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Interactions of Macromolecules with Salt Ions: AnElectrostatic Theory for the Hofmeister Effect

Huan-Xiang Zhou*Department of Physics and Institute of Molecular Biophysics and School of Computational Science, Florida State University,Tallahassee, Florida

ABSTRACT Salting-out of proteins was discov-

ered in the nineteenth century and is widely used

for protein separation and crystallization. It is gen-

erally believed that salting-out occurs because at

high concentrations salts and the protein compete

for solvation water. Debye and Kirkwood suggested

ideas for explaining salting-out (Debeye and Mac-

Aulay, Physik Z; 1925;131:2229; Kirkwood, In: Pro-

teins, amino acids and peptides as ions and dipolar

ions. New York: Reinhold; 1943. p 586 622). How-

ever, a quantitative theory has not been developed,

and such a theory is presented here. It is built on

Kirkwoods idea that a salt ion has a repulsive

interaction with an image charge inside a low dielec-

tric cavity. Explicit treatment is given for the effect

of other salt ions on the interaction between a salt

ion and its image charge. When combined with the

Debye-Huckel effect of salts on the solvation energy

of protein charges (i.e., salting-in), the characteris-

tic curve of protein solubility versus salt concentra-

tion is obtained. The theory yields a direct link

between the salting-out effect and surface tension

and is able to provide rationalizations for the effectsof salt on the folding stability of several proteins.

Proteins 2005;61:69 78. 2005 Wiley-Liss, Inc.

Key words: Hofmeister effect; salting-out; protein

solubility; protein stability; Debye-

Huckel theory

INTRODUCTION

In the nineteenth century it was discovered that varioussalts at high concentrations could precipitate proteins.1

This salting-out effect has since been found to be a verygeneral phenomenon, occurring not only on proteins but

also on amino acids and even simple gas molecules.2,3 Asystematic study of salts on the solubility of hemoglobinwas done by Green,4,5 whose data are reproduced in Figure1. These data show three characteristics: (1) an increase insolubility at low salt concentrations; (2) a decrease insolubility at high salt concentrations, with a linear slope;(3) the salting-out slope has a distinct order with respect todifferent types of salts, which is now known as theHofmeister series. It is generally accepted that character-istic (1) arises from the Debye-Huckel effect on the solva-tion energy of the protein charges. However, the situationswith characteristics (2) and (3) are much murkier.6

Hofmeister1 suggested thatsalting-out wasdue to dehydra-

tion of the protein by the added salt. This concept wasreinforced by Debye and MacAulay7 in arguing that thesalt ions would attract the highly polar water molecules.Kirkwood8 approached the salting-out problem on asounder statistical mechanical basis. He too consideredthe interaction of a salt ionwith the solvent and recognizedthat, when a salt ion is near a less polar protein molecule,an image charge is induced and a repulsive interactionbetween the salt ion and its image charge arises. Here wedevelop Kirkwoods idea further into a theory that qualita-tively explains characteristics (1) and (2).

Kirkwood made calculations for the interaction of a saltion with its image charge inside a low-dielectric sphericalcavity. The model, shown in Figure 2(a), is closely relatedto one Kirkwood9 and later Tanford and Kirkwood10 usedfor calculating the solvation energy of protein charges. Themajor difference is that a protein charge is located insidethe low-dielectric cavity, therefore interaction with itsimage charge in the solvent is attractive, whereas a saltion is located in the high-dielectric solvent, thus interac-tion with its image charge in the cavity is repulsive. Thisunfavorable interaction energy is

u i0riei

2

2ri1p

1s

l1

lR/ri2l1

l l 1s/p(1)

whereRis the radius of the low-dielectric cavity,pand sare the low and high dielectric constants, andeiandriarethe charge and the radial distance of the salt ion. Whenother salt ions are present, the interaction energy will bestrongly affected. An initial treatment of this effect, basedon the linearized Poisson-Boltzmann (PB) equation and

valid at low salt concentrations, has been presented previ-ously.11 Here extension to arbitrary salt concentrations ismade through the use of the nonlinear PB equation. Such

an extension is important because salting-out is mostly

TheSupplementary Materialsreferred to in this article canbe foundat http://www.interscience.wiley.com/jpages/0887-3585/suppmat/

Grant sponsor: The National Institutes of Health; Grant number:GM58187.

