Physiologically Relevant Mechanics of Biodegradable Polyester Nanoparticles

Abstract

Despite the extensive use of biodegradable polyester nanoparticles for drug delivery, and reports of the strong influence of nanoparticle mechanics on nano-bio interactions, there is a lack of systematic studies on the mechanics of these nanoparticles under physiologically relevant conditions. Here, we report indentation experiments on poly(lactic acid) and poly(lactide-co-glycolide) nanoparticles using atomic force microscopy. While dried nanoparticles were found to be rigid at room temperature, their elastic modulus was found to decrease by as much as 30 fold under simulated physiological conditions (i.e. in water at 37 °C). Differential scanning calorimetry confirms that this softening can be attributed to the glass transition of the nanoparticles. Using a combination of mechanical and thermoanalytical characterization, the plasticizing effects of miniaturization, molecular weight, and immersion in water were investigated. Collectively, these experiments provide insight for experimentalists exploring the relationship between polymer nanoparticle mechanics and in vivo behavior.

Graphical Abstract

Polymer nanoparticles (NPs) are extensively used for biomedical applications due to their biodegradability, biocompatibility, and highly tailorable drug loading and release capabilities.^1–4 Despite numerous reports of the impact of NP mechanics on nano-bio interactions such as internalization,^5,6 uptake,⁷ trafficking,^8–11 and degradation,¹² there has not been systematic characterization of polymer NP mechanics in conditions commensurate with their utilization. The root of this deficiency is that while atomic force microscopy (AFM) is well-suited for characterization of nanoscale materials, namely NPs,^13–15 experiments under physiological conditions (i.e. 37 °C in buffer) are challenging and require specialized equipment.^16,17 While it is possible to use bulk measurements to infer the mechanical properties of NPs to gain insight about biological functionality, this extrapolation carries the assumptions that being suspended in buffer and heated to physiological temperatures do not significantly alter NP mechanics. Such assumptions hold true for certain inorganic NPs, such as those composed of metals¹⁸ and oxides.¹⁹ Additionally, systematic studies of silica nanocapsules with different mechanical properties have found a strong dependence of phagocytosis²⁰ and tumor targeting processes^21,22 on nanoparticle stiffness.

Alternatively, there exist NP materials for which indentation experiments under physiological conditions have been conducted out of necessity due to the lack of a suitable bulk comparison, such as hydrogels composed of poly ethylene glycol (PEG) or polyester-PEG blends,^23,24 liposomes,^25,26 and dendrimers.²⁷ Polyesters, in contrast, are commonly glassy, and their properties can change drastically with particle size, molecular weight, temperature, or plasticizing absorbates such as water.^28,29 Specifically, the relatively low glass transition temperatures T_g of polyesters indicates that changes in temperature in the vicinity of room temperature may bring about changes in their mechanical properties – namely their elastic moduli – ranging over orders of magnitude.^30,31 Accordingly, the limited reports of polymeric NP mechanics available also vary over orders of magnitude for similar materials,^32–34 painting an incomplete and often confusing picture of polymer NP mechanics.

Here, we use a combination of differential scanning calorimetry (DSC) to measure the polymer T_g and AFM to explore the mechanical properties of poly(lactic acid) (PLA) and poly(lactide-co-glycolide) (PLGA) NPs. We observe that the differentiating factors between the NPs under simulated physiological conditions and bulk material, specifically particle size and immersion in water, significantly depress T_g of the NPs to, in certain cases, below physiological temperatures. For these NPs, we observe a significant softening representative of the transition of the NPs to the rubbery state, which can subsequently affect the behavior of the NPs under physiological conditions, as observed previously for virus-mimicking NPs.³⁵ Relatedly, we find that nanoindentation experiments in air can suffer from poor probe-sample thermal contact, complicating estimation of NP temperature and further motiving the study of NPs in aqueous environments to best match conditions in vivo. Both the specific results presented here as well as the methodology used to obtain them have important implications towards understanding the relationship between NP mechanics and biological environments and the design of NPs for tunable nano-bio interactions. This work concludes with a set of guidelines designed to help researchers understand what measurements are necessary to accurately estimate the stiffness of a given NP type.

