Role of Bovine Serum Albumin Addition in Micellization and Gel Formation of Poloxamer 407

The combination of the thermoresponsive polymer and protein has demonstrated great promise in its applications in drug delivery and tissue engineering fields. This study described the impact of bovine serum albumin (BSA) on the micellization and sol–gel transition behaviors of poloxamer 407 (PX). The micellization of aqueous PX solutions with and without BSA was examined using isothermal titration calorimetry. In the calorimetric titration curves, the pre-micellar region, the transition concentration region, and the post-micellar region were observed. The presence of BSA had no noticeable impact on critical micellization concentration, but the inclusion of BSA caused the pre-micellar region to expand. In addition to studying the self-organization of PX at a particular temperature, the temperature-induced micellization and gelation of PX were also explored using differential scanning calorimetry and rheology. The incorporation of BSA had no discernible effect on critical micellization temperature (CMT), but it did affect gelation temperature (Tgel) and gel integrity of PX-based systems. The response surface approach illustrated the linear relation between the compositions and the CMT. The major factor affecting the CMT of the mixtures was the concentration of PX. The alteration of the Tgel and the gel integrity were discovered to be a consequence of the intricate interaction between PX and BSA. BSA mitigated the inter-micellar entanglements. Hence, the addition of BSA demonstrated a modulating influence on Tgel and a softening effect on gel integrity. Understanding the influence of serum albumin on the self-assembly and gelation of PX will enable the creation of thermoresponsive drug delivery and tissue engineering systems with controlled gelation temperatures and gel strength.


Introduction
Over the past few years, the self-assembly of amphiphilic copolymers has increased attention. It has been considered for various applications, such as templates for nanomaterial synthesis, vehicles for drug encapsulation, and matrices for drug delivery and tissue engineering [1][2][3]. Among the several amphiphilic copolymers, poloxamers are becoming more prevalent in the biochemical and pharmaceutical fields due to their minimal immunological response and low toxicity [3][4][5]. The triblock structure of poloxamers consists of a central hydrophobic poly(propylene oxide) (PPO) block and terminal hydrophilic poly(ethylene oxide) (PEO) blocks. The amphiphilicity of poloxamers depends on the molecular weight and the number and proportion of PEO and PPO blocks [3]. The self-assembly of the unimers in an aqueous environment varies according to polymer concentration and temperature [6]. Moreover, the addition of cosolvent and some additives refines the self-assembly of poloxamers in water [4,5,7]. The worsening interaction between the hydrophobic block of the polymer chain and water with a rise in temperature triggers heat-induced self-assembly in aqueous poloxamer solutions, resulting in micelle formation [5]. The formation of the have been explored and suggested for use as an injectable platform [33]. Understanding the influence of additives on the self-assembly of PX is necessary for the rationale design of prospective thermoresponsive gels. More information is required to comprehend how BSA affects the micellization and gelation of PX.
In this study, the impact of BSA on the micellar properties and gelation of PX was examined. Using isothermal titration calorimetry (ITC), the aqueous associated colloids from PX and the mixtures were characterized, and the CMC was determined. Further, response surface methodology was applied to rationally design the experiments and statistically examine the relationship between the composition and the thermoresponsive micellization and gelation characteristics. To comprehend the phenomena of temperature-induced micellization and thermogelation of PX in the presence of BSA, differential scanning calorimetry (DSC) and rheological investigations were conducted.

Materials and Sample Preparation
PX was purchased from Sigma-Aldrich (Saint Louis, MO, USA). BSA was supplied by Fisher BioReagents (Thermo Fisher Scientific, Waltham, MA, USA). Ultrapure water was obtained from a Simplicity ® water purification system (Millipore, Molsheim, France) and used as the solvent for all samples.
The plain PX solutions were prepared using the cold method [34], which involved dispersing the desired quantity of PX in two-thirds of the required cold water while stirring to obtain a homogenous dispersion. The sample's volume was then adjusted to the desired total volume by adding the remaining cold water. To prepare the mixtures of BSA and PX, the required quantity of BSA was dissolved in the PX solution before adjusting the volume of each mixture to the final volume. In order to prepare BSA solutions, the necessary amount of BSA was dissolved in water.

