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625530ddebac3a4918d21843 | 18 | Semi-empirical determination of HSPs was also performed by dissolving the synthesized homo-/triblock copolymers at 20 g/L concentration in a library of solvents ranging from polar (protic and aprotic) to non-polar solvents (Figure ). Initially, the solubility profile of all the homopolymers was obtained. The POx based hydrophobic polymers i.e. pBuOx and pPentOx showed similar solubility profile with an exception to one solvent i.e. pBuOx and pPentOx were not soluble in toluene and sulfolane, respectively (Figure , column 1 and 2). For the POzi based homoplymers i.e. pPrOzi and pBuOzi, both exhibited a very similar solubility profile with only one exception; dimethoxy methane, in which pPrOzi was not soluble (Figure , column 3). The pMeOx homopolymer being hydrophilic, exhibited slightly different solubility profile as compared to hydrophobic homopolymers (Figure , column 5). Additionally, the solubility profile of all the selected ABA triblock copolymers was also obtained. Not surprisingly, the results showed that the solubility of triblock copolymers is strongly affected by the presence of hydrophilic pMeOx block. The solubility profile of both POx based triblocks (i.e. A-pBuOx-A and A-pPentOx-A) (Figure , column 6 and 7) was the same as that of pMeOx homopolymer. The POzi based triblocks (i.e. A-pPrOzi-A and A-pBuOzi-A) also followed the same pattern with a notable single exception to butyronitrile, where both POzi based triblocks were found soluble too (Figure , column 8 and 9). The semi-empirical SPs were obtained by utilizing the solubility score obtained as binary code, i.e. 0 (insoluble, red) and 1 (soluble, green) (Figure ) in the HSPiP software. The polymer concentration used for solubility testing was randomly chosen (i.e. 20 g/L), unfortunately, there is no defined rule for that. Important to note, different concentrations/temperatures and shaking time, may result in different solubility profile and in turn varied SPs. The semiempirical SPs determination was capable to differentiate between hompolymers which are structural isomers, because of minor differences in obtained solubility profile (Figure , column 1-4 and Table ). Within pure POx and POzi based triblock copolymers, identical SPs values were obtained because of identical solubility profile (Figure , column 6-9, Table ). |
625530ddebac3a4918d21843 | 19 | We selected a list of hydrophobic drugs for formulation development and compatibility estimation. The main criteria for the selection of drugs was their hydrophobicity and associated concerns, which can limit therapeutic outcomes. The physicochemical properties of the selected drugs are shown in table . At first, SPs of the drugs were calculated by HnV and YMB method. To proceed, initially, the molar volume of the drugs were calculated by Fedor's method and by HSPiP software. |
625530ddebac3a4918d21843 | 20 | The molar volume of drugs and polymers obtained by YMB method was higher than HnV (Figure ). The SPs of the drug library were obtained by HnV method using equation 1 to 6 and for YMB methods, the drugs SMILES were obtained by drawing the structures in ChemDraw followed by further processing in HSPiP software. The Ξ΄d, Ξ΄p, Ξ΄h and Ξ΄T of all the drugs generally followed similar trend irrespective of method i.e. HnV or YMB with the single exception of Genistein, where Ξ΄d, Ξ΄h and Ξ΄T were found higher in case of HnV method (Figure ). Overall, the HSPs values obtained by YMB are slightly lower than HnV, except for Ξ΄p, |
625530ddebac3a4918d21843 | 21 | Out of 21 drugs, the SPs determination by HnV was not possible for 11 drugs (missing black squares in Figure ) e.g. for the drugs Erlotinib, Axitinib and Bortezomib, as the Fdi, Fpi and Ehi values for C-C triple bond, -N= and borane, respectively are not available. For a better comparison of HSPs values obtained by HnV and YMB for the 10 drugs both methods were suitable, the SPs values were replotted and presented in the supporting information (Figure ). As stated previously, no major differences were observed for both group contribution methods. The calculation of molar volume for all the drugs was possible by Fedor's method because of the large number of groups enlisted with their respective values in the literature (Figure ) . The YMB method also has limitations like, it is unable to process the molecules larger than 120 heavy atoms. However, in the case of Cabazitaxel, after inserting the SMILES in the HSPiP software, the HSPs values could not be obtained, although the compound is smaller than the specified limit. The experimental determination of HSPs of drugs was not performed, as the experimental SPs values of the POx and POzi based triblock copolymer have shown the similar results (Figure and Table ). |
625530ddebac3a4918d21843 | 22 | The SPs values obtained by HnV and by experimental determination were not further processed for compatibility estimation because of the similar SPs values for the polymers (Figure and Table ). Only the SPs values obtained by the YMB method were further utilized to estimate the compatibility between polymers and drugs either by Flory-Huggins interaction parameter (Οdrug-polymer, Οdp) or by Ra calculation (equation 7 and 8, respectively). |
625530ddebac3a4918d21843 | 23 | Here, a lower value of Οdp (ideally = 0) suggests a better polymer-drug compatibility. For Οdp calculation (equation no. 7), the total solubility parameters (Ξ΄T) of drug and polymer is needed. As noted previously, the YMB method gave the similar Ξ΄T values (for PrOzi and PentOx polymer) (Table ) and molar volume values (for BuOx and PrOzi polymer) i.e. 20.8 MPa 1/2 and 145.60 cm 3 /mol, respectively (Figure ). This already gave a hint that Flory-Huggins interaction parameter would not be an appropriate method to estimate the compatibility, because of the same Ξ΄T and molar volume values. Therefore, the measurement of Ra (equation no. 8), which involves the utilization of individual Ξ΄d, Ξ΄p, Ξ΄h values was only considered for compatibility estimation. The smaller distance between polymers and drugs in Hansen space represent the higher compatibility. Importantly, Ra of the two substances in the Hansen space only provide the qualitative information of compatibility. |
625530ddebac3a4918d21843 | 24 | Initially, the solubility of drugs was tested in various solvents to select the best solvent for thin film-hydration method. In our previous studies, depending upon the solubility of the drug, the most commonly used solvent is EtOH. Herein, most of the enlisted drugs were also soluble in ethanol (EtOH) with the exception of dasatinib, clofazimine and lapatinib for which mixture of EtOH/Acetonitrile (ACN) and methanol (MeOH) were used, respectively. All the information about solubility of drugs in organic solvents is presented in Table . The drug formulations were prepared by thin film hydration method as reported previously . |
625530ddebac3a4918d21843 | 25 | Briefly, the polymer and drug solutions (prepared in organic solvent) were mixed in desired ratios (the targeted polymer concentration was kept constant at 10 g/L while the drug concentration was increased from 2 to 10 g/L) followed by solvent removal and the subsequent hydration of resultant thin-film by deionized (DI) water. A total of 1260 formulations were prepared with the in-house developed formulation assembly capable to make 24 thin films in one session (Figure ). The (dissolved) drug in the micellar formulation was quantified by HPLC, after removal of (if any) non-solubilized drug by centrifugation. All the HPLC related details i.e. standard curve, elugrams and HPLC method can be found in Figure -S28. The aqueous solubility of pristine drugs was also determined and the results are presented in Table . For the ease of readers and for better comparison, the theoretical compatibility profiles (obtained by Ra calculation) and the practical formulation results are discussed together, individually for each drug with respect to four amphiphilic triblock copolymers. Additionally, the solubility of drugs in formulations is presented in g/L to better compare with the solubility of pristine drugs (determined in-house), however for maximum solubility achieved for each drug, the corresponding loading capacities and loading efficiencies are also presented. |
625530ddebac3a4918d21843 | 26 | AXT is tyrosine kinase inhibitor (TKI), use to treat a variety of cancers such as renal cell carcinoma . It also has anti-angiogenic effect . The aqueous solubility of AXT was determined in-house to be 0.005 g/L (Table ). The compatibility estimation by Ra showed that all the 4 hydrophobic blocks and, surprisingly, the hydrophilic block has similar compatibility (Figure ). To the best of our knowledge, no POx/POzi based AXT formulations are reported so far. At the AXT feed of 2 g/L, all the four triblock copolymer yielded in similar apparent AXT solubility, i.e. β 0.2 g/L (LC β 2 wt.% and LE β 10%). With the increasing AXT feed, the differences in solubilizing capacity for triblock became apparent, especially between A-pBuOx-A and A-pPentOx-A. Like for many other drugs, A-pBuOx-A was found to be the best solubilizer and the maximum achievable solubility was around 1 g/L at 4 g/L AXT feed (LC β 7 |
625530ddebac3a4918d21843 | 27 | wt.% and LE β 25%) while its higher homologue A-pPentOx-A was found to be the least efficient in solubilizing AXT (β 0.25 g/L) (Figure ). Shi et al. recently reported polyethylene glycol-polycaprolactone (PEG-PCL) micelles which were capable to solubilize only 0.01 g/L of AXT , two orders of magnitude lower than the solubility achieved here. In the selected list of four polymers, A-pPentOx-A, which is comparatively least efficient AXT solubilizer, performed better than a previously reported PEG-PCL system. No marked differences in the solubilizing capacity of A-pPrOzi-A and A-pBuOzi-A were observed. Increasing the AXT feed did not improve the aqueous solubility. From the AXT formulation results, we can conclude that the compatibility estimation was not helpful in optimizing this formulation and stronger structure-solubilization difference was observed in case of POx than POzi based formulations. |
625530ddebac3a4918d21843 | 28 | Golgi complex . According to Ra calculation, the structural isomers i.e. A-pBuOx-A/A-pPrOzi-A and A-pPentOx-A/A-BuOzi-A exhibited similar compatibility for BRF, while the later pair are supposedly better solubilizer than former (Figure ). As expected, pMeOx being hydrophilic showed the least compatibility. In this case, the formulation results were in accordance with the compatibility profile. The structural isomer pair, A-pPentOx-A/A-BuOzi-A were found to be better and capable to solubilize β 0.40/0.33 g/L BRF (LC β 4/3 wt.% and LE β 20/8%), respectively (Figure ). The in-house BRF aqueous solubility was found to be 0.15 g/L (Table ). For the treatment of metastatic breast cancer, Yu et al. reported the nanoparticles based co-formulation of Brefeldine and celecoxib, where solubility of BRF was found to be β 0.29 g/L . Unlike other, ultra-high drug loaded POx/POzi formulations , we can say that for the BRF, POx/POzi based amphiphiles are hardly solubilizers, but still performed better than previously published systems. |
