Proton Diffusion through Bilayer Pores - The Journal of Physical

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Proton Diffusion Through Bilayer Pores Jesse Gatten McDaniel, and Arun Yethiraj J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07780 • Publication Date (Web): 14 Sep 2017 Downloaded from http://pubs.acs.org on September 19, 2017

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The Journal of Physical Chemistry

Proton Diffusion Through Bilayer Pores Jesse G. McDaniel∗,†,‡ and Arun Yethiraj† †Department of Chemistry, University of Wisconsin, 1101 University Avenue , Madison , Wisconsin 53706 ‡Current Address: School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 E-mail: [email protected] Phone: +1 (404) 894-0594

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Abstract The transport of protons through channels in complex environments is important in biology and materials science. In this work, we use multistate empirical valence bond simulations to study proton transport within a well-defined bilayer pore in a lamellar Lβ phase lyotropic liquid crystal (LLC). The LLC is formed from the self-assembly of dicarboxylate gemini surfactants in water, and a bilayer-spanning pore of ∼3-5 ˚ A radius results from the uneven partitioning of surfactants between the two leaflets of the lamella. Local proton diffusion within the pore is significantly faster than diffusion at the bilayer surface, which is due to the greater hydrophobicity of the surfactant/water interface within the pore. Proton diffusion proceeds by surface transport along exposed hydrophobic pockets at the surfactant/water interface and depends on the continuity of hydronium-water hydrogen bond networks. At the bilayer surface, there is a reduced fraction of the “Zundel” intermediates that are central to the Grotthuss transport mechanism, while the fraction of these species within the bilayer pore is similar to that in bulk water. Our results demonstrate that the chemical nature of the confining interface, in addition to confinement lengthscale, is an important determiner of local proton transport in nanoconfined aqueous environments.

1

Introduction

Proton transport in nanoconfinement is important in many biological processes, such as transport across membranes through ion channels, and in technological applications such as proton exchange membranes (PEMs). The complexity of the transport process arises from the inherent sensitivity to the lengthscale of nanoconfinement, and the special mechanism of “Grotthuss” hopping 1 in which protons migrate along water networks by rearrangement of covalent and hydrogen bonds. The presence of other ionic and non-ionic species further influence the spatial proton distributions and kinetics through electrostatic and hydrophobic interactions. 2 In this work we study proton transport through a model bilayer system using


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reactive molecular dynamics simulations. Self-assembled bilayers consisting of lipid or surfactant molecules are of particular interest, as such bilayers are the basis of both biological membranes and certain synthetic PEMs. In these systems, the ionic headgroups and hydrophobic tails are partitioned into separate domains, and nanoscale water and ion confinement occurs both within membrane pores and also within the water layers that separate closely packed bilayer surfaces. 3 In biological membranes, the ion and water transport near the membrane surface and through membrane pores or channels is essential. 4–6 Previous work has focused on mechanisms of proton transport near lipid bilayer surfaces, 7–12 through spontaneously formed membrane pores, 13 or within specific protein channels. 14–21 Complementary studies of proton transport in synthetic PEMs have largely focused on perfluorosulfonic acid (PFSA) membranes. 22–25 Theoretical studies of PFSA have examined the protonation of sulfonic acid groups in nanoconfinement, 26–40 the effect of structural morphology on ion transport, 41–43 and specific transport mechanisms 2,44–46 such as proton hopping between acid group solvation shells along the membrane surface. 47–49 Additional theoretical studies have importantly attempted to bridge the gap between nanoscale chemical detail and mesoscopic mass transport of protons in PFSA membranes. 50,51 Surfactant-based lyotropic liquid crystals (LLCs) are particularly ideal systems for studying fundamental mechanisms of proton transport in nanoconfinement due to their precise synthetic control and tunability, 52 and direct structural characterization. 53 The nanoconfinement lengthscale and topology in LLCs are readily determined by sharp X-ray scattering peaks, 54,55 and this confinement can be precisely tuned based on the surfactant weight percent. LLCs may exhibit a variety of morphologies including hexagonally-packed cylinders, bicontinuous cubic networks, or lamellar structures depending on the type of surfactant and water composition; 54,56,57 in this regard, lamellar phases are the closest analogue to biological membrane bilayers, whereas other morphologies may be more desirable for technological applications. 58–60 As with biological membranes, lamellar LLCs may exhibit either ordered



