Liquid Expanded Monolayers of Lipids As Model Systems to

J. Phys. Chem. B 2009, 113, 1447–1459

1447

Liquid Expanded Monolayers of Lipids As Model Systems to Understand the Anionic Hofmeister Series: 1. A Tale of Models E. Leontidis* and A. Aroti Department of Chemistry, UniVersity of Cyprus, Nicosia 1678, Cyprus

L. Belloni CEA/SACLAY, LIONS at SerVice de Chimie Mole´culaire, 91191-Gif-sur-YVette Cedex, France ReceiVed: October 24, 2008; ReVised Manuscript ReceiVed: NoVember 22, 2008

In this work, we use Langmuir monolayers of dipalmitoyl phosphatidylcholine (DPPC) as model systems to enhance the understanding of specific anion effects in physicochemical and biological systems. The 298 K isotherms (equation of state, EOS) of DPPC over solutions of a range of sodium salts depend strongly on the type and concentration of the salt in the subphase. We focus in particular on the liquid expanded phase region of the DPPC EOS and assume that the deviation of the isotherms over electrolyte solutions from that over pure water is due entirely to the charging of the lipid monolayer by the ions. We then examine the ability of a range of phenomenological continuum models to explain the pressure increase in the presence of electrolytes. The important finding is that insoluble lipid monolayers allow the discrimination between possible modes of ion-lipid interaction. Chemical binding models, simple or modified, cannot fit the range of data presented in this work. Both dispersion interaction and partitioning models fit most of the experimental isotherms and provide unique values for dispersion coefficients or ionic partitioning constants, respectively, even though the nature of these models is completely different (the former concentrates on the potential of mean force that acts on an ion in the double layer, while the latter concentrates on the treatment of interactions at the interface). Surprisingly, the respective fitting parameters are very highly correlated, reflecting, we believe, the effect of ion size on ionic properties and interactions. With sodium fluoride (NaF) as the subphase electrolyte, it is demonstrated that sodium exhibits a weak complexation-type interaction with the zwitterionic lipids. The simple dispersion and partitioning models cannot account for the NaF results, highlighting the need for more complex salt-lipid interaction models that account both for sodium binding and anion partitioning. This realization sets the stage for the companion paper. 1. Introduction The Hofmeister series ordering ions on the basis of their effects on protein solubility has puzzled scientists for more than a century, but no general consensus has been reached about the exact mechanism of specific ion action.1-6 Specific salt effects are important in a broad range of problems of physicochemical, biological, and environmental significance. In the past few years, research on specific salt effects has been reinvigorated by the advent of powerful new experimental methodologies and computer simulation methods. Through these recent investigations, new insights have been obtained, providing a large increase of scientific work on the origin of specific ion action at aqueous interfaces7-9 and forcing the scientific community to reconsider some traditional beliefs. For example, a major recent finding was that chaotropic ions favor surface solvation sites at the surfaces of water clusters10-14 and at electrolyte solution surfaces,15-51 challenging the old surface depletion picture of Onsager and Samaras.52 Why would chaotropic ions behave in such a counterintuitive way? A probable answer, first suggested in the seminal work of Collins53-56 and the computer simulations of Perera et al.,10,11 Jungwirth and Tobias,15-22 Karlstro¨m,13,14,23 and Dill24 and further supported by thermodynamic integration methods,28,29 may be surprisingly simple: * To whom correspondence should be addressed. E-mail: psleon@ ucy.ac.cy.

Ions are driven away from the air-water interface because of loss of water of hydration but are driven toward the air-water interface where a smaller cavity is needed to accommodate them, resulting in a smaller overall perturbation of the bulk water structure. In addition, the polarizabilities of both ions and water play an important and unexpected role, as significant dipole moments are induced on water and ions at the free water surface and the additional induced dipole interactions favor the surface sites.10,11,15-22,28,29 However, other explanations are also possible; Ninham and co-workers, who are responsible, to a large extent, for the general revival of interest in specific salt effects, have argued that the inclusion of dispersion interactions of ions with interfaces may explain most ion-specific phenomena.4,5,57,58 Ruckenstein argued that ion specificity may alternatively stem from the ionic response to the changing density and polarization of water close to an interface, proving that different mathematical formulations, based on completely different pictures of ion-interface association, can fit the surface tension of electrolyte solutions.59,60 These recent advances in our understanding of the presence of ions close to the free water surfaces of clusters and solutions can shed light into other specific salt effects. They suggest that a major part of specific ion effects may be based on collective rather than on local interactions, in contrast to “chemical” explanations of the Hofmeister series61-63 or the contact ion pair ideas put forward by Collins.53-56 This is still an open issue

10.1021/jp809443d CCC: $40.75  2009 American Chemical Society Published on Web 01/14/2009

1448 J. Phys. Chem. B, Vol. 113, No. 5, 2009

Figure 1. Three modes of specific ion interaction at a boundary between two phases, (a) local binding at available “strongly interacting” sites, (b) partitioning into the interfacial zone, and (c) inhomogeneous ion distribution due to interfacial field effects.

however: What really happens at interfaces where local ionic interactions with potential binding sites or with an adjacent phase are possible? Would the mechanism of specific ion effects be different in such cases; would the binding idea be revived? Two major problems exist when specific salt effects are examined at interfaces that contain potential binding sites. First, an electrolyte always contains an anion and a cation, which may both interact, often in distinctly different ways, with an interface. Second, one can visualize three different ways of specific ion interaction with an interface (Figure 1), (a) localized chemical binding at individual sites, (b) partitioning into the interfacial zone which behaves as a region with solvent properties different from those of the bulk, and (c) uneven distribution in response to local fields, as in the case of electrostatic interactions for ions of different sizes,64-66 or in the case of dispersion interactions,4,5,57,58 or in response to the inhomogeneous distribution of water itself, due to changing solvent polarization or changing ion hydration.59,60,67-71 In mathematical terms, binding phenomena would affect the boundary conditions of equations describing ion distributions, while dispersion and other field effects would affect the potential of mean force that an ion feels as it approaches an interface, that is, the equations themselves. Partitioning phenomena stand between these two extremes. It is difficult to devise experiments that would unequivocally discriminate between the three possibilities mentioned above; it is also critical to find proper model systems which will provide such discrimination. Recent attempts to directly measure the charge distribution at a soft lipid interface using X-ray reflectivity have provided disturbing clues that little can be learned by measuring quantities perpendicular to an interface between a lipid and an electrolyte solution because the existing experimental tools are still not refined at the scale for a few Å, with the result that interfacial fluctuations destroy vital information.72 In a way, this observation justifies Lyklema’s argument that hard surfaces should be chosen as model systems.63 The important recent work by Daillant et al.73-75 and Bergbreiter and Cremer76 has shown however that soft interfaces may provide insights, provided the proper techniques are used and the proper quantities measured. Recently, we have examined Langmuir monolayers of zwitterionic lipids at the surface of electrolyte solutions as model systems to examine specific anion effects,77,78 following a long and fruitful tradition of using Langmuir monolayers to simulate interactions at membrane surfaces.79,80 Considerable insights were gained from that exploratory experimental investigation. Working with a range of sodium salts, it could be proved that the disordered liquid expanded (LE) phase of DPPC becomes more favored in the

Leontidis et al.

