Machine learning to determine optimal conditions for controlling the size of elastin-based particles

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Effect of solution parameters on LCST

The LCST behavior of ELP in solution can be modulated by polymer concentration, NaCl content, and pH1013. An increase in the concentration of ELP decreases the LCST by increased hydrophobic interactions, and does so quantitatively as a function of the natural logarithm of the ELP concentration11. We observed similar behavior in neat ELP (Fig. 2a). Both ELP/ELP-PEI copolymer mixtures also displayed lower LCST with higher polymer concentrations (Fig. 2b,c).

Cho et al. investigated the effect of the Hofmeister series ions on the LCST of ELP and found that NaCl exhibited a linear salting-out behavior, decreasing the LCST as a function of molar NaCl concentration. The Na+ and Cl ions cause a destabilization of the water molecules’ hydrophobic hydration of the polymer structure12. The same depression of LCST by NaCl was observed for neat ELP and both ELP/ELP-PEI copolymer solutions used in our study (Fig. 2). For the ELP-PEI copolymers, this effect is likely a combination of the disruption of hydrophobic hydration and the neutralization that occurs when Cl anions interact with protonated amines of PEI, which further encourages hydrophobic folding (Figs. 1 and 5).

Altering solution pH can be used as an effective method for tuning LCST when the ELP structure has ionizable residues at the guest position10. Our copolymer design differs in that the charged aspect of the copolymer is attached as a terminal controlling end and is not integral to the ELP molecule. For the [VPGVG]40 polymer, where all X = Valine, pH was not expected to significantly influence the LCST behavior of neat ELP, as seen in Fig. 2a. In the absence of salt, increasing pH had no effect on the LCST’s of ELP/ELP-PEI800 and ELP/ELP-PEI10K (Fig. 2b,c). Trabbic-Carlson et al. found that encoding a hydrophobic, neutral target protein to an ELP terminal end will depress the LCST of the reacted protein43. Similarly, when ELP-PEI copolymers are placed in water, without the anion interference of salt, an increase in pH deprotonates the PEI blocks, and the now more neutral non-transitioning blocks of PEI are forced together at a lower temperature by hydrophobic interactions between both the PEI and ELP blocks of the copolymer5.

The molecular weight of the PEI block progressively impacts the LCST (Fig. 2) as neat ELP solutions have higher LCSTs than the ELP/ELP-PEI800 solutions, which in turn have higher LCSTs than the ELP/ELP-PEI10K solutions under similar solution environment (polymer concentration, pH, and salt concentration) (Figs. 1 and 5). MacKay et al. found that adding more positive hydrophilic amino acids in the guest residue positions of the ELP raises the LCST, allowing better water solvation and increasing the temperature necessary to make transitioning energetically advantageous10. Therefore, in pH = 3 solution, one would assume that the ELP-PEI800 and ELP-PEI10K would have a higher LCST than the uncharged neat ELP because the positive charges on the PEI block would be expected to help maintain hydration at higher temperatures. Surprisingly, we found the opposite. One major difference between our study and that of MacKay et al. is that the hydrophilic groups are localized to one side of the molecule in ELP-PEI as opposed to being distributed evenly throughout the ELP. This could help the hydrophobic ELP blocks of the ELP-PEI more easily arrange to form an inner core of the aggregate surrounded by the solvated PEI blocks. Because of the highly hydrophilic nature of the protonated amine groups of the PEI, such a core–shell aggregate can form more favorably, which is at a lower temperature than the aggregate formation of neat ELP. On average, ELP/ELP-PEI10K appears to have an LCST 3.3 °C lower than that of ELP/ELP-PEI800, and ELP/ELP-PEI800 appears to have an LCST 4.1 °C lower than neat ELP. Alternatively, as shown by Weeks et al., the ELP-PEI10K may have more than one ELP molecule conjugated to the PEI10K, which transitions at a lower temperature by virtue of its higher molecular weight44.

