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Electrostatics of phosphatidic acid monolayers: Insights from computer simulations
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
b
Departament de Fisica, Universitat Autonoma de Barcelona, Bellaterra, Spain Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, United States Available online 9 February 2007
Abstract In this paper, we argue that many of the fascinating electrostatic effects that take place in amphiphilic systems are strongly related to the particular organization of the oxygen atoms within each individual molecule. In particular, we focus on two effects: charge inversion and dielectric overscreening. For that purpose, we present molecular dynamics simulations of phosphatidic acid (DMPA2− ) in the presence of divalent counterions. Our results show that the many oxygens present in DMPA2− cooperatively create strong binding sites for counterions, which in some cases lead to charge inversion. We also present an analysis of the role of interfacial water and relate our analysis to the phenomenon of dielectric overscreening. Several experimental implications are discussed in the conclusions. © 2007 Elsevier B.V. All rights reserved. PACS: 82.45.Mp; 61.20.Qg; 82.39.Wj Keywords: Amphiphilic monolayers; Molecular dynamics simulations; Charge inversion; Ion correlations; Dielectric overscreening; Interfacial water
1. Introduction Amphiphilic interfaces (surfactant monolayers, biological membranes, . . .) in contact with aqueous solutions exhibit, under certain experimental conditions, different non-intuitive electrostatic phenomena with profound implications in their physico-chemical properties and technological or biological functionality. Two fascinating examples are charge inversion and dielectric overscreening. Charge inversion [1,2] consists in the binding of counterions in excess of the bare charge of the interface, thus leading to an interface whose effective charge has opposite sign (see Fig. 1). Dielectric overscreening (Fig. 2) has its origin in a strong orientational polarization of interfacial water leading to an electric field near the interface which is larger and opposite than the electric field generated by the amphiphiles and the counterions [3]. Traditionally, charge inversion has been analyzed in terms of specific chemical mechanisms. However, the fact that charge inversion has been observed in a large variety of different systems [4–9], suggests the existence of some general mechanism
∗
Corresponding author. E-mail address: [email protected] (J. Faraudo).
0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.02.011
responsible for charge inversion. In the case of surfaces with uniform charge distribution, charge inversion can be generated by strong lateral correlations between counterions [1,2]. In the case of amphiphilic interfaces, charge inversion is highly specific on the nature of the molecules forming the interface. As an example, monolayers with a surface charge of σ ≈ −e/20 (in ˚ 2 ) can be assembled either units of the elementary charge per A 2− with DMPA near close packing conditions (area per phos˚ 2 ) or with fatty acids. Experiments found charge pholipid ≈41 A inversion for DMPA monolayers in contact with divalent counterions [8] but not for fatty acids [10]. Theories that neglect amphiphilic specificity by describing the interface by a uniform surface charge lead to the same predictions for both DMPA and fatty acids, thus showing the necessity to include molecular details of the interface in the description of the electrostatics of many amphiphilic systems. Dielectric overscreening has been predicted to occur in different amphiphilic systems [11,12]. For example, simulations of phosphatidylcholine (PC) bilayers predict a positive electrostatic potential for the membrane (as compared with the bulk solution), while the contribution of the PC lipids is negative. The positive membrane potential results from the interfacial water, which overcompen-sates the electric field created by the PC. Dielectric overscreening contributes significantly to the electro-
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Fig. 1. Scheme of charge inversion in an amphiphilic monolayer. The charge due to bound counterions is larger an opposite in sign than the charge of the amphiphiles.
static interaction force between charged amphiphilic interfaces. In some amphiphilic systems, such as very thin SDS/water/SDS films, dielectric overscreening is the mechanism behind the socalled hydration force [13], which is responsible for the stability of the films as it has been shown in recent MD simulations [14]. Overscreening is just one example showing that interfacial water may show dramatically different properties than bulk water. We point out, however, that the properties of interfacial water are expected to be highly non-universal, as precise experiments of Langmuir monolayers of dihexadecylphosphate (DHDP) in contact with monovalent salt solution are well described by a bulk dielectric constant [15,16], while other experiments with mica surfaces show a drastic reduction of the water dielectric constant within the 10 nm next to the interface [17]. Also, hydration forces themselves are very specific, as many amphiphilic systems do not show any evidence of such forces [13]. Despite the wealth of phenomena observed, the different experimental examples mentioned so far are similar in that the
Fig. 2. Sketch of the different contributions to the electrostatic potential of a PC or PS membrane as obtained in simulations [11]. The strongly polarized water molecules generate an electric field which overcompensates that of the interface (dielectric overscreening).
charged headgroups basically consist of many oxygen atoms. How is it possible, therefore, that such similar interfaces display such disparate phenomena? Clearly, the answer to this question requires investigations taking into account the atomic details of the molecules forming the interface. In this paper, we provide a united atom simulation for a 1,2-dimyristoyl-sn-glycero-3phosphatidic acid (DMPA) monolayer in contact with a solution containing divalent Ba2+ ions. We have chosen this specific system because experimental results do report charge inversion [8]. Further interest in the properties of DMPA is provided by its biological relevance, as phospholipids with the phospatidic acid headgroup play a fundamental role in a wide range of biological processes, including signal transduction, secretion or membrane fusion. A detailed discussion on the biological implications for our results can be found in reference [18]. The organization of the paper is as follows. In Section 2, we briefly describe our simulations and discuss the mechanisms behind charge inversion in the view of simulation results. In Section 3, we discuss the role played by interfacial water in the electrostatics of this system. Finally, we end up with the conclusions. 2. Computer simulations of a DMPA monolayer 2.1. Brief description of simulations We have performed large-scale molecular dynamics (MD) simulation of DMPA2− monolayers in contact with aqueous solutions containing BaCl2 . The chemical structure of the DMPA2− molecule is shown in Fig. 3. Our MD simulations were conducted with the DLPOLY2.15 simulation package [19] running at the new BSC Supercomputing facility using 64 dual PowerPC 970FX processors. We employed the AMBER force field [20] modified according to reference [21]. Our system consisted of 100 doubly deprotonated DMPA2− molecules (charge q = −2e) placed at a water interface in contact with BaCl2 solution (150 Ba2+ , 100 Cl− and 9132 H2 O molecules) at 298 K. The partial charges of the DMPA molecule are attributed as shown in Fig. 3. Water was modelled using the SPC/E model. DMPA ˚ 2) molecules were kept at close packing (molecular area ≈41 A during the simulations, which ran over several ns. The convergence of simulations during this simulation time was ensured by using a block average analysis of the results. All technical details of simulations, including the details of the employed force fields and algorithms can be found in reference [18].