*Correspondence to: Huan-Xiang Zhou, Department of Physics andInstitute of Molecular Biophysics and School of Computational Sci-ence, Florida State University, Tallahassee, FL 32306. E-mail:zhou@sb.fsu.edu

Received 6 January 2005; Revised 2 February 2005; Accepted 4February 2005

Published online 25 July 2005 in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/prot.20500

PROTEINS: Structure, Function, and Bioinformatics 61:6978 (2005)

2005 WILEY-LISS, INC.

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manifested at high salt concentrations. It should be notedthat the PB equation is a mean field model with limita-tions such as the neglect of ionion correlations.

As is well known, the characteristics of salt effects onprotein solubility are also seen on a wide range of otherphenomena.12 One such phenomenon is the increase inwaterair surface tension by added salts. Onsager andSamaris,13 following earlier work by Wagner,14 explainedthe increase in surface tension, , as the result ofdepletion of salt ions near the water-air interface, due tothe repulsion between the salt ions and their imagecharges.increases almost linearly with salt concentra-tion. Here the use of the nonlinear PB equation is shown to

improve predictions of surface-tension increase.For a macromolecule with fixed charges embedded in-side, the effects of mobile salt ions in the solvent can beformally divided into two contributions [Fig. 2(b)]. Thefirst contribution is the work, wout (for salting-out), tocharge up the salt ions while the macromolecule is totallydischarged. The second contribution is the work,win(forsalting-in), to charge up the macromolecule in the pres-ence of the fully charged salt ions. The salt ions change thechemical potential of the macromolecule, relative to thesituation where no salt ions are present in the solvent, by

wout win (2)

win is negative because salt ions increase the magnitudesof theimage charges of protein charges andthus strengthentheir favorable interactions. This term accounts for theinitial rise in protein solubility (i.e., salting-in). wout ispositive due to the repulsive interactions between salt ionsand their image charges. The close connection betweensurface-tension increase and the salting-out work will beshown to be captured by an approximate relation,

wout kBT0A (3)

wherekBTis the product of the Boltzmann constant andthe absolute temperature, is the mean diameter of thesalt ions,0is the salt concentration, and Ais the surface

area of the macromolecule. As the salt concentrationincreases, the magnitude of wout increases more rapidlythan that ofwin, leading to salting-out. It should be notedthat there are also salts, notably those of iodide andthiocyanate (SCN), that exhibit salting-in behavior athigh concentrations.3,15 The physical origin of this salt-ing-in effect is distinct from that for winin Equation 2,and has been suggested to be some unknown chaotropic(i.e., water structure breaking) effect or favorable interac-tions with peptide groups. This second type of salting-in isoutside the scope of the present theory.

At high concentrations, many salts are found to stabilizeproteins, again with exceptions such as SCN 1619 The

Fig. 1. Dependence of the solubility of horse carbonmonoxy hemoglobin on concentrations of seven salts.Lines are drawn to guide the eye through the data points, which are taken from Green.4,5

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shown that i(rri) satisfies the nonlinear Poisson-Boltz-mann equation

irri4eir ri 4i

eiirri (9)

Note that there are three distinct regions: in both r RandR r Rithe source terms on the right-hand side areabsent, but pin the former and sin the latter; in r

Ri the source terms are present and s. At theboundaries r R and r Ri, i(rri) and the normalcomponent of i(rri) satisfy continuity conditions. Weemphasize again that, for the present calculation, salt ion iis assumed to be fixed whereas all other salt ions areassumed to be mobile.

