Understanding thermal phases in atomic detail by all-atom molecular-dynamics simulation of a phospholipid bilayer.

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Understanding Thermal Phases in Atomic Detail by All-Atom Molecular-Dynamics Simulation of a Phospholipid Bilayer Koji Ogata, Waka Uchida, and Shinichiro Nakamura J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp504684h • Publication Date (Web): 10 Nov 2014 Downloaded from http://pubs.acs.org on November 12, 2014

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The Journal of Physical Chemistry

Title: Understanding Thermal Phases in Atomic Detail by All-atom Molecular-dynamics Simulation of a Phospholipid Bilayer Koji Ogata†*, Waka Uchida†,‡, and Shinichiro Nakamura†

†

RIKEN Innovation Center, Nakamura Laboratory, 2-1Hirosawa, Wako, Saitama, Japan, 351-0198

‡

Department of Biomolecular Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa, Japan, 226-8503

Running title: All-atom simulation of lipid bilayer

ACS Paragon Plus Environment


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Abstract All-atom molecular-dynamics (MD) simulations were used to investigate the thermal phase behavior of two hydrated phospholipids DPPC and DPPE at the atomic level. The trajectories in the MD simulations clearly identified the structures of DPPC in the crystalline (Lc), gel (Lβ), ripple (Pβ) and liquid crystalline (Lα) phases and those of DPPE in the Lc and Lα phases. The physicochemical and structural properties of these phases agree well with the experimental results. Moreover, the structural transformation between phases was observed. In the Lβ phase, forces are directed in opposite directions in the upper and lower layers of the bilayer. These forces, which are due to the thermal motion of each monolayer, strongly influence a series of phase transitions from Lβ to Pβ. This MD simulation can provide understanding of the dynamics of the lipid bilayer in each thermal phase and suggest the mechanism that generates the Pβ phase.

Keywords: All-atom molecular dynamics simulation, DPPC, DPPE, Thermal phases


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Introduction Phosphatidylcholine (PC) and phosphatidylethanolamine (PE) are important lipids constituting the plasma membrane1, and a model membrane system consisting of a single lipid, either PC or PE, is generally used to understand the phase behavior of plasma membranes2-6. Temperature-dependent phase transitions have previously been studied using a model membrane system consisting of a single lipid, and the properties of each phase investigated step by step using methods like differential scanning calorimetry and X-ray diffraction2-3, 5. The phase-transition temperatures of hydrated phospholipids

have

also

been

determined

experimentally;

those

of

1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) are reported to be approx. 20 ºC (293.15 K) for Lc→Lβ (subtransition), approx. 35 ºC (308.15 K) for Lβ→Pβ (pre-transition), and approx. 41 ºC (about 314.15 K) for Pβ→Lα (main transition)

2, 4-7

,

while that of 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) is reported to be 64.3 ºC (337.5 K) for Lc→Lα (main transition)6. Although a rough picture of the phospholipid structures in each phase has been obtained after considerable study2-3, 5-6, the detailed mechanism of lipid behaviors—at the atomic level—in each phase is still unknown.

Such atomic-level details are expected to be useful for the fields of physics,

chemistry, and biology as well as nanotechnology. In particular, elucidating the structure of lipid bilayers in the atomic level will enable understanding of the



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mechanism of events occurring in the plasma membrane, and design of artificial cell membranes. Computer simulations have been used to understand the thermal phase behavior of model membrane systems8-16. These simulations aim to understand atomic behavior in different phases but not the sequence of events of phase transition from Lc to Lα in the lipid bilayer system (because of computational costs). To simulate the sequential events, including validation by repeating the simulations, MD simulations with a large time scale are needed. The coarse-grained approach (namely, applying molecular dynamics (MD) simulations based on simplified lipid models) roughly shows how the properties of bilayer conformations change with temperature17-19. In particular, Smit and his colleagues have analyzed the thermal phase behavior of lipid bilayer using coarse-grained MD simulation and observed the lipid behaviors in each phase18. This approach, however, cannot reveal the atomic-level details of the lipid structures. Elucidating the mechanism of the phase transition behavior at the atomic level is a very important and challenging task for providing insight to synthetic chemists and biologists. In light of these above-described issues, the present study used an all-atoms MD simulation to investigate the thermal phase behavior of two hydrated phospholipids


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(DPPC and DPPE) at the atomic level. The structures in each phase were clearly identified by analyzing the MD trajectories. The MD simulation links the experimentally obtained information on the structure of the lipid bilayer in each phase to all the physical events. The force generated by the conformational changes in the alkyl-chains in the Lβ phase of DPPC was studied by analyzing the MD trajectories. It is suggested that this force is essential for forming ripples in the Pβ phase. To confirm this, four additional simulations including and excluding the Lβ phase, were performed with temperature increments. On the basis of the results of these additional MD simulations, the mechanism of ripple formation is explained.



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Materials and Methods Modeling of lipid bilayer DPPC and DPPE models were constructed with extended alkyl chains in which torsional angles of saturated bonds were set at 180º so that the chains of both lipids form a parallel shape. These lipid models were aligned along the z-axis. To generate a lipid bilayer model, an 8×8 upper layer was formed by placing the lipids at grid points on the xy-plane at every 8 Å. The model had an area per lipid of 64 Å2, which was close to reported experimental results

20-21

. The lower layer was formed in the same way, but it

was rotated 180º towards the y-axis and shifted in the minus direction along the z-axis so that the average distance between head groups was 40 Å (see Figure S1a). The model was hydrated in a TIP3P water box with more than 35 water molecules per lipid molecule.

Parameterization of lipids The atom types for DPPC and DPPE from the GAFF parameter22 were set by using Antechamber programs23. The GAFFLipid parameters reported by Dickson et al24 were assigned as parameters of the alkyl chains. The partial charges at each atom were obtained in consideration of the charge distribution of various conformations of lipids because the lipid conformations changed with temperature.

Although, the optimization

procedure using QM needs considerable computational time for flexible molecules, this


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procedure does not always guarantee improvement. Therefore, the single point calculation for various conformations was adopted for obtaining atomic charges. The various conformations in the vacuum state were generated by MD simulation. The initial partial charges were then obtained by using antechamber23 at the am1bcc level for the sampling of the conformation. Note that although this partial-charge method is qualitatively inaccurate, it is accurate enough to generate various conformations in the vacuum state. AMBER package25 was used for all the MD simulations. The lipids were relaxed by optimizing them in the vacuum state. After the optimization, unconstrained MD simulation under the temperature condition of 300 K was performed for 2 ns. From the obtained MD trajectories, 2000 snapshots were extracted at time intervals of 1 ps. The 2000 snapshots were classified by a clustering method with a 1.0-Å threshold value. From those snapshots, 1130 and 1436 clusters were obtained for DPPC and DPPE, respectively. In each cluster, the conformation with the lowest energy was regarded as the representative conformation, and ESP charges were obtained by single-point calculation (by Gaussian0926) at the B3LYP/6-31G(d) level. The partial charge for the n-th atom is given as cn =

1 N n ∑ci exp{− Ei / kT} Z i=1


(1)


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where ci and Ei are the partial charge and energy at the i-th conformation, respectively, k is Boltzmann’s constant, and T is temperature. Z is summed over exp{− Ei / kT } . The partial charge was obtained in consideration of the charge distribution of the various conformations of the lipids. These parameterizations of the lipids were applied to DPPC and DPPE (Figure S2 and Table S1).

MD simulation with increasing temperature The lipid bilayer models were optimized by using the conjugate-gradient method (part of Amber1225, 27) in 10,000 steps for hydrogen atoms after 10,000 steps for all atoms. After the optimization, 100-ps MD simulation under constant volume (NVT) was performed with constraint for the lipids. In this study, all MD simulations of hydrated lipids were performed with 10 Å cutoff and Particle Mesh Ewald (PME) method at the periodic boundary condition. To generate an initial structure, 10-ns MD simulation was performed under constant pressure (1 atm) and temperature (T = 263 K) (NPT) using a Langevin thermostat with the collision frequency γ=1 and no surface tension. In this procedure, anisotropic Berendsen control28 was used with the time constant of 1ps. From the initial structure, MD simulation was started at T = 263 K and performed for 320 ns while temperature was increased 5 K every 10 ns. The snapshots were stored every 10 ps, and the temperature dependence of conformational behavior was


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determined by analyzing 32,000 snapshots. Using the final structure and velocities at T = 418 K, MD simulation was started again at T = 413 K and performed for 310 ns while temperature was decreased 5 K every 10 ns. By performing this cooling procedure, we can expect to observe the hysteresis in the phase transitions.

Heat capacity and enthalpy calculation In the constant pressure condition, heat capacity, cp, was calculated as d H c p =   dT

H2 − H   = RT 2 P

2

where R and T are gas constant and temperature, respectively

(2)

18, 29

. And H is enthalpy

defined as

H = U +PV

(3)

where U and V are entire energy and volume, respectively. Now, to calculate the heat capacity of the lipids, the enthalpy of lipids, Hlipid, can be given by

H lipid = H system − H water

(4)

Then, Hwater was calculated from the 3-ns MD simulation of the same number of water molecules at temperature range from 263 to 418 in every 5 K. At each temperature, Hwater was calculated, after which Hlipid was calculated by subtracting Hwater from Hsystem. From the heat capacity, enthalpy (∆H) and entropy changes (∆S) were defined as



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∆H = ∫ c p dT ∆S = ∫

cp T

dT

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(5) (6)

In the current MD calculation, ∆H and ∆S were obtained by summing cp at each temperature.

MD simulation of each phase To analyze the detail of the structures of Lc, Lβ and Lα phases, 250-ns MD simulation was performed for each phase using the same condition of the simulation with increasing the temperature, as mentioned above. The temperatures of the Lc, Lβ and Lα phases of DPPC are set at 273 K, 343 K and 388 K, respectively, and the Lc, and Lα phases of DPPE are set at 273 K and 388 K, respectively. These values were detected from the simulation with increasing temperature as mentioned below. To reproduce the structure of the Pβ phase, three large DPPC bilayer models containing 648 lipids (18×18×2) in a 144×144×105-Å box (DPPC648), 1296 lipids (2×DPPC648) in a 144×144×210-Å box, and 2592 lipids (36×36×2) in a 288×288×105-Å box (DPPC2592), were generated, for which MD simulation was performed. The initial bilayer model was generated in the same manner as explained in section “Modeling of lipid bilayer”. To reproduce the Lα phase, 30-ns MD simulation was performed at 313 K, which corresponds to the phase-transition temperature for Lc→Lβ, as mentioned


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below. After the 30-ns simulation, for DPPC648, 110-ns simulation was performed for the temperature range of 318 K to 368 K while the temperature was increased by 5 K at every 10 ns, and the trajectory at 368 K was analyzed. For DPPC2592 and 2×DPPC648, 60-ns simulation was performed for the temperature range of 318 K to 368 K while the temperature was increased by 5 K at every 5 ns. Next, the Tm values were detected in each simulation after analyzing the AL and RF graphs. At temperatures lower than the Tm by 5K, 15-ns simulation was performed.

Alkyl-chain order parameter The profile for the deuterium-order parameter of the alkyl chain, SCD, is a measure of the orientation of the lipids with respect to the bilayer normal. SCD is given as SCD =

1 3 cos2 θCD − 1 2

(6)

where θCD is the angle between a vector of C-H bond and the bilayer normal, and 〈 〉 denotes an ensemble average. For each simulated MD trajectory, SCD was calculated and these were compared with the experimentally measured data 30.



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Results Thermal phase transition Thermal phase transition of DPPC The DPPC bilayer structures used in the simulation have three different conformations (Figure 1). At 273 K, the alkyl chains in the upper and lower layers are mirror images in the plane of reflection at the center of the bilayer (Figure 1a). The alkyl-chain packing is similar to that in the crystal structure of the dehydrate of 1,2-dimyristoyl-sn-glycero-3-phosphocholine

(DMPC)31-32

and

1,2-dipalmitoyl-3-acetyl-sn-glycerol33, so that the structure can be assigned to the Lc phase. The structure shown in Figure 1c has disordered alkyl chains, so it is assigned to the Lα phase. Finally, the structure in Figure 1b is assigned to the Lβ phase because it is an intermediate phase, having extended alkyl chains, between the Lc and Lα phases. To confirm the signature of phase transition, area per lipid (AL) and gauche ratio in alkyl chains (RF) (Figure 2a and 2b) were evaluated in an extensive manner. In the temperature range from 263 K to 338 K, the graph of AL shows a flat shape while that of RF gradually increases. In the temperature range from 338 K to 368 K, the values of AL and RF gradually increase. In this range, the extended alkyl chains change little by little to disordered chains, but AL values of the surface of the bilayer stay constant. Moreover, a transition between 373 K and 378 K, where AL and RF dramatically


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increase, can clearly be seen; that is, |∆AL|(=|AL(T)-AL(T-5)|; T: temperature) and |∆RF| (=|RF(T)-RF(T-5)|) have obvious peaks between 373 K and 378 K (Figures. 2a’ and 2b’). In this temperature range, the surface of the bilayer expands rapidly, and the alkyl chains completely melt in a short period (Figure S3). After 378 K, AL and RF increase proportionally. The observed peaks in |∆AL| and |∆RF| can also be traced only between 373 K and 378 K by other properties that determine the phase transition: the average distance between the phosphates of the two monolayers (DPP) as well as van der Waals energy (vdW) (Figures 2c and 2d). From 263 K to 373 K, DPP increased in a stepwise fashion, and a bilayer showed the Lc→Lβ transition (see below). In this range, the vdW energy decreases as the alkyl chains become increasingly well-packed. Between 373 K and 378 K, |∆DPP| and |∆vdW| exhibit obvious peaks. The alkyl chains are melted, and the bilayer shows clear transition to the other phase. At this transition, the profile of vdW energy of waters strongly correlates to the transition profile of the other properties (Figures 2, S4b and S4c). The energies between waters and between lipid and water dramatically increased and decreased, respectively, in the same temperature range (373 K ~ 378 K). In this phase, the distance between atoms in the lipids is greater than the vdW radii. It can be



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concluded from these results that there exists a main transition temperature (Tm) between 373 K and 378 K in our simulation. For the Lc→Lβ transition, the lipid tilt angle (θtilt), the angle between the upper and lower layers (θL), and the angle between the two layers projected to the xy-plane (ϕL) indicate that the alkyl-chain packing changes at 338 K (Figures 3a-3c).

In particular,

θL and ϕL dramatically change at 338 K (Figures 3b and 3c). Thus, sub-phase transition temperature (Ts) is about 338 K. In the Lβ phase, simulated AL agrees relatively well with the experimentally measured value of 47.9 Å2 (Figure 2a)34. Furthermore, careful observation of Figure 3 reveals that the alkyl-chain packing changes at 363 K (Figures 3a-3c). This temperature is an intermediate one between the Lβ and Lα phases. It is thus assumed that the pre-phase transition temperature (Tp) in our simulation is 363 K. According to the results, the temperature difference between Ts and Tp, and that between Tp and Tm are around 25 and 10 K, respectively. These values are relatively close to the experimentally measured ones, namely, 15 and 6 K, respectively. However, it is inevitable that the simulated phase-transition temperatures are not exactly the same as the ones measured by differential scanning calorimetry (DSC)2, 5, 7. The difference between the measured and simulated temperatures, ~60 K ranges, is attributed to several reasons: water parameters, other parameters that are constant during the temperature


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changes, the fact that experimental conditions are not exactly covered (local temperature, distribution, etc.). In addition, there is also a need to consider other reasons, such as energy parameters of lipids, method of simulations such as pressure control, etc. Still, our trajectory could reproduce phase-transition behavior and show all the physical events occurring during the heating procedure. The results of our simulations are reproducible in three different simulations (Figures. S5 and S6), and these are at large independent of the size of the system (Figure S7). It is therefore concluded that the results of our simulations did not occur accidentally but were inevitably caused by the heating procedure.

Thermal phase transition of DPPE Two different conformations of lipids appear in the DPPE simulation (Figures. 1d and 1e). Comparisons with the DPPC structures at each temperature reveal that the phase in Figure 1d can be assigned to the Lc phase because the structure shown in Figure 1d is similar to Figure 1a. On the other hand, the DPPE lipid structures in Figure 1e show many disordered alkyl chains. Judging from the |∆AL| and |∆RF| values (Figures 2a’ and 2b’), the transition temperature is between 383 K and 388 K. The same tendencies are shown in the |∆DPP| and |∆vdW| graphs (Figures 2c’ and 2d’). Comparisons of the |∆AL|, |∆RF|, |∆DPP|, and |∆vdW| graphs of DPPC with those of DPPE in Figure 2 show that all



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the graphs (except that of DPP) are very similar. In the DPPC simulation, two phase transitions, Lc→Lβ and Lβ→Lα, occurred from 263 K to 373 K, but no phase transition occurred in the DPPE bilayer at the same temperature range. Moreover, in this temperature range, the alkyl-chain packing changes in DPPC, but not in DPPE (Figure 3). Reflecting this property, it is natural that the DPP graph of DPPE shows a different shape from that of DPPC. The difference of Tm values, between DPPC and DPPE in the simulation, is around 10 K, which is similar to the measured value (about 20 K). Therefore, the simulation results showed relatively good agreement with those of the experimental measurements.

Thermodynamic properties Heat capacities of DPPC and DPPE in the heating procedure showed distinct peaks at 373 K and 383 K, respectively, as shown in Figure 4. These peaks corresponded to main phase transition of DPPC and DPP in the simulation. In the cp graph for DPPC, another small peak could be found at 338 K, which is the same as the sub-phase transition temperature detected using the graphs of AL and RF. This peak therefore was identified as sub-phase transition. Table 1 shows the thermodynamic properties, ∆H and ∆S, calculated from the cp. The calculated thermodynamic properties showed good agreement with the experimental


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values. The ∆Hs and ∆Ss of the main transition of DPPC and DPPE were very similar to those of experimentally measured values. The differences were 1 kcal/mol for ∆H and 5 cal/mol for ∆S. On the other hand, ∆Hs and ∆Ss of sub- and pre-transitions in DPPC deviated largely from the experimentally measured values. This is because these phase sub- and pre-transition occurred due to the conformational changes of the lipids, which consisted of only very small rotations in the up and down directions of the bilayers. Some weak peaks were found in the graph of cp. Therefore, the cp values could contain many inevitable errors. As a consequence, the energy deviations were small and ∆Hs and ∆Ss were underestimated.

Comparison of heating and cooling behaviors The heating procedure showed a well-distinguished main phase transition behavior in DPPC and DPPE. Changes in slope were observed clearly at the Tm, as mentioned in the above. On the other hand, for the cooling procedure, the AL and RF graphs were slightly different from those for the heating procedure (Figure 2). Hysteresis found at the peaks in the graphs of |∆AL| and |∆RF| shifted to the low temperature range. For the cooling procedure, many alkyl chains remained melted below the Tm (Figure 2b). In particular, the DPP values at 263 K were slightly larger than those in the heating procedure and similar with those in the Lβ phase. These results suggest that the cooling rate in our



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simulations is insufficient for equilibrating the bilayer system. Therefore, a slower rate of decrease of temperature was needed for the cooling down procedure. The heating rate, by contrast, was adequate for analyzing the lipid conformation in each phase, because of the similar conformation with those of the 250-ns MD simulation, as mentioned below. Therefore, for the heating procedure, our protocol is sufficient for analyzing the thermal behavior of the lipid bilayer at the atomic level.

Atomic detail of each phase in DPPC

Comparison of lipid structures of 10-ns and 250-ns MD simulations Table 2 shows the structural properties of lipids on 10-ns and 250-ns MD simulations in each phase. Small differences of the properties were observed in both simulations. This means that the atomic details between short and long simulations consist of very similar behaviors in the atomic level. Therefore, we can expect that the properties at the other temperatures show similar conformations with those of long simulation. In the following analysis, the 250-ns simulation was used to analyze the structural details and the 10-ns simulation with increasing temperature was used to analyze the thermal behaviors in the phases.


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Lc phase of DPPC In the simulation of DPPC, AL in the Lc phase is constant, and RF is gradually increasing (Figures. 2a and 2b). θtilt and θL gradually decrease and increase, respectively (Figures 3a and 3b). However, the angle between the two layers projected to the xy-plane (ϕL) stays constant. The structure in the Lc phase therefore kept the mirror images in the plane of reflection at the center of the bilayer. This mirror image was confirmed in the 250-ns MD simulation at 273 K. The self-diffusion coefficient D using Einstein relation (i.e., 〈(ri(t)-r(t0))2〉/4t) calculated from the mean square displacement of the trajectory is 0.12×10−8 cm2/s, which is smaller than that of the other phases (Figure 5). The alkyl chains therefore show tight packing in hexagonal formation, and the DPPC lipids in the lipid bilayer do not move easily. Consequently, the thermal energy acquired by increasing temperature was used in the minor shape changes between the upper and lower layers.

Lβ phase of DPPC In the Lβ phase, the upper layers rotated and became parallel to each other (Figures 1a, 1b, and 3). The tilt angle, θtilt, decreased to 17º (Figure 3a), which is slightly smaller than that measured by x-ray diffraction in the Lβ phase (θtilt = about 31º at 25 ºC)35-36.



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The angle between the upper and lower layers (θL) increased and the angle between the two layers projected to the xy-plane (ϕL) also increased. Finally, the upper and lower layers became nearly parallel. This parallel image was confirmed in the 250 ns MD simulation at 343 K. The alkyl chains at 303 K (the Lc phase) were regularly ordered but those at 353 K (the Lβ phase) indicated disorder in the upper layer (Figure S8). These differences showed the alkyl-chain packing as a hexagonal shape in the Lc phase and quasi-hexagonal shape in the Lβ phase. This change affected the cell shape in the simulation. In the Lc phase, the bilayer contracted along the x axis and expanded along the y axis (Figure S9). On the other hand, in the Lβ phase, the bilayer expanded along the x axis and contracted along the y axis. The self-diffusion coefficient (D) in the Lβ phase calculated from the trajectory in our simulation was 0.5×10−8 cm2/s (Figure 5) at 358 K and 0.85×10−8 cm2/s at the average within the Lβ phase, which was slightly smaller than the value measured using spin-labeled PC (1.8×10−8 cm2/s)37. This value was slightly larger than that of the Lc phase. This difference was confirmed through the projection of the positions of the lipids to the xy-plane (Figure 6). Analysis of the trajectories of DPPC indicates that the upper and lower layers move to the opposite direction in the Lβ phase without any change in the lipid conformation of


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ordered acyl chains (see video S1). The lipid positions projected to the xy-plane also show that the lipids in the upper and lower layers moved ~10 Å to the opposite direction (Figure 6). This movement included the rotational motion of the lipid in the Lβ phase. These results suggest that the thermal energy given by increasing temperature is converted to work with force in the upper and lower layers in directions opposite to each other. We will reveal where this force was generated from and why the lipids indicated the rotational motion in the Lβ phase (see section Discussion).

Pβ phase of DPPC X-ray

diffraction

analysis38-40,

freeze-fracture

electron

microscopy41-42,

and

atomic-force microscopy43-45 have shown that ripple phases (Pβ) between the Lβ and Lα phases occur after the pre-transition of DPPC at T≈35 ºCs. The electron-density profile indicates that the distance between repeated ripples is around 141 Å39. In the simulation, the simulation system was too small to reproduce the Pβ phase, so an additional simulation for larger DPPC bilayers was carried out (see subsection MD simulation of

ripple phase). That simulation showed that lipids with disordered tails appear in the bilayer and that the surrounding lipids also have disordered alkyl chains (Figure 7). The system of



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DPPC648 shrank to 110×136×105-Å at 363 K. The structure of the bilayer had a small kink in those lipids, and the other lipids kept the extended conformation. The distance between the lipids with the disordered alkyl chains is around 110 Å, which is similar to that between the ripples in the Pβ phase observed by X-ray diffraction analysis

39

.

Analysis of the dynamics of the lipids showed that around 363 K, the upper and lower layers receive forces opposing each other (Figure 7a) occurring in the Lβ phase. In addition, a few lipids start to form disordered alkyl chains. The lipids with melted alkyl chains then reduced their force, preventing movement of other lipids. Consequently, the relatively extended lipids press against lipids with melted alkyl chains (Figure 7b). The Dpp values of the lipids with melted alkyl chains are smaller than those of the lipids with extended alkyl chains (Figure S10). The minimum DPP values of the melted lipids are about 10 Å smaller than those of the extended lipids. In this case, the part of lipids with melted alkyl chains and the surrounding lipids collapsed and rode onto the lipid bilayer. Meanwhile, the expanded AL by the melted alkyl chains also helped this event. The lipid bilayer therefore bends at the lipids with the disordered alkyl chains (Figure 7c), giving the bilayer a ripple shape on the whole (Figure 7d). For the large systems, 2×DPPC648 and DPPC2592, the events described above were observed at 358 K in both simulations (Figure 9). In the 2×DPPC648 simulation, the


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two bilayers showed a small kink during the simulation (Figure 9b). The distance between the lipids with the disordered alkyl chains is around 110 Å. The positions of the kink were not the same in the two bilayers. This may be due to the distance between the two bilayers in the 2×DPPC648 model. However, the two bilayers individually formed the ripple formation with similar wavelength to DPPC648 simulation. Therefore, the ripple formation with the similar wavelength was indeed generated reproducibly in the simulation. Moreover, in the DPPC2592 simulation, two repeated sawtooth shapes were observed (Figure 9b). This sawtooth pattern was characterized by the contourplots of the z-coordinates of phosphate atoms in the lipids bilayer. The melted and extended lipids were complemented well between the upper and lower layers (Figure S11). The wavelength between the two patterns is ~130 Å, which is similar wavelength with DPPC648. The two sawtooth patterns of DPPC2592, therefore, correspond to two sawtooth pattern of DPPC648. This result means that the ripple formation with the similar wavelength was indeed generated repeatedly in the simulation. The results of the three simulations conclusively prove that the ripple formation always appear in our simulation. It was neither coincidentally nor artificially produced in the simulation.



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Regarding the ripple formation, there is a need for further analysis of the forces generated by thermal fluctuation, which act in different directions on the upper and lower layers and thus bend the bilayer, in order to conclude that these forces contribute to the transition from the Lβ phase (see section

Discussion).

Lα phase of DPPC The surface area of the bilayer increased rapidly at Tm and gradually expanded with increasing temperature, whereas Dpp dramatically decreased. The area per lipid at 388 K, which is 10 K above Tm in the simulation, is 59.8 Å2/lipid, which is slightly smaller than the experimentally measured value of 63.3 Å2/lipid at 323.15 K, which is 10 K above Tm in the experiment. The gauche ratio of the alkyl chains in the Lα phase gradually increased, resulting in the melting of the alkyl chains, and increase in the fluidity of the lipids. The profile of deuterium order parameter of alkyl chain, SCD, calculated from the MD simulation is similar to the experimentally measured one (Figure 9). This profile indicates the orientation of the alkyl chains with respect to the bilayer normal. Therefore, in our simulation, the alkyl chains demonstrate native-like behavior. The self-diffusion coefficient (D) increases in the Lα phase. D at around 383 K, which is more than 5 K higher than Tm, is 1.6×10−7 cm2/s, which is the same order of magnitude as the experimentally measured value of ~1×10−7 cm2/s in the Lα phase 46-47.


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Moreover, the vdW energy in the Lα phase is almost constant because the alkyl chains exhibit high mobility and are separated by a distance greater than the van der Waals radius. These results reveal that the lipids flux in the lipid layer, and the interactions are almost similar.

Atomic detail of each phase of DPPE Lc phase of DPPE In the simulation of the DPPE bilayer, the tilt angle θtilt at 263 K is inconsistent with that calculated from x-ray-diffraction data; θtilt is stable (4º) at 23ºC (296.15 K)48. However, during the heating process, θtilt near the main transition temperature decreases to 20º (Figure 3a). It seems that the entire structure of DPPE does not significantly change from the native conformation. During the simulation, a significant change of θL in the Lc phase was not observed because the NH3 groups form hydrogen bonds with P=O and C=O moieties. In fact, most of NH3 groups form hydrogen bonds at 278 K, and even in the DPPE in the Lc phase, many hydrogen bonds can be found (Figure S12). The strongly connected hydrogen bonds overcome the vibration due to thermal motion and keep their conformation with extended alkyl chains. Furthermore, at the temperature corresponding to the Lβ phase in DPPC (338 to 363 K), the self-diffusion coefficient (D) of DPPE is three times smaller than that of DPPC (Figure 5). Moreover,



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later at Tm, the hydrogen bonds did not break (Figure S13), and the increasing ratio of D of DPPE is much smaller than that of DPPC. These results reveal that the hydrogen bond restriction strongly influences the thermal behavior of DPPE under the phase-transition temperature.

Lα phase of DPPE The lipid conformation in the Lα phase of DPPE showed similar behavior to that of DPPC. That is, the alkyl chains melted, and the bilayer expanded rapidly toward the xy-plane. The NH3 group in the head part of DPPE forms hydrogen bonds with P=O and C=O moieties (Figure S12b). These hydrogen bonds prevent the DPPE from moving freely on the bilayer. This is why D of DPPE is smaller than that of DPPC. The SCD calculated from the MD simulation is similar to that of DPPC (Figure 9). DPPC and DPPC have the same alkyl chains (16:0) at sn-1 and sn-2. The SCD profile of DPPE therefore shows very similar behavior to that of DPPC.


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Discussion

Mechanism of motion in Lβ phase In Results, we mentioned that the thermal energy produced by increasing temperature is converted to work associated with force in the upper and lower layers in directions opposite to each other. In this sub-section, we try to identify the origin of the force in the Lβ phase. First of all, let us consider the lipid conformation in the Lc phase. In this phase, the alkyl-chains are well-packed to each other owing to the vdW interaction, as shown in Figure 10a. By increasing the temperature, the atoms in the alkyl-chains gain energy and vibrate more. Due to the thermal vibration, the overlapping vdW area between the atoms increases and the vdW energy also increases (Figure 10b). Finally, to reduce the vdW energy, the lipids in the upper and lower layers rotate, causing the tilt angle (Figure 10c) to increase as well. Note that the simulation in Figure 10b is similar to that with the large vdW radius in the alkyl-chains, because of the increasing number of contact atoms by the large vibration of the atoms. Therefore, to clarify this assumption, we attempted simulation using a larger vdW radius in the alkyl-chains. The temperature set at 263 K and vdW radius of carbon and hydrogen atoms in the alkyl-chains were increased 0.05 Å every 10 ns.



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Increasing the vdW radius in the alkyl-chains reduces the θtilt values (Figure 11). Meanwhile the θL values become larger than those in the simulation using normal vdW radius. The increase in the θL values also increases the DPP values (Table S2). The ϕL values decrease and the lipids rotate around 30º when the vdW radius is increased more than 0.3 Å. From these values, we can confirm that the lipids in the bilayer form a mirror image similar to that by the lipids in the Lβ phase. These simulations do not directly but indirectly reproduce the thermal behavior of the lipids in the Lβ phase. The results therefore suggest that the thermal energy produced by increasing the temperature is converted to the work with force in the upper and lower layers in directions opposite to each other. The next subsection demonstrates why this force is very important for generating the ripples of the lipid in the Pβ phase.

Mechanism to be generated in Pβ phase The previous subsection described that ripples form in the Pβ phase of DPPC, and it was assumed that the force in the Lβ phase, namely, force of the upper and lower layers in opposite directions, strongly contributes to the generation of the ripples. To confirm this assumption, three additional MD simulations were performed. The Lβ phase was skipped in these simulations. In other words, the simulations were started from the Lc


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phase and rapidly went through the Lβ phase or jumped to the Pβ phase. All conditions in the simulations were the same as those in the simulation described in the subsection

“Pβ phase of DPPC”. After 30-ns MD simulation at 313 K, the three simulations were performed at the following different conditions: (1) the temperature was set at 368 K (sim_skip), (2) the temperature was increased 5 K at every 100 ps until 368 K (sim_rapid), and (3) the temperature was increased 5 K at every 500 ps until 368 K and the positions of the carbon atoms in the alkyl chains were constrained (sim_constraint). After these three simulations, the 10-ns simulations were performed at 368 K. The structures before the Pβ phase are shown in Figure S14. Here, four trajectories of the simulations are compared. In the simulation including the Lβ phase, the bilayer showed ripple formation, as mentioned above. The bilayer can clearly be observed as a smooth sawtooth wave pattern formed by the alkyl chains that have melted and extended in an orderly manner (Figure 12a). The ratio of the lipids with melted and extended alkyl chains was almost constant during the simulation (Figure S10b). Similar plots were seen in the simulation of sim_rapid and sim_constraint (Figures S15 and S16). The ratios of the lipids with melted and extended alkyl chains were also more or less constant. The bilayers formed ripples similar to those in the simulation including the Lβ phase (Figures 11c and 11d).



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Analysis of the trajectory of these simulations showed that the lipid bilayers rapidly changed to similar conformations in the Lβ phase. The θL and ϕL values indicated almost 180°, and the lipids in upper and lower layers formed a parallel shape (Figure S17). The lipid bilayers therefore formed the ripples by passing through the Lβ phase. Even the time steps in the Lβ phase are of a very short period. On the other hand, in the case of simulation of smi_skip, although the bilayer formed ripples, the ripples are not smooth (Figure 12b). That is, many melted and extended alkyl chains are arranged in a disorderly manner. Moreover, when the temperature increased from 313 to 368 K, the alkyl chain packing shape of the lipid bilayer starts to change from hexagonal to quasi-hexagonal (which is the same alkyl conformation as the Lc→Lβ phase transition). However, the temperature increase was too fast to transition to the Lβ phase, and the number of melt lipids increased, whereas that of extended lipids decreased (Figure S18). Therefore, without being forced to move in opposite directions, some alkyl chains had already melted before lipids formed in the Lβ phase. Consequently, the melted alkyl chains can be observed on both sides of the disordered layers. The distributions of the extended and melted lipids in the simulation including the Lβ and sim_skip are plotted against time in Figure 13. The melted lipids in the simulation


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including the Lβ phase are locally distributed, and the melted and extended lipids are gathered together in the bilayer. The melted lipids show a periodic pattern. The fully extended lipids remain until t of 10 ns. Interestingly, the distributions of the melted lipid patterns in the upper and lower layers are different. In the upper layer, the melted lipids distribute in the diagonal direction.

In the lower layer, the melted lipids are arranged

in the horizontal direction and look like a banding pattern. The melted lipids form a concave shape and bend the plane of the bilayer by forces generated by thermal fluctuation, acting in different directions in the upper and lower layers. These obliquely crossed melted lipids in the upper and lower layers help to form the ripples. In the simulation of sim_skip, many extended lipids are found at the beginning of the simulation at 368 K. However, they are almost all melted in 1 ns. Since the melted alkyl chains have many contacts with other lipids, they prompt the alkyl chains in the surrounding lipids to melt. Since the simulation skipped the Lβ phase, at 368 K, the bilayer started to form the Lβ phase. However, the temperature increase was too fast for transition from the Lc phase to the Lβ phase. Before the lipid bilayer had completely transitioned to the Lβ phase, the lipids started to melt their alkyl chains, as mentioned above. Therefore, the lipids with melted alkyl chains rapidly spread into the bilayer in several picoseconds (see videos S3 and S4). The small forces acting in different



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directions in the upper and lower layers occur in the bilayer, and even these small forces can provide the energy for forming the pattern of the melted alkyl chains. The lower layer shows a banding pattern that is similar to the lower layer in the simulation including the Lβ phase.

Furthermore, in the upper layer, a similar pattern of the melted

lipids in the upper layer to that shown in simulation including the Lβ phase can be vaguely observed, but it disappears after t=6 ns. In Figures 12c and 12d, at t=10 ns, a small number of extended lipids are observed, and the patterns of the melted alkyl chains in both layers partially disappear. The bilayer structure shows an almost-flat structure. It can be concluded from the above-described results that lipid conformation in the Lβ phase is needed to form the ripple structure. In particular, the motion in the Lβ phase, namely, the force of the upper and lower layers in opposite directions, strongly contributes to the formation of ripples. This force was not observed in the simulation of DPPE, which did not show the Lβ phase with the rotational motions during the simulation. The Pβ phase was not experimentally observed for the DPPE lipid bilayer at neutral pH. This fact also supports our assumption that the opposite forces of the upper and lower layers contribute to the generation of ripples. The following Conclusion describes the basic principle for elucidating the mechanism that generates ripples.


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Conclusions Thermal phase behaviors are clearly seen at the atomic level. Trajectory analysis by MD simulation revealed that alkyl-chain packing strongly contributes to change in lipid conformation at the phase-transition temperature. In particular, in the Lβ phase, the rotation of lipids on one side of a layer by opposing forces between upper and lower layers was observed. Moreover, in the Pβ phase, a few lipids melted and bowed to pressure from the other lipids. The lipid bilayer bended and formed ripples. These opposing forces are therefore important for forming ripples in the Lβ phase. Two additional MD simulations, one including and one excluding the Lβ phase, confirmed that these forces strongly contribute to the ripple formation. It can therefore be concluded that these forces are necessary for generating ripples in the Pβ phase.



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Table 1 Thermodynamics properties of phase transition Lipids

Transition

Exp. DPPC

DPPE

Sim.

∆H (kcal/mol) Exp.a Sim.b

∆S (cal/mol) Expa Sim.c

Temperature (K) a

Lc→Lβ

293.6

337

5.38

0.92

18.4

2.72

Lβ→Pα

309.0

363

1.29

0.29

4.063

0.81

Pα→Lα

314.8

373

8.7

8.92

27.73

23.88

Lc→Lα

337.5

383

17.76

18.48

52.58

48.24

a

6

Katsube et al. .

b

At phase transition temperature, ∆Hs were calculated from cp between T-5 and T+5 K.

c

At phase transition temperature, ∆Ss were calculated from cp/T between T-5 and T+5 K.


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Table 2 Comparison of the results between 10 ns and 250 ns simulations

Lipids

Temperature (K)

DPPC

273

Time

343

388

DPPE

AL (Å2)

RF

10

42.77

250

273

388

θtilt (º)

D (× ×10 cm2/s)

0.031

26.01

0.075

42.23

0.031

24.97

0.026

10

42.93

0.089

16.71

0.425

250

43.04

0.083

18.18

0.125

10

59.37

0.272

27.27

27.6

250

59.86

0.273

28.76

20.7

10

41.6

0.017

26.09

0.005

250

41.73

0.015

26.48

0.002

10

56.24

0.261

24.86

26.9

250

56.35

0.261

26.74

21.9

scale (ns)

Table 3 Comparison of ripple formation in three simulations Configration

AL (Å2)

RF

DPPC648

Wavelength (Å) ~110

2×DPPC648

46.0

0.150

~120

DPPC2592

46.1

0.155

~130


−8


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Figure Legends

Figure 1 All phase-transition structures and temperatures for (A) DPPC and (B) DPPE. Snapshots of DPPC at (a) 273 K (Lc), (b) 358 K (Lβ), and (c) 388 K (Lα) are shown in (A), and snapshots of DPPE at (d) 273 K (Lc) and (e) 388 K (Lα) are shown in (B). During the simulation, the tilt angle (measured between the upper and lower layers) of DPPC was around 26° in

Lc phase and 16° in Lβ phase, and that of DPPE in Lc phase

was around 26°. The structures of all snapshots are drawn as vdW models, and C, N, O, P, and H are colored in gray, blue, red, tan, and white, respectively. All molecular graphics figures were made using the program VMD49.

Figure 2 Temperature vs. (a) area per lipid (AL), (b) gauche ratio in alkyl chains (RF), (c) average distance of phosphates between two monolayers (DPP), and (d) van deer Waals energy (vdW) in DPPC and DPPE systems. The temperature vs. differentials of AL (|∆AL|), GF (|∆RF|), DPP (|∆DPP|), and vdW (|∆vdW|) are shown in Figures (a’), (b’), (c’), and (d’), respectively. The red and blue dotted lines indicate the Tm of DPPC and DPPE, respectively, in the simulations.


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Figure 3 Temperature vs. (a) lipid tilt angle (θtilt), (b) angle between upper and lower layers (θL), and (c) angle of two layers projected to xy-plane (ϕL) of DPPC and DPPE. The red and blue dotted lines indicate the Tm of DPPC and DPPE, respectively, in the simulations.

Figure 4 Temperature vs. heat capacities of DPPC and DPPE.

Figure 5 Temperature vs. (a) diffusion efficiencies and (b) log scaled diffusion efficiencies of DPPC and DPPE. (b) The red and blue dotted lines indicate the Tm of DPPC and DPPE, respectively, in the simulations.

Figure 6 Trajectories of lipid diffusion (mass center projected onto xy plane) of DPPC. Six lipids, (a) three from upper layers (U1-U3) and (b) the other three from lower layers (L1-L3), are randomly selected. The trajectories in the Lc and Lβ phases are colored in blue and red, respectively.

Figure 7 Mechanism producing Pβ phase of DPPC. The structure in the Lβ phase has a force (Figure 7a). Increasing the temperature melted the alkyl chain in a few lipids (colored in red) and reduced their force (Figure 7b), and the other lipids pressed against



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the melted lipids. Meanwhile, the alkyl chains surrounding the lipids were disorderly owing to the influence of the lipid and expanded the lipid surface. Finally, the part of lipid bilayer consisting of melted lipids was bent by the pressing force from other lipids (Figure 7c). The snapshot in the simulation at 363 K clearly shows the rippling lipid bilayer (Figure 7d).

Figure 8 Snapshots of structure in Pβ phase in (a) DPPC2592 and (b) 2×DPPC648. Arrows colored in blue indicate the bent position in the bilayers.

Figure 9 Alkyl-chain deuterium order parameter, SCD.

Figure 10 Motions of alkyl-chain in gel formation in MD simulations of DPPC.

