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Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 287–292

Electrostatics of phosphatidic acid monolayers:Insights from computer simulations

Jordi Faraudo a,∗, Alex Travesset b

a Departament de Fisica, Universitat Autonoma de Barcelona, Bellaterra, Spainb Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, United States

Available online 9 February 2007

bstract

In this paper, we argue that many of the fascinating electrostatic effects that take place in amphiphilic systems are strongly related to thearticular organization of the oxygen atoms within each individual molecule. In particular, we focus on two effects: charge inversion and dielectricverscreening. For that purpose, we present molecular dynamics simulations of phosphatidic acid (DMPA2−) in the presence of divalent counterions.ur results show that the many oxygens present in DMPA2− cooperatively create strong binding sites for counterions, which in some cases lead to

harge inversion. We also present an analysis of the role of interfacial water and relate our analysis to the phenomenon of dielectric overscreening.everal experimental implications are discussed in the conclusions. 2007 Elsevier B.V. All rights reserved.

ACS: 82.45.Mp; 61.20.Qg; 82.39.Wj

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eywords: Amphiphilic monolayers; Molecular dynamics simulations; Charge

. Introduction

Amphiphilic interfaces (surfactant monolayers, biologicalembranes, . . .) in contact with aqueous solutions exhibit,

nder certain experimental conditions, different non-intuitivelectrostatic phenomena with profound implications in theirhysico-chemical properties and technological or biologicalunctionality. Two fascinating examples are charge inversionnd dielectric overscreening. Charge inversion [1,2] consists inhe binding of counterions in excess of the bare charge of thenterface, thus leading to an interface whose effective chargeas opposite sign (see Fig. 1). Dielectric overscreening (Fig. 2)as its origin in a strong orientational polarization of interfacialater leading to an electric field near the interface which is larger

nd opposite than the electric field generated by the amphiphilesnd the counterions [3].

Traditionally, charge inversion has been analyzed in terms

f specific chemical mechanisms. However, the fact that chargenversion has been observed in a large variety of different sys-ems [4–9], suggests the existence of some general mechanism

∗ Corresponding author.E-mail address: jordi.faraudo@uab.cat (J. Faraudo).

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927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfa.2007.02.011

sion; Ion correlations; Dielectric overscreening; Interfacial water

esponsible for charge inversion. In the case of surfaces withniform charge distribution, charge inversion can be generatedy strong lateral correlations between counterions [1,2]. In thease of amphiphilic interfaces, charge inversion is highly spe-ific on the nature of the molecules forming the interface. Asn example, monolayers with a surface charge of σ ≈ −e/20 (innits of the elementary charge per A2) can be assembled eitherith DMPA2− near close packing conditions (area per phos-holipid ≈41 A2) or with fatty acids. Experiments found chargenversion for DMPA monolayers in contact with divalent coun-erions [8] but not for fatty acids [10]. Theories that neglectmphiphilic specificity by describing the interface by a uni-orm surface charge lead to the same predictions for both DMPAnd fatty acids, thus showing the necessity to include molecularetails of the interface in the description of the electrostatics ofany amphiphilic systems.Dielectric overscreening has been predicted to occur in

ifferent amphiphilic systems [11,12]. For example, simulationsf phosphatidylcholine (PC) bilayers predict a positive electro-tatic potential for the membrane (as compared with the bulk

olution), while the contribution of the PC lipids is negative. Theositive membrane potential results from the interfacial water,hich overcompen-sates the electric field created by the PC.ielectric overscreening contributes significantly to the electro-

288 J. Faraudo, A. Travesset / Colloids and Surfaces A: Ph

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ig. 1. Scheme of charge inversion in an amphiphilic monolayer. The chargeue to bound counterions is larger an opposite in sign than the charge of themphiphiles.

tatic interaction force between charged amphiphilic interfaces.n some amphiphilic systems, such as very thin SDS/water/SDSlms, dielectric overscreening is the mechanism behind the so-alled hydration force [13], which is responsible for the stabilityf the films as it has been shown in recent MD simulations [14].