Figure 2. Fluctuation phenomena associated with a spread lipid monolayer. Perpendicular to the interface, there exist positional and orientational lipid fluctuations and water density and polarization effects. Lateral fluctuations involve capillary waves and lipid clustering.

presence of salts but that even quite high salt concentrations do not significantly affect the lipid packing in the ordered liquid condensed (LC) phase. In addition, the effect of anions on the DPPC isotherms is strongly ion-specific and follows the established Hofmeister series.77,78 Langmuir monolayers of lipids provide a useful platform to investigate specific salt effects because the surface pressure can be precisely controlled and the effect of ions at a direction lateral to the interface can be assessed, where the interference of fluctuations can be expected to be smaller. In fact, lateral fluctuations, such as capillary waves, can be ignored since their wavelength is much larger than the relevant molecular scales. The only potentially troublesome lateral fluctuation may be inhomogeneity due to lipid clustering, but this should be minimal in the LE phase (see Figure 2). Monolayers of charged lipids have often been used in the past to investigate specific salt effects with considerable success.81-87 With zwitterionic lipids, the direct Coulombic interactions, which strongly attract one of the two ions of the electrolyte toward the interface and strongly repel the other, are subdued. In the present work, we use the DPPC monolayers as model systems in a much more quantitative way than hitherto. We focus on the liquid expanded phase of the DPPC monolayers and assume that the observed deviations of the DPPC isotherm in the presence of salts are entirely due to the ion-lipid association, which leads to double-layer formation at the lipid interface. We then apply a range of theoretical double-layer models containing appropriate ionic parameters. A model is considered satisfactory only if it can fit experimental results for a broad range of electrolyte concentrations with a single adjustable parameter for each ion. As will be seen below, this strategy allows the discrimination between binding, distribution, and partitioning phenomena. 2. Materials and Methods 2.1. Materials. The phospholipid DPPC (1,2-dipalmitoylsn-glycerophosphocholine) was obtained from Avanti Polar Lipids and used without further purification. Chloroform (p.a. grade, Merck, Germany) was used as a solvent to prepare 1 mM solutions of DPPC. Sodium salts were preferred over potassium salts in this series of experiments because some potassium salts are not very soluble and we need to reach high ionic concentrations in the Langmuir trough. All sodium salts were purchased from Merck with a purity of >99%, with the exception of the salts NaBF4 and NaSCN, the purity of which was >98%. The salts were baked in an oven at 300 °C for 2 h prior to solution preparation, with the exception of NaClO4 and

Liquid-Expanded Monolayers of Lipids As Model Systems

J. Phys. Chem. B, Vol. 113, No. 5, 2009 1449

Figure 4. Surface pressure increment of DPPC over NaF (empty symbols) and NaCl (filled symbols) solutions of various concentrations compared to that for pure water at 85 Å2 per molecule.

Figure 3. (a) Surface pressure-area isotherms of DPPC Langmuir monolayers over solutions of 0.5 M sodium salts in the area range between 80 and 90 Å2 per molecule. (b) Surface pressure-area isotherms of DPPC Langmuir monolayers over solutions of various concentrations of sodium thiocyanate.

NaSCN, which decompose at lower temperatures. At this point, it must be noted that salts obtained from different vendors contain different impurities and sometimes do not give identical DPPC isotherms or do not provide reproducible results. Salts from Merck were found to provide the most reproducible results. Salt solutions were prepared using ultrapure water (specific resistance of 18.2 MΩ cm) produced by a Millipore or a Sartorius reverse osmosis unit. 2.2. Pressure-Area Isotherms of Langmuir Monolayers. Isotherm measurements were carried out with a KSV 3000 Langmuir trough (KSV Instruments, Finland) equipped with a Wilhelmy plate for the determination of the surface pressure with an accuracy of (0.01 mN m-1. The effective trough surface area was 795 cm2, and the subphase volume was 1.2 L. All experiments were performed at (22.0 ( 0.1) °C. The temperature of the subphase was maintained constant with a Julabo recirculating thermostat. DPPC monolayers were obtained by spreading 90-100 µL of a 1 mM chloroform solution of DPPC on a painstakingly cleaned water surface. After 20 min of evaporation time for the spreading solvent, the surface pressure-area isotherms were registered while compressing the monolayers at a constant speed of 10 mm/min. Different solvent evaporation times (10-30 min) and different compression speeds (2-10 mm/min) were used as well and were found to have no systematic effect on the isotherms. For all concentrations of every salt used, the DPPC isotherms were measured as many times as necessary to obtain an accurate average isotherm. For salt experiments in a particular day, the DPPC isotherm over pure water was also measured as a basis for comparison. 3. The Experimental Database Figure 3a shows portions of the DPPC isotherms over 0.5 M sodium salt solutions in the range between 80 and 90 Å2 per

molecule. This range was chosen because the monolayer is then in the disordered liquid expanded phase, which was previously found to be clearly affected by the salts.77,78 In Figure 3a, we see that all isotherms remain roughly parallel to that over pure water in this area range. This is an important observation, implying that the change of surface pressure due to the salts is independent of the exact value of the lipid density in the liquid expanded phase. In addition, the increase of surface pressure in Figure 3a follows the series:

