Materials Science and Engineering C 58 (2016) 316–323

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Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec

Polyacrylic acids–bovine serum albumin complexation: Structure and dynamics Mohamed Othman, Adel Aschi ⁎, Abdelhafidh Gharbi Labeoratoire de Physique de la Matière Molle et Modélisation Electromagnétique, Faculté des Sciences de Tunis, Campus Universitaire, 2092, Université de Tunis El Manar, Tunisia

a r t i c l e

i n f o

Article history: Received 12 March 2015 Received in revised form 23 August 2015 Accepted 25 August 2015 Available online 5 September 2015 Keywords: Complex phase Turbidity Dynamic light scattering Nuclear magnetic resonance Electrostatic potential

a b s t r a c t The study of the mixture of BSA with polyacrylic acids at different masses versus pH allowed highlighting the existence of two regimes of weak and strong complexation. These complexes were studied in diluted regime concentration, by turbidimetry, dynamic light scattering (DLS), zeta-potential measurements and nuclear magnetic resonance (NMR). We have followed the pH effect on the structure and properties of the complex. This allowed refining the interpretation of the phase diagram and understanding the observed phenomena. The NMR measurements allowed probing the dynamics of the constituents versus the pH. The computational method was used to precisely determine the electrostatic potential of BSA and how the polyelectrolyte binds to it at different pH. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The systems involving interactions between polyelectrolytes and oppositely charged spheres are present in many areas and fields of application [1–3]. These systems are found in nature, which gives them a biological interest [4]. One of the newest and most interesting applications is the transfer of genes associated with gene therapy. In this case, the association between the DNA of vectorized gene and a cationic polymer forms the complex. The polyelectrolytes can also stabilize mineral particles in solution or encapsulate them for delivery. These encapsulation capabilities are also useful in food processing; where charged particles are biological macromolecules, mainly proteins. The grafted polyelectrolytes on surfaces can also be used to trap particles on these surfaces [5–7]. In general, the complex formation is based on electrostatic interactions between opposite charges of polyelectrolyte and protein. Various physico-chemical parameters can influence the electrostatic interactions and the complex formation. To better understand these parameters, we try to study one system where we were able to control the parameters governing the complex formation, in particular, the electric charge. We choose macroscopic studies (phase diagram) to determine the structures formed at the scale of objects based on the physicochemical parameters that can modify the interactions in the system.

⁎ Corresponding author at: Laboratoire de Physique de la Matière Molle et de la Modélisation Electromagnétique, Faculté des Sciences de Tunis, Campus Universitaire, 1060, Université de Tunis El-Manar, Tunisia. E-mail address: [email protected] (A. Aschi).

http://dx.doi.org/10.1016/j.msec.2015.08.057 0928-4931/© 2015 Elsevier B.V. All rights reserved.

This study aimed at studying the effect of pH on the structure and properties of the mixture system composed of bovine serum albumin (BSA)–polyacrylic acid (PAA). The composed systems of the polyelectrolyte and proteins are very varied and their related current studies are very important [8–12]. In our case, the chosen protein is the bovine serum albumin (BSA) that has a globular shape in native state [13,14], stable in solution and does not form oligomers. Its isoelectric pHi is equal to 4.9, which allows varying the total charge (positive/negative) on a reasonable range of pH. Finally, this protein is commercially available in large quantities and with sufficient purity. To overcome the problem of lack of system stability, making it difficult to perform experiments, we have chosen to use a polyelectrolyte; where we can control the parameters governing the formation of complexes in particular the electric charge of the chains. This is possible by using the polyelectrolyte whose charge density is pH dependent. The polyacid that we have chosen is polyacrylic acid (PAA). It is linear, flexible and has different lengths. In this article, we discuss the phase diagrams obtained at low concentration. The goal is to follow the changes in turbidity, zeta potential and the hydrodynamic radius of the complex versus pH. Still, this study was performed for three different masses of PAA (Mw = 5.7 k, 57 k and Mw = 118 k) to monitor the effect of pH on the chain length of the polyelectrolyte. We also examined the influence of the ratio r of constituent concentrations on the properties of complexes. The study of our systems by NMR will clarify the influence of the structure on the complex dynamics. Finally, we extended our work by studying the computational method of the electrostatic potential of BSA. The electrostatic potential helped us in the identification of functional sites at the surface of a protein and might be visualized by color-coding the molecular surface versus the potential values. The aim of this part of work is to