ITC Experiments
In order to ensure that the polymer concentration in the sample cell varies to span the micellization process as the titration progresses, the concentration of the amphiphilic polymer placed into the injection syringe as titrant should be higher than the CMC [35]. In addition, the heat change in each titration should not exceed the measuring capacity or be too small compared to background noise [35]. According to our preliminary study, 1.5% w/v PX was suitable for the ITC experiment. For studying the micellization of plain PX, the sample cell was initially loaded with water while 1.5% w/v PX was loaded into the syringe. Then the PX solution was successively titrated into water.
To examine the impact of BSA on PX micellization, the mixture of PX and BSA was continuously titrated into water that contained the same BSA composition as in the titrant. In this manner, the concentration of BSA remains constant during the titration procedure, and any heat change resulting from BSA dilution can be ruled out [6]. The mixtures of PX and BSA used as titrants were 0.75% and 1.5% w/v of BSA in 1.5% w/v PX.
The ITC experiments were conducted at 30 • C using a MicroCal PEAQ-ITC microcalorimeter (Malvern Panalytical, Malvern, UK). An initial small injection of 0.4 µL was followed by 38 injections of 1 µL of the titrant. Spacing was 120 s, and stirring speed was set to 750 rpm. All experiments were performed in triplicate. Data were processed and analyzed using MicroCal PEAQ-ITC Analysis Software and MATLAB 2018a (Mathworks, Natick, MA, USA). The CMC value was estimated from the maximum of the first derivative of the calorimetric titration curve, as described previously [35,36].

Response Surface Methodology
Response surface methodology with a 3-level factorial design was adopted to study how the factors affect responses including the CMT, the T gel , and the elastic modulus at 37 • C (G 37 • C ), which reflected gel strength [15]. The variables used for 3-level factorial design are represented in Table 1. The factors were the concentrations of PX and BSA in the  The actual values for low, medium, and high levels of PX  were 16, 18, and 20% w/v, respectively. The concentration of 16% w/v was chosen as the low level since it is fractionally greater than the minimum concentration that forms gel as reported in the literature [12]. According to Table 1, the chosen highest concentration of BSA was 1.5% w/v which covered the BSA concentration generally used for biomedical and pharmaceutical applications [14,37,38]. The sample notation and description are listed in Table 2. With Design-Expert ® software (version 13; Stat-Ease Inc., Minneapolis, MN, USA), thirteen runs for three levels, two factors, and five center points were produced as shown in Table 3. The relations between the factors and the experimental results of the responses were established. Analysis of variance (ANOVA) was used to figure out whether the regression model was statistically significant. Statistical significance was regarded as a p-value of less than 0.05. Table 1. Variables used for 3-level factorial design.

Factors
Actual Level (Coded Level)

Low
Medium High

DSC Experiments
The DSC investigations were conducted using a Mettler Toledo DSC 3+ model (Mettler-Toledo, Viroflay, France). Samples were placed into aluminum pans with a pinhole in the lid. Temperature scans from 5 to 45 • C under nitrogen purge were conducted at a heating rate of 1 • C/min. STARe Evaluation Software was used for data analysis. All measurements were in triplicate.

Rheological Experiments
A HAAKE MARS 40 rheometer (ThermoFisher Scientific, Bremen, Germany) was used to evaluate the rheological characteristics. By utilizing a 60 mm parallel plate geometry with a 0.5 mm gap, the dynamic moduli-the elastic modulus (G ) and viscous modulus (G )-were evaluated through temperature ramps at a heating rate of 1 • C/min from 5 to 45 • C. At a frequency of 1 Hz, the oscillation temperature ramp tests were conducted within the linear viscoelastic region. All measurements were in triplicate.