If the Boltzmann distribution in Equation 8(a) is ex-panded, and terms up to the first order are retained andassumed to be applicable even whenr ri , then oneobtains the linearized PB equation:

iLrri4eir ri s2

MriLrri (10)where the electrostatic potential is now denoted as iL(rri),

M(r) is a masking function that is 1 for r Ri and 0otherwise, and is the Debye-Huckel screening parametergiven by

2 4i

i0ei2/s (11)

The linearized PB equation can be solved analytically. Theresult can be expressed as

iLrrieigrri

For r Rione has

grriexpr ri

sr ri g1rri

l0

glr;riPlcos

(12a)

with

glr;r 2s

2l 1il1/2rAlkl1/2rkl1/2r

(12b)

and

Al Ylil1/2Ri Ll YlRiil3/2Ri/2l 1]

Mlkl1/2Ri

(12c)

where

Ll 1 l lp/s (12d)

Yl 1 p/slR/Ri2l1 (12e)

Ml Ll Ll YlRikl1/2Ri/2l 1kl1/2Ri

(12f)

and il1/2(x) and kl1/2(x) are modified spherical Besselfunctions.

The nonlinear PB equation has to be solved numerically.Here we chose to find i(rri) by iterating an implicitequation starting from iL(rri). The desired implicit equa-tion, for r Ri, is

irri iLrrid3rgrr

i

eiirri s2/4Mrirri (13)

Details of the solution are given in the SupplementaryOnline Material.

Work of Charging up a Fixed Salt Ion

When the linearized PB equation is used, the work forcharging up the fixed salt ion i at riis

uiLriei2g1riri/2 (14)

When Ri 3 R, Equation 14 reduces to a result derivedpreviously.11 With the nonlinear PB equation, one has touse a more general expression for the work, which can bederived through a charging process. It has been shownthat three different processes lead to the same result forthe work of charging up a fixed charge distribution.21 Theresult for the fixed salt ion i is21,22

uirieiiriri/2rri

d3rMrkBTi

i01

eeiirri irrii

eii0eeiirri/2 (15)

where a prime indicates that an infinite term leading tothe self-energy of the salt ion has been subtracted. Thecharging process of later interest is one in which thecharges on both the fixed salt ion and all other salt ions areincreased from zero to their respective full values. Theother salt ions will redistribute in response to the chargingprocess. The work expanded when all the charges are onlya fraction of their full values will be denoted as ui(ri;).The result in Equation 15 corresponds to 1.

One may interpret ui(ri) as the potential of mean force of

the fixed salt ion. The sign ofui(ri) will be positive becauseof the repulsive interaction with its image charge, while itsmagnitude will decrease with increasing ri. One thusexpects a depletion of salt ions near the surface of thelow-dielectric cavity. The mean density of species i saltions at ri(Ri) is given by

iri i0expuiri (16)

It is understood that any nonzero value ofui(ri) at infiniteseparation is to be subtracted from ui(ri), so ui() 30.

Throughout this work, unless otherwise indicated, pwas taken to be 4, and swas assigned the value of thedielectric constant of water at the appropriate tempera-

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ture (which is 78.5 at 25C and 63.7 at 70C). Though highsalt concentrations are known to decrease the bulk dielec-tric constant of aqueous solutions,23 given the depletion ofsalt ions near the macromolecular surface, the exact valueof the dielectric constant there is uncertain. Such complica-tions are avoided in this study.

Work of Charging Up the Equilibrium Distribution

of All Salt Ions

Consider again the process in which the charges on allsalt ions are increased from zero to their respective full

values. This time each salt ion is allowed to redistribute.Let us look at an intermediate step during this chargingprocess, at which the charge of species i is ei. When thecharge is further increased by dei for each species, theadditional work for charging up a salt ion that is of speciesi and located at r is dui(r;)/.

Considering that the density of species i ions at r isi(r;), the total work for charging up all salt ions in anequilibrium distribution is

wout 0

1

did3rir; uir;

0

1

did3ri0Mreuir;uir;

kBTi

i0d3rMr1euir (17)Note that the sum in Equation 17 is the total deficit of saltions around the low-dielectric cavity.

Work of Charging Up the Macromolecule: Spherical

Boundary

The electrostatic potential (r) originated from a fixedcharge distribution inside the macromolecule,

prj

qjr rj (18a)

satisfies the PB equation

r4pr 4i

eiir (18b)

where the density of the salt ions isir i0Mrexpeir (18c)

The work for charging up the macromolecule is21,22

win j

qjrj/2d3rMrkBTi

i01eeir

ri

eii0eeir/2 (19)

where a prime signifies elimination of the self-energy. Thequantity winappearing in Equation 2 is the difference

between Equation 19 and its counterpart when salt ionsare absent.

