Article pubs.acs.org/Langmuir
Understanding the Structural Parameters of Biocompatible Nanoparticles Dictating Protein Fouling Carlos E. de Castro,† Bruno Mattei,‡ Karin A. Riske,‡ Eliézer Jag̈ er,§ Alessandro Jag̈ er,§ Petr Stepánek,§ and Fernando C. Giacomelli*,† †
Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, Brazil Departamento de Biofísica, Universidade Federal de São Paulo, São Paulo, Brazil § Institute of Macromolecular Chemistry, Heyrovsky Sq. 2, 162 06 Prague 6, Czech Republic ‡
S Supporting Information *
ABSTRACT: The development of nanocarriers for biomedical applications requires that these nanocarriers have special properties, including resistance to nonspecific protein adsorption. In this study, the fouling properties of PLA- and PCL-based block copolymer nanoparticles (NPs) have been evaluated by placing them in contact with model proteins. Block copolymer NPs were produced through the self-assembly of PEOm-b-PLAn and PEOmb-PCLn. This procedure yielded nanosized objects with distinct structural features dependent on the length of the hydrophobic and hydrophilic blocks and the volume ratio. The protein adsorption events were examined in relation to size, chain length, surface curvature, and hydrophilic chain density. Fouling by BSA and lysozyme was considerably reduced as the length of the hydrophilic PEO-stabilizing shell increases. In contrast to the case of hydrophilic polymer-grafted planar surfaces, the current investigations suggest that the hydrophilic chain density did not markedly influence protein fouling. The protein adsorption took place at the outer surface of the NPs since neither BSA nor lysozyme was able to diffuse within the hydrophilic layer due to geometric restrictions. Protein binding is an exothermic process, and it is modulated mainly by polymer features. The secondary structures of BSA and lysozyme were not affected by the adhesion phenomena.
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size,16 surface curvature,17 surface charge,18 and surface chain density19 were reported to impact the amount and mechanism of protein adsorption. The same is valid regarding the core base material.20 Among the materials that may prevent protein adsorption, highly hydrophilic polymers have been shown to be effective.21 In this regard, well-known poly(ethylene oxide) (PEO) can effectively minimize or even prevent protein adsorption depending on chain parameters.22,23 The PEO chains are flexible and mobile and have a relatively large exclusion volume, interacting strongly with water molecules and consequently preventing protein adsorption. The protein resistance of PEO has been attributed to steric repulsion and hydration that result in a high activation energy barrier for protein adsorption.24 Specifically, the mobility of PEO chains has been shown to contribute to elastic repulsive forces, which allows the polymer layers to reduce nonspecific protein adsorption.25 Nevertheless, although the protein-repelling features of PEO are welldocumented when grafted onto planar surfaces,26,27 where prevention of protein adsorption has been demonstrated if the
INTRODUCTION The development of nanocarriers for application in drug delivery requires that these nanocarriers have special properties, such as biocompatibility and targeting capabilities. Several systems based on polymeric nanoparticles have been proposed as drug delivery vessels, including drug-loaded block copolymer micelles.1−4 In addition to the aforementioned features, one of the remaining challenges in the field of nanobiotechnology is the development of nanocarriers resistant to nonspecific protein adsorption, as nanoparticles in contact with biological fluid may become coated with a protein layer,5−8 resulting in an inability of the cells to encounter the naked particles.9,10 Therefore, the assembly of polymeric nanoparticles able to prevent or at least reduce protein adsorption is of utmost importance as it allows for a long circulation of the entities in the bloodstream 11 and an increase in their targeting capabilities.12 Commonly, protein adsorption is attributed to electrostatic, van der Waals, and hydrophobic interactions.13,14 This phenomenon is expected to be more pronounced if the surface is positively charged due to the huge quantity of proteins with residual negative charge in the bloodstream under physiological conditions. The hydrophobicity also influences the amount and identity of the adsorbed proteins.15 Furthermore, the particle © 2014 American Chemical Society