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precisely know how the polyelectrolyte binds with the protein when they have the same sign charge. 2. Materials and methods

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measured the apparent diffusion coefficient D for a large pH range. Further, D can be related to hydrodynamic radius distribution Rh by using the Stokes–Einstein equation, Rh = kBT/(6πηD); where kB, T and η are the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively.

2.1. Materials Bovine serum albumin (BSA) (essential fatty acid free) is purchased from Sigma Chemical Co and is a large globular protein (molecular weight = 67 kDa and residues = 585) with a good essential amino acid profile. The used protein concentration of complex for this study was 0.1% (w/v). The polyacid used in our experiments was polyacrylic acid (PAA) hydrogenated and deuterated. The molecular weight average weight Mw, the polydispersity I and the polymerization index N were presented in Table 1. Polyacrylic acids were obtained from Polysciences Inc. The deuterated polyacrylic acid PAA(D) was synthesized in our laboratory [15]. We used two mass ratios (r = [BSA]/[PAA]) r = 5 and r = 20. Sample solutions were made from a freshly stock solution of BSA and PAA that were dissolved in deionized and deuterated water, without adding salt. The pH of the mixture was adjusted by the addition of a strong base (NaOH) or a strong acid (HCl) and measured with accuracy pH-meter (multi-parameter analyzer Consort C862, offering a resolution up to 0.001 pH unit). A pH electrode (SP10T, 3 M KCl, pH ranged from 0 to 14. Temperature compensation: 0 °C to 80 °C) was immersed for 10 h more in 3 M of KCl solution and calibrated at 3 points (pH = 4, pH = 7 and pH = 10). The visual appearance (turbidity) of these complexes changed rapidly with time (3–4 h) to reach a stable state. Measurements of pH, turbidity, zeta potential and hydrodynamic radius performed 24 h after mixing. For some samples, these measurements were repeated after one week to ensure the stability of the complexes. 2.2. Characterization of the samples 2.2.1. Size, zeta potential In this work, the dynamic light scattering (Zetasizer Nano ZS, Malvern Instruments) was used to determine the particle sizes and the zeta potentials of the protein/polyelectrolyte complexes formed at various ratios. All dynamic light scattering (DLS) experiments were performed at a 173° scattering angle and a wavelength of 514 nm. DLS measurements have been performed in the so-called parallel mode that allowed measuring the correlation function over a wide time range. In this mode the relaxation time τ, which differs by orders of magnitude, could be probed in a single measurement. The measured intensity autocorrelation functions are related to the field autocorrelation functions through the Siegert relation:  2 g 2 ðt Þ ¼ A þ B g 1 ðt Þ