When the PB equation is linearized, the potential isgiven by9,10

Lr

jqj

pr rj

1

p

1

s

j

qj

Rl0

l 1rrj/R2lPlcosj

Ll

j

qj

sRil0

2l 1Xlrrj/Ri

2lPlcosjLlMl

(20)

forr R, wherejis the angle betweenrandrjandXlRikl1/2(Ri)/kl1/2(Ri). Note that the first two termsgive the result in the absence of salt ions and the last termgives the contribution of the salt ions to L(r). The work for

charging up the macromolecule becomeswin;L

j

qjLrj/2 (21)

The solution for r Riwill become useful shortly, whichcan be written as

Lrj

qjhrrj (22a)

where

hrrj1

sRil0

2l 1rj/Rilkl1/2rPlcosj

Mlkl1/2Ri (22b)

Solution for (r) was obtained by iteration starting fromL(r). The appropriate implicit equation is

r Lrd3rgrr

i

eiir s2/4Mrr (23)

Forr Ri,L(r) is given by Equation 22(a) andg(r|r) isgiven by Equation 12(a). Once (r) is obtained by iterationfor r Ri, it can be used in Equation 23 to calculate its

values forr R. In that regionL(r) is given by Equation20 and g(r|r) is the same as h(r|r), which is given byEquation 22(b). Details of the solution are given in theSupplementary Online Material.

Work of Charging Up the Macromolecule: Arbitrary

Boundary

It was shown previously that the values ofwin calculatedby the nonlinear and linearized PB equations were notsignificantly different.21 The reason is that, given the largedifference between sand p, the influences on the poten-tial (r) inside the macromolecule as modeled by the two

versions of PB equation are comparable. The nonlinear

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version slightly increases the magnitudes of the imagecharges of protein charges, making the first term inEquation 19 somewhat more negative. However, even thissmall change in the first term is partially offset by theaddition of the second term in Equation 19, which isalways positive. The solution of the nonlinear PB equation

for a spherical macromolecule via Equation 23 allows forfurther comparison of the results for wincalculated bythe two versions of PB equation.

For realistic modeling of the salting-in work, the linear-ized PB equation with the actual shape and charge distri-bution of horse carbonmonoxy hemoglobin was solvednumerically by the UHBD program.24 The protocol followsour previous studies.20 On the PDB entry 1g0b25 hydrogenatoms were added and energy minimized by the CHARMMforce field.26 CHARMM charges were assigned to proteinsatoms. Around the pH (6.6) where the solubility wasfound to be minimal and its salt dependences were mea-sured,4,5 hemoglobin has a net charge close to zero (with 58

Asp and Glu residues balanced by 58 Lys and Arg residues,but with some of the 28 His residues at least partiallycharged). The boundary of the low dielectric cavity wastaken as the outer van der Waals surface of the proteinmolecule. Any voids inside the outer van der Waals surfacewere assigned the low dielectric constant. The electrostaticpotentialL(r) was calculated first on a 100 100 100grid with a 1.5- spacing and then on a 140 140 140grid with a 0.5- spacing.

In ourprevious work,20 results ofwin;L fortwo cold shockproteins using their actual shapes and charge distribu-tions were calculated. These are used here to predict thetotal effect of salts on the folding stability.

RESULTS AND DISCUSSIONPotential of Mean Force of a Salt Ion Around a Low-

Dielectric Cavity

Figure 3(a) shows the potential of mean force,ui(ri), of asalt ion in a 1 M 1:1 salt with an exclusion diameter of 4 outside a 16- spherical cavity at 25C. The value ofui(ri)is0.4kBTat contact and extends about 6 . In compari-son, the potential of mean force, uiL(ri), calculated by thelinearized PB equation has a slightly higher contact value(0.5 kBT) but decays more rapidly.