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or disordered packing of hydrophobic tails within the bilayers, resulting in either Lβ or Lα phases respectively. 61–66 Furthermore the relative stability of Lα and Lβ LLCs can be controlled through synthetic modification of the surfactants, 67–69 which allows systematic characterization of water and ion dynamics for these different bilayer phases over a range of nanoconfinement lengthscales. Fundamental to proton transport in all of the above mentioned systems is the Grotthuss exchange mechanism, which is a primary process by which protons are transported in aqueous environments. 70,71 This mechanism involves thermal bond rearrangement of proton/hydrogenbond water networks, facilitated by low (∼ kcal/mole) energy barriers for transferring an excess proton from a hydronium ion to a hydrogen-bonded water molecule. 72,73 Significant advancement in the theoretical understanding of the Grotthuss mechanism has been enabled by the development and application of the multistate empirical valence bond (MS-EVB) method by Voth and coworkers, 72–84 and others. 85–92 The MS-EVB method is a reactive molecular dynamics approach that explicitly captures the bond breaking/formation events involved in Grotthuss transport, with computational efficiency that allows access to diffusive timescales, and comparably greater accuracy than alternative central-force based methods. 48,77,81 Accurate MS-EVB potentials for hydronium ions have been refined to ab initio calculations to allow for predictive accuracy of static and dynamic properties. 72–74,79,83,84 For proton transport in bulk water, the MS-EVB method has provided significant mechanistic insight including the fundamental role of “Eigen” and “Zundel” intermediates, 73,93 the importance of randomization of hydronium hydrogen bonds between proton hopping events, 70,80 and the coupling of water mobility and importance of fluctuations in the water solvation structure for successful proton transfer. 71,84 In this work we use MS-EVB simulations to study proton transport in a lamellar, Lβ LLC formed by the self assembly of dicarboxylate gemini surfactant molecules in water. To enhance computational efficiency, we implement and describe an algorithm for efficiently computing the particle-mesh Ewald (PME) 94 reciprocal space electrostatic forces of the MS-


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EVB Hamiltonian, as described in the Supporting Information. The model system consists of a lamellar LLC phase with λ ∼15 water molecules per surfactant. Due to asymmetric surfactant partitioning during the LLC self-assembly, a pore is formed within the LLC bilayer, which is metastable throughout the ∼ µs simulation; this allows direct characterization of proton transport both within the bilayer pore and along the bilayer surface. Consistent with previous work, 95 we find a high propensity for excess protons to be trapped at exposed hydrophobic surface regions of the dicarboxylate LLC bilayers, with proton transport primarily dictated by diffusion along these surface sites. Pores within the LLC bilayers exhibit a lower concentration of surfactant carboxylate headgroups, and this difference in the hydrophobicity of the pore and bilayer surface has a significant effect on the local proton dynamics, resulting in faster proton transport through the bilayer pores compared to near the bilayer surface. Within the pore, hydronium ions exhibit a distribution of “Zundel” and “Eigen” motifs quite comparable to bulk water, whereas at the bilayer surface the probability of “Zundel” formation is significantly reduced, due to the greater surface heterogeneity and disruption of water networks. The efficient proton diffusion through bilayer pores results from less disruption of interfacial hydrogen-bonded water networks due to the enhanced hydrophobicity of the pore surface, indicating that the chemical surface composition, and not just the confinement lengthscale, is an important determiner of proton transport in nanoconfinement. This mechanistic insight is an important complement to previously proposed proton transport mechanisms within nanopores obtained from studies of carbon nanotubes 96–101 as well as metastable pores in biological membranes. 13

2

Methods

We study LLCs self-assembed from dicarboxylate gemini surfactant molecules with sodium counterions in water. Such gemini surfactants consist of two single tail surfactants that are covalently bound by a linker, resulting in a greater propensity for self-assembly into micelles



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and LLCs; 56,57,102–104 specifically the self-assembly of dicarboxylate gemini-surfactants has been characterized both experimentally 52,54 and theoretically. 55,69,105,106 In this work, we focus on dicarboxylate surfactants with 15 carbon atoms in the surfactant tails, and 4 carbon atoms in the gemini linker (Figure 1), termed “CO2 -15(4)”. We consider a system composed of 134 surfactant molecules, 268 sodium counterions, and 2010 water molecules, resulting in simulation box of x/y dimensions of ∼7.6 nm and z dimension of ∼3.4 nm, with the periodic bilayer stacking along the z dimension. To self-assemble and equilibrate the CO2 -15(4) Lβ phases, we use 2µs simulated annealing simulations as described previously, 69 starting from 380 K and cooling to 300K at a rate of 0.2 K/ns. This simulation results in the selfassembly of an Lβ morphology with asymmetric surfactant partitioning between the top and bottom surfaces of the bilayer. Specifically, we find that the ratio of surfactant molecules with their headgroups at the top surface of the bilayer to those with headgroups at the bottom bilayer surface is ∼64/70 molecules. This ratio remains relatively constant after the system is equilibrated and the Lβ morphology is fully formed, with nearly negligable surfactant diffusion between the surfaces. As discussed below, this asymmetry in the bilayer causes pore formation that is stable over the entire simulation timescale. For comparison, we construct a symmetric bilayer by manually “moving” surfactant molecules from the bottom to top bilayer surface, and then requilibrating for 400 ns, resulting in a symmetric 67/67 surfactant partitioning between bilayer surfaces. We characterize the structural ording of these LLCs by computing X-ray scattering structure factors, as described previously. 106 To analyze the pore width and topology we use the HOLE software of Smart and coworkers, 107 with 1.2 ˚ A van der Waals (VDW) radii for surfactant atoms.


