We therefore and analysed the converged 340 parts of the trajectories in terms of hydrogen bond contact occupancy and RDFs, and 341 computed interaction free energies with the MM/GBSA method. To reduce the higher 342 statistical uncertainty in the computed free interaction energies for the neutral CEL:PVP- 343 VA system compared to the other simulated systems, we carried out a third replica 344 simulation for a longer time for this system. The third replica showed similar convergence 345 as regards RMSD within the first 150ns and this was maintained up to the end of this 346 simulation at 556 ns ( Fig S8e). The radius of gyration of the oligomer chain also 347 converged to a similar value to that observed for the first two replicas (see Fig. S8i). The 348 MM/GBSA energies computed for time intervals to 356 ns or to 556 ns were very similar 349 (see Table S1 and S2), indicating that the replica simulations of this system up to 356 ns 350 were of sufficient duration to investigate the properties of the neutral CEL-PVP-VA 351 aggregates. 352 The computed RDFs are shown in Figure 4. Differences in g(r) peak heights between 353 replicas reflect the transient and rather non-specific nature of hydrogen-bonding 354 interactions between the sulfonamide nitrogen and oxygen atoms of two CEL molecules, 355 or between CEL and oligomer atoms, as apparent from visual inspection of the 356 trajectories. For example, for the negatively charged celecoxib and HPMCAS system (Fig. 357 4B g-h), we observed that a hydrogen-bonding interaction between the nitrogen atom of 358 the sulfonamide group in CEL and a hydroxyl group in HPMCAS was present throughout 359 the trajectories in both replica simulations. However, this hydrogen-bonding interaction 360 did not occur between a specific pair of CEL and HPMCAS hydroxyl atoms. Rather, it 361 occurred between any of the eleven CEL molecules and the HPMCAS hydroxyl atoms. 362 Moreover, the RDFs were computed by generating histograms of the number of particles 363 found as a function of distance and normalizing by the expected number of particles at the 364 corresponding distances. Since the modelled HPMCAS chain has eight hydroxyl groups in 365 hydroxypropyl moieties but only three hydroxyl groups attached to the tetrahydropyran 366 rings, the discrepancy in the RDF peak heights in the two replicas shown in Fig. 4B  between the −NH2 group of the neutral form of CEL and all oxygen atoms of the PVP-VA 372 polymer shows a peak ( Fig. 4B (a-b), S9B) at 2.8±0.01 Å, whereas this peak is absent for 373 the anionic form of CEL. In the presence of PVP-VA, the relative g(r) value at the peaks 374 in the RDFs of the neutral CEL sulfonamide −NH2 and −SO2 groups is lower (Fig. 4A (c)) 375 than in the absence of polymer ( Fig. 4A (a)) for all replicas. Thus, the CEL:CEL 376 hydrogen-bonding interactions are weakened by the presence of the PVP-VA oligomer.
Interactions between HPMCAS and CEL. The RDF was computed for each of the five 378 individual functional groups of HPMCAS and for all the five groups together. The g(r) 379 values between the neutral form of CEL and the hydroxypropoxy and hydroxyl groups of 380 HPMCAS are the highest in both sets of simulations ( Fig. 4B (e-f)). The g(r) at a distance 381 ≤3 Å between the hydroxypropoxy group of HPMCAS and the anionic form CEL ) is less than for the neutral form of CEL, but much higher than the carbonyl oxygen 383 of the VA group of PVP-VA (Fig. 4B (c-d)). As observed for PVP-VA, the relative g(r) 384 value of the RDF peaks for the sulfonamide −NH2 and −SO2 groups of neutral CEL in the 385 presence of HPMCAS, is decreased ( Fig. 4A (e)) compared to in the absence of polymer 386 ( Fig. 4A (a)) in both replicas. Thus the CEL:CEL hydrogen-bonding interactions are also 387 weakened by the presence of the HPMCAS oligomer.  (Table S2). On the other hand, the electrostatic interaction energy between the anionic 401 form of CEL and the HPMCAS oligomer is unfavorable due to repulsive interactions 402 between the negatively charged sulfonamide group of CEL and the oxygen atoms of the 403 oligomer. Nevertheless, the overall energy of the complex is negative due to the favorable 404 van der Waals and solvation energies. 405 We found that as the strength of oligomer:CEL interaction energy increases, the 406 magnitude of the CEL:CEL interaction energy in the CEL aggregate tends to decrease. 