Determinants ofwout

The integration of 1 exp[ui(ri)] gives the salting-out

work wout (Equation17). For the case shown in Figure 3(a),wout is 3.06 kBT. If the linearized PB were used, wout wouldbe underestimated by 21%. The underestimate growswith salt concentration.

The value of woutshows a nearly linear increase withsalt concentration 0, except at low 0. Overall, the saltdependence can be fitted to [Fig. 3(b)]

wout a01/2 b0 (24)

For the 1:1 salt with 4- outside a 16- sphericalcavity, the fitting parameters are a 1.04 and b 2.00when the salt concentration is in moles (wout is dimension-less). Reducing the exclusion diameter of the 1:1 salt

results in an increase in wout. At 3 , the fittingparameters become a 1.28 and b 1.94. From theresults at 3 and 4 , one may obtain values ofwoutatother exclusion diameters by interpolation or extrapola-tion. In particular, the interpolated fitting parameters for 3.5 are a 1.16 and b 1.97. At a highertemperature, the dielectric constant of water decreases,leading to an increase in wout. At 70C, the interpolatedfitting parameters for 3.5 rise to a 1.22 and b 2.01. Later, KCl and NaCl will be modeled as 1:1 salts withexclusion diameters of 4 and 3.5 , respectively.

Fig. 3. a:The potential of mean force of an ion in a 1:1 salt with 4 at 1 M. The cavity radius is 16 . b:The dependence of the salting-outwork on salt concentration for the 1:1 salt with 4 . The curve is a fitaccording to Equation 24.

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As may be expected, woutincreases with the chargeeionthe salt ions. For a hypothetical 31/2:31/2 salt with 4 ,which mimics a 1:2 salt such as Na2SO4, the fittingparameters become a 1.33 and b 5.12 at 25C. The

value ofwout increases linearly with the surface area of thelow-dielectric cavity.

Magnitude ofwin: Modest Difference Between

Nonlinear and Linearized PB

In a previous study, it was found that the nonlinear andlinearized PB equations do not predict significantly differ-ent results in winfor typical proteins.

21 This finding isconfirmed in the present work for spherical macromol-ecules. For example, for a macromolecule with a 16-radius in a 0.1 M 1:1 salt at 25C, when 25 positive unitcharges and 24 negative unit charges are randomly distrib-uted on a interior shell 2 from the surface, winis 2.32kBTaccording to the nonlinear PB equation and 2.17 kBTaccording to the linearized equation. When there are 40

unit positive charges and 30 unit negative charges,w

inbecomes 16.9 kBTand 15.6 kBT, respectively,accordingto the two versions of PB equation. Increasing the ionicstrength further reduces the relative difference betweenthe two calculations ofwin.

The modestdifference between the nonlinearand linear-ized PB estimates ofwin is in contrast to what is found forwout. The disparity can be attributed to the fact thatthe source forwin, i.e., the protein charges, resides in thelow-dielectric cavity, whereas the source for wout, i.e., thesalt ions, resides in the high-dielectric solvent. For the re-sults presented below, winwas obtained by solving thelinearized PB equation with the actual shapes and chargedistributions of particular proteins.

Effects of Different Salts on the Solubility of

Hemoglobin

When the solution phase and crystalline phase of aprotein come to equilibrium, the protein concentration inthe solution is the solubility. The solubilities in the pres-ence and absence of salt ions, S and S0, respectively, arerelated to the change in chemical potential of the protein, of Equation 2, via

kBTlnS/S0 wout win (25)

which assumes that the chemical potential in the crystal-line phase is not affected by salts.27 In applying Equation

25, wout for a particular protein was obtained by scalingthe result for a 16- cavity with an adjustable effectiveradiusReff:

wout wout16 Reff/162 (26)

but winwas calculated through the linearized PB equa-tion using the actual protein shape and charge distribu-tion.

Figure 4 shows the calculated changes in hemoglobinsolubility by three salts: NaCl, KCl, and Na2SO4. To avoidcomplications due to small errors caused by using thelinearized PB equation for calculating win (see above)and possible salt ion binding to the protein,18 only results

at salt concentrations higher than 0.1 M are presented.Qualitative agreement with the experimental data ofGreen4,5 is obtained for all the three salts when theeffective radiusReffis taken as 23.2 .

