Molecular dynamics study of lipid bilayers modeling the plasma membranes of mouse hepatocytes and hepatomas Yoshimichi Andoh, Noriyuki Aoki, and Susumu Okazaki

,

Citation: J. Chem. Phys. 144, 085104 (2016); doi: 10.1063/1.4942159 View online: http://dx.doi.org/10.1063/1.4942159 View Table of Contents: http://aip.scitation.org/toc/jcp/144/8 Published by the American Institute of Physics

THE JOURNAL OF CHEMICAL PHYSICS 144, 085104 (2016)

Molecular dynamics study of lipid bilayers modeling the plasma membranes of mouse hepatocytes and hepatomas Yoshimichi Andoh,1 Noriyuki Aoki,2 and Susumu Okazaki1,2,a)

1

Center of Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan 2 Department of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

(Received 10 November 2015; accepted 22 January 2016; published online 26 February 2016) Molecular dynamics (MD) calculations of lipid bilayers modeling the plasma membranes of normal mouse hepatocytes and hepatomas in water have been performed under physiological isothermal–isobaric conditions (310.15 K and 1 atm). The changes in the membrane properties induced by hepatic canceration were investigated and were compared with previous MD calculations included in our previous study of the changes in membrane properties induced by murine thymic canceration. The calculated model membranes for normal hepatocytes and hepatomas comprised 23 and 24 kinds of lipids, respectively. These included phosphatidylcholine, phosphatidylethanolamine, phosphatidylserine, phosphatidylinositol, sphingomyelin, lysophospholipids, and cholesterol. We referred to previously published experimental values for the mole fraction of the lipids adopted in the present calculations. The calculated structural and dynamic properties of the membranes such as lateral structure, order parameters, lateral self-diffusion constants, and rotational correlation times all showed that hepatic canceration causes plasma membranes to become more ordered laterally and less fluid. Interestingly, this finding contrasts with the less ordered structure and increased fluidity of plasma membranes induced by thymic canceration observed in our previous MD study. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4942159]

I. INTRODUCTION

Lipids, such as phospholipids and sphingolipids, are fundamental components of biomembranes.1 They form bilayers spontaneously in water. A lipid bilayer is the basic structure of the plasma membranes of cells. From a biological point of view, much experimental and theoretical research has been performed on the physicochemical properties of phospholipid bilayers.2–7 The properties investigated include the statics and dynamics (membrane fluidity) of lipid bilayers. Although the properties of model bilayers with single, binary, or ternary composition have been investigated thoroughly, those of real plasma membranes of cells are not fully understood because of their very complex lipid composition. A variety of component lipids is found in mammalian plasma membranes.1–5 These lipids may be classified into three major categories: glycerophospholipids, sphingolipids, and cholesterol. Glycerophospholipids are classified further according to their head group into several species such as phosphatidylcholine (PC), phosphatidylethanolamine (PE), phosphatidylserine (PS), and phosphatidyl-myo-inositol (PI). In addition, each of these species show diversity of its tail group. That is, two acyl groups bonded to the glyceryl group have a number of variations in their length as well as in the number of double bonds and their location. The physicochemical properties of the phospholipid bilayers depend heavily on these head groups and tail chains. The a)Author to whom correspondence should be addressed. Electronic mail:

[email protected] 0021-9606/2016/144(8)/085104/14/$30.00

second category includes sphingolipids. In mammalian plasma membranes, sphingomyelin (SM) is the most abundant sphingolipid. Typically, SMs have a backbone of C18 sphingosine with a phosphocholine or phosphoethanolamine head group and have one saturated acyl tail amide-linked to the backbone, which gives a very similar chemical structure to PC and PE. The third category includes cholesterol. In mammalian plasma membranes, it is the most abundant lipid species (20–50 mol. % of total lipids). Cholesterol has a rigid steroid ring and one hydrocarbon tail. When added to the lipid bilayers in the fluid phase, cholesterol functions to order the sn-1 and sn-2 saturated acyl chains of the surrounding phospholipids and sphingolipids. Conversely, when added to the lipid bilayers in the gel phase, cholesterol functions to disorder the surrounding acyl chains, leading the bilayer to enter the fluid phase. This dual effect of cholesterol is generally found among the phospholipid–cholesterol binary systems regardless of the degree of unsaturation of the sn-2 tail.8–12 Cholesterol is thus considered to play a very important role in the formation of real membranes. The composition of lipids in plasma membranes depends heavily on the type of cell.1–5 In a series of investigations since the 1960s,13–15 the concentrations of the component lipids (i.e., glycerophospholipids, SM, and cholesterol) and the mole fractions of the constituent head groups and tail chains have been measured individually for various kinds of mammalian cell plasma membranes.16–22,24 The lipid composition of plasma membranes of liver cells (hepatocytes), the main topic of this article, has been investigated in the rat13–22 and mouse.16–18 The lipid

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composition of normal hepatocyte plasma membranes has also been compared with that of cancerous hepatoma membranes.16–22 Detailed analyses have been reported for mouse and rat hepatocytes.16–18 One essential and commonly observed change in plasma membrane lipid composition induced by hepatic canceration is an increase in the concentration of cholesterol, which is opposite to the situation in thymocytes and their leukemic cells.24 For example, van Hoeven and Emmelot16 reported that the ratio of cholesterol to total phospholipids (C/PL ratio) was 1.0 (50.0 mol. %) in mouse hepatoma-147042 plasma membranes, whereas it was 0.8 (44.4 mol. %) in normal hepatocyte plasma membranes. Similar observations of an increase in C/PL ratio have been made for other species of mice and rats.16,17,20,22 The head groups of the component phospholipids have also been analyzed in detail.18 In particular, the mole fractions of various glycerophospholipids, lysophospholipids, and sphingolipids to total phospholipids have been measured. Decreases in the PE and SM content were noted in mouse hepatoma plasma membranes, and these decreases were compensated by an increase in PC content (see also experimental values in Table I). Further, the length of the acyl tail chains and of the number of unsaturated bonds have been measured for the same two types of membranes.18 This analysis has shown a decrease in the concentration of saturated tail chains in hepatoma membranes from 62.1 mol. %

to 58.7 mol. %, which was compensated for by an increase in the concentration of polyunsaturated tail chains (see also Table I). The average length of the acyl tail chains was a little shorter in hepatoma plasma membranes than in hepatocyte membranes. Another important characteristic of the cell membranes is that they have asymmetric distribution of both number and species of the lipid molecules between outer and inner leaflets.1–5 It is found that, in the cell membranes of human red blood cells and erythrocytes, PCs and SMs are mainly distributed in the outer cell membranes which face extracellular space whereas PEs and negatively charged PSs and PIs are distributed in the inner cell membranes which face cytosol. Cholesterol are presumed to be commonly distributed between inner and outer membranes.5 The asymmetric distribution of lipids, and peripheral and integral membrane proteins, closely relates to biological function of cell membranes.1,3–5 However, in the experimental studies of lipid composition stated above,16–18 asymmetric distribution of lipids between outer and inner leaflets has not been clarified. Only one model of an asymmetric lipid compositions of hepatocyte and hepatoma cell membranes is proposed with a very rough assumption that hepatocyte and hepatoma cell membranes have the same asymmetric phospholipid distribution as the erythrocyte membranes.23 In the present study, we

TABLE I. Model and experimental compositions of the lipids for the hepatocyte and hepatoma cell membranes. Nlip is the number of lipid molecules, and Ntail is the number of fatty acid tails. Details of the phospholipid tails are given in Table S1 in the supplementary material.56 Hepatocyte plasma membrane