Cl- < Br- < NO3- < I- < ClO4- < SCNThis coincides with the classical Hofmeister series,1,2 although zeta potential measurements of phosphatidyl ethanolamine vesicles88 and NMR measurements of phosphatidylcholine bilayers89,90 suggest that ClO4- “associates” more strongly than SCN- with zwitterionic lipids. Similar data have been obtained at all other salt concentrations (results not shown). Figure 3b shows portions of π-Α isotherms of DPPC in the same area range, obtained over electrolyte solutions of varying NaSCN concentrations. As the salt concentration in the subphase increases, so does the surface pressure at any area in the range. This type of behavior has been observed for all salts used, with the exception of NaF. It is anticipated that fluoride ions, being very strongly solvated,91-93 do not associate with the lipids at all. In fact, the interaction of fluoride ions with phosphatidylcholine vesicles,94 with a phosphatidylcholine-loaded chromatographic column,95 and with a phosphatidylcholine-supported membrane96 were reported to be very weak. One might therefore expect no effect of NaF on the DPPC isotherm. However, a measurable effect is observed in Figure 4. The surface pressure at 85 Å2 is remarkably indifferent to NaF concentration at high salt but is higher than that over pure water. We believe this to be an indication of sodium association with the surface, as will be discussed below. NaCl behaves in an intermediate way as well, producing a rather slow increase of surface pressure at low concentrations and a gradually increasing effect at higher concentrations (Figure 4). 4. Mathematical Description of Models 4.1. Modeling Principles and Guidelines. The modeling efforts presented below address the previous experimental results and rely on the following points: (a) The lipids will be considered as a liquid expanded (LE) monolayer at 85 Å2 per molecule (roughly in the middle of the LE phase region at 22 °C). This is in fact a much larger molecular area than that attained in osmotic stress experiments on bilayer stacks97-102 or used in bilayer103-108,110,113 or mono-

1450 J. Phys. Chem. B, Vol. 113, No. 5, 2009 layer114 simulations. The latter areas range between 57 and 67 Å2 per molecule. (b) It will be assumed that the surface pressure increment with respect to that over pure water is mostly due to the ion-lipid interaction, which creates a net negative charge at the interface. Since the experimental results in Figure 3 show a Hofmeister-type anion effect, we concentrate mostly on the anion. This initial assumption is supported by equation-of-state data for DPPC lipid bilayers, where it was shown that NaCl and NaBr solutions do not provide measurable differences with respect to pure water; hence, Na+ must interact very weakly with zwitterionic lipids, if at all.101,102 Binding constants for sodium ions on zwitterionic bilayers have been reported in the literature, and they are much smaller than the corresponding values for chaotropic anions.89,90,115 (c) The lipids form a uniform, well-mixed layer on top of the electrolyte solution. Point (b) above contains, in fact, two major assumptions. Although the origin of the surface pressure increment is assumed to be purely electrostatic, other possibilities exist. A significant change of the average lipid tilt in the presence of salts could seriously affect the surface pressure,116,117 although such an explanation is hard to reconcile with the very systematic behavior observed in Figure 3a or with other similar results at higher salt concentrations. Recent molecular dynamics simulations of DPPC bilayers in the presence of NaCl, KCl, and other simple electrolytes provide rather conflicting information, on the basis of which weak salt effects on the lipid head group tilt or conformation may be expected.109,111,112 However, monolayers in the disordered liquid expanded phase are structurally quite different from bilayers. Regarding anion versus sodium binding, measurements of surface potentials of DMPC vesicles showed that the potentials become more negative in the presence of salts, supporting surface charging by anion-lipid association.94 On the other hand, sodium ions are known to associate with the carbonyl groups of glycerophospholipids,115 often forming complexes with two or more lipid molecules, as suggested by several recent MD simulations of bilayer membranes.103-113 We will see later (and especially in the companion paper) that the sodium-lipid association must in fact be invoked to explain the results obtained using subphase electrolytes with more kosmotropic anions, such as NaF. This association is also responsible for a sizable reduction of the area per molecule in bilayers, as reported by simulations.103,106,109,113 Point (c) above is also debatable, in view of the possible lipid clustering in the presence of sodium or other cations.109 The three alternative modes of specific ion-lipid interaction presented in Figure 1 will be examined in this work. The goal is to fit the surface pressure increments at 85 Å2 per molecule, at all concentrations of all electrolytes using a maximum of one parameter per ion. A sequence of local “chemical” binding models treats the situation depicted on the left-hand side of Figure 1 and follows the widely used philosophy of the chargeregulation approach.118-120 Chemical binding constants of ions to lipids are proposed as specific ionic parameters in this approach. The second method is based on the concept of ion partitioning within an active interfacial region,121 corresponding to the situation depicted in the center of Figure 1. The specific ionic parameters are now partitioning constants or chemical potential differences for the ions between the bulk electrolyte solution and the lipid-water interfacial region. Finally, we choose to study field effects by considering dispersion forces in the simplest possible way, assuming an additional Boltzmann factor for the ionic distribution in the diffuse part of the double

Leontidis et al. layer and a minimum distance of approach of the ions equal to the ionic radius.122 No other possible field effects are studied in this work. 4.1. Local Binding Models. Initially, we consider aniononly binding to the lipid head groups, which can be modeled as a chemical reaction of anion A- that binds to a neutral lipid L0 (DPPC) to form a charged lipid complex, LA-

L0 + A- f LA-

(1)

The assumption is that each anion associates with a single lipid molecule since no experimental or computational evidence exists, as far as we know, for the possible association of an anion with many lipid molecules simultaneously. In the case of DPPC, we have, of course, in mind the potential association between an anion and the choline group. The binding constant KA of the above reaction is defined as89,90,101,102,118-121

KA )

xb [LA-] ) 0 (1 - xb)C∞ exp(qeψ0 /kBT) [L ][A ]

(2)

where xb is the percentage of lipid molecules that have acquired a charge through anion binding, C∞ is the electrolyte concentration in the bulk, qe is the electron charge, kB is Boltzmann’s constant, and ψ0 is the electrostatic potential at the binding plane that is created due to anion adsorption on the lipid head groups. The surface charge density σ created by anion adsorption is given by the Grahame equation89,90,101,102,118-121

( )

σ ) √8kΒTC∞ε0ε sinh

qexb qeψ0 )2kΒT aL

(3)

where aL is the surface area per lipid molecule at the lipid-solution interface, and it is assumed for simplicity that the dielectric constant of water, ε, is everywhere equal to its bulk value. The minus sign on the right-hand side of eq 3 stems from the fact that the lipid surface acquires a negative charge upon anion adsorption (the electrostatic surface potential is negative). Working with the interfacial free energy or the grand potential for the electrolyte, one can prove that the electrostatic contribution to the surface pressure is given by an expression which also holds for a constant charge interface and is sometimes referred to as “the Davies equation” (see Appendix I)123

πsalt(aL) - πH2O(aL) ) ∆π(aL) ) 2kBT

( )

qeψ0 σ tanh qe 4kBT

(4)

For any assumed value of the binding constant KA, eqs 2 and 3 can be solved for σ, xb, and ψ0, and the surface pressure increment can then be calculated from eq 4. These equations can be easily modified to accommodate the possibility of ion pair formation in the bulk of the solution (here, C∞ must be reduced by an amount dictated by the ion pair formation constant in the bulk), a Stern layer for ions at the monolayer surface, or the possibility of independent 1:1 chemical binding of sodium to the lipids (binding of sodium to the phosphate or the carbonyl group of DPPC). In the latter case, the initial assumption that sodium is not playing a role is relaxed, but two chemical binding constants are required, one

Liquid-Expanded Monolayers of Lipids As Model Systems for the anion (KA) and one for sodium (KNa); the corresponding lipid fractions carrying a negative or a positive charge by adsorption are xb,A and xb,Na+

KA )

KNa+ )

xb,A [LA-] ) 0 (1 x x [L ][A ] b,A b,Na+)C∞ exp(qeψ0 /kBT) (5) [LNa+] ) [L0][Na+] (1 - xb,A

xb,Na+ (6) - xb,Na+)C∞ exp(-qeψ0 /kBT)

( )

qe(xb,A - xb,Na+) qeψ0 )(7) 2kΒT aL

while eq 4, which provides the surface pressure increment, remains unchanged. In this case, after assuming values for the two binding constants, one can solve the system of eqs 5-7 to obtain the surface mole fractions xb,A and xb,Na+, as well as σ and ψ0; then, from eq 4, the surface pressure increment is again calculated. 4.2. Model of Ionic Partitioning in a Diffuse Lipid Layer. Ion partitioning ideas are certainly not new, but recently, they have been applied to a variety of systems, including micelles,124-126 lipidmonolayers,78,127 bilayers,101,102,127 theair-waterinterface,128,129 and even the salting-out of peptides and proteins.130 Such models treat the interface between two adjacent “phases” as a different phase with distinctive properties, in which the ions may partition. The simplest partitioning models in the present monolayer systems are nonelectrostatic in nature and are based on the following principles: • Sodium is excluded from the monolayer “phase”. , is defined for each anion • A partitioning constant, Ki )Kbfs i i between the interfacial layer of width δ (phase “s”) and the bulk water (phase “b”).

Ki ≡

Kibfs

Cis nis ) ) C∞ AδC∞

(8)

Here Csi and C∞ are the molar concentrations of ionic species i in the surface layer and in the bulk, nsi is the number of moles of i in the surface layer, A is the total surface area of the interface, and δ the thickness of the layer available for ion penetration. • An expression for the free energy of the interfacial system is assumed, and the corresponding surface pressure difference (versus that over pure water) is obtained from

∆π ) -

water is replaced by an electrolyte solution) can be modeled in various ways. The assumption of random mixing of anions with lipids in the monolayer cannot explain the pressure difference data, as will be discussed later. Assuming however that hydrated anions i and hydrated lipid head groups mix in the lipid layer according to a regular solution scheme (although, strictly speaking, this usually applies to mixtures of molecules of similar size131), we postulate that

( ) ( )

nis nL nLnis ∆F + nL ln s + βi s ) nis ln s RT ni + nL ni + nL ni + nL (10) Combining eq 10 with eqs 8 and 9, we obtain the following expression for the surface pressure increment

Equation 3 then becomes

σ ) √8kΒTC∞ε0ε sinh


( ∂∆F ∂A )

T, δ, nL

(9)

Here, nL is the number of moles of lipid in the monolayer. Keeping δ fixed in the differentiation of eq 9 simply reflects the lack of precise knowledge about the structural changes in the monolayer upon compression in the liquid expanded phase region. ∆F (the free-energy change of the monolayer when pure

(

)

β-w_ wA∆π ) -w- ln nLRT 1 + w(1 + w-)2

w- ) K-AδC∞ (11) nL

where K_ is the anionic partition coefficient of eq 8. The first right-hand-side term in eq 11 is the ideal entropy of mixing of anions and lipid head groups in the monolayer. The “interaction term” contains an interaction parameter β_, the meaning of which is not clear since it may reflect direct anion-lipid interactions of any type or indirect interactions involving, for example, the exchange of water molecules of hydration or changes in solvation structure of one component because of the other’s presence. This lack of transparency, as well as the fact that eq 11 contains two parameters per ion (K_ and β_), renders this type of model less useful than single-parameter models. It is presented here however because, as we shall see, its parameters are correlated to those of the electrostatic model presented next. The latter is based on the concept of an active diffuse interface,121 as shown in the middle of Figure 1. The idea is that the interfacial layer “repels” hydrophilic ions while it “attracts” and partly dehydrates hydrophobic (or chaotropic) anions, reducing the free energy of the system by liberating water molecules (from the solvation shells of the hydrophobic anions), which are returned to bulk water. This model has some similarities (entropy of mixing, penetration) but also fundamental conceptual differences (nonlocal ion-lipid interaction, explicit electrostatics) from the previous regular solution model. It is also different from models of ion penetration behind surfactant head groups in monolayers, which have been used for a long time in the literature since the latter usually address counterions of charged lipids or are based on Stern-type pictures132-135 and do not assume “deeper” penetration behind the first headgroup layer.136,137 It is finally different from the models of Pegram and Record,128-130 which omit the influence of electrostatics. The present model is closer in spirit to the diffuse layer models for micelles described by Okada et al.124,125 or Baptista et al.126 and has already been applied to the interaction of anions with DPPC bilayers,78,101,102,127 while preliminary results of its application to Langmuir monolayers have also been reported.78,127 Equation 8 acquires a different form in this model, which acknowledges that even within the monolayer phase, ions are distributed unevenly due to electrostatics


(

Kibfs(x) ) exp -

Leontidis et al.

)

ziqeψ(x) + Ui Ci(x) ) kBT C∞

The interface (water-lipid) is divided in two regions. The top region (0 < x < δ) of layer thickness δ is playing an active role in the process of ion adsorption and is responsible for the ionic “selectivity” of the interface with respect to the bulk (δ < x < ∞). Specific ion partitioning is driven by a constant attraction potential Ui, which is essentially an ionic chemical potential difference between the interfacial layer and the bulk solution. The analysis is based on the solution of the Poisson-Boltzmann equation (PBE) in the two regions. To simplify the mathematics and avoid the introduction of additional parameters, we assume that the dielectric constant, ε, is everywhere equal to that of bulk water. For x > δ, the classical nonlinear PBE is applied, which has an analytical solution for a 1:1 electrolyte64

tanh

(

qeψ+U+ kΒT

)-q C e ( +

e ∞

qeψ-UkΒT

))

(14)

where Ui is taken here as a constant characteristic for each ion. By setting U+ f ∞ for 0 e x < δ, the cations are excluded from the monolayer phase. The resulting equation in this case is known to have the following analytical solution78,101,102,138

C-(x) )

C∞ cos2 Y

Y tan Y ) -κ sinh

C-(0) Yx cos2 δ

(15)

( )

where Y is defined as

)

(19)

ψδ 2

(20)

For a given U_ using a combination of eqs 17, 19, and 20, one can compute ψδ, Y, and C_(0) and then the complete ion concentration and electrostatic potential profiles. The surface pressure increment can be calculated from eq 9 through the appropriate free energy or the grand potential (see Appendix II) and is given by the following expression, if it is assumed that the partitioning constants U_ do not depend on the total area of the interface, that is, on the density of lipids in the liquid expanded phase (Appendix II)

{

(13)

where ψδ is the electrostatic potential at x ) δ and κ-1 is the Debye length. For 0 e x < δ and a 1:1 electrolyte, the PBE takes the following form

(

C-(0)

πsalt(aL) - πH2O(aL) ≡ ∆π(aL) ) kΒT 2

qeψ(x) qeψδ -κ(x-δ) ) tanh e 4kBT 4kBT

d2ψ 1 )qeC∞e2 ε ε dx 0

(

qeψδ ) U- + kBT ln

(12)

( ) }

qeψδ σ tanh + qe 4kBΤ

Y (2 tan Y - Y) (21) 2πLBδ In fact, the opposite assumption, namely, that U_ is proportional to the lipid density, hence to 1/A, leads to a different equation, which cannot fit the experimental data of the previous section. Comparing eqs 21 and 4, one finds that the first term on the right-hand side of eq 21 is identical to the right-hand side of eq 4, if ψδ replaces ψ0. This is the term that originates from the diffuse part of the double layer in the electrolyte solution. The second right-hand side term of eq 21 is a contribution from the anions penetrating the diffuse lipid layer. The complete model of eq 14 that allows sodium penetration in the lipid layer can only be solved numerically, and the surface pressure increment is then calculated from

{

C-(x) 1 + ε0εΕ2 + kBTC-(x) ln 2 C∞ C+(x) δ kBTC+(x) ln + 0 dx(C+(x)U+ + C-(x)U-) C∞

∆π )

∫0∞ dx

}

∫

∫0∞ kBT(C+(x) + C-(x) - 2Θ(x - δ)C∞) (22)

Y ) √2πLBC-(0)δ2

(16)

C_(0) is the anion concentration at x ) 0, given by

(

C-(0) ) C∞ exp

qeψ0 - UkBT

)

(17)

and LB is the Bjerrum length

LB )

q2e 4πεε0kBT

(18)

At x ) δ, the electrostatic potential and the electric field E ) -∇ψ calculated in the two regions must match. The following two conditions can then be derived

(see Appendix II). Here, Θ is a Heavyside step function. 4.3. Model of Specific Ion Distribution Due to Dispersion Forces. Ninham and Yaminski in their seminal work suggested that inclusion of dispersion forces between an ion and an interface can account for ionic specificity in several interfacial phenomena.4,5 Although the exact formalism of dispersion forces is quite complex,4,5,139,140 a simple approximate modification of the ionic potential of mean force has been suggested and used in several calculations to date.4,5,122,141-145 According to this scheme, the concentration of an ion at a distance x from a mathematically sharp interface is given by

(

Ci(x) ) C∞ exp -

ziqeψ(x) Bi kBT kBTx3

)

(23)

Bi, the dispersion coefficient, is the fitting parameter in this model. At a certain limit, related to the electronic resonance



TABLE 1: Fitted Anionic Parameters for the Regular Solution Model, the Partitioning Model (Assuming That the Penetrable Width of the Lipid Layer Is Equal to 10 Å), And the Dispersion Model (Assuming BNa ) +3 × 10-50 J m3) K_Aδ/nL /10-4 m3mol-1

ion ClCH3COOBrNO3ClO3IBF4ClO4SCNPF6-

β_

2.03 ( 0.13 2.53 ( 0.23

-2.97 ( 0.22 -3.74 ( 0.44

2.51 ( 0.25 4.60 ( 0.90 4.00 ( 0.73 3.69 ( 0.22

-6.93 ( 0.55 -3.65 ( 0.80 -5.50 ( 1.00 -8.77 ( 0.59

frequencies of ions, water, and “oil”, the Lifshitz theory provides the following approximate limiting expression for Bi close to a water-oil interface, similar to the lipid monolayer interface examined in this work4,5

(

Bi ) Ri(0) -

)

(24)

{

C-(x) 1 + ε0εwΕ2 + kBTC-(x)ln 2 C∞ C+(x) kBTC+(x)ln - kBT(C+(x) + C-(x) - 2C∞) (25) C∞

∆π )

∫a∞ dx

δ/Å U_/kBT (SCN ) U_/kBT (Br-) a

Here, Ri(0) and Rw(0) are the static polarizabilities of ions and water, respectively, υi and υw are the respective molar volumes, and ωi is a characteristic electronic frequency of ionic species i, while nw and no are the refractive indices of water and the lipid phase, respectively. From eq 24, it can be seen that, although Bi is expected to be positive for most ions at the air-water interface,4,5,141 this is not the case at an oil-water interface where no > nw. Only small ions with low polarizability may be expected to have a positive Bi coefficient (to be repelled) at the lipid-water interface. Since precise values of ionic frequencies and aqueous-phase ionic polarizabilities are not available for most ions studied in this work, we treat the anionic coefficient, B_, as a fitting parameter. BNa is of central importance in this model since it always appears for sodium salts. The current dispersion model can be competitive with other models only if the same BNa provides the optimal fit for all electrolytes. The model is numerically solved as any other double-layer problem using the Boltzmann factor of eq 23. Because the approximate dispersion potential Bi/x3 diverges as x f 0, we introduce a minimum distance of approach to the sharp interface equal to the ionic radius, a procedure used by others,122,141-146 although some authors have used complex functional forms for the dispersion potential, which do not diverge as x f 0.147,148 To simplify matters and avoid using further parameters, we have assumed the same ionic radius for all ions, equal to a ) 2 Å,143 a value representing a good average of reported ionic radii.149 We also assume that the dielectric constant of water is fixed up to the monolayer surface, although it has been found that inclusion of the actual density and dielectric profiles in a dispersion model improves its predictive behavior.146-148 With the ionic concentration and electrostatic potential in hand, the surface pressure increment is computed using eq 25 (see Appendix III for its derivation).

}

5. Discussion of Modeling Results 5.1. Fitting with the Binding Model. The application of the simple binding model (eq 4) to the DPPC isotherms in the

B_/ 10-50 J m3

-0.70 ( 0.10 -1.40 ( 0.05 -1.78 ( 0.05 -2.50 ( 0.05 -2.90 ( 0.05 -3.15 ( 0.10 -3.30 ( 0.10 -3.70 ( 0.05 -4.23 ( 0.10 -4.50 ( 0.10

-14.0 ( 0.4 -16.5 ( 0.5 -17.5 ( 0.5 -18.5 ( 0.5 -19.8 ( 0.4 -20.9 ( 0.5 -21.0 ( 0.3 -21.7 ( 0.4 -23.4 ( 0.4 -24.6 ( 0.2

TABLE 2: Fitted Values of the Partitioning Parameter U_ for Br- and SCN- Obtained by Changing the Thickness ∆ of the Lipid Layer, In Which the Anions Can Penetratea -

υi hωi 2 Rw(0) (n - n2o) υw 16 w

U_/kBT

6

8

10

12

14

-4.48 -2.10

-4.33 -1.92

-4.23 -1.78

-4.15 -1.68

-4.09 -1.59

UNa was set to +∞.

presence of various salt concentrations is presented in Figure 5 for NaBr, NaI, and NaSCN. It is obvious that the binding model cannot fit these data with a single value of the binding constant for each ion. The situation does not improve if ion pair formation is assumed for the bulk of the electrolyte (results not shown) or when a Stern layer for sodium is assumed. In the latter case, the sodium radius must be treated as an extra adjustable parameter, and reasonable fits are obtained for values of 4 Å or larger, which are unnaturally large. Furthermore, assuming that sodium can independently bind to lipid molecules in a 1:1 configuration (eqs 4-9) does not provide a solution, as is illustrated in Figure S1 in Supporting Information, in which we examine the NaI fits at 0.1 and 0.5 M and provide graphs of the binding constant of iodide versus that of sodium that fit the data in the two concentrations and find no pair of KI and KNa that can fit the data for both concentrations. The conclusion is that the simple chemical binding approximation, which has been used very extensively in colloidal and biophysical chemistry,67,89,90,118-121 cannot fit our monolayer data. A similar conclusion was reached in our recent investigations of DPC micelles121,127 and DPPC bilayer stacks.101,102,127 5.2. Fitting with the Partitioning (Ion Penetration) Model. The assumption of simple random mixing of ions and lipids in the monolayer (first right-hand side term in eq 11) will not fit the present surface pressure data. However, the full regular solution model of eqs 8-11 can provide satisfactory fits to the surface pressure increment versus concentration plots for all electrolytes (Figure S2 in Supporting Information). This is hardly surprising, of course, since the model contains two parameters per ion. The optimal values of K_δΑ/nL and β_ for the investigated anions can be found in Table 1. Although individual values of K_ and β_ are not very reliable, given the small number of data fitted for its ion (between three and six concentrations for the ions presented), the product K_β_ increases smoothly as the ions become more chaotropic. The partitioning model of eqs 13-21 is examined next. The anionic partition coefficient is not really independent of the penetrable lipid layer thickness, δ, as we shall see below, but to avoid introducing additional parameters in this model, we will assume that δ is equal to 10 Å for all concentrations of all ions. This is a reasonable average number, supported by most recent simulations of ions in DPPC bilayers.103-114 However, there is nothing fundamental about this value. Changing it will


Figure 5. Best fits of surface pressure increments for DPPC monolayers over electrolyte solutions at 85 Å2 per molecule calculated using the chemical binding model. Results for NaBr (experimental ) filled circles, model ) solid line), NaI (experimental ) open triangles, model ) dashed line), and NaSCN (experimental ) filled triangles, model ) dashed-dotted line) are shown.

Figure 6. Best fits of surface pressure increments for DPPC monolayers over electrolyte solutions at 85 Å2 per molecule calculated using the ion penetration model. Results for NaBr, NaI, and NaSCN are shown, as in Figure 5.

affect the values of the partitioning parameters U_ in a systematic way. The experimental results are fitted very well using the partitioning model with δ ) 10 Å, as can be seen in Figure 6 for three electrolytes. The success of the singleparameter partitioning model is remarkable and holds for all sodium salts examined in this study. Table 2 summarizes the values of U_ for SCN- and Br- that fit the data for a range of assumed δ values. The fits are good in all cases, and it can be observed that U_/kBT increases (becomes less negative) linearly with ln δ with a slope between 0.4 and 0.6 (Figure S3 in Supporting Information). This observation illustrates why it is reasonable to assume a single constant value of δ for all ions. Table 1 lists optimal U_ values (in kBT units) for all experimentally tested anions obtained for δ ) 10 Å. These U_ parameters are related to the parameters of the regular solution model listed in Table 1. In Figure S4 in Supporting Information, we observe a very good correlation between exp(-U_/kBT), a measure of the chemical partition constant, and the product K_β_, which suggests that the U_ parameters reflect both ion partitioning and ion-lipid (direct or indirect) interactions. Relaxing the assumption of total sodium exclusion, one can allow finite and even negative UNa values and try to fit the monolayer pressure data by applying eq 22. For most ions, it is found that only large, positive UNa values fit the data (see Figure S5 in Supporting Information, where the NaBr experimental data are presented with a number of best-fitting curves for various values of UNa). This finding highlights the weak

Leontidis et al.