In a typical indentation experiment, NPs were synthesized via nanoprecipitation³⁶ as previously reported³⁵ and drop cast on a poly-L-lysine (PLL) coated coverslip to promote adhesion of NPs to the substrate.³⁷ For indentation experiments conducted in water, NPs were kept immersed in Milli-Q water throughout synthesis, preparation, and experimentation. Water was used in lieu of buffer in indentation experiments to avoid NP detachment. To perform mechanical characterization, coverslips were placed on a Peltier heating element within the AFM system and kept at fixed experimental temperature. The AFM was then used to scan the surface in tapping mode to identify a region without NPs to conduct the probe calibration procedure,³⁸ and then scanned again to identify an isolated NP for mechanical characterization (Figure 1a). A higher resolution image of the selected NP was then collected in tapping mode to precisely identify its apex (Figure 1b). After locating the particle apex, the particle was indented to produce a force-indentation curve (Figure 1c) that was fit with a modified Hertzian contact model^39,40 (Figure S1) accounting for the NP diameter d, estimated as the height of the particle, and the AFM probe diameter, measured as the difference between the NP width w and d (Figure 1d).⁴¹ Details of fitting and verification of the contact model are provided in the Supporting Information.

Figure 1.

Typical experimental procedure for characterizing nanoparticles (NPs) using atomic force microscopy (AFM). (a) Survey image (height channel) of a collection of low molecular weight poly(lactic acid) (PLA_LMW) NPs to identify an isolated NP (dashed box). Color bar denotes height. (b) Height channel of a higher resolution AFM image of selected isolated NP from (a) and dashed line across the NP apex. Color indicates height following the color bar in (a). (c) Force curve from NP in (b) with force F vs. indentation h. Thick green line represents contact model fit from which elastic modulus E is derived. (d) Schematic of an AFM tip (white) as it scans across an NP (green) sitting on a substrate (gray). Thick black line is the cut line depicted in (b) as a dashed line. Apparent particle width w and measured NP diameter d derived from imaging was used to estimate AFM probe diameter for analysis.

To separate the contributions of the different factors that distinguish bulk samples under dry conditions and NPs under simulated physiological conditions (Figure 2a,b), a series of experiments were conducted on a model polymer, low molecular weight PLA (PLA_LMW, molecular weight M_w 18 - 28 kDa, intrinsic viscosity 0.25 - 0.35 dL/g). First, a 3 mm thick film of PLA_LMW was prepared by drop casting a solution of PLA_LMW in acetonitrile and allowing it to dry under vacuum for one month. The dried bulk film was then indented using a sphere-tipped AFM probe (radius = 920 nm) at 25 °C. The resultant elastic modulus E of the bulk polymer film, 4.7 ± 0.5 GPa, agrees well with literature values (Figure 2c).^42,43 Subsequent indentation experiments on dry NPs in air at 25 °C yielded E of 2.5 ± 1.1 GPa while similar NPs in water at 25 °C yielded E = 1.8 ± 0.5 GPa. Lastly, to best simulate in vivo experiments,³⁵ indentation experiments were conducted on NPs in water at 37 °C yielding E = 83 ± 23 MPa.

Figure 2.

Factors differentiating bulk polymer from NPs in experiments under physiological conditions. (a) Schematic of bulk dried polymer in comparison to (b) AFM height map of polymer NPs immobilized on a poly-L-lysine treated glass cover slip. Color bar denotes height. (c) Measured E for PLA_LMW in a bulk polymer film, as NPs measured in air, as NPs measured in water, and as NPs measured in water at elevated temperature, number of experiments (n) is denoted on each bar graph. (d) Differential scanning calorimetry (DSC) thermograms of PLA_LMW NPs in water and air as well as bulk PLA_LMW powder. Curves are vertically shifted for visual clarity.