2.2.2. Turbidimetry The transmittances of complexes at different composition and pH were measured, at a wavelength equal to 480 nm, with a spectrophotometer (Thermo Spectronic, Cambridge, UK). At this wavelength, strong signals were obtained from the samples. The trend of the turbidity was the same for the other wavelengths. The apparatus was equipped with a temperature unit (Peltier plate) that provided a good temperature control over an extended time. The transmittance T of the samples could be determined from the following relationship: T = It/I0, where It is the transmitted light intensity and I0 is the incident light intensity. 2.2.3. NMR measurements The NMR spectrometer super-heterodyne with two-way irradiation and a receive path H-NMR experiments were done on an AMX Bruker spectrometer operating at 400 MHz. With this device, we gained a 4 signal to noise ratio resulting in better sensitivity and a gain in time of acquisition. Spectra were recorded after an acquisition of 400 scans with a repeating delay of 4 s. 3. Results and discussion 3.1. The evolution of the hydrodynamic radius of BSA versus pH We present in Fig. 1 the variation of hydrodynamic radius Rh of the BSA versus pH. One should be reminded that these obtained values, at an angle θ = 173°, are apparent. The obtention of absolute value of Rh requires further study of the second order autocorrelation function g2(t) as a function of scattering angle θ. Nevertheless, this study provides us with an idea on the evolution of the average size of the protein and its stability. We notice that the hydrodynamic radius Rh of the protein is constant over a wide pH range, 38 b Rh b 44 Å. These values are close to those mentioned in previous studies [16–19]. The greater increase in the size of the protein at pH b 3 is evidence of the denaturation of the BSA. The change in protein conformation depending on the pH has been intensively studied by scientists, an example of which is the work of Gulam Rabbani et al. [20–22].

ð1Þ

where, B is a constant depending on the experimental setup and A is the baseline. τ is related to the apparent diffusion coefficient D by the following relationship: 1=τ ¼ Dq2

ð2Þ

The scattering wave vector q is given by q = (4πn/λ)sin(θ/2), where n is the refractive index, θ the diffusion angle and λ the wave length. We Table 1 Weight average molecular weight Mw, polydispersity I and the polymerization index N for the three PAA used.

PAA(5.7 k) PAA(57 k) PAA(118 k)

Mw (kDa)

Polydispersity I

Polymerization index N

5.7 57.5 118

1.09 1.2 1.13

79 798 1638

Fig. 1. Evolution of the apparent hydrodynamic radius Rh versus pH. [BSA] = 0.1% (w/v).

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3.2. The evolution of the electrophoretic mobility of BSA versus pH The change of protein charges as a function of pH is an essential element to understand the process of complexation. An indirect way to follow the evolution of the protein charges is to study the change of their electrophoretic mobility versus pH. In fact, another study has been carried out on H2O [23]. Here, we propose to reproduce it in H2O and D2O. We present in Fig. 2 the variation of ζ potential, deduced from the electrophoretic mobility μ by the relation of Huckel, versus pH. At higher pH, the ζ potential is negative; indicating that the overall of the protein charge is negative. As the pH decreases, the acid functions are protoned while the basic functions are in positively charge. This reflected an increase in the protein charges and thus the ζ potential. At pH = 5 ± 0.02, the positive and negative charges on the surface of the protein are compensated and the electrophoretic mobility of the protein is null: this pH corresponds to the isoelectric point (pHi). Below pHi, the positive charge of the protein increases as the pH decreases. The value of the isoelectric point is close to those encountered in the literature and obtained by different experimental methods. [24,25]. In fact, we have also measured the evolution of the zeta potential of the protein to a higher concentration, c = 0.1% in D2O, in order to maintain the same experimental conditions as those of the NMR experiments performed on the complex (Figs. 6 and 7). The variation of ζ potential as a function of pD has the same shape as that of BSA in H2O, and the value of the isoelectric point pDi = 5.3. Taking into account the measurement error (± 2 mV), the shift observed in relation to pHi is insignificant. In addition, the reservation of the protein charge sign is insensitive to the isotopic composition of water. 3.3. pH effect on BSA–PAA complex (5.7 k) We present in Fig. 3, the variation of turbidity, potential ζ and hydrodynamic radius Rh versus pH for the BSA–PAA (5.7 k) mixture. We still figure out the same curve of the hydrodynamic radius and potential ζ of the BSA alone. We remind that the turbidity, measured at 480 nm, is expressed as a function of the transmission T as 100 – T (%). It is pivotal to note that the values of Rh obtained at 173° cannot be considered as exact values, but as apparent sizes. These measures will be primarily used to monitor the complex size. Furthermore, it is important to mention that for these concentrations of polyacid, the signal to determine Rh and ζ potential of the highly charged polyacid is very low and difficult to detect. Therefore, the main signal of the measurements of complexes is essentially due to the protein. Thereafter, we will describe the variation of the different curves (Rh, turbidity and ζ potential) that follow the decrease of pH, i.e. from clear mixture to most turbid mixture. Moreover, the ratio rc of the

Fig. 2. Variation of ζ potential of BSA in: (x) H2O and (*) D2O versus pH and pD respectively.