Figure 7. Best fits of surface pressure increments for DPPC monolayers over electrolyte solutions at 85 Å2 per molecule calculated using the dispersion interaction model. Results for NaBr, NaI, and NaSCN are shown, as in Figure 5.

interaction of sodium with the DPPC monolayers in the LE phase and justifies the original assumption of omitting its interaction with the lipids. 5.3. Fitting with the Dispersion Model. For the dispersion model, we have undertaken from the beginning a two-parameter fit (BNa and Banion) for all electrolytes since the model relies on the modification of the potential of mean force in the diffuse double layer. The value of BNa was fixed at a specific value, and the value of Banion was varied to locate the minimum (leastsquares) deviation of the fit from the experimental results. Then the BNa was varied and the procedure repeated again. In most cases, depending on the quality of the actual experimental data, minimum deviations were found for positive values of BNa, ranging between 1.5 × 10-50 and 5.0 × 10-50 J m3. This is a very reasonable result, given eq 24, from which a positive BNa can be anticipated. With BNa fixed at +3.0 × 10-50 J m3, the values of the optimal dispersion coefficient for the anions are listed in Table 1, and characteristic fits are provided in Figure 7 for NaBr, NaI, and NaSCN. It is clear that the simple dispersion model can fit the surface pressure data equally well as the partitioning model. The B_ values in Table 1 are of the same magnitude as parameters reported by Boström, Deniz, and Ninham in their recent work.142,143 For example, these authors use the following B_ values to model electrolyte solutions between phosphatidylglycerol bilayers:143 -0.45 × 10-50, -3.6 × 10-50, -10 × 10-50, and -15 × 10-50 J m3 for Na+, Cl-, Br-, and SCN-, respectively. With the exception of sodium, for which we find a positive optimal value, the other numbers are quite similar to those reported in Table 1. Furthermore, Figure 8 reveals that a striking linearity exists between the ionic partitioning parameters and the ionic dispersion coefficients of Table 1. The models are widely different in other respects, as can be seen from the anion and cation concentration and potential profiles computed for 0.5 M NaI (Figure 9). In particular, the partitioning model concentrates anions within the lipid monolayers, behind the assumed position of the sharp interface used by the dispersion model. Why are the partitioning and dispersion parameters so strongly correlated? The most intuitive answer that we can offer at the moment is that both parameters reflect the ionic volume in the same way, as can be seen in Figure 10. Both the U_ and B_ parameters are similarly correlated to ionic volumes, and they correlate to each other even better! 5.4. Anions Not Interacting with DPPC. The Case of NaF. The experiments and theory discussed above concern sodium salts with chaotropic anions. It is reasonable to ask if sodium salts of hydrophilic anions have any effect on the surface


Figure 8. Correlation between the optimal anionic partitioning parameters, U_, obtained for δ ) 10 Å, and the optimal anionic dispersion coefficients, B_, obtained for BNa ) 3 × 10-50 J m3.


Figure 10. Correlations of the optimal partitioning parameters and dispersion coefficients of Table 1 with the partial limiting ionic volumes.

Figure 11. Surface pressure increments of DPPC monolayers in the presence of NaF. Optimal fitting attempts with the simple binding model (dashed line, optimal KNa ) 2.3 M-1) and the partitioning (continuous line, optimal UNa ) +0.10kBT) model.

Figure 9. Comparison of (a) anion and (b) cation double-layer profiles obtained with the partitioning (empty symbols) and the dispersion (filled symbols) model for the case of 0.1 M NaI. (c) Comparison of the corresponding electrostatic potential profiles.

pressure DPPC monolayers. It is not an easy task to select a proper salt since certain hydrophilic anions may interact with

DPPC in special ways. Sodium hydroxide cannot be used since DPPC becomes charged above a pH value of 11.115 Sodium sulfate was not used since we have opted to consider only monovalent anions in this investigation. Sodium fluoride appeared to be the most useful candidate for the examination of the effects of hydrophilic anions on DPPC monolayers. NaF induces a clearly measurable increase of the surface pressure of DPPC monolayers compared to that of pure water, as was seen in Figure 4. This is rather surprising since F- is expected to be expelled from the lipid layer. In addition, the surface pressure increase appears to be very insensitive to the concentration of NaF beyond 0.2 M, in sharp contrast to the results presented for other salts in Figure 3. This different behavior in the case of NaF can only be explained as a result of Na+ binding to the DPPC molecules. Many recent molecular simulations with a variety of force fields have demonstrated the coexistence of several complexes of sodium ions with one, two, or more lipids at DPPC bilayers.103-114 The simple 1:1 binding, the partitioning, and the dispersion model cannot fit the NaF results. The optimal curves for the binding and the partitioning model are shown in Figure 11. For the binding model, only sodium binding was assumed, while for the partitioning model, we have set UF f +∞. The two models cannot reproduce the plateau of surface pressure observed at high NaF concentrations. Regarding the dispersion model, we were obliged to take BNa ) +3 × 10-50 J m3, which is the value used to fit all other electrolytes. With this value, no large positive value for fluoride will provide even a remotely satisfactory fit for NaF; therefore, no curve obtained from the dispersion model appears in Figure 11. This failure shows that even the very successful models discussed in this

