Curvature-Induced Lateral Organization in Mixed Lipid Bilayers

May 18, 2009 - curvature regions while the ld domains stay in the highly curved regions .... to find the equilibrium free energy of the system. In the...
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J. Phys. Chem. B 2009, 113, 8049–8055

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Curvature-Induced Lateral Organization in Mixed Lipid Bilayers Supported on a Corrugated Substrate Qing Liang and Yu-qiang Ma* National Laboratory of Solid State Microstructures, Nanjing UniVersity, Nanjing 210093, People’s Republic of China ReceiVed: January 20, 2009; ReVised Manuscript ReceiVed: April 25, 2009

The organization of lipids in biological membranes is essential for cellular functions such as signal transduction and membrane trafficking. A major challenge is how to control lateral lipid composition in supported membranes, which is crucial for the design of biosensors and investigation of cellular processes involved with biomembranes. Here, we undertake the first theoretical study of the full phase behavior of lateral organization of lipids in mixed bilayers induced by a periodically corrugated substrate. A rich variety of compositional segregation of lipids is regulated by varying the roughness of substrates. Interestingly, several structures of our work are similar to the results of the recent experiments with ternary lipid bilayers supported on corrugated substrates, and two novel structures which have not been experimentally observed are also predicted. The morphology diagram, which provides a useful guidance for the future experiments to find unexpected structures, is given. Further, we analyze the microscopic mechanism of the structural formation and demonstrate that our conclusions also remain valid for the case of the substrate with arbitrarily distributed grooves. Introduction Lateral organization of lipids in biological membranes directly determines cellular functions and attracts extensive interest. The supported membrane, as an ideal biomembrane model, maintains many structural and dynamic properties of natural membranes and is widely used to reveal the lateral organization of biomembranes and design biosensors.1-6 The substrate surface can directly influence the morphology of supported membranes, and thus, one can modulate the organization of lipids by changing topological or chemical properties of the substrates to investigate some cellular processes. For example, Lee and coauthors studied lateral organization of a two-component membrane supported on a substrate with a groove and found that the two kinds of lipids with different spontaneous curvatures segregate spontaneously, where the lipid with larger spontaneous curvature (which has a bigger head group) prefers to stay in the curved regions.7,8 In addition, Yoon et al. examined the lateral organization of a ternary lipid bilayer, which is a widely investigated model for biomembranes on a rough substrate.9 In their system, the saturated lipids (sphingomyelin) and the cholesterol form more rigid liquid-ordered (lo) domains, while the unsaturated lipids (1,2-dioleoyl-sn-glycero-3-phophocholine) form less rigid liquid-disordered (ld) domains. Because of larger rigidity of the lo domains, the curved regions of the bilayer provide energy barriers for them. Thus, the macroscopic lo domains, which are aggregated by the small lo domains, emerge in the nanosmooth regions of the substrate, whereas there are only small lo domains in the nanocorrugated regions. Recently, Parthasarathy et al. also proposed a curvature-mediated modulation of phase-separated structures in membranes supported on a periodically corrugated substrate by different rigidities between the cholesterol* To whom correspondence should be addressed. E-mail: myqiang@ nju.edu.cn.

Figure 1. A schematic illustration of lateral organization in a mixed lipid bilayer supported on a periodically corrugated substrate. Each periodicity is composed of a flat step and an arc-like groove. The lipid species A and B have different effective (cylindrical and cone-shaped) shapes due to different head-tail volume ratios. The groove depth is H, and the substrate periodicity is L.

rich lo and the cholesterol-poor ld domains and found that, when the curvature of the grooves exceeds a critical value, a modulated structure with the lo domains staying in the lowcurvature regions while the ld domains stay in the highly curved regions appears.10 To the best of our knowledge, such curvature-induced lateral organization of supported membranes has rarely been considered in theoretical and computational investigations. Additionally, with current experimental technologies, it is still difficult to directly probe the laterally heterogeneous structures of membranes from tens to hundreds of nanometers in size by experiments, and consequently, still little is known about the membrane organization in very narrow widths of the substrate roughness.11,12 In this case, theoretical study no doubt becomes an efficient and crucial route to systematically explore the structural organization of supported membranes. Here, we examine the lateral organization in a mixed bilayer consisting of cylindrical and cone-shaped lipids supported on a periodically corrugated substrate (see Figure 1) by using self-consistent field theory (SCFT). By varying