We hypothesized that the observed changes in E with size and immersion in water could be understood by exploring how T_g was affected by these factors.⁴⁴ While the miniaturization of the PLA_LMW NPs from bulk results in a reduction in T_g (Figure 2d), the plasticizing effect of water on the NPs^29,45 more significantly affects T_g, notably shifting it below the physiological temperature of 37 °C. This shift can explain the substantial softening observed for NPs in water at 37 °C (above T_g of PLA_LMW NPs in water), which are in the rubbery phase.⁴⁶

As water absorption is a key factor involved in the shift in T_g (Figure 2d, S2a), it is important to further explore the role of water on the mechanics of NPs. Accordingly, air and water-based indentation experiments were conducted on PLA_LMW NPs and a second population of NPs composed of 50:50 PLGA (molecular weight 24 - 38 kDa, intrinsic viscosity 0.32 - 0.44 dL/g) as PLGA is more hygroscopic than PLA due to the presence of glycolic acid (Figure S2b,c).⁴⁷ For both PLA_LMW and PLGA NPs, immersion in water significantly decreased T_g relative to that measured in the dry state (Figure S2a), illustrating the plasticizing effect of water.^29,48 As softening behavior observed³⁵ under simulated physiological conditions for PLA_LMW and PLGA (PLA_LMW from 2.5 ± 1.1 GPa to 83 ± 23 MPa and PLGA from 2.9 ± 0.7 GPa to 58 ± 30 MPa when compared to NPs in air at 25°C) can be attributed to water uptake and entering the rubbery state, indentation experiments in water at 25°C can better elucidate the changes in mechanical properties due to water uptake alone. Interestingly, the resultant E from indentation experiments suggests that while both materials underwent a softening in the presence of water, the more hygroscopic polymer, PLGA, was more significantly affected (Figure 3a). Comparative water uptake has been previously observed for microparticles^29,49 and bulk polymer^45,50–52 and found a plasticizing effect of water that is in a similar range as observed here. Importantly, while the plasticizing effect of water was evident in the DSC thermograms, the degree to which water softened the NPs was only evident from indentation experiments. Additionally, it should be noted that although NPs at 25 °C for both PLA_LMW and PLGA were observed to soften in water, these NPs still exhibit high E, representative of the glassy state. Changes in stiffness in the GPa regime are not within the sensing threshold of soft biological tissues which are significantly softer,^53–55 with typical elasticities in the kPa regime.^56,57

Figure 3.

(a) Effect of water on NP E at 25 °C for PLA_LMW and poly(lactide-co-glycolide) (PLGA). Orange bar plots represent measured E of NPs measured in air, blue represents NPs measured in water. (b) Effect of molecular weight on NP E for PLA_LMW and a high molecular weight PLA_HMW, at 25 °C in air, orange, and at 37 °C in water, hatched blue bar plots. n is denoted on each bar plot.

To explore the role of molecular weight on NP mechanics, a series of indentation experiments were conducted on high molecular weight PLA (PLA_HMW) NPs with molecular weight of 209 kDa and intrinsic viscosity of 1.3 - 1.7 dL/g. Due to the increase in the molecular chain length, the T_g for all conditions (NPs in water, NPs in air, and bulk powder) for PLA_HMW was higher than the corresponding condition T_g for PLA_LMW, as predicted by the Flory-Fox relationship (Figure S2a).⁵⁸ While a depression of the PLA_HMW NP T_g was observed upon immersion in water commensurate with the change in T_g observed with PLA_LMW, T_g remained above 37 °C. These indentation experiments confirmed that PLA_HMW NPs in water were in their glassy state even at physiological temperatures (Figure 3b). Comparing the ratio between E at 25 and 37 °C in air and water respectively (E_{25 °C}/E_{37 °C}), we find that E_{25 °C}/E_{37 °C} = 30 for PLA_LMW is a result of both immersion in water and the polymer undergoing a glass transition while the E_{25 °C}/E_{37 °C} = 3 for PLA_HMW is a result of immersion in water alone as the polymer has not yet undergone glass transition. Similar to the experiments on NPs in water at 25 °C, factors of ~3 changes in the modulus within the GPa regime is likely imperceptible to the biological environment due to the immense difference between particle and cell or membrane stiffness.⁵³

