Structures, dynamics, and water permeation free energy across bilayers of Lipid A and its analog studied with molecular dynamics simulation.

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Structures, Dynamics and Water Permeation Free Energy across Bilayers of Lipid A and its Analog Studied with Molecular Dynamics Simulation Tao Wei, Tiefan Huang, Baofu Qiao, Mo Zhang, Heng Ma, and Lin Zhang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp508549m • Publication Date (Web): 13 Oct 2014 Downloaded from http://pubs.acs.org on October 18, 2014

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The Journal of Physical Chemistry

Structures, Dynamics and Water Permeation Free Energy across Bilayers of Lipid A and Its Analog Studied with Molecular Dynamics Simulation Tao Wei,1* Tiefan Huang,2 Baofu Qiao, 3Mo Zhang, 2 Heng Ma, 1 Lin Zhang2 1

Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX, 77710, USA 2

Key Laboratory of Biomass Chemical Engineering of MOE, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou, 310027, China

3

Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA

ACS Paragon Plus Environment

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KEYWORDS: Bilayer, Structure, Dynamics, Water Permeation Free Energy, Lipid A and its analogue, MD Simulation.

ABSTRACT

Fundamental studies of the supra-molecular layer structures, dynamics and water permeation free energy of hexa-acyl-chain lipid A and its analogue of tetra-acyl chains would be useful for polymer membranes design for endotoxin removal in water treatment, drug delivery and other biotechnologies. In this work, we studied their supra-molecular bilayer by using molecular dynamics simulations and efficient free energy computations. Our simulation accuracy was verified by the agreement between the bilayer structural properties (structure factor, bilayer thickness and the area per lipid) and lateral diffusion coefficient in our simulation and experimental measurements. More importantly, our simulation for the first time illustrated hexagonal compact packing of the hydrocarbon acyl chains within a leaflet of lipid A membrane (at 298 K and water content of wt 40%), which is consistent with experiments. In contrast, lipid A analogue is found with less ordered ripple structures at the same condition. Our study also demonstrated slower dynamics and larger and broader free energy barrier (～23 kJ/mol) for water permeation for lipid A, compared with that of lipid A analogue. Moreover, the analysis of dynamics showed that highly hydrated hydrophilic diglucosamine backbone is structurally stable, whereas the interdigitated hydrophobic acyl chain tails inside the membrane with faster dynamics screen the aqueous environment from the lipid interior and also reinforce the membrane’s structural stability.


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1. INTRODUCTION

Lipopolysaccharide (LPS), an essential amphiphilic component of the outer membranes of Gram-negative bacteria, governs the outer membrane’s permeability and activation of the host immune response. Lipid A, one of the three regions that LPS generally consists of (the other two being the O-antigen and the core)1, anchors an LPS molecule in the membrane and is therefore regarded as a toxic component of LPS.2 Due to its unique biological activity, Lipid A attracted significant interest as a candidate for medical applications, such as anticancer drugs3,

4

and

vaccine adjuvant5, 6. A fundamental understanding of lipid A bilayers will also play a key role in biosensor design7 to detect endotoxin of ultra-low concentration and polymer membrane fabrication8 using L-Serine in water treatment for endotoxin elimination.

Compared with other membrane lipids, lipid A exhibits considerable chemical complexity in that it consists of a β(1-6)-linked D-glucosamine disaccharide substituted by phosphoryl groups, and both ester-linked and amide-linked fatty acids. According to a plethora of studies on the structure-activity governing the immunological responsiveness of lipid A, Lipid A’s biological activity is highly dependent on its chemical structures9, 10, 11, e.g., acylation pattern, charges and three-dimensional supra-molecular assembly structures12, 13. Those studies also showed that an alteration of the chemical structure of the lipid A moiety may result in dramatic reduction of endotoxical activity or even render the modified lipid A antagonistic against endotoxically active LPS.9,

10, 14

For example, recent experiments done by Li, et al.,11 demonstrated that lower

acetylation in lipid A results in stronger water permeability and less stimulatory to humans at the same temperature.


