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Anisotropic protein–protein interactions due to ion binding Mikael Lund ∗ Division of Theoretical Chemistry, Lund University, PO Box 124, SE-22100 Lund, Sweden
a r t i c l e
i n f o
Article history: Received 14 April 2015 Received in revised form 11 May 2015 Accepted 13 May 2015 Available online xxx Keywords: Anisotropic interactions Protein–protein interactions Electrostatics Multipoles Monte Carlo simulation Coarse graining
a b s t r a c t Self-association of proteins is strongly affected by long-range electrostatic interactions caused by equilibrium adsorption of small ions such as protons and multivalent metals. By affecting the molecular net charge, solution pH is thus a widely used parameter to tune stability and phase behavior of proteins. We here review recent studies where the charge distribution is perturbed not only by protons, but also by other binding ions, leading to a rich and inherently anisotropic charge distribution. Focus is on coarse grained simulation techniques, coupled to experiments of protein–protein interaction at varying salt and pH conditions. Finally, and with future bio-colloidal models in mind, we discuss the validity of coarse graining charge anisotropy using electric multipoles. © 2015 Elsevier B.V. All rights reserved.
1. Introduction With their intricate three dimensional structures, proteins represent a body of molecular compounds with highly irregular interfacial properties. Acidic and basic amino acid side chains participate in proton equilibria which ultimately lead to a distinct, pH-dependent charge distribution of proteins. The chemical potential or activity of protons, i.e. pH, is thus an important handle to control intermolecular electrostatic interactions in both biological and technical contexts [1]. Protons, however, may be in competition for binding sites with other ions and solutes in the solution. For example, recent work shows that trivalent cations such as lanthane and yttrium can reverse the charge of human serum albumin by strong binding to carboxyl groups which in turn influence protein–protein interactions and phase equilibria [2–4]. Large ions with a low surface charge density such as thiocyanate or tetra-alkylammonium may bind to hydrophobic surface patches, contributing to the effective electrostatic potential emanating from the protein [5–8]. That is, pH is merely one of many parameters controlling the surface charge distribution. Due to the above complexity of ion binding, the final charge distribution is inherently anisotropic and may deviate significantly from classic colloidal models using a centro-symmetric charge [9]. Protein surface anisotropy has been shown to affect the phase equilibria of concentrated protein solutions [10,11] as well as
∗ Tel.: +46 46 222 31 67. E-mail address: [email protected]
steer biologically relevant protein complexes into place [12–14]. In this work we review anisotropic protein–protein interactions as brought about by binding ions and, in particular, we examine the validity of describing the surface charge distribution via electric multipoles. The latter can be regarded as systematic coarse graining of protein electrostatics and forms a mathematically sound scheme of expanding centro-symmetric, colloidal models. Starting chiefly from more detailed protein descriptions (amino acid level) as illustrated in the figure below (right), we investigate the validity of multipolar moments for use in bio-colloidal models (left).
2. Charge anisotropy via electric multipoles Formally, electrostatic anisotropy can be described using multipoles and for an arbitrary charge distribution, [ri , zi ], the potential at position R from the distribution center can be expanded in terms of monopoles, dipoles, quadrupoles, etc. [15,16]. This approximation is strictly valid only for |R| |ri | and at close proximity, higher order poles become increasingly important. Several authors have used twobody multipole expansions in the context of protein–protein
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2
Boltzmann averaging over the inter-protein angular space, the simplest form of the multipole-multipole interaction free energy in a salt-free environment can be approximated by [15],
Net charge (Z/e)
15 10
5
2B Za2 Cb + Zb2 Ca + Ca Cb B Za Zb ˇw(R) ≈ − R 2R2
0
Dipole moment (μ/D)
-5
−
400 o ap
200 Lysozyme
Capacitance (C/e²)
2 1.5 1 0.5 0
2
4
6
6R4
−
2B 2a 2b 3R6
+ ···
(1)
c La αCa 2+ α-L ac
300
2B Za2 2b + Zb2 2a
8
10
pH Fig. 1. Simulated net molecular charge, Z, dipole moment, , and proton capacitance, C = Z2 − Z2 = ∂Z/ln 10∂pH, as a function of pH for lysozyme, apo ˛-lactalbumin, and holo ˛-lactalbumin with bound calcium [14].
interactions [9,14,17–21] and one of the oldest works, by Kirkwood and Shumaker [17], also includes the effect of proton fluctuations due to acidic and basic side-chains [18,21,22]. Although like-charged, significant protein attraction may arise from higher order moments [23,24]. Further, electric multipolar moments due to acidic and basic side chains have been shown to correlate with the tertiary structure of globular proteins [25] and nonspherical models for electrophoretic mobility also incorporate higher order moments as a descriptor for electrostatic anisotropy [26].