Fig. 3. (▲) Changes versus pH of: turbidity (a), ζ potential (b) and hydrodynamic radius Rh of complexes (c). [BSA] = 0.1% and r = 5. (■) BSA alone. The zones (I and II), (III) and (IV) correspond respectively to soluble polymers, soluble complexes and association of complexes.

number of proteins on the number of polyacid chains presented in the solution is defined by the following relationship [26]:   r c ¼ r Mw PAA =Mw BSA

ð3Þ

and is equal to 0.43. This result is about more than two proteins per polyacid chain. Fig. 3 illustrates the change in turbidity when pH decreases and shows three distinct regimes. The first regime (5.22 b pH b 7, zones I and II) is perfectly clear. The second regime (zone III) is characterized by the great increase in turbidity at a very narrow pH range (5.05 b pH b5.22). This zone precedes the inversion of BSA charges. Finally, at pH b 5.05, the solution is highly turbid (transmission T is close to 0) and precipitates slowly. In fact, the solution abruptly passes from a regime where the mixture does not form clusters to a very complex system where the protein and the polyacid associate form a large aggregates which diffuse light strongly. The transmittance observed in the first regime (zones I and II) does not necessarily mean that the protein and the polyacid are not interacted. The evolution of Rh and ζ potential in zone II clearly shows the formation of small size complexes (primary complex). Indeed, this regime consists of two distinct zones (zones II and I) for which the evolution of the hydrodynamic radius and the complexes zeta potential are different. In zone I, the observed apparent Rh is constant (Rh = 5.8 nm) and slightly higher than that of protein alone. At pH = 6.77, the ζ

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potential of BSA alone or in the complex is same and equal to −15.8 mV. We still notice, in the zone cited above, that the potential of BSA alone increases when pH decreases; unlike to the case in the mixture where it remains constant. The constant value of Rh indicates that the components are not interacted and the overall negative charge of the protein and the polyacid are high, indicating the existence of strong repulsive interactions. On the contrary, in zone II there was an increase of Rh, which passed from 5.8 nm to 19.1 nm accompanied by a decrease in the ζ potential. In the same flow, the regime of weak complexations is called primary complexes, constituted of two proteins associated with some polyacid chains. This regime begins at critical pH (pHC = 5.7) below, with the gain of correlation energy, due to electrostatic association between the polyacid and positively charged domains of the protein, which outweighs on the macroscopic energy of electrostatic repulsion associated to the total charge Q of the complex (Q b 0).[15,27]. In fact, the total charge Q of complex can be written as Q = Q− – q+, where Q− is the total negative charge of the polyacid and the protein together and q+ is the total positive charge on the surface of the protein. This binary association between the protein and polyacid occurs when the charge of the polyacid is sufficiently reduced and the positive charge of the protein, origin of electrostatic correlations, is sufficiently increased. This transition occurs for a well-defined charge ratio Q/q+ and corresponds to pHc. The decrease of zeta potential with pH shows that the number of polyacid chains per protein increases with protein charge q+. The second regime (zone III), characterized by a strong increase in turbidity, begins at a pH value commonly noted as pHϕ [19,28]. In this case, there is an increase in Rh accompanied with a decrease of the ζ potential of complexes from a pHϕ value equal to 5.22. In this zone the samples are stable (no precipitates), the charge rate of the polyacid is 30% and that the excess of negative charges of the protein is low. We still notice that on the one hand a rapid increase of hydrodynamic radius of the complex from 19.4 nm to 184 nm when the pH decreases from pHϕ = 5.22 to pHϕ = 5.19, and on the other hand, the overall negative charge continues to increase in absolute value. This is the beginning of a very high complexation system in which the primary complex aggregates to form large size complexes. In fact, this regime is also called “condensation regime” in which the primary complex associated from a threshold is in turn called condensation regime formed by large aggregates. Paradoxically, the condensation of the primary complex occurs when the global negative charges are maximal. Contrary to expectations, the condensation reached far from the isoelectric point, corresponding to the reversal of complex charges. This phenomenon has been observed in other complexes of oppositely charged polyelectrolytes [12,29–31] and this is again an explanation within the framework of the theory of Zhang and B. Shklovskii. [32, 33]. Indeed, the primary charged complex can condense if the total electrostatic energy is reduced and then becomes like the classical cohesive energy (or Madelung energy) of a neutral species. In the present case, the decrease of the cohesive energy can offset the increase of electrostatic repulsion energy and is related to the increase of the total charge Q of the complex, Erep ∝ Qζ. We notice that the last point of this zone corresponds to an increase in the size and ζ potential of complexes. The entropic effects promote the dispersion of the complexes and can explain why condensation occurs in a narrow interval before reaching the maximum of complexation. Finally, in zone IV, the condensed complexes of large size are formed. As the pH decreases, the charge rate of the polyacid decreases and the positive charge of BSA increases. This explains why the negative charge of the complex increases and changes at the isoelectric point of the complex (pHic = 4.37). Accordingly, the regime of both kinds of constituents has charges of opposite signs. The electrostatic correlations responsible for the cohesion of the aggregates are strong and largely compensate the dispersive electrostatic forces (repulsive) associated with the global negative charge of the aggregates: the system precipitates. For pH b pHic