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O O-

O-

C15 O

Figure 1: Molecular structure of dicarboxylate gemini surfactants with 15 tail carbon atoms and 4 linker carbon atoms. To study proton transport, we conduct 8 MS-EVB simulations starting from configurations in which we randomly choose and replace a sodium ion/water molecule pair with a hydronium ion. Half of these simulations are started from configurations in which hydronium ions are proximal to the bilayer surface, and the other half are started from configurations of hydronium ions placed inside the bilayer pore; throughout the simulations, the excess protons remain in either of these “surface” or “pore” configurations respectively. The MS-EVB simulations are equiibrated for 500 ps at 300 K (starting from equilibrated Lβ structures), and production runs are ∼4 ns, with a 1 fs time step in the NVE ensemble. All MS-EVB simulations are conducted with an in-house code that utilizes an efficient implementation for calculating the PME reciprocal space forces for the different diabatic states, as described in the Supporting Information; further details of the underlying theory and implementation of the MS-EVB method can be found in the original works of Voth and coworkers. 72,73,75,81 We use the recently re-parameterized MS-EVB3.2 model 83,84 along with the SPC/Fw model 108 for describing hydronium/water interactions. The GROMOS force field 109 is used for the surfactant molecules and sodium ions, and cross interactions between the hydronium ion and surfactant groups have been parameterized in our recent work. 95 All of the standard MD simulations (non MS-EVB) are conducted with the GROMACs-4.6 sofware, 110 using the Berendsen barostat 111 with semi-isotropic pressure coupling, Nose-Hoover thermostat, 112,113



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PME 94 for electrostatics, and a 1.4 nm cutoff for VDW interactions.

3

Results and Discussion

3.1

Structure of bilayers

The CO2 -15(4) dicarboxylate Gemini surfactants (Figure 1) self-assemble into Lβ lamellar phases at hydration levels below λ ∼18 water molecules per surfactant, at 300K. 69 The surfactant tails pack in an ordered arrangement within the lamellar bilayer (see Figure 2). The two forms of packing, laterally into an ordered hexagonal lattice with ∼4-5 ˚ A spacing, and stacking of the bilayers with a several nanometer spacing, result in distinct features in the X-ray scattering spectra (Figure 3).

Figure 2: Snapshot of CO2 -15(4) Lβ lamellar phase at λ=15. The simulation box is replicated in the z-dimension to depict the bilayer stacking, and atom colors are as follows: sodium (blue), oxygen (red), carbon (cyan), hydrogen (white) . We study two different Lβ morphologies, with and without a trans-bilayer pore. We refer to the porous morphology as Lpore and the non-porous (symmetric) morphology as Lsym β β . The differences between these structures are qualitatively illustrated in Figure 3, which shows simulation snapshots of the packing of the surfactant tails along with corresponding X-ray scattering structure factors of the systems. The hexagonal packing of the tails can be clearly 8 ACS Paragon Plus Environment

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seen from these snapshots, although there is some inherent disorder. The X-ray scattering structure factors quantify the two different types of periodicity in the Lβ phases; peaks at ∼0.2 and 0.4 ˚ A

−1

correspond to the (001) and (002) reciprocal lattice vectors defining the

periodic bilayer stacking in the z-dimension, while the peak(s) at ∼1.5 ˚ A

−1

corresponds to

system is clearly seen the short-range tail packing within each bilayer. The pore in the Lpore β from the snapshot. In the vicinity of the pore, there is disorder in the tail packing, which is quantitatively illustrated by the smaller magnitude of the ∼1.5 ˚ A Lpore system relative to the Lsym system. β β


−1

scattering peak for the

S(q)

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S(q)


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1.6

0

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0.4

(a)

0.6

0.8 -1 q (Å )

1

1.2

1.4

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Figure 3: Simulation snapshots of the surfactant tails as viewed from the z-dimension for morphologies. Corresponding X-ray scattering structure factors are the a) Lsym and b) Lpore β β shown for the full systems. .


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The asymmetry of the surfactants and presence of the pore in the Lpore phase has only β a small effect on the net density distribution of the different chemical species. This is illustrated in Figure 4, where we show computed density profiles along the z-dimension (normal systems. These density profiles are quanand Lsym to bilayer stacking) for both the Lpore β β titatively similar to previously computed profiles in dicarboxylate lamellar phases; 69,95 the water and sodium distributions are Gaussian, centered at the middle of the water layer, while the surfactant carboxylate headgroup distribution is approximately a sum of two Gaussians, each centered at the different bilayer surfaces. The roughness of the surface is evident by the broad headgroup distribution, and there is non-negligable probability for headgroups to reside at the center of the water layer due to surface fluctuations, as qualitatively seen in Figure 2. Differences between these distributions in the Lpore and Lsym systems are small, β β indicating that the asymmetry between bilayer surfaces for the former system is subtle. For the Lpore system, the carboxylate peak at z > 0 (bottom bilayer surface, facing water β layer) is slightly higher than the corresponding peak at z < 0 (top bilayer surface), reflecting the asymmetric surfactant distribution. Correspondingly, the tail group density (CHn ) is slightly depleted near the top bilayer surface. In general, however, the bilayer structure and hydrophilic/hydrophobic density distributions are very similar for the Lpore and Lsym β β systems, despite the presence of the pore.



0.015

0.015 H2O carboxylate CHn

Relative Probability

Relative Probability

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-15

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H2O carboxylate CHn +

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Na

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Z (Å)

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(a)

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Figure 4: Density profiles of chemical groups along the z-dimension, normal to the bilayer stacking in the a) Lsym and b) Lpore phases. The center of the distribution corresponds to β β the center of the water layer in each system. Each distribution is separately normalized to the specific number of atoms of that type in the system.

