Article pubs.acs.org/JPCB
Coupling between the Dynamics of Water and Surfactants in Lyotropic Liquid Crystals Jesse G. McDaniel and Arun Yethiraj* Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, United States S Supporting Information *
ABSTRACT: Bilayers composed of lipid or surfactant molecules are central to biological membranes and lamellar lyotropic liquid crystalline (LLC) phases. Common to these systems are phases that exhibit either ordered or disordered packing of the hydrophobic tails. In this work, we study the impact of surfactant ordering, i.e., disordered Lα and ordered Lβ LLC phases, on the dynamics of water and sodium ions in the lamellar phases of dicarboxylate gemini surfactants. We study the different phases at identical hydration levels by changing the length of the hydrophobic tails; surfactants with shorter tails form Lα phases and those with longer tails form Lβ phases. We find that the Lα phases exhibit lower density and greater compressibility than the Lβ phases, with a hydration-dependent headgroup surface area. These structural differences significantly affect the relative dynamic properties of the phases, primarily the mobility of the surfactant molecules tangential to the bilayer surface, as well as the rates of water and ion diffusion. We find ∼20−50% faster water diffusion in the Lα phases compared to the Lβ phases, with the differences most pronounced at low hydration. This coupling between water dynamics and surfactant mobility is verified using additional simulations in which the surfactant tails are frozen. Our study indicates that gemini surfactant LLCs provide an important prototypical system for characterizing properties shared with more complex biological lipid membranes.
1. INTRODUCTION The dynamics of water and ions in nanoconfinement is of interest in a variety of biological and technological applications. In the design of proton exchange membranes, for example, the channels are only a few nanometers wide and the water dynamics under these conditions directly affects ion transport. While there has been considerable work on the effect of confinement on water dynamics, much less is known regarding the impact of the soft nature of the confining surfaces on the behavior of water. In this article we study the lamellar phases of gemini surfactants and investigate the effect of surfactant ordering (and hence dynamics) on the dynamics of the confined water. Surfactant-based thermotropic1 and lyotropic liquid crystals (LLCs)2 share many similarities with the biological lipid bilayers that constitute cell, vesicle, and liposome membranes. Lamellar phase LCs consist of surfactant molecules packed into bilayers that separate the hydrophobic tails and ionic (or polar) headgroups into alternating domains. Such lamellar phases are thus structurally analogous to biological lipid bilayers; just as lipid bilayers may exist as “fluid” or “gel” phases,3 lamellar LLCs may be of either Lα or Lβ type characterized by surfactant tails that are disordered or ordered respectively (nematic, smectic nomenclature is used in the thermotropic LC literature1). Due to the many biological, industrial, and material science applications, the fundamental physical properties of both surfactant and lipid bilayers are of complementary interest. The focus of this work is on a system where the surfactant ordering can be tuned without changing either the temperature or hydration level. Twin-tailed, “gemini” surfactants are a © 2017 American Chemical Society
specific class of molecules that have received considerable interest due to their desirable self-assembly properties and high surface activity.4−10 Geminis exhibit significantly lower critical micelle concentration, enhanced tunability, and unique LLC phase behavior compared to single tail surfactants. Of particular interest to bilayer studies, geminis can form either Lα or Lβ phases at room temperature, depending on the surfactant type.11−13 These phases are distinguished by their X-ray diffraction spectra; Lβ phases generally exhibit additional scattering peaks corresponding to ∼4.1−4.2 Å spacing,13−17 indicative of ordered hexagonal packing of alkyl chains in the bilayer.18,19 This tunability for forming either Lα or Lβ room temperature phases makes gemini