Driving Force for Water Permeation Across Lipid Membranes

Letter pubs.acs.org/JPCL

Driving Force for Water Permeation Across Lipid Membranes Baofu Qiao† and Monica Olvera de la Cruz*,†,‡ †

Department of Materials Science and Engineering and ‡Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *

ABSTRACT: The permeation of water across lipid membranes is of paramount importance in biological and technological processes. The driving force for such energetically unfavorable processes is explored here. To determine the effect of the lipid membrane conformation, water transport in both liquid-crystalline and ordered gel phases is studied in zwitterionic dipalmitoyl phosphatidylcholine (DPPC) bilayers and anionic 1,2-dilauroyl-sn-glycero-3-phosphol-L-serine (DLPS) bilayers via atomistic molecular dynamics simulations. These phases are accessed by changing the temperature in DPPC membranes and by additionally changing the valency of counterions (i.e., Na+ and Zn2+) in DLPS membranes. The membrane conformation is found to play a critical function in water permeation, regardless of the type of lipid. The fluctuations in the potential energy are found to have a significant, if not the exclusive, role in the transportation of water across lipid membranes. SECTION: Biomaterials, Surfactants, and Membranes

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achieved by increasing the cholesterol concentration, and a higher free-energy barrier for water diffusing (up to around 38 kJ/mol) is observed concomitantly. This suggests a lower water permeation in the ordered gel phase (see, e.g., ref 15). Additionally, the energetically unfavorable permeation of water across other zwitterionic lipid bilayer membranes has also been reported to be 2511 and 30 kJ/mol16 for the diphytanoyl phosphatidylcholine membrane, 25 kJ/mol for the palmitoylsphingomyelin bilayer,14 and 27 kJ/mol for the partially fluorinated lipid bilayer of 1,2-di(F8CCH8)PC.17 Regardless of its biological importance, passive permeation of water has not been investigated across ionic lipid membrane systems. In particular, in many situations, divalent ions change the tail packing. See for example, ref 18. This offers the opportunity to probe the permeation of water in different tail conformations and determine if the charged head groups influence the above results found in zwitterionic lipid bilayer membranes. Moreover, given the aforementioned progress in understanding the water passive permeation across zwitterionic lipid bilayers, one question arises that is critical to understand the process: what is the driving force for such an energyunfavorable permeation? We address here this unexplored question in different lipid bilayer systems (zwitterionic and anionic) under varying morphologies (the liquid-crystalline phase versus the gel phase) and generalize our findings to various membrane systems. Understanding the driving force will boost our capability of tuning the water permeability of cell membranes by controlling the bilayer morphology. We investigate zwitterionic DPPC and anionic 1,2-dilauroylsn-glycero-3-phosphol-L-serine (DLPS) membranes. Living

ater molecules, and many small molecules including CO2 and O2, diffuse across lipid membranes.1 The permeability of lipid membranes to these small molecules is of paramount biological and biotechnological importance. The permeation of water across lipid membrane, for example, has a significant role in regulating ionic concentrations inside of cells.2 On the other hand, the exchange of CO2 and O2 molecules between the red blood cells and the environment is critical for the respiratory system.3 The analysis of lipid membrane permeability to drugs and/or therapeutic agents is of critical importance in biotechnology. While drug uptake is desirable, the overpermeation of drug molecules can lead to the accumulation of toxic elements in cells. In fact, the passive transmembrane permeation of drug molecules has been reported to be one of the major mechanisms for their adsorption,4 where the passive permeation stands for the transportation without the assistance of proteins (or nanoparticles5) embedded in membranes. The passive permeation of drug molecules has been addressed recently via atomistic simulations6,7 and atomistic−coarse-grained hybrid simulation.8 In the present work, only the passive permeation behavior is discussed. The literature on the passive permeation of water and drugs, as well as some other small molecules, has been summarized in two excellent reviews.9,10 Various atomistic molecular dynamics (MD) simulations have determined that the free-energy barrier for water diffusing across zwitterionic dipalmitoyl phosphatidylcholine (DPPC) bilayers2,11 is up to 26 kJ/mol in the liquidcrystalline phase.12 This shows that the water transport is highly energetically unfavorable. Interestingly, this free-energy barrier is roughly independent of the hydrocarbon tail length;13 it ranges from around 21 to 23 kJ/mol in DPPC bilayers with 12, 14, and 16 carbons, all in the liquid-crystalline phase.13,14 The transition from the liquid-crystalline phase to the gel phase12 is © 2013 American Chemical Society