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Experimental studies showed that lipid A can form various supra-molecular aggregates, such as lamellar, hexagonal and cubic phases, depending on different conditions15,

16, 17, 18

in

temperature, water content and cations. Among the various supramolecular assembly structures, lamellar structure is predominant in functional biological membranes.19 Furthermore, lamellar lipid A aggregates have been shown to exhibit lower or negligible endotoxic activity than cubic inverted structure.20 Labischinski, et al., showed the presence of interdigitated bilayers of around 5-nm thickness for isolated bacterial lipid A from Salmonella minnesota Re 595 by neutron small-angle scattering in an aqueous environment.15

Molecular dynamics (MD) simulations have been widely applied to the study of biomolecular behaviors21, 22, 23, 24, 25 either in the solution or at membrane-solution interface. MD simulations can probe molecular structures with atomistic resolutions and sample molecular dynamics behavior from sub-nanoseconds to microseconds. An understanding of water permeability across the lipid membrane is of great importance for applications in biotechnologies, such as drug delivery26. The cavity insertion Widom (CIW) method23,

27, 28, 29

, which combines with MD

simulations, has been demonstrated to have sufficient convergence and high sampling efficiency to investigate the permeation free energy barrier of small solute, such as water molecules in condensed lipid membrane interior, where lipid molecules exhibit slow dynamics and the water concentration is ultra-low. In the CIW computations, free energy barrier can be estimated using trajectories available from the MD simulation, with no need to perform additional multiple MD simulations like directed MD. The unique advantage of the efficiency makes CIW especially suitable for systems with large dimensions.


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Despite decades of advancement in experimental studies on lipid A, theoretical studies are still highly desired to rationalize materials design. Drawing on recent development of force field parameters, typically for the residues of glucosamine and disaccharide of complex structures, several works

18, 30, 31, 32

using MD simulations have attempted to tackle the supra-molecular

structures of lipid A or LPS and their interactions of proteins as functions of temperature, ion valence, chemical structures and so on.

Passive water trans-membrane permeation without the assistance of protein-embedded membrane is of paramount importance in biological systems and biotechnologies, such as drug delivery and the design of industrial microorganism membrane structures to enhance permeability and product yield. Experiments rationalized that lipid A plays an important role in maintaining the outer membrane permeability because of strong lateral interactions11. In this work we performed MD simulations combined with highly efficient CIW method to study water passive permeability across the bilayer membrane as well as bilayer’s polymorphism and dynamics at the room temperature of 25 ℃ for lipid A from Escherichia coli with hexa-acyl fatty chains (LP6) and its analogue, tetra-acyl lipid A (LP4), as shown in Figure 1. There are two reasons why we chose the room temperature: one is that for the polymer membrane project in water treatment, the system involves LP6 usually at the room temperature of 25 ℃; the other reason is that, for lipid A analogue-based drug delivery project, the research interest focuses on a narrow temperature range from room to physiological temperature, i.e., 25 ～ 37 ℃. This theoretical study will pave the road for our on-going research on the polymer membrane design in water treatment to eliminate endotoxin 8, which is related with LP6, and lipid A analogue (such as LP4)-based drug delivery. The results in this study would also be useful for broader


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applications, such as designing bacterial membrane structure and developing lipid A vaccine adjuvant.

Figure 1. Chemical structures of lipid A (LP6) (left) and its analogue, tetra-acyl lipid A analogue (LP4) (right).

2. METHODS 2.1. Molecular Dynamics Simulations Parallel fully atomistic MD simulations were performed with the software package of Gromacs (version 4.5.5)33 supported with MPI on super computer clusters. The vdW and intra-molecular interactions in the systems were described by the CHARMM36 force field34 and the literature reports35,

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about polysaccharide, carbohydrate and glycosidic linkages, combined with the

TIP3P water model37. Partial charges were adopted from the CHARMM36 force field34 and the literature38. A spherical cutoff distance of 1.2 nm was imposed on Lennard-Jones interactions. The long-range electrostatic interactions were calculated using the smooth Particle Mesh Ewald (PME) method with a direct space cutoff of 1.2 nm and a Fourier grid spacing of 0.12 nm. The long-range dispersion corrections to potential energy and pressure are also employed.