1456 J. Phys. Chem. B, Vol. 113, No. 5, 2009 paper have clear limitations, when applied to hydrophilic anions, and that a more general model, properly treating both anion and cation effects, must be constructed. This will be the task of the companion paper. 6. Conclusions In this work, DPPC monolayers at the air-water surface have been proposed as model systems to understand specific anion effects at interfaces. Sodium electrolytes had been shown before to affect the surface pressure isotherms of the monolayers and to promote the LE phase over the LC phase.77,78 We have opted to model the surface pressure of DPPC in the LE phase, assuming that the difference measured in the presence of electrolytes is a result of interfacial charging and not of a net change of the average head group dipole tilt. The results of the modeling efforts are illuminating. It turns out that simple or enhanced binding models, which assume that anions bind to the lipid head groups at a binding plane, cannot fit the experimental data by themselves. The data are instead very well fitted by a model which assumes that anions can partition within the lipid layer, in a region from which cations are excluded. This model is related to regular solution models, which assume cation exclusion from the lipid monolayer. The partitioning ionic parameters, U_, extracted from the data do not depend on actual lipid density (see Appendix II). This is indeed anticipated by the experimental fact that the DPPC isotherms in the presence of electrolytes remain roughly parallel to each other in the liquid expanded range. Do the current results prove that no anion-lipid binding takes place at these interfaces? Certainly not, but we get a strong indication that anion binding, if it exists, is not the dominant mode of interaction in this model system. Making more complex models, in which both binding and partitioning contribute, would not make sense since these would introduce at least two parameters per ion and would make interpretation of the results very difficult. A model based on dispersion forces, using a simple Sternlike minimum approach distance of the ions from a sharp interface, is similarly quite successful. In fact, the anionic fitting parameters derived from the two models are surprisingly strongly correlated to each other, even though the two models are based on different physical principles. We attribute this to the fact that they both reflect in practically identical ways the ionic volume; eq 24 implies that B_ should be roughly proportional to the ionic volume, if the frequencies ωi are of similar magnitude for most ions since the polarizabilites Ri(0) are roughly proportional to the volume. In addition, partitioning chemical potentials contain a cavity contribution150,151 that scales with solute area or volume.152,153 Although ion solvation is well approximated by a Born-like expression,154,155 if the cavity term dominates the association of the ions with the monolayer, then U_ may be expected to be roughly proportional to ionic volume. This point will be taken up in the companion paper. NaF was used as a prototype sodium salt with a hydrophilic anion. The surface pressure plot is very different in this case, and we were unable to explain it using the simple-minded models developed in this work, which either exclude cations or treat anions and cations on the same basis. Unfortunately, the two ions of an electrolyte are quite unsymmetrical with respect to their interactions with polar and nonpolar, hard or soft interfaces.1-5,53-56 Standard DLVO theory, which discriminates ions on the basis of charge only, cannot address this complexity,4-6,63,67,139 while using Stern layers with different widths for different ions63,139 simply introduces more and more fitting parameters that obscure all physical reality.

Leontidis et al. With the recent insights from molecular simulations of DPPC bilayers, we might have chosen to carry out this investigation with potassium instead of sodium salts since potassium is now believed to associate with lipids much more weakly.109,113 On the other hand, having chosen sodium instead, we are faced with a possibly more complex and more demanding modeling situation, which provides more insights into the actual nature of specific ion-lipid interactions. In the companion paper, we take up this challenge; we explain the NaF results with multiple binding models and formulate a more complex model which accounts both for multiple lipid binding to sodium ions and chaotropic anion penetration between the lipids. From this model, we then go on to sharpen our understanding of the effects of ions on zwitterionic lipid monolayers. Acknowledgment. The corresponding author would like to thank the University of Cyprus for a generous 3 year internal research grant (2005-2007) that enabled him to carry out this work. Appendix I Many ways exist to derive the Davies equation,123 but here, we use a free-energy technique in order to be compatible with the partitioning model outlined in Appendix II. The electrostatic excess contribution to the surface pressure is simply a derivative of the grand potential, Ω, with respect to the interfacial area, A, at constant temperature, total system volume, and number of lipid molecules (or surface binding sites)

∆πele ) -

( ∂Ω ∂A )

(A.I.1)

T,V,nL

The grand potential is given by

Ω ) U - TS -

∑ µiNi

(A.I.2)

i

where the energy, entropy, and chemical potential terms are given by

U)

-TSbulk ) kBT

kBT aL

A

∫ ε0εE2(x)dV

[( ( xb

(A.I.3)

{ (

∑ ∫ i

-TSsurf )

1 2

)}

µi0 Ci + ln xi - 1 dV kBT

(A.I.4)

)

0 µsite + ln xb - 1 + (1 - xb) kBT 0 µsite 0

kBT

{

µiNi ) (µi0 + kBT ln C∞)

)]

+ ln(1 - xb) - 1 dA (A.I.5) x

}

∫ CidV + A aLb dA

(A.I.6)

where the summations in eqs A.I.2 and A.I.4 go over all the ions. Equation A.I.4 is derived from the simple ideal entropy of mixing of ions in the diffuse layer. Equation A.I.5 is also an



ideal entropy of mixing of “sites” with bound ions and free sites at the binding plane. Similarly, in eq A.I.6, the contributions from ions in the bulk and those at the surface are clear. Now, we use the charge regulation expression for the anions

xb [LA-] KA ) 0 - ) (1 - xb)C∞ exp(qeψ0 /kBT) [L ][A ]

(2)

(

Ci ) C∞ exp -

Ω ) kBT

(A.I.7)

and the PBE ansatz for the ions in solution

(

ziqeψ Ci)C∞ exp kBT

)

(A.I.8)

to simplify the expression for the grand potential

[

(

qeψ qeψ 1 εε0(∇ψ)2 + 2C∞ sinh 2 kBΤ kBΤ kBT qeψ [xb ln xb + (1 - xb) ln(1 cosh + 1 dV + kBΤ aL

Ω ) kBT

∫

)]

A

0 xb) - xb ln(KAC∞) + µsite 0 /kBT - 1]dA (A.I.9)

The volume integral is identical to that obtained in the constant surface charge density case. Equation A.I.9 can acquire its most useful form by using eqs 2 and 3 of the main body of the paper and the Poisson-Boltzmann equation itself to carry out further simplifications. The result, after some mathematical work, is

Ω)

(

)

qeψ0 AkBT 0 2xb tanh + ln(1 - xb) + µsite 0 /kBT - 1 aL 4kBT (A.I.10)

Differentiating Ω with respect to A at constant T, V, and nL provides the Davies equation (eq 4 of the main body of the paper). Appendix II The derivation of the grand potential and the surface pressure contribution due to the ions is carried out using the methodology outlined in Appendix I. The first difference is the existence of an extra “energy” term because of the excess interaction potential of the ions with the lipids

U)

1 2

∫bulk εε0Ε2(x)dV + ∑ ∫surf layer CiUidV i

(A.II.1) The bulk mixing entropy is given by eq A.I.4, but there is no surface mixing term. Similarly, there is no surface term in eq A.I.6 this time. The PBE holds for the ions in the bulk, but inside of the lipid layer, we make a new ansatz

)

0

Liquid Expanded Monolayers of Lipids As Model Systems to

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