Fig. 3. Chemical structure of the DMPA molecule and its assignation of electrical charges. A, B, S, 2 symbols are used to distinguish among elements with different charge attributions.
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Fig. 4. Number of bound Ba2+ ions as a function of time. The time average is also shown as a solid line. Inset: Probability that an ion bound at t = 0 remains bound at a subsequent time t. The solid line shows an exponential fit to the probability distribution.
2.2. Presence of charge inversion in the DMPA monolayer In analyzing our simulation results, we consider a counterion as bound if it has a DMPA oxygen within its first coordination ˚ In this way, we idenshell (a maximum separation rmin = 3.5 A). tify a Stern layer formed by bound counterions and a diffuse layer of bulk counterions. The number of bound Ba2+ in the Stern layer is shown in Fig. 4 as a function of time. The average number of bound Ba2+ , computed as its time average over equilibrium configurations, yields bound /N NBa DMPA = 1.07 ± 0.01. Thus, the negative charge of the DMPA2− is overcompensated by bound counterions leaving a positive interfacial charge of q = 0.14e per phospholipid. The fact that the fluctuations in the instantaneous value of the number of bound Ba2+ are rather small is an evidence of a very strong binding of the counterions with the phospholipids at the Stern layer. Another evidence supporting this observation of strong binding is provided by the probability p(t) that a counterion bound at t = 0 remains in the Stern layer at a subsequent time t. We show the results in the inset of Fig. 4, which are consistent with an exponential decay p ≈ exp(−t/τ) with a fitted characteristic time of about τ ∼ 16 ns. The presence of charge inversion at the interface can also be shown by analyzing the charge distribution in the diffuse layer adjacent to the interface. In Fig. 5, we show the electric charge density distributions along the direction perpendicular to the interface due to bulk ions (Ba2+ and Cl− ) and the phospholipid molecules. The diffuse layer shows an excess of negative charge (Cl− ) next to the interface, in agreement with our previous finding of a positively charged Stern layer: the system exhibits charge inversion. In the inset of Fig. 5, we also show the charge distributions within the Stern layer, showing that Ba and DMPA2− distributions are very similar, with the counterion distribution slightly shifted toward the aqueous solution, thus providing
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Fig. 5. Absolute value of the charge density (elementary charges per nm3 ) due to free ions (diffuse layer) (Cl− squares, Ba2+ circles) and DMPA2− as a function of the distance from the interface z (we show only the part of the diffuse layer closer to the interface). The position z = 0 is defined so that it corresponds to the maximum of the probability distribution of the P atoms of the phospholipids. Inset: Charge density due to DMPA2− phospholipids (triangles) and bound Ba2+ ions (Stern layer).
additional evidence that Ba ions are tighly bound to DMPA headgroups. 2.3. Complex formation and binding sites for counterions In our simulations, we observe that the binding of counterions induce a significant restructuring to the DMPA interface. The distribution of bound counterions is not homogeneous as can be observed in the snapshot shown in Fig. 6. Typically, a Ba2+ ion is bound to an average of 6.2 oxygen atoms from 3 to 4 DMPA2− molecules. Also, some oxygen atoms from 3 to 4 DMPA2− molecules are shared by 2 counterions, as can be seen in Fig. 6. The system as a whole contains many complexes and holes, defined as regions without phospholipid headgroups (an example of a hole can be seen in Fig. 6). Given that the simulations where performed at the close packing density of hydrocarbon chains, the presence of holes is indicative of the strong structuring induced by the binding of divalent ions. The origin of the complexes formed by counterions and phospholipids can be traced to the oxygen atoms within the DMPA molecules, which create binding sites for counterions. In order to provide some insight on the structure of these effective binding sites for counterions, we have computed the cumulative charge near a bound counterion. As shown in Fig. 7, the charge in ˚ is about −4.5, concontact with bound counterions (r ≈ 3 A) sistent with each counterion binding to an average of 6 oxygen atoms with charges −0.7 or −0.8. Positive partial charges from DMPA and neighbouring counterions increase the cumulative charge significantly, reaching a plateau of −4 at distances about ˚ At larger distances (not shown in Fig. 7) the cumulative r ∼ 7 A. charge approaches the total charge of the interface. This interpretation for the formation of complexes at the interface is also consistent with the observed radial distribution functions gOBa2+ (r) between counterions and oxygen atoms from phospholipid molecules. A simple approximation to
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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 are Ba2+ 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 interface as seen from the aqueous solution (top view). In this patch, it can be clearly seen a hole without headgroups or counterions, a DMPA2− bound to 4 counterions (A) and counterions bound to 4 or 3 DMPA2− (labeled with B and C, respectively). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
gOBa2+ (r) assumes an effective electrostatic energy between a eff counterion and a binding site E/kT ≈ 2Qeff I lB /r, where QI ≈ 2 ˚ is the Bjerrum length −4 and the parameter lB = e /4πεkT ≈ 7 A [22]. Then, the radial distribution function gOBa2+ (r) is given by: gOBa2+ (r) ∼ exp(−2Qeff lB /r).