Surface-Tension Increases by Different Salts

The low-dielectric cavity is equivalent to an air bubble.When the radius R 3 , the surface of the cavity becomean infinite flat air-water interface. Technically it is moreappropriate to assign a dielectric constant of 1 to air.However, as Onsager and Samaris13 noted, the depen-dence of the salting-out work has only a weak dependenceon p (due to the large s/p ratio). Indeed Onsager andSamaris carried out their calculations specifically for p0, for which the mathematics is significantly simplified.Calculations here with the spherical cavity also confirmedthe very weak dependence ofwoutonp.

Qualitatively, the positive potentials of mean force ofsalt ions around the low-dielectric cavity lead to a deficit

around the cavity (Equation 17). This deficit in turnresults in an increase in surface tension. If the total deficitof salt ions per unit surface area is , then the surfacetension can be determined from28

d di (27)

whereiis the mean chemical potential of the salt ions.Neglecting the contribution of the activity coefficient ofsalt ions, one has

i kBTln0 (28)

Integrating Equation 27, one obtains for the surface-tension increase

kBT0

0

/0d0 (29)

Equation 17 gives the deficit of salt ions for r Ri R /2. It should be noted that salt ions are completelyexcluded between R and Ri. This salt-free layer alsocontributes to the deficit of salt ions. The contribution ofthe salt-free layer has been widely invoked.2932 Thedeficit of salt ions per unit area due to the salt-free layeramounts to 0. Together with Equation 17, one has

0 wout/A (30)

whereA 4R2 is the surface area of the spherical cavity.Note that since woutincreases linearly with A, the ratiowout/A is independent of the size of the cavity. Forconcreteness, calculations of were made using theresults for the 16- cavity. With the salt dependence ofwoutgiven in Equation 24, one obtains

kBT0 2a01/2 b0/A (31a)

k BT0 wout/A (31b)

Rearrangement of Equation 31(b) leads to the result givenin Equation 3.

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Using the values of the fitting parametersaandblisted

earlier, the surface-tension increases are found to be 1.42,1.51, and 1.99 dynes/cm, respectively, at 1 M solutions ofNaCl, KCl, and Na2SO4. The corresponding experimentaldata are 1.62.1, 1.6 1.9, and 2.93.0 dynes/cm.33,34 Thepresent study improves the work of Onsager and Sa-maris13 in two respects: (1) the salt-free layer is explicitlytaken into consideration; (2) the nonlinear PB equationinstead of the linerized version is used. The first improve-ment was also made in the recent work of Ohshima andMatsubara.32 The use of the nonplinear PB equation heremoves electrostatic theories of surface tension one stepfurther. The remaining discrepancy with experimentaldata perhaps can be attributed to lost dispersion interac-tions suffered by salt ions when they are near the air-water interface (in bulk solution each salt ion is sur-rounded by the solvent in all directions; not so when it isnear the interface).35

Effects of NaCl on the Stabilities of Cold Shock

Proteins

When a protein is unfolded by denaturation, salt ionswill affect the native and denatured states differently,resulting in a shift in the folding equilibrium. The changein free energy in one mole of protein molecules by salt ionsin either the native or denatured state is

G wout win

(32)

where the superscript N for the native and D for the

denatured states. The second term, win

, has been specifi-cally studied in previous work.20 In the native state,inN is

the difference in the work of charging up a folded proteinmolecule in the presence and absence of salt ions. Thedenatured state has been modeled as individually solvatedresidues plus residual electrostatic interactions betweencharged residues:20,36

winDwin(residue)win(interaction) (33)

Only charged residues are included in the calculation ofwin

D . For calculating win(residue), a charged residue iscarved from the folded molecule and solvated. The residualinteraction energy,win(interaction), between two charged

residues in the denatured state, is calculated as theaverage of the Debye-Huckel interaction potential be-tween two point charges,

win(interaction) qjqj

srjjerjj (34)

over a Gaussian distribution for the residue-residue dis-tance rjj.