Statistical Analysis
ANOVA together with post hoc test was used to assess whether there were significant differences between the groups. A statistical difference was considered significant for p-value < 0.05.

ITC Measurements on the Self-Organization of PX into Micelles
ITC analysis is a precise method for monitoring the self-organization of the amphiphilic molecules and for determining CMC [35,39]. This method enables the observation of micellization in real time without the addition of dye molecules or measurements of surface tension [39]. Small amounts of a concentrated polymeric surfactant solution are titrated into the sample cell containing dispersion medium. This causes demicellization with every injection until the polymer concentration reaches CMC, which can be evaluated from the calorimetric titration data.
3.1.1. PX Self-Organization in Water Figure 1a represents the raw ITC thermogram of aqueous micellar PX solution titrated into water. Each injection caused a negative heat flow that deviated from the baseline, suggesting that the injection of micellar PX solution into water produced the exothermic heat flow effect. The concentration of the PX solution in the syringe was much higher than the expected CMC of PX; therefore, it may be inferred that the polymer solution in the syringe consisted of micellar colloids due to the self-organization. After the first injection of micellar solution from the syringe into the dispersion medium, the concentration of PX in the sample cell was far below CMC owing to the dilution of the injected PX solution. The dilution of the injected PX solution inside the sample cell destabilized the micellar colloids and triggered the micelle dissociation into unimers. This particular phenomenon is described as demicellization [35]. Therefore, the first few injections resulted in a large heat release (Figure 1a), which was attributed to the micelle dilution, the dissociation of the injected micelles into unimers, and the unimer dilution [35]. With subsequent injections, the magnitude of the observed heat release decreased. Eventually, the heat flow became almost constant for the last few injections. micellar colloids and triggered the micelle dissociation into unimers. This particular phe-nomenon is described as demicellization [35]. Therefore, the first few injections resulted in a large heat release (Figure 1a), which was attributed to the micelle dilution, the dissociation of the injected micelles into unimers, and the unimer dilution [35]. With subsequent injections, the magnitude of the observed heat release decreased. Eventually, the heat flow became almost constant for the last few injections. The normalized titration curve was obtained by integrating the heat effect over time and subsequent normalization per amount of polymer. According to Figure 1b, the normalized titration curve of aqueous micellar PX solution titrated into water has a sigmoidal shape, which can be divided into three regions: a pre-micellar region, a transition concentration region, and a post-micellar region [35,39,40]. In the pre-micellar region, the concentration of PX in the sample cell was much below the CMC, and the observed enthalpy change was associated with the breakup of the added micelles as well as the dilution of unimers. As more of the concentrated PX was injected, the concentration of PX in the sample cell increased to the transition concentration region. The majority of injected micelles remained in the micellar form, with only a small portion dissociating into unimers in this region. The micelles gradually depress dissociating in this concentration range, as evidenced by the progressive decline in the enthalpy change magnitude. The PX concentration in the sample cell reaches the CMC in the transition concentration region. The differential curve (Figure 1b) was obtained by calculating the first derivative of the titration profile, and the CMC value was taken to be the concentration at which the differential curve reached its maximum. The CMC value of PX determined in this study was 0.057 ± 0.003 mM (0.072 ± 0.004 % w/v) which is in line with the previously reported range of CMC values [10,11,41]. In the post-micellar area, a plateau was reached on the titration curve. The predominant process occurring in the post-micellar region is the dilution of the PX micelles when the micelles no longer dissociate into unimers. The small heat release in this region reflected the dilution enthalpy of micelles. The normalized titration curve was obtained by integrating the heat effect over time and subsequent normalization per amount of polymer. According to Figure 1b, the normalized titration curve of aqueous micellar PX solution titrated into water has a sigmoidal shape, which can be divided into three regions: a pre-micellar region, a transition concentration region, and a post-micellar region [35,39,40]. In the pre-micellar region, the concentration of PX in the sample cell was much below the CMC, and the observed enthalpy change was associated with the breakup of the added micelles as well as the dilution of unimers. As more of the concentrated PX was injected, the concentration of PX in the sample cell increased to the transition concentration region. The majority of injected micelles remained in the micellar form, with only a small portion dissociating into unimers in this region. The micelles gradually depress dissociating in this concentration range, as evidenced by the progressive decline in the enthalpy change magnitude. The PX concentration in the sample cell reaches the CMC in the transition concentration region. The differential curve (Figure 1b) was obtained by calculating the first derivative of the titration profile, and the CMC value was taken to be the concentration at which the differential curve reached its maximum. The CMC value of PX determined in this study was 0.057 ± 0.003 mM (0.072 ± 0.004 % w/v) which is in line with the previously reported range of CMC values [10,11,41]. In the post-micellar area, a plateau was reached on the titration curve. The predominant process occurring in the post-micellar region is the dilution of the PX micelles when the micelles no longer dissociate into unimers. The small heat release in this region reflected the dilution enthalpy of micelles.