Received: August 13, 2013 Accepted: September 12, 2013 Published: September 12, 2013 3233

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cells have both DPPC and DLPS components.19 In Scheme 1, we show the structures of these two types of lipids. In each of Scheme 1. Schematic Representation of the Anionic Lipid DLPS and Zwitterionic Lipid DPPC

Figure 1. (a) Snapshot of one water molecule (highlighted in the VDW drawing method under VMD21) that is located in the hydrophobic interior of a DLPS membrane. (b) The permeation process of a single water molecule (highlighted) across a DLPS membrane. The trajectory of this water molecule within 7.8 ns is drawn in the same illustration with the dashed line to guide the eyes and some typical occupations labeled with the time. The other water molecules are removed for clarity. The fluctuation of the lipid membrane is small here in order to display only one frame (see the movie in the SI for the complete trajectory).

the membrane systems, the effect of the ordered gel phase of the hydrocarbon tails is compared to that of the less ordered liquid-crystalline phase. Moreover, the effect of the valency of the counterions, that is, monovalent Na+ versus Zn2+, is investigated for the bilayers consisting of anionic DLPS lipids. The enhanced electrostatic interaction in the presence of Zn2+ has been previously reported to compact the bilayer structure20 and is thus expected to affect the water permeation. We perform classical MD simulations, followed by the calculation of the excess free energy as describe in the simulation methodology (Supporting Information (SI)). Five membrane structures are investigated, two DPPC membrane structures, one at 298 K in the gel phase and the other at 323 K in the liquid-crystalline phase, and three DLPS membrane structures, DLPS-Na+ at 317 K in the liquid-crystalline phase, DLPS-Na+ at 310 K in the gel phase, and DLPS-Zn2+ at 310 K in the gel phase. Each of the simulations is performed for a duration of 100 ns for the DPPC systems or 400 ns for the DLPS systems, which are long enough to reach the desire phases, as supported by the temporal calculation of the area per lipid. (Figures S2 and S3 in the SI show the area per lipid as a function of time and the structures of the last simulation frames for DPPC at 298 and 323 K, respectively.) The phase transition of DLPS membranes has been calculated previously based on the obtained scatter structure factor20 and can also been determined from the values of the area per lipid (Table S1 in the SI). The diffusion of water into (or across) the hydrophobic interior of a DLPS membrane is verified in Figure 1a and b. In particular, illustrated in Figure 1b is the collective trajectory that the highlighted water molecule transports across the membrane within 7.8 ns. See also a corresponding movie (SI) for the complete trajectory of the diffusion process. It is also suggested in Figure 1b that there exists a metastable state in the gap region between the two leaflets by virtue of the relatively higher distribution of the water molecule there. The ordered structure of the hydrocarbon tails in the gel phase is evident in Figure 1. Not surprisingly, the probability of water molecules distributed inside of the lipid bilayers is very low. The region less than 1 nm from the midplane of the bilayer is chosen as the interior region to get an estimate of the water local density inside of the hydrophobic interior of the lipid membrane. In

comparison with the number density in bulk water, which is around 33 nm−3, the number density in the interior region is 0 for DPPC at 298 K, (4 ± 3) × 10−2 nm−3 for DPPC at 323 K, (4 ± 12) × 10−3 nm−3 for DLPS-Na+ at 310 K, (6 ± 5) × 10−2 nm−3 for DLPS-Na+ at 317 K, and (4 ± 28) × 10−4 nm−3 for DLPS-Zn2+ at 310 K. Though the fluctuations in these calculated water local densities are large, these data suggest that the water density inside of the hydrophobic interior is orders of magnitude smaller than the corresponding value in the bulk water region. In order to predict the local distribution probability in the hydrophobic interior of lipid membranes, we need to resort to the free energy via ΔG(z) = −RT ln(ρ(z)/ρbulk),2 where R is the gas constant, T stands for the temperature, and ρ(z) and ρbulk denote the local density and the density in the bulk water region, respectively. We employ the Cavity Insertion Widom method3,14 to obtain the excess free energy of insertion of one test water molecule. The results are shown in Figure 2. Under the aforementioned definition, the free energy in the bulk water region is chosen as the reference, that is, ΔG(|z| → ∞) = 0 ideally. The average free energy in the bulk water region is employed as the reference value, that is, ⟨ΔGbulk⟩ = 0. The angle brackets stand for the average over all of the free energies in those slabs that are located more than 3 nm away from the midplane in all five systems, which was originally calculated to be −23 ± 2 kJ/mol and shifted to 0 subsequently. The original chemical potential profile is also provided in Figure S4 in the SI, where the differences between the bulk water regions in the five systems investigated are shown to be overshadowed by the error bars of the free energies. That is, the type of lipid (DPPC or DLPS with varying counterions) and the morphologies of the lipid bilayers (the liquid-crystalline phase or the gel phase) have roughly negligible effect on the excess free energy in the bulk water region within the framework of the present work. It is shown that the test water molecule needs to surmount a free-energy barrier of about 23−28 kJ/mol to reach the membrane midplane from the bulk water region. The freeenergy barrier in the DPPC membrane at 323 K is around 23 kJ/mol, which is in good agreement with the reported data, ranging from 2114 to 26 kJ/mol.2,11 The corresponding value 3234