It should be noted that it would be difficult if not impossible to use bulk data to extrapolate the NP stiffness under physiological conditions. Specifically, the E_{25 °C}/E_{37 °C} ratio (both in air due to lack of studies conducted in water) was calculated from a collection of studies exploring the temperature dependent properties of bulk PLA.^59–68 Due to the high T_g values of bulk polymer across a variety of molecular weights ranging between the molecular weight of PLA_LMW and PLA_HMW, E_{25 °C}/E_{37 °C} was found to be consistently ~1 (Figure S3a,b). In fact, even comparing the bulk polymer mechanics at temperatures above and below their respective T_g did not recapitulate the softening observed for NPs in water with an average ratio of 5 ± 3 compared with the experimentally observed value of 31 ± 8 from this study (Figure S3c). These comparisons suggest that the library of bulk polymer mechanical properties can only be applied to NPs under physiological conditions if the NP T_g measured in water is well above physiological temperatures, as is the case for PLA_HMW. These results highlight the complementary utility of thermoanalytical and mechanical characterization of NPs. More specifically, a combination of both techniques is critical towards understanding the physiological behavior of NPs with transition temperatures close to physiological temperatures.

Nanomechanical characterization in water is complicated by adhesion between NPs and the underlying substrate being lower in water than in air,⁶⁹ often leading to particle dragging and accumulation.^70,71 While particle dragging and accumulation can make it difficult to identify individual particles, once these particles are identified with appropriate imaging conditions, they can be robustly characterized. Nevertheless, it is less challenging to perform nanomechanical characterization in air where capillary effects make particles less prone to tip-directed motion. Therefore, we investigated the ability to observe rubbery NP mechanics in air. To do so, we conducted indentation experiments at temperatures T above the dry NP T_g for PLA_LMW and PLGA. Specifically, T selected for PLA_LMW and PLGA were 49.4 °C and 48 °C respectively, representing a temperature shift ΔT above the T_g of NPs in air commensurate with the difference between the T_g measured for NPs in water and 37 °C. Interestingly, indentation experiments conducted on dry NPs above their T_g yielded E values in the GPa range (Figure 4a), suggesting that the NPs were still in their glassy state, even though DSC results indicated that T > T_g. Details regarding the models used to fit force-indentation curves in air (Figure S4) are given in the Supporting Information.

Figure 4.

Indentation experiments at elevated temperatures in air. (a) Measured E for PLA_LMW (top) and PLGA (bottom) NPs in air. Solid green data points represent AFM stage set point temperatures T_S. Dotted lines represent peak glass transition temperature T_g for each NP in air (see Figure S2). For the right-most data point in both panels, upper vertical bound represents fitting with a modified Hertzian model while the lower vertical bound represents a JKR-based model (see Supporting Information section v). White dot represents calculated AFM probe temperature T_P from (b) where T_P is plotted vs. T_S taken in water (black) with corresponding linear fit (dashed line) of 0.9 × T_S + 3.1 °C and in air (white) with corresponding linear fit (dotted line) of 0.5 × T_S + 10.7 °C Continuous black line represents T_P = T_S for reference. Slope from the experiments in air used to determine the left-most bound for horizontal error bar in (a) to account for AFM tip cooling. (c) Schematic of AFM probe indenting NPs in water and (d) in air with heating from stage underneath the coverslip substrate (represented by red arrows).