Effect of BSA on PX Self-Organization
The normalized titration curves of PX in the absence and presence of BSA are shown in Figure 2. The titration curves of PX in the presence of BSA exhibited a negative enthalpy change, indicating that the demicellization of PX in the presence of BSA remained the exothermic attribute. While having the sigmoidal shape, the concentration range of the pre-micellar region of PX in the presence of BSA was greater than that of plain PX. Using the concentration at the intersection of the extrapolated initial and linear ascent lines (inset of Figure 2) [42], the end of the pre-micellar region was estimated. The concentrations at the end of the pre-micellar region for plain PX, PX containing 0.75% w/v BSA, and PX containing 1.5% w/v BSA were 0.017 ± 0.001, 0.028 ± 0.000, and 0.026 ± 0.002 mM, respectively. Both samples containing BSA had significantly higher concentrations at the end of the pre-micellar region than plain PX (p < 0.05). The CMC of PX containing 0.75% w/v BSA, and PX containing 1.5% w/v BSA were 0.054 ± 0.003 and 0.052 ± 0.003 mM, respectively. For the CMC values, there was no statistical difference among plain PX, PX containing 0.75% w/v BSA, and PX containing 1.5% w/v BSA. The interaction between BSA and PX unimers may play a role in the shift of the transition from the pre-micellar region to the transition concentration region. It has been suggested that the hydrophobic interaction between PPO residues of PX unimers and BSA induced the PPO globule of PEO-PPO-PEO block copolymers to expand in water [43]. The corresponding interaction might retard the association between PPO blocks at low concentrations of PX. Therefore, the presence of BSA extended the concentration range of the pre-micellar region.
of Figure 2) [42], the end of the pre-micellar region was estimated. The concentrations at the end of the pre-micellar region for plain PX, PX containing 0.75% w/v BSA, and PX containing 1.5% w/v BSA were 0.017 ± 0.001, 0.028 ± 0.000, and 0.026 ± 0.002 mM, respectively. Both samples containing BSA had significantly higher concentrations at the end of the pre-micellar region than plain PX (p < 0.05). The CMC of PX containing 0.75% w/v BSA, and PX containing 1.5% w/v BSA were 0.054 ± 0.003 and 0.052 ± 0.003 mM, respectively. For the CMC values, there was no statistical difference among plain PX, PX containing 0.75% w/v BSA, and PX containing 1.5% w/v BSA. The interaction between BSA and PX unimers may play a role in the shift of the transition from the pre-micellar region to the transition concentration region. It has been suggested that the hydrophobic interaction between PPO residues of PX unimers and BSA induced the PPO globule of PEO-PPO-PEO block copolymers to expand in water [43]. The corresponding interaction might retard the association between PPO blocks at low concentrations of PX. Therefore, the presence of BSA extended the concentration range of the pre-micellar region.

