Water at hydrophobic interfaces delays protonsurface-to-bulk transfer and provides apathway for lateral proton diffusionChao Zhanga,1, Denis G. Knyazevb,1, Yana A. Vereshagaa,1, Emiliano Ippolitia, Trung Hai Nguyena,Paolo Carlonia,c,2, and Peter Pohlb

aComputational Biophysics, German Research School for Simulation Sciences, 52425 Jülich, Germany; bInstitute of Biophysics, Johannes Kepler UniversityLinz, 4040 Linz, Austria; and cComputational Biomedicine, Institute for Advanced Simulations, Forschungszentrum Jülich, 52425 Jülich, Germany

Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved May 1, 2012 (received for review December 23, 2011)

Fast lateral proton migration along membranes is of vital impor-tance for cellular energy homeostasis and various proton-coupledtransport processes. It can only occur if attractive forces keep theproton at the interface. How to reconcile this high affinity to themembrane surface with high proton mobility is unclear. Here, wetested whether a minimalistic model interface between an apolarhydrophobic phase (n-decane) and an aqueous phase mimics thebiological pathway for lateral proton migration. The observed dif-fusion span, on the order of tens of micrometers, and the high pro-ton mobility were both similar to the values previously reportedfor lipid bilayers. Extensive ab initio simulations on the samewater∕n-decane interface reproduced the experimentally derivedfree energy barrier for the excess proton. The free energy profileGHþ adopts the shape of a well at the interface, having a width oftwo water molecules and a depth of 6� 2RT . The hydroniums indirect contact with n-decane have a reduced mobility. However,the hydroniums in the second layer of water molecules are mobile.Their in silico diffusion coefficient matches that derived from our invitro experiments, ð5.7� 0.7Þ × 10−5 cm2 s−1. Conceivably, theseare the protons that allow for fast diffusion along biological mem-branes.

hydrophobic liquid ∣ hydrophilic liquid interface ∣ surface acidity ∣free energy calculations

Proton transfer is only fairly understood in bulk water (1, 2) buthas not been comprehended along biological interfaces, even

though the process is of vital importance for cellular bioener-getics and membrane transport processes, as has been postulateda long time ago (3). Convincing evidence revealing the membranesurface as a major pathway for proton transport was obtained bythe observation that protons that were released on one side of apurple membrane fragment appeared first at the opposing inter-face and only afterwards in the corresponding bulk solution(4). Unfortunately, it remained unclear whether proton mobilityis reduced at the membrane surface. The reported lateral diffu-sion coefficients D varied between 9.6 × 10−7 cm2 s−1 (4) and3 × 10−5 cm2 s−1 (5).

It was believed that the protons moved by jumping along themembrane surface between titrable groups. Their proton attrac-tion was deemed responsible for the delayed proton surface-to-bulk transfer (6). In line with these considerations, measure-ments of the protonation kinetics served to predict the protonsurface diffusion coefficient (7). According to such a calculation,D was more than an order of magnitude smaller than the diffu-sion coefficient of a proton carrier in bulk. In contrast, directmeasurements on simple planar bilayers devoid of proton accept-ing proteinaceous residues revealed a D that was 10 times higherand proton residence times at the interface on the order of hun-dreds of milliseconds (8). Moreover, lateral diffusion along thosebilayers persisted upon removal of titrable lipid groups. In thepresence of such groups, D appeared to depend only weakly ontheir pK (9). The observed size of the isotope effect strongly sup-

ported the conclusion that the protons may travel along surfacebound water (9).

Proton movement along hydrogen-bonded water molecules isa scenario known from narrow membrane channels, where thesewaters bridge the distance between titrable amino acids (10). Themechanism of proton hopping between protonation sites on themembrane surface may be quite similar (11, 12). However, theprotons on the membrane surface lack the geometrical confine-ment of a narrow pore, which raises the question of why the pro-tons remain for hundreds of milliseconds on the surface insteadof being released into the bulk. Molecular dynamics simulationsusing the multistate empirical valence bond (MS-EVB) modelsuggested that the protons may be trapped by charged groupssuch as the phosphate moieties of phospholipids. In this case,they would move together with the lipids (13, 14). The mobile(untrapped) fraction of surface protons faces a shallow energybarrier. Accordingly, they are released from the interfacial regionin less than one nanosecond (13, 14).