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. Figure 2. Initial lipid bilayers configuration projected on Z-Y plane (acyl chains are colored grey, and phosphorus is colored red) in water (oxygen/hydrogen is colored red/white) and K+ counterions (in green). Z-axis is normal to the lipid surface. It should be noted that the final simulation system was obtained by expanding the initial system 4 times on X-Y plane.

As shown in Figure 2, 42 lipid molecules were initially randomly distributed into two layers, with a gap distance of 0.4 nm, given the fact that self-assembly process starting from randomly distributed molecules are beyond the capability of our atomistic MD simulations. Each leaflet is composed of 21 lipid molecules. At pH 7.0, the phosphate groups of LP6 and LP4 are deprotonated to H2PO4-1. Because of the ionic nature of lipid A in an aqueous environment, 84 K+ counterions were included to neutralize the system. Initially 2848 water molecules were distributed outside the interior of lipid bilayers (Figure 2). For both systems of LP6 and LP4, three different initial configurations were used. The system was first relaxed in a canonical ensemble (NVT) by constraining atom positions (including lipid, water and ions) in the direction normal to the lipid bilayer surface (Z-axis) and keeping them mobile in X and Y axes. Second,


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after the system was relaxed in an isobaric-isothermal ensemble (NPT) for up to 200 ns at 298.15 K and 1 bar, the system was further relaxed with a stepwise heating/annealing protocol. Third, the initial system dimensions were periodically expanded four times than the original size on the X-Y plane. The expanded system, which consists of 168 lipid molecules, 11392 water molecules and 336 K+ ions, was then equilibrated for another 132 ns at the same temperature and pressure as these of the small system. The equilibrium properties were collected in the final 66 ns. For such size of the system, the performance of parallel computation with 128 processors is about 20 ns per day.

In the simulations on lipid A bilayers, the temperatures of lipid molecules, counterions and water molecules were separately scaled using the Nose-Hoover thermostat (the characteristic time of 0.5 ps) in combination with the semi-isotropic Parrinello-Rahman barostat algorithm (the characteristic time of 4 ps; the reference pressure 1 bar; the compressibility 4.5 × 10-5 bar-1). The integration of the dynamic equations was performed by using the Velocity Verlet algorithm, with a time step of 1 fs. In all the simulations, three-dimensional periodic boundary condition (PBC) was employed to mimic the infinite large lipid bilayers in an aqueous environment. Since the thickness of water layers both above and underneath the lipid bilayers was more than 1.5 nm, the interactions between lipid molecules and their periodic images in Z-axis direction were effectively removed.

2.2. Free Energy Calculation of Water Permeation across Lipid Bilayers We employed the cavity insertion Widom (CIW) method23, 27, 28, 29 to estimate the free energy profile for water molecules along the surface normal by analyzing the trajectories from MD


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simulations. The free energy profile, ∆G(z), was calculated by using the excess chemical potentials, , at position z along the bilayer normal and reference position at position in Eq. (1), ∆ = − (1) We chose the water layers, which were 1.5 nm away from the bilayer surface, as the reference state, . The expression of the excess chemical potential, in NPT ensemble is

= − ln 〈 exp

∆

〉 − ln〈"#$% 〉 (2)

where P, V, T and N respectively represent pressure, volume, temperature and the atom number in the system; R is the gas constant; ∆U(z) stands for the intermolecular interaction energy between an inserted water molecule at z and all the molecules in the system; Pcav(z) denotes the probability of a cavity at z, and the angle brackets represent time average. The final equilibrated configurations from MD simulations were used for the estimation of the excess chemical potential profile and the calculation of the cavity probability. To search cavities, the total simulation cell was first divided into 0.2 nm-wide bins along the z-direction. Inside each bin, the space was further uniformly gridded by a small grid size of 0.05 nm, which is empirically regarded small enough to produce the accurate cavity probability profile23, 27, 28, 29. A cavity grid is then identified by taking into account the atom size, which is defined as half of an atom’s van der Waals (vdW) radius. The value of the configuration energy, exp[-∆U(z)/(RT)] in Eq. (2), is estimated with trial insertions of a randomly oriented and translated water molecule inside cavity grids within each bin. For each bin of every configuration, 3000 trial insertions were executed. The averaged free energy and the associated error bar were obtained by calculating the average value and the standard deviations of 6 simulation runs, each of which included a trajectory of 8 ns (i.e., totally 4000 configurations) obtained from MD simulations. Based on previous


