Possible Origin of the Inverse and Direct Hofmeister Series for

ARTICLE pubs.acs.org/Langmuir

Possible Origin of the Inverse and Direct Hofmeister Series for Lysozyme at Low and High Salt Concentrations Mathias Bostr€om,*,†,‡ Drew F. Parsons,*,‡ Andrea Salis,*,† Barry W. Ninham,‡ and Maura Monduzzi† †

Department of Chemical Science, University of Cagliari-CSGI and CNBS, Cittadella Universitaria, S.S. 554 bivio Sestu, 09042 Monserrato (CA), Italy ‡ Research School of Physical Sciences and Engineering, Australian National University, Canberra 0200 Australia ABSTRACT:

Protein solubility studies below the isoelectric point exhibit a direct Hofmeister series at high salt concentrations and an inverse Hofmeister series at low salt concentrations. The efficiencies of different anions measured by salt concentrations needed to effect precipitation at fixed cations are the usual Hofmeister series (Cl
> NO3
> Br
> ClO4
> I
> SCN
). The sequence is reversed at low concentrations. This has been known for over a century. Reversal of the Hofmeister series is not peculiar to proteins. Its origin poses a key test for any theoretical model. Such specific ion effects in the cloud points of lysozyme suspensions have recently been revisited. Here, a model for lysozymes is considered that takes into account forces acting on ions that are missing from classical theory. It is shown that both direct and reverse Hofmeister effects can be predicted quantitatively. The attractive/repulsive force between two protein molecules was calculated. To do this, a modification of Poisson
Boltzmann theory is used that accounts for the effects of ion polarizabilities and ion sizes obtained from ab initio calculations. At low salt concentrations, the adsorption of the more polarizable anions is enhanced by ion
surface dispersion interactions. The increased adsorption screens the protein surface charge, thus reducing the surface forces to give an inverse Hofmeister series. At high concentrations, enhanced adsorption of the more polarizable counterions (anions) leads to an effective reversal in surface charge. Consequently, an increase in co-ion (cations) adsorption occurs, resulting in an increase in surface forces. It will be demonstrated that among the different contributions determining the predicted specific ion effect the entropic term due to anions is the main responsible for the Hofmeister sequence at low salt concentrations. Conversely, the entropic term due to cations determines the Hofmeister sequence at high salt concentrations. This behavior is a remarkable example of the charge-reversal phenomenon.

1. INTRODUCTION 1.1. Background. Specific ion effects abound in physical chemistry, biochemistry, and biology.1
3 Phenomena such as enzyme activities,4
6 ion binding to micelles,7 forces between polyelectrolyte molecules,8 neutral lipid membrane interactions,9 colloidal charge reversal,10 anion affinities and surface tensions at the air
water interface,11,12 protein monolayers,13 buffer pH,14 protein surface charge,15 protein precipitation,16 and adsorption on mesoporous materials17 are all ion-specific.18,19 Such Hofmeister effects are not explained by standard electrostatic theories of colloidal particle interactions. They have been known for over a century.2,19,20 The phenomena have been subsumed and characterized but not explained with terms such as the lyotropic series, kosmotropicity, and chaotropicity. For an account of the present state of affairs, see two recent books.19,21A partial r 2011 American Chemical Society

systemization has been achieved by Collins through a phenomenological law of “matching water affinities”.22
24 The standard theories of molecular and colloidal particle forces cannot explain the phenomena. One reason for this can be seen by considering the classical (DLVO) description of forces between idealized planar colloidal particles. There is a separation of forces into two kinds. An electrostatic double-layer component is due to an inhomogeneous profile of ions at the interfaces. The opposing attractive quantum mechanical forces are described by a van der Waals
Hamaker
Lifshitz attraction. The latter is a linear theory that ignores the ion profiles and the ion-specific quantum mechanical dispersion forces acting on ions.25 Received: May 31, 2011 Revised: June 17, 2011 Published: June 21, 2011 9504