Received: June 4, 2014 Revised: July 26, 2014 Published: July 28, 2014 9770
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software. Averaged intensity correlation functions g2(t) were analyzed using the algorithm REPES29 (incorporated in the GENDIST program), resulting in distributions of relaxation times, A(τ). The hydrodynamic radius (RH) of the nanoparticles was determined by using the Stokes−Einstein relation with D = τ−1q−2:
interfacial PEO chain density in planar coatings is higher than 0.1 chain/nm2,28 the spherical symmetry of nanoparticles introduces the influence of surface curvature, and the stealth properties of these entities are essentially dependent on the shielding promoted by the outer corona. The length and density of the hydrophilic chains may impact protein adsorption. The thickness and the chain density of the PEO layer are apparently the most relevant parameters in protein resistance. The thickness must be large enough to block protein−particle interactions, and the density must be sufficient to block the protein diffusion within the corona toward the core surface. Primarily, a lengthy hydrophilic chain and a high surface chain density20 are prerequisites of injectable nanocarriers that resist protein adsorption. In this study, the fouling properties of polylactic acid (PLA)and polycaprolactone (PCL)-based nanoparticles have been evaluated by putting them in contact with model proteins bovine serum albumin (BSA) and lysozyme. Nanometer-sized block copolymer nanoparticles (NPs) have been produced through the self-assembly of PEOn-b-PLAm and PEOn-b-PCLm block copolymers. This self-assembly yielded particles with distinct structural features dependent on the length of the hydrophobic and hydrophilic blocks and the volume ratio. It also resulted in block copolymer NPs with distinct core and shell sizes, as well as hydrophilic chain densities. These studies have been conducted by using scattering techniques, isothermal titration calorimetry (ITC), and circular dichroism spectroscopy (CD). Scattering techniques were used, as they are extremely sensitive to the presence of aggregates and small changes in dimension and molecular weight, whereas ITC was primarily utilized to assess stoichiometry, affinity, and enthalpy changes in the protein−nanoparticle interactions.15 Circular dichroism spectroscopy was used to probe protein conformational changes. The experimental data have been examined in relation to size, surface curvature, zeta potential, hydrophilic chain density, and the core nature of the nanoparticles. It was thus possible to probe how such features influence protein binding and adsorption events.
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RH =
kBTq2 τ 6πη
(1)
kB is the Boltzmann constant, T is the absolute temperature, q is the scattering vector, η is the viscosity of the solvent, and τ is the mean relaxation time related to the diffusion of the nanoparticles. For this study, the distributions of relaxation times were also converted to distributions of RH by using the Stokes−Einstein equation. The polydispersity of the nanoparticles was accessed by using the cumulant analysis30 of the correlation functions measured at 90o as μ ln g1(t ) = ln C − Γt + 2 t 2... (2) 2 where C is the amplitude of the correlation function and Γ is the relaxation frequency (τ−1). The parameter μ2 is known as the secondorder cumulant and was used to compute the polydispersity index of the samples (PDI = μ2/Γ 2). Static Light Scattering (SLS). The SLS measurements were carried out by varying the scattering angle (θ) from 30 to 150° with a 5° stepwise increase. At each angle, the light-scattering intensity was measured in triplicate, and the average values along with standard deviation (error bars) are reported. The molecular weight (Mw(NPs)) and the radius of gyration (RG) of the block copolymer NPs were estimated using the partial Zimm approach as R 2q2 ⎤ Kc 1 ⎡ ⎢1 + G ⎥ = Rθ M w(NPs) ⎣ 3 ⎦ where the concentration c is given in mg mL constant expressed by
4π 2n2 K=
(3) −1
and K is the optical
2
( ddnc )
NAλ 4
(4)