407 The strength of the oligomer:CEL interaction is several-fold higher per CEL molecule 408 than that of the CEL:CEL interaction in the CEL aggregate for both neutral and anionic   [51] . In contrast, the CEL-K-HPMCAS ASSD showed higher solubility 452 than the CEL-Na-HPMCAS ASSD throughout the measurement time despite having a 453 slightly higher Tg value. This is because the comparatively hydrophobic nature of 454 HPMCAS causes slower or low salt release in water but the release of the larger K + ions, 455 with higher aqueous solubility than Na + , has a greater structure-breaking effect on the 456 water [47] . The overall higher solubility for K + -containing salt formulations is attributed to 457 the higher polarizability of the K + ion than Na + ion [52] . The CEL embedded in the 458 formulations is in amorphous form, as supported by DSC and XRD spectra (see In vitro dissolution studies In vitro dissolution studies were performed to understand the 467 release behaviour of pure crystalline CEL and CEL from amorphous ASD and ASSD 468 formulations under sink (pH 12) and non-sink conditions (pH 11). The pKa of CEL is 11.1 469 so crystalline CEL remains unionized throughout the GIT at pH values below 11. At pH 470 11, CEL is ~50% ionized and at pH 12, CEL is more ionized, causing enhanced solubility. 471 Indeed, the equilibrium solubility of pure crystalline CEL in pH 12 dissolution medium was measured to be 569.80 μg/mL, which is much higher than the solubility at pH 11 473 (28.09 µg/mL). Hence, dissolution studies were performed at both pH 11 and pH 12. respectively. The dissolution rate is dependent on the release of drug from the diffusional 501 double layer around the dissolving particle in the medium. The salt alters the pH of the 502 microenvironment around the dissolving drug particle and promotes its ionization and 503 faster dissolution as compared to free acid or base [53] . 504 Dissolution under non-sink conditions Dissolution studies under non-sink conditions were 505 performed at pH 11 using tribasic sodium phosphate buffer. These conditions are preferred 506 for discriminating the drug release of amorphous formulations and crystalline CEL, for 507 direct evaluation of ASDs and ASSDs for enhancing solubility and maintaining 508 supersaturation as supersaturation is better sustained in non-sink conditions, and for 509 ensuring product quality and in vitro and in vivo performance [54] . The equilibrium 510 solubility of CEL in this buffer was found to be 28.09 μg/mL. Therefore, the entire 100 511 mg dose of the CEL cannot be solubilized in one third of the volume of the dissolution 512 medium and the system corresponds to non-sink conditions and provides a more realistic 513 estimate of the ability of amorphous solid based formulations to increase the release of 514 PWSD in the GIT. Crystalline CEL showed a low release rate of 6.96 % in pH 11 buffer 515 after 120 min because of its low solubility and poor wetting behavior. Because of its 516 hydrophobic nature, CEL tended to float on the surface of the dissolution medium during 517 the study period. The CEL release exhibited by the CEL-PVP-VA ASD was 518 approximately 70.62 % after 120 mins, which was considerably lower than for the PVP-VA ASSD. On the other hand, the CEL release from the CEL-HPMCAS binary ASD was 520 higher at 81.32 % compared to that for the CEL-Na-HPMCAS and CEL-K-HPMCAS 521 ASSDs for which the CEL release was 78.53 % and 68.08 %, respectively after 120 522 minutes ( Fig. 6B), indicating slow and incomplete release from the HPMCAS polymeric 523 matrix. However, both the CEL ASSD formulations displayed approximately 12-fold 524 enhancement in the percentage of drug release compared to pure crystalline CEL. 525 CEL-Na-PVP-VA and CEL-K-PVP-VA ASSD formulations exhibited a similar pattern of 526 maximum drug release, with 85.09 % and 85.98 % release after 120 mins (Fig. 6B). 527 Moreover, a difference of approximately 40 % was observed in the release profiles of 528 CEL-PVP-VA ASD and its ASSD for the initial 10 min, with the difference falling to 15 529 % after 120 min. Apart from strong ionic interactions in amorphous salts, strong CEL-530 polymer interactions in both the ASSDs prevented the aggregation of CEL particles from 531 the supersaturated solution. Under non-sink conditions, the ASSD prepared with 532 HPMCAS did not generate supersaturation greater than its binary ASD. The CEL release 533 from both the ASSDs was gradual and the ASSD and ASD prepared using PVP-VA 534 exhibited better drug release than HPMCAS. We attribute this difference to the higher 535 CEL-PVP-VA miscibility ( Fig S1) which results in better inhibition of CEL crystallization 536 and prolonged maintenance of supersaturation in CEL-PVP-VA amorphous formulations 537 ( Fig S7). Moreover, due to the controlled-release and hydrophilic nature of PVP-VA, 538 swelling of the polymer matrix occurred followed by slow erosion after complete 539 hydration [55][56][57] , leading to more drug release.. The higher dissolution of ASSD 540 formulations corresponded to their in vivo biopharmaceutical performance. 541 The release of CEL from CEL-Na-HPMCAS ASSD was much faster than CEL-K-542 HPMCAS ASSD at both pH 11 and pH 12 because of the low Tg value of the former. 