dx.doi.org/10.1021/la202023r | Langmuir 2011, 27, 9504–9511

Langmuir The separation of forces can be shown to be thermodynamically inconsistent.25 The matter is not academic. The introduction of effective potentials to subsume this difficulty can be used to skirt over it, but it is not predictive. For consistency, even within a primitive model of electrolytes, the missing ion-specific dispersion potentials acting on ions have to be included at the same (nonlinear) level as the electrostatic forces acting on ions. This can be done in a first approximation either within a Poisson
Boltzmann equation description or with Monte Carlo simulations.26 Such an approach was invoked to account for a number of ion specific-effects but only at a qualitative level.19 The magnitude of the dispersion forces was such that it seemed clear that they could not be ignored. Further quantitative progress was inhibited by the lack of accurate values for ionic dynamic polarizabilities and consistent definitions of ion sizes. The required data has now been obtained from ab initio quantum mechanics for a whole suite of ions.27
31 The inclusion of ionic dispersion forces is one part of but not the whole story. The short-range hydration profile around ions is also a consequence of both electrostatic and dispersion forces acting in concert. This is a necessary extension of ab initio calculations that allows for both strongly hydrated ions (kosmotropes) and weakly hydrated ions (chaotropes) and is also now accessible from ab initio treatments. Even this is not enough to pin down Hofmeister effects. The hydration of interacting surfaces is also sometimes necessary. These extensions have permitted a quantitative comparison with experiment that gives confidence that such a theoretical approach is on the right track.27
34 1.2. Direct and Reverse Hofmeister Series. A long-standing mystery attending Hofmeister effects concerns the observation of both direct and reverse Hofmeister series: when a protein is suspended in an aqueous medium, its surface charge depends both on the solution pH and on the type of different ions in solution.35,36 Attempts to include ion-specific interactions between the ions and protein surfaces appeared to offer at least a partial explanation of this old issue of why an inverse or a direct Hofmeister series is found. This depended on whether the solution pH was lower or higher than the protein isoelectric point,35,37 but the explanation used an arbitrary choice of ionic radii and estimated polarizabilities, leaving it open to justifiable criticism. The source of such a reversal and/or reordering of the Hofmeister series remained an open question. It occurs, for example, in the cutting efficiency of DNA with restriction enzymes.6 The order changes upon changing the buffer from cacodylate to phosphate. With glass electrode pH measurements for given anion sequence and a fixed buffer, the Hofmeister sequence of salt-induced pH changes reverses upon exchanging potassium for sodium.14 A very interesting effect is that typified by a recent study by Zhang and Cremer.38,39 The cloud-point temperatures in lysozyme suspensions follows an inverse Hofmeister series at low salt concentrations ( SCN
> I
> NO3
> Br
> Cl
. There is a maximum in the cloud-point temperature at about 0.3
0.5 M salt concentration, a crossing point in the concentration range of 0.8
1.5 M, and a direct Hofmeister series at high salt concentrations (>1.5 M): SCN
< I
< ClO4
< Br
< NO3
< Cl
. Robertson, as long ago as 1911, suggested that this is simply a “particular instance of the general rule that the salts may act as precipitants and as coagulants at low and at high concentrations respectively, acting as solvents at intermediate concentrations”.40 What that statement means is unclear, but it is, in any case, only a phenomenological observation.

ARTICLE

With that as a background, this work focuses on the demonstration that the direct/reverse Hofmeister series of anions with respect to the force between model lysozyme macromolecules can be explained provided that the ion-specific potentials and ion sizes, quantified from ab initio quantum mechanics, are brought into play. A simple model system with two interacting surfaces taken to mimic the dielectric properties and charge density as a lysozyme will be considered. The calculated forces between two spherical lysozyme proteins obtained with the Derjaguin approximation will be compared with recently obtained experimental results. 38All salts used by Zhang and Cremer will be considered to show both the strengths and limitations of our modeling.

2. THEORETICAL SECTION 2.1. Modified Double-Layer Theory. To model the system, two planar bodies a distance L apart separated by an electrolyte are first considered. Each has the dielectric properties and surface charge density of a lysozyme protein. The charge density is taken from the charge of the protein that is calculated at pH 9 and then divided by the surface area of the protein.35 The Derjaguin approximation was then used to calculate the force between spherical proteins.41,42 The aim is to explain the switch from a reverse Hofmeister series to a direct Hofmeister series as the salt concentration is increased. To model the specific ion effects, a calculation of the ion profiles near the interacting surfaces is required. The distribution of ions between the surfaces is determined by a modified Poisson
Boltzmann equation that includes both electrostatic potentials and nonelectrostatic (NES) potentials acting on the ions,25,28,43

d2 j ¼
dx2

e

∑i zi ci, 0 exp½
ðzi ejðxÞ + Ui ðxÞÞ ε0 εw ð0Þ

ð1Þ

where ci,0 and zi denote the bulk concentration and valency of ionic species i, respectively,. The modified Poisson
Boltzmann equation has been solved numerically using a constant charge boundary condition, dj
σ 0 j ¼ dx x ¼ 0 ε0 εw ð0Þ