According to simulations carried out with nonbiological mod-els (15–21), well-defined binding sites may be not required forproton attraction to interfaces between high and low dielectricregions. For example, for the water/vapor interface, ab initio andMS-EVB simulations revealed the acidification of the top surfacewater layer as compared to bulk water (15–18). Free energyminima about 3 Å wide from the interface were also found inMS-EVB simulations at water/carbon nanotubes (19) and water∕CCl4 interfaces (20). However, the affinity of the hydronium toa hydrophobic interface came at the cost of reduced mobility ashas been observed in ab initio simulations for the hydroniumclose to the water-graphene interface (21).

How to reconcile the high affinity to the membrane-waterinterface with high proton mobility is, thus, totally unclear. Toexplain both the high surface diffusion coefficient and the longlateral diffusion span (5, 8, 22), the membrane-water interfacemust possess a feature that has thus far escaped notice. The sim-plest explanation would be that, in the absence of titrable groups(9), polar groups might stabilize the proton close to the interface.Since their attraction is weaker than the one of titrable groups,the proton retains high mobility. To test this hypothesis, we de-veloped a minimalistic model that lacks the polar groups. Ourexperimental observation of long-range proton diffusion betweenrelease and detection spots on a water-n-decane interface sug-

Author contributions: P.C. and P.P. designed research; C.Z., D.G.K., Y.A.V., and T.H.N.performed research; C.Z., D.G.K., Y.A.V., and E.I. analyzed data; and C.Z., D.G.K., E.I., P.C.,and P.P. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1These authors contributed equally to this work.2To whom correspondence should be addressed. E-mail: p.carloni@grs-sim.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1121227109/-/DCSupplemental.

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gests that a free energy barrier ΔGHþ is intrinsic to any interfaceseparating hydrophobic and hydrophilic phases. This supports theopinions from previous simulations (15–21). Proton retentionclose to the surface decreases interfacial pH at the first two waterlayers by about 2–3 units below bulk pH, as indicated by ourextensive 75 ps-long ab initio metadynamics-based free energysimulations, including 1,707 atoms. At least in the case of a liquidhydrophobic phase, proton mobility in the second interfacialhydration shell is not impaired. Its high mobility coincides withthe observed fast surface proton diffusion in the experiment.

ResultsLong-Range Proton Diffusion on Hydrophobic Liquid-Water Interfaces.We designed a model system containing a buffered water dropletsurrounded by n-decane and a pH-sensitive dye (Oregon Greendihexadecyl phosphatidyl ethanolamine), which accumulated atthe interface (Fig. 1). The dye concentration was so low that twodye molecules were >20 Å apart from each other (assuming ex-clusive interfacial localization). The dye responded to decreasedpH with a decrease in fluorescence intensity F.

The observed fluorescence signal is FðtÞ¼Fðt¼0Þ−Bσðx; tÞ,where σðx; tÞ is the proton surface density, x is the distance tothe sink, and B is a proportionality factor. σðx; tÞ reaches a max-imum at time t ¼ τmax. We tested proton transport by (i) micro-injecting protons on a spot at the water∕n-decane interface and(ii) measuring the kinetics of their arrival at a distant position onthe same interface. Assuming that surface diffusion is decoupledfrom bulk, we fitted FðtÞ for σðx; tÞ by the solution of a two-dimensional diffusion equation (23):

σðx; tÞ ¼ A4πDt

exp�−

x2

4Dt

�expð−k1tÞ: [1]

Here, parameter k1 is a mere fitting parameter. It combines sev-eral phenomena that affect proton escape. Fitting Eq. 1 to the

experimental traces recorded at 0.1 mM buffer resulted in D ¼ð5.7� 0.7Þ × 10−5 cm2 s−1 for 35 μm ≤ x ≤ 85 μm (Fig. 2). D isclose to values obtained from similar experiments on top of lipidbilayers (8, 9).