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research23 for a system of similar dimensions and our investigation of the current system, our method, as discussed above, ensures the converged results of chemical potentials. By using parallel computation, the total free energy computation can be finished in less than 3 hours.

2.3. Lipid Bilayer Mobility Analysis Lipid mobility is known to highly correlate with lipid structural stability and critical for cellular membrane activity. To examine the dynamics of the lipid molecule in a bilayer, we calculated the chains’ mobility with self-part of Van Hove correlation function39 for lipid chain atoms by using the following time autocorrelation function, N

∑ δ [r + r (0) − r (t )] j

j

j =1

(3) N where δ is the Dirac delta function; rj represents j atom’s position vector; t is time; N is the total

G s (r , t ) =

chain atom number. By using Fourier conversion, the intermediate incoherent inelastic structure factor39, I(q,t), can then be obtained by the following, I (q, t ) = ∫ G s (r , t )e iq.r dr

(4)

By measuring the dynamic incoherent inelastic structure factor over a relatively long time interval and longer spatial scales, we can achieve insight into bilayer mobility at the molecular level, typically valuable to compare with neutron scattering experiment.40

3. RESULTS AND DISCUSSION 3.1. Structure of Bilayer Assembly In this study, we first compared the structures of both lipid (LP6 and LP4) bilayers using fully atomistic MD simulations in an aqueous environment at pH 7.0 at room temperature of 25 ℃.


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The simulations were performed at the condition of water weight content (40% for LP6 and 46% LP4) consistent with the experimental condition19. Figure 3 (a) and (b) display snapshots of the same equilibrated LP6 bilayer structure viewed from two different angles by rotating the configuration along the Z-axis, which is normal to the surface. By changing the angles, we observed an ordered alignment of acyl chains in each leaflet. The project of bottom atoms of acyl chains in the X-Y plane in the inset of Figure 3 (d) shows clear hexagonal structures in a leaflet. To prevent initial configuration-bias in the simulation, two more duplicated simulations were performed with different initial scratch configurations as stated in the previous section. All three simulations consistently showed that the fatty chains of LP6 in the bilayer, which were arranged rather regularly, exhibited all-trans configuration and formed an ordered hexagonal alignment which is named gel phase (Lβ-phase)41, in each leaflet. The diffraction curve of the hydrocarbon atoms of acyl chains in Figure 3 (d) also demonstrates the presence of hexagonal structures. An primary peak is identified around 14.9 nm-1, corresponding to the Bragg distance of 0.424 nm. Moreover, there exist two additional small peaks at q ≈ 25.8 and 29.8 nm-1, which correspond to the second (√q) and third (2q) peaks of a hexagonal packing structure respectively. The hexagonal structure within a leaflet of lipid A was also experimentally observed by X-ray measurement

42

, where the Bragg distance for LP6 bilayer structure was 0.425 nm, with which

our simulation result well agrees. This important feature of hexagonal packing in a leaflet of lipid A bilayer, has never been elucidated by previous theoretical molecular modeling, according to our knowledge. It is also noteworthy that in all three parallel simulations, hexagonal structures for the top and bottom leaflets are twisted for about 30-36 degrees to achieve the equilibrium state. The physical origin of the twisting requires further investigation. Figure 3 (c) displays an equilibrated LP4 bilayer structure which is very different from that of LP6. LP4 lipid is featured