3.2

Pore structure

We calculate the width of the pore using a Monte Carlo (MC) sampling approach as implemented in the the HOLE software. 107 The z-dimension (normal to biliayer) is discretized, and for each of the resulting 2D planes, an (x,y) coordinate is found which lies inside the pore. Starting from this point, random MC moves are made within the x-y plane to generate new points, and the radius of the largest sphere centered at each point that doesn’t overlap with any surfactant atom is computed. The center and radius of the pore for a given z-coordinate is then given by the center and radius of the largest such sphere, and the pore channel is defined by tracing a line through all of these center points. In Figure 5, the pore radius as a function of distance from the bilayer center is shown along with a corresponding snapshot illustrating the pore topology. The pore spans the entirety of the ∼2 nm surfactant bilayer, with an “hourglass-like” shape, such that it is wider near the water layer opening, and narrower at the center of the bilayer. Away from the opening, the pore has a radius of ∼3-5 ˚ A, as calculated assuming circular cross sections and thus should be considered a minimum limit. Throughout several hundred nanoseconds of the simulation, the fluctuations in pore radius are < 1 ˚ A indicating that the pore is “stable” and well-defined. 12 ACS Paragon Plus Environment

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10 5

Z (Å)

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0 -5 -10 2

3

4

5

6

7

8

Pore Radius (Å)

Figure 5: Pore radius as a function of distance from center of surfactant bilayer, as computed from final 400 ns of the NPT trajectory. Fluctuations are defined by the standard deviation of the radii (for a given z position) as computed from the different simulation snapshots. We note that the reference of the z-axis (Z=0) corresponds to the center of the bilayer, which is different than the reference of Figure 4. In the simulation snaphot, the pore is depicted by its space-filling volume colored in blue, and colors of atoms are the same as in Figure 2. The green band across the pore denotes the position of minimum pore width. .

3.3

Water dynamics

The dynamics of both water and ions are much slower in these confined LLCs compared to bulk aqueous systems. Diffusion coefficients of water and sodium are given in Table 1, computed from 100 ns of the MD trajectory. The water diffusion coefficient is ∼20 times smaller in these LLCs than in the bulk. 108 The slow water dynamics is due to both nanoconfinement and high ionic concentration, and for such LLCs the quantitative diffusion rates primarily depend on the specific hydration level. 55,69 In Table 1, we additionally report diffusion coefficients calculated for 2D in-plane motion parallel to the bilayer plane (Dxy ) and 1D motion normal to the bilayer stacking (Dz ). From this comparison, we find that the difference in the water and ion dynamics between the systems is entirely due to diffusion through the pore, along the z-dimension. The in-plane diffusion along the bilayer surface and within the water layers is identical in the two phases, while Dz is effectively zero for the xy non-porous system at long time (for Lsym are only due to 3D β , differences between D and D



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vs 2D normalization). This comparison indicates that the only significant difference in the net dynamics between Lpore and Lsym phases is the additional mechanism of mass transport β β through the pore in the former system. We note that quantitative differences between the water diffusion coefficients reported here, and in previous work, 69 are due to the different employed water models (SPC/Fw vs SPC). Table 1: Diffusion Coefficients for Sodium Ions and Water in Lβ phases.

3.4

(10−5 cm2 /s)

DN a+

Dxy N a+

DzN a+

DH2 O

Dxy H2 O

DzH2 O

Lsym β

0.035

0.052

0.000

0.127

0.191

0.000

Lpore β

0.040

0.053

0.013

0.135

0.182

0.041

Proton transport

Proton diffusion within the pore is generally faster than proton diffusion at the surface of the bilayer. The dynamics of an excess proton in the Lpore phase is quantified by the proton mean β square displacement (MSD) as computed from 4 ns MS-EVB simulations. The proton MSDs from the 8 independent simulations are illustrated in Figure 6a; half of the trajectories are for protons proximal to the bilayer surface (red), while the other half are for protons within the bilayer pore (black). Statistically averaged MSDs are only obtained for short times (∼50 ps), thus precluding the calculation of diffusion coefficients. As there is only one excess proton in the system, each trajectory exhibits a unique sampling of the surface/confinement environment, resulting in quantitatively different MSDs for each trajectory. The surface proton that diffuses almost as fast as the pore protons is spatially located near the pore entrance at the bilayer surface (vide infra). Enhanced proton transport within the bilayer pore relative to the surface is surprising because these protons are more confined. Confinement at the bilayer surface and within the pore are dimensionally different, as the former exhibits confinement in only one dimension (water layer) while the latter exhibits confinement in two dimensions (pore channel, or 14 ACS Paragon Plus Environment