A tenfold increase in mobile buffer concentration decreasedthe range of surface diffusion. The increased τmaxðxÞ (Fig. 3) in-dicated a combination of surface and bulk diffusion. Thus, slowbulk diffusion of the proton carrier Mes [2-(N-morpholino)etha-nesulfonic acid] (DMes ≈ 6.0 × 10−6 cm2 s−1) decreased theapparent diffusion coefficient Dapp ¼ x2∕4τmax to ð2.2� 0.7Þ ×10−5 cm2 s−1 (Fig. 3, Inset).

Fig. 1. Experimental scheme for fluorometrical detection of lateral protondiffusion. On top of a water droplet (140 μl) containing 0.1 or 1 mM Mes weadded n-decane (280 μl) containing 0.7 μM of fluorescent dye Oregon Green488 1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine, which accumu-lated at the interface. The protons were injected at a distance <1 μm fromthe interface through a glass pipette with a tip diameter of ≈1 μm filledwith 0.7% HCl. The injection volume was rather small (approximately 1fl) sothat convection had negligible effect on diffusion (22). We excited the dyeat 485 nm via an objective (20 ×) and collected the fluorescence via thesame objective after a long pass filter (515 nm). The fluorescent microscope(Olympus IX70, Tokyo, Japan) was equipped with two sets of diaphragms(TILL Photonics, Munich, Germany), which allowed the selection of the emis-sion (5 × 5 μm) and excitation (10 × 10 μm) areas.

Fig. 2. Kinetics of proton diffusion over different distances x. Each trace isthe average of at least 20 records. The midpoint of the detection area waslocated at distances x ¼ 45 (blue), 65 (red), and 85 (green) μm from the areaof proton release. The H2O buffer contained 0.1 mM Mes and 100 mM NaCl,pH 6.3. We found a linear dependence of x 2 on τmax (Inset), as predictedfrom a model of two-dimensional diffusion between a point source and apoint sink. The slope of the cyan line corresponds to Dapp ¼ ð6� 1Þ ×10−5 cm2 s−1. Fitting equation Eq. 1 with D ¼ ð5.7� 0.6Þ × 10−5 cm2 s−1 andk1 ¼ 0.4� 0.1 s−1 to the experimental traces resulted in the black solid lines.Fitting the conventional three-dimensional diffusion equation to the dataresulted in the dashed lines, which correspond to a bulk diffusion coefficientDbulk of ð3.8� 0.6Þ × 10−5 cm2 s−1. The Dbulk exceeds sixfold the diffusioncoefficient of the main proton carrier Mes ∼0.6 × 10−5 cm2 s−1, indicatingthat the conventional bulk diffusion model cannot be used to describeour experimental observation.

Fig. 3. Kinetics of fluorescence changes on the water∕n-decane interfacedue to lateral proton migration. The observation area was located atx ¼ 65 μm from the proton release area. The τmax linearly depended on x 2

(Inset). Increasing buffer capacity or replacing H2O by D2O decreased Dapp

from 6 to 2 or 3 × 10−5 cm2 s−1, respectively. The black line denotes the fitof Eq. 1 to the data. The glass pH electrode reading was 6.3 in H2O andin D2O. Because the pK value of Mes increases by approximately 0.4 unitsin D2O, and the glass pH electrode reading deviates from the true pD ofD2O solutions by 0.4 units, the effects cancel each other out. The buffer con-tained 100 mM NaCl and the indicated Mes concentrations.

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Substituting H2O for D2O (i) increased τmax twofold and (ii)halved Dapp (Fig. 3), as does an increased buffer capacity. Thisdifference is too big to be explained by an increased viscosityof D2O. The increased strength of hydrogen bonds in D2Oconceivably slowed down proton hopping. Alternatively, somedeuterons may have reached the measurement spot via bulkdiffusion. Both the buffer and the isotope effect rule out thepossibility that microinjecting protons caused convection, sinceeither changing the isotope or the buffer would not significantlyalter drift velocity (22). We conclude that the water∕n-decane in-terface captures key features of proton migration along the water/membrane interface, and thus the contribution of dipolar lipidmoieties to ΔGHþ is not required.