ð2Þ

The model protein
mimetic surfaces have positive surface charge densities at pH 9 that are calculated to be around σ0 = 3.4  10
2 C/m2.35 To compare with previous calculations on the Hofmeister reversal with changes in pH below and above the isoelectric point, we have also estimated the surface charge density at pH 12 to be around σ0 =
3.63  10
2 C/m2.35 Besides the electrostatic self-consistent potential (j(x)), each ion experiences nonelectrostatic potentials (Ui(x, L)) because of its dispersion interactions with planar surfaces a distance L apart. We here consider one cation (Na+) and several anions (Cl
, NO3
Br
, ClO4
, I
, and SCN
). Cations and anions with no polarizability are also considered to compare our Hofmeister results with the classical DLVO result. The NES potential acting between each polarizable ion with finite size and each of the planar charged surfaces is28 Uðx, LÞ ¼ 9505

Bf ðxÞ Bf ðL
xÞ + x3 ðL
xÞ3

ð3Þ

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511

Langmuir

ARTICLE

Table 1. Ion Sizes, a, and Dispersion Constants, B, for the Ions Used in This Studya,b a (Å)

R1* (Å3)

Na+ (hydrated)

2.25


0.44945


0.20

Cl
NO3


1.86 2.01

1.1284 0.67581


1.26
1.23

alternate approach was also tested and found to model the protein system less satisfactorily. Comparison with the experimental result suggests that the hard excluded volume formed by the ion-excluded model does not apply to protein surfaces. When ion distributions between two parallel charged colloidal surfaces are used, the total modified DLVO pressure (modified to include the ionic dispersion forces) becomes47

Br


1.97

1.3615


1.70

ClO4


0.63117


1.53

Ptot ¼ Pentropic + Pionic dispersion + PHamaker

2.17

I


2.12

2.2483


2.49

SCN


2.18

1.5898


2.27

ion

B (10
50 J m3)

Pentropic ¼ kT

For reference, ionic polarizabilities, R1*, are also given (at the lowest optical frequency used in the calculation of B). B has been summed over all frequencies; see eq 5. b Ion sizes indicate Gaussian radii. Far from a single interface, the NES potential takes the following asymptotic form: Udispersion(x) = B/x3.

∑i ½ci ðL=2Þ
c0, i 

a

Pionic dispersion ¼
2

∑i

Z

L=2

ci 0

dUi ðx, LÞ dx dL

ð6aÞ ð6bÞ

ð6cÞ

A ð6dÞ 6πL3 Here c0,i, ci(L/2), and Ui are the ion density in bulk solution, the ion density at the midplane between the two surfaces, and the ionic dispersion potential (eq 3) acting between each ion and the two interacting surfaces, respectively. The Hamaker constant (A = 3.52kT) was calculated using Lifshitz theory45 by applying the same dielectric models for water44 and protein26 used to calculate the ionic NES potentials. The first contribution to the pressure is simply the classical entropic pressure between equal plates. It is modified here because of the presence of ion-specific potentials that influence the ion concentration at the midpoint between the two surfaces. The second term is due to the direct NES interactions between the ions in the nonlinear ion profile and the two surfaces. The third term is the direct Hamaker
van der Waals interaction between two protein surfaces across water, which depends only weakly on ionic species. The force between proteins that are not too far apart can then be obtained using the Derjaguin approximation.41,42 This will be discussed in the Results section. 2.2. Ab Initio Calculations of Ion Polarizabilities. The model for the nonelectrostatic (NES) potential is based on having a polarizability that is spatially spread in line with the electron cloud of the ion.30 The electron density of small ions can be described by a Gaussian sphere with radius a. Here, one cation (Na+)27,28 and several anions are considered. The NES potential uses excess polarizabilities, which describe the difference between the intrinsic dielectric response of the ion from that of the surrounding medium (water)30 PHamaker ¼


where

! " #   " # 2x 2x2
x2 4x4 x
1 + 4 erfc
1 exp f ðxÞ ¼ 1 + pffiffiffi 2 2 a a a πa a ð4Þ " # kT R/ ðiωn Þ εw ðiωÞ
εp ðiωÞ B¼ ð2
δ0, n Þ 4 n¼0 εw ðiωn Þ εw ðiωÞ + εp ðiωÞ