(1)
The gOBa2+ (r) computed from simulations is shown in Fig. 8. As expected, it vanishes for distances smaller than the crystallo˚ The approximation given graphic radius of Ba2+ and O (≈3 A). by Eq. (1) describes very well the first peak observed in the simulations with Qeff ≈ −4, in agreement with our analysis of the cumulative charge around bound counterions (Fig. 7). We point out that this effective charge is twice the nominal charge of the DMPA molecule. This doubling of the charge is possible because of the many oxygen atoms within conformational degrees of freedom, which optimize the binding of counterions. The charge inversion in our simulations results from the formation of electrostatic complexes at the interface. The observed charge inversion is about 1.07 Ba2+ ions per DMPA. An obvious
Fig. 8. Plot of the pair distribution functions gOBa2+ (r) as a function of r, for O2 and OS oxygens (see Fig. 3).
question is the maximum amount of charge charge inversion that can be observed with PA. This is estimated from the observation that each Ba2+ counterion is typically bound to 6 oxygen atoms from 3 to 4 different DMPA2− molecules. There are 8 oxygens per DMPA molecule and only 6 of them are, on average, used for binding, but a few O are shared by two Ba2+ , as shown in Fig. 6. In a hypothetical situation were all oxygens were used, charge reversal would reach a value Nupper ≈ 6/8 = 1.4NDMPA . Obviously, this maximum charge reversal would imply that all O are used for binding, which may be prevented from packing constraints and the connectivity of the hydrocarbon chains, but at the same time, it is observed that some oxygens are shared, which might roughly compensate for the packing constraints. 3. Role of interfacial water 3.1. Interfacial water
Fig. 7. Total charge within a distance r from a bound Ba2+ counterion due to phospholipid molecules and neighbouring counterions. In this calculation, the charge of the counterion at r = 0 is not included. The solid line is only a guide to the eye.
The first step in order to study the effects of interfacial water is to compute the amount of hydration water of the interface, Nw . The calculation of this quantity is difficult, because one needs to take into account not only the hydration of counterions but also
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water molecules. Hence, counterions lose roughly half of their hydration sheaths in binding to O, replacing about 5 oxygen atoms from water molecules by an average of 6 oxygen atoms from DMPA molecules. This replacement of oxygens from water molecules by oxygens from another molecule is somewhat reminiscent of ion selectivity in ion channels [24]. Further details of hydration shells and its relation to biological processes is discussed in reference [18]. It is also interesting to note that some of the hydration water molecules are shared by several counterions. This effect can be clearly shown by noting that if they were not shared the interface would contain about 4.45 × 1.07 ≈ 4.76 water molecules per phospholipid, which is larger than our previous estimate of 3.4 water molecules per phospholipid. 3.2. Effect of interfacial water in the electrostatic potential Fig. 9. Number of oxygen atoms from water molecules in the first coordination shell of Ba2+ ions (for the cases of bound ions and bulk ions) as a function of time and number of interfacial water molecules per phospholipid. The time average is also shown in the figure.
the hydration of the charged groups in the phospholipids. For this reason, we have evaluated Nw following a simple procedure that was introduced and tested in reference [23] for SDS/water interfaces. The basic idea of the method is as follows. First, one s with z > 0 (we computes the number of water molecules Nwh recall here that z = 0 was defined as the position of the maximum of the density distribution for P atoms). These water molecules correspond to the hydration of the “inner” side of the monolayer, in contact with the hydrocarbon region. The hydration in the opposite side of the monolayer (z < 0) is more difficult to obtain because we have both water molecules corresponding to hydration layers and bulk water molecules. However, it has been shown [23] that a reasonable estimation of Nw can be obtained by assuming that the interface is similarly solvated in both sides, so the amount of solvation water will be approximately given by Nw ≈ 2Nwhs . As expected, the results for Nw as a function of time (Fig. 9) show small fluctuations around a mean value, demonstrating that the system contains a well-defined amount of interfacial water. The equilibrium value for Nw is then computed as a time average over equilibrium configurations. Our results give an equilibrium amount of interfacial water about 3.4 water molecules per phospholipid molecule. For comparison, let us recall that a SDS monolayer (a system which shows strong effects due to interfacial water) typically contains 2.2 water molecules per amphiphilic molecule [23]. The reason for this large amount of interfacial water is the presence of bound divalent ions which retain, after binding, a significant part of their hydration shell. In order to quantify this effect, we have computed the number of oxygen atoms from water molecules in the first coordination shell of bulk and bound counterions as a function of time. As expected, the results (Fig. 9) show only small fluctuations around equilibrium values, demonstrating that both bulk and bound counterions have well defined hydration shells. Free counterions have 9.4 water molecules in their first hydration shell, whereas bound counterions have 4.45
In order to investigate the possible presence of dielectric overscreening in our system, we have computed the electrostatic potential using the integrated form of the Poisson equation: φ(z) = φf (z) + φw (z) −1 z z 1 z z = ρf (z ) dz − ρw (z ) dz dz , ε0 zB zB ε0 zB zB
(2)
where ρf (z) is the charge density due to charged species (DMPA and ions), ρw (z) the charge density due to water molecules and zB is a reference point in the electrolyte solution, far from the interface, in which the potential is defined to be zero. The electrostatic potential ϕ(z) and the contributions ϕf (z) from the charged species (DMPA and ions) and ϕw (z) from water molecules are shown in Fig. 10. The main contribution to ϕ(z) is due to the charged species and is positive (we recall that there is charge inversion in our simulations). On the other hand, the contribution of water molecules is negative and is significantly smaller than the contribution from ions and phospholipids (see
Fig. 10. Different contributions to the electrostatic potential obtained in simulations for the DMPA monolayer: contribution from interfacial water (dashed line), from ions and amphiphiles (dotted line) and total potential (solid line). Note that in this case no dielectric overscreening is observed.
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Fig. 10). Hence, the total electrostatic potential ϕ(z) is positive and increases monotonically from a reference value of zero in the electrolyte solution toward a constant potential at the hydrocarbon region of about 2.5 V. This increase in the electrostatic potential is generated within a very thin region of a few A near the phospholipid headgroups. It is also interesting to note that the surface potential (∼2.5 V) is only slightly smaller than the bare potential generated by the DMPA and the ions (which is about 3.3 V), which is essentially generated at the Stern layer. The contribution of water to the surface electrostatic potential is modest, only about −0.8 V. This water contribution is, in absolute value, much smaller than the contribution from ions and phospholipds and reflects that no dielectric overscreening takes place. The differences in the electrostatic potential between systems showing dielectric overscreening (such as PC and PS− bi-layers) and our results can be clearly observed by comparing Fig. 2 with Fig. 10. 4. Conclusions We reported a MD simulation of a DMPA2− monolayer in contact with an aqueous solution containing BaCl2 . Our results show the exceptional ability of DMPA to create binding sites for counterions. These binding sites consist of arrangements of oxygen atoms, which as a result of its strong electronegativity, retain significant electric charge even when they are part of neutral groups (see Fig. 3). The strongly cohesive binding sites lead to charge inversion by formation of electrostatic complexes involving several counterions and other atoms from DMPA2− . We predict a maximum charge inversion of 1.4 counterions per DMPA, in agreement with the experimental result of 1.3–1.5 counterions bound per DMPA reported for this system [8]. Our results suggest that charge inversion is a common effect in amphiphilic systems that contain many oxygen (or other electronegative atoms) within groups that have conformational degrees of freedom. The electrostatic mechanism observed in our simulations allows them to create highly cohesive binding sites for multivalent ions. The fact that fatty acids do not exhibit charge inversion despite having the same surface charge as DMPA, can be understood from the fact that fatty acids only have two oxygens per molecule compared with the eight oxygens in DMPA. A similar situation also occurs for DHDP (dihexadecyl hydrogen-phosphate) [16], which has four available oxygens. On the other hand, it should be expected that charge inversion is a common effect in membranes of biologically relevant charged phospholipids, such as phosphatidyl serine (PS), phosphatidylinositol or glycolipids, such as the gangliosides, which contain more than 10 oxygens per molecule and can become multiply charged. Charge inversion in PS has been observed experimentally [4] and can be theoretically explained as a result of electrostatic binding [25]. Another result obtained in our simulations is the absence of dielectric overscreening by interfacial water. The results show a small contribution of water in the electrostatic potential, a surprising result in view of previously published results concerning electrostatics of membranes, monolayers and thin films [11,12].
The main conclusion that can be obtained from these results is that the electrostatic effects of interfacial water are highly specific, and strongly depend on the chemical structure of the amphiphiles involved and possibly on the specific counterions. There are many other interesting phospholipids with important biological function that show fascinating electrostatic effects. Investigations on phosphatidyl-inositol-biphosphate are currently under way. We expect to report more in the near future. Acknowledgements We acknowledge D. Vaknin for his many insightful remarks and C. Lorenz and M. Losche for discussions. J.F. acknowledges many discussions with R. Kjellander at the XIIIth International Conference on Surface Forces in Moscow. A.T. acknowledges many discussions with S. Lemay, T. Nguyen, F. Pincus and B. Shklovskii at the Aspen Center for Physics. This work is supported by NSF grant DMR-0426597, the Spanish Government Grant No. FIS2006-12296-C02-01, the UAB grant IEME200546 and partially supported by DOE through the Ames lab under contract no. W-7405-Eng-82. The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Barcelona Supercomputing CenterCentro Nacional de Supercomputacion. References [1] A.Yu. Grosberg, T.T. Nguyen, B.I. Shklovskii, Rev. Mod. Phys. 74 (2002) 329. [2] Y. Levin, Rep. Prog. Phys. 65 (2002) 1577. [3] D.A. Cherepanov, Phys. Rev. Lett. 93 (2004) 266104. [4] S. McLaughlin, Annu. Rev. Biophys. Chem. 18 (1989) 113. [5] K. Besteman, M.A.G. Zevenbergen, H.A. Heering, S.G. Lemay, Phys. Rev. Lett. 93 (2004) 170802. [6] K. Besteman, M.A.G. Zevenbergen, S.G. Lemay, Phys. Rev. E 72 (2005) 061501. [7] J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 2000. [8] D. Vaknin, P. Kr¨uger, M. L¨osche, Phys. Rev. Lett. 90 (2003) 178102. [9] J. Pittler, W. Bu, D. Vaknin, A. Travesset, D.J. McGillivray, M. Losche, Phys. Rev. Lett. 97 (2006) 46102. [10] C. Kjaer, et al., J. Phys. Chem. 93 (1989) 3200. [11] M.L. Berkowitz, D.L. Bostick, S. Pandar, Chem. Rev. 106 (2006) 1527. [12] J. Faraudo, F. Bresme, Phys. Rev. Lett. 92 (2004) 236102. [13] S. Leikin, V.A. Parsegian, D.C. Rau, Annu. Rev. Phys. Chem. 44 (1993) 369. [14] J. Faraudo, F. Bresme, Phys. Rev. Lett. 94 (2005) 77802. [15] W. Bu, D. Vaknin, A. Travesset, Phys. Rev. E 72 (2005) 60501. [16] W. Bu, D. Vaknin, A. Travesset, Langmuir 22 (2006) 5673. [17] O. Teschke, G. Ceotto, E.F. de Souza, Phys. Rev. E 64 (2001) 11605. [18] J. Faraudo, A. Travesset, Biophys. J. 92 (2007) 2806. [19] T.R. Forester, W. Smith, DLPOLY Package of Molecular Simulations, version 2.15, Daresbury Lab, 2005. [20] W.D. Cornell, J. Am. Chem. Soc. 117 (1995) 5179. [21] A. Smondyrev, M.L. Berkowitz, J. Comput. Chem. 20 (1999) 531. [22] S. Safran, Statistical Thermodynamics of Surfaces Interfaces and Membranes, Perseus Publishing, New York, 1994. [23] F. Bresme, J. Faraudo, Langmuir 20 (2004) 5127. [24] B. Alberts, et al., Molecular Biology of the Cell, Garland Science, New York, 2002. [25] A. Travesset, D. Vaknin, Europhys. Lett. 74 (2006) 181.
Electrostatics of phosphatidic acid monolayers: Insights from computer simulations Jordi Faraudo a,∗ , Alex Travesset b a
b
Departament de Fisica, Universitat Autonoma de Barcelona, Bellaterra, Spain Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, United States Available online 9 February 2007
Abstract In this paper, we argue that many of the fascinating electrostatic effects that take place in amphiphilic systems are strongly related to the particular organization of the oxygen atoms within each individual molecule. In particular, we focus on two effects: charge inversion and dielectric overscreening. For that purpose, we present molecular dynamics simulations of phosphatidic acid (DMPA2− ) in the presence of divalent counterions. Our results show that the many oxygens present in DMPA2− cooperatively create strong binding sites for counterions, which in some cases lead to charge inversion. We also present an analysis of the role of interfacial water and relate our analysis to the phenomenon of dielectric overscreening. Several experimental implications are discussed in the conclusions. © 2007 Elsevier B.V. All rights reserved. PACS: 82.45.Mp; 61.20.Qg; 82.39.Wj Keywords: Amphiphilic monolayers; Molecular dynamics simulations; Charge inversion; Ion correlations; Dielectric overscreening; Interfacial water
1. Introduction Amphiphilic interfaces (surfactant monolayers, biological membranes, . . .) in contact with aqueous solutions exhibit, under certain experimental conditions, different non-intuitive electrostatic phenomena with profound implications in their physico-chemical properties and technological or biological functionality. Two fascinating examples are charge inversion and dielectric overscreening. Charge inversion [1,2] consists in the binding of counterions in excess of the bare charge of the interface, thus leading to an interface whose effective charge has opposite sign (see Fig. 1). Dielectric overscreening (Fig. 2) has its origin in a strong orientational polarization of interfacial water leading to an electric field near the interface which is larger and opposite than the electric field generated by the amphiphiles and the counterions [3]. Traditionally, charge inversion has been analyzed in terms of specific chemical mechanisms. However, the fact that charge inversion has been observed in a large variety of different systems [4–9], suggests the existence of some general mechanism
∗
Corresponding author. E-mail address: [email protected] (J. Faraudo).
0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.02.011
responsible for charge inversion. In the case of surfaces with uniform charge distribution, charge inversion can be generated by strong lateral correlations between counterions [1,2]. In the case of amphiphilic interfaces, charge inversion is highly specific on the nature of the molecules forming the interface. As an example, monolayers with a surface charge of σ ≈ −e/20 (in ˚ 2 ) can be assembled either units of the elementary charge per A 2− with DMPA near close packing conditions (area per phos˚ 2 ) or with fatty acids. Experiments found charge pholipid ≈41 A inversion for DMPA monolayers in contact with divalent counterions [8] but not for fatty acids [10]. Theories that neglect amphiphilic specificity by describing the interface by a uniform surface charge lead to the same predictions for both DMPA and fatty acids, thus showing the necessity to include molecular details of the interface in the description of the electrostatics of many amphiphilic systems. Dielectric overscreening has been predicted to occur in different amphiphilic systems [11,12]. For example, simulations of phosphatidylcholine (PC) bilayers predict a positive electrostatic potential for the membrane (as compared with the bulk solution), while the contribution of the PC lipids is negative. The positive membrane potential results from the interfacial water, which overcompen-sates the electric field created by the PC. Dielectric overscreening contributes significantly to the electro-
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Fig. 1. Scheme of charge inversion in an amphiphilic monolayer. The charge due to bound counterions is larger an opposite in sign than the charge of the amphiphiles.
static interaction force between charged amphiphilic interfaces. In some amphiphilic systems, such as very thin SDS/water/SDS films, dielectric overscreening is the mechanism behind the socalled hydration force [13], which is responsible for the stability of the films as it has been shown in recent MD simulations [14]. Overscreening is just one example showing that interfacial water may show dramatically different properties than bulk water. We point out, however, that the properties of interfacial water are expected to be highly non-universal, as precise experiments of Langmuir monolayers of dihexadecylphosphate (DHDP) in contact with monovalent salt solution are well described by a bulk dielectric constant [15,16], while other experiments with mica surfaces show a drastic reduction of the water dielectric constant within the 10 nm next to the interface [17]. Also, hydration forces themselves are very specific, as many amphiphilic systems do not show any evidence of such forces [13]. Despite the wealth of phenomena observed, the different experimental examples mentioned so far are similar in that the
Fig. 2. Sketch of the different contributions to the electrostatic potential of a PC or PS membrane as obtained in simulations [11]. The strongly polarized water molecules generate an electric field which overcompensates that of the interface (dielectric overscreening).
charged headgroups basically consist of many oxygen atoms. How is it possible, therefore, that such similar interfaces display such disparate phenomena? Clearly, the answer to this question requires investigations taking into account the atomic details of the molecules forming the interface. In this paper, we provide a united atom simulation for a 1,2-dimyristoyl-sn-glycero-3phosphatidic acid (DMPA) monolayer in contact with a solution containing divalent Ba2+ ions. We have chosen this specific system because experimental results do report charge inversion [8]. Further interest in the properties of DMPA is provided by its biological relevance, as phospholipids with the phospatidic acid headgroup play a fundamental role in a wide range of biological processes, including signal transduction, secretion or membrane fusion. A detailed discussion on the biological implications for our results can be found in reference [18]. The organization of the paper is as follows. In Section 2, we briefly describe our simulations and discuss the mechanisms behind charge inversion in the view of simulation results. In Section 3, we discuss the role played by interfacial water in the electrostatics of this system. Finally, we end up with the conclusions. 2. Computer simulations of a DMPA monolayer 2.1. Brief description of simulations We have performed large-scale molecular dynamics (MD) simulation of DMPA2− monolayers in contact with aqueous solutions containing BaCl2 . The chemical structure of the DMPA2− molecule is shown in Fig. 3. Our MD simulations were conducted with the DLPOLY2.15 simulation package [19] running at the new BSC Supercomputing facility using 64 dual PowerPC 970FX processors. We employed the AMBER force field [20] modified according to reference [21]. Our system consisted of 100 doubly deprotonated DMPA2− molecules (charge q = −2e) placed at a water interface in contact with BaCl2 solution (150 Ba2+ , 100 Cl− and 9132 H2 O molecules) at 298 K. The partial charges of the DMPA molecule are attributed as shown in Fig. 3. Water was modelled using the SPC/E model. DMPA ˚ 2) molecules were kept at close packing (molecular area ≈41 A during the simulations, which ran over several ns. The convergence of simulations during this simulation time was ensured by using a block average analysis of the results. All technical details of simulations, including the details of the employed force fields and algorithms can be found in reference [18].