625530ddebac3a4918d21843 | 29 | CAR is an anticonvulsant drug, primarily used for the treatment of neuropathic pain and epilepsy . Based on the calculated Ra, CAR compatibility with the four different hydrophobic blocks was in the following order i.e. pBuOzi > pPrOzi β pPentOx > pBuOx (Figure ). The experimentally determined solubility of CAR was found to be 0.005 g/L (Table ). At 2 g/L CAR feed, no significant difference in solubility (β 0.7 g/L) (LC β 6.5 wt.% and LE β 35%) was observed for all four triblock copolymers (Figure ). However with the further increase in CAR feed, slight improvement in solubilizing capacity of A-pPrOzi-A (β 1.5 |
625530ddebac3a4918d21843 | 30 | g/L at 6 g/L CAR feed) (LC β 13 wt.% and LE β 25%) was observed, the rest of the picture did not change significantly. The study by showed the maximum solubilizing capacity of Pluronics micelles for CAR to be 1.18 g/L . It is apparent that no correlation was observed between compatibility estimation and formulation results. |
625530ddebac3a4918d21843 | 31 | Like AXT, DSA is also a TKI, used for the treatment of variety of cancers such as leukemia . The Ra calculation revealed that the hydrophilic block pMeOx has supposedly the highest compatibility with DSA while for the hydrophobic blocks, the compatibility was in the following order, pBuOx > pPentOx β pPrOzi > pBuOzi (Figure ). |
625530ddebac3a4918d21843 | 32 | Experimentally, the best solubilizer was found to be A-pBuOzi-A (solubility of DSA β 2.8 g/L at 4 g/L DSA feed) (LC β 22 wt.% and LE β 70%), diametrially opposite to the prediction. The aqueous solubility of DSA was found to be 0.003 g/L (Table ), meaning a 930-fold increase of the apparent solubility could be achieved. For A-pBuOx-A, increase in DSA feed did not improve the solubility (remained β 2 g/L at all DSA feeds), on the contrary, a weak trend was observed with respect to decrease in solubility of DSA for A-pPentOx-A and A-pBuOzi-A with the increasing DSA feed (Figure ). The A-pPrOzi-A was found to be the least efficient solubilizer for DSA (solubility β 0.2 g/L at 4 g/L DSA feed) (LC β 2 wt.% and LE β 5%). According to Li et al., PEG-PCL micelles were capable to solubilize only 0.19 g/L of DSA . A strong polymer-drug specificity is apparent for A-pBuOzi-A and A-pPrOzi-A, although both differ from each other by just one methylene unit in the side chain of the hydrophobic block. Again, the obtained formulation results were not in line with compatibility trend expected from Ra calculation. |
625530ddebac3a4918d21843 | 33 | The Ra calculation suggests a compatibility in the following order: pBuOzi > pPrOzi β pPentOx > pBuOx (Figure ). The experimental formulation results showed that A-pPentOx-A and A-pPrOzi-A formulation completely precipitated and ERL amounts were below the limit of detection in HPLC. For A-pBuOx and A-pBuOzi-A, the solubilizing capacity was also very low. |
625530ddebac3a4918d21843 | 34 | The maximum achievable soluble ERL was found to be 0.2 g/L by A-pBuOzi-A triblock copolymer at 4 g/L ERL feed (LC β 2 wt.% and LE β 5%) (Figure ) while the in-house ERL aqueous solubility was found to be 0.007 g/L (Table ). Overall, the Ra, successfully identified the (comparatively) best solubilizer (i.e. A-pBuOzi-A) but the overall picture was not consistent with the compatibility estimation. The presently employed POx/POzi polymers and thin film hydration are clearly not well suited for ERL solubilisation. |
625530ddebac3a4918d21843 | 35 | The SUN is also a multi-targeted TKI used for treatment of cancers like renal cell carcinoma . The Ra calculation showed the following compatibility estimation with the increasing order, i.e. pBuOx > pPrOzi > pPentOx > pBuOzi (Figure ). Like ERL, the formulation results showed that none of the triblock copolymer were capable to significantly solubilize SUN (Figure ). Maximum apparent solubility was observed for A-pBuOx-A triblock copolymer (β0.6 g/L at 6 g/L SUN feed) (LC β 5.5 wt.% and LE β 10%). The aqueous solubility of SUN was determined in-house to be 0.023 g/L (Table ). Streets et al. reported methoxy-PEG-PCL nanoparticles, which were capable to solubilize 0.32 g/L of SUN . The A-pPrOzi-A triblock was found to be a non-solubilizer for SUN. Overall, the Ra, successfully identified the (comparatively) better solubilizer, but the rest of the trend was not consistent with the compatibility estimation. |
625530ddebac3a4918d21843 | 36 | Along with rifampicin and dapsone, the CFZ is used for the treatment of leprosy . CFZ has dark brown colour. According to Ra calculation, both POzi based hydrophobic blocks showed higher and equal compatibility for CFZ (Figure ), when compared to POx based polymers. The order of compatibility was found to be, i.e. pPrOzi β pBuOzi > pPentOx > pBuOx. The maximum achievable formulation solubility of CFZ was 0.2 g/L by A-pBuOzi-A, A-pPentOx-A and A-pBuOx-A at 4, 4 and 6 g/L CFZ feed, respectively (Figure ). The in-house aqueous solubility determination was not possible, because CFZ was found completely insoluble in water (Table ). The A-pPrOzi-A triblock was found to be the worst solubilizer. Once again, the compatibility results are not consistent with the formulation profile. |
625530ddebac3a4918d21843 | 37 | The CRI is a protein kinase inhibitor, used for the treatment of variety of cancers like non-small cell lung carcinoma . The order of compatibility was found to be i.e. pBuOzi > pPrOzi β pPentOx > pBuOx (Figure ). The formulation results showed A-pBuOx-A to be the best solubilizer for CRI (β 1.15 g/L at 2 g/L feed) (LC β 10 wt.% and LE β 57%) (Figure ), which according to Ra calculation should be the least efficient in solubilizing CRI. The inhouse CRI aqueous solubility was found to be 0.08 g/L (Table ). No increase in solubility was observed with the further increase in CRI feed. At CRI feed of 4 to 10 g/L, A-pPentOx-A and A-pBuOzi-A, being structural isomers, exhibited similar solubilizing capacity i.e. β 0.6 to 0.8 g/L. |
625530ddebac3a4918d21843 | 38 | In combination with statins, EZE is administered to treat lipid abnormalities . Both of the structural isomers, A-pPentOx-A and A-pBuOzi-A has a suggested higher and similar compatibility for EZE as compared to their lower homologue pair (Figure ). However, the formulation results presented a slightly different picture, where all the four triblock copolymer showed somewhat similar solubilizing capacity for EZE (β 1.4 -1.6 |
625530ddebac3a4918d21843 | 39 | g/L at 2 g/L EZE feed) (LC β 12-14 wt.% and LE β 70-80%) (Figure ). The EZE aqueous solubility was determined in-house to be 0.01 g/L (Table ). With further increase in EZE feed, solubility was decreased and remained in the range of 0.4 -0.7 g/L for all the tested ratios except for A-pPrOzi-A, where apparent solubility significantly dropped to 0.02 g/L. No clear correlation between compatibility estimation and formulation results was observed. |
625530ddebac3a4918d21843 | 40 | VOR is histone deacetylase inhibitor (HDI) and used for the treatment of skin related manifestations like cutaneous T-cell lymphoma . Like DAS, VOR also exhibited higher compatibility for hydrophilic pMeOx as compared to hydrophobic blocks. The increase in compatibility for the hydrophobic blocks was observed in following order, i.e. pBuOx > pPentOx > pPrOzi > pBuOzi (Figure ). The maximum achievable aqueous solubility of VOR was found to be 2 g/L (LC β 16 wt.% and LE β 100%) with A-pPentOx-A triblock copolymer while its structural isomer, A-pBuOzi-A (appearing as least efficient solubilizer by compatibility estimation) could solubilize 1.8 g/L (at 2 g/L VOR feed) (LC β 15 wt.% and LE β 90%) while the second structural isomer pair i.e. A-pBuOx-A/A-pPrOzi-A exhibited similar solubilizing capacity (i.e. β 1.7/1.7 g/L, respectively) (LC β 14 wt.% and LE β 85%) (Figure ). |
625530ddebac3a4918d21843 | 41 | Rompicharla et al. also showed that PEG-PLGA micelles are capable to solubilize around 1.8 g/L of VOR , similar, albeit lower than achieved here. Further increase in VOR feed, did not improve the solubility, in fact it fell below 2 g/L. For A-pBuOx-A, the solubility of VOR remained around 2g/L while a slight decrease was observed in the case of A-pPentOx-A (β 1.1 g/L) and A-pBuOzi-A (β 1.0 g/L) at higher VOR feed. For A-pPrOzi-A, a dramatic decrease was observed from 2 to 6 g/L VOR feed (solubility dropped from 1.7 to 0.4 g/L). Further increase in VOR feed led to complete precipitation of formulation and no further quantification was possible. |
625530ddebac3a4918d21843 | 42 | Like VOR, BEX being a third generation retinoid is also an anticancer agent used for the treatment of cutaneous T-cell lymphoma . According to Ra calculation, the compatibility should be in the order pBuOzi > pPentOx > pPrOzi > pBuOx (Figure ). In contrast, experiment showed that pBuOx based triblock showed the highest solubilizing capacity for BEX (β 1.1 g/L at 4 g/L BEX feed) (LC β 10 wt.% and LE β 55%) (Figure ). The aqueous solubility of BEX was found to be 0.004 g/L (Table ). In all other triblock copolymers, solubility of BEX fell below 0.5 g/L. No clear trend between the four individual polymers was observed in formulation experiments when compared to compatibility estimation. |
625530ddebac3a4918d21843 | 43 | 3.3.12. Cabazitaxel (CBZ): CBZ, being 3rd generation, semi-synthetic derivative of natural taxoids, is a microtubule inhibitor and is used for the treatment of various cancers like prostate cancer . As mentioned previously, the compatibility estimation of CBZ was not possible because of limitation in HSPiP software, incapable to process large size SMILES. The formulation results revealed that A-pBuOx-A was capable to solubilize all provided drug, i.e. up to 10 g/L (Figure ) (LC β 50 wt.% and LE β 100%). The crash point of this formulation was not determined by further increasing the CBZ feed. The aqueous solubility of CBZ was found to be 0.007 g/L (Table ). For A-pPentOx-A and A-pBuOzi-A, the CBZ solubility also kept on increasing with the increasing feed (until 8 g/L feed) and the achievable soluble CBZ was β 6.8 g/L, while at 10 g/L CBZ feed, A-pPentOx-A gave 8.5 g/L and for A-pBuOzi-A, the solubility dropped to 5.3 g/L. Like for many other tested drugs, A-pPrOzi-A displayed comparatively, poor performance to solubilize the CBZ and the maximum soluble CBZ obtained was 1.5 g/L and also significant decrease in solubility was observed with the increasing CBZ feed. Thus, a strong polymer drug specificity was observed for the structural isomer pair i.e. A-pBuOx-A/A-pPrOzi-A, where the former appeared to be best solubilizer while the latter showed poor performance, very similar to the situation with paclitaxel, the first generation taxoid. |
625530ddebac3a4918d21843 | 44 | BTZ is a proteasome inhibitor, used for treatment of various cancers like multiple myeloma and mantle cell lymphoma . Like DSA and VOR, upon Ra calculation, the hydrophilic pMeOx supposedly exhibits a higher compatibility for BTZ in comparison to hydrophobic blocks. Amongst those, , the estimated compatibility was in the order of pBuOx > pPentOx > pBuOzi β pPrOzi (Figure ). Previously, Schulz et al. reported the A-pBuOx-A based formulations are capable to solubilize around 3.1 g/L BTZ . Here, we obtained similar results for the A-pBuOx-A triblock (i.e. 3.1 g/L soluble BTZ at 6 g/L feed). At 8 g/L BTZ feed, A-pBuOx-A gave BTZ solubility of around 3.9 g/L. However, the A-PentOx-A, its higher homologue, was found to be the best solubilizer, giving a BTZ solubility of 4.7 g/L (at 10 g/L feed) (LC β 32 wt.% and LE β 47%) (Figure ). The BTZ solubility in plain water was found to be relatively high with 0.75 g/L (Table ). A-pBuOzi-A showed a similar performance like A-pBuOx-A and gave a BTZ solubility of 3.8 g/L (at 10 g/L feed). Compared to other drugs, A-pPrOzi-A performed better in solubilizing BTZ, but the achieved solubility (β 2.7 g/L) was less than other polymers in the series. The suggested compatibility profile was not corroborated by formulation experiments, instead of A-pBuOx-A, the A-pPentOx-A was found to be best solubilizer and A-pPrOzi-A and A-pBuOzi-A showed differences in solubilizing BTZ, which became more apparent at higher BTZ feed. |