2 2 where Z = zi is the mean net charge number; C = Z − Z is the fluctuation around the mean charge [21]; = | i ri zi | is the dipole moment scalar; B is the Bjerrum length; and ˇ = 1/kB T is the inverse thermal energy. The first two terms, Z and C are clearly isotropic and account for the direct monopole-monopole and induced monopole interactions, respectively. The remaining, higher order moments, and – potentially – their fluctuations [27], describe deviations from centro-symmetric geometry; here truncated after the ion–dipole and dipole–dipole terms. An example of how bound protons influence multipolar moments of three globular proteins is shown in Fig. 1. Here pH = − log aH+ controls proton binding equilibria and as the proton activity, aH+ , is increased, all moments are affected. In particular, at neutral pH, lysozyme and the milk protein ˛-lactalbumin (˛-lac) have roughly equal but opposite charge, while the dipole moments differ by a factor of three. That is, lysozyme mimics a cationic monopole; ˛-lac an anionic monopole plus a notable dipole of 400 Debye [14]. Binding of calcium to ˛-lac obviously affects the net charge, but also the dipole moment is significantly influenced. As already outlined, the protein charge distribution is affected not only by protons, but by any binding species. This complexity connects to the original Hofmeister series where protein–protein interactions are influenced by the particular type of salt [6]. For example, sodium thiocyanate gives rise to a lower osmotic second virial coefficient for lysozyme than does sodium chloride [5,8,28]. By treating general ion binding to surface sites using a two-state model – as has been done for protons for a century – a more complete electrostatic picture emerges that prove useful in rationalizing ion-specific effects. Fig. 2 shows simulated, twodimensional titration curves of the eye-lens protein -crystallin as a function of both pH and salt concentration [8]. In this approach, no specific binding is assumed for chloride, while thiocyanate is able to bind to hydrophobic groups with strengths obtained from experimental data [29]. Thus, in sodium chloride solution, the iso-electric point is to a good approximation insensitive to the salt concentration, while in the case of thiocyanate, the charge reverses with salt while keeping pH constant. This suggests a Hofmeister
Fig. 2. Net charge of the eye-lens protein -crystallin as a function of proton and anion concentration (chloride and thiocyanate). The dotted lines mark the iso-electric point. Obtained using Monte Carlo simulations where proton and anion binding is treated by a two-state binding model to specific amino acid residues [8].
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Fig. 3. Lysozyme distribution (brown iso-density surface) around ˛-lactalbumin (ghosted). The arrow shows the direction of the molecular dipole moment (pH 7) of the latter, while residues marked in red are those most perturbed upon binding as measured using NMR [31].
reversal for protein–protein interactions, which is indeed also observed experimentally [30]. 3. Protein–protein interactions In the previous section, electrostatic anisotropy was described in terms of multipolar moments and the question is if this simplification is valid for describing the interaction between globular proteins? For this purpose we maintain focus on the lysozyme/˛lac system and investigate their mutual interaction in both dilute and dense solution. As mentioned, lysozyme and ˛-lac can be seen as two monopoles with equal but opposite magnitude, plus an additional dipole on ˛-lac. Metropolis Monte Carlo (MC) simulations of the pair interaction indeed indicate that the proteins align as expected from this simplified picture[14]. Fig. 3 shows the distribution of the overall cationic lysozyme around ˛-lac and it is evident that there is a preference for the negative pole. This theoretical prediction was based on a continuum electrostatic model where salt and counter ions were treated explicitly, while the protein was constructed by a collection of interaction sites, each representing amino acid residues[14] – see Fig. 4, top model. NMR experiments, where lysozyme is titrated into a solution of ˛-lac, later confirms [31] the anisotropic protein–protein interaction (also shown in Fig. 3). Vice versa, when ˛-lac is experimentally titrated into a lysozyme solution, uniform perturbation of lysozyme residues is observed, supporting weak or only high order electrostatic anisotropy of lysozyme. Counter ions and salt particles are expected to influence the electrostatic interaction between proteins. Monovalent salt at low concentration gives rise to simple screening as captured i.e. by continuum electrostatics at the Debye-Hückel level. Multivalent salt, however, leads to qualitatively different behavior and both experiment and simulation with explicit salt particles predict attractive electrostatics even between proteins of high, equal charge [3,32]. Fig. 4, top, shows the angularly averaged interaction free energy as a function of lysozyme/˛-lac mass center separation in aqueous 1:1 salt solution. As can be seen, increasing the salt concentration leads to reduced electrostatic interaction which is captured by models using three levels of molecular detail. Notably, the transition from explicit to implicit salt brings about the largest deviation and the most coarse grained model – consisting of charges and a single volume-excluding sphere – gives a surprisingly accurate description. The inter-protein alignment is also affected by salt as traced by the ensemble averaged scalar product between the ˛lac dipole moment vector and the mass center separation vector connecting to the lysozyme monopole, Rab · a (Fig. 4, bottom). Here perfect dipole–monopole alignment is indicated by unity,
Fig. 4. Angularly averaged potential of mean force (top) and ion–dipole correlation function (bottom) as a function of mass center separation, R, between lysozyme and ˛-lac at neutral pH [10]. Three levels of detail were used: explicit salt (–); implicit salt (•); and implicit salt with a crude protein description (◦). Grey spheres correspond to charged interaction sites representing titratable residues, distributed as in the crystal structure.