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with uneven thickness of the bilayer, undulations and ripple structure, which is similar to the undulated ripple phases of dipalmitoyl phosphatidylcholine (DPPC) lipids43. The fatty acid chains are arranged in a way that the order-disorder structures coexist. At the center of the bilayer, the fatty acid chains of both leaflets are highly interdigitated. As shown in Figure 3 (d), the intensity of the peak at 15 nm-1 on the diffraction curve of LP4 bilayer becomes much weaker than that of LP6. In addition, the second ( q√3 ) and third (2q) peaks of a hexagonal packing structure disappear. It indicates that LP6 is in the gel phase (Lβ) whereas LP4 is prone to other phases, such as liquid crystalline (Lα) phase or ripple phase like in DPPC. Previous studies12, 44 found that LP6 have higher value of Lβ↔Lα transition temperature, Tc at 43 ℃ and LP4 around 20 ℃, by measuring the acyl chain dynamics. Our current study only focused on both lipid structures at 25 ℃, which is between both lipids’ Tc, in order to serve our motivation in this study to investigate water passive permeation across the bilayer, and to establish an accurate fully atomistic model for our on-going research projects (polymer membrane for water treatment and lipid A analogue-based drug delivery). While it is obvious that the variation of temperatures above/below Tc causes phase transition, experiments also suggest that membrane water permeability is sensitive to lipid A acylation pattern11, which can result in phase morphology change. Our simulation results of different structural behaviors for both lipids are in agreement with previous experimental observations, which will be further discussed in later sections. Due to the computation loads in the current study, we have not examined and decoupled the factor of temperature effect from the acylation pattern on phase morphologies. We will tackle this issue of temperature and further investigate supra-molecular formation mechanism in our future research.


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(a)

(b)

(c)

Figure 3. Snapshots of the equilibrated LP6 bilayer structures ((a) and (b) are viewed from different angles), LP4 bilayer structure (c) and scattering structure factor (d) for the carbon atoms of acyl chains for LP6 (in black) and LP4 (in red). The inset in (d) is X-Y projection of end atoms of acyl chains in a leaflet of LP6. Note: the overlapping of carbon atoms on the inset arises from the projection of different layers of carbon atoms; water molecules and counter ions are not shown on the snapshots for the purpose of clarity; 3 principle peaks (q, q√3 and 2q) are identified with dashed lines.

To gain more insights into the supra-molecular bilayer structures, we compared the packing of both lipids in an aqueous environment as shown in Fig 4 (a) and (b). In both cases, hydrophobic fatty chains form a hydrophobic interior, while the hydrophilic head groups of glucosamine disaccharide is exposed to water environment. Figure 4 (a) and (b) also compare the two lipids’ atom density profiles (carbon and phosphorus of lipids, oxygen of water, and K+ ions) along the


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direction of Z-axis, which is normal to the membrane surface, and show that the density distributions for both systems display fairly symmetrical patterns. This symmetry is characteristic of a lamellar arrangement, which further demonstrates that lipid A, with six or four fatty acid chains, exhibited a stable bilayer structure under the condition of our simulation. Our results agree with experimental observation19, 45, which verified the presence of bilayer structure at the same water content and temperature. The water density profiles show that water molecules penetrated more deeply in LP4 bilayers than in LP6 bilayers. However, water molecules were absent from the hydrophobic interior of LP6 membrane, but for LP4 membrane, occasional diffusion of few water molecules was detected within a hundred nanoseconds of simulations. In contrast, the bilayers are fairly permeable with water molecules at the outer region of the membrane, i.e., the hydrophilic parts involving the groups of polysaccharide, glycosidic linkages and phosphates. It is worth noting that even though water density is zero in the bilayer interior obtained from MD simulations, it does not necessarily exclude the occurrence of water permeations. The dynamics of water permeation can be slow and cannot be sampled in our hundred-nanosecond simulations due to the free energy barrier, which will be discussed in the next section. In addition, for ultra-low water concentration, due to limited size of the simulation system, water molecules number is negligible. The most recent study23 showed that the driving force of water permeation across the lipid membrane is related with the factors of membrane morphology as well as the magnitude of potential energy fluctuations compared with the free energy barrier. Similar lipid A packing structures have also been identified by other published research work using molecular modeling

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and neutron scattering experiments for LPS

membranes of Pseudomonas aeruginosa 46, 47. Counterions of K+ are observed to be concentrated adjacent to lipid phosphate groups (H2PO4-1) due to the Columbic interactions. It should be noted