Effect of solution parameters on Rh

The pH had no statistically significant effect on the Rh of neat ELP. This was expected as the ELP variant used in this study contains no ionizable groups. McKay et al. have previously noted this behavior and developed an ELP that contained evenly spaced ionizable residues. However, they performed optical density measurements which do not measure Rh10. The aggregate radii of neat ELP were only affected by NaCl concentration and polymer concentration (Fig. 3a). Increasing salt and polymer concentration has been known to affect the Rh. For example, Ghoorchian et al. found that by incrementally increasing the salt concentration from 5 to 60 mM, they could systematically increase the Rh of a three-armed star ELP from 13 to 78 nm45. The mechanism associated with the increase in Rh with increased salt concentration can be attributed to the same phenomena that depresses LCST. ELP is inherently hydrophobic, but remains thermodynamically stable at colder temperatures. As the temperature is increased, the salt decreases the thermodynamic stability of the ELP, and forces the hydrophobic sections to interact in order to decrease ELP’s contact with the surrounding water12. Non-miscible substances decrease their surface area with a solute, ultimately forming smaller particles. Salt is known to increase the surface tension of water and increase the amount of interaction between protein molecules. This increase in surface tension from the salt likely allows the insoluble ELP to form larger aggregates than in water alone. ELP polymers that form smaller Rh’s (< 200 nm) than what is found in this study, and are coupled to other hydrophilic moieties, are thought to form micelles35,36,37,38,39,40. The hydrophobic sections occupy the core of the micelle where they can minimize the interaction with water, while the hydrophilic section remains soluble. Tuning the size ratio of hydrophobic to hydrophilic sections determines the micelles stability in water and the nm size of the micelle. The aggregates formed in our study are larger than 200 nm which indicates that they are true aggregates and not micelles. This means that the ELP and PEI sections are randomly dispersed within the aggregated structure. Conjugation of a PEI block to the non-ionizable ELP allows the Rh to be incrementally controlled by polymer concentration, salt concentration, and pH (Fig. 3b,c). ELP/ELP-PEI solutions at pH = 3 show the largest mean Rh at 870 ± 51 nm for ELP/ELP-PEI800 and 755 ± 37 nm for ELP/ELP-PEI10K versus 655 ± 66 nm and 638 ± 53 at pH 7 for the two polymers respectively (p < 0.05). This suggests that at pH = 3, there may be electrostatic repulsion of the entirely protonated PEI block driving the larger Rh46.

As with LCST, an increase in pH to 10 decreases the Rh in the 0 M and 0.2 M NaCl solutions of ELP/ELP-PEI800 and ELP/ELP-PEI10K. As salt is added, it neutralizes the charges on the PEI blocks, and ionic disruption of solvation becomes the dominating factor in controlling the aggregate radius. ELP/ELP-PEI800 and ELP/ELP-PEI10K show statistically similar trends in regard to salt concentration (p > 0.05), with pH becoming a less important modulator of Rh at 1 M NaCl. Note that both ELP-PEI polymers were adjusted to have an equivalent number of amine groups, thus giving them an equal ability to be affected by salt concentration. Polymer concentration showed consistent trends for all three polymers with an increase in concentration resulting in a larger Rh.

K-means cluster analysis

To out knowledge, this research is the first time the K-means cluster analysis has been used to find patterns in polymer particle data. K-means is a simple but powerful algorithm that was able to quickly elucidate the relationship between salt concentration and Tt and Rh. It should be noted that traditional subjective means of data exploration, as noted in Fig. 5, can also be used to find these relationships; however, K-means allows for a fast, un-biased way to begin breaking down complex data into understandable groups. A weak correlation was shown for Tt and Rh (Fig. 5a). The relationship between Rh and Tt was explored using K-means cluster analysis, which revealed the primary driver for both outcomes to be salt concentration followed by polymer type (Fig. 5b,c). In water, the effects from polymer concentration and pH were more pronounced with Tt varying over a 22 °C range and the Rh varying over a 621 nm range (Fig. 5b). The Tt range decreases from 22 to 13 °C, but the Rh range increases from 621 to 714 nm for 0.2 M samples (Fig. 5b). This indicates that salt concentration becomes the primary driver of Tt, while a combination of salt and polymer type begins to influence the Rh with minor contributions from polymer concentration and pH (Fig. 5b). This trend continues for 1 M NaCl, with a decrease in Tt driven by salt, and an increase in Rh attributed to salt and polymer type with small variability driven by polymer concentration and pH (Fig. 5b). ELP and ELP/ELP-PEI800 are shown to have an inverse linear relationship between Tt and Rh, which means that as either Rh or Tt is increased, the other is decreased (Fig. 5d,e). ELP/ELP-PEI10K shows linearity for 0 M and 0.2 M but deviates at 1 M NaCl to lower Rh values (Fig. 5f). This indicates that the effect salt concentration has on ELP/ELP-PEI10K with respect to Rh decreases from 0.2 to 1 M compared to ELP and ELP/ELP-PEI800.