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barrier and subsequently a lower probability of water across the membranes. In summary, water has to overcome a free-energy barrier to transport into (or across) the hydrophobic interior of lipid membranes regardless of the types of lipids investigated and the morphologies of the bilayers. To determine the driving force for such an energy-unfavorable process, we resort to the analysis of thermal fluctuations. The calculation of the fluctuation of the potential energy indicates that the energy fluctuation most probably provides such a driving force. The obtained total potential energy is −305150 ± 570 kJ/mol for DPPC at 298 K, −372800 ± 640 kJ/mol for DPPC at 323 K, −399350 ± 620 kJ/mol for DLPS-Na+ at 310 K, −394300 ± 630 kJ/mol for DLPS-Na+ at 317 K, and −469700 ± 590 kJ/ mol for DLPS-Zn2+ at 310 K, where the standard deviations are due to energy fluctuations. These energy fluctuations are more than 1 order of magnitude higher than the free-energy barrier of 23−28 kJ/mol, which thus provides a big enough driving force for water to transport across lipid membranes. We note that the overall potential energy is an extensive thermodynamics property. To eliminate the effect of system size, the potential energy is rescaled by the cross-sectional area (parallel to the bilayer). The rescaled potential energies are listed in Table 1, as well as the free-energy barriers for water Table 1. Rescaled Potential Energy and Its Fluctuation, and Free-Energy Barrier for Water Permeation

Figure 2. Free-energy profile of a water molecule across (a) DPPC and (b) DLPS membranes with Na+ or Zn2+ counterions.

energy (kJ/mol/nm2) a

DPPC (298 K) DPPC (323 K)b DLPS-Na+ (310 K)a DLPS-Na+ (317 K)b DLPS-Zn2+ (310 K)a

for the DPPC membrane in the gel phase (298 K) with an area per lipid of 0.437 nm2 is about 28 kJ/mol, which is also consistent with the reported value of around 27 kJ/mol14 at a similar area per lipid in the presence of cholesterol. No reported free energy is available for comparison for anionic DLPS bilayer systems. In regard to the effect of the type of lipid, no remarkable difference is observed in Figure 2 between the free-energy profile in the zwitterionic DPPC system and that in the anionic DLPS system with the error bar taken into account, as long as they have the same morphology (the liquid-crystalline phase or the gel phase). Meanwhile, Figure 2 suggests that in contrast with the membranes in the liquid-crystalline phase (DPPC at 323 K and DLPS-Na+ at 317 K), there exists a metastable state for water in the proximity (|z| < 0.5−0.6 nm) of the membrane midplane in the ordered gel phase (DPPC at 298 K, DLPS-Na+ at 310 K, and DLPS-Zn2+ at 310 K), which is consistent with the trajectory shown in Figure 1b. It is also indicated in Figure 2 that the free-energy barriers in the membranes in the gel phase are around 5 kJ/mol higher than those in the liquidcrystalline phase. The enhanced free-energy barriers are attributed to the higher condensed packings of the lipid molecules. The values of the area per lipid have been obtained to be 24% smaller in the gel phase than those in the liquidcrystalline phase, 0.437, 0.452, or 0.442 nm2 in the gel phase versus 0.59 or 0.56 nm2 in the liquid-crystalline phase (see Table S1 in the SI). This finding is in agreement with a recent experimental work22 that shows that the water permeation across lipid membranes composed of phosphatidylcholine (PC) or phosphatidylserine (PS) is strongly related to the lipid molecular packing, that is, the area per lipid. Meanwhile, atomistic MD simulations14 have demonstrated that a higher condensed packing of the DPPC membrane, triggered by the addition of cholesterol molecules, leads to a higher free-energy

a

−10810 −9860 −13640 −10980 −16610

± ± ± ± ±

80 220 160 240 110

ΔG (kJ/mol) 23 28 23 28 28

Gel phase. bLiquid-crystalline phase.

