1. science

Current Opinion in Colloid and Interface Science 9 (2004) 48–52
Why the properties of proteins in salt solutions follow
a Hofmeister series
¨ a,*, D.R.M. Williamsb, B.W. Ninhamb,c
M. Bostrom
b
a
¨
¨
Department of Physics and Measurement Technology, Linkoping
University SE-581 83, Linkoping,
Sweden
Research School of Physical Sciences and Engineering, Institute of Advanced Studies, Canberra, Australia 0200
c
Departments of Chemistry, Universities of Florence, Italy, and Regensburg, Germany
Abstract
The physical properties of hen-egg-white lysozyme, and other globular protein, in aqueous solutions depend in a complicated
and unexplained way on pH, salt type and salt concentration. One important and previously neglected source of ion specificity is
the ionic dispersion potential that acts between each ion and the protein. We present model calculations, performed within a
modified ion-specific double layer theory, that demonstrate the large effect of including these ionic dispersion potentials.
䊚 2004 Elsevier Ltd. All rights reserved.
Keywords: Hofmeister effect; Ionic dispersion forces; Lysozyme; Salt solution
1. Introduction
Colloid science and membrane biology can often be
described remarkably well using the electrostatic meanfield double-layer theory w1x. The only ionic property
included in this theory is the ionic charge. However,
there is nothing ion specific in this theory that can
explain why for example protein protonation depends
on the choice of background salt solution. Hofmeister
effects that are common in biology have presented a
mystery for more than 100 years w2●●,3● x. One important
source of ion specificity missed in the classical doublelayer theory is the ionic dispersion potential that acts
between an ion and an interface. Ions have in general a
different polarizability than the surrounding water (specific for each ion) and hence experience a very specific
dispersion potential near an interface w4●●,5x. At high
salt concentrations, where electrostatic potentials
become more and more screened, these ionic dispersion
potentials dominate the interaction completely. We have
in a series of publications demonstrated the importance
of including these ionic dispersion potentials in calculations of the air–water surface tension increment with
added salt w6●,7x, double layer forces w8x, ion condensation on micelles w9x and polyelectrolytes w10x, binding
*Corresponding author. Tel.: q46-13-28-8958; fax: q46-13137568.
¨
E-mail address: mabos@ifm.liu.se (M. Bostrom).
of peptides to membranes w11x, pH measurements
w12●●x, and the net charge of lysozyme w13●x.
In this paper we re-examine in some detail the role
of the dispersion force between a protein and the ions
in the surrounding ion cloud. The outline is as follows.
We describe in Section 2 the ion-specific double layer
theory that we use to model the properties of a globular
protein in a salt solution. We show why the net charge
is different in the presence of chloride and thiocyanate
salt solutions in Section 3. The apparent experimental
pKa values of ionisable groups have been shown to
depend on salt concentration and ionic species. We
demonstrate that this observation to a large degree is an
artefact of not taking ionic dispersion potentials into
account. We interpret the experimental observation in
terms of concentration and ion-specific surface pH (and
a constant pKa). We end in Section 4 with a few
concluding remarks.
2. Theory
We consider an aqueous solution of negatively
charged anions and positively charged cations each with
bulk concentration c and charge e outside a globular
protein. The protein is modelled as a homogeneously
˚ with
charged dielectric sphere of radius rp (16.5 A)
ionisable surface groups w14x. The calculations that we
present are for a hen-egg-white lysozyme at 25 8C, in a
1359-0294/04/$ - see front matter 䊚 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cocis.2004.05.001
¨ et al. / Current Opinion in Colloid and Interface Science 9 (2004) 48–52
M. Bostrom
sodium acetate buffer (cB"(`)s40 mM), and pH 4.3.
pH is defined as ylog10(cH gH), where cH is the
hydronium bulk concentration and gH is the activity
coefficient. We neglect any changes in the hydronium
ion bulk activity coefficient (i.e. we take Hq
s f
q
y4.3
Hq
M). The charge groups
r expŽybef., and Hr f10
of the lysozyme protein and the pKa values of these
groups are given in Refs. w13●,14x. While the pKa values
of the ionisable groups may change with salt concentration w15,16x, this effect is neglected since we here focus
on other effects of added salt. The average charge of an
acid group (qy) is given by the fractional dissociation
of the group qysyewH q xs y(wH q xs qKa ). Similarly, the
average charge of a basic group is qqseKa y(wH qxsq
Ka). The net protein charge, and the surface concentration of hydronium ions, must be determined selfconsistently with the non-linear Poisson–Boltzmann
equation,
´0´w d B 2 df E
Cr
FsyewycqŽr.ycyŽr.qcBqŽr.ycByŽr.z~
r2 dr D dr G
x
|
(1)
49
Fig. 1. The separation dependence of the ionic dispersion coefficient
(normalized to 1 far from the interface) as a function of distance
between ion and interface w17x. Four different model ions are consid˚ solid line); Cly (rions1.81 A,
˚ longered w18x: OHy (rions1.33 A,
˚ dashed line); and Iy (rions2.20 A,
˚
dashed line); Bry (rions1.96 A,
dotted line). Ion size effects will be considered in some detail in a
manuscript in preparation.