surfactants ideal prototypical systems for studying the fundamental influence of surfactant tail ordering on the resulting bilayer properties. While such physics has been explored in corresponding gel and fluid phases of lipid bilayers,3,20−24 the different temperature stability regimes of these phases render direct comparison of dynamical properties difficult. The characterization of gemini bilayer properties is additionally essential for the many proposed biological applications of these surfactants. Gemini surfactants have received considerable interest for applications as antimicrobials,25−31 and as liposome constituents for both drug delivery32−35 and DNA transfection;36−49 in these applications, the surfactant/lipid bilayer interaction is of primary importance. Several mechanistic Received: March 17, 2017 Revised: April 24, 2017 Published: April 26, 2017 5048
DOI: 10.1021/acs.jpcb.7b02551 J. Phys. Chem. B 2017, 121, 5048−5057
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The Journal of Physical Chemistry B studies of the interaction between geminis and lipid membranes have been reported. In a series of combined computational and experimental studies, Almeida et al.50−52 studied the influence of alkylammonium geminis on DPPC, DPPC/cholesterol, and DODAB lipid membranes. These authors found that the surfactants promoted either bilayer disorder/order when surfactant tails were comparatively shorter/longer than the lipids, and that the linker length had an important influence on the insertion depth and surface electrostatics. Teixeira et al.35 reported a complementary result, finding that cationic, serinebased geminis created more disorder in DPPC bilayers for shorter tail surfactants. A computational study by Nunes et al. examined a coarse-grained gemini surfactant/lipid bilayer system,53 and found that the surfactant spacer length modulated the lipid headgroup organization through both electrostatic and excluded volume effects. Computational studies provide important microscopic detail of bilayer properties; while many such studies exist for biological lipid bilayers,23,24,54−61 to our knowledge, there are no computational studies that systematically compare the properties of gemini surfactant Lα and Lβ phases. In addition, previous experimental characterization of ordered Lβ phases of gemini surfactants have primarily focused on cationic alkylammonium surfactants;11−14 characterization of such phases in anionic gemini surfactants, which exhibit unique and interesting phase behavior,62,63 is largely absent. In this work, we present a thorough computational study of the properties of both Lα and Lβ phases of anionic, dicarboxylate gemini surfactants. We systematically compare the structural and dynamic properties at various hydration levels, and focus on differences that result from the fundamental influence of ordered bilayer packing. Using molecular dynamics (MD) simulations, we study Lα and Lβ phases of dicarboxylate gemini surfactants with varying tail length, and characterize the X-ray scattering structure factor, headgroup surface area, bilayer structure, and the surfactant, ion, and water dynamics at 300 K. We find that the ordered tail packing of the Lβ phase results in a hydration independent surface area, in contrast to the Lα phase which compresses significantly with increasing hydration. These structural differences affect the surfactant mobility in the bilayer, which subsequently alters the water and ion dynamics. At low to moderate hydration, the greater surfactant mobility in the disordered Lα phase leads to water diffusion coefficients that are ∼20−50% larger than in the Lβ phase as a result of coupled motion. For both phases, the water dynamics is extremely sensitive to the bilayer surface mobility, as demonstrated with additional simulations employing frozen bilayers. This physical insight complements the comparatively large literature on the physics of bilayer phases in biological lipid membranes. Furthermore, we show that gemini surfactants provide ideal prototypical systems for computational bilayer studies, as equilibration of Lβ phases is comparatively much easier than for corresponding gel lipid phases.
Figure 1. Structure of dicarboxylate gemini surfactants studied in this work.