∑

ð5Þ

ωn = 2πkTn/p and k and T are the Boltzmann constant and the temperature. εw(iω) and εp(iω) are the dielectric functions of water44 and the protein26 surface, respectively. R*(iω)is the excess polarizability of the ion. The excess polarizability describes the difference between the intrinsic dielectric response of the ion from that of the surrounding medium (water). The magnitudes, and even the signs, of the dispersion potentials near the two interfaces depend in a sensitive way on these frequency-dependent entities. The calculations of ionic excess polarizabilities have been treated elsewhere,30 and here a brief summary is given in the following section. The complicated form factor in eq 4 takes account of an assumed Gaussian electron cloud and polarizability of a finite-sized ion.45 The ionic parameters (B values and ion sizes30) are given in Table 1. Note that a slightly larger ion radius was used for the Cl
than that given in ref 26 (1.86 Å rather than 1.69 Å). The larger value is generated using the least-squares algorithm of ref 6, where the smaller value was obtained by an equality algorithm (eq 7 in ref 26). It seems to reproduce the halide Hofmeister series more faithfully (the smaller radius yields Cl
> I
> Br
instead of I
> Br
> Cl
). Strongly hydrated kosmotropic ion Na+ was taken to be explicitly hydrated with three water molecules46 in the sense that the waters of hydration were included explicitly in the ab initio calculations of the size and polarizability of the hydrated ion cluster. This should be more realistic than an earlier cruder hydration model that simply added the thickness of the hydration shell to the ion size and the polarizability of the water molecules to the ion polarizability.34 We use an ion-embedded model; that is, the ion can take the full range of distance from the surface, from x = 0 to L. These boundary values imply that the ion is permitted to embed into the interface, which may be justified on the grounds that the actual protein surface contains pits and bumps. An alternate approach is an ion-excluded model, constraining ions with a distance of closest approach no closer than one ionic radius from x = 0. This

RðiωÞ ¼

3V i ½εi ðiωÞ
εw ðiωÞ 4π ½εi ðiωÞ
2εw ðiωÞ

ð7Þ

The intrinsic dielectric response of the ion, εi(iω), is derived from ab initio quantum mechanical calculations of the intrinsic polarizability R(iω) of the ion in vacuum, εi ðiωÞ ¼ 1 + 4πni RðiωÞ

ð8Þ

ni is the number density of an isolated ion (i.e., ni = 1/Vi). This equation is used rather than a more sophisticated Clausius
Mossotti description48 to avoid any unphysical values in εi if the ionic volume (Vi) has been underestimated.30 Ion volumes and ion radii are taken from quantum chemically derived estimates.30 Ab initio calculations of the intrinsic polarizabilities R(iω) of the ions in vacuum were performed31 with electron correlation provided at the coupled cluster singles and doubles (CCSD) 9506

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511

Langmuir

ARTICLE

Figure 1. Double-layer pressure (eqs 6b and 6c, i.e., not including the direct Hamaker
Lifshitz pressure) between two surfaces 20 Å apart with lysozyme-like properties. (a) pH 12 and (b) pH 9.

Figure 2. Pressure from eqs 6b and 6c (i.e., not including direct Hamaker
vdW
Lifshitz pressure) between two plates with lysozyme-like properties at pH 9. (a) 0.1 and (b)1.5 M salt solutions.

level of theory for all ions except perchlorate, for which density functional theory (DFT) was applied using the PBE0 functional.49 The aug-cc-pV*Z family of basis sets50 was used.

3. RESULTS AND DISCUSSION 3.1. Using Model Systems to Understand Hofmeister Reversal with Changes in pH and Concentration. Tardieu

and co-workers36 showed that protein
protein interactions in different salt solutions follow different Hofmeister series for pH < pI and pH > pI. This work is in agreement with older results that are mentioned in ref 33. A theoretical explanation of this effect in terms of ion-specific dispersion potentials was offered by Bostr€om et al.35 Later work by Wernersson and Kjellander confirmed the importance of ionic dispersion potentials for the pH dependent reversal of Hofmeister series.51 Our intention now is to improve this modeling by using ab initio ionic polarizabilities31 and including ion size dependence in the dispersion potentials, so making the dispersion potentials finite at shortrange.30,31 In what follows, it will be shown that a reversal of the Hofmeister series occurs when either the pH or concentration is changed and that these are related. Figure 1 shows the pressure (as a function of salt concentration) between two plates 20 Å apart at pH 12 (anions are co-ions) and pH 9 (anions are counterions). The recent Zhang and Cremer experiments38 that measured the lysozyme cloud-point temperatures were

conducted at pH 9, below the pI. Ion-specific effects due to the buffer (20 mM tris(hydroxymethyl) aminomethane in the Zhang and Cremer experiments) are neglected here. The buffer identity has its own role to play in the phenomenon of Hofmeister inversion.14 At low salt concentrations, the conclusions drawn by Bostr€om et al.35 and Wernersson and Kjellander51 remain valid. The entropic contribution, the first term in eq 6a, to the surface pressure, which is directly related to the ion-specific concentrations at the midpoint, gives rise to a reverse Hofmeister sequence at pH 9 (where anions are counterions) and a direct Hofmeister sequence at pH 12 (where anions are co-ions). Figure 1 shows pressures at a surface separation of 20 Å. We demonstrate that the Hofmeister reversal at low salt concentration (for pH 9) is independent of surface separation by showing the pressure as a function of separation at pH 9 with a salt concentration of 0.1 M in Figure 2a and 1.5 M in Figure 2b. The inverted series at 0.1 M concentration is found to be consistent at all separations, as is the direct series at 1.5 M concentration. A smaller specific ion effect was observed when the separation is larger than 35 Å (Figure 2). There are in fact long-range specific ion effects present, but the dominating effect comes from the force between surfaces at short distances.47 Such long-range effects have been observed experimentally, where they have been described as secondary hydration forces.52 3.2. Anion and Cation Contributions to the Entropic Part of Pressure Explains the Hofmeister Reversal. To understand 9507