while zero is obtained for an uncorrelated system. In the present case, the two proteins strongly align at low salt concentration and at close separation, while the effect is suppressed with added salt due to screening. Mixing lysozyme with ˛-lac in a 1:1 ratio yields micro-spheres in which the proteins form a liquid phase in equilibrium with the surrounding, dilute solution [33]. Experiment as well as isobaric, many-body simulations show that increasing the salt concentration or adding small amounts of calcium ions, strongly suppress micro-sphere formation, underlining the importance of electrostatics. Interestingly, artificially suppressing anisotropy (but maintaining shape and net-charge) in the coarse grained protein model, completely obstructs phase separation [10]. While Eq. (1) neglects salt screening, this can be included by considering the Debye-Hückel approximation when performing the two-body multipole expansion [18,20]. This leads to the interesting result [20] that for a fixed set of moments, the contribution from the individual terms varies with salt such that i.e. ion–ion repulsion dominates at low salt, while dipole–dipole attraction takes over beyond a certain salt threshold. This observation was recently used to interpret a non-monotonic variation of the virial coefficient, B2 , for monoclonal antibody [34]. That is, at low ionic strengths, isotropic ion–ion repulsion dominates B2 , while at elevated salt concentrations, anisotropic interactions set in as close contact configurations become populated. As will be shown in the following section, similar behavior is observed for the interaction between lactoferrin globules. 4. Beyond multipoles The interaction between hen-egg white lysozyme and the whey protein ˛-lac used in the previous section is of limited biological relevance and the ion–dipole analogy may well be too simplistic to capture the often highly specific protein–protein interaction developed in living cells. In this section we present examples where anisotropy play a crucial role, approaching the upper limit of patchy spherical models.
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Fig. 5. Left: Electrostatic components of the thermally averaged interaction energy between lysozyme and HyHEL-5 antigen–antibody H-L complex [14]. Triangles: ion–ion (ii) plus ion–dipole (id) energy. Circles: Ion–ion, ion–dipole, and ion–quadrupole (iq) energy. Full drawn lines: Protein–protein (pp) electrostatic energy calculated by explicitly summing over all charged groups. Right: Distribution of lysozyme around the HL complex. The arrows show the dipole moments of the heavy and light chains, respectively, ultimately forming a quadrupole.
Fig. 5 shows ensemble averages over orientations and salt positions for the electrostatic energy contribution to the interaction between lysozyme and the HyHEL-5 antigen–antibody H-L complex [14]. At short separation, the sum of multipolar terms – sampled during MC simulation – deviate from the exact electrostatic contribution, but becomes more and more accurate at larger protein–protein separations, as expected. While dipole–dipole interactions (not shown) are negligible, the ion–quadrupole term is crucial to capture the minimum at 6 nm. Thus, even in this biologically relevant complex, the multipolar approach seems promising albeit in this particular example, short ranged van der Waals interactions couple with the electrostatics [14,35], complicating the development of patchy-sphere models. As a final example of electrostatic anisotropy on protein self-assembly, we turn to the multifunctional protein lactoferrin which – as the previously mentioned monoclonal antibody [34] – displays a non-monotonic variation of B2 with monovalent salt concentration [36]. At low salt and at pH 7, where the protein is positively charged, B2 is positive, indicating overall repulsion – see Fig. 6. As further salt is added, B2 reaches a minimum whereafter it again increases to a plateau. Two-body protein simulations have shown that lactoferrin forms highly specific dimers, stabilized by a combination of charge complementarity and short range interactions of non-electrostatic origin [37]. A single point mutation is sufficient to dissolve the ∼1400 amino acid residue complex, hinting at specific interactions, hard to capture by a few multipolar moments. When the screening length falls below the protein size, i.e. when D/a 1, the electrostatic patch contributes significantly to the angularly averaged interaction free energy, leading to a B2 minimum. As further salt is added, the patch attraction is eventually screened and B2 levels off to a slightly negative value. This
Fig. 6. Osmotic second virial coefficient, B2 /B2hs , for lactoferrin as a function of the Debye screening length, D, normalized with the protein size, a. Observed in both static light scattering (SLS) experiments and CG Monte Carlo simulations [36]. B2hs = 2a3 /3.