We consider hydration levels of λ = 6.1, 10, 12.9, 13.9, and 18, where λ is the number of water molecules per surfactant. While shorter tail dicarboxylate surfactants may form a variety of LLC phases including hexagonally packed cylinders and bicontinuous cubic (gyroid) phases at higher hydration level,62−64 the longer tail surfactants employed in this study form stable lamellar phases at all hydration levels investigated (with the exception of CO2-10(4) and CO2-12(4) at λ = 18). All MD simulations are conducted using the GROMACs-4.6 software package.65 Simulations are run at 300 K using the Nose− Hoover thermostat,67,68 and semi-isotropic pressure coupling is used to keep the xy-dimensions of the box equal, and the pressure is maintained at 1 bar in both the normal and lateral directions using the Berendsen barostat.66 After equilibration, production runs are carried out in the NVT ensemble; we note that the Nose−Hoover thermostat does not significantly perturb the dynamics.69 The particle mesh Ewald (PME) algorithm70 is used for electrostatics, and long-range van der Waals (VDW) interactions are cutoff at 1.4 nm. The GROMOS force field71 is used for the surfactant and sodium ions, in conjunction with the SPC model72 for water. Each LLC system is composed of 134 surfactant molecules, 268 sodium counterions, and either 823, 1340, 1729, 1863, or 2412 water molecules for hydration levels λ = 6.1, 10, 12.9, 13.9, and 18 respectively. The lamellar LLC structures are prepared as follows. Initially, lamellar LLC phases of CO2-12(4) surfactants are selfassembled at the various hydration levels. After several hundred nanoseconds, the density, unit cell aspect ratio, and scattering structure factors appeared equilibrated; however, an unequal number of surfactants partitioned between the top and bottom of the lamellar bilayer (up to ∼5% difference). We manually equate the bilayer surface concentration by moving surfactant molecules between bilayer surfaces, and then re-equilibrate the systems. These equilibrated CO2-12(4) lamellar systems are used to generate initial structures for the other systems by either adding or removing carbon atoms to/from the surfactant tail. After manually fixing the surfactant concentration at both bilayer surfaces, we find that this distribution is maintained throughout the course of the simulation. At 300 K, the CO2-10(4) and CO2-12(4) surfactants form Lα phases, whereas the longer tail CO2-15(4) and CO2-17(4) surfactants form Lβ phases (Section 3); equilibration of the latter Lβ phases requires further care. We employ ∼1−2 μs simulated annealing to equilibrate the Lβ LLCs, ramping the temperature to 380 K and then slowly cooling back down to 300 K at a rate of ∼0.2 K/ns (based on preliminary simulations, we observe melting of the Lβ phase at temperatures above ∼350 K for the CO2-15(4) systems); note that a similar cooling rate has been used to equilibrate gel-phase DPPC lipid membranes.59 After cooling, the simulation is run for at least
2. METHODS The LLCs studied in this work are composed of dicarboxylate gemini surfactants, sodium counterions, and water molecules. The four different types of dicarboxylate gemini surfactants we investigate have varying tail length of 10, 12, 15, and 17 carbon atoms (Figure 1); these surfactants have four carbon linker atoms between the headgroups, and are thus denoted CO210(4), CO2-12(4), CO2-15(4), and CO2-17(4), respectively. 5049
DOI: 10.1021/acs.jpcb.7b02551 J. Phys. Chem. B 2017, 121, 5048−5057
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The Journal of Physical Chemistry B 1 μs at 300 K. Equilibration of the Lβ phase is deemed adequate when the system exhibits constant density and unit cell aspect ratio, and converged scattering intensity in the characteristic ∼1.5 Å−1 regime (vide inf ra). We note that while the above procedure is seemingly adequate for our systems, this would be insufficient for equilibrating gel-phases of biological lipid membranes; for example, DPPC membranes may require either hundreds of μs simulations or special techniques for gelphase equilibration using a comparable force field.24,59 We speculate that faster equilibration in this case is due to a combination of the simpler surfactant topology and mobility of the sodium counterions in the Lβ phase. All equilibrated unit cell parameters of the LLC systems are given in Table 1. The Xray scattering structure factors characterizing the LLC periodicity are computed using the methodology described by Mantha et al.73