625530ddebac3a4918d21843 | 45 | CBD is phyto-cannabinoid used for the treatment of epileptic seizures and in neuropathic pains . CBD solubility was below our limit of detection, and therefore practically insoluble in plain water (Table ). According to Ra calculation, the order of compatibility is pBuOzi > pPentOx > pPrOzi > pBuOx (Figure ). In general, the POzi based triblocks were found to be better solubilizer for CBD. The formulation results also revealed A-pBuOzi-A to be the best solubilizer for CBD, i.e. 3.3 g/L CBD (at 4 g/L feed), (LC β 25 wt.% and LE β 82%). However, with the further increase in CBD feed, a dramatic decrease in solubility was observed (i.e 0.1 g/L soluble CBD at 6 g/L feed) (Figure ). Berrocoso et al. reported the CBD loaded PEG-PLGA nanoparticles with the LC of 12 wt.% . Instead of A-pPentOx-A, as estimated by Ra calculation, the second best solubilizer was found to be A-pPrOzi-A (3 g/L soluble CBD at 4 g/L feed). The maximum achievable soluble CBD with A-pBuOx-A triblock was around 2 g/L at 8 g/L CBD feed. The A-pPentOx-A was found to be the least efficient solubilizer and gave only 1 g/L soluble CBD at 2 g/L feed. At 10 g/L CBD feed, all the four triblock formulations precipitated and, the soluble CBD level fell below 0.2 g/L. The results obtained by compatibility estimation are partially consistent with the formulation results. |
625530ddebac3a4918d21843 | 46 | CXB is a cyclooxygenase (COX2) inhibitor and a nonsteroidal antiinflammatory drug . According to Ra calculation, pPrOzi hydrophobic block was supposed to be most compatible, pPentOx/pBuOzi showed similar and intermediate while pBuOx should exhibit the least compatibility for CXB (Figure ). On the contrary, the A-pBuOx-A gave the maximum achievable aqueous solubility for CXB i.e. 4.8 g/L (at 6 g/L CXB feed) (LC β 32 wt.% and LE β 80%) (Figure ). The solubility of CXB was experimentally found to be 0.004 g/L (Table ). At 2 and 4 g/L CXB feed, all the triblock copolymers gave the similar solubility, except for A-pPentOx-A, which showed a slight decrease (β 3.8 g/L) in solubilizing CXB at 4 g/L feed. Above 6 g/L feed, all the four triblock copolymer showed different solubilizing capacity and a general decrease in solubility for CXB was observed. Compared to other triblock copolymers, a dramatic decrease was observed in the case of A-pPrOzi-A triblock copolymer (solubility of CXB dropped to 0.1 g/L). The compatibility results for CXB are not consistent with the formulation experiments. The triblock copolymer concentration was kept constant at 10 g/L with the increasing feed of drug from 2 to 10 g/L. The triblock copolymers are represented according to their hydrophobic blocks only. All the formulation were prepared in triplicate and the results are presented as means Β± standard deviation. |
625530ddebac3a4918d21843 | 47 | CTZ is an imidazole derivative with antifungal activity. It is used for the treatment of various infections like pityriasis and vaginal yeast infection . The estimation with Ra displayed the following decreasing order of compatibility, i.e. pBuOzi > pPrOzi β pPentOx > pBuOx (Figure ). Our experiments showed that the CTZ is essentially insoluble in plain water (Table ). The formulation experiments revealed A-pPentOx-A to be the best solubilizer for CTZ. At the highest tested feed ratio of 10 g/L, the formulation was completely clear and all of the added drug was solubilized (LC β 50 wt.% and LE β 100%) (Figure ). In contrast, the A-pPrOzi-A was found to be the least efficient in solubilizing CTZ and at all tested CTZ feed ratios, solubility fell below 0.2 g/L. Catenacci et al. recently reported the CTZ loaded hyaluronic acid capable to solubilize 0.018 g/L CTZ [71], 3.5 orders of magnitude lower compared to the apparent solubility achieved here. Again, the CTZ formulation results obtained are completely opposite to the compatibility estimation, where a similar level of compatibility for A-pPrOzi-A/A-pPentOx-A was observed. The A-pBuOx-A and A-pBuOzi-A showed intermediate solubilizing capacity for CTZ i.e. 2.6 and 4.4 g/L, respectively and with the increasing drug feed minor increase in solubility was observed. |
625530ddebac3a4918d21843 | 48 | The GEN is a naturally occurring isoflavone. It is TKI and topoisomerase II inhibitor. It also exhibits anti-tumor, anthelmintic and anti-inflammatory properties . Like DSA, VOR and BTZ, upon Ra calculation, the hydrophilic pMeOx was supposed to show higher compatibility for GEN in comparison to hydrophobic blocks while for hydrophobic blocks, the estimated compatibility was in the order of pBuOx > pPentOx > pBuOzi > pPrOzi (Figure ). The experimentally determined GEN solubility in water was found to be 0.007 g/L (Table ). The formulation experiments revealed, at 6 g/L feed, both A-pBuOx-A and A-pBuOzi-A were capable to solubilize around 4.2 (LC β 29 wt.% and LE β 70%) and 4.3 g/L (LC β 30 wt.% and LE β 71%) of GEN, respectively (Figure ). A direct relationship was observed between GEN feed and solubilized GEN up to 6 g/L feed for all the triblock copolymers, with the exception of A-pPentOx-A (for which a slight decrease in GEN solubility was observed), while with the further GEN increase, the solubilizing capacity for all the triblock copolymer dropped to around 1.3 g/L. At 2, 8 and 10 g/L GEN feed, no significant differences in solubility was observed for all the four triblock copolymers. However, at 4 and 6 g/L GEN feed, higher level of polymer drug specificity can be observed. The compatibility results obtained by Ra calculation are partially consistent with the formulation results. As predicted, the A-pBuOx-A exhibited higher solubilizing capacity for GEN, but at the same time A-pBuOzi-A, which was predicted as third best solubilizer also showed similar solubilizing capacity like A-pBuOx-A at 6 g/L feed. While the A-pPentOx-A being predicted as second best solubilizer, appeared last in the row with the least formulation efficiency. |
625530ddebac3a4918d21843 | 49 | Experimentally, the formulation results revealed significant differences in solubilizing capacities of all triblock copolymer at varying LAP feed. The A-pPentOx-A gave maximum solubility of 5.5 g/L at 6 g/L feed (LC β 35 wt.% and LE β 91%) (Figure ). The further increase in the LAP feed did not improve the solubility, and it remain between 5 and 6 g/L. The similar behaviour was observed for A-pBuOx-A and A-pBuOzi-A, however the maximum achievable soluble LAP was 3.4 and 2.8 g/L, respectively. The A-pPrOzi-A was found to be least efficient in solubilizing LAP (β 1.5 g/L). The obtained formulation results are not in correspondence with the estimated compatibility profile. |
625530ddebac3a4918d21843 | 50 | The kinase inhibitor SRF is used for the treatment of renal and hepatocellular carcinoma . It is practically insoluble in plain water (Table ). According to Ra, the hydrophilic pMeOx should exhibit a higher compatibility with SRF than hydrophobic blocks. For the hydrophobic blocks, the order of compatibility was found to be pBuOx > pPrOzi > pPentOx > pBuOzi (Figure ). On the contrary, the formulation results showed that the best solubilizer for SRF is A-pPrOzi-A giving a solubility of 5.6 g/L at 8 g/L SRF feed (LC β 36 wt.% and LE β 70%) (Figure ). A-pBuOzi-A, the higher homologue of A-pPrOzi-A appeared to be least efficient solubilizer for SRF and solubility fell below 0.7 g/L at all the employed feed of SRF. The A-pPentOx-A appeared to be the second best solubilizer (4.1 g/L) while A-pBuOx-A, being best solubilizer for paclitaxel and many other drug herein, could solubilize SRF only to 1.6 g/L Overall, no correlation was observed between the estimated compatibility and formulation results. |
625530ddebac3a4918d21843 | 51 | The VSM is a hedgehog signalling inhibitor used for the treatment of basal cell carcinoma . Like DSA, VOR, GEN and BTZ, upon Ra calculation, the hydrophilic pMeOx showed higher compatibility for VSM in comparison to hydrophobic blocks while for hydrophobic blocks, the estimated compatibility was in the order of pBuOx β pPrOzi > pPentOx > pBuOzi (Figure ). Experimentally, VSM was essentially insoluble in plain water (Table ) but with the A-pPentOx-A triblock copolymer, we were capable to solubilize around 8.8 g/L (at 10 g/L VSM feed) (LC β 47 wt.% and LE β 88%) (Figure ). The A-pBuOx-A and A-pBuOzi-A also exhibited very high solubilizing capacity of 7.2 and 7.5 g/L, respectively, albeit less than A-pPentOx-A. Utilizing the A-pBuOx-A triblock, very recently, Hwang et al. also reported the VSM formulation capable to solubilize around 7.5 g/L VSM (at 8 g/L feed) , |
625530ddebac3a4918d21843 | 52 | MT is a drug of choice for adrenocortical carcinoma . According to Ra calculation, the extent of compatibility between MT and triblocks was supposed to be in following order i.e. pBuOzi > pPrOzi β pPentOx > pBuOx (Figure ). The measured aqueous MT solubility was found to be 0.0004 g/L (Table ). The formulation results revealed A-pPentOx-A to be the best solubilizer, yielding an aqueous MT solubility of around 7.2 g/L at 10 g/L MT feed (LC β 42 wt.% and LE β 72%) (Figure ). The second and third best solubilizer was found to A-pBuOx-A and A-pBuOzi-A with MT solubility of around 5.7 and 4.3 g/L (at 10 g/L MT feed) (LC β 36 and 30 wt.%). The A-pPrOzi-A displayed relatively low solubility for MT i.e. 1.4 g/L (at 6 g/L feed) . Apparently, there is no correlation between compatibility estimation and formulation results. So far, the correlation between HSP based predicted compatibility and experimental formulation results for four polymers vs one drug were presented. To analyse the compatibility of 21 drugs for single polymer, the obtained results were replotted to present this trend to the readers (Figure ). On the left Y-axis Ra values are plotted with the decreasing order of compatibility between each polymer and drugs, while on the right Y-axis the actual solubility of drugs (as a formulation) is plotted. No correlation was observed between Ra based compatibility trend and the formulation results of 21 drugs with individual polymer. |
625530ddebac3a4918d21843 | 53 | The non-covalent supramolecular affinities (such as hydrogen bonding, hydrophobic interaction, Ο-Ο stacking and van der Waals interactions) between polymers and drugs play a very important role in overall organization and colloidal stability of such assemblies. The efficient and stable encapsulation of cargo into the micelles is not only governed by cargo polymer interaction, but certain innate properties of cargo like chemical composition, rigidity, conformation, molecular weight (Table ) and/or most importantly interfacial structure between cargo and polymer also play a very important role. It is becoming more evident that the ultra-high drug loading reported for the majority of the tested drugs with POx/POzi based amphiphiles is partly because of hydrophilic pMeOx . The A-pPrOzi-A/curcumin and A-pBuOx-A/paclitaxel have been investigated thoroughly in this regard. Previously, investigating the ultra-high curcumin loaded A-pPrOzi-A formulation with solid state NMR spectroscopy , PΓΆppler et al. |