Investigation on the Temperature-Induced Micellization and Gelation
The response surface methodology based on the three-level factorial design is a practical approach that uses a reasonable number of experiments and statistical analysis to establish a model correlating the casual factors with studied responses [44]. The potential effect of BSA on the temperature-induced micellization and gelation of PX was explored using the response surface approach. The DSC experiments were performed to monitor the temperature-induced micellization, and the thermoresponsive viscoelasticity of the samples was evaluated to describe the temperature-induced gelation.
The three-level factorial design was implemented to statistically identify and quantify the impact of two factors, the concentrations of PX (X1) and BSA (X2), on the responses including the CMT (Y1), the Tgel (Y2) and the G′37°C (Y3). The three-level factorial design and response data are shown in Table 3. The sample notation is also listed in Table 3.

Investigation on the Temperature-Induced Micellization and Gelation
The response surface methodology based on the three-level factorial design is a practical approach that uses a reasonable number of experiments and statistical analysis to establish a model correlating the casual factors with studied responses [44]. The potential effect of BSA on the temperature-induced micellization and gelation of PX was explored using the response surface approach. The DSC experiments were performed to monitor the temperature-induced micellization, and the thermoresponsive viscoelasticity of the samples was evaluated to describe the temperature-induced gelation.
The three-level factorial design was implemented to statistically identify and quantify the impact of two factors, the concentrations of PX (X 1 ) and BSA (X 2 ), on the responses including the CMT (Y 1 ), the T gel (Y 2 ) and the G 37 • C (Y 3 ). The three-level factorial design and response data are shown in Table 3. The sample notation is also listed in Table 3.

DSC Thermograms and Temperature Ramp Rheograms
The temperature-dependent micellization of PX in the presence and absence of BSA was investigated using DSC. The DSC thermograms for plain PX samples-16PX, 18PX, and 20PX-are depicted in Figure 3. The temperature-induced dehydration of PX molecules led to the association of the hydrophobic PPO blocks, resulting in the formation of PX micelles composed of PPO cores and PEO coronas [5,13]. A broad endotherm observed in the DSC thermogram of PX could be attributed to the micellization [13,22]. In response to heating, the onset of the endothermic signal corresponded to the initiation of micelle formation, and the end of the endotherm reflected the completion of the micellization process. In general, the CMT is defined as the temperature at which the endothermic signal reaches its peak [5,45]. Evidence for this temperature-induced micellization was provided by the endothermic traces for all plain PX as shown in Figure 3. The CMT as indicated by arrows in Figure 3 was slightly shifted to lower temperature with increasing PX concentration, indicating the concentration-facilitated self-association of amphiphilic co-polymers as previously described [46,47]. Figure 4 displays the DSC traces for the temperature-induced micellization of PX in the presence of BSA. The thermal characteristic of PX micellization was not noticeably altered by the addition of BSA. by the endothermic traces for all plain PX as shown in Figure 3. The CMT as indicated by arrows in Figure 3 was slightly shifted to lower temperature with increasing PX concentration, indicating the concentration-facilitated self-association of amphiphilic co-polymers as previously described [46,47]. Figure 4 displays the DSC traces for the temperatureinduced micellization of PX in the presence of BSA. The thermal characteristic of PX micellization was not noticeably altered by the addition of BSA.   Temperature ramp rheometry was performed to examine how BSA affected the thermoresponsive gel formation of PX. The variation of the dynamic moduli with temperature for plain PX and the mixtures of PX and BSA is depicted in Figures 5 and 6. All samples exhibited thermogelation behavior. At low temperatures, the values of G′ were below Temperature ramp rheometry was performed to examine how BSA affected the thermoresponsive gel formation of PX. The variation of the dynamic moduli with temperature for plain PX and the mixtures of PX and BSA is depicted in Figures 5 and 6. All samples exhibited thermogelation behavior. At low temperatures, the values of G were below those of G for all plain PX ( Figure 5). This reflected the liquid stage of the sample. Both dynamic moduli increased with increasing temperature, and the values of G became superior to those of G at high temperatures. The predominant G at high temperatures revealed the gel characteristic of all samples. The liquid-to-gel transition took place in the temperature range at which the abrupt increase in G was detected, and the temperature at which the crossover of G and G was observed was denoted as the T gel [13,22]. From Figure 5, increasing PX concentration caused the crossover points of G and G to shift to a lower temperature. This indicated that the thermoresponsive gelation was facilitated by raising the concentration of PX. On the contrary, the presence of BSA resulted in a shift of the crossover points of G and G to a higher temperature ( Figure 6). The gelation of PX could be attributed to the inter-micellar entanglements caused by raising the temperature [48]. The high concentration of PX produced a large number of micelles available for the formation of the gel structure; therefore, the increase in the PX concentration facilitated the temperature-induced gelation. The increase in gelation temperature with the incorporation of BSA could be associated with the steric hindrance of serum albumin. The relationship between the micellization and gelation characteristics, and the concentration of each component was further determined using response surface methodology based on the three-level factorial design.