Phase transitions and Rh

As mentioned in the methods section, some of the polymer solutions exhibited multimodal phase transitions. ELP/ELP-PEI800 solutions almost exclusively exhibited a single-phase transition, whereas ELP/ELP-PEI10K exhibited bimodal transitions, except in the presence of high salt concentrations (Fig. 1). We suspect that the aggregates formed by the ELP/ELP-PEI copolymer solutions are a mixture of ELP-PEI copolymers and the neat ELP, as in any given solution, the fraction of ELP-PEI800 and ELP-PEI10K is only 15% and 1.3% respectively, with the rest of the polymers in the solution being neat ELP. We posit that there could be a hierarchical formation of early structures where ELP-PEI copolymers transition first and provide a thermodynamically favorable substrate that the neat ELP surrounding them can easily fold around. For the bimodal transitions of ELP/ELP-PEI10K, we surmise that when the Rh is reached for aggregates containing both ELP-PEI10K and neat ELP, the remaining ELP stay suspended in solution and transition later at a higher temperature almost equivalent to the LCST of neat ELP tested at those same conditions (Fig. 1). In contrast, the ELP-PEI800 exhibits a single-phase transition in all but three of the twenty-seven solution conditions tested. This is likely because the larger 17,000 g/mol ELP blocks in ELP-PEI800 and the neighboring neat ELP molecules can negotiate around the smaller non-transitioning 800 g/mol PEI blocks to continue to condense together.

Overall, the ELP/ELP-PEI solutions formed smaller aggregates than neat ELP in any given solution condition. Even though the ELP-PEI copolymers have a larger molecular weight and a smaller mole fraction in solution than the ELP, the electrostatic repulsion of the small portion of PEI copolymers makes it more difficult for the transitioning ELP blocks of ELP-PEI and the neat ELP polymers to coalesce. As previously stated, as pH increases, there is less protonation of the amines of PEI, and the ELP-PEI copolymers become a more neutral hydrophobic molecule that should behave similarly to neat ELP. At pH = 10, both ELP/ELP-PEI800 and ELP/ELP-PEI10K aggregate radii are closer in size to the Rh of neat ELP under the same solution conditions.

In this study, we have shown that ELP/ELP-PEI800 systematically forms nano-aggregates with a radius of 276 nm to microaggregates with a radius of 1141 nm with a range of LCST from 22 to 48 °C (Figs. 2b and 3b). These aggregates were achieved using the same chemistry of copolymer synthesis, but with careful manipulation of the solution environment. The same is true for ELP/ELP-PEI10K, where we can form nano-aggregates with a radius from 250 nm to microaggregates with a radius of 1114 nm with a range of an LCST from 20 to 42 °C (Figs. 2c and 3c). The PEI block also provides the ability to crosslink the copolymers and achieve a stable particle radius after formation in harsh environments (Fig. 4). These observations are schematically represented in Fig. 6.

Figure 6
figure6

ELP/ELP-PEI800 and ELP/ELP-PEI10K systematically form nano-and micro-aggregates above LCST when the solution conditions of salt concentration, polymer concentration, and pH are carefully controlled. The PEI block provides the ability to crosslink the copolymers and to achieve particles that remain stable below LCST even after removal of the harsh (high salt or pH) conditions used to create them.

In the future, ELP/ELP-PEI could serve as a modifiable platform that combines ELP’s capability for thermally induced self-aggregation and biocompatibility with the transfection efficiency and control of particle radius conferred by adding a block of PEI. ELP-PEI copolymers thus have potential as a biotherapeutic delivery agent whose dosage can be controlled by crosslinking the particles at the desired nano- or macromolecular size. This study serves as an initial investigation of the copolymers’ functionality, and more complex ELP-PEI copolymers can be created using the same chemistry. For this study, we chose the ELP with a repeat unit of VPGVG, but moving forward, alteration of the guest residue of ELP could provide further particle size and LCST customization of ELP-PEI copolymers. Similarly, chain length (molecular weight) is another quantifiable determinant of ELP behavior and may be an avenue for further modification. There are likely more complexities to the particle formation of the ELP-PEI copolymers to be explored, including isolation of pure copolymers (compared to the ELP/ELP-PEI mixtures used in this study) and an investigation of the early micelle structures formed in different environments before the aggregation takes place. This study provides the first step in understanding how the ELP-based copolymers behave in solution and shows their potential as functional biopolymers in an increasingly popular field of nanomolecular applications in biology and medicine.

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