625530ddebac3a4918d21843 | 54 | demonstrated that polymer carbonyl moieties acting as hydrogen bond acceptor were highly sensitive to presence of curcumin (a proton donor). After a certain curcumin feed, the amide groups of hydrophilic corona also start to involve in solubilizing the cargo, leading to physical crosslinking and finally causing colloidal instability and precipitation of the whole system. In the case of POx/POzi based amphiphiles library, LΓΌbtow et al. observed that the drugs with higher proton donor count yielded the highest drug loading and vice versa, however the library was relatively small consisting of only 5 hydrophobic compounds . Herein, no correlation was observed between high proton donor count in drugs structure and higher drug loading. Out of 21 drugs, bortezomib which has the highest number of proton donor group i.e. 4 (Table ) has shown the intermediate loading capacity of 32 wt.% (Table ) while the two other drugs i.e. clotrimazole and mitotane having zero proton donor groups (Table ) |
625530ddebac3a4918d21843 | 55 | have shown the highest loading capacity of 50 and 42 wt.%, respectively (Table ). The six drugs i.e. dasatinib, sunitinib, vorinostat, cabazitaxel, genistein and sorafenib with three proton donor groups (Table ) have shown a varied loading capacity of 22, 5, 16, 50, 30 and 36 wt.%, respectively (Table ). Additionally, water molecules also have strong influence on the conformation and aggregation morphology of many drug delivery vehicle . The simple mathematical calculations like solubility parameters determination for such kind of complex system is obviously insufficient to get realistic compatibility profile. So the discrepancy between experiment formulation results and the compatibility estimation by aforementioned group contribution methods are likely due, in part, to the absence of such factors in general calculation. |
625530ddebac3a4918d21843 | 56 | To investigate the shelf-life, the freshly prepared formulations were stored at ambient conditions with the initial precipitate (if any). The samples were collected at day 0, 1, 5 and 30 and quantified by HPLC. The drugs which exhibited very poor loading capacity were excluded from this study. Accordingly, the stability studies of six drugs is presented namely CBZ, CXB, CTZ, CBD, LAP and MT. Previously, we had observed A-pBuOx-A/PTX and A-pPrOzi-A/curcumin exhibited an excellent stability for several months. However, in few cases, POx/POzi based formulation were also found to be less stable . |
625530ddebac3a4918d21843 | 57 | In case of CBZ formulations, initially a slight reduction in solubility (β 10-15 %) was observed in all the four triblock copolymers from day 0 to day 1 (24 h) (Figure ). The A-pBuOx-A and A-pBuOzi-A showed relatively stable formulations until day 30 and gradual minor decrease in solubility was observed, i.e. 10 to 7.2 g/L and 5.3 to 3.9 g/L, respectively at 10 g/L CBZ feed. |
625530ddebac3a4918d21843 | 58 | In the case of CXB formulation, all the four triblock copolymer (at all the tested CXB ratios) exhibited very good stability and only minor loss in solubility was observed until day 30 (Figure ). In the case of A-pBuOx-A, A-pPentOx-A and A-pPrOzi-A (at 6 g/L CXB feed) the solubility decreased from 4.8 to 4.3, 3.7 to 2.5, 3.5 to 3.2 g/L, respectively from day 0 to 30 while in the case of A-pBuOzi-A formulation (at 4 g/L CXB feed), the solubility decreased from 4.0 to 2.7 g/L. In the case of CTZ formulations, the A-pBuOx-A triblock copolymer presented as highly stable formulation at all the tested ratios and a minor loss in solubility was observed (< 5%) although the solubility never exceeded β 2 g/L at any of the employed CTZ feed (Figure ). |
625530ddebac3a4918d21843 | 59 | A-pBuOzi-A based formulations followed the similar trend until day 5, however slightly higher loss in solubility was observed at day 30 (β 30-40 %). The A-pPrOzi-A displayed very poor solubilizing capacity for CTZ so it was not further considered for long term stability study. In the case of A-pPentOx-A triblock copolymer, all the employed CTZ was completely solubilized in freshly prepared formulation. However, the formulation tend to agglomerate or precipitate fast and at day 1, a solubility loss of around 50% was observed and until day 30 this loss further increased to 90%. |
625530ddebac3a4918d21843 | 60 | The CBD formulations followed a somewhat similar pattern like CXB formulations, i.e. minor loss in solubility (< 5%) was observed at day 1 at all the tested ratios and until day 30 no significant loss was further observed (Figure ). However, in freshly prepared formulations, the solubility of CBD never exceeded 1.5 and 3.4 g/L in POx and POzi based triblock copolymers, respectively. |
625530ddebac3a4918d21843 | 61 | For LAP, the A-pPentOx-A triblock also exhibited the similar stability pattern as for CTZ i.e. rapid reduction in solubility was observed at day 1 and until day 30, an 80% decrease in LAP solubility was observed (Figure ). In contrast, for A-pBuOx-A, A-pBuOzi-A and A-pPrOzi-A triblock copolymers, a minor loss in solubility (< 10%) was observed until day 30. |
625530ddebac3a4918d21843 | 62 | In the case of POx/POzi based formulations, it is becoming more evident that the after a certain threshold drug feed, the hydrophilic corona start to interact with the hydrophobic drug and this association may lead to high drug loading and/or eventually the formulation agglomeration and precipitation. In majority cases, the drug was found to be amorphous in these agglomerate/precipitates with the exception of A-pBuOx-A/MT formulation where at 6 g/L MT feed, the rapid crystallization of drug was observed. The differential scanning calorimetry (DSC) measurement further confirmed the presence of crystalline mitotane. Herein, for MT formulations, we can also speculate the similar phenomena, particularly for A-pBuOzi-A triblock based formulations, where a rapid formulation instability can be observed even at lower MT feed i.e. 4 g/L (Figure ). While, the poor instability in the case of the A-pPentOx-A triblock copolymer might hint towards different mechanism, as we have observed this poor stability problem in most of the other drug presented herein. |
625530ddebac3a4918d21843 | 63 | Compared to the other triblock copolymers used in this study, A-pPentOx-A has been been much less explored for formulation development. Recently, an ultra-high drug loaded A-pPentOx-A/BT-44 formulations (BT-44 solubility β 9 g/L at 10 g/L polymer feed) was reported. At all the tested ratios, the solubility of BT-44 was decreased by 90% by day 30. This poor stability was further investigated in detail to confirm, if the drug BT-44 is crystallizing like previously reported A-pBuOx-A/MT formulation or this decreased in solubility is because of the formulation agglomeration. The DSC measurements confirmed the presence of amorphous BT-44. Additionally, the dynamic light scattering experiments (at 173Β°, at room temperature) revealed the relatively bigger hydrodynamic diameter (Dh) of 115 nm for plain polymer at 10 g/L concentration. The results obtained by DLS were further corroborated by cryo-TEM analysis where the plain polymer at 10 g/L and BT-44 formulation at 10/2 g/L polymer/BT-44 feed, appeared as worm like structures. In general, based on these recent findings, the poor stability of A-pPentOx-A formulation for the majority of drugs tested here, can be correlated to the polymer aggregation/agglomeration behaviour. Recently, depending upon the drug feed, Lim et al. observed the transition of freshly prepared A-pBuOx-A/Olaparib spherical micelles (Dh β 10-30 nm) to worm like structures (Dh β 200 nm) in the time span of 72 hours . While, the small angle neutron scattering (SANS) revealed the core shell morphologies in the case of plain A-pBuOx-A polymer . |
625530ddebac3a4918d21843 | 64 | In general, it is now evident that, such morphology transition is usually driven by presence of certain level of hydrophobic environment in the whole system assembling together, which in the case of A-pBuOx-A triblock copolymer is provided by a specific threshold drug concentration while in the case of A-pPentOx-A triblock copolymer, the hydrophobicity of pPentOx block is sufficient to induce this transition which is further substantiated with the drug addition leading to rapid formulation agglomeration. The direct comparison of A-pBuOx-A and A-pPentOx-A micellar formulations utilizing the analytical tools like solid state NMR and SANS can give us much deeper understanding of polymer drug interactions resulting in specialized micellar architecture, however such analysis is beyond the scope of current contribution. |
625530ddebac3a4918d21843 | 65 | A considerable library of structurally diverse 21 hydrophobic drugs was tested with four POx/POzi based triblock copolymer which differ from each other by one methylene unit (shuffling either in the side chain or backbone) rendering them the structural isomers of each other (i.e. pBuOx/pPrOzi and pPentOx/pBuOzi, respectively). The results obtained by compatibility estimation (by group contribution method i.e. HnV and YMB) were not in accordance with the obtained formulation results with only a few exceptions, which can be considered as more coincidental rather than systematic. The practical weakness of this approach is the limited number of functional groups available in the literature and most importantly the impact of secondary factors like thermodynamics, hydrophilic lipophilic balance, drug structure, drug rigidity, interfacial tension, polymer and drug concentration, the solvent and the method for formulation development, which are not taken into consideration in such approaches. In particular, also the block copolymer nature is not at all taken into account. Thus, the theoretical prediction based on the assumption that majority of the drug is located in the core of polymeric micelles is not comprehensive and should be practised with caution. Therefore, it is extremely essential to build a theoretical method, capable to bring most of the factor discussed above into consideration, for drug-polymer compatibility evaluation to guide the formulation design of polymeric micelles. |
625530ddebac3a4918d21843 | 66 | Nevertheless, we have successfully solubilized the majority of the hydrophobic drugs in the library specifically, 11 out of 21 drugs exhibited the loading capacity > 20 wt.% (Table ), which is typical upper limit for many systems reported in the literature. Even for those that did not perform well, the apparent solubility was still in most cases higher then previously reported in literature. Similar to previously reported POx based triblock copolymers formulation , we anticipate that variety of formulations presented herein will allow the parenteral administration and will help to alleviate the problem associated with the use of hydrophobic drugs like, poor pharmacokinetics and use of toxic excipients for parenteral administration, overall improving the therapeutic outcomes of treatment. |
625530ddebac3a4918d21843 | 67 | Table The partial and total solubility parameters of drugs and polymers obtained by Yamamoto molecular break method by utilizing the SMILES in commercially available HSPiP software. The dash (-) is representing the solubility parameters were not possible to obtain because of very large SMILES and software was not capable to process. |
625530ddebac3a4918d21843 | 68 | Figure The stability study of the cabazitaxel formulations prepared with 4 different triblock copolymers used in this study (at constant polymer feed of 10 g/L and increasing drug feed from 2 to 10 g/L). The formulations were stored at ambient conditions with initial precipitate. The quantification was done by HPLC at day 0, 1, 5 and 30. All the formulations were centrifuged at 10.000 rpm prior to collecting the sample. |
625530ddebac3a4918d21843 | 69 | The stability study of the celecoxib formulations prepared with 4 different triblock copolymers used in this study (at constant polymer feed of 10 g/L and increasing drug feed from 2 to 10 g/L). The formulations were stored at ambient conditions with initial precipitate. The quantification was done by HPLC at day 0, 1, 5 and 30. All the formulations were centrifuged at 10.000 rpm prior to collecting the sample. |
625530ddebac3a4918d21843 | 70 | The stability study of the clotrimazole formulations prepared with 4 different triblock copolymers used in this study (at constant polymer feed of 10 g/L and increasing drug feed from 2 to 10 g/L). The formulations were stored at ambient conditions with initial precipitate. The quantification was done by HPLC at day 0, 1, 5 and 30. All the formulations were centrifuged at 10.000 rpm prior to collecting the samples. |
625530ddebac3a4918d21843 | 71 | The stability study of the cannabidiol formulations prepared with 4 different triblock copolymers used in this study (at constant polymer feed of 10 g/L and increasing drug feed from 2 to 10 g/L). The formulations were stored at ambient conditions with initial precipitate. The quantification was done by HPLC at day 0, 1, 5 and 30. All the formulations were centrifuged at 10.000 rpm prior to collecting the sample. |
625530ddebac3a4918d21843 | 72 | The stability study of the lapatinib formulations prepared with 4 different triblock copolymers used in this study (at constant polymer feed of 10 g/L and increasing drug feed from 2 to 10 g/L). The formulations were stored at ambient conditions with initial precipitate. The quantification was done by HPLC at day 0, 1, 5 and 30. All the formulations were centrifuged at 10.000 rpm prior to collecting the samples. |
625530ddebac3a4918d21843 | 73 | The stability study of the mitotane formulations prepared with 4 different triblock copolymers used in this study (at constant polymer feed of 10 g/L and increasing drug feed from 2 to 10 g/L). The formulations were stored at ambient conditions with initial precipitate. The quantification was done by HPLC at day 0, 1, 5 and 30. All the formulations were centrifuged at 10.000 rpm prior to collecting the sample. |
63dd124d6d032916bb55dc43 | 0 | Wood and other forms of lignocellulosic biomass constitute an abundant natural resource with a tremendous capacity to provide sustainable fuels, chemicals, and materials for a variety of applications . Biorefineries seek to employ conversion strategies to deconstruct lignocellulosic biopolymers into smaller molecules that can be subsequently converted into fuels or platform chemicals, recreating the petrochemical products with a smaller temporal gap between photosynthesis and utilization . These conversion strategies employ biochemical processes such as enzymatic hydrolysis and fermentation, and thermochemical pathways such as pyrolysis and catalytic upgrading, to drive transformation of biomass-derived molecules into desirable products. Wood is also intrinsically valuable as a sustainable construction material for a wide range of applications, including furniture, tools, and buildings . More recently, mass timber products like crosslaminated timber panels have been developed and become viable alternatives to nonrenewable steel and concrete materials for the construction of mid-to high-rise buildings . |
63dd124d6d032916bb55dc43 | 1 | Understanding and controlling transport of ions and small molecules throughout wood and lignocellulosic biomass is critical to both biorefining and materials applications. For example, biological conversion scenarios use thermochemical pretreatments to enhance the yields of enzymatic hydrolysis . Such pretreatments involve infiltration of the biomass with mineral acids and bases such as sulfuric acid and sodium hydroxide, which diffuse into cell walls to depolymerize non-structural polysaccharides and thereby provide better access for cellulase enzymes during saccharification . Similarly, biomass fractionation processes often require diffusion of small molecular solvents into the cell walls to enable extraction of select biopolymer components . |
63dd124d6d032916bb55dc43 | 2 | For construction material applications, transport processes through woody cell wall materials is also important for creating durable adhesive bonds , chemically modifying wood , and wood preservation treatments . Wood degradation mechanisms, such as fungal decay and metal fastener corrosion , are also controlled by transport. These types of degradation limit the utility of wood in high moisture environments. An improved understanding of transport mechanisms would accelerate the development of more environmentally friendly wood preservation treatments and improved resistance to degradation, thereby expanding the market for sustainable wood construction materials . |
63dd124d6d032916bb55dc43 | 3 | Wood tissue exhibits a hierarchical structure which provides structural support while enabling transport of water and nutrients . The microstructure is highly porous and varies extensively between species. Bulk transport of water and ions is effectively facilitated by the macroporosity of wood , however intra-cell wall diffusion requires infiltration into the complex assembly of lignocellulosic polymers. Quantitatively discerning the precise nanostructure of lignocellulosic biomass is still an active area of research ; however, it is generally accepted that bundles of several dozen cellulose chains are assembled into larger fibrils which are decorated with hemicellulose and further ensheathed with lignin , and that the internal structure and dynamics change as a function of hydration . |
63dd124d6d032916bb55dc43 | 4 | Many studies have investigated molecular transport within wood and other types of biomass with computational and experimental methods. Given suitable structural characterization of the macroporosity of wood tissue, often by imaging methods, bulk transport throughout the interconnected pores can be well-described by direct numerical simulation considering the structure explicitly, and coupling this structure to reduced order approximations for bulk transport in porous media . However, characterizing diffusive transport within the cell wall has proven far more challenging largely because the length scale at which intra-cell wall diffusion occurs (~ 10 -5 m) and the difficulty of decoupling intra-cell wall diffusion from bulk diffusion through the macropores precludes most bulk measurement techniques. From a materials perspective, unmodified lignocellulosic cell walls are solid polymers and intra-cell wall transport is expected to be a solid polymer diffusion process , with motions at the atomic scale by the individual polymers in the cell wall together with hydration levels controlling diffusion. |
63dd124d6d032916bb55dc43 | 5 | Recent experimental work on latewood loblolly pine cell wall layers strongly supports that diffusion through unmodified wood cell walls is a solid polymer diffusion process, where motions within the polymer structure are limiting to transport. Using synchrotron X-ray fluorescence microscopy (XFM) and a custom-built RH chamber, Zelinka and coworkers directly observed that there is a 60-85% RH threshold for mineral ion diffusion in individual wood cell wall layers . At levels below this level of hydration, there is simply no room in the wood nanostructure to permit diffusion, whereas enough water intercalates into the wood structure at greater humidity to plasticize the wood polymers and facilitate mineral ion diffusion. Interestingly, the 60-85% RH range also corresponds to the 50-85% RH range for the moistureinduced glass transition in amorphous polysaccharides . Using nanoindentation dynamic mechanical analysis, it is possible to assess the moisture-and time-dependence of the molecular relaxations corresponding to the glass transition . These molecular relaxations correlate directly to ionic conductivity measurements made on similar wood cell wall layers, demonstrating that ionic conductivity is being controlled by the molecular relaxations . This manifests concretely in time-lapse XFM imaging, from which it is possible to determine moisture-dependent ion diffusion constants . The direct connection to moisture content highlights how structural changes at the atomic scale propagate forward to higher order observables. |
63dd124d6d032916bb55dc43 | 6 | With this experimental context in mind, the current study aims to use the power of molecular simulation to act as a computational microscope to identify how interactions in intact biomass respond to changes in hydration (Figure ). Using prior experiments as a benchmark for comparison , we can compute diffusion coefficients for multiple ion species (Na + , K + , Cu 2+ , and Cl -) within our models. We find that the diffusion coefficients determined from atomistic simulation models show the same trends found experimentally. Using the detailed structural information available only from an atomic model, we find that increasing hydration reduces contacts between individual biopolymers within a cell wall, creating the space for rapid diffusion along hydrated tracks parallel to the hemicellulose strands once water molecules account for 10-15% of the total mass for the cell wall. The detailed molecular picture also identifies interactions between carboxylate groups that decorate the hemicellulose and positive ions. These interactions impede diffusion even further beyond what the crowded conditions require within the cell wall. |
63dd124d6d032916bb55dc43 | 7 | The secondary cell wall model used here contains the three major polymers, cellulose, hemicellulose, and lignin, in approximately the ratio found in hardwood (Table ). The cellulose model contains four 18-chain cellulose IΞ² bundles with DP (degree of polymerization) of 40 in the 234432 motif (Figure ). Decorated xylan molecule with DP of 40 was used to represent hemicellulose. Experimental studies suggest that ~40-70% of the xylose residues are acetylated on C2 or C3 positions and D-glucuronic acid groups are also linked to C2 or C3 in ~10% of the xylose residues . In our xylan model, the D-glucuronic acid groups are linked to C2 in every one of eight xylose residues, whereas the acetyl groups are linked to C2 in every other xylose residue. In models where the C2 has been occupied by a D-glucuronic acid group, the acetyl group is linked to C3. All the substitution groups are located on the even-numbered xylose residues, leading to a xylan molecule with all decorations on the same side (Figure ). A schematic lignin 20-mer model proposed by for hardwood was used to construct the structure of the lignin polymer model, which contains 13 syringol units and 7 guaiacol units (S:G = 65:35) (Figure ). While the individual polymers were repeated to fill the simulation volume (Table ), and therefore the polymer distribution is not polydisperse like it would be in intact biomass, the system approximately represents intact biomass to within the limitations of current modeling approaches. The individual components were assembled using PACKMOL into a rectangular simulation volume. The generated PCW model was compressed slowly by decreasing the simulation box dimensions until a desired density of 1.5 g/cm 3 determined experimentally from dried wood was achieved at a box size of 78.8 Γ
x 78.8 Γ
x 210.6 Γ
. Sodium ions were added to maintain the total charge of the system to be neutral. |
63dd124d6d032916bb55dc43 | 8 | The initial model described above was generated such that water was 3 weight percent of the total simulation system. To generate alternative systems with different hydration levels, the hemicellulose and lignin polymers were moved such that the center of geometry each individual molecule was multiplied by a constant factor, effectively moving each polymer away from cellulose fibril without introducing ring penetrations. Additional water molecules were added into the interstitial spaces after rewrapping the lignocellulose using the solvate plugin to VMD. By empirically varying the constant factor by which the system was expanded, we obtain models that are 0, 3, 5, 10, 15, 20, 25, or 30 percent water by weight (100% x mass water / mass total) (Figure ) and range from approximately 120,000 atoms to 190,000 atoms in size. Converting to equilibrium moisture content, these systems have an equilibrium moisture content of 0, 3. .9%, respectively. This range of hydration spans hygroscopic measurements for wood at across all humidity levels up to the fiber saturation point . To track ion diffusion within the system, ions were added by replacing water molecules within the system. Three ionization models were prepared for each level of hydration, shown in Figure . In the first case, only neutralizing sodium ions were added to each model. To directly compare against experimental findings, 100mM KCl, and CuCl2 salts were added to the hydrated neutralized models using the autoionize plugin to VMD to create two alternative systems. |
63dd124d6d032916bb55dc43 | 9 | Other simulation parameters are shared. The CHARMM36 force field was used to describe interactions between carbohydrates , lignin , water , and ions . Following CHARMM36 standards, we used a 12 Γ
cutoff and a force switching function after 10 Γ
. Long range electrostatics was treated using particle mesh Ewald with a 1.2 Γ
grid spacing . To enable a 2fs timestep between force evaluations, covalent bonds to hydrogen atoms were treated using the RATTLE algorithm . The Langevin thermostat was set to maintain a temperature of 300K using a 5ps -1 damping coefficient . A Langevin barostat semi-isotropic with respect to the cellulose fibril axis was set to maintain 1 atm pressure . |
63dd124d6d032916bb55dc43 | 10 | In the analysis of our trajectories, we quantified key observables such as diffusion coefficients and intermolecular contacts using scripts written for python-enabled alpha versions of VMD 1.9.4 . Leveraging python libraries such as NumPy , SciPy , and matplotlib , we use Einstein's relation to quantify diffusion from the mean-squared displacement . To analyze diffusion, we leverage the long trajectories by analyzing multiple 50ns trajectory snippets to determine a diffusion distribution. In this analysis, the trajectories are aligned to the cellulose fibril to eliminate drift based on thermostat fluctuations and the initial velocities. The diffusion coefficient within an individual snippet is determined from the slope of the linear fit between mean squared displacement and time (π· = |
63dd124d6d032916bb55dc43 | 11 | (,)01( (1) This contact sum captures the essential close-contact interactions between cell wall components and is less sensitive to an arbitrary cutoff choice than other alternative metrics. To determine the contact number in the dense, periodic system, we used the KDtree implementation in Scipy to determine contact distances between atoms within the periodic system using a minimum image convention. |
63dd124d6d032916bb55dc43 | 12 | Here, we present the results from independent all-atom molecular dynamics (MD) simulations of the plant secondary cell wall (Animation S1) with different water weights, ranging from 0 -30 wt% water, which span the realistic range for wood moisture content. First, we calculate the diffusion coefficient (D) of cell wall polymers, ions, and water at different water weights. In addition, we calculate the diffusion coefficient of ions (Na + , K + , Ca 2+ , Cl -) in the cell wall and find that our results agree well with previously reported X-ray fluorescence microscopy measurements . Next, we quantify the contacts between different cell wall polymers using Eq. 1. Both molecular diffusion and measured contacts between cell wall polymers exemplify changes in the mechanical properties of secondary cell wall at varying moisture levels. Visually, the increase in diffusion is immediately apparent from our trajectories. As shown in supporting animation S2, cell walls with low moisture content appear to be essentially static over the microsecond long trajectory animations. By contrast, increasing hydration creates trajectories that are visibly more dynamic (Animation S3), even if the overall structure remains relatively consistent over the simulation timescale. |
63dd124d6d032916bb55dc43 | 13 | The measured diffusion rates across the different cell wall models vary considerably and are dependent on hydration within the plant cell wall (Figure ). Higher moisture content is observed to broadly increase diffusion by more than an order of magnitude across the hydration levels tested. Following general trends for diffusion in solution, larger polymers diffuse more slowly than ions or water, and ions move more slowly than the water molecules that lubricate the interpolymer spaces within the model. |
63dd124d6d032916bb55dc43 | 14 | The water within the model exhibits slower dynamics than it would in bulk solution. Whereas the expected diffusion coefficient for the TIP3 water model is 6 x 10 -5 cm 2 /s , we find that water diffusion within the confines of the cell wall is at least an order of magnitude slower (Figure ). Slower water dynamics compared to bulk with a similar order of magnitude difference have been observed previously through quasielastic neutron scattering measurements . |
63dd124d6d032916bb55dc43 | 15 | Among the cell wall polymers, cellulose is observed to have the slowest diffusion (Figure ). The cellulose fibril is on aggregate the largest single entity in the simulation system at approximately 470 kDa. Its size and slow motion made cellulose the natural choice for aligning the overall trajectory prior to measuring the mean squared displacements needed to calculate the diffusion coefficients reported in Figure . Without this realignment, correlated drifts for the center of mass of the whole system pollute the diffusion measurement, substantially accelerating diffusion for the slowest components. The lignin and hemicellulose fractions have similar diffusion profiles, owing to the similar molecular weights for each individual molecule within the system, 4.5kDa for lignin fragments, and 7.1 kDa for each hemicellulose chain. However, size is not the only determinant for diffusion, as hydrophilic hemicelluloses demonstrate slightly larger gains in diffusion coefficient with increasing hydration than amphipathic lignin polymers do. The exception to this is cellulose, which is the largest single polymer component within the cell wall model and was used as the reference to eliminate center of mass drift from the trajectory. |
63dd124d6d032916bb55dc43 | 16 | Figure : Ion diffusion as a function of moisture index in secondary cell wall of woody plants. We calculate the diffusion of cations (Na + , K + and Cu 2+ ) and anion (Cl -). Overall, ion diffusion increases as the moisture index increases. For KCl and CuCl2 at 0.1 M initial concentration, diffusion coefficients were previously measured using time-lapse X-ray fluorescence microscopy (XFM) . Scatter circles and triangles with no face color represent the experimental data for the respective cation (K + and Cu 2+ ) and anion (Cl -). Atomic level molecular diffusion agrees within an order of magnitude with microscale scale diffusion measurements. Similar to observations reported in XFM experiments, we find in MD simulations that K + diffuses faster than Cu 2+ ions. |
63dd124d6d032916bb55dc43 | 17 | To tie the diffusion results to reality, we can compare ion diffusion coefficients from within our model directly to diffusion coefficients determined from time-lapse X-ray fluorescence microscopy (XFM) experiments . Figure reports the diffusion of ions calculated from MD simulations, replicating information from Figure , and directly compares the measured diffusion with the imputed diffusion coefficients from XFM. The time-lapse XFM ion maps were collected in a preconditioned 2 ΞΌm thick section of loblolly pine (Pinus taeda) held at 70%, 75%, or 80% relative humidity, which is 14 -16% equilibrium moisture content . The diffusion determined via simulation is approximately one order of magnitude faster than the experimental references. Multiple factors may contribute to this discrepancy. On the technical side, the selected water model within our simulation system is known to have faster diffusion by roughly a factor of two, with a diffusion coefficient of approximately 4-6 x 10 -5 cm 2 /s depending on temperature rather than 2.3 x 10 -5 cm 2 /s . Likewise, the initial ion distribution is different between the homogenous initial distribution from the simulation compared with the ion wavefront from a single source that was tracked in XFM. Since local charge neutrality needs to be maintained, both cations and anions diffuse at similar rates as measured by XFM , but can move independently in the periodic simulation volume. This is seen mostly explicitly in the Cl anions (Cl -), which diffused as similar rates regardless of counterion in simulation but exhibited diffusion that matched the associated cation measured with XFM . Together, we anticipate that the coupled nature of diffusion in XFM would slow diffusion of the wavefront relative to a tissue already impregnated with ions. Since we recapitulate the key trends found experimentally, that K + diffuses much more rapidly than Cu 2+ (Figure ), with magnitudes that are reasonable given the different conditions seen between the two experiments, our simplified cell wall model recapitulates the essential dynamics of ion permeation into cell walls. |
63dd124d6d032916bb55dc43 | 18 | Having established the correspondence with experiment, the widely varying water content from simulation can be used to establish trends over a wide range of conditions, including those that may be inaccessible experimentally. We observe that the diffusion coefficient of inorganic ions increases with the water weight in the cell wall of woody plants. At low water weight, akin to low moisture content, the diffusion is slow (~ 10 -9 cm 2 /s) but grows by almost three orders of magnitude (10 -6 cm 2 /s) for wood with 30 wt.% water. The wide range observed in the diffusion of ions can be attributed to the interactions between inorganic ions and the local secondary cell wall environment with different water weights. As the water weights increase, the ions appear in a more hydrated environment, and diffusion approaches values observed for bulk diffusion in solution. |
63dd124d6d032916bb55dc43 | 19 | The diffusion for individual ions appears to be related to the hydration shell radius. Within the MD simulation trajectories, we observe that similarly charged ions may have different diffusion coefficients. For instance, the sodium ion (Na + ) diffusion is a factor 2-3 slower compared to potassium ion (K + ) (Figure ). This correlates with measures of the hydration shell radius, as measures for K + (3.31 Γ
) or Cl -(3.32 Γ
) are similar, followed by Na + (3.6 Γ
) and then Cu 2+ , which has a larger hydration shell (4.1 Γ
) . This relationship mechanistically suggests that rapid ion diffusion depends on solvating the ion within the relatively mobile water within the cell wall environment. |
63dd124d6d032916bb55dc43 | 20 | Figure : Quantifying average contact between cell wall components at different water weights (A, B) Atomistic models illustrating low and high moisture content, 5% and 30% water weights respectively in secondary cell wall in plants. In this figure, the cellulose microfibril is represented in blue, hemicellulose in green and lignin in orange. To maintain the same aspect ratio for the systems represented in panels (A) and (B), panel A is zoomed in further due to the smaller dehydrated system. The water is represented by red (oxygen atom) and white (two hydrogen atoms). (C) The average number of contacts between individual cell wall components -cellulose, hemicellulose, and lignin. The average number of contacts reduces as the moisture level increases, as water molecules diffuse in between the spaces impeding interaction between individual components. Figures 6A and 6B represent a molecular system of the plant secondary cell wall at low and high moisture content, 5 and 30 water weight percent respectively. Even after extensive equilibration under constant pressure conditions, we see that there may be large voids in between individual cell wall components. This is particularly true for models with lower water content, as water can more readily fill in gaps within the cell wall structure for hydrated cell walls. As a consequence, close contacts between different cell wall polymers goes down with increasing hydration (Figure ). By hydrating the system and removing interpolymer contacts, water acts as a lubricant to polymer motion within the cell wall. Fundamentally, the reduction in contacts demonstrated by Figure drives the increase in biopolymer motion first characterized in Figure . Figure also demonstrates why cellulose-hemicellulose and especially cellulose-lignin interactions have been historically so difficult to quantify, since there are just many more hemicellulose-lignin interactions, even in the absence of covalent linkages between the polymers. and Cu 2+ (orange) and snap shots of their interactions with the carboxylate functional group in hemicellulose shown in sticks with gray, red and white colors representing the carbon, oxygen, and hydrogen atoms respectively. Ion interaction reduces with increase in moisture content. Interaction between ions and hemicellulose are always higher compared to the interaction with either lignin or cellulose. Cations have a strong affinity towards hemicellulose, as it interacts strongly with the carboxylate group in hemicellulose. As the zoom levels while rendering the molecular structures were not the same, K + cation appears bigger than Na + and Cu 2+ cations. |
63dd124d6d032916bb55dc43 | 21 | Demonstrating at a global scale that water reduces contacts with the surroundings by lubricating the cell wall interior, we again focus on the ions and what drives their differential diffusion. Figure and supporting animations S4 -S6 illustrates as well as quantifies typical cation -cell wall polymer interactions. When the water weight of the plant's secondary cell wall system increases, the contacts between cations and the cell wall polymers are generally reduced. In a solid system, the coordination number of the ions will be approximately constant, and thus the decrease in contacts to biopolymers leads to an increase in contacts to water molecules. For sodium or potassium (Figure and), the changes in contact number are monotonic. Similar trends where contacts are reduced at higher moisture levels are observed for Cu 2+ interaction with cellulose and lignin, but not when interacting with hemicellulose (Figure ). Instead, we find that the reduction in number of contacts between the cation and hemicellulose is not monotonous. Instead, the cation-hemicellulose contacts increase beyond 15% water weight. We attribute this to the strong electrostatic interaction between the cation and carboxylate functional group in hemicellulose in our secondary cell wall model, with representative snapshots shown in Figures . We would anticipate that other divalent cations would have similar strong interactions with hemicellulose carboxylate groups and may need to be avoided when optimizing for diffusion within wood. Overall, for different salts used in this study, we find the cation interaction with hemicellulose is relatively stronger when compared to interactions with lignin or cellulose, due to the carboxylate functional group in hemicellulose. |
63dd124d6d032916bb55dc43 | 22 | It is generally understood that diffusion through solid polymers including wood depends on molecular motions of the polymer, free volume in the polymer matrix, diffusant dimensions, and solubility of the diffusant in the polymer matrix . Diffusant transport is generally controlled by the motion of similar-sized features of the polymer matrix. Smaller diffusants, such as water molecules, are controlled by uncoordinated local motions, whereas larger chemicals, like mineral ions, are controlled by cooperative motions. As a hygroscopic material, water absorbs in the cell wall and acts as plasticizer that increases molecular motions and free volume. It is generally understood that diffusion is promoted by increases in water plasticization. Of particular interest is an ambient temperature moistureinduced glass transition that current evidence indicates occurs in the amorphous polysaccharides when wood is conditioned between 50 and 85% RH, which corresponds to 10-15% moisture content. Diffusion of larger chemicals, like mineral ions, are only expected to appreciably occur through rubbery polymers above their glass transition that have cooperative motions. |
63dd124d6d032916bb55dc43 | 23 | Within our simulations, where we identify a linear trend on a logarithmic scale (Figure ), it would appear at first glance that we do not see a clear moisture-induced glass transition. However, if we replot Figure on a linear scale (Figure ), this same ion and polymer diffusion information shows a clear transition at between 10-15% moisture content, where the diffusion goes from effectively zero to growing approximately linearly. Based on this simplified depiction of the plant cell wall and the observation of piecewise linear ion and polymer diffusion, we suggest that below 15% water weight the system behaves as though it were effectively static. Above that moisture threshold, internal motions become appreciable, and the material transitions to a more "rubbery" state rather than a glass. This observation of a moisture-induced glass transition, based on diffusion coefficients calculated from atomistic simulations agrees well with previously reported XFM experiments . Below this threshold, the diffusion for any permeant will be slow within a tightly bound arrangement of secondary cell wall biopolymers. However, once there is sufficient hydration, the diffusion approaches the maximum observed in an approximately linear fashion. Maintaining hydration above this transition point will be critical for applying penetrating treatments to woody biomass, and may contribute to vastly different cell wall diffusion measures across plant tissues . ). Ion diffusion in the plant secondary cell wall agrees well with previously reported X-ray fluorescence microscopy (XFM) experiments . |
63dd124d6d032916bb55dc43 | 24 | Demonstrating this importance quantitatively, we can estimate the diffusion length and timescale for penetrating wood treatments, such as ions. For Fickian ion diffusion within in the secondary cell wall, the diffusion length for a given time is estimated by this formula: πΏ # = β2π· π‘. Here, D is the diffusion coefficient and time t is how long one is willing to wait. Over short 50 ns timescales, Cu 2+ has a corresponding diffusion length of less than 1 nm, even at the highest hydration level simulated. A single xylan monomer is about 0.9 nm large. Thus, divalent copper cations tend to remain bound to a single hemicellulose polymer in the cell wall for a considerable duration within our simulation. Similarly, for monovalent sodium and potassium cations, the diffusion lengths are less than 1 nm at below 15% water wt. and between 1 -4 nm at higher levels of hydration in wood. Using these diffusion lengths, we estimate that treatments in dried wood would require timescales on the order of years to permeate 1 inch but may only take a month or two to diffuse within hydrated wood samples. In practice, where the initial concentration gradient is large rather than zero as it is in these simulations, practical treatments would take only hours in water-saturated wood. |
63dd124d6d032916bb55dc43 | 25 | The singular experience of how carboxylate groups on hemicellulose can impede divalent cation motion through strong ionic bonds illustrates potential strategies for modulating diffusion in woody tissues. For instance, modifying hemicellulose synthesis to eliminate carboxylates would likely lead to accelerated cation diffusion, as the cations would not interact as strongly with a carbonyl or hydroxyl as they would with the carboxylate. Similarly, lignin acetylation would be expected to make lignin even more hydrophobic than it already is, altering transport dynamics . Further study on both the experimental and modeling frontiers will be needed to couple together cell wall chemistry to the impact on dynamics at the molecular level. |
63dd124d6d032916bb55dc43 | 26 | The ion diffusion results also have direct impact on the electrical conductivity of wood. Typical dried wood used as building materials is a good insulator. However, measured diffusions correlates with electrical conductivity of wood based on the Nernst-Einstein equation . Thus, when an electric field is applied to wood with a moisture content above 10-15% or so, substantial ion diffusion may permit wood to act as a conductor, with conductivity spanning 6 orders of magnitude . Increasing hydrophobicity of wood polymers, such as treatments via low molecular weight phenol-aldehyde resins to exclude water and thus reduce ion movement, would be expected to significantly reduce conductance. |
63dd124d6d032916bb55dc43 | 27 | Diffusion in plant cell wall is dependent on moisture levels. The diffusion of inorganic ions in plant cell wall measured from MD simulation increases with cell wall hydration, and agrees well with prior XFM experiments . Diffusion for all species, but particularly K + and Cu 2+ is observed to have a moisture-induced glass transition at 15% equilibrium moisture content in wood. Generally, cation diffusion within the cell wall is slower compared to anion diffusion, because of strong interactions between carboxylate groups on the hemicellulose and cation retard the free diffusion of positively charged permeants. Armed with this mechanism, it is possible to design and engineer pathways to alter the mechano-chemical properties of lignocellulosic biomass, catering to applications in sustainable, chemical, and biomedical engineering. The insights obtained from our molecular simulations provide key guidelines for future experimental and computational studies, where we anticipate extending this model to explore the effects of cell wall polymer heterogeneity and acetylation on the diffusivity and ionic conductivity in plant biomass at different hydration index. |
63dd124d6d032916bb55dc43 | 28 | The MD simulations further provide a detailed mechanistic view to relate moisture content to diffusive processes within plant secondary cell walls. One of the strongest conclusions is that the moisture-induced glass transition between at between 10 -15 wt% water is a natural extension of existing trends in hydration space, where additional water facilitates polymer separation and ion solvation. Such quantitative and qualitative evaluation of molecular diffusion provides evidence towards the atomistic origins of cell wall being a barrier to diffusive transport, both for small and large diffusants, such as mineral ions and enzymes respectively. Hence strategies are being developed to engineer the cell wall microenvironment to ameliorate diffusion process, with an aim to create durable and sustainable plant-based biomaterials, to build a circular bioeconomy . |
6549f26248dad231203fd0e0 | 0 | As ββG values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue pK a s in practice. We demonstrate that our approach and a previously proposed microscopic pK a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein pK a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that n Γ€ively computed pK a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the pK a values of both uncoupled and coupled residues. |
6549f26248dad231203fd0e0 | 1 | Protein function is known to depend on the acidity of the medium. Such a pH dependence is caused by the (de)protonation of amino acid residues, whereby a proton is added or removed from an amino acid side chain. As this process is pH-dependent, at certain pH levels, the event will be more or less favorable and, by definition, at the pK a , it will be equally probable (i.e., βG prot = 0). Knowledge of the residue pK a values in a protein is essential for understanding function. It not only allows for a rationalization of protein properties (e.g., stability, solubility, etc.) and interactions at a specific pH, but in the context of enzymatic and redox reactions, pK a values can provide insight into how favorable a proton transfer will be under certain conditions. As alluded to, the pK a is fundamentally a free energy relationship; for an isolated, protonatable group, the value is proportional to the free energy of protonation: |
6549f26248dad231203fd0e0 | 2 | βG prot = RT log (10) (pH -pK a ) . (1) This relationship suggests that the free energy is linearly dependent on the solution pH; as the pH moves farther away from pK a , the free energy required to (de)protonate also shifts. A purely linear relationship between pH and βG implies a joint relationship with the probability of finding a protonatable group i in a given state; this follows from the rearranged Henderson-Hasselbalch (HH) equation: pK i a = pH + log 10 |
6549f26248dad231203fd0e0 | 3 | where β¨x i β© is the probability that residue i is protonated. However, such a curve, when computed from experiment, may be flatter or irregularly shaped, often necessitating the application of specialized fitting procedures. In such cases, not only does the curve suggest a non-linear dependence, an analysis of the complete pH-dependent behaviour is often more insightful than defining the residue by a single pK a value. |
6549f26248dad231203fd0e0 | 4 | In proteins and, in particular, enzymes, protonatable residues can, in only a few cases, be separated from their interactions with one another. Although these associations will be more pronounced at an active site, even more distant residues can experience some degree of coupling, interacting more or less strongly depending on their microenvironment, the pH of the solution, and their own protonation state. |
6549f26248dad231203fd0e0 | 5 | Indeed, this could result in a more challenging resolution of "the pK a "; however, such interactions may provide insight into a reaction mechanism or suggest the functional importance of a residue pair. In these scenarios, a modified HH-curve may still yield two clear inflection points; however, the assignment of pK a values to specific residues could remain a challenge. Moreover, the protonation probability of a coupled residue, although potentially described by an HH-curve, is nonetheless a composite probability of microstates. As Edsall and co-workers, and more recently G. Matthias Ullmann and co-workers have helped formalize, these states are in a pH-dependent equilibrium with each other and collectively comprise the macroscopic probability observed experimentally. This knowledge gap between the measurable macrostates and the cryptic microstates suggests a potential role for theoretical and computational methods, which may help to resolve both the macroscopic pK a and the microscopic pK a values. |
6549f26248dad231203fd0e0 | 6 | In this work we explore the effects of coupling on the shifts in pK a between spatially neighbouring residues. We begin by illustrating the potential magnitude of such effects on a set of toy systems by systematically altering coupling strength. We then focus on two proteins where similar coupling behaviour between amino acid residues are observed. We demonstrate that explicitly accounting for the coupling between titratable sites significantly improves accuracy of the pK a prediction and highlight the potential insights associated with coupling analysis (e.g., buffering between residues). Finally, we provide a practical guide for using alchemical free energy calculations to: 1) account for pK a shifts in coupled residues based on the formalism derived in this work; and 2) compute the probabilities of individual protonation microstates based on an existing partition function framework. |
6549f26248dad231203fd0e0 | 7 | While from the perspective of statistical mechanics the behaviour of coupled titratable sites is well understood, the subsequent challenge arises: What is the best way to extract information about changes in residue protonation using existing computational approaches? Molecular dynamics (MD) simulations offer an attractive solution to this question by providing efficient sampling of well defined thermodynamic ensembles. Over the years, several approaches have emerged to quantify pK a shifts based on MD simulations, among the most popular are constant-pH simulations (CpHMD) and alchemical free energy calculations. While CpHMD explicitly models protonation changes dynamically over the course of a simulation, an alchemical approach considers discrete protonation states and computes the free energies between them (see Appendix A for additional details). Here, we focus on the latter approach and demonstrate how to connect double free energy differences with a statistical mechanics description of population changes in coupled residue protonations. |
6549f26248dad231203fd0e0 | 8 | Consider the thermodynamic cycle given in Figure . To calculate the absolute protein pK a value of a single residue (A), we must consider the free energy of proton transfer from the gas (g) phase into the solution (s) phase and then from the solution into the protein (p) phase. However, for many model compounds, the free energy associated with the proton transfer in solution is known. Using this reference pK a value (pK β’ a ) allows us to only consider the free energies associated with the rightmost cycle, thus reducing our problem to solving ββG s,p (A H β A -) -the free energy difference between a deprotonation event in the solution phase and in the protein phase -which is related to the protein pK a by |
6549f26248dad231203fd0e0 | 9 | From here we will refer to ββG s,p (A H β A -) as ββG. Equation 3 implicitly contains two terms, which we here call ββG env and βG titr , following the notation of Sharp and Honig . The first (ββG env ) represents the free energy of dissociating a proton within a protein relative to the solvent environment, which we represent by a capped peptide. It is assumed that the protein is fixed in some protonation state and, based on Tanford and Kirkwood, has often been taken to be the state in which all titratable sites in the protein are neutralized. Because these sites are fixed to some state, this free energy is pH-independent. The second free energy component (βG titr ) reintroduces pH dependence by capturing how the free energy of dissociating the proton within the protein will be more or less favorable, depending on the states of the other protonatable sites. |
6549f26248dad231203fd0e0 | 10 | Although the pK int is pH-independent, it may still provide a strong estimate of the true pK a depending on the reference protonation state assigned to the protein. Indeed, recent work has demonstrated that alchemical free energy calculations can resolve protein pK a values relying on the assumption: pK a β pK int . Nevertheless, it is inevitable that in some instances this will break down, and only by considering βG titr (pH) can an accurate pK a be resolved. Here, we investigate whether coupling can be meaningfully resolved within an alchemical free energy framework and assess the relative importance of this contribution for computing protein pK a values. |
6549f26248dad231203fd0e0 | 11 | As alluded to the introduction, both the macroscopic and microscopic pK values are of interest. A partition function approach can account for coupling between residues and the microscopic pK values between individual states. Note that the (de)protonation of the sidechain of an amino acid can be described using a standard equilibrium binding formalism. Specifically, the "binding" of protons can be fully described by the proton concentration (c) and the binding constant (K), from which it follows that the grand partition |
6549f26248dad231203fd0e0 | 12 | Unlike in the single-site case, we now include an (un)cooperativity term that follows from the fact that: 1) the cycle is closed (i.e., K 1 + K 3 = K 2 + K 4 ), and 2) there is an "interaction free energy", w, associated with the second (de)protonation event given the first. Given that we can define the standard free energy of deprotonation as: |
6549f26248dad231203fd0e0 | 13 | Here, ββG 0 corresponds to ββG env : the free energy of deprotonating residue A while in the presence of protonated B. Similarly, ββG 3 corresponds to the deprotonation of A in the presence of deprotonated B. For all branches in the cycle, the remaining protonatable sites in the protein are fixed to their model states at pH 7.4. Notice that ββG 1 and ββG 2 will shift the populations of "reactants" and "products" with respect to ββG 0 and ββG 3 . Following a derivation provided in Appendix A, we resolve a pH-dependent ββG(pH): |
6549f26248dad231203fd0e0 | 14 | βG protein (pH) = ββG(pH) + βG(pH), (8) where βG(pH) corresponds to Equation 1 with a reference pK β’ a corresponding to residue A. Equation 8 provides a family of solutions that depend on the pH value. To determine the pK a , we find the point where βG protein (pH) = 0. This pH corresponds to the pK a that would be observed in a titration experiment and follows from the Henderson-Hasselbalch equation (Equation ). |
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