Overscreening is just one example showing that interfacialater may show dramatically different properties than bulkater. We point out, however, that the properties of interfa-

ial water are expected to be highly non-universal, as precisexperiments of Langmuir monolayers of dihexadecylphosphateDHDP) in contact with monovalent salt solution are wellescribed by a bulk dielectric constant [15,16], while otherxperiments with mica surfaces show a drastic reduction of theater dielectric constant within the 10 nm next to the interface

17]. Also, hydration forces themselves are very specific, asany amphiphilic systems do not show any evidence of such

orces [13].Despite the wealth of phenomena observed, the different

xperimental examples mentioned so far are similar in that the

ig. 2. Sketch of the different contributions to the electrostatic potential of a PCr PS membrane as obtained in simulations [11]. The strongly polarized waterolecules generate an electric field which overcompensates that of the interface

dielectric overscreening).

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ysicochem. Eng. Aspects 300 (2007) 287–292

harged headgroups basically consist of many oxygen atoms.ow is it possible, therefore, that such similar interfaces display

uch disparate phenomena? Clearly, the answer to this questionequires investigations taking into account the atomic details ofhe molecules forming the interface. In this paper, we provide

united atom simulation for a 1,2-dimyristoyl-sn-glycero-3-hosphatidic acid (DMPA) monolayer in contact with a solutionontaining divalent Ba2+ ions. We have chosen this specific sys-em because experimental results do report charge inversion [8].urther interest in the properties of DMPA is provided by itsiological relevance, as phospholipids with the phospatidic acideadgroup play a fundamental role in a wide range of biologicalrocesses, including signal transduction, secretion or membraneusion. A detailed discussion on the biological implications forur results can be found in reference [18].

The organization of the paper is as follows. In Section 2,e briefly describe our simulations and discuss the mechanismsehind charge inversion in the view of simulation results. Inection 3, we discuss the role played by interfacial water in

he electrostatics of this system. Finally, we end up with theonclusions.

. Computer simulations of a DMPA monolayer

.1. Brief description of simulations

We have performed large-scale molecular dynamics (MD)imulation of DMPA2− monolayers in contact with aqueousolutions containing BaCl2. The chemical structure of theMPA2− molecule is shown in Fig. 3. Our MD simulationsere conducted with the DLPOLY2.15 simulation package [19]

unning at the new BSC Supercomputing facility using 64 dualowerPC 970FX processors. We employed the AMBER forceeld [20] modified according to reference [21]. Our system con-isted of 100 doubly deprotonated DMPA2− molecules (charge= −2e) placed at a water interface in contact with BaCl2 solu-

ion (150 Ba2+, 100 Cl− and 9132 H2O molecules) at 298 K. Theartial charges of the DMPA molecule are attributed as shownn Fig. 3. Water was modelled using the SPC/E model. DMPA

olecules were kept at close packing (molecular area ≈41 A2)uring the simulations, which ran over several ns. The conver-

ence of simulations during this simulation time was ensured bysing a block average analysis of the results. All technical detailsf simulations, including the details of the employed force fieldsnd algorithms can be found in reference [18].

ig. 3. Chemical structure of the DMPA molecule and its assignation of elec-rical charges. A, B, S, 2 symbols are used to distinguish among elements withifferent charge attributions.

J. Faraudo, A. Travesset / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 287–292 289

Fig. 4. Number of bound Ba2+ ions as a function of time. The time average isalso shown as a solid line. Inset: Probability that an ion bound at t = 0 remainsbp

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Fig. 5. Absolute value of the charge density (elementary charges per nm3) due tofree ions (diffuse layer) (Cl− squares, Ba2+ circles) and DMPA2− as a functionof the distance from the interface z (we show only the part of the diffuse layercloser to the interface). The position z = 0 is defined so that it corresponds to themIi

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This interpretation for the formation of complexes at the

ound at a subsequent time t. The solid line shows an exponential fit to therobability distribution.