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that in this work counterions were added for the purpose of neutralizing the simulation. The wellknown effect of divalent cation’s ionic valence and radius on the packing of lipid A or LPS 18, 30 are beyond our concern in this study. For both lipid biayers, the carbon density profile along the direction normal to the lipid surface exhibits a similar shape of central trough, representing a decrease in carbon density around the bilayer midplane. The differences between the two systems also merit attention. In particular, the depth of the central trough for LP4 is shallower than for LP6, which indicates that the fatty acyl chains of LP4 are more interdigitated, compared with those of LP6 (see Fig. 4). The interdigitation between bilayer leaflets has also been reported when the composition of amphiphiles with larger headgroups increases.48 Our simulation showes, at the lipid-water equilibrium inside the bilayer, a LP4 molecule is smaller than a LP6 molecule (LP6: 0.21 × 0.14 × 0.25 nm3; LP4: 0.17 × 0.14 × 0.23 nm3). (a)

(b)

Figure 4. Snapshots of lipid bilayer for LP6 (a) and LP4 (b) and the corresponding atom density distributions of water oxygen (blue), lipid carbon (green), lipid phosphorus (red) and counterions


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(black) along Z-axis which is normal to the bilayer surface. The counter ions of K+ are colored green and water is colored red in the snapshots. Noted: The black points are the atoms across the cross section.

The supra-molecular structure as a function of molecular chemical structures can generally be described by comparing the properties of the thickness and the area per lipid for both bilayer membranes. The thickness of the lipid bilayer can be estimated from phosphor and carbon density distribution profiles (see Figure 4 (a) and (b)). The LP6 bilayer was observed to have the thickness of 4.8 - 4.9 nm, which is close to the experimental neutron scattering measurement (～ 5.0 nm)15 in an aqueous environment and the X-ray measurement (4.8 - 5.1 nm)42, 49 in a dry state. In contrast, relative shorter thickness (4.4 - 4.5 nm) is detected for LP4 bilayers, mainly due to the interdigitation of two LP4 leaflets. For LP6 bilayer, the area per lipid is estimated at about 1.29 ± 0.01 nm2. The experimental values

45

of the area per lipid A with six fatty acid

chains in the gel phase ranged between 1.26 nm2 (at 20 ℃) and 1.29 nm2 (at 40 ℃).45 Moreover, according to the experimental rule of thumb44 regarding the space requirement of the hydrophobic moiety and the critical chain length, the area per lipid A is 1.273 nm2. For LP4, our simulation showed the area per lipid to be 1.11 ± 0.01 nm2, which is close to the estimation of 1.04 nm2 by Snyder, et al

50

. The affinity between our simulations and reported experimental

measurements confirms the reliability of our simulations and the forcefield parameters we adopted.

3.2. Free Energy Profile for Water Permeation across Lipid Bilayer


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The chemical potential difference between bulk water and the lipid interior yields a free energy barrier for water permeation across the membrane. The local chemical potential is known to be sensitive to lipid molecule conformation29. Our discussions in Section 3.1 demonstrate that LP6 and LP4 lipids display different packing structures possibly due to the difference in acylation patterns (LP6: six non-hydroxy fatty chains; LP4: four hydroxyl fatty chains). In this study, we compared the water permeation free energy for both lipid membranes, using the efficient CIW method. Figure 5 shows the free energy profile of a water molecule transporting across LP6 and LP4 bilayer membranes. In the region of bulk water (i.e., ≤ 0.6 nm and ≥ 6.4 nm ), which was chosen as a reference, ∆G fluctuates around 0 kJ/mol as expected. In the bilayer interior (1 nm < < 6 01), ∆G is significantly higher than in the water region. Around the midplane ( ~ 3.5 nm) of the membranes, the free energy profiles show fairly good convergence of the excess chemical potential. For both lipids, the associated error bars are less than 2 kJ/mol. A small different free energy barrier is observed for a water molecule to transport from the bulk water region to the membrane midplane: ～23 kJ/mol for LP6 and ～20 kJ/mol for LP4. It is necessary to note that the obtained free energy barriers of water permeations for the lipid-A and its analogue membranes are slightly lower than those for phosphorus lipid membranes (e.g., ～28 kJ/mol in the gel phase and ～ 23 kJ/mol in the liquid-crystalline phase for dipalmitoyl phosphatidylcholine, DPPC, membranes).23 This possibly indicated a slightly higher water permeation in Lipid A (or Lipid A analogue) membranes than in DPPC lipid membranes. Such a higher permeation may be related to the toxic feature of lipid-A membranes. It also should be noted that different force field parameters can also possibly result in the variance in free energy28.