Hepatoma plasma membrane

mol. %

mol. %

Lipid composition

Nlip

Present calculation

Experiment16–18

Nlip

Present calculation

Experiment16–18

PC PE PS PI Lyso-PC Lyso-PS SM CH

20 14 10 2 6 2 18 56

15.6 10.9 7.8 1.6 4.7 1.6 14.1 43.7

15.3 11.4 7.6 2.2 4.5 1.1 13.5 44.4

24 8 10 4 6 2 10 64

18.8 6.3 7.8 3.1 4.7 1.5 7.8 50.0

18.3 6.7 7.7 3.3 4.1 1.8 8.1 50.0

Ntail

Present calculation

Experiment16–18

Ntail

Present calculation

Experiment16–18

68 14 36

57.6 11.9 30.5

62.1 11.3 26.6

58 14 38

52.7 12.7 34.6

58.7 11.8 29.5

Present calculation

Experiment16–18

Present calculation

Experiment16–18

28.8 37.3 11.9 16.9 5.1

28.7 34.5 10.4 18.4 8.0

25.5 43.6 18.2 9.1 3.6

26.8 42.7 14.7 11.7 4.1

mol. % Degree of unsaturation Saturated Monounsaturated Polyunsaturated Length of the tail 16 18 20 22 24 Total number of lipid species Number of water molecules Number of Na+ ions Total number of atoms

34 44 14 20 6

23 6 400 14 32 684

mol. %

28 48 20 10 4

24 6 400 16 32 206

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assumed symmetric distribution between two leaflets as an approximation. However, we believe that this does not affect much the qualitative discussion here. The changes in lipid composition described above must cause a change in the physicochemical properties of plasma membranes. This is very interesting from both the physical chemistry as well as the pharmaceutical and physiological perspectives. However, because of difficulties in conducting experiments, the physical properties have rarely been compared between hepatoma membranes and healthy hepatocyte membranes. Measurement of the fluorescence depolarization of fluorescence probe molecules incorporated into membranes is one of a few such investigations performed to date. The most reliable property at the molecular level obtained by fluorescence depolarization measurement is the order parameter of the molecular tilt of fluorescence probe molecules in membranes.25–28 Diphenylhexatriene (DPH), which has rigid molecular structure and hydrophobic nature, is frequently used as the probe molecule, giving the order parameter SDPH. Theories to extract the relaxation time of the wobble motion of fluorescence probes and wobbling diffusion constant have also been established.25–28 However, few investigations have provided these dynamic properties as measured in real plasma membranes. van Blitterswijk et al. reported that the values of SDPH for rat hepatocytes and hepatoma 484A cell plasma membranes were 0.74 and 0.77, respectively.29 The increase in SDPH indicates that the DPH molecule is orientationally more ordered in the hydrophobic region of hepatoma plasma membranes than in that of hepatocyte membranes. Since SDPH is considered to be a reciprocal of membrane fluidity,29 the assumption is made that plasma membranes are less fluid in hepatomas than in hepatocytes. However, SDPH is only a static aspect of the fluidity of the membrane, and the measurements are not related to the membranes themselves. The indirect nature of the measurements prevents a clear, unambiguous understanding of the difference in membrane fluidity between the two membranes. It would be rewarding to obtain a new molecular understanding of the structure and dynamics of normal and tumor cell membranes. Based on the rapid progress in supercomputers, longtime molecular dynamics (MD) calculations for more than 100 ns have become a standard tool for analyzing membrane properties, even for very large and complex systems. Calculation at this time scale allows the investigation of the structure and dynamics of membranes, such as the lipid–lipid lateral distribution functions and lateral diffusion constant of the lipid molecules.30–33 Several theoretical investigations have reported on lipid bilayers.34–44 However, most of these papers were based on single-component membranes or, at most, binary or ternary component membranes containing cholesterol. Recently, we performed all-atom MD calculations of lipid bilayer modeling the plasma membranes of normal murine thymocytes and spontaneous leukemia of GR mice (GRSL) cells.45 The lipid composition of thymocyte and leukemic model membranes was matched to experimentally

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measured lipid compositions24 as nearly as possible for more than 20 kinds of lipid species included in the bilayers. This approach first provided information about the molecular aspects of the changes in the structural and dynamic properties induced by canceration, in particular, in murine thymic leukemias. Other MD studies have also focused on model lipid bilayers for real plasma membranes.46–49 In particular, Klähn and Zacharias performed all-atom MD calculations of lipid bilayers modeling plasma membranes of healthy and cancerous erythrocytes,49 which considered the asymmetric distribution of the lipid species. These recent all-atom MD calculations may be the first theoretical studies of real plasma membranes from the physical chemistry as well as the pharmaceutical and physiological perspectives. Furthermore, to handle slow dynamics of membranes and large lateral fluctuation of concentration of lipid species in membranes by molecular simulations, there are two trends. The first is to use the Anton special purpose MD machine50 which enables it easy to perform over 1 µs all-atom MD calculations of membrane systems.51,52 Sodt et al. identified substructure within the liquid-ordered phase of lipid bilayers (i.e. local hexagonal order of saturated hydrocarbon tails) by a 10 µs all-atom MD simulation.51 The second is to use coarse-grained model to describe interactions between lipids and lipid-solvent. Recently, Ingólfsson et al. performed large-scale coarse-grained (CG) MD calculations of plasma membrane models with over 60 kinds of lipid species with an asymmetric lipid composition based on the MARTINI CG model.53 MacDermaid et al. discussed the formation of lateral microdomains in bilayers of ternary mixture of PCs and cholesterol based on the Shinoda-DeVane-Klein CG model.54 However one general problem of the CG models is that they cannot reproduce dynamics of the lipid molecules omitting the detail of interatomic interactions. Thus, it is still important to explore the dynamics of complicated membrane systems by all-atomistic MD calculations. In the present study, MD calculations based on the newest all-atom lipid force field, the CHARMM36,57 were performed for normal mouse hepatocyte plasma membranes and hepatoma membranes to clarify at the molecular level the changes in the physical properties of membranes induced by hepatic canceration. Symmetric distribution of both lipid number and the lipid species was assumed, although real hepatocyte and hepatoma plasma membranes might have asymmetric distribution.23 The lipid compositions of model lipid bilayers adopted in the present calculations were the experimentally determined compositions described previously,16–18 which included 23 and 24 species of component lipids for hepatocyte and hepatoma membrane models, respectively. Molecular trajectories were analyzed for as long as 250 ns to evaluate both the static properties of the membranes, such as the lateral structure and order parameters, as well as the dynamic properties related to membrane fluidity, such as the lateral self-diffusion constant and rotational correlation times. An inclusion of the asymmetricity and the membrane proteins in our model membranes will make our MD calculations more realistic. However, in general, the asymmetric distribution of molecule species induces asymmetric lipid

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packing between the two monolayers, resulting in unusual surface tensions or different spontaneous curvature of each monolayer of a planer bilayer as discussed in a recent paper.55 Effect of the mismatch in surface area per lipid between two monolayers on bilayer properties is mild when the mismatch is less than 5%-10%. However, further increase of the mismatch results in notable unstabilization of the bilayers. It will cost huge calculation time with trials and errors to determine the asymmetric distribution of lipid species and lipid numbers to obtain zero surface tensions for each monolayer of planer bilayers by all-atom MD calculations. It is out of scope of this paper. Therefore, we performed the present MD calculation study with tensionless planer bilayers with symmetric distribution of lipid number and species without membrane proteins as a simplified model of hepatocyte and hepatoma plasma membranes. In Section II, details of our model membranes and calculation conditions are presented. Section III presents our analysis of both the static and dynamic properties of the membranes and the comparisons between hepatocyte and hepatoma membranes. The results of this study were also compared with our previous MD study45 to clarify whether and how the trend in physical property changes induced by canceration is related to the type of cancer (hepatoma and thymic leukemia). Finally, we describe our conclusions in Section IV. II. CALCULATIONS