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“cylinder”). Qualitatively, however, water and ions at the bilayer surface are “less-confined” than similar species within the bilayer pore; this is inferred from comparing the water layer thickness between bilayer surfaces (∼ 5-10 ˚ A, Figure 4) to the pore width (∼ 3-5 ˚ A, Figure 5). Previous studies on similar lipid/surfactant systems have generally concluded that the water and ion dynamics is slower with more narrow confinement. 114–121 Our finding that proton diffusion is faster within the more narrowly confined bilayer pore is thus an interesting and important result. We note that while facile proton transport can occur for single water chains within nanopores, 96–100,122 such an effect is very specific to ∼ 2˚ A confinement lengthscales, 96,123 and is not of primary mechanistic importance in the present system. The transport of protons is much faster than that of sodium ions, and the transport of water molecules lies in between that of surface and pore protons. Figure 6b, compares the proton MSDs for the different sites to MSDs of water molecules and sodium ions over the same 50 ps time scale (in this figure the proton MSDs have been averaged over like trajectories). The faster transport of protons can be attributed to the special Grotthuss transport mechanism in aqueous environments. 73 Interestingly, the relative mobility of protons compared to water molecules depends on the specific local environment within the Lpore system; β within the pore, proton diffusion is enhanced relative to diffusion of water molecules, similar to the situation for excess protons in bulk water, but the protons proximal to the bilayer surface have comparatively lower mobility. While proton diffusion is generally faster than water diffusion in aqueous environments, the presence of ionic species in the dicarboxylate Lpore system leads to slower proton transport rates, similar to the effect demonstrated for β aqueous salt solutions. 124,125



20

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H3O Surface

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+

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time / ps

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Figure 6: a) Mean square displacement (MSD) of excess protons in Lpore computed from 4 β ns MS-EVB simulations. Red curves denote trajectories of protons proximal to the bilayer surface, and black curves are trajectories of protons within the pore. b) Averaged MSDs from proton trajectories compared to MSDs for water molecules and sodium ions. . The surface protons move along the surface of the bilayer, with very limited excursion into the center of the water layer, but the pore protons sample most of the pore volume. Figures 7 and 8 depict spatial diffusion maps of the protons from the 8 different simulations. In these figures, the water, surfactant, and sodium molecules/ions are frozen from a single snapshot, and all spatial sites visited by the proton during the 4 ns simulation are denoted by spheres, with different colors (orange, yellow, tan, purple) corresponding to the different trajectories. Figure 7 shows the proton “surface’ trajectories, from both a top view of the bilayer surface and a side view of the water layer separating the bilayers. The central important feature of these trajectories is that the protons are strongly attracted to the bilayer surface, and diffusion occurs primarily by transport along the surface rather than at the center of the water layer. This interesting qualitative result was reported in our previous study of proton transport in similar dicarboxylate Lα phase LLCs; 95 we found that protons were attracted to hydrophobic pockets at the surfactant/water interface, and the interaction strength between protons and the hydrophobic surface sites strongly modulated proton transport rates. This physics is identically important for proton transport in the present Lpore system. In Figure β 7, the proton trajectory corresponding to the yellow spatial diffusion map exhibits enhanced


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transport compared to the other three trajectories, corresponding to the outlier red curve in Figure 6; for this particular trajectory, the proton diffuses along the surface at the edge of the pore entrance, and enhanced transport occurs due to identical mechanisms as for protons within the pore (vide infra). In Figure 8 we show the similar diffusion maps for the proton trajectories within the pore. It is evident that the protons diffuse along the entire length of the pore, but in no trajectory does the proton completely diffuse out of the pore and into the water layer separating the bilayer surfaces. The extent of spatial diffusion is consistent with the proton MSDs (Figure 6), as the protons exhibit significantly greater spatial diffusion (in 4 ns) within the pore than at the bilayer surface. We note that the spatial diffusion maps in Figure 8 artificially exaggerate the width of the pore because only a single snapshot of the bilayer is shown and thus fluctuations in the pore channel position are not illustrated.

as viewed from top Figure 7: Proton diffusion trajectories (4 ns) for surface sites of Lpore β and side of bilayer. Spatial diffusion maps for the protons are shown for each independent trajectory, as tan, yellow, orange, and purple spheres; surfactant and water atoms are colored as carbon (cyan), oxygen (red), hydrogen (white). .



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Figure 8: Proton diffusion trajectories (4 ns) for pore sites of Lpore as viewed from side of β bilayer. Spatial diffusion maps for the protons are shown for each independent trajectory, as tan, yellow, orange, and purple spheres; surfactant and water atoms are colored as carbon (cyan), oxygen (red), hydrogen (white). . There are significant hydrophobicity differences between the pore surface and bilayer surface, which subsequently affects the water hydrogen bond (H-bond) network and probability distribution for important intermediates involved in the Grotthuss transport. Figure 9a shows the radial distribution function, g(r), between the oxygen atoms of the surfactant carboxylate headgroups and hydrogen atoms of the hydronium ions, computed from both protons within the pore (black) and at the surface of the bilayer (red). It is clear that there is a much greater probability for protons to be proximal to carboxylate headgroups at the bilayer surface than within the bilayer pore. The major peak at ∼4 ˚ A corresponds to a water-mediated interaction between the proton and headgroup, in which a water molecule separates the two ionic pairs. As demonstrated in our previous work, 95 these water-mediated headgroup/proton surface interactions are typical configurations in dicarboxylate LLCs, in which the oxygen atom of hydronium “buries” into hydrophobic pockets at the bilayer surface, and the hydronium hydrogen atoms orient towards the water layer, donating H-bonds from below. Such configurations are energetically favorable because the hydronium ion is amphiphillic, 82,83,124,125 with the oxygen atom tending to interact with hydrophobic groups 18 ACS Paragon Plus Environment

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as it has only a small propensity to accept H-bonds. In Figure 9b, we replicate the snapshot of the bilayer pore from Figure 5, but remove water molecules and highlight the carboxylate headgroups. This rendering qualitatively illustrates the enhanced hydrophobicity of the pore surface compared to the bilayer surfaces facing the water layers. The surface of the pore is mostly composed of the hydrophobic groups of the surfactant tails, and there is a much lower density of headgroups; this is the reason for the much reduced correlation between protons and carboxylate groups for protons within the pore (Figure 9a).

3

Pore Surface

head

3

/HH O

4

g(r) O

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2 1 0 0

2

4

R(Å)

6

8

(a)

(b)

Figure 9: a) Radial distribution function between oxygen atoms of carboxylate headgroups and hydrogen atoms of hydronium ions for protons located within the bilayer pore (black curve) and protons located at the bilayer surface (red curve). b) Snapshot of bilayer pore in which only the surfactant atoms are shown, and the carboxylate headgroups are highlighted. The enhanced hydrophobicity of the pore surface and lower probability for proton/carboxylate interactions has an important effect on the proton/water H-bond network and Grotthuss transport. Efficient Grotthuss transport involves protons hopping along a water wire connected by hydrogen bonds, and relies on well-formed hydrogen bond networks proximal to the hydronium ions. 96,98,125,126 However, for protons at the bilayer surface, the water Hbond network originating at the hydronium ion is disrupted after the first or second water molecule by interactions with the carboxylate headgroups; in the pore, the lower concentration of headgroups facilitates more continuous H-bond water networks through which the proton can diffuse by Grotthuss hopping. We quantify this effect by computing the number 19 ACS Paragon Plus Environment


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of H-bonds that a given water molecule participates in as a function of the location along a proton-water H-bonding chain (H-bonds are defined by standard distance and angle metrics: ROO ≤3.5 ˚ A and θHOO ≤30◦ ). This quantitative analysis is shown in Figure 10, indicating the number of donated H-bonds (Figure 10a) and accepted H-bonds (Figure 10b) for water molecule chains originating at protons within the pore or at the surface of the bilayers; for comparison, we compute the analogous quantities for an excess proton in bulk water. It is important to note that our analyzed proton-water H-bond chains are asymmetric, in that water molecules are only added to the chain if they accept a H-bond from a previous molecule in the chain (but not if they donate a H-bond to the previous molecule); this definition is utilized because Grotthuss proton transport involves H-bond accepting water molecules. We find that the number of accepted H-bonds along the proton-water chain is comparable between the Lpore system and bulk water. The hydronium ion accepts only ∼0.1 H-bonds on β average, and nearest neighbor water molecules accept only ∼0.1-0.3 H-bonds in addition to the H-bond accepted from the hydronium ion (∼1.1-1.3 total). By the second and third water molecule in the chain, the number of accepted H-bonds nearly converges to the bulk water value of ∼1.8. The reason that the nearest neighbor water molecules have a lower number of accepted H-bonds is because of the delocalization of the excess proton, in which the excess positive charge “repels” H-bond donors (in this analysis, we have used the largest amplitude diabatic state to define the location of hydronium). In contrast to accepted H-bonds, the number of donated H-bonds by water molecules within the chain is significantly lower in the Lpore system compared to bulk water, due to the β presence of carboxylate groups. This is shown in Figure 10a, in which the average number of donated H-bonds from a water molecule in the chain to another water molecule is only ∼1.11.2 in the Lpore system compared to the average value of ∼1.8 in bulk water. It is important β to note that in Figure 10a, only H-bonds involving water and hydronium are counted, and Hbonds between water molecules and carboxylate head groups are omitted. The inequivalence of the number of H-bonds donated and accepted in Figure 10 is due to the asymmetry of the


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defined chains (vide supra), such that all of the H-bond donors contributing to the averages are not necessarily included in the chains. (the absolute number of donating and accepting H-bonds in the full system is necessarily the same). The hydronium ion donates ∼3 H-bonds to water molecules in all cases, indicating a low probability for primary interactions between hydronium and carboxylate groups. However, the number of donated H-bonds for the first and second water molecules in the chain is determined by a subtle interplay between the proton delocalization and interaction with carboxylate headgroups. Proton delocalization results in a tendency for first neighbor water molecules to donate a greater than average number of H-bonds, but the high probability for first and second water neighbors to interact with carboxylate groups (Figure 9a) lowers the number of H-bonds donated to water for these molecules. Comparing the water chains originating from protons within the bilayer pore (black curve) to the chains originating from protons at the bilayer surface (red curve), it is evident that there is a significant difference in the network connectivity at the first and second chain water molecules. Protons at the bilayer surface exhibit more broken water chains, evidenced by a smaller number of donated H-bonds for the nearest water molecules; this is due to the higher concentration of carboxylate groups at the surface, which interrupt the water H-bond networks. This structural difference in H-bond connectivity along water networks for protons within the pore and at the surface of the bilayer is the primary reason for the difference in proton transport rates (Grotthuss hopping) in these different regions of the Lpore system. β