.2. Presence of charge inversion in the DMPA monolayer

In analyzing our simulation results, we consider a counterions bound if it has a DMPA oxygen within its first coordinationhell (a maximum separation rmin = 3.5 A). In this way, we iden-ify a Stern layer formed by bound counterions and a diffuseayer of bulk counterions.

The number of bound Ba2+ in the Stern layer is shown in Fig. 4s a function of time. The average number of bound Ba2+, com-uted as its time average over equilibrium configurations, yieldsboundBa /NDMPA = 1.07 ± 0.01. Thus, the negative charge of theMPA2− is overcompensated by bound counterions leaving aositive interfacial charge of q = 0.14e per phospholipid. The facthat the fluctuations in the instantaneous value of the number ofound Ba2+ are rather small is an evidence of a very strong bind-ng of the counterions with the phospholipids at the Stern layer.nother evidence supporting this observation of strong binding

s provided by the probability p(t) that a counterion bound at= 0 remains in the Stern layer at a subsequent time t. We showhe results in the inset of Fig. 4, which are consistent with anxponential decay p ≈ exp(−t/τ) with a fitted characteristic timef about τ ∼ 16 ns.

The presence of charge inversion at the interface can also behown by analyzing the charge distribution in the diffuse layerdjacent to the interface. In Fig. 5, we show the electric chargeensity distributions along the direction perpendicular to thenterface due to bulk ions (Ba2+ and Cl−) and the phospholipidolecules. The diffuse layer shows an excess of negative charge

Cl−) next to the interface, in agreement with our previous find-ng of a positively charged Stern layer: the system exhibits chargenversion. In the inset of Fig. 5, we also show the charge distri-

utions within the Stern layer, showing that Ba and DMPA2−istributions are very similar, with the counterion distributionlightly shifted toward the aqueous solution, thus providing

iba

aximum of the probability distribution of the P atoms of the phospholipids.nset: Charge density due to DMPA2− phospholipids (triangles) and bound Ba2+

ons (Stern layer).

dditional evidence that Ba ions are tighly bound to DMPAeadgroups.

.3. Complex formation and binding sites for counterions

In our simulations, we observe that the binding of counte-ions induce a significant restructuring to the DMPA interface.he distribution of bound counterions is not homogeneous asan be observed in the snapshot shown in Fig. 6. Typically, aa2+ ion is bound to an average of 6.2 oxygen atoms from 3

o 4 DMPA2− molecules. Also, some oxygen atoms from 3 toDMPA2− molecules are shared by 2 counterions, as can be

een in Fig. 6. The system as a whole contains many complexesnd holes, defined as regions without phospholipid headgroupsan example of a hole can be seen in Fig. 6). Given that theimulations where performed at the close packing density ofydrocarbon chains, the presence of holes is indicative of thetrong structuring induced by the binding of divalent ions.

The origin of the complexes formed by counterions and phos-holipids can be traced to the oxygen atoms within the DMPAolecules, which create binding sites for counterions. In order to

rovide some insight on the structure of these effective bindingites for counterions, we have computed the cumulative chargeear a bound counterion. As shown in Fig. 7, the charge inontact with bound counterions (r ≈ 3 A) is about −4.5, con-istent with each counterion binding to an average of 6 oxygentoms with charges −0.7 or −0.8. Positive partial charges fromMPA and neighbouring counterions increase the cumulative

harge significantly, reaching a plateau of −4 at distances about∼ 7 A. At larger distances (not shown in Fig. 7) the cumulativeharge approaches the total charge of the interface.

nterface is also consistent with the observed radial distri-ution functions gOBa2+(r) between counterions and oxygentoms from phospholipid molecules. A simple approximation to

290 J. Faraudo, A. Travesset / Colloids and Surfaces A: Physicochem. Eng. Aspects 300 (2007) 287–292

Fig. 6. Snapshot showing a lateral view of the phospholipd monolayer and bound counterions. Red and yellow balls are O and P atoms from DMPA, blue balls areBa2+ counterions. For clarity, hydrocarbon chains are shown as thin lines and water molecules are not shown. Also, we show a magnification of a patch of the interfacea n a hole without headgroups or counterions, a DMPA2− bound to 4 counterions (A)a ). (For interpretation of the references to colour in this figure legend, the reader isr

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s seen from the aqueous solution (top view). In this patch, it can be clearly seend counterions bound to 4 or 3 DMPA2− (labeled with B and C, respectivelyeferred to the web version of the article.)

OBa2+(r) assumes an effective electrostatic energy between aounterion and a binding site E/kT ≈ 2Qeff

I lB/r, where QeffI ≈

4 and the parameter lB = e2/4πεkT ≈ 7 A is the Bjerrum length22]. Then, the radial distribution function gOBa2+(r) is giveny:

OBa2+(r) ∼ exp(−2QefflB/r). (1)

he gOBa2+(r) computed from simulations is shown in Fig. 8.s expected, it vanishes for distances smaller than the crystallo-raphic radius of Ba2+ and O (≈3 A). The approximation giveny Eq. (1) describes very well the first peak observed in theimulations with Qeff ≈ −4, in agreement with our analysis ofhe cumulative charge around bound counterions (Fig. 7). Weoint out that this effective charge is twice the nominal chargef the DMPA molecule. This doubling of the charge is possi-le because of the many oxygen atoms within conformational

egrees of freedom, which optimize the binding of counterions.

The charge inversion in our simulations results from the for-ation of electrostatic complexes at the interface. The observed

harge inversion is about 1.07 Ba2+ ions per DMPA. An obvious

ig. 7. Total charge within a distance r from a bound Ba2+ counterion due tohospholipid molecules and neighbouring counterions. In this calculation, theharge of the counterion at r = 0 is not included. The solid line is only a guideo the eye.

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ig. 8. Plot of the pair distribution functions gOBa2+(r) as a function of r, for

2 and OS oxygens (see Fig. 3).

uestion is the maximum amount of charge charge inversion thatan be observed with PA. This is estimated from the observationhat each Ba2+ counterion is typically bound to 6 oxygen atomsrom 3 to 4 different DMPA2− molecules. There are 8 oxygenser DMPA molecule and only 6 of them are, on average, usedor binding, but a few O are shared by two Ba2+, as shown inig. 6. In a hypothetical situation were all oxygens were used,harge reversal would reach a value Nupper ≈ 6/8 = 1.4NDMPA.bviously, this maximum charge reversal would imply that allare used for binding, which may be prevented from packing

onstraints and the connectivity of the hydrocarbon chains, butt the same time, it is observed that some oxygens are shared,hich might roughly compensate for the packing constraints.

. Role of interfacial water

.1. Interfacial water

The first step in order to study the effects of interfacial waters to compute the amount of hydration water of the interface, Nw.he calculation of this quantity is difficult, because one needs to

ake into account not only the hydration of counterions but also

J. Faraudo, A. Travesset / Colloids and Surfaces A:

Fig. 9. Number of oxygen atoms from water molecules in the first coordinationsai

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wazissato the charged species and is positive (we recall that there ischarge inversion in our simulations). On the other hand, thecontribution of water molecules is negative and is significantlysmaller than the contribution from ions and phospholipids (see

hell of Ba2+ ions (for the cases of bound ions and bulk ions) as a function of timend number of interfacial water molecules per phospholipid. The time averages also shown in the figure.