3. RESULTS/DISCUSSION 3.1. Structural Characterization. The equilibrium phase changes from Lα to Lβ as the tail length of the dicarboxylate gemini surfactants is increased (at 300 K). The shorter tail CO2-10(4) and CO2-12(4) surfactants form Lα LLCs while the longer tail CO2-15(4) and CO2-17(4) surfactants form Lβ LLCs over the investigated hydration range, λ = 6.1−18 (with the exception of the CO2-10(4) and CO2-12(4) systems at λ = 18, in which the lamellar phases are unstable). These different phases are depicted in Figure 2, which shows snapshots from the MD simulations along with their corresponding scattering structure factors for representative systems (structure factors for all systems are given in the Supporting Information). All of the LLCs in this work exhibit the characteristic scattering signature of lamellar phases, which are the low-q features corresponding to the periodicity between the lamellar planes, (100) and higher indices thereof.74 In addition to these lamellar scattering peaks, the Lβ phase exhibits additional scattering peak(s) at higher wavevector, ∼ 1.5 Å−1, that is absent in the Lα phase; this additional peak corresponds to the ordering of the hydrophobic tails within the lamellar bilayer and is the clear signature of the Lβ phase. Simulation snapshots (Figure S2) indicate that the surfactant tails pack into a 2D hexagonal lattice that is nearly perpendicular to the lamellar plane normal (slightly tilted tails). The observed hexagonal packing and spacing of ∼4.2 Å between alkyl tails is in very good agreement with experimental characterization of similar Lβ phases.18 Because of the ordered packing, the Lβ
Table 1. Unit Cell Dimensions of Lamellar LLC Phasesa λ = 6.1 CO2-10(4) CO2-12(4) CO2-15(4) CO2-17(4)
7.25, 7.21, 7.18, 7.33,
2.64 2.94 3.27 3.31
λ = 10 7.62, 7.58, 7.43, 7.39,
2.63 2.90 3.28 3.50
λ = 12.9
λ = 13.9
7.85, 7.77, 7.49, 7.49,
7.89, 7.80, 7.47, 7.48,
2.65 2.94 3.38 3.62
2.68 2.96 3.49 3.71
λ = 18 N/Ab N/Ab 7.58, 3.67 7.52, 3.96
Tetragonal unit cell is specified by length “a” = “b” tangential to lamellar plane, and length “c” perpendicular to lamellar plane (length in nm). bThe CO2-10(4), CO2-12(4) lamellar phases are unstable at λ = 18.
a
Figure 2. Structure factor and corresponding simulation snapshot for (a) Lα phase of CO2-12(4), at λ = 10 and (b) Lβ phase of CO2-15(4), at λ = 10. The additional visible ordering of the Lβ phase is characterized by the scattering intensity marked with “*” at ∼1.5 Å−1. 5050
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hydration dependent expansion/contraction for the fluid phase.3,20,21,54 We note that the calculated headgroup surface area is approximate, as it does not consider bilayer fluctuations (see Supporting Information).20 In Figure 5 we show the 1D probability distribution of different chemical groups for the dimension normal to the bilayer surface at intermediate hydration, λ = 12.9. For this hydration level and resulting confinement length scale, surface effects are dominate and there is no clearly defined bulk-like regime within the water layer. The water and ion distributions are Gaussian at the center of the water channel, and the carboxylate headgroup distribution is approximately a sum of two Gaussian contributions from the top and bottom bilayer surface. The significant overlap of the carboxylate headgroup distribution with the water distribution indicates the surface roughness, and fluctuations result in a non-negligable probability for head groups to reside at the center of the water layer. The hydration dependence of the water layer width is shown in Figure 6, which plots the water density across the water channel for both the Lα and Lβ phases. Interestingly, at hydration levels λ ≤ 10, the density never reaches a bulk-water like value, and is less than 1 g/cm3 even at the center of the layer; we note that due to the fluctuating surface, a more precise evaluation of the local water density rather than this averaged quantity may be a more appropriate metric, but here we are primarily interested in structural characterization. While the thickness of the water layer expectedly increases with hydration, the magnitude of this trend is somewhat different for the Lα and Lβ phases as seen by the tails of the distributions. For the Lβ phase, because the headgroup surface area is relatively independent of hydration (Figure 4), the water layers become thicker than those in the Lα phase at higher hydration; this is also evident in the ion