permeation across the corresponding membranes. It is shown that regardless of the systems investigated here, the rescaled fluctuations of the potential energies are always bigger than the free-energy barrier for water permeation across the bilayers. It is also indicated that the anionic DLPS bilayer systems have a relatively larger energy fluctuation than the zwitterionic counterparts of DPPC membranes under the same morphology of the liquid-crystalline phase or the gel phase, which results from the dynamic balance between the counterions associated and those dissociated with the DLPS membrane. On the other hand, as expected, the membranes in the gel phase show remarkably smaller fluctuations in contrast to the membranes in the liquid-crystalline phase, irrespective of the types of the lipids. In comparison with the presence of water inside of the hydrophobic interior of membranes, there are no ions (Na+ or Zn2+) distributed inside of the central region (|z| < 0.6, 0.3, and 1.3 nm from the midplane for DLPS-Na+ at 310 K, DLPS-Na+ at 317 K, and DLPS-Zn2+ at 310 K, respectively) of the membranes throughout the simulations here. Therefore, the free-energy barriers for ion permeation across DLPS membranes are expected to be larger than the corresponding energy fluctuations. This assumption can be supported by the strong hydration of the ions. The hydration enthalpy is −405 and −2044 kJ/mol for Na+ and Zn2+, respectively.23 Furthermore, the free-energy barriers for passive permeation of ions have been reported to be around 230 kJ/mol for Na+ and 210 kJ/ 3235

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mol for Cl− utilizing the umbrella sampling MD method.24 (See also ref 9 for a related review.) The permeation of water has been verified across the hydrophobic interior of zwitterionic DPPC membranes, as well as across that of anionic DLPS membranes in the presence of monovalent counterions Na+ and in the presence of divalent counterions Zn2+ in both the liquid-crystalline phase and the gel phase. The free-energy barriers for one water molecule diffusing across DPPC or DLPS membranes have been obtained to be around 23−28 kJ/mol. The morphology of the hydrocarbon tails plays a dominant role in enhancing the free-energy barrier from ∼23 kJ/mol in the liquid-crystalline phase to ∼28 kJ/mol in the gel phase. In contrast, the effects of the type of lipid (DPPC versus DLPS) or of the counterions of the DLPS lipid (Na+ versus Zn2+) are negligible under the same morphology. The driving force for such an energy-unfavorable process is depicted here to be most probably due to the fluctuation of the potential energy. Consistently, the morphology is again found to play a critical role in the fluctuation of the potential energy, with a minor attribution to the type of lipid. It is worth noting that the classical atomistic MD simulation approach is employed here in unveiling the driving force of water permeation across lipid membranes. Even though it is the most frequently used approach in related studies, there are some limitations, such as the polarization effect of ions not being accounted for, and the implementation of different classical force fields has been expected to affect the calculated value of the free-energy barrier.14 Apart from lipid membrane structures, water also diffuses into the hydrophobic pores of carbon nanotubes.25 Even though a hydrogen bonding chain was reported for water inside of carbon nanotubes (see, e.g., refs 26 and 27), which leads to an equal water free energy inside and outside of the carbon nanotube,28 the driving force that leads to the formation of the hydrogen bonding chain has not been addressed. The present work may provide a clue for the phenomenon. Meanwhile, the passive permeation of drugs and other nonelectrolyte molecules, as well as the lack of passive permeation of ions, can also be explained based on the present work. That is, the permeation occurs when the free-energy barrier is less than the energy fluctuation. We note that for some molecules, for example, CO2, O2, CO, and NO, even though a free-energy well,3,13 rather than a free-energy barrier, allows their diffusion from the water phase into the hydrophobic interior of the membrane (i.e., water phase → membrane), the permeation across the membrane (i.e., water phase → membrane → water phase) involves a free-energy barrier when diffusing from the interior of the membrane back to the water phase. Therefore, the present work is also informative for these phenomena.

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the support from the Office of the Director of Defense Research and Engineering (DDR & E) under Award No. FA9550-10-1-0167.

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ASSOCIATED CONTENT

S Supporting Information *

Simulation methodology, some simulation data and results, the cavity probability across the membrane, the excess potential profile, the obtained area/lipid as a function of time, and the structures of the last frames for DPPC systems. A movie shows that one water molecule diffuses across the bilayer in DLPSZn2+ (310 K). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 3236

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