non-monotonic behavior – caused by salt screening of repulsive and attractive electrostatics at different length scales – was initially predicted by coarse grained Monte Carlo simulations, where the proteins were described at the amino acid level. The mechanism is supported by static light scattering measurements [36] and although no microscopic information can be inferred from such experiments, complete qualitative agreement with simulations were obtained for the dependence of the virial coefficient with 1:1 salt concentration. This example highlights challenges in using patches to dress up spherical models for anisotropy. Sensitivity to point mutations may require a large number of higher order moments and a projection of all charges onto a sphere [38] may be more convenient. The coupling of electrostatics and short-range interactions such as van der Waals and excluded volume (shape) [14,35] seem more testing and although this may by a nonissue for many protein complexes, it is difficult to quantify a priori. Nevertheless, for a number of systems, electric multipoles do provide a phenomenological sound picture and may well be used to dress up spheres. Such models may pioneer unknown territories in solution space, before instating more elaborate models, based in dressed down proteins. Acknowledgements The following agencies are greatly appreciated for financial support: Södra Research foundation, the Swedish Research Council, and the Swedish Foundation for Strategic Research. References [1] Z. Zhang, S. Witham, E. Alexov, On the role of electrostatics in protein–protein interactions, Phys. Biol. 8 (2011) 035001. [2] F. Zhang, M. Skoda, R. Jacobs, S. Zorn, R. Martin, C. Martin, G. Clark, S. Weggler, A. Hildebrandt, O. Kohlbacher, F. Schreiber, Reentrant condensation of proteins in solution induced by multivalent counterions, Phys. Rev. Lett. 101 (2008) 3–6. [3] F. Roosen-Runge, B.S. Heck, F. Zhang, O. Kohlbacher, F. Schreiber, Interplay of pH and binding of multivalent metal ions: charge inversion and reentrant condensation in protein solutions, J. Phys. Chem. B 117 (2013) 5777–5787. [4] F. Roosen-Runge, F. Zhang, F. Schreiber, R. Roth, Ion-activated attractive patches as a mechanism for controlled protein interactions, Sci. Rep. 4 (2014). [5] M. Bostrom, D.R.M. Williams, B.W. Ninham, Specific ion effects: why the properties of lysozyme in salt solutions follow a Hofmeister series, Biophys. J. 85 (2003) 686–694. [6] Y. Zhang, P.S. Cremer, The inverse and direct Hofmeister series for lysozyme, Proc. Natl. Acad. Sci. U. S. A. 106 (2009) 15249–15253. [7] J. Heyda, J. Dzubiella, Ion-specific counterion condensation on charged peptides: Poisson Boltzmann vs. atomistic simulations, Soft Matter 8 (2012) 9338. [8] A. Kurut, M. Lund, Solution electrostatics beyond pH: a coarse grained approach to ion specific interactions between macromolecules, Faraday Discuss. 160 (2013) 271. [9] C. Yigit, J. Heyda, J. Dzubiella, Charged patchy particle models in explicit salt: ion distributions, electrostatic potentials, and effective interactions, J. Chem. Phys. (2015) (in press). [10] A. Kurut, B.a. Persson, T.A. kesson, J. Forsman, M. Lund, Anisotropic interactions in protein mixtures: self assembly and phase behavior in aqueous solution, J. Phys. Chem. Lett. 3 (2012) 731–734. [11] C. Gogelein, G. Nagele, R. Tuinier, T. Gibaud, A. Stradner, P. Schurtenberger, A simple patchy colloid model for the phase behavior of lysozyme dispersions, J. Chem. Phys. 129 (2008), http://dx.doi.org/10.1063/1.2951987, arXiv: 0901.4916. [12] X. Song, The extent of anisotropic interactions between protein molecules in electrolyte solutions, Mol. Simul. 29 (2003) 643–647. [13] A. Spaar, V. Helms, Free energy landscape of protein–protein encounter resulting from Brownian dynamics simulations of Barnase:Barstar, J. Chem. Theory Comput. 1 (2005) 723–736. [14] a. Persson, B. Jonsson, M. Lund, Enhanced protein steering: cooperative electro static and van der Waals forces in antigen–antibody complexes, J. Phys. Chem. B 113 (2009) 10459–10464. [15] A.J. Stone, Int. Ser. Monogr. Chem., vol. 32, 2nd ed., Oxford University Press, Oxford, 2013, pp. 339. [16] T. Hoppe, A simplified representation of anisotropic charge distributions within proteins, J. Chem. Phys. 138 (2013), http://dx.doi.org/10.1063/1.4803099 [17] J.G. Kirkwood, J.B. Shumaker, Forces between protein molecules in solution arising from fluctuations in proton charge and configuration, Proc. Natl. Acad. Sci. 38 (1952) 863–871. [18] G.D.J. Phillies, Excess chemical potential of dilute solutions of spherical polyelec-trolytes, J. Chem. Phys. 60 (1974) 2721.
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[19] M.L. Grant, Nonuniform charge effects in protein–protein interactions, J. Phys. Chem. B 105 (2001) 2858–2863. [20] D. Bratko, A. Striolo, J.Z. Wu, H.W. Blanch, J.M. Prausnitz, Orientation-averaged pair potentials between dipolar proteins or colloids, J. Phys. Chem. B 106 (2002) 2714–2720. [21] M. Lund, B. Jonsson, Charge regulation in biomolecular solution, Q. Rev. Biophys. 46 (2013) 265–281. [22] N. Adzic, R. Podgornik, Field-theoretic description of charge regulation interaction, Eur. Phys. J. E 37 (2014), 10.1140/epje/i2014-14049-6. [23] R.B. McClurg, C.F. Zukoski, The electrostatic interaction of rigid, globular proteins with arbitrary charge distributions, J Colloid Interface Sci 208 (1998) 529–542. [24] A. Patil, H. Nakamura, The role of charged surface residues in the binding ability of small hubs in protein–protein interaction networks, Biophysics (Oxf.) 3 (2007) 27–35. [25] H. Nakamura, A. Wada, Nature of the charge distribution in proteins. III. Electric multipole structures, J. Phys. Soc. Jpn. 54 (1985) 4047–4052. [26] J.Y. Kim, S.H. Ahn, S.T. Kang, B.J. Yoon, Electrophoretic mobility equation for protein with molecular shape and charge multipole effects, J. Colloid Interface Sci. 299 (2006) 486–492. [27] J.G. Kirkwood, J.B. Shumaker, The influence of dipole moment fluctuations on the dielectric increment of proteins in solution, Proc. Natl. Acad. Sci. 38 (1952) 855–862. [28] R. Piazza, Protein interactions and association: an open challenge for colloid science, Curr. Opin. Colloid Interface Sci. 8 (2004) 515–522. [29] K.B. Rembert, J. Paterova, J. Heyda, C. Hilty, P. Jungwirth, P.S. Cremer, Molecular mechanisms of ion-specific effects on proteins, J. Am. Chem. Soc. 134 (2012) 10039–10046.
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[30] S. Finet, F. Skouri-Panet, M. Casselyn, F. Bonnete, A. Tardieu, The Hofmeister effect as seen by SAXS in protein solutions, Curr. Opin. Colloid Interface Sci. 9 (2004) 112–116. [31] D.B. Salvatore, N. Duraffourg, A. Favier, B.A. Persson, M. Lund, M.-M. Delage, R. Silvers, H. Schwalbe, T. Croguennec, S. Bouhallab, V. Forge, Investigation at residue level of the early steps during the assembly of two proteins into supramolecular objects, Biomacromolecules 12 (2011) 2200–2210. [32] F. Tavares, D. Bratko, J. Prausnitz, The role of saltmacroion van der Waals interactions in the colloid–colloid potential of mean force, Curr. Opin. Colloid Interface Sci. 9 (2004) 81–86. [33] Y. Desfougeres, T. Croguennec, V. Lechevalier, S. Bouhallab, F. Nau, Charge and size drive spontaneous self-assembly of oppositely charged globular proteins into micro-spheres, J. Phys. Chem. B 114 (2010) 4138–4144. [34] D. Roberts, R. Keeling, M. Tracka, C.F. van der Walle, S. Uddin, J. Warwicker, R. Curtis, The role of electrostatics in protein–protein interactions of a monoclonal antibody, Mol. Pharm. 11 (2014) 2475–2489. [35] L.J. Quang, S.I. Sandler, A.M. Lenhoff, Anisotropic contributions to protein–protein interactions, J. Chem. Theory Comput. 10 (2014) 835–845. [36] W. Li, B.A. Persson, M. Morin, M.A. Behrens, M. Lund, M. Zackrisson Oskolkova, Charge-induced patchy attractions between proteins, J. Phys. Chem. B 119 (2015) 503–508. [37] B.A. Persson, M. Lund, J. Forsman, D.E.W. Chatterton, T. Akesson, Molecular evidence of stereo-specific lactoferrin dimers in solution, Biophys. Chem. 151 (2010) 187–189. [38] F. Carlsson, M. Malmsten, P. Linse, Monte Carlo simulations of lysozyme selfassociation in aqueous solution, J. Phys. Chem. B 105 (2001) 12189–12195.
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Contents lists available at ScienceDirect
Colloids and Surfaces B: Biointerfaces journal homepage: www.elsevier.com/locate/colsurfb
Anisotropic protein–protein interactions due to ion binding Mikael Lund ∗ Division of Theoretical Chemistry, Lund University, PO Box 124, SE-22100 Lund, Sweden
a r t i c l e
i n f o
Article history: Received 14 April 2015 Received in revised form 11 May 2015 Accepted 13 May 2015 Available online xxx Keywords: Anisotropic interactions Protein–protein interactions Electrostatics Multipoles Monte Carlo simulation Coarse graining
a b s t r a c t Self-association of proteins is strongly affected by long-range electrostatic interactions caused by equilibrium adsorption of small ions such as protons and multivalent metals. By affecting the molecular net charge, solution pH is thus a widely used parameter to tune stability and phase behavior of proteins. We here review recent studies where the charge distribution is perturbed not only by protons, but also by other binding ions, leading to a rich and inherently anisotropic charge distribution. Focus is on coarse grained simulation techniques, coupled to experiments of protein–protein interaction at varying salt and pH conditions. Finally, and with future bio-colloidal models in mind, we discuss the validity of coarse graining charge anisotropy using electric multipoles. © 2015 Elsevier B.V. All rights reserved.
1. Introduction With their intricate three dimensional structures, proteins represent a body of molecular compounds with highly irregular interfacial properties. Acidic and basic amino acid side chains participate in proton equilibria which ultimately lead to a distinct, pH-dependent charge distribution of proteins. The chemical potential or activity of protons, i.e. pH, is thus an important handle to control intermolecular electrostatic interactions in both biological and technical contexts [1]. Protons, however, may be in competition for binding sites with other ions and solutes in the solution. For example, recent work shows that trivalent cations such as lanthane and yttrium can reverse the charge of human serum albumin by strong binding to carboxyl groups which in turn influence protein–protein interactions and phase equilibria [2–4]. Large ions with a low surface charge density such as thiocyanate or tetra-alkylammonium may bind to hydrophobic surface patches, contributing to the effective electrostatic potential emanating from the protein [5–8]. That is, pH is merely one of many parameters controlling the surface charge distribution. Due to the above complexity of ion binding, the final charge distribution is inherently anisotropic and may deviate significantly from classic colloidal models using a centro-symmetric charge [9]. Protein surface anisotropy has been shown to affect the phase equilibria of concentrated protein solutions [10,11] as well as
∗ Tel.: +46 46 222 31 67. E-mail address: [email protected]
steer biologically relevant protein complexes into place [12–14]. In this work we review anisotropic protein–protein interactions as brought about by binding ions and, in particular, we examine the validity of describing the surface charge distribution via electric multipoles. The latter can be regarded as systematic coarse graining of protein electrostatics and forms a mathematically sound scheme of expanding centro-symmetric, colloidal models. Starting chiefly from more detailed protein descriptions (amino acid level) as illustrated in the figure below (right), we investigate the validity of multipolar moments for use in bio-colloidal models (left).