10.1021/jp9005789 CCC: $40.75  2009 American Chemical Society Published on Web 05/18/2009

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the substrate roughness, the model not only allows us to obtain a variety of structures which are similar to the structures observed in a series of recent experiments with the ternary lipid bilayers9,10 but also allows us to predict two new lipid bilayer structures that, so far, remain unexplored in experiments. The results may provide a new route to modulate the lateral organization of the supported lipid bilayers and may help experimentalists better probe the lipid distribution on a wide range of length scales of nanometers.11 Model and Method Section We present a lipid bilayer composed of a volume fraction φ1 of lipid species A and a volume fraction φ2 of lipid species B dispersed in a volume fraction (1 - φ1 - φ2) of hydrophilic homopolymer solvents,13 supported on a periodically corrugated substrate (see Figure 1). The head group volumes of lipid species A and B are Vh1 and Vh2 (Vh1 < Vh2), respectively, and their tails are equal-length, consisting of Nt segments of segment volume F0-1.14 The solvent chain consists of Ns segments with the same segment volume F0-1. We choose Nt ) Ns ) N without loss of generality. The system is translational invariant in the y-direction,10 and the surface of the corrugated substrate is characterized by choosing a periodical function

S(x) )

{(

x 1 en+ L 2 1 x if n + < e n + 1 2 L

if n
0, which implies that the substrate is attractive to the head groups of the lipids and repulsive to the tails of the lipids.26,28 If the substrate shows different attraction to the two kinds of lipids, the distribution of the lipids could be influenced directly by the substrate. For example, when the difference of the adsorption strength between the two kinds of lipids and the substrate is large enough, the lipids which are more attractive with the substrate would be adsorbed on the substrate, while the lipids with weaker attraction prefer to distribute in the upper leaflet of the supported bilayer.29 Here, for the sake of simplification, we assume that the substrate shows the same adsorption property to the two kinds of lipids, and thus, the effect of the substrate adsorption on the lateral organization of the mixed bilayer is negligible. By minimizing the free energy (eq 2) with respect to the density functions, the fields, and ξ(r), we obtain the following self-consistent equations

wh1(r) ) χNγ1(φt1(r) + φt2(r)) + χ12Nγ1φh2(r) γ1K(r)N + γ1ξ(r) (3)

Mixed Lipid Bilayers Supported on a Corrugated Substrate

wt1(r) ) χN(φh1(r) + φh2(r) + φs(r)) + χ12Nφt2(r) + K(r)N + ξ(r) (4) wh2(r) ) χNγ2(φt1(r) + φt2(r)) + χ12Nγ2φh1(r) γ2K(r)N + γ2ξ(r) (5) wt2(r) ) χN(φh1(r) + φh2(r) + φs(r)) + χ12Nφt1(r) + K(r)N + ξ(r) (6) ws(r) ) χN(φt1(r) + φt2(r)) - K(r)N + ξ(r)

φ1f1V ∂Ω1 Ω1 ∂wh1(r) φ1f1V q (r, 1)q†1(r, 1) ) Ω1 1

(7)

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qi(r, s) )

qi†(r, s) )

∫ DrR,iP [rR,i, 0, s]δ(r - rR,i(s)) × s exp{- ∫0 wti(rR,i(t))dt}

(16)

∫ DrR,iP [rR,i, s, 1]δ(r - rR,i(s)) × 1 exp{-whi(rR,i(1)) - ∫s wti(rR,i(t))dt}

(17)

where rR,i(s) is a spatial curve describing the conformation of the Rth i-type lipid. The ∫DrR,i denotes a functional integral over all of the possible configurations of the Rth i-type lipid, and P[rR,i,0,s] is the probability distribution of the conformation for the 0-s part of the Rth lipid.15 The qi(r,s) and q†i (r,s) satisfy the modified diffusion equations