3

3

# H-Bonds Accepted

Pore Surface Bulk Water

2.5

# H-Bonds Donated

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2 1.5 1


2.5 2 1.5 1 0.5

0.5 0 0

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1

2

3

4

5

6

7

0 0

1

2

3

4

5

6

7

# H2O Chain

# H2O Chain

(b)

(a)

Figure 10: Number of a) donated and b) accepted water-water (or hydronium-water) hydrogen bonds for a given molecule along a water hydrogen bond network originating at a hydronium ion. The different data sets are for hydronium ions within the bilayer pore (black), at the bilayer surface (red), and for comparison, in bulk water (blue). The indices on the x-axis denote the position of the molecule within the hydrogen bond chain, such that index “0” is the hydronium ion, index “1” denotes water molecules directly accepting hydrogen bonds from hydronium, index “2” are water molecules accepting hydrogen bonds from index “1” water molecules, etc. Additional mechanistic understanding of the different proton transport rates within the bilayer pore and at the bilayer surface comes from analysis of the expansion coefficients of diabatic states in the MS-EVB state. In particular, such an analysis reflects the probability for protons to be in either “Zundel” or “Eigen” configurational motifs. In Figure 11, we show snapshots of representative Eigen and Zundel configurations from the simulations, as well as the probability density for the two largest diabatic state expansion coefficients (c21 and c22 ) for the excess protons in the different environments. In Eigen form (Figure 11a), the excess proton is largely localized as a central hydronium ion, donating hydrogen bonds to three water molecules in a symmetric configuration; this motif corresponds to values of c21 ∼0.6 and c22 ∼0.13 in bulk water. 73 The Zundel configuration (Figure 11b) is an important intermediate for proton transfer events, 70 characterized by the excess proton shared equivalently by two 2 2 water molecules and forming an H5 O+ 2 complex; the Zundel form has values of c1 ∼ c2 ∼

0.45 in bulk water. The distribution of the MS-EVB expansion coefficients for a proton in bulk water (Figure 11c) shows large peaks corresponding to the Eigen configuration (c21 ∼0.6, 22 ACS Paragon Plus Environment

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c22 ∼0.13), and lower probability tails corresponding to Zundel-like configurations (c21 ∼ 0.40.55, c22 ∼ 0.3-0.45). We find that the Eigen and Zundel distributions are very similar for protons within the bilayer pores compared to the corresponding distributions for protons in bulk water. Interestingly, however, there are significant differences in the distributions for protons at the bilayer surface; there is greater probability for the Eigen configuration, with the c21 peak shifted to larger values (∼0.66), and there is significantly reduced probability for the Zundel configuration as indicated by the less prominent shoulders of the c21 and c22 distributions. These distribution differences are due to the high concentration of carboxylate headgroups at the bilayer surface (Figure 9), which affect the proton structure in a similar manner as previously discussed in terms of the hydrogen bond water networks (Figure 10). As the Zundel configuration is the primary intermediate state in the Grotthuss hopping mechanism, 70 the lower probability of the Zundel state correlates with the lower proton transport rates for protons at the bilayer surface. It is important to note that the above mentioned trend in the Eigen/Zundel distribution is primarily due to the differences in chemical composition of the bilayer pore/surface interfaces rather than differences in confinement lengthscale. For very small water channels, it has previously been shown that confinement stabilizes the Zundel state because the Eigen configuration exhibits a bulkier solvation structure so that it does not sterically fit into very narrow channels. However, this effect was most prominent for channels of 2-3 ˚ A in radius, and largely diminishes for channels of radius ≥ 4-5 ˚ A. 96 The bilayer pore in the Lpore system β is comparable in size to the larger limit, ∼ 3-5 ˚ A, especially considering that the dimensions reported in Figure 5 should be considered a lower bound, since the pore is not a smooth cylinder but has significant interfacial roughness. Additionally, the Eigen/Zundel stability trends depicted in Figure 11 are qualitatively opposite from the confinement-mediated effect, and the consistency with the trends in hydrogen bond network (Figure 10) and headgroup correlation (Figure 9) clearly indicate that the effect is due to differences in the surface chemical composition.




8

(a)

Probability Density

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6

c2

2

c1

2

4

2

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 ci

(b)

(c)

Figure 11: Snapshots of representative a) Eigen and b) Zundel proton configurations. In the Eigen configuration, the dashed red lines denote hydrogen bonds. c) Probability distribution of primary (c21 ) and second largest (c22 ) MS-EVB expansion coefficients, for protons within the bilayer pore (black curve), at the bilayer surface (red curve), and for protons in bulk water (blue curve), for comparison. The solid lines are distributions for c21 , and dashed lines are distributions for c22 . There is a higher probability of finding the protons at the center of the pore than at the entrance. Figure 12 depicts the probability density for finding a proton along the pore zdimension, which is calculated by constructing a histogram from the four pertinent MS-EVB trajectories. This histogram should be interpreted only semi-quantitatively as the trajectories are too short to ensure converged sampling, and biased free-energy calculations (e.g. umbrella sampling) are necessary for quantitative accuracy. Comparing this distribution with the pore dimensions (Figure 5), the clear qualitative conclusion is that protons are more likely to be localized at the midpoint of the bilayer pore rather than at either of the pore entrances. This is due to the concentration of carboxylate headgroups along the pore dimension, with higher concentration near the pore entrance, (Figure 9) and the resulting attraction of hydronium ions to the more hydrophobic surfactant/water interface at the center