Experimental Data and Response Surface Modeling of Three-Level Factorial Design
The experimental data presented in Table 3 were fitted to linear, two-factor interaction (2FI), and quadratic models to obtain the regression equation. For checking model adequacy, the comparative values of sequential p-value, lack of fit p-value, correlation coefficient (R 2 ), adjusted R 2 , and predicted R 2 are summarized in Table 4. When the sequential p-value is lower than 0.05 and a non-significant lack of fit (p-value > 0.05) is obtained, the model is considered to be adequate [49]. In addition, the feasibility of the model is determined by the values of R 2 , adjusted R 2 , and predicted R 2 . The adjusted R 2 and the predicted R 2 should be close to the same or different by no more than 0.2 [50,51]. All R 2 values of the satisfactory model should fall within the range of 0.7 to 1.0, and the adjusted R 2 should be close to 1.0 [50,51]. Accordingly, the response Y 1 was found to follow the linear model, while the quadratic models were selected to describe the effects of the factors on the responses Y 2 and Y 3 .   The relationship between the CMT and the concentrations of PX and BSA was represented by the following linear model in terms of coded factors.
whereas a negative sign of a factor denotes an inverse relationship between the factor and the response, a positive sign of a factor signifies a positive effect of the factor on the response. In an equation, any term with statistical significance is bolded. As illustrated in Figure 7a, the plot of experimental response against predicted response shows an adequate correlation and behaves with a uniform distribution of data points around the 45 • line. A high correlation between predicted and actual experimental data indicated that the model was reliable [52]. According to the response surface plot in Figure 7b, the CMT was mainly dependent on the concentration of PX. As the concentration of PX increased, the CMT decreased in a linear fashion. Although the concentration of BSA also had a negative effect on the CMT, the effect of BSA concentration on the response Y 1 was minor and insignificant.
The insignificant influence of BSA on the CMT found in this study is in accordance with a study by Perinelli et al., which investigated the effect of BSA on the CMT of PX at low PX concentrations (2.5% and 5% w/w) in phosphate buffer and found no notable effect on the CMT value of PX [30].
The coefficient of a linear term (X1 or X2) represents the effect of a particular factor, whereas the coefficients of an interactive term (X1X2) and a quadratic term (X1 2 or X2 2 ) describe the interaction between two factors and quadratic effect, respectively. In Equation (2) X1, X2, X1X2, and X1 2 were significant model terms, as highlighted in bold. When the experimental response is plotted against the predicted response (Figure 8a), the data points are close to the straight line. This reflected an adequate agreement between the experimental data and the predicted responses. According to Equation (2), both PX and BSA concentrations significantly impacted on the Tgel. The increase in the PX concentration lowered Tgel, as revealed by the negative coefficient of its linear term. This is consistent with the gelling behavior of PX reported by Liu et al. [48]. With the increase in PX concentration, the polymer solution gains in density and volume fraction of micelles. As a result, the distance between micelles was reduced, favoring the temperature-induced formation of a micellar network [48]. Hence, the increase in PX concentration gave rise to the reduction of Tgel. The positive coefficient for the linear term of BSA, on the other hand, showed that increasing the concentration of BSA shifted Tgel to higher values. As a result, these two factors have opposing effects. However, the curvature depicted on the response surface plot (Figure 8b) indicates the complexity of the interaction between the components in the mixtures. The influence of one component may vary depending on the amount of another in the mixture. At the lower level of PX, BSA had a more noticeable effect on Tgel increase. The steric hindrance caused by the additives may be responsible for the increase The relationship between the T gel and the concentrations of PX and BSA was represented by the following quadratic model in terms of coded factors.