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Figure 5. Free energy profile across lipid bilayers (LP6 and LP4) for water permeation.

Figure 5 also displays a remarkable difference in the shapes of the free energy profiles for both lipid membranes. For LP6, the free energy reaches the maximum at 2.7 nm < < 4.3 01 with a small trough, which is similar to its hydrocarbon density distribution. Compared with LP4, the enhanced free energy barrier of LP6 is attributable to the higher condensed packing of lipid hydrocarbon tails in the gel phase. In contrast, the free energy of LP4 displays a narrow peak in the middle of the bilayer 3.2 nm < < 3.8 01, which is attributed to the more disordered structure inside LP4 membrane (see Figure 3 (c) and (d)) and the deeper water permeation across the bilayer (see Figure 4 (b)). The free energy profile of the LP6 system obtained from our simulations is typical for lipid bilayers in the gel phase, while that of the LP4 system is characteristic for membranes in the liquid-crystalline phase.23, 28 The higher and broader free energy barrier for LP6 bilayer suggests lower water permeation and also indicates that LP6 acyl tails have more compact packing.


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It should be noted that the large magnitude of energy fluctuations around lipid-water interface actually is attributed to the fluctuation and undulation of the membrane interface (see Figure 4). We will further examine the lipid dynamics in the following sections.

3.3. Dynamic Behavior of Bilayer Assembly Lipid mobility is known to highly corelate with lipid structral stability and critical for cellular membrane activity. As we discussed in the previous section, acyl chains can affect bilyer structural stability. To study the lipid acyl chain dynamics, we calculate their incoherent inelastic structural factors, I(q,t). The apparent difference in the decay of I(q,t) for both lipids, as shown in Figure 6, can be identified over a large distance, i.e., at q=7.14 nm-1, after we investigated a certain range of q (5-8 nm-1). LP6 bilayers experience longer relaxation time (~4 ns) than LP4 bilayers ( ～ 2 ns). The slower mobility of LP6 bilayers is consistent with its more ordered structures which as demonstrated before.

q=7.14 nm-1

Figure 6. Incoherent inelastic structural factor for chain atoms of LP6 and LP4 at q=7.14 nm-1.


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We proceed to measure the chain’s local mobility by dividing the chain atoms into three regions according to their relative positions to calculate their incoherent inelastic structural factors for both LP6 and LP4 bilayers, at q = 7.14 nm-1 in Figure 7 (a) and (b). The result demonstrates that atoms at the tail positions adjacent to the bilayer center experience faster dynamics compared with atoms at the top and middle parts, which are closer to the diglucosamine backbone. LP4 top and middle atoms inside bilayers experience very slight difference in mobility. Similarly, negligible difference is observed for different parts of LP6 bilayer. The distinct mobility of carbon atoms at different positions arises from variations in the local environment. The hydrated diglucosamine backbone in bilayers have pronounced structural rigidity. Consequently, the upper parts of the chains adjacent to the backbone are effectively rendered relatively immobile. In contrast, the lower part of the hydrocarbon of chains undergoes faster dynamics due to their conformational transitions at the bilayer central part, where two leaflets interdigitate.

Figure 7. Incoherent inelastic structural factor for chain atoms at different positions for LP6 (left) and LP4 (right) at q=7.14 nm-1. Bottom part refers to the position which is most farther away from lipid head group of polysaccharide. Note: for LP6, both curves of Top and Middle seems to overlap because of negligible difference.