Fig. 3. Chemical structure of the DMPA molecule and its assignation of electrical charges. A, B, S, 2 symbols are used to distinguish among elements with different charge attributions.
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Fig. 4. Number of bound Ba2+ ions as a function of time. The time average is also shown as a solid line. Inset: Probability that an ion bound at t = 0 remains bound at a subsequent time t. The solid line shows an exponential fit to the probability distribution.
2.2. Presence of charge inversion in the DMPA monolayer In analyzing our simulation results, we consider a counterion as bound if it has a DMPA oxygen within its first coordination ˚ In this way, we idenshell (a maximum separation rmin = 3.5 A). tify a Stern layer formed by bound counterions and a diffuse layer of bulk counterions. The number of bound Ba2+ in the Stern layer is shown in Fig. 4 as a function of time. The average number of bound Ba2+ , computed as its time average over equilibrium configurations, yields bound /N NBa DMPA = 1.07 ± 0.01. Thus, the negative charge of the DMPA2− is overcompensated by bound counterions leaving a positive interfacial charge of q = 0.14e per phospholipid. The fact that the fluctuations in the instantaneous value of the number of bound Ba2+ are rather small is an evidence of a very strong binding of the counterions with the phospholipids at the Stern layer. Another evidence supporting this observation of strong binding is provided by the probability p(t) that a counterion bound at t = 0 remains in the Stern layer at a subsequent time t. We show the results in the inset of Fig. 4, which are consistent with an exponential decay p ≈ exp(−t/τ) with a fitted characteristic time of about τ ∼ 16 ns. The presence of charge inversion at the interface can also be shown by analyzing the charge distribution in the diffuse layer adjacent to the interface. In Fig. 5, we show the electric charge density distributions along the direction perpendicular to the interface due to bulk ions (Ba2+ and Cl− ) and the phospholipid molecules. The diffuse layer shows an excess of negative charge (Cl− ) next to the interface, in agreement with our previous finding of a positively charged Stern layer: the system exhibits charge inversion. In the inset of Fig. 5, we also show the charge distributions within the Stern layer, showing that Ba and DMPA2− distributions are very similar, with the counterion distribution slightly shifted toward the aqueous solution, thus providing
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Fig. 5. Absolute value of the charge density (elementary charges per nm3 ) due to free ions (diffuse layer) (Cl− squares, Ba2+ circles) and DMPA2− as a function of the distance from the interface z (we show only the part of the diffuse layer closer to the interface). The position z = 0 is defined so that it corresponds to the maximum of the probability distribution of the P atoms of the phospholipids. Inset: Charge density due to DMPA2− phospholipids (triangles) and bound Ba2+ ions (Stern layer).
additional evidence that Ba ions are tighly bound to DMPA headgroups. 2.3. Complex formation and binding sites for counterions In our simulations, we observe that the binding of counterions induce a significant restructuring to the DMPA interface. The distribution of bound counterions is not homogeneous as can be observed in the snapshot shown in Fig. 6. Typically, a Ba2+ ion is bound to an average of 6.2 oxygen atoms from 3 to 4 DMPA2− molecules. Also, some oxygen atoms from 3 to 4 DMPA2− molecules are shared by 2 counterions, as can be seen in Fig. 6. The system as a whole contains many complexes and holes, defined as regions without phospholipid headgroups (an example of a hole can be seen in Fig. 6). Given that the simulations where performed at the close packing density of hydrocarbon chains, the presence of holes is indicative of the strong structuring induced by the binding of divalent ions. The origin of the complexes formed by counterions and phospholipids can be traced to the oxygen atoms within the DMPA molecules, which create binding sites for counterions. In order to provide some insight on the structure of these effective binding sites for counterions, we have computed the cumulative charge near a bound counterion. As shown in Fig. 7, the charge in ˚ is about −4.5, concontact with bound counterions (r ≈ 3 A) sistent with each counterion binding to an average of 6 oxygen atoms with charges −0.7 or −0.8. Positive partial charges from DMPA and neighbouring counterions increase the cumulative charge significantly, reaching a plateau of −4 at distances about ˚ At larger distances (not shown in Fig. 7) the cumulative r ∼ 7 A. charge approaches the total charge of the interface. This interpretation for the formation of complexes at the interface is also consistent with the observed radial distribution functions gOBa2+ (r) between counterions and oxygen atoms from phospholipid molecules. A simple approximation to
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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 are Ba2+ 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 interface as seen from the aqueous solution (top view). In this patch, it can be clearly seen a hole without headgroups or counterions, a DMPA2− bound to 4 counterions (A) and counterions bound to 4 or 3 DMPA2− (labeled with B and C, respectively). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
gOBa2+ (r) assumes an effective electrostatic energy between a eff counterion and a binding site E/kT ≈ 2Qeff I lB /r, where QI ≈ 2 ˚ is the Bjerrum length −4 and the parameter lB = e /4πεkT ≈ 7 A [22]. Then, the radial distribution function gOBa2+ (r) is given by: gOBa2+ (r) ∼ exp(−2Qeff lB /r).