To test whether the lateral migration of protons depends ontheir recombination with molecules known to adsorb at hydro-phobic boundaries (24), we varied the chloride concentrationsin the buffer solution (Fig. S1). We found that lateral surface pro-ton diffusion persisted when chloride was not at all present. Thisobservation indicates that lateral proton migration is intrinsic tothe boundary of hydrophobic and hydrophilic liquids.

For an experimental evaluation of ΔGHþ , we measured k1 attemperatures ranging from 287 K to 316 K. The resulting Arrhe-nius plot of ln k1 versus 1∕T is nonlinear, similar to what wasshown in previous work (25). The plot is composed of two tem-perature regimes (Fig. 4). Assuming that proton delivery to mem-brane channels occurs by surface migration, the activation energyfor transmembrane proton transport must show similar tempera-ture dependence. Indeed, concave Arrhenius plots have alreadybeen observed for proton transport through membrane channelsat comparable temperatures (26, 27). In the temperature regimearound 310 K, for which simulations have been carried out (seethe next section), we find that ΔGHþ ≃ 8.7 RT.

Mechanistic Insights. We performed density functional theory(DFT)-based molecular dynamics (MD) simulations (28) to in-vestigate the molecular details of proton diffusion at the surface.

DFT-MD calculations are well suited for the study of protontransfer in complex systems (29, 30). Their accuracy, however,dramatically depends on the choice of the exchange-correlationfunctional. Here we use the Becke–Lee–Yang–Parr (BLYP) func-tional, along with Grimme’s correction for the dispersion forces(31), which turned out to be reasonably accurate yet computa-tionally affordable for our system, which is very large. The BLYPfunctional consists of 25 n-decane molecules, 302 water mole-cules in slab geometry, and one excess proton, making1,707 atoms in total (see Materials and Methods).

The free energy profile GHþ is calculated by 75 ps-long ab in-itio simulations based on metadynamics (32) at 310 K. GHþ is afunction of the distance L from the excess proton to the water∕n-decane instantaneous interface (33) (SI Text and Fig. S2). A wideminimum ofGHþ is located within 6 Å from the hydrophobic sur-face with a depth of 6 RT (Fig. 5) and an estimated statisticalerror of approximately 2 RT (Figs. S3 and S4). This is in reason-able agreement with the experimental estimate ofGHþ describedbefore (approximately 8.7 RT). Within this minimum, two popu-lations of the excess proton I and II (Fig. 5) are observed. Inpopulation I, the hydronium ion is in direct contact with then-decane surface. Its electron lone pair is oriented towards n-de-cane (Fig. 5, Inset), consistent with the fact that it is a weak H-bond acceptor (Fig. S5) (15, 21). The hydronium ion forms threeH-bonds with surrounding water molecules [the so-called ‘Eigenstructure’ (34)]. Similar asymmetric amphiphile-like solvationpatterns through both hydrophilic and hydrophobic interactionshave previously been found for the excess proton in methanol-water solutions (35, 36). Its electronic density is significantlypolarized by the first and second solvation shells (Fig. 5, Inset).

Fig. 4. Experimental estimation of the free energy barrier for proton surfaceto bulk escape. (A) Kinetics of surface proton concentration change in a spotat distance x ¼ 45 μm from the proton release area. The left and right panelswere recorded at T ¼ 287.5 K and 316 K, respectively. The buffer contained1 mM Mes (pH 6.3) and 100 mM NaCl. Fitting of Eq. 1 (main text) to the dataresulted in the red lines. The parameters were D ¼ 4.3 × 10−5 cm2s−1,k1 ¼ 0.2 s−1 and D ¼ 9.5 × 10−5 cm2 s−1, k1 ¼ 31.9 s−1, for the left and rightpanels, respectively. (B) Experiments similar to those shown in (A) were per-formed at temperatures between 287 and 316 K. Subsequently we used thefitting parameter k1 to build the Arrhenius plot. In order to extract ΔGHþ , wetreated the data at low and high temperature regimes separately. The slope ofthe linear regression at 310 K corresponds to ΔGHþ ¼ 8.7 RT.