tion approximation be written
with the ion concentrations is given by
w
y
c"Žr.scexpŽyb "efqU"Žr.
x
z
~
.
|
(2)
with similar expressions for the sodium acetate buffer
(cB"(r)). Here bs1ykBT, kB is Boltzmann constant, T
is temperature, and ´w is the dielectric constant of salt
solution. Furthermore, f is the self-consistent electrostatic potential experienced by the ions, and U"(r) is
the interaction potential experienced by the ions. Our
purpose is to demonstrate effects of including ionic
dispersion potential that acts between ions and interface
(in general there will also be contributions from image
potentials; electrostatic; hard-core; and ionic dispersion
interactions between ions, and between ion and water
molecule). The boundary conditions follow from global
charge neutrality. The first boundary condition is that
the electric field vanishes at infinity faster than 1yr2.
The second is that
Žrpqrion.2
df
drrsrpqrion
i
syŽ8iq"
.y4p´0´w
(3)
Here we have made the plausible assumption that the
ions cannot get any closer to the effective protein surface
than one ion radius (rion). Usually, the difference in ion
size for similar ions is quite small and to highlight the
effects of dispersion potentials we take it to be the same
˚ The dispersion interaction between a
for all ions (2 A).
point particle and a sphere can within the pair summa-
U"s
B"
z
Žryr . 1qŽryrp.3yŽ2rp3.~
3w
p y
x
(4)
|
where the dispersion coefficient (B") will be different
for different combinations of ion and protein. We can
calculate it from the corresponding planar interface as a
sum over imaginary frequencies (ivnsi2pØkBTny",
where " is Planck’s constant) w4●●x
`
B"s 8
Ž2ydn,0.a"Živn.wy´wŽivn.y´oilŽivn.z~
x
4b´wŽivn.wy´wŽivn.q´oilŽivn.z~
x
ns0
|
(5)
|
One reason for introducing a cut-off distance between
ion and protein surface is that the dispersion potential
diverges on contact. In fact in a complete theory of
dispersion interactions the potential does not diverge on
contact. Mahanty and Ninham w17x demonstrated that
the effect of a finite ion radius could be taken into
account by multiplying the dispersion coefficient with a
function g(ryrp) shown in Fig. 1. We are currently
exploring how inclusion of finite size effects influences
surface tension of electrolytes and other specific ion
effects. Here we assume that the ions cannot get any
closer to the effective protein surface than one ion radius
and that g(ryrp)s1 all the way up to contact.
We model the excess polarizability of the ions using
the London approximation (assuming a single adsorption
frequency),
50
¨ et al. / Current Opinion in Colloid and Interface Science 9 (2004) 48–52
M. Bostrom
Fig. 2. Theoretical netcharge of a lysozyme globular protein as a function of salt concentration for the same system considered in Fig. 1.
As comparison we have added two experimental data points w5x (at
pHs4.5) for the netcharge in 0.1 M KCl (cross) and 0.1 M KSCN
(circle).
a"Živn.sa"Ž0.yŽ1qvn2 yv02.
(6)
The literature values for the static excess polarizabil˚ 3 for Kq, 2.10 A
˚ 3 for Cly, and
ities are w18x: 0.49 A
3
y
˚ for SCN . The effective resonance frequencies
4.59 A
(v0) for different ions are not known, but should be of
the order 1–2=1016 radys. We recently found similar
values for the excess polarizability using refractive index
changes with added salt w13●x. These estimates agree
reasonably well with a recent simulation of the polarizability of a chloride ion in water w19●● x. Using a model
dielectric function w20x for calf serum protein (most
proteins have similar densities and composition) and for
water we estimate that the dispersion coefficient for
SCNy near a protein should be of the order y5 to
y25=10y50 J m3. Similar but smaller magnitudes are
expected for Kq and Cly. Considering the approximations used this only give us an order of magnitude
estimate for the ionic dispersion potential.
(dotted line). The calculated net protein valency (Zp) as
a function of salt concentration is shown in Fig. 2.
There is a large degree of ion specificity found for the
net protein charge. The cross (circle) in Fig. 2 represents
the experimentally obtained net charge of lysozyme at
pH 4.5 in a 0.1 M KCl (KSCN) salt solution. We see
that inclusion of the ionic dispersion potential can
explain the observed ion-specific charge.
It is the surface pH, rather than bulk pH, that is
important for surface groups. The surface pH is highly
ion-specific w13● x. Lee et al. w15x found that the apparent
pKa values of histidines depend on salt concentration
and ionic species. Since surface pH depends on both
salt concentration and ionic species it is natural to
question the origin of the salt sensitivity of the pKa
values. We will now explore how the average net
valency (zq) of a histidine charge group in our model
globular protein, as a function of bulk pH, varies with
the choice of salt and with concentration. The average
net valency is
zqs
10ypHs
10
q10ypKa
ypHs
(7)
where as before we take the pKas6.0. The average net
valency as a function of bulk pH is shown in Fig. 3.