(1)
The gOBa2+ (r) computed from simulations is shown in Fig. 8. As expected, it vanishes for distances smaller than the crystallo˚ The approximation given graphic radius of Ba2+ and O (≈3 A). by Eq. (1) describes very well the first peak observed in the simulations with Qeff ≈ −4, in agreement with our analysis of the cumulative charge around bound counterions (Fig. 7). We point out that this effective charge is twice the nominal charge of the DMPA molecule. This doubling of the charge is possible because of the many oxygen atoms within conformational degrees of freedom, which optimize the binding of counterions. The charge inversion in our simulations results from the formation of electrostatic complexes at the interface. The observed charge inversion is about 1.07 Ba2+ ions per DMPA. An obvious
Fig. 8. Plot of the pair distribution functions gOBa2+ (r) as a function of r, for O2 and OS oxygens (see Fig. 3).
question is the maximum amount of charge charge inversion that can be observed with PA. This is estimated from the observation that each Ba2+ counterion is typically bound to 6 oxygen atoms from 3 to 4 different DMPA2− molecules. There are 8 oxygens per DMPA molecule and only 6 of them are, on average, used for binding, but a few O are shared by two Ba2+ , as shown in Fig. 6. In a hypothetical situation were all oxygens were used, charge reversal would reach a value Nupper ≈ 6/8 = 1.4NDMPA . Obviously, this maximum charge reversal would imply that all O are used for binding, which may be prevented from packing constraints and the connectivity of the hydrocarbon chains, but at the same time, it is observed that some oxygens are shared, which might roughly compensate for the packing constraints. 3. Role of interfacial water 3.1. Interfacial water
Fig. 7. Total charge within a distance r from a bound Ba2+ counterion due to phospholipid molecules and neighbouring counterions. In this calculation, the charge of the counterion at r = 0 is not included. The solid line is only a guide to the eye.
The first step in order to study the effects of interfacial water is to compute the amount of hydration water of the interface, Nw . The calculation of this quantity is difficult, because one needs to take into account not only the hydration of counterions but also
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water molecules. Hence, counterions lose roughly half of their hydration sheaths in binding to O, replacing about 5 oxygen atoms from water molecules by an average of 6 oxygen atoms from DMPA molecules. This replacement of oxygens from water molecules by oxygens from another molecule is somewhat reminiscent of ion selectivity in ion channels [24]. Further details of hydration shells and its relation to biological processes is discussed in reference [18]. It is also interesting to note that some of the hydration water molecules are shared by several counterions. This effect can be clearly shown by noting that if they were not shared the interface would contain about 4.45 × 1.07 ≈ 4.76 water molecules per phospholipid, which is larger than our previous estimate of 3.4 water molecules per phospholipid. 3.2. Effect of interfacial water in the electrostatic potential Fig. 9. Number of oxygen atoms from water molecules in the first coordination shell of Ba2+ ions (for the cases of bound ions and bulk ions) as a function of time and number of interfacial water molecules per phospholipid. The time average is also shown in the figure.
the hydration of the charged groups in the phospholipids. For this reason, we have evaluated Nw following a simple procedure that was introduced and tested in reference [23] for SDS/water interfaces. The basic idea of the method is as follows. First, one s with z > 0 (we computes the number of water molecules Nwh recall here that z = 0 was defined as the position of the maximum of the density distribution for P atoms). These water molecules correspond to the hydration of the “inner” side of the monolayer, in contact with the hydrocarbon region. The hydration in the opposite side of the monolayer (z < 0) is more difficult to obtain because we have both water molecules corresponding to hydration layers and bulk water molecules. However, it has been shown [23] that a reasonable estimation of Nw can be obtained by assuming that the interface is similarly solvated in both sides, so the amount of solvation water will be approximately given by Nw ≈ 2Nwhs . As expected, the results for Nw as a function of time (Fig. 9) show small fluctuations around a mean value, demonstrating that the system contains a well-defined amount of interfacial water. The equilibrium value for Nw is then computed as a time average over equilibrium configurations. Our results give an equilibrium amount of interfacial water about 3.4 water molecules per phospholipid molecule. For comparison, let us recall that a SDS monolayer (a system which shows strong effects due to interfacial water) typically contains 2.2 water molecules per amphiphilic molecule [23]. The reason for this large amount of interfacial water is the presence of bound divalent ions which retain, after binding, a significant part of their hydration shell. In order to quantify this effect, we have computed the number of oxygen atoms from water molecules in the first coordination shell of bulk and bound counterions as a function of time. As expected, the results (Fig. 9) show only small fluctuations around equilibrium values, demonstrating that both bulk and bound counterions have well defined hydration shells. Free counterions have 9.4 water molecules in their first hydration shell, whereas bound counterions have 4.45
In order to investigate the possible presence of dielectric overscreening in our system, we have computed the electrostatic potential using the integrated form of the Poisson equation: φ(z) = φf (z) + φw (z) −1 z z 1 z z = ρf (z ) dz − ρw (z ) dz dz , ε0 zB zB ε0 zB zB
(2)
where ρf (z) is the charge density due to charged species (DMPA and ions), ρw (z) the charge density due to water molecules and zB is a reference point in the electrolyte solution, far from the interface, in which the potential is defined to be zero. The electrostatic potential ϕ(z) and the contributions ϕf (z) from the charged species (DMPA and ions) and ϕw (z) from water molecules are shown in Fig. 10. The main contribution to ϕ(z) is due to the charged species and is positive (we recall that there is charge inversion in our simulations). On the other hand, the contribution of water molecules is negative and is significantly smaller than the contribution from ions and phospholipids (see
Fig. 10. Different contributions to the electrostatic potential obtained in simulations for the DMPA monolayer: contribution from interfacial water (dashed line), from ions and amphiphiles (dotted line) and total potential (solid line). Note that in this case no dielectric overscreening is observed.