Fh1(r) ) -

φh1(r) ) γ1Fh1(r)

φ1f1V ∂Ω1 Ω1 ∂wt1(r) φ1f1V 1 q (r, s)q†1(r, s)ds ) Ω1 0 1

(8)

(9)

φt1(r) ) -

∫

(10)

(11)

φh2(r) ) γ2Fh2(r)

(12)

φ2f2V ∂Ω2 Ω2 ∂wt2(r) φ2f2V 1 q (r, s)q†2(r, s)ds ) Ω2 0 2

φt2(r) ) -

∫

(13)

(1 - φ1 - φ2)V ∂Ωs Ωs ∂ws(r) (1 - φ1 - φ2)V 1 q (r, s)qs(r, 1 - s)ds ) 0 s Ωs

φs(r) ) -

∫

(14) 2

∑ [φhi(r) + φti(r)] + φs(r) ) Φ0(r)

(15)

i)1

Here, qi(r,s) and q†i (r,s) (s changes continuously along the lipid from 0 at the end of the lipid tail to 1 at the head group) are the end-segment distribution functions of the i-type lipids and are defined by15

(18)

∂qi† R20 ) - ∇2qi† + wtiqi† ∂s 6

(19)

where R0 ≡ a(N)1/2 is the natural length of lipids and a is the statistical segment length. The initial conditions are qi(r,0) ) 1 and q†i (r,1) ) exp(-whi(r)); qs(r,s) has the analogous definition for the solvent, which satisfies eq 18 with wti replaced by ws and the initial condition qs(r,0) ) 1. With qi and qs, the partition functions of the individual lipids and solvent can be written as

Ωi )

φ2f2V ∂Ω2 Ω2 ∂wh2(r) φ2f2V q (r, 1)q†2(r, 1) ) Ω2 2

Fh2(r) ) -

R20 ∂qi ) ∇2qi - wtiqi ∂s 6

∫ qi(r, s)qi†(r, s)dr

Ωs )

i ) 1, 2

∫ qs(r, s)qs(r, 1 - s)dr

(20) (21)

The resulting self-consistent equations (eqs 3-15) together with eqs 18 and 19 can be numerically solved by the combinatorial screening method proposed by Drolet and Fredrickson.16 The minimization of the free energy corresponds to the possible equilibrium structures of the lipid bilayer. We first generate the random initial values of whi(r), wti(r), and ws(r), with which the field ξ(r) is obtained from eqs 3-7 combined with eq 15, and the modified diffusion eqs 18 and 19 as well as the similar equation for the solvents are also resolved to find qi(r,s), q†i (r,s), and qs(r,s). Then, the partition functions of single lipid A, B, and solvent as well as the local distribution of the components are found through eqs 20 and 21 and eqs 8-14, respectively. The obtained local densities and the incompressibility field ξ(r) are then used to find the new whi(r), wti(r), and ws(r). Next, the old and the new fields are mixed with a certain ratio to update the fields to start the new iteration as mentioned above. The calculation is continued until eq 15 is satisfied with an acceptable precision. Finally, the resulting local fields, densities, and the partition functions of the individual lipids and solvent are used to find the equilibrium free energy of the system. In the present paper, to facilitate the formation of a bilayer structure, we adopt the scenario proposed in ref 21 by introducing an external field favoring the lipid tails in the initial stage of the self-consistent calculation, which enforces the bilayer membrane formed along the substrate surface profile. When the bilayer is formed, the external field is turned off, and the

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Figure 2. (a-e) Summary of all observed morphologies for head group density profiles of lipid spcies A (φh1) and B (φh2) and the corresponding schematic illustrations; (a) homogeneously mixed lipid bilayer (HMLB), (b) macrosegregated lipid bilayer (MSLB), (c) component-modulated lipid bilayer (CMLB), (d) component-modulated lipid domain (CMLD), and (e) coalesced long lipid droplet (CLLD); the color scale bar shows the local density values of the head group of lipid species A and B. (f) Morphology diagram of the mixed lipid bilayer supported on a periodically corrugated substrate.