In the present study, the MD calculations for model lipid bilayers of the normal hepatocyte and hepatoma plasma membranes were performed to investigate the changes in physical properties of membranes induced by hepatic canceration. We prepared three initial configurations each for hepatocyte and hepatoma membranes among which lateral mixing was different. Three independent MD calculations starting from different initial configurations enhanced a reliability of the calculated physical properties. As discussed in Sec. III, convergence of membrane properties was very similar among the three runs. Deviations in physical properties calculated from three MD runs were small enough to discuss the difference between normal hepatocyte and hepatoma model membranes. In this section, we give the details of the model systems investigated here, and we describe the MD calculations used in the analyses. A. Model systems

We modeled the plasma membranes of mouse normal hepatocytes and hepatomas (hepatoma-147042) using their experimentally determined lipid composition.16–18 As in our previous study,45 we constructed our model systems such that three experimentally known properties of the membranes’ lipid compositions were reproduced. The first was the molar ratio of cholesterol to the whole phospholipids. The second was the head group mole fraction in which the experimentally found major phospholipids, PC, PE, PS, PI, SM, lyso-PC, and lyso-PS were all considered. The third was the composition of the fatty acid residues of the lipids.

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In the present calculations, one leaflet comprised 64 lipid molecules. The lipid compositions of the hepatocyte and hepatoma cell membranes are listed in Tables I and S1 in the supplementary material56 together with the experimental values.16–18 First, the mole fractions of cholesterol were 43.7 mol. % for the hepatocyte plasma membranes and 50.0 mol. % for the hepatoma membranes in the present calculation. These corresponded well to the experimental values of 44.4 mol. % and 50.0 mol. %,16 respectively. Second, the mole fractions for PC, PE, PS, PI, SM, lyso-PC, and lysoPS of the present system were taken to be the same as those in the experimental system. For the above two mole fractions, the difference between the experiments and the present study reflects the rounding to integers. Here, the derivative of C18 sphingosine with a head group of phosphocholine was adopted for SMs. Because PS, PI, and lyso-PS are monovalent anionic phospholipids, the same number of Na+ ions was introduced as counterions to neutralize the calculation systems. The manner by which the fatty acid residues of the phospholipid tails were determined is described in the supplementary material.56 As is shown in Table S1 in the supplementary material,56 some phospholipid molecules such as PI and lyso-PS are contained only one molecule per leaflet in our model membranes. Further, number of phospholipid molecules with the same head group and the same two acyl tails is one per leaflet for some phospholipids (e.g. PC with sn-1 chain of 16:0, and sn-2 chain of 16:0 in the hepatocyte membranes). Therefore, clustering of the lipids and formation of lateral microdomains54 are out of scope of the present calculations. B. Molecular dynamics calculations

Three 300 ns-long independent MD calculations were executed for both the hepatocyte and hepatoma model membranes. The fully flexible MD unit cell contained 128 lipid molecules, 6400 water molecules, and Na+ counterions as shown in Table I. The CHARMM36 force field57 was adopted for PC, PE, PS, lyso-PC, and lyso-PS. For PI, the parameters for the myo-inositol head group were imported from the CHARMM35 parameter set for sugar-related molecules.58 For SM, the parameters for the backbone were imported from a previous report,59 while keeping the other parameters identical to those of CHARMM36. For cholesterol, an early version of CHARMM36 potential model referred as “C36” in Ref. 62 based on the model by Pitman et al.39 was adopted. The rigid TIP3P and Na+ potential models60,61 listed in the standard CHARMM36 topology file were adopted for water and Na+ counterions, respectively. Current newer versions of the CHARMM force field for SM52 and cholesterol (referred as “C36c” in Ref. 62) have been released. However, to enable direct comparisons between the previous study of murine thymocyte and leukemic cell plasma membranes and the present study of mouse hepatocyte and hepatoma plasma membranes, we adopted the same force field set as used in Ref. 45 described above. The Lennard-Jones (LJ) interaction was cut off at 12 Å by applying a switching function from 8 to 12 Å on the potential function, while the original CHARMM36 paper57 suggests that a choice of the forcebased switching function is most appropriate. The long-ranged

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FIG. 1. Snapshots of the equilibrated (a) hepatocyte and (b) hepatoma membranes from the present MD calculations at t = 300 ns. The figure was drawn by the VMD.72

Coulombic interaction under the three-dimensional periodic boundary condition was calculated by the particle mesh Ewald (PME) method63,64 with a relative error in forces of 10−5. To reproduce the hydrostatic pressure of the system, all production MD runs were performed in an NPT ensemble with full MD unit cell fluctuations. The hydrostatic pressure P and temperature T were controlled to be 1 atm and 310.15 K by the Parrinello–Rahman65 and Nosé–Hoover chain66–68 methods, respectively. Time constants of the thermostat and barostat were chosen to be 0.5 ps and 1.0 ps, respectively. Newton’s equation of motion for each atom was solved numerically using RESPA.69,70 A single time interval of the numerical integration, ∆t, was adopted to be 2 fs by constraining the length of chemical bonds, including hydrogen atoms, by SHAKE/ROLL and RATTLE/ROLL.70 The whole calculation was executed with the PME version of our originally developed MD software package MODYLAS.71 After the potential energy minimization of the initial configuration, velocity scaling was applied to increase the system temperature stepwise to 310.15 K. Then, a 300 ns production run in the NPT ensemble with full MD unit cell fluctuations was executed for the two kinds of systems. Three independent runs using different initial configurations were performed for each kind of system (0.9 µs for each in total), and the results were averaged to give the calculated values for the physical properties of the membranes.

The trajectories in the following 250 ns (0.75 µs in total) were analyzed to obtain the structural and dynamical properties of these membrane systems. Figure 1 shows snapshots of the hepatocyte and hepatoma membranes in an equilibrium state from the present MD calculations. From the figure, we see that the width of the MD unit cell was a little smaller for hepatoma membranes than for hepatocyte membranes. In Secs. III A 2–III B 3, we examine in detail the differences in the structure, level of order, and membrane fluidity between the two kinds of membranes. 2. Geometric properties

The geometric properties of the MD unit cell and the lipid bilayer averaged over the last 250 ns are listed in the Table II. In the table, A is membrane area per lipid molecule, and hl and Vl are the height and volume of the lipid bilayer, respectively. hl was defined by the z—distance between the averaged positions of the phosphorus atom in two leaflets of the bilayer, and Vl was the product of S and hl . The table shows that hepatic canceration resulted in a small decrease in S of about 2%, which contrasts with the 20%

TABLE II. Calculated structural membrane properties averaged over the last 250 ns. The error represents the difference between the maximum and minimum values calculated in the three independent MD calculations. Hepatocyte membrane

Hepatoma membrane

S (103 Å2) A (Å2) h (Å) h l (Å) V (105 Å3) Vl (105 Å3) χ TS (m2 J−1) V (10−9 m3 J−1) χT

2.73 ± 0.01 42.7 ± 0.1 114 ± 1 41.6 ± 0.1 3.14 ± 0.01 1.14 ± 0.01 1.7 ± 0.3 0.55 ± 0.01

2.68 ± 0.01 41.9 ± 0.1 115 ± 1 40.6 ± 0.1 3.09 ± 0.01 1.09 ± 0.01 1.2 ± 0.1 0.54 ± 0.01

χ T l (10−9 m3 J−1)

2.3 ± 0.1

2.3 ± 0.2

III. RESULTS AND DISCUSSION A. Structural properties 1. Convergence

Time evolution of membrane area S (the base area of the MD unit cell), and the height of the MD unit cell h, and volume of the MD unit cell V starting from three independent initial configurations for hepatocyte and hepatoma membranes is shown in Figs. S1–S3 of the supplementary material.56 From the figures, we judged the first 50 ns was spent in equilibration.

