J. Phys. Chem. B 2008, 112, 1963-1967
1963
Inclusion-Mediated Lipid Organization in Supported Membranes on a Patterned Substrate Qing Liang and Yu-qiang Ma* National Laboratory of Solid State Microstructures, Nanjing UniVersity, Nanjing 210093, China ReceiVed: July 3, 2007; In Final Form: October 25, 2007
We theoretically investigate the effects of inclusions on the domain formation in mixed lipid bilayers supported on a geometrically patterned substrate. It is found that the inclusions may distribute quite differently with varying volume fraction and size of inclusions. The distribution of inclusions will effectively change the spontaneous curvature of the inclusion-rich lipid domains, and consequently can sort the lipid domains in the supported bilayers. By varying the volume fraction and size of inclusions, we obtain a rich variety of laterally organized lipid bilayers and reveal some interesting transitions between these structures. The present model provides a possible strategy to control the domain formation in the supported membranes, and may yield some theoretical insight into the design of biosensors by the reorganization of lipids and inclusions.
1. Introduction Supported lipid bilayers have attracted extensive interest in recent years because of their importance in the fundamental investigation of cellular membranes and their potential applications in the design of biosensors.1-6 Compared to the freely suspending lipid bilayers, supported lipid bilayers possess better stability and can be controlled more easily by changing the geometrical and/or chemical properties of the substrates. For example, a series of recent experiments manipulated the lipid distribution in the supported lipid bilayers through geometrically patterning the substrates,7-9 and the authors found that, because of their different rigidities, the cholesterol-enriched liquidordered (Lo) domains and liquid-disordered (Ld) domains prefer to stay in the flat regions and curved regions, respectively. Additionally, in a very recent experiment, Zhou et al.10 produced a supported membrane over a carbon nanotube to study the influence of membrane curvature on the diffusion of lipids and bound proteins, and found that the lipids can freely diffuse across the carbon nanotube, whereas the proteins can not. On the other hand, some experiments have revealed that the addition of inclusions (e.g., metal nanoparticles or fullerene C60) can greatly improve the mechanical, electrical, and optical properties of the supported membranes, and, consequently, this kind of modified supported lipid bilayers presents a novel system for biosensor design.11-14 All of these studies provide extensive experimental fundamentals for the design of biosensors and the investigation of cellular processes involved with membrane organization. However, these kinds of systems are far from being completely understood because of the complex influences of the inclusions and/or curvature on the organization of the lipids in the supported membrane, and how to manipulate the lipid organization through combination of the effects of substrate topography and the existence of inclusions is still a big challenge. In this article, using self-consistent field theory (SCFT), we undertake the first theoretical study of lateral organization of the lipid bilayers composed of two-component lipids (lipids A and lipids B) and inclusions supported on a geometrically patterned substrate (see Figure 1a). The inclusions are generally * Author to whom correspondence should be addressed. Electronic mail:
[email protected].
assumed to be strongly hydrophobic, relatively stiff, and have different affinities for different lipid domains. By varying the volume fraction and size of the embedded hydrophobic inclusions that have a preferential affinity to the lipids A, we systematically study the influences of the inclusions on the spontaneous curvature of the membrane and the domain formation in the membrane supported on such a geometrically patterned substrate. 2. Model and Methods The supported lipid bilayer consists of n1 lipid species A, n2 lipid species B, and np spherical rigid inclusions (radius R), and is dispersed in ns hydrophilic homopolymer solvents with polymerization index N (Figure 1a).15,16 The two kinds of lipids have the same shape with a headgroup (volume Vh) and an N-segment tail.17 The segment volumes of solvents and lipid tails are both F0-1, and the statistical length of the segment is R. If we assume that the system is translationally invariant in the y-direction,8,18 then the surface of the patterned substrate can be characterized by a periodical function S(x), which is only dependent on x. In our calculation, we choose S(x) as
{
1 x en+ L0 2 S(x) ) 2π(x - L0/2) x 1 if n + < e n + 1 H0 sin 2 L0 L0 0
(
)
if n