Fig. 5. The free energy profile of the excess proton GHþ and density profilesof water and n-decane molecules as a function of the distance L to thewater∕n-decane interface (see SI Text for the definition of L). In the back-ground, water molecules are shown in CPK representation and n-decanemolecules are represented as green rods. The blue vertical stripe indicatesthe instantaneous interface between water and n-decane. The system fullytreated with DFTconsists of 25 n-decane molecules, 302 water molecules, and1 excess proton (Fig. S8). Free energy simulations were 75 ps-long and per-formed with a thermostat at T ¼ 310 K. See SI Text and Figs. S3 and S4 fortechnical discussion. (Inset) Electron density differences of the two excess pro-ton populations at the surface (I and II), Δρ ¼ ρsystem − ρH3Oþ − ρrest. Systemrefers to the whole ab initio simulation system; Rest refers to the rest ofthe whole simulation system without H3Oþ. Purple refers to positive Δρand yellow is for the negative Δρ.

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The first peak of the water density profile lies behind the positionof population I at about 1.5 Å, as shown in Fig. 5. Therefore, thehydronium ion is closer to the n-decane surface than the watermolecules. In population II, the ion forms solvent-separatedcontacts with the n-decane surface. It is located in the secondlayer of water molecules without a specific orientation.

In our 10 ps-long unbiased DFT-MD simulations, the excessproton diffuses and remains in the interfacial region (Fig. S6A).The calculated proton lateral diffusion coefficient is ð8� 2Þ ×10−5 cm2s−1 (Fig. S6B). This is in agreement with our experi-mental value ð5.7� 0.7Þ × 10−5 cm2 s−1. Very importantly, po-pulation II represents the main species that diffuses quickly alongthe interface (Fig. 6), because its adjacent water molecules formmore H-bonds, on average, than the water molecules adjacent topopulation I do (Fig. S5).

DiscussionSimulations and experiments provide a consistent picture indicat-ing that (i) the hydronium ion forms attractive interactions atthe water∕n-decane interface, and that (ii) the hydronium ion re-tains high mobility that exceeds bulk mobility of proton carriers.Moreover, both the in vitro and in silico results indicate that theinterfacial energy barrier adopts the form of a well. If the protonwould face a barrier upon approaching the interface from thebulk water, proton microinjection (Fig. 1) would not result insurface diffusion spans and mobilities that are comparable tothose obtained upon proton photo-release from the hydrophobicinterface (8, 9).

Free Energy Minimum at the Interface. To understand the origin ofthe free energy well involving two water layers, we consider keycontributions to GHþ as functions of the proton distance L fromthe interface (Fig. 7D and SI Text). The first stabilizing contribu-tion Gbind is the excess binding free energy of a hydronium ionto the n-decane surface. An approximate estimate for Gbind byconsidering only the enthalpy can be tabulated by ab initio cal-

culations. The binding energy of the hydronium ion to the n-de-cane surface amounts to approximately −25 RT (Fig. 7A), whichexceeds that of a water molecule (approximately −4 RT) sixfold(Fig. 7B). This leads to the value of Gbind approximately −21 RTat the minimum (SI Text).

The next stabilizing contribution Gstrain is due to the watermolecules solvating the excess proton. The latter strains thehydrogen-bond pattern of the surrounding liquid water, as dis-cussed already for water/vapor (17), water/carbon nanotubes(19), or water∕CCl4 interfaces (20). The strain is much smaller atthe boundary because of the reduced number of hydrogen bonds(Fig. S5). At present, no simple way to quantify Gstrain has beenfound.

Then, we consider the destabilizing contribution of Born freeenergy and the free energy costs for polarization of the interfaces(image energy), i.e. GBorn-image. This contribution arises frommoving a proton from the hydrophilic environment of bulk water(ε approximately 80) to the more hydrophobic environmentadjacent to the interface (ε approximately 10–20). We use con-tinuum electrostatics for the calculation of this contribution(SI Text).

Finally, we consider the destabilizing contribution GΦ ofsurface electrostatic potential Φ across two dielectric phases(SI Text). Φ is analogous to the so-called dipole potential of bio-logical membranes and lipid bilayers, which is positive inside themembrane (37, 38). Although somewhat larger in size, Φ has thesame orientation at the water∕n-decane interface. Our ab initiosimulations provide an estimation, showing that the potential

Fig. 6. A lateral diffusion path of the excess proton at the water∕n-decaneinterface extracted from a 10 ps-long NVE ab initio MD simulation.(Inset) Simulation snapshots of the excess proton and its coordinating watermolecules at the interface. The n-decane molecules and remaining watermolecules are not plotted for clarity. The blue area represents the instanta-neous water∕n-decane interface, the same as in Fig. 5. The background coloris set to green.

Fig. 7. (A) and (B) Calculated binding energies of a hydronium ion and awater molecule to the n-decane slab as a function of the distance to the inter-face, respectively. The n-decane slab was extracted by removing the watermolecules from the equilibrated water∕n-decane system. No geometricoptimization has been performed. (C) Calculated average electrostaticpotential Φ of the water∕n-decane system as a function of the distance tothe interface from a 10 ps-long NVT ab initio MD simulation. ΦðLÞ ¼1A

RRRdxdydzhΦðrÞδðl − LÞi, where ΦðrÞ is the electrostatic potential of the sys-

tem at the position r, and A is the area of the interface. ΦðrÞ ¼ ∑BZB

jRB−rj−∫ dr 0 ρðr 0 Þ

jr 0−rj, in which ZB is the charge on nucleus B located at RB, and ρðrÞ isthe electron density of the system at the position r in the real space grid.(D) Gbind, GΦ, GBorn-image and their sum Gsum, comparing with GHþ as a func-tion of the distance to the interface. Gbind stems from the excess short-rangeattractive interactions of a hydronium ion with the n-decane surface. The GΦis the electrostatic energy of the proton due to the surface electrostatic po-tential. GBorn-image is due to Born energy of the excess proton and the inter-action with its image in continuum electrostatics. The GHþ is the profilegenerated from DFT-MD free energy simulations.

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increases by approximately 1.2 V from the water phase to the n-decane phase (Fig. 7C).

In the absence of analytical expression for Gstrain, we calculateGsum ¼ Gbind þGBorn-image þGΦ.Gsum reproducesGHþ surpris-ingly well (Fig. 7D), althoughGbind represents the only stabilizingcontribution. This observation suggests that (i) Gstrain might notbe very large; (ii) the minimum of the free energy spans over twowater layers (Fig. 5) because, beyond that, Gbind ¼ 0 (Fig. 7A);(iii) since our calculated value of the free energy barrier ΔGHþ ¼6� 2 RT is not very different from those calculated for water/vapor (17, 18), water/carbon nanotube (19), and water∕CCl4 (20)interfaces, some of these findings may be general to dielectricmismatched interfaces.

Fast Diffusion at the Interface. The free energy barrier provided byour in vitro and in silico studies on the n-decane interface (ΔGHþ

of about 6 to 8 RT) is similar to that of MS-EVB calculations onthe membrane interface (ΔGHþ of about 6.7 to 8.3 RT) (14).In that case, these protons localize in the deep interface regionof a phospholipid membrane and move essentially with the lipid(14). Our simulations allow us to suggest a different picture forthe n-decane interface. Here, the protons in the second interfa-cial hydration layer retain their high mobility, although they aresubjected to attractive forces large enough to prevent their fastrelease into the bulk. This observation is in perfect agreementwith the experiment, where the highly mobile excess proton staysin the interfacial region for tens and hundreds of milliseconds(Figs. 2 and 3).