The coefficient of a linear term (X 1 or X 2 ) represents the effect of a particular factor, whereas the coefficients of an interactive term (X 1 X 2 ) and a quadratic term (X 1 2 or X 2 2 ) describe the interaction between two factors and quadratic effect, respectively. In Equation (2) X 1 , X 2 , X 1 X 2 , and X 1 2 were significant model terms, as highlighted in bold. When the experimental response is plotted against the predicted response (Figure 8a), the data points are close to the straight line. This reflected an adequate agreement between the experimental data and the predicted responses. According to Equation (2), both PX and BSA concentrations significantly impacted on the T gel . The increase in the PX concentration lowered T gel , as revealed by the negative coefficient of its linear term. This is consistent with the gelling behavior of PX reported by Liu et al. [48]. With the increase in PX concentration, the polymer solution gains in density and volume fraction of micelles. As a result, the distance between micelles was reduced, favoring the temperature-induced formation of a micellar network [48]. Hence, the increase in PX concentration gave rise to the reduction of T gel . The positive coefficient for the linear term of BSA, on the other hand, showed that increasing the concentration of BSA shifted T gel to higher values. As a result, these two factors have opposing effects. However, the curvature depicted on the response surface plot (Figure 8b) indicates the complexity of the interaction between the components in the mixtures. The influence of one component may vary depending on the amount of another in the mixture. At the lower level of PX, BSA had a more noticeable effect on T gel increase. The steric hindrance caused by the additives may be responsible for the increase in T gel of the PX-based mixtures [15,30]. The presence of BSA could produce steric hindrance and hinder the temperature-induced organization of PX micelles into the inter-micellar packing, causing a positive effect on T gel . As discussed previously, the density and volume fraction of PX micelles depended on the concentration of PX. The micellar volume fraction of PX at low concentration may be low compared with that of PX at high concentration. Therefore, the addition of BSA to PX at a low concentration had a more pronounced effect on T gel . X1, X2, X1X2, and X1 2 were significant terms for the storage modulus at 37 °C. Negative coefficients of X2 and X1 2 indicated the inverse relationship for the G′37°C while other terms showed a positive effect on the G′37°C. The adequate agreement between the experimental data and the predicted responses is demonstrated in Figure 9a. The response surface plot is depicted in Figure 9b to further highlight the relationship between these factors and the response. As can be seen, increasing the concentration of PX led to a significant increase in the G′37°C. For PX-based gels, the increment of the elastic characteristic is associated with the increase in inter-micellar entanglements, which promote the deformation resistance of the gels [53]. The increase in PX concentration produced more entanglements in the gel structure, enhancing the gel strength. The surface response of the G′37°C tended to tilt down with increasing BSA concentration. In addition, the complexity of the interplay between the components was shown by the curvature of the response surface plot. At the lower level of PX, the effect of BSA on the G′37°C is more prominent. The reduction in elasticity of gels has been reported for the mixtures of PX and poly(acrylic acid) and the mixtures of PX and HSA [23,32]. This softening effect could be explained by the attachment of the macromolecules to the micelles, which in turn limited the movement of the micelles and obstructed inter-micellar entanglements. (3) X 1 , X 2 , X 1 X 2 , and X 1 2 were significant terms for the storage modulus at 37 • C. Negative coefficients of X 2 and X 1 2 indicated the inverse relationship for the G 37 • C while other terms showed a positive effect on the G 37 • C . The adequate agreement between the experimental data and the predicted responses is demonstrated in Figure 9a. The response surface plot is depicted in Figure 9b to further highlight the relationship between these factors and the response. As can be seen, increasing the concentration of PX led to a significant increase in the G 37 • C . For PX-based gels, the increment of the elastic characteristic is associated with the increase in inter-micellar entanglements, which promote the deformation resistance of the gels [53]. The increase in PX concentration produced more entanglements in the gel structure, enhancing the gel strength. The surface response of the G 37 • C tended to tilt down with increasing BSA concentration. In addition, the complexity of the interplay between the components was shown by the curvature of the response surface plot. At the lower level of PX, the effect of BSA on the G 37 • C is more prominent. The reduction in elasticity of gels has been reported for the mixtures of PX and poly(acrylic acid) and the mixtures of PX and HSA [23,32]. This softening effect could be explained by the attachment of the macromolecules to the micelles, which in turn limited the movement of the micelles and obstructed inter-micellar entanglements.