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511

Langmuir

ARTICLE

Figure 3. Double-layer pressure between two surfaces 20 Å apart with model lysozyme-like properties at pH 9. (a) Entropic part (eq 6b). (b) NES part.

Figure 4. Electrostatic potential at the protein-like surfaces considered in Figure 3 as a function of salt concentration for different ionic species.

the concentration-dependent reversal observed in protein solutions when pH < pI, we show in Figure 3 the entropic and NES contributions to the double-layer pressure shown in Figure 1b, again at a separation of 20 Å. At low salt concentrations, more polarizable anions adsorb more strongly because of ion
surface dispersion interactions. They therefore better screen the protein surface charge and thereby reduce the surface pressure, giving rise to a reverse Hofmeister series. The strength of the entropic contribution is attenuated as the concentration increases until a minimum pressure is reached. At high salt concentrations, enhanced adsorption of the counterions (anions) driven by ion-surface dispersion interactions leads to an increase in the entropic contribution. This behavior is a nice example of the charge-reversal phenomenon. The reversal of the Hofmeister series with increasing concentration is related to the reversal with changing pH (i.e., with the sign of the effective surface charge). This charge reversal is illustrated in Figure 4, where the surface electrostatic potential is shown at the proteinlike surfaces considered in Figure 3a. Close to the proteinlike surface, the magnitudes of the surface electrostatic potential have different Hofmeister series for low and high salt concentrations! Both the pressure and surface electrostatic potentials in the highconcentration limit, when pH < pI, behave in a similar way to the corresponding results for pH > pI. Some examples of co-ion adsorption at high salt concentrations are illustrated in Figure 5. As compared with the other anions, the more polarizable counterions (iodide ions) cause an

Figure 5. Normalized cation profiles (in 2.5 M salt solutions) between two surfaces 20 Å apart with lysozyme-like properties at pH 9.

increase in the number of co-ions (sodium ions) in between the surfaces. This gives rise to the observed reversal of the Hofmeister series at high concentrations in our simple model system, as will be shown. The cation profiles at 0.1 M salt concentration follow the same Hofmeister series as in the highsalt-concentration limit, but the cations are depleted from the positively charged surface (data not shown). The corresponding entropic contributions (given by midpoint concentrations, eq 6b) due to the cation and anion are shown as a function of concentration in Figure 6. The reverse Hofmeister series at low concentrations is evidently due to the anion component. The series in the anion component remains reversed at high salt concentration. The onset of the direct Hofmeister series at high salt concentration is, rather, due to the dominance of the cationic component. A similar decomposition of the NES contribution to the surface pressure both for anions and cations is shown in Figure 6b. By comparing the magnitudes of the dispersion with the entropic contributions, we see that the entropic component dominates. Indeed, although the dispersion component is always attractive (Figure 6b), the total force is repulsive. 3.3. Concentration Dependence of Forces Between Model Protein Molecules for pH < pI. Let us consider the calculations for pH < pI (i.e., pH 9) only. Lysozyme protein molecules occur as roughly spherical colloidal particles. Therefore, for comparison with experimental transition concentrations from the reverse to direct Hofmeister series, it is more appropriate to 9508

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511

Langmuir

ARTICLE

Figure 6. Decomposition of (a) entropic contribution Pentropic and (b) NES contribution PNES to the surface pressure, showing the separate components due to the cation and anion. Calculated from two flat surfaces 20 Å apart with lysozyme-like properties at pH 9.

Figure 7. Schematic drawing of two spherical protein globules showing separation L as used in the Derjaguin approximation.