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Fig. 10). Hence, the total electrostatic potential ϕ(z) is positive and increases monotonically from a reference value of zero in the electrolyte solution toward a constant potential at the hydrocarbon region of about 2.5 V. This increase in the electrostatic potential is generated within a very thin region of a few A near the phospholipid headgroups. It is also interesting to note that the surface potential (∼2.5 V) is only slightly smaller than the bare potential generated by the DMPA and the ions (which is about 3.3 V), which is essentially generated at the Stern layer. The contribution of water to the surface electrostatic potential is modest, only about −0.8 V. This water contribution is, in absolute value, much smaller than the contribution from ions and phospholipds and reflects that no dielectric overscreening takes place. The differences in the electrostatic potential between systems showing dielectric overscreening (such as PC and PS− bi-layers) and our results can be clearly observed by comparing Fig. 2 with Fig. 10. 4. Conclusions We reported a MD simulation of a DMPA2− monolayer in contact with an aqueous solution containing BaCl2 . Our results show the exceptional ability of DMPA to create binding sites for counterions. These binding sites consist of arrangements of oxygen atoms, which as a result of its strong electronegativity, retain significant electric charge even when they are part of neutral groups (see Fig. 3). The strongly cohesive binding sites lead to charge inversion by formation of electrostatic complexes involving several counterions and other atoms from DMPA2− . We predict a maximum charge inversion of 1.4 counterions per DMPA, in agreement with the experimental result of 1.3–1.5 counterions bound per DMPA reported for this system [8]. Our results suggest that charge inversion is a common effect in amphiphilic systems that contain many oxygen (or other electronegative atoms) within groups that have conformational degrees of freedom. The electrostatic mechanism observed in our simulations allows them to create highly cohesive binding sites for multivalent ions. The fact that fatty acids do not exhibit charge inversion despite having the same surface charge as DMPA, can be understood from the fact that fatty acids only have two oxygens per molecule compared with the eight oxygens in DMPA. A similar situation also occurs for DHDP (dihexadecyl hydrogen-phosphate) [16], which has four available oxygens. On the other hand, it should be expected that charge inversion is a common effect in membranes of biologically relevant charged phospholipids, such as phosphatidyl serine (PS), phosphatidylinositol or glycolipids, such as the gangliosides, which contain more than 10 oxygens per molecule and can become multiply charged. Charge inversion in PS has been observed experimentally [4] and can be theoretically explained as a result of electrostatic binding [25]. Another result obtained in our simulations is the absence of dielectric overscreening by interfacial water. The results show a small contribution of water in the electrostatic potential, a surprising result in view of previously published results concerning electrostatics of membranes, monolayers and thin films [11,12].
The main conclusion that can be obtained from these results is that the electrostatic effects of interfacial water are highly specific, and strongly depend on the chemical structure of the amphiphiles involved and possibly on the specific counterions. There are many other interesting phospholipids with important biological function that show fascinating electrostatic effects. Investigations on phosphatidyl-inositol-biphosphate are currently under way. We expect to report more in the near future. Acknowledgements We acknowledge D. Vaknin for his many insightful remarks and C. Lorenz and M. Losche for discussions. J.F. acknowledges many discussions with R. Kjellander at the XIIIth International Conference on Surface Forces in Moscow. A.T. acknowledges many discussions with S. Lemay, T. Nguyen, F. Pincus and B. Shklovskii at the Aspen Center for Physics. This work is supported by NSF grant DMR-0426597, the Spanish Government Grant No. FIS2006-12296-C02-01, the UAB grant IEME200546 and partially supported by DOE through the Ames lab under contract no. W-7405-Eng-82. The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Barcelona Supercomputing CenterCentro Nacional de Supercomputacion. References [1] A.Yu. Grosberg, T.T. Nguyen, B.I. Shklovskii, Rev. Mod. Phys. 74 (2002) 329. [2] Y. Levin, Rep. Prog. Phys. 65 (2002) 1577. [3] D.A. Cherepanov, Phys. Rev. Lett. 93 (2004) 266104. [4] S. McLaughlin, Annu. Rev. Biophys. Chem. 18 (1989) 113. [5] K. Besteman, M.A.G. Zevenbergen, H.A. Heering, S.G. Lemay, Phys. Rev. Lett. 93 (2004) 170802. [6] K. Besteman, M.A.G. Zevenbergen, S.G. Lemay, Phys. Rev. E 72 (2005) 061501. [7] J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London, 2000. [8] D. Vaknin, P. Kr¨uger, M. L¨osche, Phys. Rev. Lett. 90 (2003) 178102. [9] J. Pittler, W. Bu, D. Vaknin, A. Travesset, D.J. McGillivray, M. Losche, Phys. Rev. Lett. 97 (2006) 46102. [10] C. Kjaer, et al., J. Phys. Chem. 93 (1989) 3200. [11] M.L. Berkowitz, D.L. Bostick, S. Pandar, Chem. Rev. 106 (2006) 1527. [12] J. Faraudo, F. Bresme, Phys. Rev. Lett. 92 (2004) 236102. [13] S. Leikin, V.A. Parsegian, D.C. Rau, Annu. Rev. Phys. Chem. 44 (1993) 369. [14] J. Faraudo, F. Bresme, Phys. Rev. Lett. 94 (2005) 77802. [15] W. Bu, D. Vaknin, A. Travesset, Phys. Rev. E 72 (2005) 60501. [16] W. Bu, D. Vaknin, A. Travesset, Langmuir 22 (2006) 5673. [17] O. Teschke, G. Ceotto, E.F. de Souza, Phys. Rev. E 64 (2001) 11605. [18] J. Faraudo, A. Travesset, Biophys. J. 92 (2007) 2806. [19] T.R. Forester, W. Smith, DLPOLY Package of Molecular Simulations, version 2.15, Daresbury Lab, 2005. [20] W.D. Cornell, J. Am. Chem. Soc. 117 (1995) 5179. [21] A. Smondyrev, M.L. Berkowitz, J. Comput. Chem. 20 (1999) 531. [22] S. Safran, Statistical Thermodynamics of Surfaces Interfaces and Membranes, Perseus Publishing, New York, 1994. [23] F. Bresme, J. Faraudo, Langmuir 20 (2004) 5127. [24] B. Alberts, et al., Molecular Biology of the Cell, Garland Science, New York, 2002. [25] A. Travesset, D. Vaknin, Europhys. Lett. 74 (2006) 181.