V

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increase in S caused by thymic canceration as found in our earlier study.45 This change should result from the difference in the lipid composition between the two types of membranes. First, cholesterol increased from 43.7 mol. % for hepatocyte membranes to 50.0 mol. % for hepatoma membranes in our calculation. Second, this increase was accompanied by a decrease in the number of saturated tails in two leaflets in the MD unit cell from 68 for the hepatocyte membranes to 58 for the hepatoma membranes. By contrast, the total number of mono- and polyunsaturated tails did not differ much between the two membranes: 50 for hepatocyte membranes and 52 for hepatoma membranes. The increase in the proportion of cholesterol molecules with relatively small sectional area accompanied by a decrease in lipid molecules with saturated tails must induce a decrease in S. The increase in the level of order of the lipid tail conformation induced by the greater amount of cholesterol in hepatoma membranes than in hepatocyte membranes, as shown in Sec. III A 6, also contributed to the decrease in S. The table also shows that hl becomes slightly thinner for hepatoma membranes than for hepatocyte membranes. Qualitatively, this finding is inconsistent with the decrease in S discussed above because the decrease in S usually leads to an increase in hl if the density or volume of the lipid bilayer is unchanged. However, we note that in the present case, the length of the acyl tails of the lipids also differs between the two types of membranes. The average carbon number of phospholipid acyl chains for hepatoma membranes, 18.5, was smaller than that for hepatocyte membranes, 18.8. An increase in the mol. % of unsaturated tails in hepatoma membranes also contributes to the thinning of the membrane because unsaturated tails have a more disordered conformation and a shorter effective tail length than do saturated tails with the same carbon number. These changes should lead to a thinning of the hepatoma membranes. The smaller membrane area and higher conformational order observed reflect a tightly packed structure, which must be closely related to the fluidity of the membranes. 3. Compressibility

Fluctuation of the MD unit cell constant provides further information about the softness of the membrane. The isothermal area compressibility χTS under a hydrostatic pressure condition may be calculated by χTS =

1 ⟨(∆S)2⟩ N, P,T , kBT ⟨S⟩ N, P,T

(1)

where kB is the Boltzmann constant, ⟨S⟩ the average of S, and ⟨(∆S)2⟩ = ⟨(S − ⟨S⟩)2⟩ the fluctuation of S. In a similar way, the isothermal volume compressibility χVT and that for the V lipid bilayer itself χT l were calculated by the fluctuation in V and Vl . Table II also lists the calculated values of χTS , χVT , and Vl χT , by which the fluctuations were evaluated for each 250 ns trajectory. The small errors for these values clearly show a good correspondence between the three trajectories for each system. The χTS value was 29% smaller for hepatoma

membranes than for hepatocyte membranes, which indicates that the former is stiffer in the lateral direction than the latter. The lower χTS for hepatoma membranes could be attributed to a more ordered lateral arrangement of lipid molecules and their tails in the membranes compared with normal hepatocyte membranes, as discussed in Sec. III A 7. These calculated χTS values were similar to those calculated for ternary lipid bilayers containing DOPC:SM:CHOL = 1:1:1 at 305–308 K73 in one uniform liquid phase with less fluidity than that of the liquid crystalline phase.74 Interestingly, this change in χTS induced by hepatic canceration was opposite to that by induced thymic canceration, where χTS showed twofold increase for leukemic cell membranes compared with normal thymocyte membranes.45 Further, the calculated χTS for hepatocyte membranes, 1.7 m2 J−1, is similar to that for normal thymocyte membranes, 1.9 m2 J−1.45 This close correspondence suggests that the plasma membranes of normal cells may commonly have proper stiffness, which helps to maintain their normal functions. V By contrast, the differences in χVT and χT l between the two systems were not obvious. The much greater value V of χT l than the bulk volume compressibility of water (0.44 × 10−9 m3 J−1 at 310.15 K and 1 atm75) indicates that the bilayers were quite soft in the solution. 4. Electron density profile

We next performed a series of structural analyses of the lipid bilayer. First, we investigated the distribution of atoms along the normal to the bilayer (the z axis) and the resultant electron density profile. Figure 2(a) shows the electron density profile along the z axis, ρe(z), where the origin of z is taken to be the mass center of the lipid bilayer. The distribution was almost symmetric with respect to z = 0 Å for both systems. There were slight but clear differences in ρe(z) between two types of membranes. The height of the peaks found around |z| = 23 Å was lower for hepatoma membranes than for hepatocyte membranes. By contrast, the altitude of the humps ranged from |z| = 8 Å to 16 Å for hepatoma membranes, which was greater than that for hepatocyte membranes. The well at z = 0 Å was a little deeper for hepatoma membranes than for hepatocyte membranes. Origin of these differences in ρe(z) between the two types of membranes was explored by dividing ρe(z) into the contributions from each atom type. Fig. 2(a) shows the partial ρe(z) contributed by each atom type. From the panel, we can see the lower peaks around |z| = 23 Å in Fig. 2(a) for hepatoma membranes came from decreases in partial ρe(z) at the same position contributed by carbon, oxygen, and phosphate atoms (green, cyan, and black lines, respectively), which should stem from the lower amount of phospholipid molecules in hepatoma membranes than in hepatocyte membranes. It is interesting that the decrease in electron density was partially compensated by the electron density of the oxygen and hydrogen of water molecules (gray and orange lines, respectively), denoting that more water molecules penetrated into hepatoma membranes than into hepatocyte membranes at the same z.

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FIG. 2. Calculated electron density profile for hepatocyte (solid line) and hepatoma (dotted line) plasma membranes. Panel (a) represents the profiles averaged over all atom species. Panel (b) represents partial electron density profiles contributed from the atoms; carbon (green), hydrogen (blue), nitrogen (purple), oxygen (sky blue), and phosphorus (black) in the lipid molecules; hydrogen (orange) and oxygen (gray) in water; and sodium ion (red). In panel (c), the contributions from the phospholipid and the cholesterol molecules are presented separately as phospholipid carbon (dark green), cholesterol carbon (yellow-green), phospholipid oxygen (dark sky blue), and cholesterol oxygen (cyan).

Further, Fig. 2(b) shows clearly that the humps in the region |z| = 8 Å to 16 Å and the well at |z| = 0 in Fig. 2(a) originated from the carbon atom of the lipids (green lines). In Fig. 2(c), the profiles of carbon and oxygen were divided further into the contributions from phospholipid and cholesterol molecules. The figure shows clearly that the cholesterol carbon profile had humps in the region |z| = 8 Å to 16 Å (yellow-green lines), whereas the phospholipids carbon profiles were almost flat in the same region (dark-green lines). Panels (b) and (c) of Fig. 2 show clearly that altitude of the humps of total ρe(z) in Fig. 2(a) was predominantly determined by the sum of the cholesterol and phospholipid carbon electron densities. Thus, the larger hump altitude in hepatoma membranes than in hepatocyte membranes can be attributed to the greater cholesterol carbon electron density in the region |z| = 8 Å to 16 Å. Enlargement of the well depth at |z| = 0 in hepatoma membranes can be explained by the opposite pattern. 5. Tilt

Second, the degree of order of molecular tilt was investigated. As described in the Introduction, the order parameter of fluorescence probe DPH SDPH was higher in