calculation continues until the equilibrium state of the system is reached. To avoid the finite size effects, we perform several repeated calculations of the same L and H with different simulation box sizes by varying the lateral length of the system.28,30 Furthermore, we carefully scan the L-H parameter space to systemically investigate the influence of roughness of the substrate on the lateral organization of the lipid bilayer. We set f1 ) 0.6, f2 ) 0.45, χN ) 20, N ) 50, a ) 1, F0-1 ) 1, and thus Vh1 ) 33, Vh2 ) 61, and R0 ) a(N)1/2 = 7. In order to conveniently compare our results with the experiments, all of the lengths involved in our work are scaled by R0. In our model, the effective molecular shapes of lipids are determined by χN and fi (i ) 1,2).15 With the chosen parameters, lipid species A and B form lamellar and hexagonally cylindrical phases in bulk, respectively.20 This means that lipid species A has a cylindrical head/tail shape (i.e., a zero spontaneous curvature), while lipid species B is cone-shaped with a nonzero spontaneous curvature. To form a mixed lipid bilayer, we take the overall volume fractions of lipid species A and B as φ1 ) φ2 ) 0.12. The repulsive interaction between the two kinds of lipids is chosen as χ12N ) 3. This is a crucial parameter; if χ12N is too small, the two kinds of lipids will mix homogenously in any case; however, if χ12N is too large, the two kinds of lipids will segregate from each other in any case. Therefore, χ12N should be weakly repulsive and just near the critical demixing value as chosen in this work. In real experimental systems, χN may be much stronger compared to χ12N. In that case, a larger χN without changing χ12N can also be chosen, but fi should be correspondingly changed to obtain the lipids with the same effective shapes. The strength of surface field is taken to be ΛN ) 1. Results and Discussion We examine the formation of all of the possible bilayer structures by varying the groove depth (H) and the substrate periodicity (L), and the results are summarized in Figure 2a-e. Here, the height of system is fixed to be 5.71R0, which is large enough not to influence the morphology of the lipid bilayer, and the lateral length ranging from 14.29R0-71.43R0 is adjusted to search the stable phases by the free-energy minimization. Figure 2f shows a diagram of the structures. The substrate periodicity changes from L ) 1.43R0 to 14.29R0, and the groove depth changes from H ) 0 to 1.43R0, which are either

comparable to or several times larger than the natural size of the lipids (R0), and therefore, the involved scale of lateral organization is within the nanometer size. When the groove depth H is vanishingly small, the perturbation from the substrate is negligible. In this case, whether the two kinds of lipids mix or separate into domains is determined by the competition between the repulsive interaction and the mixing entropy of lipids.31 The repulsive interaction favors the segregation of the two kinds of lipids, while the mixing entropy favors the homogeneous mixing phase. Because the repulsive interaction between the two kinds of lipids is weak (χ12N ) 3), the mixing entropy wins the competition and drives the two kinds of lipids to mix uniformly. Thus, a homogeneously mixed lipid bilayer (HMLB) is formed (Figure 2a). With the increase of H, the substrate becomes slightly rough, and lipid species B start to aggregate in the grooves because of their bigger spontaneous curvature. As lipid B-rich islands (nuclei) initiate from the grooves, a lateral expansion of the islands on the substrate appears and eventually leads to the formation of a macrosegregated lipid bilayer (MSLB) with the help of the lipid A-B interfacial energy (Figure 2b). When H is increased to modest values where the curvature of grooves becomes comparable to the spontaneous curvature of lipid species B, both lipid species B and A will, respectively aggregate, in the grooves and on the flat steps because of their individual preferred spontaneous curvatures. Thus, a componentmodulated lipid bilayer (CMLB) structure appears, as shown in Figure 2c. Comparing our results with the experiments of refs 7-10, we can find that, although the systems are different, the component-modulated lipid bilayer is very similar to the experimental results observed in refs 7-10, while the macrosegregated lipid bilayer presented in the lower-curvature regions corresponds to the macroscopic lo domains that emerged in nanosmooth regions in ref 9. However, it is notable that the microscopic mechanism of the structural formation in our results is different from that of experimental results. In our model, the formation of various structures is mainly induced by the interplay between the effective shapes of lipids and the roughness of the substrate, while in the experiments, the formation of the structures is mainly dominated by the interplay between the rigidities of the lipid domains and the roughness of the substrate. Additionally, in real biological systems, it was reported