Rθ (Rayleigh ratio) is the normalized scattered intensity (toluene was used as the standard solvent), n is the refraction index of the solvent, dn/dc is the refractive index increment determined on a classical BricePhoenix differential refractometer, and NA is Avogadro’s number. Hence, by measuring Kc/Rθ at a given angular range for one single diluted concentration, we estimated the value of RG from the slope of the curve, and as q → 0, the apparent molecular weight (Mw(NPs)) was extracted from the inverse of the intercept. Small Angle X-ray Scattering (SAXS). The SAXS experiments were conducted at the SWING SAXS beamline of Synchrotron SOLEIL (Gif-sur-Yvette, France). The samples were loaded into sealed borosilicate capillaries (∼2 mm diameter). The collimated beam (λ = 1.033 Å) crossed the samples toward an evacuated flight tube and was scattered to a 17 cm × 17 cm PCCD-170170 CCD detector (Aviex). The sample-to-detector distance was chosen in such a way that the q range of 0.03−2.0 nm−1 could be covered. At each measurement, 10 frames of 0.1 s exposure times were collected. These were further normalized by the sample transmission, subsequently averaged and then converted to I(q) vs q profiles using Foxtrot software. The resulting I(q) vs q scattering curves were corrected by the subtraction of the scattering of pure solvent and could be fitted by using the form factor of homogeneous spheres or the spherical copolymer micelle model developed by Pedersen and Gerstenberg,31 depending on the scattering contrast. The fitting procedures were performed using the SASfit software, which makes use of the leastsquares fitting approach for minimizing the squared chi (χ 2). The SASfit software package was developed by Kohlbrecher.32 Electrophoretic Light Scattering (ELS). ELS measurements were used to determine the average zeta potential (ζ) of the nanoparticles, which were collected using a Zetasizer Nano-ZS ZEN3600 instrument
EXPERIMENTAL SECTION
Materials and Reagents. The PEOn-b-PLAm and PEOn-b-PCLm block copolymers were purchased from Polymer Source Inc. The molecular characteristics of the whole set of block copolymers investigated are given in Table S1 of the Supporting Information File. The subscripts refer to the mean degree of polymerization of each block, and the weight fraction of PEO (wPEO) was determined on the basis of the Mn of each block. The water used was ultrapure Milli-Q. Acetone and protein samples of bovine serum albumin (BSA) and lysozyme were purchased from Aldrich and used as received. Preparation of the Nanoparticles. Monodisperse block copolymer micelles (c = 2.5 mg mL−1) were produced by nanoprecipitation. Typically, 12.5 mg of the solid block copolymers was dissolved in acetone. The micellization was then induced by injecting the organic phase into 5.0 mL of water. The organic solvent was further removed by evaporation at room temperature. Scattering Characterization of the Nanoparticles. Dynamic Light Scattering (DLS). DLS measurements were performed using an ALV/CGS-3 compact goniometer system consisting of a 22 mW HeNe linearly polarized laser operating at a wavelength of 633 nm, an ALV 7004 digital correlator, and a pair of avalanche photodiodes operating in the pseudo-cross-correlation mode. The samples were placed in 10-mm-diameter glass cells and maintained at a constant temperature of 25 ± 1 °C. The autocorrelation functions reported are based on three independent runs of 60 s counting time. The data were collected and further averaged by using the ALV Correlator Control 9771
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Figure 1. Scattering characterization of PEO105-b-PLA236 nanoparticles: (A) autocorrelation function and respective distribution of relaxation times, (B) static light scattering (Kc/Rθ vs q2), (C) SAXS data and corresponding curve fitting, and (D) zeta potential distribution for 2.5 mg mL−1 in PBS (pH 7.4 at 37 °C). (Malvern Instruments, U.K.). This instrument measures the electrophoretic mobility (UE) and converts the value to a ζ potential (mV) through Henry’s equation UE =
2εξf (ka) 3η
lysozyme solution was injected into the sample cell containing only PBS buffer. The resulting data set was fit whenever possible with the two-site model of the ITC analysis module of the MicroCal Origin 7.0 software. This model assumes two sites of nanoparticle−ligand interaction with distinct molar enthalpy (ΔH), stoichiometry of binding (N), and equilibrium association constant K. The changes in free energy (ΔG) and entropy (ΔS) associated with the process were obtained from the fundamental thermodynamic relation ΔG = −RT ln K = ΔH − TΔS. The experiments showed good reproducibility although only one data set for each condition is shown. Circular dichroism spectroscopy (CD) measurements were carried out in a Jasco J-815 circular dichroism spectrometer using quartz cuvettes with a 1.0 mm optical path. The jumble of spectra was collected in the range of 190−260 nm at room temperature and corrected by subtracting the solvent background (PBS buffer).