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and for the same reasons, the positive charge of the complex increases when pH decreases.

3.4. The influence of the polyacid length The realized study with short PAA (5.7 k) was reproduced with two long polyacids (PAA (57 k) and PAA (118 k)). The variation of turbidity, hydrodynamic radius Rh and ζ potential versus pH of three PAA is shown in Fig. 4. We remind that at fixed pH, the charge rate of the polyacid does not depend on the polymerization index [34]. The rates of protein number per polyacid chain are rc = 4.42 for PAA (57 k) and rc = 9.1 for PAA (118 k). The turbidity curves of PAA–BSA complexes (118 k) and BSA–PAA (57 k) versus pH show again the clear and turbid regimes separated by a narrow zone of pH. The pHϕ value corresponding to the beginning of a strong regime of complexation is the same for PAA 57 K and PAA 118 K (Phϕ = 5.9) and is greater than that observed in PAA (5.7 k) (pHϕ = 5.07). In the case of BSA–PAA (57 k) complex, the regime of weak complexation appears at pHc = 6.5 and exactly presents the same evolutions in the size and ζ potential of complexes. The increase of the chain length of polyanion induces an increase in pHc value and a broadening of pH zone corresponding to the formation of primary complexes (pHϕ b pH b pHc). The multiplication of chains length by a factor 10 may be the cause of the great reduction of the polyanion translational entropy, thus promoting its complexation with the protein. During the association of polyanion with protein, the loss of translational entropy of long polyacid is much lower than that of short polyacid. Therefore, the minimum charge required for the protein to bind to PAA (57 k) is less than that to PAA (5.7 k).

Fig. 4. Evolution versus pH of: (a) turbidity, (b) ζ potential and (c) hydrodynamic radius Rh complexes: (■) BSA–PAA (118 k) (•) BSA–PAA (57 k) (▲) BSA–PAA (5.7 k). [BSA] = 0.1%, r = 5. The dashed line corresponds to pHi.

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As in the case of PAA (5.7 k), the condensation threshold at pHϕ corresponding to the minimum of ζ potential of complexes coincides with a dramatic increase of hydrodynamic radius (Rh: 20 nm → 700 nm). As we have noted on the turbidity curve, the increase of the length of polyelectrolyte chains moves the condensation threshold to a higher pH, i.e. for lower positive charge q+ of the protein. This is again a demonstration of entropic effects. Due to the confinement of the chains in large aggregates, the condensation of the primary complex is accompanied by a further decrease of the translation entropy of polyacid. This loss of entropy, which opposes the condensation, is less important in the case of the longer polyacid. Moreover, at the approach to pHϕ, the long chains of polyacid can easily bind to primary complexes than short chains and lead their condensation. In the case of pH b pHϕ, the evolution of complexes little depends on chain length. 3.5. Effect of molar ratio Our results have shown that the association is controlled by the protein charges, confirming the previous work performed on similar systems. [35–42]. An additional manner commonly used to confirm this hypothesis is to vary the total charge supplied by the polyanion via modifying its mass concentration. We present in Fig. 5 a comparative study between a complex formed by BSA–PAA (5.7 k) at r = 5, discussed above, and another complex that differs only by a lower polyacid concentration, r = 20. The changes in the complexes size (Rh) versus pH for r = 20 reveal the same characteristics to that of r = 5 and exhibit two regimes of weak and strong complexation with a transition that occurs at the same pH = pHϕ. This indicates that the condensation of the primary complex is only controlled by the charge of the protein. We noticed, for the weak complexation regime, that the number of available polyacid chains is, in this case, lower than that of protein (rc = 1.72 to r = 20) i.e. some proteins are not complexed. The increase in hydrodynamic radius and the decrease of the ζ potential of primary complexes are lower than the case of r = 5. The shift of the minimum of ζ potential to high pH is probably due to the depletion of the reservoir of free polyacid chains.

Fig. 5. Evolution versus pH (a): turbidity; (b): ζ potential and (c): hydrodynamic radius Rh of complexes BSA–PAA(5.7 k). (•): r = 20; (▲): r = 5. [BSA] = 0.1%.

In the condensed regime (pH b pHϕ), the size of condensed complex is around 2000 nm and is independent of the ratio r. However, for r = 20, the transition is invisible on the turbidity curve. It is found that the increase in turbidity is achieved when the pH decreases progressively. Indeed, this indicates that the number of condensed aggregates increases with the positive charge of the protein and this can occur only if the number of polyacid chains in the aggregates decreases with pH. 3.6. Dynamic NMR study The study of the complex by proton NMR allows us to obtain information about the dynamics of complexes. The association between protein and polyelectrolyte is accompanied by a change of dynamic at large-scale (the diffusion of components is slowed). Indeed, the movement of chain segments is restricted by the complexation. This diffusion reduction and the slowdown of movements cause an increase of the correlation time τr of chain segments. The slowdown in the local dynamics is reflected in NMR by a faster relaxation of the transverse magnetization. If the static magnetic field B0 is sufficiently uniform, the width at half- height δν of the resonance spectrum is connected to the transverse relaxation time T2 by the following relationship: δν = 1/πT2. The decrease of the relaxation time is directly manifested by a line broadening of the NMR spectrum. Thus, it is possible to qualitatively follow the evolution of the constituents local dynamics. The samples are the same as those studied by dynamic light scattering and turbidity. The protein concentration in D2O is 0.1% and the molar ratio r = 5. We can therefore directly realize a comparative study on structural and dynamic properties of the complexes. Measurements are performed at room temperature one week after sample preparation. The variation versus pD of the NMR spectra of the mixture and those of the constituents are presented in Figs. 6 and 7. 3.6.1. BSA–PAA complex (5.7 k) The NMR spectrum of BSA–PAA complex (5.7 k) is illustrated in Fig. 6. The NMR spectrum of PAA (5.7 k) alone in solution presents two isolated peaks at δ = 2.4 ppm and δ = 1.2 ppm, corresponding respectively to the group of CH and CH3. Another massive of three peaks (1.5 ppm b δ b 2 ppm) corresponds to CH2 group. At pD = 7.43, the position and peak width of the polyacid remain unchanged. The dynamic of polyanion is not affected by the presence of the protein: the polyacid chains remain free in solution. In the clear zone (5.63 b pD b 7.43) and when the pD decreases, a slight enlargement of the resonance peaks is appeared. This effect clearly demonstrates a reduction of chain mobility of polyacid when the BSA–PAA interaction increases. The observed widening is slightly marked because

Fig. 6. Proton NMR complexes BSA–PAA (5.7 k) versus pD. [BSA] 0.1%, r = 5.

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(pD = 5.89 and pD = 5.69), the resonance of peaks relative to the PAA (118 k) gradually disappears under the effect of line broadening. We deduce that, as the case of the BSA–PAA (5.7 k) complex, and the dynamics of PAA chain are practically frozen. In the weak complexation domain, The NMR spectrum of the protein is weakly modified by the interactions with PAA (118 k). For the most complexed samples (pD = 5.87 and pD = 5.69), we observe a strong broadening which results in the overall decrease in the intensity of the NMR spectrum. This effect shows the same reduction in the mobility of residues of protein surface observed on the PAA (5.7 k).

4. Computational methods

Fig. 7. Proton NMR complexes BSA–PAA (118 K) versus pD. [BSA] = 0.1%, r = 5.

the polyacid chains are weakly complexed with the protein. In this primary complexes regime, the polyelectrolyte chains move quickly from one complex to another (fast exchange situation). The broadening of resonance lines is much more dramatic in the case of strong complexation regime (5.46 b pD b 5.57) for which there is a gradual disappearance of peaks as the pD decreases. In the case of most complexed samples, the lines of polyacid almost disappear due to their strong broadening. In the latter case, the dynamics of the PAA chains, confined between proteins, are practically frozen. This development also shows that there are no free chains in solution. These observations may confirm the interpretations of our previous experiences and regenerate the existence of a regime of weak complexation in which the polyacid chains interact weakly with the protein, followed by a strong complexation where the polyacid occupies interstitial space between the aggregated proteins. The NMR spectrum of the protein is not modified by the interaction with the polyacid except at pD = 5.46. The slow dynamic of hydrated residues on the surface of the protein is not affected by the complex formation. In the case of the most complexed sample (pD = 5.46), a strong broadening is observed, which results in an overall decrease in the intensity of the NMR spectrum. This situation of strong interaction, where the components are confined in large aggregates, induces a dramatic reduction in the mobility of surface residues of the protein. In all cases, the NMR shows that the protein remains in a conformation close to its native state. In fact, there was no denaturation of BSA. 3.6.2. BSA–PAA complex (118 k) The NMR spectrum of BSA–PAA complex (118 k) is presented in Fig. 7. The spectrum of single polyanion PAA (118 k) shows the same characteristics as that of PAA (5.7 k). The peak of the terminal CH3 group is no longer visible. The NMR spectra of the BSA and the polyacid PAA (118 k) in the complex have the same general trend as that observed in short polyacid. There is an overall reduction of polyacid chain mobility when the complexation increases. In addition, the peaks of the spectra of long polyacid are, at the same pD, larger than those of short polyacid. This is particularly the case of the complexes obtained at pD = 6 and corresponding to the regime of weak complexation. In the regime of weak complexation (7.4 b pD b 6), the progressive fixation of protein on a long chain of polyacid and the formation of “pearl necklaces” may be explained by significant reduction in chain mobility. The observed effect is more pronounced than that of PAA (5.7 k). In this regime, unlike to the short polyacid, the long polyelectrolyte is always associated with several proteins. The exchanges between the complexes are therefore slower. In the strong complexation regime