Results ofwinN and win

D for a pair of cold shock proteins,Bc-Csp and Bs-CspB, have been presented in our previousstudy.20 These two proteins differ in only 11 of 66 posi-tions, with Bc-CspB also having an extra residue at the Cterminal. The net charges at pH 7 are very different, 2e

Fig. 4. Solubility of hemoglobin calculated according to Equation 25.winwas calculated by numericallysolving the linearized PB equation with the actual shape and charge distribution of hemoglobin. wout wasobtained from the result for a 16- cavity by scaling according to Equation 26, with Reff 23.2 . NaCl and KClwere modeled as 1:1 salts with exclusion diameters of 3.5 and 4 , respectively; Na 2SO4was modeled as asymmetric salt with charges 31/2eand an exclusion diameter of 4 . The results at 0.1 M salts were used asreference. Experimental data are as shown in Figure 1.

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for Bc-Csp and6efor Bs-CspB. It was assumed that thesalting-out contribution

Gout woutDwout

N

to the unfolding free energy is identical for the twohomologous proteins. The differential effects of NaCl onthe unfolding free energies of the two proteins, measuredby Perl and Schmid,17 were rationalized by the salting-incontribution

Gin

winD

winN

A main cause for the differential effects of NaCl on thefolding stabilities was attributed to the difference in netcharges.20,37

The Goutterm can now be calculated. For this purpose,the folded molecule is modeled as a cavity with an effectiveradiusReffand wout

N is evaluated according to Equation 26.For the denatured state, each residue (charged or neutral)is modeled as a small cavity, with an effective radius reff.The total salting-out work in the denatured state is

woutD nreswout16 reff/162 (35)

wherenresis the number of residues in the protein. WithReff11.5 and reff2.4 , it is possible to reproducewell the experimental salt dependences of the unfoldingfree energies of both cold shock proteins (Fig. 5). Since thedenatured state has a larger surface area (nresreff

2 Reff2 ),

the salting-out work favors the native state and ultimatelyleads to its stabilization. A similar calculation withReff16 and reff 2.4 has been found to reproduceexperimental data for the effect of KCl on the stability ofthe 107-residue FK506 binding protein.38

CONCLUSIONS

We have developed an electrostatic theory for the inter-actions of macromolecules with salt ions. Salt ions are

found to have two opposing effects on the chemical poten-tial of the macromolecule. A salting-in effect arises be-cause salt ions strengthen the favorable interactions be-tween macromolecular charges with the solvent. A salting-out effect arises because salt ions induce repulsiveinteractions with image charges inside the low-dielectric

macromolecular cavity. Two kinds of experimental dataare analyzed: protein solubility and stability. Rationaliza-tions are provided in both cases. A direct link betweensalting-out and surface-tension increase is also obtained.

Do interactions other than the electrostatic type consid-ered herealso playimportant roles? In consideringsurface-tension increase by salt ions, lost dispersion interactionsnear air-water interface have been implicated. However,around a macromolecular surface, lost dispersion interac-tions with solvent are replaced by gained dispersioninteractions with the macromolecule. Thus to a crudeapproximation the loss and gain cancel each other andthere is no net effect from dispersion interactions. How-ever, the cancellation may not be complete and there couldbe subtle effects from dispersion interactions. These subtleeffects may well be specific to each ion species and there-fore contribute to the ordering of the Hofmeister series[characteristic (3) listed in Introduction]. In particular,anions such as I and SCN appear to have excessivesalting-in effects.3,15 These have been attributed to achaotrope mechanism or to favorable interactions withpeptide groups.

The electrostatic theory for salt ions developed here isbased on a continuum solvent model. Molecular dynamicssimulations with explicit water are providing insights onthe details of the interactions of salt ions with water andmacromolecules.3944 These insights may spur further

theoretical developments for the effects of salt ions.In conclusion, the electrostatic theory presented heremay find applications in understanding the effects of saltions on a wide range of properties of proteins, includingaggregation, crystallization, and halophilicity.

ACKNOWLEDGMENTS

I thank Robert L. Baldwin for discussion. This work wassupported in part by NIH grant GM58187.

REFERENCES

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