(5)
where ε is the dielectric constant of the medium and η is the viscosity. Furthermore, f(ka) is the Henry’s function, which was calculated through the Smoluchowski approximation f(ka) = 1.5. Each ζpotential value reported in the manuscript is an average of 10 independent measurements with a repeatability of ±2%. Nanoparticle−Protein Investigations. The stability of the nanoparticles and nanoparticle−protein interactions was investigated by placing them in contact with model proteins BSA and lysozyme dissolved in PBS. Typically, 2.5 mg mL−1 of the block copolymer micelles solution was placed in contact with the model proteins at concentrations of 40.0 (BSA) and 60.0 mg mL−1 (lysozyme). The dynamic and static light scattering experiments were performed before and just after the protein contact to monitor the stability of the systems (size, size distribution, and molecular weight) in the presence of the biological entities. The thermodynamic parameters of the interaction among the proteins, BSA and lysozyme, and the different nanoparticles were determined through isothermal titration calorimetry (ITC) by using a MicroCal VP-ITC instrument. The reference cell was filled with water, the sample cell was filled with a 2.5 mg mL−1 block copolymer solution, and the syringe was filled with 2.0 mg mL−1 BSA or lysozyme solution. The titrations were performed by injecting 10 μL of protein solution into the sample cell every 600 s. The temperature was kept constant at 25 °C. The ITC raw data, which consists of peaks of power delivered to the sample cell during the titration, was integrated from a baseline to give the heat per injection as a function of the protein-tonanoparticle weight ratio. The heat of dilution of the protein solution was negligible, as determined in a blank experiment where BSA or
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RESULTS AND DISCUSSION Characterization of the Nanoparticles. The protein-free nanoparticles were first characterized by scattering techniques (SDLS, ELS, and SAXS). The representative data for PEO105-bPLA236 are given in Figure 1. The scattering data related to the remaining samples are given in the Supporting Information (Fig S1−S3). The dynamic light scattering data showed monomodal distributions of size in all cases, which were related to the presence of polymeric nanoparticles. The average hydrodynamic radius (RH) and polydispersity (μ2/Γ2) were determined. It is important to note here that RH increased as the PEO length was reduced, which was a consequence of the greater aggregation of PEO45-based nanoparticles. The aggregation number is defined by a set of multifaceted contributions that likely includes the strongest influence coming from the length 9772
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Table 1. Structural Characteristics of the Polymeric Nanoparticles as Determined by Scattering Techniques entry
RH(nm)
μ2/Γ2
dn/dc (mL g−1)
RG(nm)
RG/RH
RC(nm)
RL(nm)
ζ (mV)
Mw(NPs) × 107 g mol−1
Nagg
PEO105-b-PLA236 PEO45-b-PLA174 PEO113-b-PCL118 PEO45-b-PCL118
28.4 45.9 25.2 32.8
0.14 0.12 0.13 0.10
0.114 0.113 0.134 0.144
23.8 43.0 18.4 30.1
0.84 0.94 0.73 0.92
15.0 21.1 12.3 17.0
13.4 24.8 12.9 15.8
−28.6 −19.8 −23.7 −13.2
0.59 1.49 0.33 0.60
273 1027 178 387