distributions of Figure 5. The corresponding hydration dependence of the sodium counterion distribution within the water channels is shown in Figure 7. The most probable location of sodium counterions is at the center of the water channels, and the hydration dependence of the ion distribution largely mirrors that of the water molecules. Only at the highest hydration level (λ = 18) in the Lβ phase does the sodium distribution start to become bimodal, reflecting both the increasing width of the water channels and preference of the counterions for the negatively charged bilayer surfaces. Similar to the water distribution, there are small quantitative differences in the sodium distribution of the Lα and Lβ phases, which can be attributed to the differences in headgroup surface area of the phases and are most apparent at higher hydration levels. It is interesting to note that these ion distributions deviate from that predicted by mean-field theory (Gouy−Chapman) for two separated, charged surfaces. In such confined systems, however, comparison with theoretical predictions of ideal, flat interfaces is somewhat ill-posed, due to the lack of a well-defined bulk region, the roughness of the interfaces, and the very significant surface fluctuations. The hydration dependence of the headgroup surface area and the water layer thickness in the lamellar phases indicates that surface wetting is an important component of the relative Lα and Lβ bilayer stability. Additionally, this surface wetting is not restricted to the ionic surfactant headgroups but also involves a significant contribution from hydrophobic surface regions of the lamellar bilayers, as inferred from a previous study75 in which it was demonstrated that exposed hydrophobic surface regions exhibited a particularly high affinity for hydronium ions. The amount of exposed hydrophobic surface area increases as
phases are characteristically more dense than the Lα phases, as shown in Figure 3. For the Lα phase the system density
Figure 3. Density of LLC systems at hydration level λ = 12.9.
generally decreases with increasing tail length as the relative hydrophobic/hydrophilic domain sizes are altered, but there is a sharp increase in density at the Lα to Lβ transition, independent of hydration level (Table S1). The surfactant bilayers of the Lα phase compress with increasing hydration level, whereas the bilayer thickness of the Lβ phase is relatively insensitive to hydration. The dimensions of the surfactant bilayer are inferred from the unit cell dimensions listed in Table 1, noting that there is one lamellar bilayer per unit cell. For λ = 6.1−13.9, the magnitude of the unit cell “c” vector (normal to lamellar plane) is relatively constant for the Lα phases due to offsetting increasing water layer thickness and decreasing bilayer thickness, while the “a/b” lengths increase with hydration; this tangential expansion compensates the thickness compression to maintain relatively constant density of the bilayer. The change in aspect ratio of the Lα phase bilayers directly corresponds to a change in the effective surface area per surfactant headgroup. As shown in Figure 4, the surface area per surfactant headgroup for the Lα phase monotonically increases with hydration, up to λ ∼ 14, which is a direct consequence of bilayer expansion tangential to the lamellar plane. For the Lβ phase, both the bilayer thickness and corresponding headgroup surface area are relatively independent of hydration level. It is interesting to note the similarity to phospholipid bilayers, which exhibit a similar
Figure 4. Surface area per carboxylate headgroup in each LLC lamellar phase. The dashed lines indicate hydration mediated trends and are to guide the eye. 5051
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Figure 5. Probability distribution of chemical groups in the CO2-12(4) Lα and CO2-17(4) Lβ phases at λ = 12.9. The origin of the distribution corresponds to the center of the water layer, and each distribution is normalized by the number of atoms of that type in the system.
Figure 6. Density distribution of water molecules spanning the bilayer channel in the CO2-12(4) Lα and CO2-17(4) Lβ phases at different hydration levels. The origin of the distribution corresponds to the center of the water layer.
Figure 7. Density distribution of sodium ions spanning the bilayer channel in the CO2-12(4) Lα and CO2-17(4) Lβ phases at different hydration levels. The origin of the distribution corresponds to the center of the water layer.