use sphere
sphere forces rather than flat surface pressures. Sphere
sphere forces (fs) may be estimated from flat surface pressures by applying the Derjaguin approximation, normalized against the radius (Rp) of the protein molecules,41,42,53 Z ∞ fs ðLÞ ¼ πUtot ðLÞ ¼ π Ptot ðLÞ dL ð9Þ Rp L Here, L is the closest surface separation as defined in Figure 7. The Derjaguin approximation is valid when the distance between two spherical colloid particles is much lower than their respective radii. Lysozyme is a small globular protein, so the Derjaguin approximation should not be strictly valid. Nevertheless, previous work showed that the use of a modified Poisson
Boltzmann theory using two-sphere geometry was found to be in good qualitative agreement with the simpler Derjaguin approximation.54 Hence, the use of the Derjaguin approximation gives qualitatively correct results. However, the calculations used in the present work demonstrate the underlying fundamental origin of the Hofmeister reversal with increasing salt concentrations. Zhang and Cremer38 found that the cloud-point temperature for the liquid
liquid phase transition of lysozyme at about pH 9 followed two distinct Hofmeister series depending on salt concentration.38Below the cloud point, protein molecules aggregate into a cloudy protein-rich phase, and above it, the protein molecules are dispersed into a clear solution. The temperature at which the cloud point occurs should correlate with the forces acting between protein molecules. In particular, the higher the temperature at which the cloud point occurs, the stronger the

Figure 8. Total force (normalized with protein radius) versus salt concentration for two lysozyme proteins with the closest distance 20 Å apart at pH 9.

attractive forces between proteins will be (or the weaker the repulsive forces will be). Zhang and Cremer related these effects to the expected electrostatic contributions along with ion-specific variations of surface tension and ion polarizabilities.38,39 Our model was chosen according to the experimental conditions (pH 9, salt concentrations up to 2.5M) used to investigate the lysozyme phase transition. The calculations should be taken as indicative rather than predictive because a simple generic model for the protein dielectric response26 was applied rather than a dielectric function specific to lysozyme. Figure 8 shows the force (normalized with respect to the protein radius) between two globular proteins with a fixed separation of L = 20 Å for different salt concentrations. In good agreement with experimental results, we found that the interaction between proteins in a lysozyme suspension follows a reverse Hofmeister series at low salt concentrations ( SCN
> Br
>Cl
> ClO4
> NO3
> DLVO. There is a minimum force at about 0.5
0.8 M salt concentration, a crossing point in the concentration range of 0.8
1.5 M, and a direct Hofmeister series at high salt concentrations (>1.5 M): I
< SCN
< Br
≈ ClO4
< NO3
≈ Cl
. For high salt concentration, almost the same Hofmeister series found by Zhang and Cremer is observed.38 The limitations of the model at low salt concentrations for ClO4
and NO3
will be discussed later. Also, 9509

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511

Langmuir iodide and thiocyanate curves come in the wrong sequence. First it should be observed that the trends found in flat surface pressures are sustained in sphere
sphere forces. That is, at low salt concentrations the more polarizable anions are more successful in compensating for the positive surface charge. Anion binding due to ion
surface dispersion interactions reduces the entropic repulsion between protein molecules and makes it easier for them to aggregate. As a consequence, the cloud-point temperature of lysozyme will rise as the anion polarizability increases. Thus, our modeling is consistent with the explanation of Zhang and Cremer in the low-salt-concentration limit.38,39 As more salt is added, at a certain concentration, the force curves reveal a minimum that is ion-specific similar to the experimental maximum in cloud-point temperatures. The transition between lowand high-concentration salt behavior comes at a similar salt concentration in the theoretical curves compared to the experimental results, around 0.5
1.0 M. This gives the opposite Hofmeister series at high salt concentrations, again in agreement with the experiments. Our results also show that at low salt concentration the series for the halides matches experiment, but NO3
, SCN
, and ClO4
are found more or less out of sequence. (The experimental sequence at low concentration is ClO4
> SCN
> I
> NO3
> Br
> Cl
). This discrepancy suggests that some physical properties not considered here may dominate at low concentrations, chiefly anisotropic effects29 (affecting SCN
and NO3
) and higher multipolar (quadrupole and octupole) dispersion interactions. The polyatomic ions (SCN
, NO3
, and ClO4
) all have a significant quadrupole moment. In the ionic nonelectrostatic interaction used here, eq 3, only induced dipole interactions are included, without higher multipole contributions. The multipole dispersion interactions supply a substantial additional attractive force expected to get SCN
in the right place relative to I
. Likewise, it would push ClO4
and NO3
toward I
as seen in experiments.

4. CONCLUSIONS The results presented in this work, obtained by solving the modified Poisson
Boltzmann equation with ion-specific NES potentials (using excess ion polarizabilities obtained from ab initio calculations), give a possible explanation of the concentration dependence of the Hofmeister series. At low salt concentrations, more polarizable anions are more strongly adsorbed because of nonelectrostatic ion
surface dispersion interactions. They therefore screen the protein surface charge more strongly, resulting in a reduction of inter protein forces and in a reverse Hofmeister series. At high salt concentrations, the effective surface charge is reversed in sign; that is, the electrostatic potential switches from positive to negative. Consequently, coions (cations) are pushed in between proteins, resulting in an increase in the entropic pressure. The inversion of the Hofmeister series with increasing concentration is related to the inversion that occurs with changing pH (again, a change in the sign of the effective surface charge). The Hofmeister series reversal in surface forces must be a contributor to and the possible origin of the Hofmeister series inversion observed experimentally in lysozyme cloud-point temperatures. Levin and Diehl demonstrated by Monte Carlo simulation that charge reversal may take place at a colloid surface because of electrostatic interactions and ion
ion correlations when a multivalent counterion is present at sufficiently high concentration.10 By contrast, we find here an onset of charge reversal even in a