Figure 11 Increasing vdW vs. (a) lipid tilt angle (θtilt), (b) angle between upper and lower layers (θL), and (c) angle of two layers projected to xy-plane (ϕL) of DPPC. The vdW radii of carbon and hydrogen in the alkyl-chain were increased 0.05 Å at every 10 ns in the simulation.


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Figure 12 Snapshots of structure in Pβ phase obtained by (a) simulation including Lβ phase, (b) sim_skip, (c) sim_rapid, and (d) sim_constraint.

Figure 13 Distributions of extended and melted lipids of (a) upper layer and (b) lower layer of simulation including Lβ phase and of (c) upper layer and (d) lower layer of simulation excluding Lβ phase. The phosphate atoms in the lipid were drawn by the vdW model, of which the radius of atom is four times larger than the original one. The figures show the images replicated along the ±x and ±y axes; i.e., a total of nine replicated images are shown. The vdW models were colored by the gauche ratio in the alkyl chains.



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ASSOCIATED CONTENT

Supporting Information. Supporting figures and movies. These materials are available free of charge on the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author * Koji Ogata

RIKEN Innovation Center, Nakamura Laboratory, 2-1 Hirosa-wa, Wako, Saitama 351-0198, Japan

Email: [email protected]

Author Contributions W.U. performed MD simulations, collected data, analyzed the results, and wrote the paper. S.N. designed the study, overall project strategy and management, and wrote the paper. K.O. performed MD simulations, analyzed the results, wrote the paper, and was involved in the design of the study.


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Acknowledgments We thank the KAITEKI Institute (Mitsubishi Chemical Holdings) for their support and Dr. T. Iitaka at RIKEN for his fruitful discussions. Some of the calculations in this study were performed at the RIKEN Integrated Cluster of Clusters (RICC) facility.



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(A) DPPC

Crystalline (Lc) phase

Experiment

T  293.15 K T  338 K

Simulation

Gel (Lb ) phase

~26º

~15º

~26º

~17º T = 273 K

Liquid crystalline (La) phase

293.15 K  T  308.15 K 314.15 K  T 338 K  T  363 K 373 K - 378 K  T (b) (c)

(a)

Snapshots

Figure Page1A 46 of 61 Ogata et al.

T = 343 K


T = 388 K

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Figure 1B Ogata et al.


(B) DPPE

Crystalline (Lc) phase

T  337.5 K Simulation T  383 K - 388 K (d) Snapshots ~26º Experiment

Liquid crystalline (La) phase

337.5 K  T 383 K - 388 K  T (e)

~25º T=273 K


T=388 K

Figure Page2ab 48 of 61 Ogata et al.


(b)

RF

AL (Å2)

(a)

(a’)

(b’)

|DRF|

|DAL| (Å2)

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Temperature (K)

Temperature (K) ACS Paragon Plus Environment

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DPP (Å)

vdW (×103 kcal/mol)

(c)

(c’)

|DvdW| (kcal/mol)

|DDPP| (Å)

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Figure 2cd Ogata et al.


Temperature (K)

(d)

(d’)


Figure Page350 of 61 Ogata et al.

qtilt (º)

Temperature (K)

qL (º)

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jL (º)


Temperature (K)


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Heat capacity (kcal/molK)

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Figure 4 Ogata et al.

Log10D (cm2/s)

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D (×10−8 cm2/s)


(a)

(b)



Page 53 of 61

(a)

(b)

U1 U2

Y position (Å)

L1 Y position (Å)

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L2

L3

U3

X position (Å)

X position (Å)




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(a)

Lb phase

(b)

(c)

Bend

Melt

Force Press

Pb phase

Press Press

Force (d)

Force

Expand

Bend

Bend Simulation box ACS Paragon Plus Environment

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(a)

(b)


Simulation box



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-SCD


Carbon number ACS Paragon Plus Environment


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(a)

Lc phase

(b)

(c)

Lb phase

Force

Alkyl chains

qtilt



Contact

Force Temperature


Figure Page11 58 of 61 Ogata et al.


(b)

Increase vdW radius (Å)

(c)

jL (º)

(a)

qL (º)

qtilt (º)

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(a)

(b)

(c)

(d)



Figure Page13 60 of 61 Ogata et al.


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(a)

0.5 (b)

(c)

(d)

0.0

0

1

2

3

4

5

6

Time (ns)


7

8

9

10

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Table of Contents artwork


Ogata et al.

Molecular dynamics simulation of interlayer water embedded in phospholipid bilayer.

Lipid-Bilayer Dynamics Probed by a Carbon Dot-Phospholipid Conjugate.

Electrolyte effects on bilayer tubule formation by a diacetylenic phospholipid.

Structure-based prediction of drug distribution across the headgroup and core strata of a phospholipid bilayer using surrogate phases.

Phospholipid exchange between bilayer membranes.

Possible mechanism of adhesion in a mica supported phospholipid bilayer.

Experimental demonstration of a bilayer thermal cloak.

Kinetics of phospholipid exchange between bilayer membranes.

Robustly Engineering Thermal Conductivity of Bilayer Graphene by Interlayer Bonding.

Phospholipid exchange between bilayer membrane vesicles.

Fluorescence quenching of Ca2+-ATPase in bilayer vesicles by a spin-labeled phospholipid.

A Unified Detail-Preserving Liquid Simulation by Two-Phase Lattice Boltzmann Modeling.

Topological phases in the zeroth Landau level of bilayer graphene.

Localization of molecular halothane in phospholipid bilayer model nerve membranes.

Thermal conductivity of twisted bilayer graphene.

Probing interactions between β-glucan and bile salts at atomic detail by ¹H-¹³C NMR assays.

Lipid-alginate interactions render changes in phospholipid bilayer permeability.

Glycophorin-induced cholesterol-phospholipid domains in dimyristoylphosphatidylcholine bilayer vesicles.

Probing the Huntingtin 1-17 membrane anchor on a phospholipid bilayer by using all-atom simulations.

Asymmetry of the phospholipid bilayer of rat liver endoplasmic reticulum.

Atomic-scale control of competing electronic phases in ultrathin LaNiO₃.

The mechanism of action of DNP on phospholipid bilayer membranes.

The intrinsic structural asymmetry of highly curved phospholipid bilayer membranes.

Preparation of large monodomain phospholipid bilayer smectic liquid crystals.