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of the pore. This conclusion is consistent with our previous findings that protons are significantly attracted to hydrophobic pockets of dicarboxylate surfactant bilayers. 95 Presently, our simulation timescales and current statistics do not allow for accurate quantitative evaluation of this free energy profile, and this will be a subject of future research. 0.005 +

Probability Density

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0.004

H3O Pore

0.003 0.002 0.001 0

-10

0

-5

5

10

Z (Å)

Figure 12: Spatial probability distribution of protons along the bilayer pore, in which z=0 corresponds to the center of the surfactant bilayer.

4

Conclusion

The chemical nature of the confining interface has a significant effect on local proton transport rates in nanoconfined water channels. This surface sensitivity for proton transport is due to the amphiphilic nature of hydronium ions, and the resulting tendency for the oxygen atom of hydronium to be attracted to hydrophobic surfaces. 82,83 These conclusions are based on our simulations of dicarboxylate surfactant LLCs, in which a significant fraction of the bilayer interface consists of exposed hydrophobic hydrocarbon groups, 69 resulting in a heterogeneous interface. The effect of confinement on proton transport can be counter-intuitive because of two possible effects. The dynamics of water and ions slow down with increasing confinement, 114,116,117,119 and in the absence of the Grotthuss transport mechanism, one would expect similar trends 25 ACS Paragon Plus Environment


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to hold for proton transport. In addition, slower water dynamics can diminish Grotthuss transport rates, since this mechanism depends on reorganization of water solvation structures. 70,73,84 It is also possible for confinement to alter the hydrogen-bond networks in a manner that is advantageous for proton hopping. Previous studies of proton transport in carbon nanotubes and other hydrophobic pores 96–100,122 have shown that single water wire networks in small diameter pores may exhibit very fast Grotthuss proton transport rates. Thus both the confinement-mediated structure and dynamics of water networks near hydronium ions can affect proton transport in different ways, and the resulting quantitative enhancement/reduction in dynamics may be specific to the microscopic properties of the system. We find that proton transport is significantly enhanced in the pore compared to the surface of the bilayer because the hydrogen bond water network near a hydronium ion has greater connectivity in the latter case.. Additionally, the probability for formation of Zundel proton configurations is reduced near the bilayer surface, which is significant as these are important intermediates in the Grotthuss transport mechanism. The difference in protonwater network structure at the bilayer pores and bilayer surface is largely due to the relative hydrophobicity of the interface, rather than differences in the confinement lengthscale. The bilayer pore walls exhibit enhanced hydrophobicity and lower concentration of carboxylate head groups compared to the top bilayer surface, and the lower carboxylate concentration leads to more continuous proton-water hydrogen bond networks. While previous studies have largely focused on the effect of confinement lengthscale, our results indicate that the specific surface roughness and chemical functionalization of the interface can have a significant influence on the proton transport rates through nanopores. Our results have potentially important implications for both artificial PEM materials as well as biological membranes. The permeation of protons through lipid bilayers is an important biological process, and the mechanism for both pore formation and proton transport through the bilayers is an ongoing topic of investigation. 9,13 For artificial PEM materials con-


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structed from self-assembled surfactants, the presence of metastable pores spanning bilayers or other hydrophobic domains may have an important effect on the resulting conductivity; pores in lamellar LLCs enable three-dimensional ion transport, extended from the two dimensional transport within each bilayer-separating water layer. PEMs composed of LLCs may thus exhibit ion transport that is more isotropic than would be predicted strictly based on the structural periodicity of the LLC, if the formation of pore networks through hydrophobic domains is facile. One can also envisage the creation of pores of desired functionality by the incorporation of oils and single-tailed surfactants into LLC forming phses, allowing for the rational design of materials with enhanced proton transport.

Acknowledgements This research is supported by Department of Energy, Basic Energy Sciences through grant DE-SC0010328. Computational resources were provided by the Center for High Throughput Computing at the University of Wisconsin. The CHTC is supported by UW-Madison, the Advanced Computing Initiative, the Wisconsin Alumni Research Foundation, the Wisconsin Institutes for Discovery, and the National Science Foundation, and is an active member of the Open Science Grid, which is supported by the National Science Foundation and the U.S. Department of Energy’s Office of Science.. This research was supported in part by National Science Foundation Grant CHE-0840494. Additional computational resources were provided through Extreme Science and Engineering Discovery Environment (XSEDE) allocations under grant number TG-CHE090065.

Supporting Information Available Description of algorithm for efficiently computing the particle-mesh Ewald (PME) reciprocal space electrostatic forces for the numerous diabats of the MS-EVB Hamiltonian.



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Proton Diffusion through Bilayer Pores - The Journal of Physical

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