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Lipid molecular lateral diffusion coefficient inside the membrane is important for membrane fluidity. We estimate lateral diffusion coefficients, Dlat, using atoms’ mean square displacement in the plane of bilayer surface, i.e., in X and Y directions, for both lipid molecules using the following time autocorrelation function,

lim [r (t + ∆t ) − r (t )] = ∆t → ∞ 4∆t

2

Dlat

(5)

where r is atoms’ position vectors and t is time. The difference in lateral diffusion coefficient Dlat (lipid A: 2.22×10-7 cm2/s, its analogue: 5.57×10-7cm2/s) indicates that the bilayer of LP4 has higher fluidity than that of LP6, which is consistent with our analysis above of the different phases of the two bilayer systems.

4. CONCLUSIONS Considering the structural complexity of lipid A molecule, the system dimension and the computational load demanded, our atomistic simulations with large-scale parallel computations in this study were started with pre-assembled bilayer structure rather than from a random distribution of lipids in the water phase. Nevertheless, the overall agreement between our simulations with reported experimental measurements confirms the reliability of our simulations. Our simulated properties of lipid membranes (including molecular packing structure, bilayer thickness, the area per lipid, and selected chemical atoms density distributions) and lateral diffusion coefficient match published experimental results.


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Most interestingly and importantly, our simulation is so far the first theoretical molecular modeling work to elucidate the presence of hexagonal structures within a lipid leaflet, which matches the reported experimental observation. LP6 with six acyl fatty chains is observed to form a more ordered and stable bilayer structure of gel phase, compared with the analogue, LP4, with four acyl fatty chains. The LP4 tail chains are highly interdigitated, whereas the two leaflets of LP6 are fairly separated. A slightly higher and significantly broader free energy barrier and slower dynamics of acyl chains for LP6 membrane than that of LP4 are observed. The hydrophilic diglucosamine backbone is highly hydrated at lipid-water interface and provides structural rigidity for the membrane, whereas the interdigitated hydrophobic hydrophobic acyl chain tails with faster dynamics play the role of screening the aqueous environment from the lipid interior and also reinforce the membrane’s structural stability.

Our current study focused on the bilayer behavior, typically the water passive permeation at room temperature. Although it cannot be concluded that lipid A acylation pattern is the ultimate factor causing all the differences (lipid morphology, hydrocarbon acyl chain packing structure, dynamics and water permeation) without further investigation of temperature effects on phase behavior, our current study would be useful future research in polymer design for endotoxin removal and drug design, as well as broader applications.

ACKNOWLEDGEMENTS Tao Wei thanks the support of computational resources from Texas Advanced Computing Center (TACC) and the program of Extreme Science and Engineering Discovery Environment


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from National Science Foundation (XSEDE/NSF). Lin Zhang acknowledges the support of National Natural Science Foundation of China (No. 20946003); Zhejiang Provincial Natural Science Foundation of China (No. LR12B06001). We thank Dr. Robert A Riggleman for the helpful discussion.

Corresponding Author *Email: [email protected]

Notes The authors declare no competing financial interest.

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TOC

Hexa-acyl

LipidA

Water Permeation Tetra-acyl analogue at 25 ℃


30

Mechanical properties of lipid bilayers from molecular dynamics simulation.

Molecular dynamics simulations of water permeation across Nafion membrane interfaces.

Structural properties of archaeal lipid bilayers: small-angle X-ray scattering and molecular dynamics simulation study.

Phase-transition properties of glycerol-dipalmitate lipid bilayers investigated using molecular dynamics simulation.

A model of lipid-free apolipoprotein A-I revealed by iterative molecular dynamics simulation.

Receptor-guided 3D-QSAR studies, molecular dynamics simulation and free energy calculations of Btk kinase inhibitors.

Free Energy Profile of APOBEC3G Protein Calculated by a Molecular Dynamics Simulation.

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Molecular dynamics simulation of interlayer water embedded in phospholipid bilayer.

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Molecular Dynamics Simulations of Ceramide and Ceramide-Phosphatidylcholine Bilayers.

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Passive one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation.