# Fluorescence Correlation Spectroscopy Measurement Based on Fiber Optics for Biological Materials
## 1 Introduction  
Fluorescence correlation spectroscopy (FCS) is a technique used to quantitatively measure the concentration and diffusion coefficient of fluorescently labeled molecules [1, 2, 3]. Because FCS measurement can be performed inside living cells, FCS has been mainly used in biology to analyze changes in apparent molecular size due to intermolecular interactions and the expression of specific proteins, even in cells. The diffusion coefficient of fluorescently labeled probe molecules can be changed by intermolecular interactions because the apparent size of the probe and interactant complex becomes larger than that of the probe. FCS can separately measure the amount and size of the free probe molecule and those of the complex of the probe molecule. There are numerous reports on the measurement of biological molecules using FCS in academic research. [PERSON] et al. performed FCS measurements to characterize the interaction dynamics of \(\alpha\)-bungarotoxin labeled using tetramethyl rhodamine with acetylcholine receptors. The equilibrium constants and dissociation rate constants of the solution were successfully determined [4]. [PERSON] et al. performed FCS measurement on a green fluorescent protein (GFP) fused glucocorticoid receptor (GFP-GR) in cells and their lysates. The dissociation constants of the GFP-GR homodimer were successfully determined based on the concentration and fluorescence brightness of the GFP-GR monomer and homodimer measured using FCS [5]. Recently, FCS has also been used as a tool for medical diagnosis. FCS was used to detect interferon-gamma for the diagnosis of M. tuberculosis infection [6]. [PERSON] et al. used FCS to detect contactin-2 in the cerebrospinal fluid of patients with Alzheimer's disease [7]. [PERSON] et al. performed FCS and fluorescence cross-correlation spectroscopy (FCCS), which is an advanced variant of FCS, to detect prion protein. They found that thesensitivity of FCCS in detecting abnormal isoforms of prion protein was greater than that of FCS and comparable to the sensitivity of enzyme-linked immunosorbent assay (ELISA) [8]. Thus, FCS/FCCS is suitable for the measurement of fluorescently labeled specific particles, even in crude samples such as solutions containing impurities, cell lysates, and living cells. However, the available FCS systems are generally large and expensive. Furthermore, it is recommended that the FCS system be placed in a darkroom. FCS is a useful tool; however, the widespread adoption of FCS could be difficult for the aforementioned reasons. In most FCS systems, an excitation laser is focused on the samples, and only the fluorescence emitted from the focal region is detected using a pinhole (confocal detection optics). A core of a multimode optical fiber is often used as a pinhole [9]. Samples are generally solutions containing fluorescently labeled molecules/particles of interest or cells containing fluorescently labeled targets. Target molecules/particles diffuse in the sample and randomly enter or leave the confocal region of the excitation laser. As a result, the detected fluorescence temporally fluctuates owing to the diffusion of the target, reflecting the diffusion coefficient of the target. Because of this principle of FCS, the obtained parameters depend on both the size and shape of the confocal region. This makes the fine adjustment of the pinhole position very important in FCS; however, this is usually troublesome, and misarrangement can cause artifacts. [PERSON] et al. developed an alignment-free FCS system [10]. They connected the focusing unit to a wavelength division multiplexer unit, which was consist of a dichroic mirror and three lenses, by a single-mode optical fiber. Because the focal spot of the excitation laser is always imaged on the core of the single-mode optical fiber, the alignment of the pinhole was not needed in the system. They also achieved the compact size of the FCS system.