## Appendix B  
To confirm the proposed calculation, a Monte Carlo simulation was performed. Fluorescence intensity fluctuations detected by confocal fluorescence detection in fluorescence solutions were generated. The point spread function (PSF) of the confocal system is defined as follows [3]:  
\[W(x,y,z)=\exp\left[-2\frac{x^{2}+y^{2}}{w_{0}^{2}}-2\frac{z^{2}}{z_{0}^{2}} \right], \tag{105}\]  
where \(w_{0}\) and \(z_{0}\) denote the lateral radius and axial radius of the confocal volume, respectively. The z-axis represents the optical axis of the system. The effective measurement volume \(V_{\rm eff}\) of the FCS measurement [18] is defined as  
\[V_{\rm eff}=\pi^{\frac{3}{2}}w_{0}^{2}z_{0}. \tag{106}\]  
The cuboid volume of interest in the simulation was defined as \(-L_{x}/2\leq x\leq L_{x}/2\), \(-L_{y}/2\leq y\leq L_{y}/2\), and \(-L_{z}/2\leq z\leq L_{z}/2\). The widths in \(x\)- and \(y\)-axis are \(L_{x}\) and \(L_{y}\), respectively. The height was \(L_{z}\). In this case, the number of molecules in the volume of interest \(N_{0}\) is  
\[N_{0}=CN_{\rm A}\times 1000V_{\rm eff}, \tag{107}\]  
where \(C\) denotes the molar concentration of the target molecules.  
In this simulation, the positions of each of \(N_{0}\) molecules were randomly determined, and the fluorescence intensity to be detected was calculated using the position and the PSF. The position of the \(i\)-th molecule (\(x_{i}\), \(y_{i}\), \(z_{i}\)) at time point \(n\) is calculated as follows:  
\[x_{i,\ n+1}=x_{i,n}+R_{\rm N}\Big{(}0,\sqrt{2D\Delta t}\Big{)}, \tag{108}\]  
\[y_{i,\ n+1}=y_{i,n}+R_{N}\Big{(}0,\sqrt{2D\Delta t}\Big{)}, \tag{109}\]  
\[z_{i,\ n+1}=z_{i,n}+R_{N}\Big{(}0,\sqrt{2D\Delta t}\Big{)}, \tag{110}\]  
where \(R_{N}\Big{(}0,\sqrt{2D\Delta t}\Big{)}\) represents a random number obeying a normal distribution with a mean of 0 and a standard deviation of \(\sqrt{2D\Delta t}\). \(D\) denotes the diffusion coefficient of the target molecules, and \(\Delta t\) is the time interval of the simulation. The initial positions of the molecules were determined by uniform random numbers within the volume of interest. If a molecule exits to the outside of the volume, the molecule enters from the opposite of the volume.  
The fluorescence intensity to be detected at the \(n\)-th time point can be calculated as  
\[I_{n}=\sum_{i=1}^{N_{0}}I_{i,n}, \tag{10}\]  
\[I_{i,n}=\varepsilon_{0}W(x_{i,\ n},y_{i,\ n},z_{i,\ n}), \tag{11}\]  
where \(I_{i,n}\) is the fluorescence intensity of the \(i\)-th molecule. \(\varepsilon_{0}\) denotes the brightness of the target molecule at the origin (the focal point of the system). The brightness obtained by the FCS measurement (CPM) \(\varepsilon\) is  
\[\varepsilon=\gamma\varepsilon_{0}, \tag{12}\]  
\[\gamma=\frac{\int\!\int\!\int[W(x,y,z)]^{2}dxdydz}{\int\!\int\!\int\!W(x,y,z)dxdydz}, \tag{13}\]  
where \(\gamma=\sqrt{2}/4\) for the 3D gaussian PSF defined by Equation (10).  
If there are two or more species with different brightness levels, the fluorescence intensity for each species is superimposed.  
We calculated the apparent parameters and the corrected parameters from the FCS analysis of the generated fluorescence intensity based on the method described in Appendix A. Finally, the results and the given parameters were compared.