PAPER
www.rsc.org/softmatter | Soft Matter
Polyelectrolyte–protein complexation driven by charge regulation Fernando Luı´s Barroso da Silva*ab and Bo J€ onssonb Received 30th January 2009, Accepted 13th May 2009 First published as an Advance Article on the web 15th June 2009 DOI: 10.1039/b902039j The interplay between the biocolloidal characteristics (especially size and charge), pH, salt concentration and the thermal energy results in a unique collection of mesoscopic forces of importance to the molecular organization and function in biological systems. By means of Monte Carlo simulations and semi-quantitative analysis in terms of perturbation theory, we describe a general electrostatic mechanism that gives attraction at low electrolyte concentrations. This charge regulation mechanism due to titrating amino acid residues is discussed in a purely electrostatic framework. The complexation data reported here for interaction between a polyelectrolyte chain and the proteins albumin, goat and bovine a-lactalbumin, b-lactoglobulin, insulin, k-casein, lysozyme and pectin methylesterase illustrate the importance of the charge regulation mechanism. Special attention is given to pH y pI where ion– dipole and charge regulation interactions could overcome the repulsive ion–ion interaction. By means of protein mutations, we confirm the importance of the charge regulation mechanism, and quantify when the complexation is dominated either by charge regulation or by the ion–dipole term.
I.
Introduction
Although the Coulomb’s law is an old and clear physical concept known since 1785, when it is applied to (bio)colloidal systems a rich diversity of peculiar mechanisms come into play. The combination of its characteristics with the chemical properties of the colloidal constituents, pH and salt concentration results in a unique collection of interparticle forces of importance for molecular organization and function.1–9 Despite different system geometries, electrostatic phenomena in macromolecular solutions are usually classified according to the coupling regime:10–12 (a) weak coupling regime (wcr), where the counter-ions and added salt are monovalent particles screening the electrostatic interactions, and the system is characterized by repulsive forces between the charged macromolecules (as given by the DLVO theory13), and (b) strong coupling regime (scr), where multivalent ions give rise to attractive forces due to ion–ion correlation.14–16 This is a somewhat simplified picture, since even in the wcr, anomalous behaviour, i.e. attraction between like charged objects can be observed. We will focus here on biological systems in the weak coupling regime where attraction can be seen instead of the expected repulsive behaviour. The idea of such a phenomenon goes back to Kirkwood’s structure sensitive electrostatic forces,17 where attractive forces between biomolecules arise from fluctuations in proton charge due to the acid–base equilibrium. The attraction is pH-dependent and a result of an intrinsic physical property of the macromolecule, the capacitance, determining its ability for charge regulation.9,18–21
a Department of Physics and Chemistry, Faculty of Pharmaceutical Sciences at Ribeira˜o Preto – University of Sa˜o Paulo, Av. do caf e, s/no., 14040–903 Ribeira˜o Preto, SP, Brazil. E-mail:
[email protected]; Fax: +55 (16)3602 48 80; Tel: +55 (16)3602 42 19 b Department of Theoretical Chemistry, Chemical Center – University of Lund, POB 124, S-221 00 Lund, Sweden. E-mail: Bo.Jonsson@teokem. lu.se
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Employing different model systems and experimental conditions, we aim here to illustrate the charge regulation mechanism in some biomolecular systems in the weak coupling regime. The purpose of this work is twofold: (i) to demonstrate that the complexation between polyelectrolytes and protein molecules at their isoelectric point (pI) can occur by a purely electrostatic mechanism, and (ii) to quantify when the picture is dominated either by the charge regulation or by the ion– dipole term.
II. Theoretical modelling Invoking a minimum set of parameters, a coarse-grained model within the continuum solvent framework has been devised and solved by Monte Carlo (MC) simulations.22,23 In all the MC simulations, the charged species are confined inside an electroneutral spherical cell as shown in Fig. 1, whose radius, Rcell, is determined by the protein concentration cP. This corresponds to the so-called cell model.24–26 The physical assumption behind the model is that the solution can be divided into cells, each containing one macromolecule [as seen in Fig. 1a (or one macromolecule and a polyelectrolyte as seen in Fig. 1b)] and the accompanying electrolytes (counter-ions and added salt). There is no explicit interaction between different electroneutral cells. The only manner macromolecule–macromolecule interactions are taken into account is by the definition of Rcell. Each mobile ion k with valency zk is treated explicitly as a hard sphere of radius Rk, while the solvent is treated as a structureless dielectric medium characterized by a relative dielectric permittivity 3s. The same uniform static dielectric permittivity 3s is assigned to all charged species interior, including the macromolecule and the polyelectrolyte.27–29 The macromolecule is a rigid body kept fixed at the center of the cell. The interaction potential energy between any two particles (or interaction sites) i and j (either a protein fixed charge, a mobile ion or a polyelectrolyte monomer) is given by, This journal is ª The Royal Society of Chemistry 2009
and the polyelectrolyte carry the same charge. This has been interpreted as if the ion–dipole interaction can overcome the repulsive ion–ion interaction, and was called complexation ‘‘on the wrong side’’ in several theoretical and experimental studies.36–39 In order to support this initial physical view, it was necessary to invoke local regions with high complementary charge density on the protein surface, so-called ‘‘charge patches’’.37,38,40–43 As suggested by Kirkwood & Shumaker,17 and later validated by numerical simulations,9,19,20 pH can induce an attraction between two titratable objects that result in macromolecular association. That is, for an ionizable protein and a non-titratable polyelectrolyte (valency Za), the electrostatic free energy [A(R)] for the complexation may be written in a perturbation theory framework as a function of their separation (R) as ! 2 C hZi0 hmi0 2 2 þ lB Z a (2) bAðRÞzlB Za 2R2 6R4 R where b ¼ 1/kBT (kB is the Boltzmann constant and T is the temperature), lB ¼ e2/4p303skBT is the Bjerrum length, hZi0 is the P protein average valency, hmi0 ¼ | iziri| the average dipole moment number and finally C is a measurement of the charge fluctuations due to the acid–base equilibrium. This is an intrinsic protein property called the protein charge capacitance:19 vZ Ch Z2 0 hZi20 f vpH
Fig. 1 Schematic representation of the model system. A protein in atomic detail in a spherical electroneutral cell (radius Rcell) is seen surrounded by counterions and added salt particles (radii R+ and R). Positive and negatively charged protein atoms (radii Ra) are represented in blue and red, respectively. (a) Top panel: system with no polyelectrolyte. (b) Bottom panel: a polyanion with 21 monomers (radii Rmon) carrying a monovalent charge is also present in the system.
8 < u rij ¼ :
N qi qj 4 p 30 3s rij
;
rij # Ri þ Rj
;
otherwise
(1)
where 30 is the vacuum permittivity, qi ¼ zie and qj ¼ zje (e is the elementary charge) denote the charges on particles i and j, respectively, and rij their separation. The Coulombic collapse is avoided by the hard-core overlap restriction [u(rij) ¼ N] imposed when rij # Ri + Rj.
Structure sensitive electrostatic forces Both natural and synthetic polyelectrolytes form strong complexes with a variety of proteins.30–39 One peculiar phenomenon is the association that can take place even when the protein This journal is ª The Royal Society of Chemistry 2009
(3)
If the polyelectrolyte is allowed to titrate, the attractive term of eqn (2) will be enhanced, and even larger effects can be observed. At pH ¼ pI, hZi0 ¼ 0 and the leading term in eqn (2), the ion– ion interaction, vanishes, and the charge regulation and the ion– dipole terms are left. It is interesting to note that the charge regulation term has a 1/R2 (more long ranged) dependence while the ion–dipole interaction, the term related to the ‘‘patch theory’’,37,38,40–42 has a 1/R4 dependence. Therefore, depending on the values of C and hmi0, the major attractive contribution may come more easily from the proton fluctuations. In any case, the charge regulation term will always dominate at long range. A number of proteins with different capacitances and dipole moments are compared in Table 1. The comparison demonstrates that the charge regulation is a general phenomenon and that it also often dominates the interaction at the isoelectric point. It should be pointed out that the charge regulation mechanism has also been observed as a key interaction for other systems (e.g. the adsorption of albumin in a planar poly(acrylic acid) brush layer).21 The protein data reported here are from albumin (alb), goat (a-lac1) and bovine a-lactalbumin (a-lac2), b-lactoglobulin (b-lac), insulin (ins), k-casein (k-cs), lysozyme (lys) and pectin methylesterase (met). Their coordinates in the native state were taken from the Protein Data Bank,44,45 (PDB identities are 1AO6, 1HFY, 1F6S, 1BEB, 1APH, 2LZT, and 1GQ8 for alb, a-lac1, a-lac2, b-lac, ins, lys and met, respectively). No X-ray structure was available for k-cs, instead a molecular modeling one was used.46 Following de Vries38 and experimental data,47 b-lac was assumed to be a dimer at neutral pH while the other proteins were treated as monomeric. Theoretical mutations were done in a particular a-lactalbumin structure (PDB id 1HFY) neutralizing Soft Matter, 2009, 5, 2862–2868 | 2863
Table 1 Charge capacitance (C) and dipole moment number (m) for the investigated proteins at their isoelectric points. Rp is an estimate of the protein radius. bA(R) is the minimum value of the free energy observed at the protein–polyanion separation distance R during the Monte Carlo simulations. All The three last columns give the interaction between the protein and the polyelectrolyte at contact, that is, bAreg ¼ lB2Z2aC/2(Rp + radii are given in A. Rpe)2, bAdip ¼ lB2Z2am2/6(Rp + Rpe)4, and bAreg/bAdip, where Rpe has been chosen as half the end-to-end separation of the corresponding neutral and Za ¼ 21 polymer (30 A)
Albumin a-Lactalbumina a-Lactalbuminb,c b-Lactoglobulinc,e Insulin k-Caseind Lysozymec Pectin methylesterase a-Lacb (mutation K62) a-Lacb (mutation K94) a-Lacb (mutation K98) a-Lacb (mutation H68) a-Lacb (mutation R70) a-Lacb (all 5 mutations)
Residues
pI
C
m
bA(R)
R
Rp + Rpe
bAreg
bAdip
Areg/Adip
585 123 123 324 41 169 129 319 123 123 123 123 123 123
5.5 4.8 5.4 4.5 5.4 5.9 10.9 9.5 5.0 5.0 5.0 5.0 5.0 4.1
3.2 1.5 1.0 4.5 0.4 1.3 1.7 2.4 1.2 1.3 1.2 1.2 1.2 2.5
297 101 82 128 49 151 24 60 78 69 65 74 65 61
15.8 6.0 6.1 10.2 2.6 4.7 2.3 6.7 4.1 3.4 2.7 3.6 3.5 6.9
25 16 19 22 22 27 25 24 21 22 24 19 19 16
81 57 58 73 51 84 58 68 58 58 58 58 58 58
5.5 5.0 3.3 9.4 1.7 2.0 5.6 5.8 4.0 4.3 4.0 4.0 4.0 8.3
7.7 3.3 2.2 2.1 1.3 1.7 0.2 0.6 2.0 1.6 1.4 1.8 1.4 1.2
0.7 1.5 1.5 4.4 1.3 1.2 29.8 9.2 2.0 2.8 2.9 2.2 2.9 6.8
a Organism bovine (Bos taurus). b Organism goat (Capra hircus). c Simulation parameters are chosen as in ref. 20. d Protein structure computationally obtained by Kumosinski et al.46 e Dimer.
a collection of positive charges [residue.position.atom (label): LYS.62.NZ (K62), LYS.94.NZ (K94), LYS.98.NZ (K98), ARG.70.NH1 (R70) and HIS.68.ND1 (H68)] suggested by de Vries (38) as forming the ‘‘charge patch’’ in order to prove that the ‘‘patch mechanism’’ is not the key contribution to the complexation. These mutations were done by deleting the positive charges on the side chains and not letting them titrate. All protein atoms present in the three dimensional structure (from X-ray or modeling data) are described by hard spheres of and valency za, and are not allowed to move radius Ra ¼ 2 A during the calculations. Charges are varied according to the pH and the acid–base equilibrium.48 The reader is referred to ref. 27,48,49 for more details. A single flexible polyelectrolyte is introduced as a real species into the simulation cell together with the protein and monovalent free ions [counter-ions (Nc) and added salt (Ns)] – see Fig. 1b). The polymer is free to move in the cell and is modeled as a chain with of Nmon ¼ 21 charged hard spheres of radius Rmon ¼ 2 A fixed valency zmon ¼ 1 (non-titratable). The spheres are connected by harmonic springs. That is, the bond interaction potential (bubond) between neighbouring monomers is, bubond ¼
mon 1 lB NX ðri;iþ1 Þ2 3 2rmin i¼1
(4)
where ri, i + 1 is the separation between the consecutive monomers i and i + 1, and rmin is the separation corresponding to the energy minimum for a dimer. Following a previous study,20 rmin was which results in an average monomer– assigned a value of 4 A, that reflects the monomer separation of approximately 7.4 A electrostatic interactions between all charged monomers and the thermal fluctuations. Free cations and anions were modeled by Rk ¼ 2.125 A. Initially, physico-chemical properties of each protein immersed in a aqueous electrolyte solution with Ns ¼ 20 ion pairs as well as Nc neutralizing counterions at different pH values were measured in simulation runs without the polyanion (see Fig. 1a). In a second set of simulations, the negatively charged 2864 | Soft Matter, 2009, 5, 2862–2868
polyelectrolyte was introduced in the cell (see Fig. 1b), and the complexation study was carried out. Protein and salt concentrations were fixed at 58.7mM and 1.2 mM, respectively. The simulations were performed in a semi-grand canonical ensemble using the standard Metropolis Monte Carlo algorithm23 with random displacements of mobile species (salt, counterions and polyanion beads) within the electroneutral cell The conformation distribution for a flexible (Rcell ¼ 189 A). molecule in a solvent is known to be a special problem in molecular simulations50 and the manner the polyelectrolyte configurations are sampled followed a protocol described in previous publications.20 A pre-equilibration phase with at least 108 simulation cycles was used. Afterwards, ten times longer equilibration and production runs were carried out and the latter were used for sampling properties.
III.
Results and discussion
Physical chemistry properties of the proteins such as pI, C and m are listed in Table 1. These were obtained from simulations of a single protein in solutions of low salt concentrations. Experimental data for pI is scattered in the literature due to several reasons (e.g. experimental uncertainties, different salt concentration regimes, tendency for oligomer formation, presence of genetic variants, etc.). In general, the theoretical predicted pI numbers are closed with experimental measurements. However, the results for b-lac are too low in comparison with experiments (ca. 5.2).51–56 We can see three sources for this discrepancy. One is that the experimental determinations are usually performed at elevated salt and buffer concentrations. For example, the addition of 150 mM salt to an b-lac solution decreases pI by approximately 0.3 units. The second is that the standard pK0 values used in the simulations might be too low. This problem has been investigated by Persson et al.57 Another point is related with the protein three dimensional structure. We have used X-ray protein coordinates obtained from the RCSB Protein Data Bank. As discussed by other authors,58,59 such crystal structures This journal is ª The Royal Society of Chemistry 2009
Fig. 2 The simulated charge number of the proteins as a function of pH. The salt concentration is 1.2 mM and the protein concentration is 58.7 mM. (a) Top panel: data for a-lac1 (filled circle), lys, a-lac2 (open circle) and ins. (b) Bottom panel: data for b-lac, k-cs,46 met and alb.
may have artifacts and deviations from their structure on solution where the pI measurements are usually taken. Plots of the protein net charge as a function of pH are shown in Fig. 2(a) and (b). A similar plot for the protein capacitance varying with pH is given in Fig. 3(a) and (b). The capacitance varies with pH as a consequence of the number of amino acid residues that titrate around each pH. Since charge fluctuations are largest when pH y pKa of a certain residue, the capacitance of a protein rich in say, aspartic acid will peak at pH 4 (pKaasp z 4.060). At some pHs, the values can be three–four times larger than the ones calculated at pI. The largest capacitance found in the present study at pI is for b-lac, while insulin has the smallest value. At other pHs, albumin has substantially larger capacitance. Both albumin and b-lac have large C and m and it is expected that these proteins should attract other charged molecules at pI by a combination of charge regulation and ion-dipole interaction. On the other extreme, lys has the smallest dipole moment. Its capacity to attract another molecule will mostly come from the C term. This is also seen in the semi-quantitative analyses included in the last three columns of Table 1. These interaction free energies were calculated according to eqn (2), revealing the magnitude of the charge regulation and ion–dipole terms at contact. Except for albumin where the ion–dipole contribution is larger than the charge regulation term, in all the other polyelectrolyte–protein complexes the main attractive force comes from charge regulation. The ratio Areg/Adip is a simple manner to quantify the different contributions. Proteins as b-lac that might exist in more oligomerization states may have even large attraction due to the charge regulation mechanism. Increasing This journal is ª The Royal Society of Chemistry 2009
Fig. 3 The simulated protein capacitance of the proteins studied here as a function of pH. The salt concentration is 1.2 mM and the protein concentration is 58.7 mM. (a) Top panel: data for a-lac1 (filled circle), lys, a-lac2 (open circle) and ins. (b) Bottom panel: data for b-lac, k-cs,46 met and alb.
the oligomerization state of proteins will increase the number of amino acids that peak in their characteristics pKas. As a consequence, this enlarges their capacitances. Dynamic light scattering and turbidimetry experiments associated with Poisson–Boltzmann calculations studying albumin (Areg/Adip ¼ 0.7) systems were used to support the ‘‘patch’’ interaction as the main interaction behind the observed complexation with hyaluronic acid.32 Similar conclusions were drawn for albumin–heparin and albumin–poly(dimethyldially1ammonium chloride) complexes based on turbidimetric pH titration and frontal analysis continuous capillary electrophoresis.43,61 Recent turbidity measurements performed on a mixture of albumin and sodium polystyrene sulfonate also show the same trends.62 This is in agreement with the simulated capacitances and dipole moments presented in Table 1, from which one can conclude, even before performing any complex simulation, that albumin will form strong complexes with the polyanion due to its very high dipole moment. An experimental comparison between alb and b-lac based on potentiometric and turbidimetric titration and photon correlation spectroscopy experiments shows similar complexation behavior63 despite the differences of their dipole moment numbers (297 and 128 for alb and b-lac, respectively), which indicates that other attractive mechanisms (i.e. charge regulation) contribute to the complexation for b-lac. For lys, the Areg/ Adip ratio is the largest value observed for all systems studied here confirming that the charge regulation term (ca. 30 times larger than the patch term) is the main origin for the attraction. Soft Matter, 2009, 5, 2862–2868 | 2865
