J. Phys. Chem. B 2008, 112, 4393-4400
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Release of Lysozyme from the Branched Polyelectrolyte-Lysozyme Complexation Ran Ni, Dapeng Cao,* and Wenchuan Wang DiVision of Molecular and Materials Simulation, Key Lab for Nanomaterials, Ministry of Education, Beijing UniVersity of Chemical Technology, Beijing 100029, People’s Republic of China ReceiVed: August 7, 2007; In Final Form: January 15, 2008
On the basis of the discretely charged sphere model of lysozyme, the release behavior of lysozyme from the branched polyelectrolyte-lysozyme complexation is investigated by adding salt and changing the pH values of the solution. It is found that, with the increase of the salt ionic strength of the solution, the lysozymes are gradually released from the oppositely charged polyelectrolyte as a result of the screening of electrostatic attraction between the two ionic species by adding the salt. Interestingly, there exists a critical salt ionic strength at which all proteins are released from the branched polyelectrolyte, and the polyelectrolyte-protein complexation is broken completely. Beyond the critical value, the increase of the salt ionic strength causes self-association of the proteins released from the branched polyelectrolyte-protein complexation. The selfassociation of the protein is detrimental in biological systems. By calculating the second virial coefficient, we found that the optimal salt content for the dispersion of proteins coincides with the critical ionic strength, because the second virial coefficient reaches its maximum at the critical ionic strength. Similarly, increasing the pH value of the solution can also release the lysozymes from the polyelectrolyte, because the increase of pH value of the solution changes the charge distribution and net charge of the lysozyme, weakens the attraction between lysozymes mediated by polyelectrolyte, and finally leads to the dissolution of the complexation of branched polyelectrolyte with lysozymes in strong alkaline solution. In addition, by exploring the effect of architecture of the polyelectrolyte on the release behavior of proteins, we found that it is more difficult to release proteins from the branched polyelectrolyte than from the linear polyelectrolyte.
1. Introduction Since Fleming first found that a substance in nasal mucosa can lyse some bacteria,1 lysozyme has been crystallized,2 and the complexation of a protein and a polyelectrolyte has been extensively investigated by experimental3-6 and theoretical approaches7,8 because of its importance in a variety of fields such as protein purification,3,4,9,10 drug delivery systems,11,12 and food technology.13 In the past decades, the experimental studies on the electrostatically driven protein-polyelectrolyte complexes mainly focused on the formation of the complex and phase separation,3,5,14 and on the key factors influencing the conformation of the complex, such as the protein-polyelectrolyte interaction,15,16 the nature of the protein,17the stiffness of the polyelectrolyte,18 the salt concentration,19,20 and the pH value of the solution.21 The behavior of complexation of a protein and a polyelectrolyte is analogous to that of the system containing a macroion and an oppositely charged polyelectrolyte,8,22 where the macroion is modeled as a charged hard sphere and the polyelectrolyte is represented by a sequence of oppositely charged connected hard spheres.23 Numerous theoretical investigations concerning such macroion-polyelectrolyte systems have been performed in past decades. On the basis of a coarse-grained model, Muthukumar and co-workers derived the critical condition for the adsorption of polyelectrolytes on uniformly charged24 and heterogeneously positively charged surfaces.25 Recently, Winkler and Cherstvy26 gave analytical solutions of the critical adsorption radius and critical surface charge density for the * Corresponding author. E-mail:
[email protected] and cao_dp@ hotmail.com.
adsorption of polyelectrolyte on a charged spherical surface. The self-consistent field theory (SCFT)27 and phenomenological theory28 were also employed to investigate adsorption, the complexation of a polyelectrolyte and an oppositely charged macroion, and the charge inversion phenomena. On the basis of the SCFT, Gurovitch and Sens27 found that the connectivity between polyelectrolyte beads enhances the intensity of charge inversion. The overcharged complexation may tend to adsorb other charged macroions, which is known as the bridging mediated by the polyelectrolyte for aggregation of oppositely charged macroions.29 Podgornik and co-workers30,31 recently presented a self-consistent theory for the polyelectrolytemediated bridging for oppositely charged macroions. Moreover, the dependence of the complexation on the stiffness and the chain length of the polyelectrolyte, ionic concentration, particle size, and surface charge density of macroion were systematically explored by theoretical approaches32-35 and molecular simulation.22,23,36-43 Experimental approaches confirmed that the greater the flexibility of a polyelectrolyte, the stronger the binding of that polyelectrolyte (i.e., poly(styrene sulfonate)) to proteins (i.e., BLG),18 which is in line with the theoretical results on macroion-polyelectrolyte complexations. Recently, these theoretical and simulation investigations on the macroionpolyelectrolyte complexations were reviewed by Stoll and coworkers,44 and de Vries and co-workers,45 and several comprehensive reviews on experiments of polyelectrolyte and protein complexations have been addressed.13,15,16,46 Although regarding the proteins as a uniformly charged hard sphere is a theoretically reasonable simplification to some extent, experiments show that the charge heterogeneity of a protein is significantly important. By comparing the formation of com-
10.1021/jp076348z CCC: $40.75 © 2008 American Chemical Society Published on Web 03/15/2008
4394 J. Phys. Chem. B, Vol. 112, No. 14, 2008 plexes between potassium poly(vinyl alcohol) sulfate and lysozyme vs ribonuclease, Kokufuta and co-workers17 found that the difference in the aggregation degree of the two complexes is attributed to the difference in charge distribution between lysozyme and RNAse (the latter being more heterogeneous). Muthukumar and co-workers advanced their theories by considering a surface with a distribution of positive and negative charge, and derived the critical condition for the adsorption of polyelectrolyte on the patterned charged surface.47 Furthermore, de Vries et al.48 attempted to elucidate the effect of charge anisotropy of a protein on the protein-polyelectrolyte interaction by considering the protein as a randomly charged (annealed) sphere, and developed a rough analytical theory to estimate the critical pH of the soluble complex containing polyelectrolytes of low linear charge. The macroion-polyelectrolyte system, therefore, is not adequate to capture essential physical features of the complexation of a protein and an oppositely charged polyelectrolyte. Linse and co-workers proposed a hard sphere model with the discretely embedded charges beneath the spherical surface to represent the protein (i.e., lysozyme), owing to the sphere-like nature of lysozyme.49 They also investigated the effect of adding salt on the complexation of lysozyme and a linear polyelectrolyte7 on the basis of the embedded charge spherical model of lysozyme. Their simulation results show that the addition of salt in an aqueous solution containing negatively charged polyelectrolyte and lysozyme makes the lysozymepolyelectrolyte complexation looser. In the spherical model of Linse and co-workers for lysozyme, the embedded charges represent the ionized amino acids, and the positions of all embedded charges were constructed based on an X-ray diffraction study of crystalline hen egg white lysozyme.50 The detailed construction of this model was described elsewhere.7 By using the above model, Linse and coworkers derived the parameter of hydrophobic interaction by fitting the calculated second virial coefficient B2 to experimental data. Furthermore, Lund and Jonsson51 used both atomic and amino acid representations to develop more complicated mesoscopic models, aiming to describe the protein-protein interaction in aqueous solution reasonably. Recently, McGuffee and Elcock52 performed an atomically detailed simulation of protein solution, and their simulation results are mainly in analogy with that of Linse and co-workers,49 which suggests that the hard sphere model with discretely embedded charges proposed by Linse and co-workers7 is a reasonable simplification of the atomically detailed model, since the simplified spherical model can capture the essential features of charge heterogeneity of the lysozyme. To our best knowledge, previous research mainly focused on the complexations of protein and linear polyelectrolyte, except for these investigations on the adsorption of a protein on a star polyelectrolyte brush from Ballauff and co-workers.53-56 They experimentally demonstrated that the interaction between proteins and the star polyelectrolyte brush is very strong, and almost no free proteins disperse in solution,53 which is very important in many biological applications, such as drug delivery. In recent years, many polyelectrolytes with complex architectures, such as branched, star-shaped, and dendritic polyelectrolytes, were synthesized and applied to drug delivery systems and biological realms.57 However, there were few theoretical investigations on the complex of proteins and polyelectrolytes with nonlinear geometries, and on the difference between the protein-linear polyelectrolyte and protein-nonlinear polyelectrolyte complexes. In this work, on the basis of the discretely charged sphere model, we use Monte Carlo simulations to
Ni et al.
Figure 1. The model of a branched polyelectrolyte, where the branched polyelectrolyte contains Nf side chains of length Ns, and two side chains are separated by Ng beads along the backbone. For the model, Nf ) 11, Ns ) 7, and Ng ) 1.
Figure 2. RDFs between the centers of the protein and the segment of the branched polyelectrolyte at different ionic strengths.
investigate the release behavior of lysozymes from the branched polyelectrolyte-lysozyme complexation by adding salt and changing the pH value of the solution, and explore the effect of the architecture of the polyelectrolyte on the release of lysozymes. The remainder of this article is organized as follows. We first describe the computational method of a Monte Carlo simulation, including molecular models and simulation details. Then, we present the simulation results on the complexation of branched polyelectrolyte and lysozyme and its dependence on the salt content. Finally, some discussion is addressed. 2. Models and Simulation Methods In this work, the protein (i.e., lysozyme) is modeled as a discretely charged hard sphere with radius RProt ) 18.54 Å, and the charges representing the ionized amino acids are embedded 2 Å beneath the spherical surface. The number of positive and negative charges at a given pH is determined by the pKa values of all titrating amino acids of lysozyme.7,58 The positions of charges are constructed on the basis of the coordinates of lysozyme crystal structure from X-ray diffraction in the Brookhaven Protein Data Bank, entry 2LZT,50 and this detailed protein model was described elsewhere.7 The branched polyelectrolyte is represented by a charged hard-sphere chain with a branched architecture, as shown in Figure 1. The branched polyelectrolyte contains Nf side chains. Each side chain length is Ns, and the branched points of the grafting side chain are
Release of Lysozyme from Polyelectrolyte-Lysosyme
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separated by Ng beads along the backbone. The total number of sites, M, in one molecule is given by M ) (Ng + Ns + 1)Nf + Ng, and the number of segments along the backbone, Mb, is given by Mb ) M - Nf‚Ns. The bond length and hard-sphere diameter are fixed and equal to σb ) 1 nm. The solvent (i.e., water) is not considered explicitly in our model, but enters the model just through its relative dielectric permittivity. The total energy of the system in our simulation is given by
U ) Ubond + Uhs + Uel + Ushort all beads
)
∑ i
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Figure 8. Number of lysozymes complexed on the branched polyelectrolyte at different Zprot.
Figure 7. RDFs between the center of the protein and the segment of the branched polyelectrolyte at different Zprot: (a) IS ) 0.0372 M and (b) IS ) 0.0492 M.
0.1 M), there exists a contact peak in gprot-prot(r) again, as shown in the inset of Figure 6. Moreover, the height of the contact peak increases with the salt ionic strength, which is due to the fact that the hydrophobic attraction between proteins plays a more dominating role in the case of higher ionic strength. It can be observed from Figures 5 and 6 that, with the increase of the salt ionic strength, proteins are released from branched polyelectrolyte first, and then self-association of the released proteins occurs. Moreover, we are also interested in the influence of pH values on the complexation of lysozyme and branched polyelectrolyte. Since, in the lysozyme model used in this work, the pH value just monotonically affects the charge distribution and net charge of the lysozyme, we performed Monte Carlo simulations at Zp ) + 19, +10, +6, -1, and -13, which means that the pH value in the solution increases from pH ) 1 (Zp ) +19) to pH ) 13 (Zp ) -13). Two fixed salt contents of IS ) 0.0372 M and 0.0492 M are considered, and the RDFs between lysozymes and segments in the branched polyelectrolyte are shown in Figure 7. It can be observed from the figure (panels a and b) that, in the strong acidic solution corresponding to Zprot ) +19, there is a high contact peak in gprot-branch(r), and with the increase of the pH in the solution (corresponding to the decrease of Zprot), the height of the contact peak gradually decreases. For the cases of Zprot < 0, i.e., Zprot ) -1 and -13, an apparent depletion appears in gprot-branch(r), which is due to the net electrostatic repulsion between lysozyme and branched polyelectrolyte. To further observe the dissolution of proteins
Figure 9. The gyration radius of the branched polyelectrolyte at different Zprot.
from branched polyelectrolyte with the pH value, we also calculated the number of lysozymes complexed to the branch polyelectrolyte at different Zprot, as shown in Figure 8. With the increase of the pH value of the solutions (corresponding to the decrease of the Zprot), the lysozymes are gradually released from the branched polyelectrolyte. The changing trends of Ncprot vs Zprot in salt solutions of IS ) 0.0372 M and 0.0492 M are the same, but the values of Zprot at IS ) 0.0372 M are apparently larger than those at IS ) 0.0492 M for the same pH value. This may be because the screening of the salt content strengthens the release of the lysozymes from the complexation. To consider the effect of pH value on the conformational change of the branched polyelectrolyte with Zprot, we calculated the gyration radius of the branched polyelectrolyte, 〈Rg2〉1/2
〈Rg2〉1/2 )
x
1
M
M
〈
|ri - rcm|2〉 ∑ i)1
(3)
where ri and rcm denote the position vectors of the segment i and the mass center of the branched polyelectrolyte, respectively. The calculated gyration radii of the branched polyelectrolyte are shown in Figure 9. It can be observed that, with the increase of pH value, corresponding to the decrease of Zprot, the gyration radius of branched polyelectrolyte increases gradually, which means that, after the lysozymes are released from the branched
Release of Lysozyme from Polyelectrolyte-Lysosyme
Figure 10. Second virial coefficients at different Zprot.
polyelectrolyte, the branched polyelectrolyte swells gradually. When Zprot decreases from +19 to +6, 〈Rg2〉1/2 at IS ) 0.0492 M is larger than that at IS ) 0.0372 M. While Zprot decreases to be less than 0, 〈Rg2〉1/2 at IS ) 0.0492 M is smaller than that at IS ) 0.0372 M. This is due to the fact that, when Zprot > 0, there are a number of lysozymes complexed on the branched polyelectrolyte, which mainly determines the conformation of the branched polyelectrolyte. When Zprot decreases to be less than 0, there are almost no lysozymes on the branched polyelectrolyte, and the conformation of the polyelectrolyte is determined by the screening of the salt content. In addition, to elucidate the effect of pH values on the net interaction between lysozymes, we calculated the second virial coefficients of the lysozymes, B2, as shown in Figure 10. It can be observed from Figure 10 that, when Zprot ) +19, the value of B2 is less than 0, which means that the net interaction between lysozymes is attraction. With the increase of the pH value of the solution, i.e., the decrease of Zprot, the second virial coefficient of lysozymes increases monotonically, and when Zprot ) -13, the values of B2 at IS ) 0.0372 M and 0.0492 M both become positive, which means that the attraction between lysozymes mediated by polyelectrolyte decreases monotonically with the increase of the pH value of the solution, and finally turns to a repulsive interaction in strong alkaline solution. It is noted that when Zprot > 0, B2 at IS ) 0.0372 M is smaller than that at IS ) 0.0492 M, which is due to the electrostatic screening of the salt content. 4. Conclusions We used canonical Monte Carlo simulation to investigate the microscopic properties of the branched polyelectrolytelysozyme complexation at different salt contents based on the discretely charged sphere model of lysozyme,7 where the embedded charges represent the ionized amino acids, and the positions of all embedded charges were constructed on the basis of an X-ray diffraction study of crystalline hen egg-white lysozyme.50 The effect of adding salt in the solution on the microscopic behavior of the complexation was studied. It is found that, with the increase of the salt ionic strength of the solution, the lysozymes were gradually released from the oppositely charged polyelectrolyte due to the screening of electrostatic attraction between the two ionic species by the added salt. Interestingly, there exists a critical ionic strength at which all proteins are released from branched polyelectrolytes and the polyelectrolyte-protein complexation is broken completely. Beyond this critical value, the increase of the ionic