The program, Adaptive Poisson-Boltzmann Solver (APBS), was used to calculate the potential map and write it out in a file [43], which can be then read into Chimera software [44]. The structure was prepared for APBS calculations by reconstructing missing heavy atoms, adding hydrogens, and assigning atomic charges and radius. These tasks have been done with Protein Data Bank to Protein atomic partial Charge Q and radius R (PDB2PQR) software [45,46]. PDB2PQR uses protein pKa server (PROPKA) [47] to assign protonation states at desired pH. The resulting electrostatic potential map will be introduced as a new model in Chimera and the Electrostatic Surface Coloring tool for coloring molecular surfaces by the potential that is going to appear. The dielectric constants of the solvent and the protein were set to 78.54 and 2.5, respectively. By calculating the protein net-charge [47] based on the pKa values for the individual amino acids, the charges of the protein at different pH values could be estimated. Fig. 8 shows the electrostatic potential contour at the surface of the protein as a function of pH and corresponding net charges Zp. The protein crystal structures with Protein Data Bank identifications 3V03 (BSA) were taken from the Research Collaboratory for Structural Bioinformatics, RCSB Protein Data Bank (http://www.rcsb.org). The values of electrostatic potential were color-coded from red to blue on the molecular surface. In fact, this result helped us to determine the pH dependence of complexation observed in Fig. 3 and comparer the electrostatic potential on the surface of BSA (a) pH = 4.3; Zp = 80, (b) pH = 4.9; Zp = 36, (c) pH = 5.2; Zp = 20, (d) pH = 5.7; Zp = 2, (e) pH = 7; Zp = −30, and (f) pH = 9.7; Zp = −84. The orientation of the protein was the same in all cases to facilitate comparison. The electrostatic potential was given in units of KBT/e. In fact, two isosurfaces were shown, red: −0.5 KBT/e and blue: +0.5 KBT/e.

Fig. 8. (a) Electrostatic potential contour +0.5 kT/e (blue) and −0.5 kT/e (red) around the BSA at ionic strength 0 M. (b) pH values and corresponding net charges Zp are presented. Calculation based on protein data bank identifier, pdb id: 3V03.

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We notice that the number of negatively charged surface residues was increased with increasing the pH value. The region around BSA displayed the strongest positive potentials (Fig. 8a), making it a good candidate to interact with a negatively charged potentials at the surface of polyelectrolyte. At pH 5, close to pI, BSA showed approximately high positive charge, as seen in Fig. 8b and c. In Fig. 8d(pH = 5.7). The positively charged character of a BSA chain in basic pH was shown by little “patches” in blue. This demonstrated how the protein interacts with the polyelectrolyte even with negative net charges. 5. Conclusion We studied the complexation of BSA with various masses of polyacrylic acids versus pH and we found two complexation regimes. In the presence of a short polyacid, one or two proteins associated to polyacid chain to form a stable complex with small size. When the polyanion was much longer, the proteins bound with polymer chains to form “pearl necklaces”. During the regime of weak complexation, there was an electrostatic association between polyelectrolyte and proteins of the same charge. This phenomenon was ascribed to the attraction between polyelectrolyte charges and oppositely charged patches on the protein surface. The structure of condensed complexes observed for pH b pHϕ depends strongly on the chain length. When the polyacid was short, we observed the formation of aggregates of increasing size. The condensation of the primary complex formed by a long-chain of polyacid and several proteins also resulted in the formation of complexes of increasingly dense when the pH decreased. In this case, the aggregates consisted of protein clusters whose size increased as the BSA charges decreased. These protein clusters interconnected by the chains of polyacid represented the nodes of a three-dimensional network. Whatever the regime of complexation, the length of polyacid chain has a decisive influence on the structure of forming assemblage. Finally, we can conclude, that short polyelectrolyte is recommended for the encapsulation and the stabilization of globular proteins as the BSA. Acknowledgments – This research was supported by the Ministry of Higher Education and Scientific Research in Tunisia (MHESRT). – The authors thank the Laboratory of Physique of Solids, CNRSUMR8502, Paris-sud University, F-91405 Orsay, France for access to NMR experiment.

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