the surfactant bilayer expands along the “a/b” unit cell vectors, which may be energetically driven by the increased separation of the negatively charged headgroups. However, this surface area expansion depends on wetting, and at low hydration levels there is higher surface tension and reduced surface area. The importance of hydrophobic wetting is demonstrated by subsequent simulations, in which the Lennard-Jones interaction between exposed hydrophobic CH2 groups and the SPC water molecules is switched to a corresponding WCA repulsive potential.76 Although the pairwise Lennard-Jones well-depth was only ∼0.5 kJ/mol, this reduced water/hydrophobic interaction had a pronounced effect, causing a Lα to Lβ phase transition for the CO2-12(4), λ = 12.9 system. This transition was driven by the reduced wetting ability from the WCA CH2/
SPC interaction, as the Lβ phase exhibits reduced surface area and greater hydrophobic density. 3.2. Dynamics. Due to the structural ordering, there is significantly lower surfactant mobility in the Lβ phases compared to the Lα phases. Figure 8 shows the mean square displacement (MSD) of surfactant molecules in both the Lα and Lβ phases, and for a given hydration level, it is clear that the surfactant mobility is much lower in the Lβ phase. Interestingly, the surfactant MSD is coupled to hydration level, and increases significantly for both the Lα and Lβ phases with increasing hydration. The different Lα and Lβ surfactant mobility is related to the different compressiblities of the phases, and the loss of mobility in the Lβ phase is due to the enhanced density and ordered packing of the bilayers. In Figure 9, we show the separation of the total surfactant MSD into components parallel 5052
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Table 2 (italic numbers). Two conclusions are drawn from this additional data: Water diffusion is dramatically reduced in the frozen-tail simulations for both the Lα and Lβ phases, indicating a strong coupling of the water dynamics and surfactant mobility. Additionally, there is only minor difference between the water dynamics in the Lα and Lβ phases when the surfactant molecules are frozen, indicating that the enhancement of water and ion dynamics in the Lα phase relative to the Lβ phase is primarily due to the enhanced surfactant mobility. At higher hydration levels (λ = 13.9), differences in the water diffusion coefficients from the frozen surfactant simulations reflect the increasingly pronounced differences in headgroup surface area between the Lα and Lβ phases. The enhancement of water dynamics due to surfactant mobility is graphically depicted in Figure 10, which plots the ratio of the water diffusion coefficients from the normal and frozen-tail simulations. We note that only the relative enhancement should be interpreted, as the absolute enhancement depends sensitively on which specific surfactant atoms are frozen (e.g., additionally freezing the linker atoms slows down the water dynamics even more). It is evident that the surfactant mobility has a greater enhancement on water diffusion rates at low hydration, and this effect diminishes in magnitude as the hydration level increases. This is because at higher hydration there is less confinement and a smaller fraction of the water molecules are near the surface of the bilayer interface compared to the center of the water channels (Figure 6). In Figure 10, it is somewhat surprising that the normal and frozen-tail simulations give significantly different water diffusion rates for the Lβ phases, considering their already reduced surfactant mobility (Figure 8). To further investigate this effect, we computed an additional metric of surfactant mobility, namely the MSD of the carboxylate headgroups which reside at the hydrophobic/hydrophilic interface; this is shown in Figure 11 for both phases as a function of hydration level. In contrast to the MSD of the surfactant center of mass, the MSD of the carboxylate groups is comparatively similar for the Lα and Lβ phases at a given hydration level, especially over shorter time scales (tens of picoseconds). This indicates that the short-time bilayer surface dynamics is more dependent on the hydration level than on the specific LLC phase, with the surface dynamics clearly coupled to the water dynamics. Obviously for long time scales, the headgroup MSD is correlated with the surfactant center of mass MSD, but this need not (and is not) the case for shorter time scales. Overall, the Lβ phase exhibits somewhat
Figure 8. Mean square displacement of center of mass of surfactant molecules for CO2-12(4) Lα and CO2-17(4) Lβ phases at different hydration levels.