2. Charge anisotropy via electric multipoles Formally, electrostatic anisotropy can be described using multipoles and for an arbitrary charge distribution, [ri , zi ], the potential at position R from the distribution center can be expanded in terms of monopoles, dipoles, quadrupoles, etc. [15,16]. This approximation is strictly valid only for |R| |ri | and at close proximity, higher order poles become increasingly important. Several authors have used twobody multipole expansions in the context of protein–protein
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Please cite this article in press as: M. Lund, Anisotropic protein–protein interactions due to ion binding, Colloids Surf. B: Biointerfaces (2015), http://dx.doi.org/10.1016/j.colsurfb.2015.05.054
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2
Boltzmann averaging over the inter-protein angular space, the simplest form of the multipole-multipole interaction free energy in a salt-free environment can be approximated by [15],
Net charge (Z/e)
15 10
5
2B Za2 Cb + Zb2 Ca + Ca Cb B Za Zb ˇw(R) ≈ − R 2R2
0
Dipole moment (μ/D)
-5
−
400 o ap
200 Lysozyme
Capacitance (C/e²)
2 1.5 1 0.5 0
2
4
6
6R4
−
2B 2a 2b 3R6
+ ···
(1)
c La αCa 2+ α-L ac
300
2B Za2 2b + Zb2 2a
8
10
pH Fig. 1. Simulated net molecular charge, Z, dipole moment, , and proton capacitance, C = Z2 − Z2 = ∂Z/ln 10∂pH, as a function of pH for lysozyme, apo ˛-lactalbumin, and holo ˛-lactalbumin with bound calcium [14].
interactions [9,14,17–21] and one of the oldest works, by Kirkwood and Shumaker [17], also includes the effect of proton fluctuations due to acidic and basic side-chains [18,21,22]. Although like-charged, significant protein attraction may arise from higher order moments [23,24]. Further, electric multipolar moments due to acidic and basic side chains have been shown to correlate with the tertiary structure of globular proteins [25] and nonspherical models for electrophoretic mobility also incorporate higher order moments as a descriptor for electrostatic anisotropy [26].
2 2 where Z = zi is the mean net charge number; C = Z − Z is the fluctuation around the mean charge [21]; = | i ri zi | is the dipole moment scalar; B is the Bjerrum length; and ˇ = 1/kB T is the inverse thermal energy. The first two terms, Z and C are clearly isotropic and account for the direct monopole-monopole and induced monopole interactions, respectively. The remaining, higher order moments, and – potentially – their fluctuations [27], describe deviations from centro-symmetric geometry; here truncated after the ion–dipole and dipole–dipole terms. An example of how bound protons influence multipolar moments of three globular proteins is shown in Fig. 1. Here pH = − log aH+ controls proton binding equilibria and as the proton activity, aH+ , is increased, all moments are affected. In particular, at neutral pH, lysozyme and the milk protein ˛-lactalbumin (˛-lac) have roughly equal but opposite charge, while the dipole moments differ by a factor of three. That is, lysozyme mimics a cationic monopole; ˛-lac an anionic monopole plus a notable dipole of 400 Debye [14]. Binding of calcium to ˛-lac obviously affects the net charge, but also the dipole moment is significantly influenced. As already outlined, the protein charge distribution is affected not only by protons, but by any binding species. This complexity connects to the original Hofmeister series where protein–protein interactions are influenced by the particular type of salt [6]. For example, sodium thiocyanate gives rise to a lower osmotic second virial coefficient for lysozyme than does sodium chloride [5,8,28]. By treating general ion binding to surface sites using a two-state model – as has been done for protons for a century – a more complete electrostatic picture emerges that prove useful in rationalizing ion-specific effects. Fig. 2 shows simulated, twodimensional titration curves of the eye-lens protein -crystallin as a function of both pH and salt concentration [8]. In this approach, no specific binding is assumed for chloride, while thiocyanate is able to bind to hydrophobic groups with strengths obtained from experimental data [29]. Thus, in sodium chloride solution, the iso-electric point is to a good approximation insensitive to the salt concentration, while in the case of thiocyanate, the charge reverses with salt while keeping pH constant. This suggests a Hofmeister
Fig. 2. Net charge of the eye-lens protein -crystallin as a function of proton and anion concentration (chloride and thiocyanate). The dotted lines mark the iso-electric point. Obtained using Monte Carlo simulations where proton and anion binding is treated by a two-state binding model to specific amino acid residues [8].
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Fig. 3. Lysozyme distribution (brown iso-density surface) around ˛-lactalbumin (ghosted). The arrow shows the direction of the molecular dipole moment (pH 7) of the latter, while residues marked in red are those most perturbed upon binding as measured using NMR [31].