Mixed Lipid Bilayers Supported on a Corrugated Substrate

J. Phys. Chem. B, Vol. 113, No. 23, 2009 8053 formation and distribution of lipid domains in real cellular membranes.34 To further address the underlying mechanisms driving such structural transitions, we examine the evolution of free energy with the substrate roughness. For convenience, we distill the following three parts which directly influence and dominate the lateral organization of the lipid bilayer from the free energy eq 2 of the system

Figure 3. Free-energy contributions from the entropy (FA) of lipid species A (O), the entropy (FB) of lipid species B (b), and the interfacial energy (FAB) between the mixed lipids (2). (a) L ) 5.71R0; (b) H ) 0.86R0.

that, during the formation of membrane fusion pores, the coneshaped nonlamellar lipids, such as phosphatidylethanolamine (PE), are spontaneously concentrated at high-curvature regions.32 This also provides indirect experimental evidence implying the validity of a component-modulated lipid bilayer in the real biomembrane systems. When the groove depth H is large, the groove curvature becomes larger than the spontaneous curvature of lipid species B at the small or modest L region. In this case, if the bilayer structure is still maintained, on one hand, lipid species B in the lower leaflet prefer to fill in the grooves; on the other hand, the bilayer would be curved strongly in the regime of grooves, and thus, the conformations of lipid species B in the upper leaflet must be changed strongly and lose plenty of conformational entropy because the curvature of the upper leaflet is in contrast to their bulk curvature. As a result, the lipid bilayer may be ruptured by the extremely rough substrate; the componentmodulated lipid domains (CMLD) appear at modest L, and the coalesced long lipid droplets (CLLD) with spreading lipid A droplets are formed at smaller L (see Figure 2f). For the large L region, where the groove curvature becomes comparable to the spontaneous curvature of lipid B, a component-modulated lipid bilayer is formed again. As we take a close look at the component-modulated lipid domain and coalesced long lipid droplet structures, we can find that the lipid species B almost fill up the grooves in these two structures, and therefore, for lipid species A, the substrate now becomes a chemically patterned one which is composed of alternating more-wettable hard-wall parts and less-wettable lipid B parts. Thus, the problem can be highlighted by templating of thin films on chemically patterned substrates;33 when the periodicity of the patterned substrate is beyond a critical length, the thin film pattern closely replicates the substrate surface pattern, namely, dewetting occurs on every less-wettable part of the patterned substrate, just as shown in Figure 2d, where lipid species A are localized on more-wettable hard-surface parts. On the contrary, when the periodicity is smaller than the critical length, the dewetting effect may be partially suppressed, and the long droplet of thin films spans across the remaining less-wettable sites, exactly like the morphology of lipid A droplets shown in Figure 2e. Importantly, by changing positions of grooves for given H and L, we find that at arbitrary spatial distribution of grooves, the above conclusions remain unchanged, independent of the positions of the grooves. Thus, such substrate-mediated organization of lipids provides a controllable mechanism for spatial sorting of membrane components by varying the substrate roughness. This is also helpful to understand how the membrane geometry and the effective molecular shapes of lipids affect the

( )

∫ dr[wh1(r)Fh1(r) +

( )

∫ dr[wh2(r)Fh2(r) +

NFA Ω1 1 ) -φ1f1 ln F0kBTV Vφ1f1 V

NFB Ω2 1 ) -φ2f2 ln F0kBTV Vφ2f2 V

NFAB 1 ) F0kBTV V

wt1(r)φt1(r)] (22)

wt2(r)φt2(r)] (23)

∫ dr[χN(φh1(r)φt2(r) + φh2(r)φt1(r)) + χ12N(φh1(r)φh2(r) + φt1(r)φt2(r))] (24)

Here, FA and FB are the entropic free energies of lipids A and B, respectively, and FAB is the interfacial energy between lipids A and B. Figure 3a shows the variation of the three free-energy contributions of the system with the groove depth H for the substrate periodicity L ) 5.71R0. We can clearly find that, with the formation of the macrosegregated lipid bilayer at small H (e.g., H ) 0.14R0-0.43R0) and the component-modulated lipid domains at large H (e.g., H ) 1.14R0-1.43R0), lipids A and B separate strongly, and the interfacial energy (FAB) decreases, while with the formation of homogeneously mixed lipid bilayer at H ≈ 0 and the component-modulated lipid bilayer at middle values of H (e.g., H ) 0.57R0-1.0R0), the interfacial energy increases due to the increase of the contact between lipids A and B. Therefore, the interfacial energy favors the structures of the macrosegregated lipid bilayer and the component-modulated lipid domains and governs the formation of these structures. However, it disfavors the structures of the homogeneously mixed lipid bilayer and the component-modulated lipid bilayer. The curve of the entropic free energy of lipids A (FA) varies slowly with H. This is because, with the formation of different structures via varying the substrate roughness, the lipids A almost always stay in the flat regions, and such a flat sorting just matches the spontaneous curvature of lipids A. On the other hand, a reduction of the entropic free energy of lipids B (FB) at middle values of H signifies that the curvature of the grooves approximately matches the curvature of the lipids B. Such a match can release the entropy of lipids B and drives the formation of the component-modulated lipid bilayer structures. We should also point out that the conformational entropy of lipids B plays a significant role in the formation of the component-modulated lipid domain or the coalesced long lipid droplet structure because of the existence of the energetic penalty for curving the membrane away from the spontaneous curvature. This can be realized through changing the conformation of flexible lipid B tails. If the conformational degree of freedom of lipid tails is reduced, these two structures could be more difficult to form, namely, the phase regions of structures of the component-modulated lipid domains and the coalesced long lipid droplets may shrink.35 This indicates that, in real experiments,

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the structures of the component-modulated lipid domains and the coalesced long lipid droplets may easily occur with relatively flexible lipid tails on a rougher substrate. Additionally, the role of conformational entropy is also emphasized to understand the stripe pattern formation of short immiscible ligands coadsorbing on a nanoparticle.36 Figure 3b shows the variation of the free-energy contributions with L for H ) 0.86R0. A significant change of the curves of the interfacial energy and entropic free energy of lipids B shows that the lipid bilayer is either a component-modulated structure for small L (e.g., L ) 1.43R0-10.0R0) due to different spontaneous curvatures of lipids A and B or a macroseparated one for large L (e.g., L ) 11.43R0-14.29R0), where the interfacial energy is decreased. Similarly, no obvious change in the entropic free energy of lipids A is observed. Thus, our results demonstrate that a rich variety of composition segregation of lipids formed through varying the substrate roughness is dominated by the complex interplay among the interfacial energy of lipids, different spontaneous curvature of lipids, and the mixing and conformational entropy of lipids. Finally, to give a more intuitive physical picture of our results, we can describe our system with the phenomenological model which has been widely used to study the morphology of membranes and vesicles37,38 as well as the wetting behavior of the membrane supported on a rough substrate.39 The phenomenological Hamiltonian of the supported bilayer in our model, A B + Ead + Ead . E, can be written as37,38 E ) EbA + EbB + EAB l Here, EbA(B) ) ∫σA(B) dA(κA(B)/2)(C1 + C2 - 2C0A(B))2 is the bending energy of domains of lipids A (B), where κA and κB are the respective bending rigidities of lipid A and lipid B domains, C1 and C2 are the local principal curvatures, and C0A and C0B are the respective spontaneous curvatures of lipid A and lipid B. The spontaneous curvatures C0A and C0B are determined by the effective molecular shapes of lipid A and lipid B in our model. The surface integrals run over the total ) ∫lAB dlλ area of lipid A (σA) and lipid B (σB) domains. EAB l is the interfacial energy between lipid A and lipid B domains, and λ(>0) is the line tension between the domains of lipids A and B, and the curve integral extends over the total length of the boundary (lAB) of the domains of lipids A and B. The last A(B) ) -∫σA(B) dAΛ, are the adsorption energy two terms, Ead between the lipids A (B) and the substrate, and Λ(>0) is the adsorption strength, as mentioned in the Model and Method Section. In our system, because the adsorption between the substrate and the two kinds of lipids is identical, the sum of the last two adsorption energies is a constant and thus has no influence on the lateral organization of the lipid bilayer. From this phenomenological Hamiltonian, we can clearly find that the lateral organization of the supported lipid bilayer is mainly dominated by the competition between the bending energy and the interfacial energy. The bending energy favors the lipid domains to bend to their spontaneous curvatures, namely, the lipids A with zero spontaneous curvature tend to maintain a flat sorting, while the lipids B with nonzero spontaneous curvature prefer to sort in the curved regions. On the other hand, the interfacial energy favors the segregation of the two kinds of lipids. In our system, when the depth of the grooves is small, the curvature of the groove is unable to be comparable with the spontaneous curvature of lipid B domains. In this case, if the grooves are completely occupied by the lipids B, the decrease of the bending energy cannot compensate for the increase of the interfacial energy due to the increased domain boundaries separating different lipids. Therefore, the interfacial