to be able to diffuse within the hydrophilic brushes of each produced NP. Behavior in the Protein Environment. Dynamic Light Scattering. The behavior of the whole set of nanoparticles was investigated in different protein environments (BSA and lysozyme) to identify specific characteristics of the aggregates or biological entities that may be important in protein adsorption events. The serum albumin protein is the most abundant plasma protein in mammals, and bovine serum albumin (BSA), which is a large globular protein (Mw = 66.0 kDa), was chosen as the model serum albumin. This protein corresponds to about half of the blood serum proteins, and the value of the albumin concentration in mammals is approximately 40 mg mL−1.33 This high physiological concentration was the motivation to perform the experiments at such a high protein concentration. The isoelectric point of BSA is 4.7− 4.9;34 therefore, it is slightly negatively charged in the healthy physiological environment (pH 7.4). The distribution of RH of PEO105-b-PLA236, PEO45-b-PLA174, PEO113-b-PCL118, and PEO45-b-PCL118 in a BSA-free medium (full circles) and in the presence of BSA at 40.0 mg mL−1 (open circles) is given in Figure 2. The distributions were always bimodal in the presence of BSA. The population centered at around RH = 4.2 nm is related to the presence of free BSA. The results in Figure 2 note that the mean average size related to the presence of the polymeric nanoparticles in the BSA environment were very similar to the hydrodynamic dimension monitored in the protein-free environment in the cases of PEO105-b-PLA236 and PEO113-bPCL118. In contrast, the size increased when PEO45-b-PLA174 and PEO45-b-PCL118 nanoparticles were in the presence of BSA. The quantitative values are given in Table S2 of the Supporting Information. The same approach has been applied to investigate the behavior in a lysozyme environment. The distribution of RH for PEO105-b-PLA236, PEO45-b-PLA174, PEO113-b-PCL118, and PEO45-b-PCL118 in a lysozyme-free medium (full circles) and in the presence of lysozyme at 60.0 mg mL−1 (open circles) is given in Figure 3. The behavior was very similar to that reported for BSA, with the results suggesting that lysozyme adsorption was prevented at PEO113-b- PCL118 and PEO105-bPLA236 surfaces, whereas a size increase was evidenced for PEO45-b- PLA174 and PEO45-b-PCL118. The average distance between PEO chains at the core surface was always smaller than 3.3 nm (Table 2). Considering the hydrodynamic dimensions of BSA (DH = 8.4 nm) and lysozyme (DH = 4.2 nm), the distance between neighboring hydrophilic chains was below the dimensions of the protein molecules in all cases. It is therefore reasonable to accept that both biomacromolecules were too large and were not able to diffuse within the PEO layer to adsorb onto the hydrophobic PLA or PCL core surface. Hence, in cases where the increase in size was noticed, protein molecules were likely adsorbed onto the outer surface
of the core-forming block, and it should also scale with the degree of polymerization (DP) of the soluble block as Nagg ≈ (ln DPPEO)−6/5, in the case of starlike micelles (i.e., Nagg is expected to decrease as the length of the corona-forming block increases). In the present study, this consideration was experimentally shown, as Nagg increased when the PEO length decreased or the solvophobic block length (or weight fraction of thereof) increased, which consequently led to an increase in the hydrodynamic dimension of the self-assemblies. The values of molecular weight (Mw(NPs)), aggregation number (Nagg = Mw(NPs)/Mw(polymer)), and radius of gyration (RG) were determined from SLS. The summary of the structural characteristics of the NPs as determined by scattering techniques is given in Table 1. The dimensionless structure-sensitive parameter (RG/RH) was determined always to be below 1.0, which is compatible with the formation of spherical objects. The SAXS profiles, along with the SLS data, gave insightful information on the inner structure of the polymeric nanoparticles. Depending on the scattering contrast, the SAXS profiles could be satisfactorily fitted by using the form factor of homogeneous spheres or the spherical copolymer micelle model formerly developed by Pedersen and Gerstenberg. The solid line in Figure 1C corresponds to the best fittings achieved by using the abovementioned model. From the fittings, it was possible to determine the dimensions of the core (RC), and by subtraction from RH (RH − RC), the shell dimension (RL) was estimated. These parameters are also given in Table 2. Table 2. Structural Properties of Scattering Nanoobjects Calculated from the Scattering Data entry PEO105-bPLA236 PEO45-bPLA174 PEO113-bPCL118 PEO45-bPCL118
Ac (nm2)
Nagg/Ac (chains/nm2)
average distance between hydrophilic chains (nm)
2827
0.10
3.2
5595
0.18
2.3
1901
0.10
3.3
3632
0.11
3.1
The core surface area (Ac) was then calculated as
Ac = 4πR C 2
(6)
The core surface area available per each hydrophilic PEO segment (Nagg/Ac) could be further estimated for the whole set of polymeric nanoparticles (Table 2). Parameter Nagg/Ac is named the surface chain density throughout the manuscript. Inversely, the available area at the hydrophobic core available per each hydrophilic PEO chain could also be calculated (Ac/ Nagg); therefore, the average distance between the hydrophilic chains could be estimated as (Ac/Nagg)0.5. Such calculations allowed us to evaluate whether the biomolecules were too large 9773
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Figure 2. Distribution of RH for (A) PEO105-b-PLA236, (B) PEO45-b-PLA174, (C) PEO113-b-PCL118, and (D) PEO45-b-PCL118 in a BSA-free medium (full circles) and in the presence of BSA at 40.0 mg mL−1 (open circles).
Figure 3. Distribution of RH for (A) PEO105-b-PLA236, (B) PEO45-b-PLA174, (C) PEO113-b-PCL118, (D) and PEO45-b-PCL118 in a lysozyme-free medium (full circles) and in the presence of lysozyme at 60.0 mg mL−1 (open circles).
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of the entities, even though the surface chain density was very high for the whole group of NPs (>0.1 chains/nm2). Static Light Scattering. The static light scattering of protein−polymer mixtures is far from being easy. However, when properly and carefully treated, the molecular weight of the complex can be determined and compared to the molecular weight of the protein-free NPs. The amount of protein adsorbed onto the surface of the nanoobjects may then be estimated. The straightforward Zimm equation can be applied as suggested by Kokufuta et al.35 In such a case, the weight concentration of the complex and its molecular weight are replaced by the weight concentration of the polymer and its molecular weight by ccomplex = c polymer(1 + β)
(7)
Mcomplex = NaggM polymer(1 + β)
(8)
Figure 4. K′cpolymer/Rθ vs q2 for 2.5 mg mL−1 PEO45-b-PLA174 in the presence of 40.0 mg mL−1 BSA (○) and in the presence of 60.0 mg.mL−1 lysozyme (●) in PBS (pH 7.4, 37 °C).