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hepatoma plasma membranes than in normal hepatocyte plasma membranes:29 SDPH = 0.77 and 0.74 for rat hepatoma 484A and normal hepatocytes, respectively. In the experiment, rod-like DPH molecules are assumed to lie parallel to acyl tails of phospholipid molecules in membranes. Thus, a larger SDPH indicates that the probe DPH molecules had, on average, a smaller tilt angle in hepatoma membranes than in hepatocyte membranes. Although the present calculation systems did not contain the DPH molecule, we discuss the level of order of molecular tilt by examining the tilt angle distribution of cholesterol molecules, as done in our previous study.45 The steroid ring skeleton of cholesterol and the DPH molecule are of similar size and rigidity. We defined the tilt angle θ tilt as the angle between the z axis and the vector connecting steroid carbons 3 and 17 (see the inset in Fig. 3). Further, order of the tails of each phospholipids are also discussed. Fig. 3 shows the calculated probability distributions P(θ tilt) for hepatocyte and hepatoma membranes. Both functions have a maximum at θ tilt ≃ 10◦. That is, cholesterol molecules were, on average, aligned parallel to the z axis with their hydroxyl groups oriented toward the water phase. The difference in P(θ tilt) between the two types of membranes was very small but obvious as is shown in the top panel of the figure: P(θ tilt) for hepatoma membranes became larger than that for hepatocyte membranes in the range of θ tilt ≤ 15◦, whereas it became smaller in the range of θ tilt > 15◦. An average of θ tilt was 13.70◦ ± 0.01◦ for hepatocyte membranes and 13.17◦ ± 0.01◦ for hepatoma membranes, respectively.

FIG. 3. Calculated tilt angle distribution of cholesterol, P(θ tilt). The tilt was defined by the angle between the normal to the bilayer and the vector connecting steroid carbons 3 and 17. Open circles, hepatocyte plasma membrane; closed circles, hepatoma plasma membrane. Top subpanel represents difference in the probability distribution between the two types of membranes based on normal hepatocyte membranes, ∆Phep−nor. Error bars represent the standard errors (68% confidence intervals) estimated from six independent leaflets.

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This result indicates clearly that the cholesterol molecule is tilted less in hepatoma membranes than in hepatocyte membranes. We next calculated the order parameter of molecular tilt of cholesterol by   1 2 (2) Schol = (3cos θ tilt − 1) . 2 The value was 0.893 ± 0.005 and 0.901 ± 0.003 for hepatocyte and hepatoma membranes, respectively (see also Table V 2 where C∞ = Schol are listed). Here, errors in Schol were defined by the standard error of an average over six independent leaflets. A slight increase in the Schol value for the hepatoma membranes is caused by higher peak of P(θ tilt) for hepatoma membranes. It is interesting that the higher level of tilt order of cholesterol molecules in hepatoma membranes than in hepatocyte membranes is opposite to the trend of change induced by thymic canceration. Schol was 0.88 and 0.79 for normal and leukemic cell membranes, respectively,45 which indicates that the cholesterol molecule tilt order was markedly lower in leukemic cell membranes. Order of the tails of each phospholipid was evaluated by the order parameter of the vector connecting the carbon atom at the root of a phospholipid tail to that at the end of the tail, Stail. Stail was calculated by the same equation with Eq. (2), whereas θ tilt was defined as the angle between the z axis and the root-to-end vector. As shown in Fig. S8 in the supplementary material,56 Stail increased in the all categories of the tail (saturated, mono-unsaturated, and poly-unsaturated tails). Stail for mono-unsaturated tails showed most remarkable increase in the hepatoma membranes: from 0.797 ± 0.006 in the hepatocyte membranes to 0.827 ± 0.004 in the hepatoma membranes. These results together with Schol qualitatively corresponded to the experimental observation for SDPH noted above. Further analysis of molecular tilt in relation to the wobbling dynamics of the cholesterol is given in Sec. III B 3 where the square of the order parameter of molecular tilt is used to estimate an asymptotic value of the time autocorrelation function which describes orientational relaxation by wobble motion. 6. Conformational order of the tail

Third, the order parameter of the C–H vector located in acyl tails, SCH, was calculated to investigate the conformational order of the lipid tails. As in our previous study,45 we obtained an order parameter profile as a function of z, SCH(z), without distinguishing between different phospholipids,   1 2 SCH(z) = (3cos θ(z) − 1) , (3) 2 where ⟨· · · ⟩ denotes the ensemble average over each slab sliced along the x- y plane. Here, θ(z) is the angle between the normal to the bilayer and the C–H vector located at z. The calculated order parameter profile SCH(z) is presented in Fig. 4(a). Here, note that ensemble averages of SCH(z) were taken over six independent leaflets. In Figs. S4–S7 of the

FIG. 4. Calculated C–H order parameter profiles for hepatocyte (solid line) and hepatoma (dotted line) plasma membranes. Panel (a) represents the profiles averaged over the whole phospholipid tails without distinction between the number of double bounds. Panel (b) represents the profiles for saturated and unsaturated phospholipid tails with n double bonds; red, n = 0; green, n = 1; blue, n = 2; purple, n = 3; orange, n = 4; and black, n = 6. Note that tails with n = 5 was not included in the present systems. Panel (c) shows the profiles for cholesterol; dark green: methyl group at carbons 18 and 19. Brown: methyl, methylene, and methine groups at the hydrocarbon tail of n (z) were calculated for phospholipids cholesterol. Note that SCH(z) and SCH which belonged to one leaflet. Time averages were taken over per leaflet, then ensemble averages were taken over six independent leaflets. Negative z values indicate the opposite side of the leaflet into which phospholipid tail ends protrude. Error bars represent the standard errors estimated from six independent leaflets.

supplementary material,56 SCH is also presented as a function of carbon number of acyl tails for each phospholipid species. Fig. 4(a) shows that the difference in SCH(z) between the two types of membranes was small. One noticeable difference between the two is that SCH(z) was smaller in the region 16 Å ≤ z ≤ 26 Å for hepatoma membranes than for hepatocyte membranes. From Fig. 2(b), we can see that this region corresponds to the interface between the hydrophobic region of membranes and the water phase. That is, the level of conformational order of the lipid tails in hepatoma membranes decreased at the interface. By contrast, the level of the conformational order within hydrophobic region was not largely altered by hepatic canceration. To investigate the behavior of the order parameter in greater detail, the profile was calculated independently for

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n each degree of unsaturation n of the acyl chain, SCH (z). The result is presented in Fig. 4(b) from n = 0–6 without 5 for the phospholipids. First, Fig. 4(b) shows that the functions 0 for the saturated tails, SCH (z), (red lines) had a peak at the center of a leaflet, whereas the functions for the tails having double bond(s) (the other lines) showed mainly a peak that had shifted to the upper part of the leaflet. Thus, it can be said that the peaks of the total SCH(z) in Fig. 4(a) stem mainly 0 from the peak of SCH (z). 0 2 Further, it is apparent that SCH (z) and SCH (z) were larger at the middle of the leaflet for hepatoma membranes than 1 for hepatocyte membranes. The peak height of SCH (z) at 1 the middle of the leaflet did not change, whereas SCH (z) decreased at the hydrophobic region/water interface for 3 4 6 hepatoma membranes. SCH (z), SCH (z), and SCH (z) did not show clear differences between two types of membranes. The 0 2 increases in SCH (z) and SCH (z) in hepatoma membranes would be caused by a higher cholesterol content in the membranes. From panel (b), the reduction in total SCH(z) in Fig. 4(a) at the hydrophobic region/water interface could be attributed to the 1 large reduction in SCH (z) in this region. As for the conformation of polyunsaturated tails, 3 4 6 SCH (z), SCH (z), and SCH (z) were not different in hepatoma membranes compared with hepatocyte membranes. This may be because the effect of cholesterol, which increases the order of surrounding polyunsaturated tails, had already reached saturation even in hepatocyte membranes. By contrast, in our previous study,45 a change in cholesterol content from 23.4 mol. % (leukemic cell plasma membranes) to 42.2 mol. % 3 (thymocyte plasma membranes) caused increase in SCH (z), 4 6 0 1 2 SCH(z), and SCH(z) as well as in SCH(z), SCH(z), and SCH(z). As is presented in Fig. 4(c), the order parameter profile for the C–H vector in the tail of cholesterol had a peak at 2 3 z = 5 Å. It is interesting that SCH (z) and SCH (z) in Fig. 4(b) also had an additional peak at the same position (z = 5 Å) in both types of membranes. This close correlation between the two peak positions, which was also observed in our previous study,45 suggests that both the cholesterol steroid ring and the cholesterol tail chain could increase the order of the surrounding polyunsaturated phospholipid tail chains when lipid molecules are packed densely in the lateral direction.