(MSDxy) and perpendicular (MSDz) to the plane of the lamellar bilayer. From this analysis, it is evident that the majority of the surfactant mobility enhancement in the Lα phase comes from diffusion tangential to the bilayer surface. This is easily rationalized based on the structural characteristics discussed earlier; hexagonal packing of the hydrophobic tails in the Lβ phase prohibits surfactant diffusion along the tangential dimension, whereas there is no such constraint in the Lα phase. The relative surfactant mobility in the Lα and Lβ phases correspondingly affects the water and ion dynamics. Selfdiffusion coefficients for water and sodium ions in each of the LLCs are given in Table 2 and 3. There are similar trends for the sodium and water diffusion, and thus we primarily focus our discussion on the water dynamics. It has previously been shown64 that the dynamics of water in LLCs is significantly slower than in bulk water, and is primarily dependent on the hydration level. At fixed hydration, however, there is on average ∼50% and ∼20−30% enhancement in the rate of water diffusion in the Lα phase compared to the Lβ phase for λ = 6.1 and λ = 10−12.9, respectively. These differences in water diffusion rates are primarily due to the reduced surfactant mobility in the Lβ phase. To demonstrate this, we conduct additional simulations in which the tails of the surfactant molecules are frozen, and only the linker and headgroup surfactant atoms are allowed to move (see Supporting Information for simulation details). The water diffusion coefficients for these “frozen-tail” simulations are given in
Figure 9. Mean square displacement of center of mass of surfactant molecules (a) parallel to lamellar plane (xy) and (b) perpendicular to lamellar plane (z) for CO2-12(4) Lα and CO2-17(4) Lβ phases at different hydration levels. 5053
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The Journal of Physical Chemistry B Table 2. Water Diffusion Coefficients (10−5 cm2/s) in Lα and Lβ LLCsa λ = 6.1 CO2-10(4) CO2-12(4) CO2-15(4) CO2-17(4) a
0.026 0.022 0.017 0.015
λ = 10
(0.006) (0.007) (0.006) (0.006)
0.090 0.074 0.063 0.063
λ = 12.9
(0.032) (0.030) (0.030) (0.029)
0.169 0.153 0.132 0.121
(0.089) (0.086) (0.085) (0.079)
λ = 13.9 0.208 0.171 0.195 0.184
(0.115) (0.120) (0.143) (0.137)
λ = 18 N/A N/A 0.426 (0.377) 0.453 (0.421)
The diffusion coefficients given in italic are computed from simulations in which the tails of the gemini surfactants were frozen.
Table 3. Sodium Diffusion Coefficients (10−5 cm2/s) in Lα and Lβ LLCs CO2-10(4) CO2-12(4) CO2-15(4) CO2-17(4)
λ = 6.1
λ = 10
λ = 12.9
λ = 13.9
λ = 18
0.006 0.004 0.003 0.002
0.025 0.018 0.017 0.015
0.042 0.037 0.030 0.030
0.057 0.044 0.039 0.044
N/A N/A 0.081 0.078
reduced in the Lβ phase due to hexagonal packing of the surfactant tails. Despite the ordered tail-packing, however, the Lβ phase exhibits much less reduced bilayer surface mobility compared to the Lα phase as characterized by the short-time MSD of the carboxylate groups, and it is primarily this bilayer surface mobility that couples to the water and ion dynamics within the water channels. Such coupling is demonstrated by the frozen-tail simulations, which exhibit significantly reduced water diffusion rates especially at low hydration. Overall, the greater surface mobility of the Lα phase bilayers result in ∼20− 50% faster water diffusion at hydration λ = 6.1−12.9 compared to the Lβ phases.
