## 1 Introduction  
Lipid bilayers are the fundamental structure of plasma membranes and play important roles as a reaction field for various membrane reactions such as the transport of material, energy, and information into and out of cells [1; 2; 3]. Artificial lipid bilayer membranes such as the black membrane, vesicle, and supported lipid bilayer (SLB) have been used as cell membrane model systems to understand the behaviors of lipids, peptides, and proteins in and on lipid bilayers [4; 5; 6; 7; 8]. The artificial lipid bilayer system at the interface between a solid substrate and an aqueous solution is the SLB. The lipid bilayer exists in the vicinity of approximately 1 nm to the substrate, and thus, has a high technical affinity with functionalized surfaces and sensors [9; 10; 11; 12]. SLBs on functional materials are valuable as a platform for investigating the function of membrane proteins because the lateral and vertical distribution, and assembly of lipids and proteins, significantly affect the efficiency of the transportation reaction though cell membranes [2; 3].  
Graphene oxide (GO) is a chemical derivative of graphene, which is a two-dimensional atomic sheet of sp2-carbon. GO is a single-atomic sheet comprising aromatic carbons modified with oxygen functional groups such as hydroxy, epoxy, and carboxy groups [13; 14]. Because of these functional groups, GO becomes hydrophilic and is available in aqueous systems, whereas pristine graphene is hydrophobic. Recently, various biological applications of GO, utilizing its unique properties, were reported [14; 15; 16; 17; 18; 19; 20; 21; 22]. GO possesses a unique fluorescence quenching ability that works independently of the wavelength of a donor fluorescence probe and presents a longer effective range than that of general molecular acceptors [23]. The quenching function of GO has been applied to biosensing based on fluorescence resonance energy transfer (FRET) for DNA hybridization and protein binding [15; 16; 24; 25]. In the theoretical calculation based on the Forster mechanism, the efficiency of fluorescence quenching by the two-dimensional graphene-based materials has the dependence to the minus forth power of the distance between the donor molecule and GO [26,27], while dye molecules assumed as a point dipole have that to the minus sixth power of the distance. The former shows a longer effective range compared to the latter (Figure 1). The fluorescence lifetime measurement for fluorescence-tagged DNA molecules at the different positions demonstrated that the quenching efficiency of GO was expressed as Equation (1) [28]:  
\[E=\frac{1}{1+\left(\frac{d}{d_{0}}\right)^{4}} \tag{1}\]  
where \(d\) is the distance between GO and a fluorescent probe, and \(d_{0}\) is the Forster distance, at which the quenching efficiency becomes 0.5. The estimated \(d_{0}\) of GO is 7.5 nm [28]. It is larger than the \(d_{0}\) of typical dye molecules, approximately 5 nm at maximum.  
We aim to apply the fluorescence quenching of GO to detect lipids and protein molecules in and on lipid bilayers. A typical thickness of a lipid bilayer is approximately 5 nm. Therefore, the quenching effect of GO reaches to the other side of the lipid bilayer that is formed on GO (Figure 1). We have reported that a single lipid bilayer or double bilayers form on GO flakes after the SLB formation by the vesicle fusion method [29,30]. However, fluorescence single particle tracking (SPT) showed that dye molecules labeled to lipids are quenched too effectively to be detected in the SLB on GO [30]. As a first step for detecting the quenching efficiency of a single molecule by the SPT, we demonstrated the single particle observation of the quantum dot (QD) in this study. We expected that the fluorescence intensity of a QD is sufficiently high for the SPT even under the quenching effect of GO.