7. Lateral structure

Fourth, the lateral structure of a lipid bilayer may be evaluated by the two-dimensional lateral radial distribution function on the x- y plane. In the following, two kinds of lateral radial distribution functions were calculated. The first total was for the center of mass of each lipid molecule, g2D (r), where the species of lipids were not distinguished. The second was a radial distribution function measuring the center of mass of the phospholipid acyl tail from that of the cholesterol steroid ring. In the latter, for simplicity, we classified the acyl tail into three categories according to their degree of unsaturation: saturated tails, tails with one double bond, and tails with more than one double bond. Consequently, we calculated three p 0 1 partial radial distribution functions, g2D (r), g2D (r), and g2D(r), for the cholesterol steroid ring–saturated tail, cholesterol steroid ring–monounsaturated tail, and cholesterol steroid

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FIG. 5. Calculated lateral radial distribution function of the center of mass of the whole lipid molecule. Solid lines: hepatocyte plasma membrane and dotted lines: hepatoma plasma membrane. Error bars represent the standard errors estimated from six independent leaflets.

total ring–polyunsaturated tail pairs. g2D (r) represents the total 0 level of structural order of the membranes, whereas g2D (r), p 1 g2D(r), and g2D(r) indicate the specific correlation between the cholesterol steroid ring and the surrounding saturated and unsaturated lipid tails. total Fig. 5 shows the averaged g2D (r) values over three independent MD runs for hepatocyte membranes and hepatoma membranes. Similar to the other structural properties discussed in the previous sections, there was small but evident difference between the two types of membranes. For both types of membranes, the function showed oscillatory behavior in which at least four peaks and wells were observed. This indicates that there is a long-range structural correlation between the center of mass of lipid molecules. The amplitudes of the all peaks and wells were larger in hepatoma membranes than in hepatocyte membranes, which indicates that hepatoma membranes have a more highly ordered lateral structure compared with hepatocyte membranes. 0 1 By contrast, Fig. 6 shows the calculated g2D (r), g2D (r), p total and g2D(r). As with g2D (r), the partial distribution functions exhibited oscillatory behavior in both types of membranes. This denotes that there is also a long-range structural correlation between the cholesterol steroid ring and lipid tails. The larger amplitude of these partial functions compared with the total function shows that the lateral packing unit of the membranes is not a pair of acyl tails but an individual acyl tail. For the all partial distribution functions, the first, second, and third peaks were located at r = 5.5–6.0 Å, 10.0–11.0 Å, and 15.0–16.0 Å, respectively. These peaks should be one of total the origins of the first, second, and third peaks of g2D (r) in 0 Fig. 5. The heights of the first peaks were greater in g2D (r) p and g2D(r) for hepatoma membranes than for hepatocyte total membranes. The higher first peak of g2D (r) in hepatoma 0 membranes could be explained by higher peaks in g2D (r) and

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its time scale (greater than a microsecond3) is beyond the present simulation time of 300 ns. In Secs. III B 1–III B 3, the translational and rotational dynamics of the lipid molecules are analyzed in detail for the two types of membranes. As for rotational dynamics, rotation around the molecular long axis of the lipid molecules and the wobbling of the molecular long axis itself were both investigated. 1. Lateral diffusion

The lateral self-diffusion coefficient, DL, may be calculated by ⃗ x y (t)|2⟩ ⟨|∆ R , t→ 0 4t

DL = lim

FIG. 6. Lateral radial distribution function calculated between the center of mass of the cholesterol steroid ring and that of the phospholipid acyl tail. 0 (r ), Panels (a), (b), and (c) represent the functions for the saturated tails g 2D p 1 mono-unsaturated tails g 2D(r ), and polyunsaturated tails g 2D(r ), respectively. Solid line, hepatocyte plasma membrane; dotted line, hepatoma plasma membrane. Error bars represent the standard errors estimated from six independent leaflets.

p

g2D(r). The heights of the second peaks were also greater in p 0 g2D (r) and g2D(r) for hepatoma membranes than for hepatocyte membranes. On the other hand, the first and second peaks in 1 g2D (r) were smaller in hepatoma membranes than in hepatocyte membranes, indicating that the lateral packing of monounsaturated tails around the cholesterol was more perturbed in the former than in the latter. Perturbed lateral packing of monounsaturated tails may cause a decrease in 1 SCH (z) for hepatoma membranes, as shown in Fig. 4(b). B. Membrane fluidity

Fluidity is one of the most important physical properties of membranes.1–5 Membrane fluidity is usually discussed from two different perspectives:4 the translational degree of freedom and the other degree of freedom of the lipid molecules themselves. The former may be represented by the self-diffusion coefficient, and the latter by the rotational correlation time of the lipids. For the latter, we excluded flip-flop motion of the lipids in the present analysis because

(4)

⃗ x y (t)|2⟩ is the lateral mean square displacement where ⟨|∆ R (MSD). This coefficient functions as a measure of the translational fluidity. Typical examples of the lateral trajectory of the center of mass of the lipid molecules are shown in Fig. S9 of the supplementary material56 where lateral self-diffusion of the molecules over 250 ns was observed. The calculated ⃗ x y (t)|2⟩ were also shown in Fig. S10.56 According to the ⟨|∆ R previous papers,76,77 contribution from the collective slipping ⃗ x y (t)|2⟩ motion of each leaflet was eliminated from ⟨|∆ R to evaluate pure self-diffusive lateral displacement of lipid molecules due to thermal motion. An effect of periodic ⃗ x y (t)|2⟩ has been boundary condition and system size to ⟨|∆ R 77,78 under discussion. Every function plotted in the figure panels was almost linear from t = 10 ns to 50 ns. Thus, we used the weighted least-squares fitting method to estimate the DL from the slopes of these lines. Table III lists the values of the calculated DL. We see that the total self-diffusion coefficient was 18% smaller in hepatoma membranes than in hepatocyte membranes. DL was 19% and 20% smaller for phospholipid and cholesterol molecules, respectively, in hepatoma membranes than in hepatocyte membranes. DL for lysophospholipids showed smallest (10%) reduction in hepatoma membranes. These results show clearly that hepatoma model membranes are less fluid than hepatocyte model membranes with respect to the translational degree of freedom. Experimental measurements of DL by pulsed-field gradient (PFG)-NMR,79–85 fluorescence correlation

TABLE III. Calculated lateral self-diffusion coefficient of the lipids. The coefficient was evaluated from the slope of the linear line fitted to the averaged ⃗ x y (t)|2 over three independent trajectories. mean-squared displacements |∆ R The error is the weighted least-squares fitting error. D L (10−12 m2 s−1)

Total Phospholipids Lysophospholipids Cholesterol

Hepatocyte membrane

Hepatoma membrane

2.8 ± 0.1 2.6 ± 0.1 3.0 ± 0.1 3.0 ± 0.1

2.3 ± 0.1 2.1 ± 0.1 2.7 ± 0.1 2.4 ± 0.1

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spectroscopy (FCS),86–88 and fluorescence recovery after photobleaching89 commonly indicate that DL is of the order of 10−14–10−13 m2 s−1 for pure bilayers in the gel phase, of the order of 10−12 m2 s−1 for mixed bilayers with medium cholesterol content in the fluid phase (or liquid-ordered phase), and of 10−11 m2 s−1 for pure bilayers in the liquid crystalline phase and for mixed bilayers with very low cholesterol content in the liquid-disordered phase at physiological temperature (∼310 K). Our calculated DL for hepatocyte and hepatoma membranes correspond to the second case. Thus, we judged that both types of membranes were in the liquid-ordered phase with intermediate fluidity. The lower value for DL for hepatoma membranes with higher cholesterol content compared with hepatocyte membranes may be explained by the cholesterol effect, which decreases membrane fluidity in the fluid phase.1,3,4 As was observed in our previous study,45 the DL values for cholesterol were larger than those for the phospholipids shown in Table III. This was also observed experimentally by PFG-NMR for DPPCd62/cholesterol binary systems in the fluid phase at 308 K, which was attributed to the smaller mass of the cholesterol molecule than for phospholipid molecules.82

FIG. 7. Rotational autocorrelation function of cholesterol based on the vector connecting cholesterol carbons 8 and 11. Open circles, hepatocyte plasma membranes; closed circles, hepatoma plasma membranes. Error bars represent the standard errors estimated from six independent leaflets. TABLE IV. Calculated rotational relaxation time, τ rot, of cholesterol. The errors are propagated errors of least-squares fitting errors.

2. Rotation

Next, membrane fluidity with respect to the rotational degree of freedom was evaluated by orientational relaxation through rotation of a whole lipid molecule around its long axis. The cholesterol molecule was chosen as the probe molecule to measure the rotational relaxation because it is incorporated in a hydrophobic region of the lipid bilayer, as is DPH when used for fluorescence depolarization measurements of the SDPH for rat hepatocyte and hepatoma plasma membranes.29 Rotational relaxation around the long axis may be evaluated by the time autocorrelation function of a vector perpendicular to the long axis, Crot(t) = ⟨cos φ(t)⟩ ,

(5)

where φ(t) is the angle swept by the vectors from t = 0 to t = t. Here, we chose the two-dimensional vector projected on the x- y plane, which connects two carbon atoms in the cholesterol molecule, i.e., carbons 8 and 11 (see Fig. 7), because they are a part of the rigid ring skeleton of the molecule. It is evident that ⟨cos φ(t)⟩ = 0 when the vectors are uniformly distributed at t → ∞ limit in two-dimensional polar coordinates. Fig. 7 presents the calculated Crot(t) where the average was taken over six independent leaflets. We obtained very similar functions to those in the figure with another choice of vector between carbon atoms in the steroid ring. This indicates that the steroid ring behaves as a rigid ellipsoid in the bilayer and supports the validity of the present choice of cholesterol as the probe molecule instead of DPH. The calculated Crot(t) for both hepatocyte and hepatoma membranes showed the almost exponential decay at large t. Crot(t) decayed more slowly for hepatoma membranes than for hepatocyte membranes. However, the difference between the two was not so large when compared with the difference between thymocyte and leukemic cell membranes.45

τ rot (ns)

Hepatocyte membrane

Hepatoma membrane

3.5 ± 0.1

3.7 ± 0.1

Further, the correlation time of Crot(t) defined by ∞ τrot = 0 Crot(t)dt was estimated in the same way in our previous paper45 in order to compare quantitatively the decay rate between the two types of membranes. Detail of τrot estimation is summarized in Table S2 in the supplementary material.56 Table IV lists the estimated correlation times. τrot was 6% larger for hepatoma membranes than for hepatocyte membranes. This indicates quantitatively that the rotation of the cholesterol molecules was slightly suppressed by hepatic canceration. This contrasts with the variation induced by thymic canceration, where the rotation of the cholesterol molecules was accelerated.45 The enlargement of τrot indicates that hepatoma model membranes have less membrane fluidity compared with hepatocyte model membranes in terms of the rotational degree of freedom of a cholesterol molecule about its long axis. 3. Wobble

To obtain another measure of membrane fluidity, we analyzed the orientational relaxation by wobbling motion. Wobbling relaxation may be evaluated by the time autocorrelation function of the molecular long axis,  1

3cos2θ(t) − 1 , (6) 2 where θ(t) is the angle swept by molecular long axes from t = 0 to t = t. The molecular long axis was defined as the Cwob(t) =

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J. Chem. Phys. 144, 085104 (2016) TABLE V. Asymptotic values C ∞ of C wob(t) at long t, which correspond to 2 , and the calculated correlation time of wobble, τ Stilt wob. The errors for C ∞ represent the standard errors estimated from six independent leaflets. Those for τ wob represent the propagated errors. τ wob (ns)

C∞

Total Phospholipids Lysophospholipids Cholesterol

FIG. 8. Wobbling autocorrelation function for the hepatocyte plasma membrane (panel (a)) and the hepatoma plasma membrane (panel (b)). Solid line, total lipids; broken line, phospholipids; dot–dashed line, lysophospholipids; dotted line, cholesterol. The asymptotic value of the autocorrelation function C ∞ is listed in Table V. Error bars represent the standard errors estimated from six independent leaflets.

eigenvector of the inertia tensor with the smallest eigenvalue, where the molecule was considered to be a rigid body at each frame. Figures 8(a) and 8(b) show the calculated Cwob(t) for the hepatocyte and hepatoma membranes, respectively, where the average was taken over six independent leaflets. Unlike Crot(t), every Cwob(t) did not converge to zero, which reflects the restricted motion of the lipid molecule’s long axis within each monolayer over 300 ns. To quantify the orientational relaxation by wobble motion, we used a framework of the theory of the time-dependent measurement of fluorescence anisotropy r(t).25–27 That is, the wobbling diffusion constants of each lipid species were estimated from the effective relaxation time of wobble motion and order parameter of molecular tilt. In the wobbling in a cone model25,26 adopted in the theory, each fluorescence probe molecule in the membrane is assumed to wobble in a restricted space of an inverted cone shape. This assumption is plausible because the measurement period of r(t), typically a few 10 ns,29 is much smaller than the time scale of the flip-flop motion of the surrounding lipids. In such a case, r(t)/r(0) converges to the nonzero value r ∞/r(0),25–27 where r(0) is a normalization factor. In MD calculations of a few 100 ns duration, the lipid molecules also did not show flip-flop motion. Therefore, as for r(t)/r(0), Cwob(t) should be of the following form: ′ Cwob(t) = (1 − C∞)Cwob (t) + C∞.

(7)

Here, C∞ corresponds to the squared order parameter of  2 2 the molecular long axis,25–27 Stilt = 12 ⟨3cos2θ tilt − 1⟩ , where

Hepatocyte membrane

Hepatoma membrane

0.796 ± 0.002 0.801 ± 0.003 0.746 ± 0.005 0.798 ± 0.004

0.808 ± 0.001 0.814 ± 0.002 0.750 ± 0.004 0.810 ± 0.002

Hepatocyte Hepatoma membrane membrane 5.0 ± 0.1 8.1 ± 0.1 5.8 ± 0.1 2.2 ± 0.1

4.6 ± 0.1 8.2 ± 0.1 6.1 ± 0.1 2.0 ± 0.1

θ tilt is the tilt angle between the molecular long axis and ′ the z axis. The effective relaxation time of Cwob (t) may be ∞ ′ evaluated by integrating the function τwob = 0 Cwob(t)dt. By ′ this procedure, τwob can be evaluated even when Cwob (t) cannot be described by a single exponential function. Detail of τwob estimation is summarized in Table S3 in the supplementary material.56 Table V lists the calculated C∞ and τwob values. The calculated C∞ values averaged for all lipid molecules were slightly larger for hepatoma membranes than for hepatocyte membranes: 0.808 ± 0.001 versus 0.796 ± 0.002. An increase in C∞ was most remarkable for phospholipid molecules. This trend agrees qualitatively with the SDPH measured for rat hepatocyte and hepatoma membranes,29 where its value increased from 0.74 for hepatocytes to 0.77 for hepatomas, although the probe molecules were different from those used in our study. The higher C∞ value for hepatoma membranes represents a more ordered alignment of the molecular long axis of the lipids. This is the static aspect of the fluidity of the membranes. All of the C∞ values for normal hepatocyte membranes (0.796, 0.801, 0.746, and 0.798 for total, phospholipids, lysophospholipids, and cholesterol, respectively) correspond to those for normal thymocyte membranes45 (0.79, 0.80, 0.73, and 0.78, respectively). This close correspondence of C∞ between two kinds of normal cell membranes implies that they have a similar level of order in the alignment of the lipid molecules long axis. Thus, a proper level of order in the lipid molecules alignment seems to be essential to retaining the normal functions of cell membranes. Table V shows that the calculated τwob averaged over phospholipid molecules and lysophospholipids molecules was larger in hepatoma membranes than in hepatocyte membranes. The increase in τwob for phospholipids and lysophospholipids, which are the main component of these membranes, implies that the membrane fluidity with respect to the wobbling motion is suppressed in hepatoma membranes. In contrast, τwob for cholesterol was a little smaller in hepatoma membranes than in hepatocyte membranes. Consequently, τwob for total lipids was smaller in hepatoma membranes. However, it should be noted that all C∞ values in the table differed between the two types of membranes. The larger C∞ in hepatoma membranes indicates that the lipid molecules wobble in an inverted cone with a narrower opening angle, θ 0, compared with hepatocyte membranes. To take this difference

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TABLE VI. Wobbling diffusion constant, Dwob, within the framework of the diffusion in a cone model.27,28 Values in parentheses are the opening angle of the cone, θ 0, with a unit of degree estimated from C ∞. D wob and θ 0 for normal thymocyte membranes and leukemic membranes45 obtained in the same way are also listed. The errors in the table represent propagated errors. Dwob (×10−3 ns−1)

Total Phospholipids Lysophospholipids Cholesterol

Total Phospholipids Lysophospholipids Cholesterol

Hepatocyte membrane

Hepatoma membrane

8.2 ± 0.9 (22.1) 5.0 ± 0.6 (21.8) 9.0 ± 0.8 (25.0) 18.4 ± 2.2 (22.0)

8.5 ± 1.0 (21.4) 4.6 ± 0.6 (21.0) 8.4 ± 0.8 (24.8) 19.0 ± 2.3 (21.3)

Thymocyte membrane45

Leukemic membrane45

9.4 ± 1.1 (22.7) 6.1 ± 0.7 (22.1) 8.2 ± 0.7 (25.9) 25.8 ± 5.1 (23.2)

17.3 ± 1.1 (31.9) 15.0 ± 0.9 (32.2) 17.0 ± 1.2 (30.6) 37.2 ± 2.9 (31.3)

in the range of wobble into account, Lipari and Szabo derived an equation that relates τwob, C∞, and the wobbling diffusion constant, Dw, within the framework of the Smoluchowski description of the dynamics.27,28 The calculated Dw values based on Eq. (24) in Ref. 27 are listed in Table VI together with θ 0 evaluated from the relation C∞ = [ 21 cos θ 0(1 + cos θ 0)]2.25 In the table, the calculated Dw for phospholipids and lysophospholipids was smaller in hepatoma membranes than in hepatocyte membranes, whereas the value for cholesterol was larger in the former than in the latter. Dw for total phospholipids was a little larger in the hepatoma membranes. Considering the framework of wobbling in a cone model, we conclude that the wobbling fluidity of phospholipids and lysophospholipids is less in hepatoma membranes than in hepatocyte membranes, whereas that of cholesterol is slightly greater in the former than in the latter. Consequently, the total wobbling fluidity does not appear to be largely changed by hepatic canceration. Interestingly, Table VI also shows that, as in thymocyte membranes, all Dw values were increased markedly by thymic canceration. This indicates that the wobbling fluidity of lipid molecules is accelerated entirely by thymic canceration. Thus, we concluded that the trend in the change in the wobbling fluidity induced by canceration depends strongly on the kind of cancer, as well as the static and dynamic properties of membranes, as discussed in Secs. III A 1–III B 2.

The calculations showed first that hepatic canceration leads to a smaller membrane area and lower isothermal area compressibility in hepatoma membranes than in hepatocyte membranes. That is, the membranes were more shrunken and stiff in the lateral direction in the hepatoma membranes than in hepatocyte membranes. Second, the two-dimensional lateral radial distribution function of the center of mass of the lipid molecules showed that the hepatoma membranes were laterally more structured than the hepatocyte membranes. The calculated order parameter profile of the C–H vectors in the acyl chains of the lipid molecules indicated that the level of conformational order with hydrophobic region of membranes was not altered by hepatic canceration, whereas that at the hydrophobic region/water interface was lowered. The detailed analysis showed that the conformational order of the saturated and diunsaturated acyl chains of phospholipid molecules was higher. This may be caused by the greater amount of cholesterol in hepatoma membranes than in hepatocyte membranes. Third, the fluidity of the membranes was also investigated from two perspectives: the translational and rotational degrees of freedom. The calculated lateral selfdiffusion coefficients of the lipids were 10%–20% smaller in hepatoma membranes than in hepatocyte membranes. The rotational relaxation of the cholesterol molecule around its long axis was slightly suppressed in hepatoma membranes compared with hepatocyte membranes. The wobbling diffusion of phospholipid and lysophospholipid molecules, which are main component of lipid bilayers, was slowed in hepatoma membranes, whereas that of cholesterol was accelerated in the membranes. The wobbling diffusion of total lipids does not appear to be changed largely by hepatic canceration. The present calculations have demonstrated the molecular detail of the reduction in the membrane fluidity induced by hepatic canceration. These changes contrast with the changes in the physicochemical properties of membranes induced by thymic canceration. Thymic canceration resulted in laterally more bulky and softer membranes, disordering of the membrane structure, and a large increase in the membrane fluidity.45 That is, when taken together, our MD calculation studies have demonstrated that the trend in the changes in the physicochemical properties induced by canceration differs considerably between kinds of cancers, or at least between hepatomas and thymic leukemias. ACKNOWLEDGMENTS

IV. SUMMARY

A series of MD calculations have been performed for the lipid bilayers to model mouse hepatocyte and hepatoma plasma membranes according to the experimentally derived chemical composition of membrane lipids. The observed difference in the level of ordering of the acyl tail alignment of the phospholipid molecules and the long-axis alignment of the lipid molecules between hepatocyte and hepatoma membranes showed good qualitative correspondence to the experimental observations obtained for rat hepatocyte and hepatoma plasma membranes.

This work was supported by the Theoretical and Computational Chemistry Initiative (TCCI)/Computational Materials Science Initiative (CMSI) in the Strategic Programs for Innovative Research, Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Calculations were performed mainly at the Institute for Solid State Physics, the University of Tokyo, and partly at the Research Center for Computational Science, Okazaki, Japan and the Supercomputer Center. Calculations were partly performed using the K-computer at RIKEN Advanced Institute for Computational Science (Proposal No. hp150222).

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1D. Voet and J. G. Voet, Biochemistry, 4th ed. (Wiley-Interscience, New York,

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