where β represents the mass ratio of bound protein to the NPs. The dn/dc of the complex is related to the dn/dc of the polymer and the protein as
respectively. By using the values of B, we assessed the values of β, which are the mass ratio of bound protein to polymeric nanoparticles (Table 3). Because the Mw(NPs) of each block copolymer nanoparticle in a protein-free environment was known, as was the mass ratio of bound protein to polymeric nanoparticle (β) and the molecular weight of each protein (66.0 kDa [BSA] and 14.4 kDa [lysozyme]), it was possible to estimate the number of adsorbed BSA and lysozyme molecules per each nanoparticle, and by considering the estimated nanoparticle surface area (4πRH2), the degree of coverage of the nanoparticles could be estimated. These considerations are quantitatively given in Table 3. The experimental data suggest that some structural dimensions of the NPs seem not to have a great influence on the adsorption behavior. This is evidenced if one compares PEO105-b-PLA236 and PEO45-b-PCL118 NPs (Tables 1 and 2), which are structurally similar regarding RH, RC, RL, Nagg/Ac, and the average distance between hydrophilic chains. However, protein absorption was mainly evidenced on the surface of PEO45-b-PCL118 NPs. It therefore suggests that these are not the parameters governing protein adsorption. Additionally, although the hydrophilic chain density (Table 2) is similar in all investigated systems (>0.1 chain/nm2), the adsorption took place only on the surface of PEO45-based NPs. Therefore, when we consider the investigated spherical objects in contrast to the case of hydrophilic polymer-grafted planar surfaces, the experimental data suggest that the adsorption event is chiefly governed by the PEO length whereas the hydrophilic chain density seems not to influence the behavior markedly. Additionally, the chemical nature of the core was assumed to influence the adsorption events, as the BSA and lysozyme adsorption were more pronounced in PEO45-b-PLA174 than in PEO45-b-PCL118. The ζ potential of the polymeric nanoparticles in PBS at pH 7.4 was slightly more negative for PLAbased nanoparticles (Table 1). Specifically considering BSA, its isoelectric point is at 4.7−4.9, and its effective charge is always negative for higher pH values, being z = −8.4 at pH 6.8.36 Hence, weak electrostatic forces may contribute to avoiding BSA adsorption, although the main reason for the antibiofouling property was presumably related to the extensive hydration layer conferred by the hydrophilic chains, where a negative ζ potential has, if any, a minor influence on these phenomena. The nanoparticles were consequently assumed to be well protected against protein adsorption at Mw(PEO) ≈ 5000 g· mol −1 . Nevertheless, although PEO is known to be
⎛ dn ⎞ β ⎛ dn ⎞ 1 + β ⎛ dn ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = + ⎝ dc ⎠complex β ⎝ dc ⎠ polymer 1 + β ⎝ dc ⎠ protein (9)
and the substitutions yield K ′c polymer Rθ
=
⎡ R 2q2 ⎤ ⎢1 + G ⎥ 3 ⎦ NaggM polymerB ⎣ 1
2
(10)
where B=
⎛ dn ⎞ ⎛ dn ⎞ ⎜ ⎟ + β⎜ ⎟ ⎝ dc ⎠ polymer ⎝ dc ⎠ protein
K′ =
4π 2n2 NAλ 4
(11)
(12)
Thus, the SLS data can be analyzed without the use of the concentration and the refractive index increment of the complex. The extrapolation to q → 0 has been applied in the same way as in the Zimm plot for polymer solutions to determine the molecular weight of the complex (Mcomplex), which is related to the number of biomacromolecules on the surface of the NPs. Because the systems have a bimodal distribution of size (one related to free protein and the other related to the presence of the polymeric nanoparticles or the polymer−protein complex), prior to the static light scattering data treatment the intensity contribution of the protein-free population was subtracted from the total light scattering at each scattering angle by considering the amounts determined from DLS. The reported K′cpolymer/ R(θ) vs q2 profiles in the presence of protein already considers the intensity contribution only of the larger particles (whether NP−protein complexes or NPs). The representative data for PEO105-b-PLA174 in the presence of BSA and lysozyme are given in Figure 4. The remaining data are given in the Supporting Information File (Figure S4). The dn/dc values for BSA and lysozyme in PBS buffer were determined as 0.181 and 0.186, respectively. The intercept of the y axis gave a value equal to (Mw(NPs)B2)−1. Because the values of Mw(NPs) were known (Table 1), the values of B could be determined. The data are summarized in Tables S3 and S4 of the Supporting Information for BSA and lysozyme, 9775
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Table 3. Mass Ratio of Bound Protein (β), Estimated Number of Adsorbed Proteins, and Estimated Surface Coverage entry
β (BSA)
number of adsorbed BSA molecules
surface covered (%)
β (lysozyme)
number of adsorbed lysozyme molecules
surface covered (%)
PEO105-b-PLA236 PEO45-b-PLA174 PEO113-b-PCL118 PEO45-b-PCL118
0.017 0.163 0.004 0.109
negligible 37 negligible 10