Our in silico system contains neither ions nor buffer molecules.This omission is unlikely to distort the principal molecular picturethat emerged from the simulations because varying the concen-tration of both kinds of molecules in the experimental system didnot induce dramatic effects on either lateral diffusion span or onits speed. Although chloride ions may adsorb at the interface(24), proton binding to interfacial Cl− is not essential for lateralproton migration (Fig. S1). An increase in mobile buffer concen-tration seems to inhibit surface diffusion, most probably by a re-combination of the mobile buffer with the excess proton (Fig. 3).

We may thus be confident that the in vitro and in silico studieshave captured the same process. Moreover, we have found aproper explanation for how the requirements for proton attrac-tion and high proton transport rate, which at first glance appearconflicting, may actually both be realized at the same time. Thesimulations show that the hydroniums in direct contact with thehydrophobic liquid are indeed immobile. However, the hydro-niums in the second layer of water molecules are capable ofmigrating along the surface given that they encounter a weakerbinding force. We expect proton attraction to be an intrinsic prop-erty of all water/hydrophobic interfaces and that, at least for hy-drophobic liquid phase, fast surface proton diffusion is retained.

Consequently, these findings may have wide implications beyondmembrane transport (39).

Materials and MethodsThe 1,707 atom system was set up with classical MD (SI Text, Figs. S7 and S8)and underwent ab initio Car-Parrinello MD simulations (28) in the NVT andNVE ensembles, where N is the number of particles, V is volume, and T is tem-perature.

The quantum problem was solved within density functional theory (DFT),using the BLYP exchange-correlation functional and Grimme’s correction forthe London dispersion interactions (31). The accuracy of the correction wasinvestigated by comparing dispersion-corrected DFT calculations with MP2calculations as well as with results from the highly accurate dispersion-cor-rected atom-centered potentials (DCACP) (40) (SI Text and Fig. S9). The elec-tronic wave functions were expanded by plane wave basis sets within anenergy cutoff of 70 Ry. A fictitious electron mass of 400 a.u. and a timestepof 4 a.u. (approximately 0.1 fs) were used.

For the NVT simulations, the Nosé-Hoover chains thermostat (41) was usedto keep the temperature at T ¼ 310 K.

First, several simulated annealing steps and then a 3.0 ps-long ab initioMD equilibration in the NVT ensemble were carried out. Then, based onthe last ab initio MD snapshot, three production simulations were per-formed.

1. We performed 75 ps-long ab initio multiple-walker metadynamics simula-tions (42) in the NVT ensemble to reconstruct the free energy profile as afunction of an appropriate collective variable (CV). The method allowsthe system to escape the free energy minima and scales linearly on a mas-sively parallel supercomputer (42). The CV identifies the distance from theexcess proton to the interface (SI Text). The key parameters of themethod(42, 43) are the width of Gaussian ‘hills’ added to the history-dependentbiasing potential, the height of Gaussian hills, and the frequency at whichthe hills are added. These parameters were set to 0.25 Å, 0.2 RT, and4.84 fs, respectively, similar to what was done in previous applicationsof the method (42, 43).

2. A 10 ps-long ab initio MD simulation in the NVE ensemble was performed.The lateral diffusion coefficient of the excess proton at the water∕n-de-cane interface was calculated. The averaged temperature of this simula-tion is 318� 5 K.

3. A 10 ps-long ab initio MD simulation in the NVT ensemble, at T ¼ 310 K,was carried out. Electrostatic potential was calculated from 200 equallyspaced snapshots. The real-space grid was 360 × 240 × 256. Density pro-files of water and n-decane molecule as a function of the distance to theinterface were also calculated from this simulation.

All the ab initio simulations were performed by using the CPMD code(44). For metadynamics simulations, the PLUMED-CPMD interface was em-ployed (45).

ACKNOWLEDGMENTS. C.Z. and E.I. thank Fabio Pietrucci for providing thePLUMED-CPMD interface for free energy simulations and Giovanni Bussifor the discussions of recovering canonical probability from metadynamicssimulations. We acknowledge that this work has been achieved using thePRACE (http://www.prace-project.eu/) research infrastructure resource JU-GENE hosted by Forschungszentrum Jülich in Germany.

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