Conclusions
The micellization of PX in the presence and absence of BSA was investigated using ITC. The pre-micellar region, the transition concentration region, and the post-micellar region were observed in the calorimetric titration curves. The presence of BSA did not show a discernible effect on the CMC of PX. However, the addition of BSA caused the extension of the pre-micellar region. This could be attributed to the hydrophobic interaction between PPO residues of PX unimers and BSA. In addition to the self-organization of PX at a certain temperature, the temperature-dependent micellization and gelation of PX were also investigated. The presence of BSA did not show a significant effect on the CMT but altered the Tgel as well as the gel integrity of PX-based solutions. Response surface methodology represented the linear relationship between the composition and the CMT. The change in the CMT of the mixtures was mainly attributed to the concentration of PX. The complex interplay between PX and BSA was found for the Tgel and the G′37°C. BSA interfered in the inter-micellar entanglements into gel structure. Accordingly, the presence of BSA showed the modulation effect on the Tgel and the softening effect on the gel integrity. Understanding the impact of serum albumin on the self-assembly and gelling characteristics of PX would allow the development of thermoresponsive systems with controlled gelation temperatures and viscoelasticity for drug delivery and tissue engineering.

Conclusions
The micellization of PX in the presence and absence of BSA was investigated using ITC. The pre-micellar region, the transition concentration region, and the post-micellar region were observed in the calorimetric titration curves. The presence of BSA did not show a discernible effect on the CMC of PX. However, the addition of BSA caused the extension of the pre-micellar region. This could be attributed to the hydrophobic interaction between PPO residues of PX unimers and BSA. In addition to the self-organization of PX at a certain temperature, the temperature-dependent micellization and gelation of PX were also investigated. The presence of BSA did not show a significant effect on the CMT but altered the T gel as well as the gel integrity of PX-based solutions. Response surface methodology represented the linear relationship between the composition and the CMT. The change in the CMT of the mixtures was mainly attributed to the concentration of PX. The complex interplay between PX and BSA was found for the T gel and the G 37 • C . BSA interfered in the inter-micellar entanglements into gel structure. Accordingly, the presence of BSA showed the modulation effect on the T gel and the softening effect on the gel integrity. Understanding the impact of serum albumin on the self-assembly and gelling characteristics of PX would allow the development of thermoresponsive systems with controlled gelation temperatures and viscoelasticity for drug delivery and tissue engineering.