A single mutation on a-lac (1HFY) neutralizing each of the basic residues [K62, K94, K98, R70 and H68] that form the positive charge patches shifts down pI to 5.0 and m to the interval [65–78]. There is virtually no reduction of the binding affinity in terms of b(Areg + Adip) at the estimated contact. Moreover, since both C and m decrease after mutation, there is no reason to favor one or another interaction. Neutralizing all five charges has a more pronounced effect on pI (reducing it from 5.4 to 4.1) and more than double the protein capacitance (from 1.0 to 2.5). The final effect is contrary to what could be predicted from the patch theory: the ion–dipole interaction becomes less important, and the charge regulation term controls the attraction. Areg/Adip changes from 1.5 (wild type structure) to 2.0 (mutation K62) and even 3.0 (mutations R70 and K98). The ratio is even larger (Areg/ Adip ¼ 6.8) when all the five charged residues are neutralized. A high capacitance means that a protein, like b-lac, can acquire a significant negative charge and still have a net attractive interaction with a polyanion. A simple numerical example, based on the numbers given in Table 1, shows that as long as Zb-lac > 4 the attractive charge regulation term will dominate over the repulsive Coulomb interaction. Fig. 4 and 5 show the simulated potential of mean force, w(R), for the eight wild type proteins and the six mutated a-lactalbumin proteins at their respective pI. These data were obtained in a second set of simulations where the polyelectrolyte was included in the cell. All plots show a clear minimum which are summarized in Table 1 together with the corresponding separation. Although the relative strength of the minima are only in qualitative agreement with the
Fig. 5 The potential of mean force between the centers of mass of the single and quintuple (K62, K94, K98, R70 and H68) mutated a-lactalbumin proteins and the polyelectrolyte obtained from MC simulations. Basic residues that would define a ‘‘charge patch’’ were neutralized.
analytical predictions, the same trends are observed: large capacitance gives more stable complexes. This is a confirmation of the importance of the charge regulation mechanism for protein complexes. A separation between the polyelectrolyte center of mass and the protein (R) close to zero means that the polyanion wraps around the protein. Depending on the protein size and geometry, this can be an entropically unfavourable situation for the polyelectrolyte chain, which leads to a repulsive potential of mean force. For a-lac (1HFY and 1F6S structures), bA(0) is still attractive but for all other proteins bA(0) > 0.
IV.
Concluding remarks
By means of Monte Carlo simulations and semi-quantitative analyses based on perturbation theory, we have demonstrated the importance of charge regulation. This mechanism induced by pH results in attractive forces due to electrostatic interactions. The charge regulation mechanism is a consequence of the protein’s ability to regulate its charge as a result of the acid–base equilibrium. This makes possible the complexation of protein– polyelectrolytes (and also the protein–protein complexation) with high affinity even when the pH solution is at the protein’s pI cancelling out the Coulombic charge–charge interactions. The ion–dipole term also contributes to the formation of these complexes. Nevertheless, as quantified here, the dominating term is often the charge-induced charge interaction. Addition of salt screens the electrostatic interactions and the charge regulation and thermally average ion–dipole term will also be effectively screened out, not by exp(kR) but by exp(2kR), since they appear in the second order in the perturbation analysis. The inverse screening length (k) is proportional to the square root of the salt concentration.64 In the MC simulations presented here we have neglected the attractive van der Waals interaction. Inclusion of such a term can further emphasize the attraction coming from the charge regulation term. The presented theoretical mutational data might also stimulate new experimental studies with proteins obtained from mutagenesis experiments. Fig. 4 The potential of mean force between the centers of mass of the proteins and the polyelectrolyte obtained from MC simulations. The salt concentration is 1.2 mM and the protein concentration is 58.7 mM. (a) Top panel: data for a-lac1 (filled circle), lys, a-lac2 (open circle) and ins. (b) Bottom panel: data for b-lac, k-cs,46 met and alb.
2866 | Soft Matter, 2009, 5, 2862–2868
Acknowledgements It is a pleasure to express our gratitude to Prof. Farrell and his co-authors that kindly provided us the k-cs coordinates. This This journal is ª The Royal Society of Chemistry 2009
work has been supported in part by the Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol ogico (CNPq), Fundac¸a˜o de Amparo a Pesquisa do Estado de Sa˜o Paulo (Fapesp) and the Swedish Research Council through a Linnaeus grant.
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