4. CONCLUSION We have characterized lamellar LLC phases of four dicarboxylate gemini surfactants that differ in tail length, over a range of hydration levels. At 300 K, the two shorter tail surfactants form disordered Lα phases, while the two longer tail surfactants form ordered Lβ phases, allowing for the direct determination of the influence of tail ordering on the structural and dynamic properties of the bilayers. Our resulting analysis provides interpretation for the phase behavior of these LLCs and additionally expands the general understanding of bilayers within the complementary framework of surfactant/lipid systems. For the Lα phases, the surface area per headgroup is hydration dependent due to a significant compression of the bilayer, normal to the interface. This effect may provide an important explanation for certain LLC phase behavior. Specifically, seven-carbon tail dicarboxylate surfactants exhibit a transition from the Lα phase to a bicontinuous cubic phase at λ ∼ 6−8,62,63 which is significantly lower hydration than the stability limit of the longer tail dicarboxylate Lα phases in this work. The longer tails provide a greater range of compression/ expansion of the bilayer that is necessary for stability at higher hydration, while the shorter tails may prohibit bilayers of higher headgroup surface area, reducing the stability of Lα phases at λ > 8. Comparison to previous work77 indicates that the headgroup separation in the shorter tail bicontinuous cubic phase is very similar to that in the longer tail Lα phase at λ = 12.9, suggesting that hydration-dependent surface area may be general across morphologies. The driving force for the hydration induced change in surface area results from a combination of hydrophobic wetting and electrostatic interactions between headgroups, counterions, and water,73 but optimizing these energetics can be limited by packing constraints of surfactant tails in certain phases (e.g., short tails in Lα bilayers). Beyond this insight into the LLC phase behavior, our study has illuminated fundamental physical properties general to bilayers. Specifically, we have shown that the dynamic properties of the gemini dicarboxylate Lα phases exhibit similarities with biological phospholipid bilayers. For the latter systems, MD studies of DMPC78 and POPC65 bilayers have
Figure 10. Ratio of water diffusion coefficients for normal and frozentail simulations for the Lα and Lβ phases as a function of hydration level. Lα phase data is the average of the CO2-10(4) and CO2-12(4) water diffusion coefficients, and the Lβ phase data is the average of the CO2-15(4) and CO2-17(4) water diffusion coefficients.
Figure 11. Mean square displacement of oxygen headgroup atoms of surfactant molecules for CO2-12(4) Lα and CO2-17(4) Lβ phases at different hydration levels.
lower surface mobility compared to the Lα phase, but these differences are not nearly as dramatic as the loss of tangential surfactant (center of mass) mobility in the Lβ phase due the ordered packing of the tails. We summarize our dynamic analysis of the LLC bilayers and the important differences between the Lα and Lβ phases. The most significant difference between the phases is the tangential mobility of the surfactant center of mass which is greatly 5054
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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 TGCHE090065.
demonstrated the coupling of water and lipid dynamics, which is increasingly important at low hydration levels and is largely mediated by headgroup-water hydrogen bonds. Similar to our present results, simulations of DOPC bilayers56 found dramatically reduced water dynamics when the lipid bilayers were frozen. While these are important comparisons that generalize the influence of bilayer mobility on water dynamics, such previous studies have only focused on the fluid phase of phospholipid bilayers. By presenting a direct comparison of the bilayer dynamics in Lα and Lβ phases of gemini surfactants, we have extended the analysis to quantify the influence of ordered tail packing on the resulting surfactant and water dynamics. Dynamical differences between the Lα and Lβ phases include both the bulk surfactant diffusion and bilayer surface mobility, with the latter effecting the water dynamics and resulting in ∼20−50% faster water diffusion at hydration λ = 6.1−12.9 in Lα compared to the Lβ phases. Future biological applications of gemini surfactants may benefit from similar studies of pure surfactant bilayers. For example, the effect of incorporating gemini surfactants into phospholipid membranes may be partially deduced from the relative stability of pure surfactant Lα and Lβ phases. Upon incorporation, surfactants that prefer Lα/Lβ phases may promote bilayer disorder/order under similar thermodynamic conditions. Such a correlation would be important to examine, as we have demonstrated that computational equilibration of ordered Lβ phases is significantly faster than corresponding simulations of ordered, gel-phase phospholipid systems.24,59 Because of this advantage, gemini surfactants may be ideal for computational characterization of additional bilayer phenomena, such as the importance of local bilayer order on the assembly of transmembrane proteins.60
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b02551. Further computational details concerning surface area calculations and methodology for frozen surfactant simulations; densities of all LLC systems; snapshot showing hexagonal tail packing in Lβ phases; scattering structure factors for all LLC systems; mean square displacement of surfactants in all LLC systems (PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Arun Yethiraj: 0000-0002-8579-449X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS 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, 5055
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