reversal for protein–protein interactions, which is indeed also observed experimentally [30]. 3. Protein–protein interactions In the previous section, electrostatic anisotropy was described in terms of multipolar moments and the question is if this simplification is valid for describing the interaction between globular proteins? For this purpose we maintain focus on the lysozyme/˛lac system and investigate their mutual interaction in both dilute and dense solution. As mentioned, lysozyme and ˛-lac can be seen as two monopoles with equal but opposite magnitude, plus an additional dipole on ˛-lac. Metropolis Monte Carlo (MC) simulations of the pair interaction indeed indicate that the proteins align as expected from this simplified picture[14]. Fig. 3 shows the distribution of the overall cationic lysozyme around ˛-lac and it is evident that there is a preference for the negative pole. This theoretical prediction was based on a continuum electrostatic model where salt and counter ions were treated explicitly, while the protein was constructed by a collection of interaction sites, each representing amino acid residues[14] – see Fig. 4, top model. NMR experiments, where lysozyme is titrated into a solution of ˛-lac, later confirms [31] the anisotropic protein–protein interaction (also shown in Fig. 3). Vice versa, when ˛-lac is experimentally titrated into a lysozyme solution, uniform perturbation of lysozyme residues is observed, supporting weak or only high order electrostatic anisotropy of lysozyme. Counter ions and salt particles are expected to influence the electrostatic interaction between proteins. Monovalent salt at low concentration gives rise to simple screening as captured i.e. by continuum electrostatics at the Debye-Hückel level. Multivalent salt, however, leads to qualitatively different behavior and both experiment and simulation with explicit salt particles predict attractive electrostatics even between proteins of high, equal charge [3,32]. Fig. 4, top, shows the angularly averaged interaction free energy as a function of lysozyme/˛-lac mass center separation in aqueous 1:1 salt solution. As can be seen, increasing the salt concentration leads to reduced electrostatic interaction which is captured by models using three levels of molecular detail. Notably, the transition from explicit to implicit salt brings about the largest deviation and the most coarse grained model – consisting of charges and a single volume-excluding sphere – gives a surprisingly accurate description. The inter-protein alignment is also affected by salt as traced by the ensemble averaged scalar product between the ˛lac dipole moment vector and the mass center separation vector connecting to the lysozyme monopole, Rab · a (Fig. 4, bottom). Here perfect dipole–monopole alignment is indicated by unity,
Fig. 4. Angularly averaged potential of mean force (top) and ion–dipole correlation function (bottom) as a function of mass center separation, R, between lysozyme and ˛-lac at neutral pH [10]. Three levels of detail were used: explicit salt (–); implicit salt (•); and implicit salt with a crude protein description (◦). Grey spheres correspond to charged interaction sites representing titratable residues, distributed as in the crystal structure.
while zero is obtained for an uncorrelated system. In the present case, the two proteins strongly align at low salt concentration and at close separation, while the effect is suppressed with added salt due to screening. Mixing lysozyme with ˛-lac in a 1:1 ratio yields micro-spheres in which the proteins form a liquid phase in equilibrium with the surrounding, dilute solution [33]. Experiment as well as isobaric, many-body simulations show that increasing the salt concentration or adding small amounts of calcium ions, strongly suppress micro-sphere formation, underlining the importance of electrostatics. Interestingly, artificially suppressing anisotropy (but maintaining shape and net-charge) in the coarse grained protein model, completely obstructs phase separation [10]. While Eq. (1) neglects salt screening, this can be included by considering the Debye-Hückel approximation when performing the two-body multipole expansion [18,20]. This leads to the interesting result [20] that for a fixed set of moments, the contribution from the individual terms varies with salt such that i.e. ion–ion repulsion dominates at low salt, while dipole–dipole attraction takes over beyond a certain salt threshold. This observation was recently used to interpret a non-monotonic variation of the virial coefficient, B2 , for monoclonal antibody [34]. That is, at low ionic strengths, isotropic ion–ion repulsion dominates B2 , while at elevated salt concentrations, anisotropic interactions set in as close contact configurations become populated. As will be shown in the following section, similar behavior is observed for the interaction between lactoferrin globules. 4. Beyond multipoles The interaction between hen-egg white lysozyme and the whey protein ˛-lac used in the previous section is of limited biological relevance and the ion–dipole analogy may well be too simplistic to capture the often highly specific protein–protein interaction developed in living cells. In this section we present examples where anisotropy play a crucial role, approaching the upper limit of patchy spherical models.
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Fig. 5. Left: Electrostatic components of the thermally averaged interaction energy between lysozyme and HyHEL-5 antigen–antibody H-L complex [14]. Triangles: ion–ion (ii) plus ion–dipole (id) energy. Circles: Ion–ion, ion–dipole, and ion–quadrupole (iq) energy. Full drawn lines: Protein–protein (pp) electrostatic energy calculated by explicitly summing over all charged groups. Right: Distribution of lysozyme around the HL complex. The arrows show the dipole moments of the heavy and light chains, respectively, ultimately forming a quadrupole.
Fig. 5 shows ensemble averages over orientations and salt positions for the electrostatic energy contribution to the interaction between lysozyme and the HyHEL-5 antigen–antibody H-L complex [14]. At short separation, the sum of multipolar terms – sampled during MC simulation – deviate from the exact electrostatic contribution, but becomes more and more accurate at larger protein–protein separations, as expected. While dipole–dipole interactions (not shown) are negligible, the ion–quadrupole term is crucial to capture the minimum at 6 nm. Thus, even in this biologically relevant complex, the multipolar approach seems promising albeit in this particular example, short ranged van der Waals interactions couple with the electrostatics [14,35], complicating the development of patchy-sphere models. As a final example of electrostatic anisotropy on protein self-assembly, we turn to the multifunctional protein lactoferrin which – as the previously mentioned monoclonal antibody [34] – displays a non-monotonic variation of B2 with monovalent salt concentration [36]. At low salt and at pH 7, where the protein is positively charged, B2 is positive, indicating overall repulsion – see Fig. 6. As further salt is added, B2 reaches a minimum whereafter it again increases to a plateau. Two-body protein simulations have shown that lactoferrin forms highly specific dimers, stabilized by a combination of charge complementarity and short range interactions of non-electrostatic origin [37]. A single point mutation is sufficient to dissolve the ∼1400 amino acid residue complex, hinting at specific interactions, hard to capture by a few multipolar moments. When the screening length falls below the protein size, i.e. when D/a 1, the electrostatic patch contributes significantly to the angularly averaged interaction free energy, leading to a B2 minimum. As further salt is added, the patch attraction is eventually screened and B2 levels off to a slightly negative value. This
Fig. 6. Osmotic second virial coefficient, B2 /B2hs , for lactoferrin as a function of the Debye screening length, D, normalized with the protein size, a. Observed in both static light scattering (SLS) experiments and CG Monte Carlo simulations [36]. B2hs = 2a3 /3.