J. Phys. Chem. B, Vol. 112, No. 14, 2008 4399 strength causes self-association of the proteins released from the branched polyelectrolyte-protein complexation. The selfassociation of proteins is detrimental in biological systems. Accordingly, it is significant to seek the optimal salt content at which the proteins exhibit the best dispersion. By calculation of the second virial coefficient, which can be measured experimentally, we found that the optimal salt content for the dispersion of proteins coincides with the critical ionic strength, at which the second virial coefficient reaches its maximum. Moreover, we also investigated the influence of pH value on the conformation of the complexation of branched polyelectrolyte with lysozymes in salt solutions. Our simulation results show that increasing pH value can also release the lysozymes from the branched polyelectrolyte, because the increase of pH value leads to a decrease of the net charge of the protein. Similarly, increasing pH value monotonically weakens the attraction between lysozymes mediated by polyelectrolyte, and finally turns the attraction between lysozymes to a repulsive interaction in strong alkaline solution. To consider the effect of architecture on the microscopic properties of the polyelectrolyte-proteins complexation, the linear polyelectrolyte-protein system was also simulated. It is found that the branched and linear polyelectrolytes show the same behavior with the increase of salt ionic strength, i.e., proteins are released from the polyelectrolyte first, and then the released proteins form self-association. However, the architecture can affect the release degree of proteins. The branched polyelectrolyte provides a lot of positions for proteins adsorption on its branches, which lead to a more prominent second peak in RDF between proteins, and it is also the reason the release of proteins from the branched architecture is much more difficult than that from the linear polyelectrolyte at the same salt content. Acknowledgment. We thank Prof. Per Linse at Lund University for providing the structure of lysozyme and helpful discussion. This work is supported by the National Natural Science Foundation of China (Nos. 20776005 and 20736002), the Beijing Novel Program (2006B17), NCET from the Ministry of Education (NCET-06-0095), and the “Chemical Grid Program” and Excellent Talent Foundation from BUCT. References and Notes (1) Fleming, A. Proc. R. Soc. London 1922, B 93, 306. (2) Abraham, E. P.; Robinson, R. Nature 1937, 140, 24. (3) Mattison, K. W.; Brittain, I. J.; Dubin, P. L. Biotechnol. Prog. 1995, 11, 632. (4) Wang, Y.; Gao, J. Y.; Dubin, P. L. Biotechnol. Prog. 1996, 12, 356. (5) Park, J. M.; Muhoberac, B. B.; Dubin, P. L.; Xia, J. Macromolecules 1992, 25, 290. (6) Cousin, F.; Gummel, J.; Ung, D.; Boue, F. Langmuir 2005, 21, 9675. (7) Carlsson, F.; Linse, P.; Malmsten, M. J. Phys. Chem. B 2001, 105, 9040. (8) Carlsson, F.; Malmsten, M.; Linse, P. J. Am. Chem. Soc. 2003, 125, 3140. (9) Morawetz, H.; Hughes, W. L., Jr. J. Phys. Chem. 1952, 56, 64. (10) Sternber, M.; Hershber, D. Biochim. Biophys. Acta 1974, 342, 195. (11) Hubbell, J. A. Science 2003, 300, 595. (12) Malmsten, M. Surfactants and Polymers in Drug DeliVery; Marcel Dekker: New York, 2002. (13) Tolstoguzov, V. B. Food Hydrocolloids 1991, 4, 429. (14) Xia, J.; Dubin, P. L.; Kim, Y.; Muhoberac, B. B.; Klimkowski, V. J. J. Phys. Chem. 1993, 97, 4528. (15) Doublier, J. L.; Garnier, C.; Renard, D.; Sanchez, C. Curr. Opin. Colloid Interface Sci. 2000, 5, 202. (16) Turgeon, S. L.; Beaulieu, M.; Schmitt, C.; Sanchez, C. Curr. Opin. Colloid Interface Sci. 2003, 9, 1794. (17) Takahashi, D.; Kubota, Y.; Kokai, K.; Izumi, T.; Hirata, M.; Kokufuta, E. Langmuir 2000, 16, 3133.
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