ARTICLE

univalent electrolyte as a result of the dispersion forces of the counterion. More recently, Levin et al. demonstrated the role of hydrated ion size and dehydration in reproducing surface tension increments at the air
electrolyte interfaces.12 We similarly invoke finite ion sizes (with kosmotropic ions taken as strongly hydrated) but assume that dehydration does not play a large role at the lysozyme interface. Our model includes ionic dispersion (van der Waals and induced dipole
induced dipole) forces, missing in Levin’s treatment, which includes ion polarizability through a small induction force (permanent charge-induced dipole) only. Future work addressing Hofmeister effects clearly needs to proceed along the lines that we have outlined in this article combined with the work of Levin and co-workers. In other words, a complete model will include the finite ion size, ion-sizedependent dispersion forces acting between ions and surfaces and between ions, the surface dehydration of certain ions, and ion
ion correlations. In conclusion, the most significant result of this work is represented by the demonstration that among the different contributions determining the predicted specific ion effect the entropic term due to anions is mainly responsible for the Hofmeister sequence at low salt concentrations. Conversely, the entropic term due to cations determines the Hofmeister sequence at high salt concentrations.

’ AUTHOR INFORMATION Corresponding Author

*(M.B.) E-mail: [email protected]. (D.F.P.) E-mail: [email protected]. (A.S.) E-mail: [email protected]. Tel: +39 070 6754362. Fax: +39 070 6754388.

’ ACKNOWLEDGMENT A.S. and M.M. thank MIUR, PRIN 2008, for financial support. M.B. thanks the program Visiting Professor 2010, which was financed by RAS. D.F.P. acknowledges the financial support of the Australian Research Council’s Discovery Projects scheme and the computational support of the NCI National Facility at the Australian National University. We also thank Tim Duignan for bringing to our attention the vital role of multipolar dispersion interactions in polyatomic ions. ’ REFERENCES (1) Kunz, W. Curr. Opin. Colloid Interface Sci. 2010, 15, 34. (2) Zhang, Y.; Cremer, P. S. Curr. Opin. Chem. Biol. 2006, 10, 658. (3) Ball, P. Chem. Rev. 2008, 108, 74. (4) Bilanicova, D.; Salis, A.; Ninham, B. W.; Monduzzi, M. J. Phys. Chem. B 2008, 112, 12066. (5) Salis, A.; Bilanicova, D.; Ninham, B. W.; Monduzzi, M. J. Phys. Chem. B 2007, 111, 1149. (6) Kim, H.-K.; Tuite, E.; Norden, B.; Ninham, B. W. Eur. Phys. J. E 2001, 4, 411. (7) Romsted, L. R. Langmuir 2007, 23, 414. (8) Rau, D. C.; Lee, B.; Parsegian, V. A. Proc. Natl Acad. Sci. U.S.A. 1984, 81, 2621. (9) Petrache, H. I. Z., T.; Belloni, L.; Parsegian, V. A. Proc. Nat. Accad. Sci. U.S.A. 2006, 103, 7982. (10) Diehl, A.; Levin, Y. J. Chem. Phys. 2006, 125. (11) Cheng, J.; Vecitis, C. D.; Hoffman, M. R.; Colussi, A. J. J. Phys. Chem. B 2006, 110, 25598. (12) Levin, Y.; dos Santos, A. P.; Diehl, A. Phys. Rev. Lett. 2009, 103, 257802. 9510