We consider two different model salt solutions (Bqs
0=10y50 J m3) and two different concentrations: Bys
0 J m3 (circles); Bysy20=10y50 J m3 (squares);
0.1 M (solid symbol) and 0.5 M (open symbol). For
comparison we have also added a curve when the surface
pH is replaced with the bulk pH (crosses). If Fig. 3 had
3. Hofmeister effects in lysozyme
The pH dependent lysozyme net charge in KCl
solutions has been deduced from titration experiments
w16x. There is nothing in the ordinary double-layer
theory that explains why the lysozyme net charge at pH
4.5 is 10 for 0.1 M KCl and 10.5 for the same
concentration of KSCN w21x. As we will demonstrate a
new understanding begins to emerge when we include
ionic dispersion potentials.
We consider a charged lysozyme under the conditions
described in Section 2. We consider four different cases
(Bqs0 J m3): Bys0 J m3 (solid line); Bys
y10=10y50 J m3 (dashed line); Bysy15=10y50 J
m3 (dashed–dotted line); and Bysy20=10y50 J m3
Fig. 3. The average net valency of histidine as a function of pH in
the bulk reservoir. We consider two different model salt solutions (as
before we take Bqs0=10y50 J m3) and two different concentrations:
Bys0=10y50 J m3 (circles); Bysy20=10y50 J m3 (squares); 0.1
M (solid symbol) and 0.5 M (open symbol). For comparison we have
also added the corresponding curve when the surface pH is replaced
with the bulk pH (shown as crosses).
¨ et al. / Current Opinion in Colloid and Interface Science 9 (2004) 48–52
M. Bostrom
shown experimental titration curves the natural conclusion w15x would have been to assume that the histidine
pKa (note: pHsspKa when zqs1y2, the apparent pKa
can be taken to be equal to pHr at this point) depend
on concentration and on the ionic species. We are not
saying that the pKa values of histidine and other ionizable charge groups on proteins never change with added
salt, or that they cannot follow a Hofmeister series.
However, it appears that concentration and ion-specific
changes in surface pH due to ionic dispersion potentials
can by itself account for the experimental observation.
One very important reason that the apparent pKa values
are higher in thiocyanate than in chloride is that thiocyante anions are much more attracted by ionic dispersion potentials towards the protein surface than chloride.
These attractive potentials reduce surface pH, so that
one must go to a higher bulk pH to obtain the same
effect. The importance of ionic dispersion potentials
becomes increasingly important as the salt concentration
increases, consistent with the observation that the importance of Hofmeister effects increase with concentration.
4. Conclusions
Ninham and Yaminsky w4x proved that the standard
DLVO theory of colloid science—and by immediate
extension the Onsager Samaris theories of interfacial
tension and of the double layer, standard theories of
electrolyte activities and solubility and pH are all fundamentally incorrect even at the level of the primitive
model. This is because by treating electrostatics at a
non-linear theory and quantum electrodynamic forces in
a linear theory (Lifshitz or its extensions) they violate
the Gibbs adsorption equation and gauge condition on
the electromagnetic field. The theory becomes consistent, and an understanding of the Hofmeister effect is
emerging, when ionic dispersion potentials are included
in the theory.
While we get the right order of magnitude for the
surface tension of electrolytes w6x when we include ionic
dispersion potentials it appears that the theoretical Hofmeister sequence is in the wrong order compared to the
experimental result. One reason for this must be that it
is not sufficient to only take image potentials and ionic
dispersion potentials into account. We will discuss a
few possible additional effects later. Nonetheless the
point is that we can no longer ignore dispersion forces.
A very important point is that our theory has the
limitation of the primitive model, i.e. the assumption
that an interface can be modeled by treating the solvent
as if it has bulk properties up to the interface. This
approximation is shared by standard treatments of electrostatic contributions. The interfacial tension problem
requires the inclusion of a profile of solvent not just by
correct treatment of the Gibbs dividing surface, but also
the modification through, e.g. the inclusion of ion-
51
induced surface dipole correlations. The importance of
this has been clearly demonstrated in simulations by
Jungwirth and Tobias w19x. It is now clear how to make
further progress in the theory by taking into account the
change in dielectric properties of water near the interface. We will come back to this vital question shortly
in a subsequent publication.
There may of course be other effects that can influence the Hofmeister effect. A few examples include:
water structure w22x; different ion size; co-ion and
counterion exclusion w23x; and dissolved gas w24x. There
will also be an important role for ionic dispersion
potentials acting between ions w25●●x and between ions
and water molecules. A detailed theoretical understanding of the Hofmeister effect most likely also requires
that one include hydration forces. We do not role out
the possibility that there may also be some influence
from the effective interaction between an ion and a
hydrophobic particle caused by a large dipole moment
¨ w26x.
of medium molecules as argued by Karlstrom
However, we have clearly demonstrated that ionic dispersion potentials have an important rule for the
observed ion specificity of, for example, globular proteins w13●x, membrane bound proteins w27x, and
membrane potentials w28x.
Acknowledgments
Financial support from the Swedish Research Council
is gratefully acknowledged.
References and recommended reading
● of special interest
●● of outstanding interest
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