543 While the smaller Na + ion might be expected to interact more strongly with CEL than the 544 larger K + ion, the K + ion has a lower ionization enthalpy and may therefore have a greater 545 tendency to form ionic interactions with CEL in the amorphous form leading to slower 546 drug release. Whereas the CEL release profile for CEL-HPMCAS ASD is very similar at 547 pH 11 and pH 12, for the ASSDs, the extent of CEL release is lower than the CEL-548 HPMCAS ASD at pH 11 and higher at pH 12, and the rate of CEL release increases from 549 pH 11 to pH 12. This difference in CEL release behaviour might be explained by the 550 relative differences in ionization tendencies of the salt and the drug at the two pH values, 551 with more CEL being in the ionized form at pH 12, as well as tendency of the ASSDs to 552 form ionic interactions with CEL in the amorphous form leading to slower drug release. 553 HPMCAS, being rather hydrophobic in nature [58] , is unlikely to affect the differences in 554 ionization of the drug and the salt at these pH values. ng/mL and 116 ng/mL, respectively, at 12 h whereas the CEL-Na-HPMCAS ASSD 563 attained a Cmax of 84 ng/mL at 1 h, which further reduced with time. Also, the CEL-K-HPMCAS ASSD acquired a lower Cmax of 60 ng/mL, even at 12 h (Fig. 6C). Thus, CEL-565 K-PVP-VA and CEL-Na-PVP-VA ASSDs had approximately 8.0 and 5.6-fold higher 566 Cmax, respectively, than crystalline CEL. Moreover, the extent of enhancement in Cmax and 567 other pharmacokinetic parameters was much greater for the ASSD than the binary ASD, 568 see Table 3. Both the ASSD formulations of CEL with PVP-VA possessed a higher 569 plasma concentration of CEL for 12 h due to maintenance of supersaturation for a 570 prolonged period (synergistic effect of amorphization and salt form), enhanced solubility 571 and dissolution, and increased intermolecular drug-polymer interactions in the ionic state 572 than in the neutral state, thereby inhibiting drug-drug aggregation as revealed from the 573 experimental and in silico computational interaction studies. This may be ascribed to 574 generation of CEL-rich nano-droplets or a colloidal system in equilibrium with the 575 molecularly dissolved CEL [59] . Also, the PVP-VA matrix allowed higher CEL loading, 576 and enabled carrier-controlled release for continuous dissolution of CEL through gel-like 577 layer of PVP-VA, and absorption into the blood stream gradually over a longer time 578 period [57] . However, the binary ASD showed lower supersaturation potential then the 579 ASSD due to weak intermolecular interactions between CEL and PVP-VA, resulting in a 580 lower Cmax (56 ng/mL). Additionally, the formulations with HPMCAS did not prove better 581 than PVP-VA, indicating the lower supersaturation potential of HPMCAS that is evident 582 from its pH-dependent solubility, i.e., lower solubility at acidic pH (< 10% below pH 4 583 and ~50% at or above pH 5) [50] . Notably, the solid dispersion of paclitaxel (PTX) with 584 HPMCAS-MF failed to improve the oral bioavailability of PTX in Sprague Dawley (SD) 585 rats despite maintenance of in vitro supersaturation [60] . 586 The better relative bioavailability of the ASSDs compared to the ASD for PVP-VA versus 587 HPMCAS is due to the much better performance of the PVP-VA ASSDs, which correlates 588 with their higher solubilities and higher drug release in dissolution media. These here provide a basis for probing the determinants of CEL-polymer excipient interactions. 653 We focused on ASDs containing CEL, and one of two established polymer excipients -654 PVP-VA or HPMCAS -with or without Na + or K + salts. While classical empirical models 655 showed adequate miscibility of CEL and both polymers, they were unable to correctly 656 identify the best drug-salt-polymer combination. In contrast, more stable drug-polymer 657 intermolecular interaction energies computed from the atomically detailed MD 658 simulations were found to correlate with prolonged stability of supersaturated amorphous 659 drug-salt-polymer systems in aqueous medium. MD simulations revealed that the PVP-and experiments for ASSDs, in which the anionic form of CEL is favored, revealed that it 662 was a better polymer than HPMCAS for inhibiting precipitation and maintaining 663 supersaturation of CEL for a prolonged time. All simulations of CEL-containing systems 664 were performed in the presence of NaCl and, as no direct effects of the Na + ions on the 665 CEL:CEL or CEL:oligomer interactions were observed, similar behaviour would be 666 expected in classical MD simulations with K + ions. Molecular simulations to capture the 667 differences between these cations would likely require the use of a polarizable force field 668 or a quantum-mechanics-based model. However, experiments did show some differences 669 in solubility between ASSDs with the two cations, likely due to differences in the size and 670 polarizability of the cations, whereby K + has a higher polarizability than Na + , and their 