Liang and Ma energy drives the segregation of the two kinds of lipids, and the macrosegregated lipid bilayer is formed. However, if the curvature of the grooves is comparable to the spontaneous curvature of lipids B as the groove depth becomes moderately large, the decrease of the bending energy can completely compensate for the increase of the interfacial energy when the lipids B stay in the grooves and lipids A stay on the flat steps, and consequently, the component-modulated lipid bilayer is formed. Unfortunately, the phenomenological models are not suitable to study the topological structure changes22 with the formation of pores in the component-modulated lipid domains and the coalesced long lipid droplets, although they can be extended to consider the membrane structures with high curvature.40-42 Furthermore, because the phenomenological model describes the lipid bilayers as infinitely thin sheets, it cannot consider the conformational variation and mixing entropy effect of lipids. Therefore, the component-modulated lipid domain and the coalesced long lipid droplet as well as the homogeneously mixed lipid bilayer are absent in this model. Through comparing the phenomenological model and our coarse-grained microscopic model, we can find that the conformational entropy in our coarse-grained microscopic model plays a similar role as the bending energy in the phenomenological model in the formation of the macrosegregated and component-modulated lipid bilayers. However, the role of the entropy is more extensive and may also contribute to the formation of the other three structures. Therefore, the investigation of the internal structure of the lipid bilayer is necessary and very important. The shape and the entropy effect of lipids, which can be properly described by our coarse-grained microscopic model, play important roles in the lateral organization of the lipid bilayers. Conclusion We carried out a thorough investigation of the lateral organization of a two-component lipid bilayer supported on a periodically corrugated substrate by using self-consistent field theory. By adjusting the groove depth and the substrate periodicity, the interfacial energy, spontaneous curvature, and mixing and conformational entropy interplay complexly and consequently result in the formation of a rich variety of laterally organized lipid structures. Although parts of our results are similar to the results of the recent experiments,7-10 the microscopic mechanism of these two systems is different. Therefore, our model may provide another route to modulate the lateral organization of the supported membranes. Most importantly, we also predict, for the first time, the formation of the coalesced long lipid droplet and component-modulated domain structures in large roughness regions, which may provide insight into future experiments with the improvement of visualization techniques toward smaller scales of geometry. Finally, we further examine the microscopic mechanism of lateral organization of lipids in the mixed bilayer supported on the periodically corrugated substrate, which may yield some theoretical insight into the curvature-induced organization of lipids in the natural cellular membranes. Acknowledgment. This work was supported by the National Basic Research Program of China (No. 2007CB925101) and the National Natural Science Foundation of China (Nos. 20674037 and 10629401). References and Notes (1) Sackmann, E. Science 1996, 271, 43–48. (2) Tanaka, M.; Sackmann, E. Nature 2005, 437, 656–663.

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