non-monotonic behavior – caused by salt screening of repulsive and attractive electrostatics at different length scales – was initially predicted by coarse grained Monte Carlo simulations, where the proteins were described at the amino acid level. The mechanism is supported by static light scattering measurements [36] and although no microscopic information can be inferred from such experiments, complete qualitative agreement with simulations were obtained for the dependence of the virial coefficient with 1:1 salt concentration. This example highlights challenges in using patches to dress up spherical models for anisotropy. Sensitivity to point mutations may require a large number of higher order moments and a projection of all charges onto a sphere [38] may be more convenient. The coupling of electrostatics and short-range interactions such as van der Waals and excluded volume (shape) [14,35] seem more testing and although this may by a nonissue for many protein complexes, it is difficult to quantify a priori. Nevertheless, for a number of systems, electric multipoles do provide a phenomenological sound picture and may well be used to dress up spheres. Such models may pioneer unknown territories in solution space, before instating more elaborate models, based in dressed down proteins. Acknowledgements The following agencies are greatly appreciated for financial support: Södra Research foundation, the Swedish Research Council, and the Swedish Foundation for Strategic Research. References [1] Z. Zhang, S. Witham, E. Alexov, On the role of electrostatics in protein–protein interactions, Phys. Biol. 8 (2011) 035001. [2] F. Zhang, M. Skoda, R. Jacobs, S. Zorn, R. Martin, C. Martin, G. Clark, S. Weggler, A. Hildebrandt, O. Kohlbacher, F. Schreiber, Reentrant condensation of proteins in solution induced by multivalent counterions, Phys. Rev. Lett. 101 (2008) 3–6. [3] F. Roosen-Runge, B.S. Heck, F. Zhang, O. Kohlbacher, F. Schreiber, Interplay of pH and binding of multivalent metal ions: charge inversion and reentrant condensation in protein solutions, J. Phys. Chem. B 117 (2013) 5777–5787. [4] F. Roosen-Runge, F. Zhang, F. Schreiber, R. Roth, Ion-activated attractive patches as a mechanism for controlled protein interactions, Sci. Rep. 4 (2014). [5] M. Bostrom, D.R.M. Williams, B.W. Ninham, Specific ion effects: why the properties of lysozyme in salt solutions follow a Hofmeister series, Biophys. J. 85 (2003) 686–694. [6] Y. Zhang, P.S. Cremer, The inverse and direct Hofmeister series for lysozyme, Proc. Natl. Acad. Sci. U. S. A. 106 (2009) 15249–15253. [7] J. Heyda, J. Dzubiella, Ion-specific counterion condensation on charged peptides: Poisson Boltzmann vs. atomistic simulations, Soft Matter 8 (2012) 9338. [8] A. Kurut, M. Lund, Solution electrostatics beyond pH: a coarse grained approach to ion specific interactions between macromolecules, Faraday Discuss. 160 (2013) 271. [9] C. Yigit, J. Heyda, J. Dzubiella, Charged patchy particle models in explicit salt: ion distributions, electrostatic potentials, and effective interactions, J. Chem. Phys. (2015) (in press). [10] A. Kurut, B.a. Persson, T.A. kesson, J. Forsman, M. Lund, Anisotropic interactions in protein mixtures: self assembly and phase behavior in aqueous solution, J. Phys. Chem. Lett. 3 (2012) 731–734. [11] C. Gogelein, G. Nagele, R. Tuinier, T. Gibaud, A. Stradner, P. Schurtenberger, A simple patchy colloid model for the phase behavior of lysozyme dispersions, J. Chem. Phys. 129 (2008), http://dx.doi.org/10.1063/1.2951987, arXiv: 0901.4916. [12] X. Song, The extent of anisotropic interactions between protein molecules in electrolyte solutions, Mol. Simul. 29 (2003) 643–647. [13] A. Spaar, V. Helms, Free energy landscape of protein–protein encounter resulting from Brownian dynamics simulations of Barnase:Barstar, J. Chem. Theory Comput. 1 (2005) 723–736. [14] a. Persson, B. Jonsson, M. Lund, Enhanced protein steering: cooperative electro static and van der Waals forces in antigen–antibody complexes, J. Phys. Chem. B 113 (2009) 10459–10464. [15] A.J. Stone, Int. Ser. Monogr. Chem., vol. 32, 2nd ed., Oxford University Press, Oxford, 2013, pp. 339. [16] T. Hoppe, A simplified representation of anisotropic charge distributions within proteins, J. Chem. Phys. 138 (2013), http://dx.doi.org/10.1063/1.4803099 [17] J.G. Kirkwood, J.B. Shumaker, Forces between protein molecules in solution arising from fluctuations in proton charge and configuration, Proc. Natl. Acad. Sci. 38 (1952) 863–871. [18] G.D.J. Phillies, Excess chemical potential of dilute solutions of spherical polyelec-trolytes, J. Chem. Phys. 60 (1974) 2721.
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