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511

Langmuir

ARTICLE

(13) Chen, X.; Flores, S. C.; Lim, S.-M.; Zhang, Y.; Yang, T.; Kherb, J.; Cremer, P. S. Langmuir 2010, 26, 16447. (14) Salis, A.; Pinna, M. C.; Bilanicova, D.; Monduzzi, M.; Lo Nostro, P.; Ninham, B. W. J. Phys. Chem. B 2006, 110, 2949. (15) Gokarn, Y. R.; Fesinmeyer, R. M.; Saluja, A.; Razinkov, V.; Chase, S. F.; Laue, T. M.; Brems, D. N. Protein Sci. 2011, 20, 580. (16) Curtis, R. A.; Ulrich, J.; Montaser, A.; Prausnitz, J. M.; Blanch, H. W. Biotechnol. Bioeng. 2002, 79, 367. (17) Salis, A.; Bhattacharyya, M. S.; Monduzzi, M. J. Phys. Chem. B 2010, 114, 7996. (18) Loeb, J. Science 1920, LII, 449. (19) Ninham, B. W.; Lo Nostro, P. Molecular Forces and Self Assembly: In Colloid, Nano Sciences and Biology; Cambridge University Press: Cambridge, U.K., 2010. (20) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. 1888, 24, 247. (21) Kunz, W. Specific Ion Effects; World Scientific Publishing: Singapore, 2010. (22) Collins, K. D. Methods 2004, 34, 300. (23) Collins, K. D.; Neilson, G. W.; Enderby, J. E. Biophys. Chem. 2007, 128, 95. (24) Lund, M.; Jagoda-Cwiklik, B.; Woodward, C. E.; Vacha, R.; Jungwirth, P. J. Phys. Chem. Lett. 2010, 1, 300. (25) Ninham, B. W.; Yaminsky, V. Langmuir 1997, 13, 2097. (26) Tavares, F. W.; Bratko, D.; Blanch, H.; Prausnitz, J. M. J. Phys. Chem. B 2004, 108, 9228. (27) Salis, A.; Parsons, D. F.; Bostrom, M.; Medda, L.; Barse, B.; Ninham, B. W.; Monduzzi, M. Langmuir 2010, 26, 2484. (28) Parsons, D. F.; Bostr€om, M.; Maceina, T. J.; Salis, A.; Ninham, B. W. Langmuir 2010, 26, 3323. (29) Parsons, D. F.; Deniz, V.; Ninham, B. W. Colloids Surf., A 2009, 343, 57. (30) Parsons, D. F.; Ninham, B. W. J. Phys. Chem. A 2009, 113, 1141. (31) Parsons, D. F.; Ninham, B. W. Langmuir 2010, 26, 1816. (32) Parsons, D. F.; Ninham, B. W. Colloids Surf., A 2011, 383, 29. (33) Ninham, B. W.; Duignan, T. T.; Parsons, D. F. Curr. Opin. Colloid Interface Sci. 2011, DOI:10.1016/j.cocis.2011.04.006 (34) Parsons, D. F.; Ninham, B. W. Langmuir 2010, 26, 6430. (35) Bostr€om, M.; Tavares, F. W.; Finet, S.; Skouri-Panet, F.; Tardieu, A.; Ninham, B. W. Biophys. Chem. 2005, 117, 217. (36) Finet, S.; Skouri-Panet, F.; Casselyn, M.; Bonnete, F.; Tardieu, A. Curr. Opin. Colloid Interface Sci. 2004, 9, 112. (37) Lund, M.; Jungwirth, P. J. Phys.: Condens. Matter 2008, 20, 4. (38) Zhang, Y.; Cremer, P. S. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 15249. (39) Zhang, Y.; Cremer, P. S. Annu. Rev. Phys. Chem. 2010, 61, 63. (40) Brailsford Robertson, T. J. Biol. Chem. 1911, 9, 303. (41) Rentsch, S.; Pericet-Camara, R.; Papastavrou, G.; Borkovec, M. Phys. Chem. Chem. Phys. 2006, 8, 2531. (42) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. (43) Boinovich, L. Curr. Opin. Colloid Interface Sci. 2010, 15, 297. (44) Dagastine, R. R.; Prieve, D. C.; White, L. R. J. Colloid Interface Sci. 2000, 231, 351. (45) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: London, 1976. (46) Marcus, Y. Pure AppI. Chem. 1987, 59, 1093. (47) Edwards, S.; Williams, D. Phys. Rev. Lett. 2004, 92, 248303. (48) Netz, R. R. Curr. Opin. Colloid Interface Sci. 2004, 9, 192. (49) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158. (50) Woon, D. E.; Dunning, T. H. J. Chem. Phys. 1994, 100, 2975. (51) Wernersson, E.; Kjellander, R. J. Chem. Phys. 2006, 125, 154702. (52) Pashley, R. M.; Quirk, J. P. Colloids Surf. 1984, 9, 1. (53) Chan, D. Y. C.; Pashley, R. M.; White, L. R. J. Colloid Interface Sci. 1980, 77, 283. (54) Lima, E. R. A.; Biscaia, E. C., J. R.; Bostr€om, M.; Tavares, F. W. Force Between Two Similar and Two Dissimilar Charged Globular Proteins; Eleventh International Conference on Properties and Phase Equilibria for Product and Process Design - PPEPPD, 2007, Hersonissos, Creta. 9511

dx.doi.org/10.1021/la202023r |Langmuir 2011, 27, 9504–9511