he hydration of the charged groups in the phospholipids. Forhis reason, we have evaluated Nw following a simple procedurehat was introduced and tested in reference [23] for SDS/waternterfaces. The basic idea of the method is as follows. First, oneomputes the number of water molecules Ns

wh with z > 0 (weecall here that z = 0 was defined as the position of the maximumf the density distribution for P atoms). These water moleculesorrespond to the hydration of the “inner” side of the mono-ayer, in contact with the hydrocarbon region. The hydration inhe opposite side of the monolayer (z < 0) is more difficult tobtain because we have both water molecules corresponding toydration layers and bulk water molecules. However, it has beenhown [23] that a reasonable estimation of Nw can be obtainedy assuming that the interface is similarly solvated in both sides,o the amount of solvation water will be approximately giveny Nw ≈ 2Nhs

w . As expected, the results for Nw as a functionf time (Fig. 9) show small fluctuations around a mean value,emonstrating that the system contains a well-defined amountf interfacial water. The equilibrium value for Nw is then com-uted as a time average over equilibrium configurations. Ouresults give an equilibrium amount of interfacial water about.4 water molecules per phospholipid molecule. For compari-on, let us recall that a SDS monolayer (a system which showstrong effects due to interfacial water) typically contains 2.2ater molecules per amphiphilic molecule [23].The reason for this large amount of interfacial water is the

resence of bound divalent ions which retain, after binding, aignificant part of their hydration shell. In order to quantify thisffect, we have computed the number of oxygen atoms fromater molecules in the first coordination shell of bulk and bound

ounterions as a function of time. As expected, the results (Fig. 9)

how only small fluctuations around equilibrium values, demon-trating that both bulk and bound counterions have well definedydration shells. Free counterions have 9.4 water molecules inheir first hydration shell, whereas bound counterions have 4.45

FllN

Physicochem. Eng. Aspects 300 (2007) 287–292 291

ater molecules. Hence, counterions lose roughly half of theirydration sheaths in binding to O, replacing about 5 oxygentoms from water molecules by an average of 6 oxygen atomsrom DMPA molecules. This replacement of oxygens from waterolecules by oxygens from another molecule is somewhat rem-

niscent of ion selectivity in ion channels [24]. Further detailsf hydration shells and its relation to biological processes isiscussed in reference [18].

It is also interesting to note that some of the hydration waterolecules are shared by several counterions. This effect can be

learly shown by noting that if they were not shared the inter-ace would contain about 4.45 × 1.07 ≈ 4.76 water moleculeser phospholipid, which is larger than our previous estimate of.4 water molecules per phospholipid.

.2. Effect of interfacial water in the electrostatic potential

In order to investigate the possible presence of dielectric over-creening in our system, we have computed the electrostaticotential using the integrated form of the Poisson equation:

(z) = φf(z) + φw(z)

= −1

ε0

∫ z

zB

∫ z′

zB

ρf(z′′) dz′ − 1

ε0

∫ z

zB

∫ z′

zB

ρw(z′′) dz′′ dz′,

(2)

here ρf(z) is the charge density due to charged species (DMPAnd ions), ρw(z) the charge density due to water molecules andB is a reference point in the electrolyte solution, far from thenterface, in which the potential is defined to be zero. The electro-tatic potential ϕ(z) and the contributions ϕf(z) from the chargedpecies (DMPA and ions) and ϕw(z) from water moleculesre shown in Fig. 10. The main contribution to ϕ(z) is due

ig. 10. Different contributions to the electrostatic potential obtained in simu-ations for the DMPA monolayer: contribution from interfacial water (dashedine), from ions and amphiphiles (dotted line) and total potential (solid line).ote that in this case no dielectric overscreening is observed.

2 A: Ph

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branes, Perseus Publishing, New York, 1994.[23] F. Bresme, J. Faraudo, Langmuir 20 (2004) 5127.

92 J. Faraudo, A. Travesset / Colloids and Surfaces

ig. 10). Hence, the total electrostatic potential ϕ(z) is posi-ive and increases monotonically from a reference value of zeron the electrolyte solution toward a constant potential at theydrocarbon region of about 2.5 V. This increase in the elec-rostatic potential is generated within a very thin region of aew A near the phospholipid headgroups. It is also interesting toote that the surface potential (∼2.5 V) is only slightly smallerhan the bare potential generated by the DMPA and the ionswhich is about 3.3 V), which is essentially generated at the Sternayer.

The contribution of water to the surface electrostatic poten-ial is modest, only about −0.8 V. This water contribution is, inbsolute value, much smaller than the contribution from ionsnd phospholipds and reflects that no dielectric overscreeningakes place. The differences in the electrostatic potential betweenystems showing dielectric overscreening (such as PC and PS−i-layers) and our results can be clearly observed by comparingig. 2 with Fig. 10.

. Conclusions

We reported a MD simulation of a DMPA2− monolayer inontact with an aqueous solution containing BaCl2. Our resultshow the exceptional ability of DMPA to create binding sitesor counterions. These binding sites consist of arrangementsf oxygen atoms, which as a result of its strong electroneg-tivity, retain significant electric charge even when they areart of neutral groups (see Fig. 3). The strongly cohesive bind-ng sites lead to charge inversion by formation of electrostaticomplexes involving several counterions and other atoms fromMPA2−. We predict a maximum charge inversion of 1.4 coun-

erions per DMPA, in agreement with the experimental resultf 1.3–1.5 counterions bound per DMPA reported for this sys-em [8]. Our results suggest that charge inversion is a commonffect in amphiphilic systems that contain many oxygen (or otherlectronegative atoms) within groups that have conformationalegrees of freedom. The electrostatic mechanism observed inur simulations allows them to create highly cohesive bind-ng sites for multivalent ions. The fact that fatty acids do notxhibit charge inversion despite having the same surface charges DMPA, can be understood from the fact that fatty acids onlyave two oxygens per molecule compared with the eight oxygensn DMPA. A similar situation also occurs for DHDP (dihexade-yl hydrogen-phosphate) [16], which has four available oxygens.n the other hand, it should be expected that charge inver-

ion is a common effect in membranes of biologically relevantharged phospholipids, such as phosphatidyl serine (PS), phos-hatidylinositol or glycolipids, such as the gangliosides, whichontain more than 10 oxygens per molecule and can becomeultiply charged. Charge inversion in PS has been observed

xperimentally [4] and can be theoretically explained as a resultf electrostatic binding [25].

Another result obtained in our simulations is the absence of

ielectric overscreening by interfacial water. The results show amall contribution of water in the electrostatic potential, a sur-rising result in view of previously published results concerninglectrostatics of membranes, monolayers and thin films [11,12].

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ysicochem. Eng. Aspects 300 (2007) 287–292

he main conclusion that can be obtained from these resultss that the electrostatic effects of interfacial water are highlypecific, and strongly depend on the chemical structure of themphiphiles involved and possibly on the specific counterions.

There are many other interesting phospholipids with impor-ant biological function that show fascinating electrostaticffects. Investigations on phosphatidyl-inositol-biphosphate areurrently under way. We expect to report more in the near future.

cknowledgements

We acknowledge D. Vaknin for his many insightful remarksnd C. Lorenz and M. Losche for discussions. J.F. acknowledgesany discussions with R. Kjellander at the XIIIth Internationalonference on Surface Forces in Moscow. A.T. acknowledgesany discussions with S. Lemay, T. Nguyen, F. Pincus and B.hklovskii at the Aspen Center for Physics. This work is sup-orted by NSF grant DMR-0426597, the Spanish Governmentrant No. FIS2006-12296-C02-01, the UAB grant IEME2005-6 and partially supported by DOE through the Ames labnder contract no. W-7405-Eng-82. The authors thankfullycknowledge the computer resources, technical expertise andssistance provided by the Barcelona Supercomputing Center-entro Nacional de Supercomputacion.

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