671 ability to polarize their surroundings, which is greater for Na + than K + [52] . Thermal It should be noted that the ASSD technology is not suitable for non-ionizable drugs due to 681 their inability to form a salt. In addition, due to the higher hygroscopicity of ASSDs than 682 ASDs (Fig. S14) because of their amorphous nature and the presence of the Na + or K + 683 salts which are very hygroscopic [61] , their applicability could be challenging for more 684 hygroscopic drugs. The ASSD technology remains to be explored for permeability 685 enhancement of BCS class IV drugs, that have both low permeability and low solubility. formulations was previously explained in detail [27] . Briefly, CEL (pKa 11.1) and 758 counterions {K + (KOH (pKa 14.7)) or Na + (NaOH (pKa 15.7))} were dissolved in 759 methanol in a 1:1 molar ratio to generate Na + and K + salt solutions. The salt formation is 760 attributable to the pKa difference of more than 2 between CEL and the counterions. The and PXRD. The sample preparation for DSC studies was done as described previously [27] . in cubic periodic boxes using the Gromacs [76] insert-molecules command and then TIP3P 861 water molecules were added to the system using the tleap module of AMBER. To avoid 862 periodicity artifacts, the box dimensions were greater than the lengths of oligomers (see 863   Table 1). 4 excess Na+ ions were added to neutralize the HPMCAS oligomer. The MD 864 simulation protocol is given below. The last snapshot from each trajectory was extracted 865 and used as the starting structure for drug-polymer simulations. The simulation lengths, 866 box sizes and the numbers of water, ions are listed in Table 2 (systems a and b).

867
Simulation of CEL aggregation. To simulate a supersaturated solution of CEL, 868 we generated periodic boxes with the same number of CEL molecules as used for the 869 drug-oligomer systems described below. 11 and 13 CEL molecules, which were modelled 870 in either neutral or anionic forms, were inserted randomly in cubic periodic boxes of water 871 molecules with a box-length of 106 and 112 Å, respectively, using the Gromacs insert-872 molecules and gmx solvate commands. Na + ions were added to neutralize each system and 873 thus the Na + :CEL mass-ratio for each simulated system with anionic CEL molecules was 874 0.0603:1, while in the experiments, the NaOH:CEL ratio was 0.105:1. Note that the 875 hydroxide anions (OH -) are expected to extract the proton from the CEL sulfonamide 876 nitrogen at higher pH values, and therefore the simulated systems did not contain 877 hydroxide ions. In addition, further Na + and Clions were added to all the simulation 878 boxes to generate ~0.01M ionic solutions (see Table 2). Then, the system was set up for 879 simulation with AMBER using the tleap program for which it was necessary to first 880 remove the hydrogen atoms from the water molecules and change the residue name of 881 water from "SOL" to "WAT". All-atom explicit solvent energy minimization and MD   [77] .Thus, the stomach is a supersaturated system with CEL concentration 1650 908 times higher than its experimental equilibrium solubility (3.46 mg/L) [27] . Even considering 909 half the dose of CEL and administration of the drug with water, the CEL concentration 910 would still be supersaturated in the stomach. In order to restrict the simulation box size, 911 we approximated the maximal CEL concentration. Thus, one PVP-VA 34-mer and 13 912 CEL molecules were inserted in a cubic box of length 112 Å, and one HPMCAS 15-mer 913 and 11 CEL molecules were inserted in a cubic box of length 106 Å. Afterwards, Na + and 914 Clions were added (see Table 2), and the systems were re-solvated with the tleap module 915 of AMBER as aforementioned and then, all atom explicit solvent energy minimization 916 followed by MD simulations and post-facto trajectory analysis were performed. 917 MD simulation protocols. All the systems were energy minimized using the 918 AMBER v14 and v20 software [68] . Energy minimization was carried out by restraining 919 non-hydrogen solute atoms with a force constant that gradually decreased from 1000 to 0 920 kcal/mol·Å 2 . During energy minimization, the maximum number of cycles was set to 921 14000 steps: 1400 steps steepest descent followed by 12600 steps conjugate gradient.

922
Minimization was stopped when the root mean square energy gradient for the input 923 coordinates was less than 0.00001 kcal/mol/Å.

924
MD equilibration and production runs were performed using the AMBER v20  Table S1).   CEL without oligomer is shown for system e but in system f, which also lacked 1439 oligomer (Table 2), no aggregation of anionic CEL molecules was observed in a 1440 simulation of 1042 ns duration).  Table S1, their decomposition is 1480 given in Table S2, and the results of bootstrapping of the computed energies are 1481 given in Table S3.