To explain the apparent glassy state of NPs when T > T_g, we hypothesize that the AFM probe was cooling the NPs in air during indentation. To investigate this potential heat transfer, we measured the AFM probe temperature T_P with changing AFM stage set point temperature T_S using a series of power spectral density (PSD) measurements and the equipartition theorem (Figure S5).^72,73 When the probe was immersed in water, the slope of the linear fit of T_P vs. T_S is 0.9 ± 0.3 (65% confidence interval) (Figure 4b), which indicates that heat from the stage was effectively transferred to the probe through the water. In contrast, when the same measurements were repeated for the AFM probe in air, the slope of the linear fit was 0.5 ± 0.3 (65% confidence interval), indicating that air was not effectively conducting heat between the probe and heated sample. It is important to note that these PSD measurements were taken while the probes were 40 μm away from the substrate, which, while further from the substrate than the NPs, present a lower bound of probe temperature during indentation.

Validating the probe cooling phenomenon has critical implications for indentation experiments at elevated temperatures in air. Namely, it suggests that the NP is not isothermal when in contact with both the AFM probe and substrate (Figure 4c,d). This finding is particularly concerning for experiments where the internal thermal gradient of the NP ranges from below T_g to above T_g, which suggests that the particle is partially in its glassy state and partially in its rubbery state. The resulting stiffness gradient within the NP could alter the contact behavior in a manner that is not accurately captured by any existing contact model. While these results indicate that extreme caution is warranted in interpreting mechanical measurements at elevated temperatures in air, the good correspondence between probe and sample temperatures in water indicate that such artifacts are absent in water.

The experiments presented here provide insight for researchers exploring the relationship between polymer NP mechanics and in vivo behavior. Namely that initial thermoanalytical techniques can be used to determine T_g, whose relationship to the utilization temperature determines the classes of experiments necessary for accurate quantification of particle mechanics. For glassy polymer NPs with T_g above physiological temperatures, an approximation of the mechanics can be determined from bulk material properties. This approximation is valid only if the polymer’s glassy phase exhibits stiffnesses significantly beyond what is perceptible to cells (e.g. in the GPa regime). Notably, although all the polymers studied here underwent softening at room temperature associated with water uptake, the effect was not significant enough to be discernible by soft biological cells.⁵³ Conversely, if the measured T_g of the NPs in water is below the utilization temperature, then direct NP characterization is necessary to determine the mechanical properties of the NP in water. While experiments in air revealed the presence of a temperature gradient which complicates accurate determination of mechanics – further justifying the better controlled experiments in water – it also highlights the need for more advanced contact mechanics models and opportunities for potentially using such systems for studying thermal transport through nanoparticles. Despite its difficulties, direct NP mechanical characterization is warranted by the drastic changes in mechanics observed here. It should be noted that many nanoparticles used in drug delivery applications feature functional coatings such as PEG or lipids to lengthen circulation times.⁷⁴ Such coatings are unlikely to change the mechanics of the core material, but this hypothesis warrants further study.

Taken together, the results provide a nuanced perspective of the mechanical characterization of polymeric NPs that undergo drastic changes in their mechanical properties due to glass transition. Depending on the NP composition, changes in environmental conditions such as temperature and water absorption can have significant impact on T_g, which can subsequently affect the behavior of the NPs under physiological conditions. For some materials, this dramatic (measured here to be as much as 50-fold) change in the measured modulus relative to bulk materials makes it challenging to accurately extrapolate relevant properties from those collected under different conditions. Taking these mechanical studies together with the prior work showing the disparate biological outcomes of particles based solely on their stiffness,³⁵ this work has the fascinating implications that, despite all particles studied herein being stiffer than biological tissue, cells can somehow sense the difference between 80 MPa and several GPa. This highlights open questions in the biological community regarding how cells perceive nanoparticle stiffness and underscores the importance of robust mechanical characterization under conditions relevant to the cell biology. The methods and challenges described here can serve as a guide for the estimation of polymer NP mechanics, which is critical to understanding and controlling NP behavior in nano-bio interactions spanning uptake, trafficking, and degradation.