# Optimization of Optical Trapping and Laser Interferometry in Biological Cells
## 4 Experimental Results and Discussions
### LI Sensitivity Depending on Optical Properties
The LI sensitivity is the largest for melamine particle (Figure 4b). We then turn to measure the LI sensitivity in living HeLa cells. Since cells are highly crowded with concentrated biopolymers, their refractive indices are largely different from that of the solvent and are not known exactly. The calibration procedure using a reference material as written above is not appropriate. In this study, therefore, the sensitivity \(S\) was directly measured in living cells as the ratio of the amplitude of the QPD output \(V\) to that of the probe displacement \(x\)[23; 15]. While sinusoidally moving the piezo-mechanical sample stage, the QPD signal and the video of microscopic image of the probe were recorded [15]. Since a probe in a living cell spontaneously moves during the calibration  
Figure 4: **(a)** Normalized LI sensitivity \(A\equiv S/S_{40}\) in aqueous glycerol with \(2a=1\) μm probe particles (green: silica, blue: latex, red: melamine). Symbols (open squares, triangles and circles) are experimental data. Solid and broken curves are obtained based on geometrical optics [Equation (4)] and Rayleigh scattering [Equation (5)] approximations, respectively. In the range of explored conditions, approximated theories agree to experimental data that are provided by symbols with the same color. (b) LI sensitivities \(Af_{\text{R}}(n_{40},\,n_{\text{p}})\), which is free of uncontrollable factor \(G\), are shown as a function of \(\Delta n\), together with the predictions \(f_{\text{R}}(n,\,n_{\text{p}})\) made by Rayleigh scattering approximation (solid curves). Error bars represent standard deviations of the mean (N = 10). owing to the vigorous cytoplasmic fluctuations, movement of the piezo stage was controlled with 3D feedback as expressed in the materials and methods section. Even if this direct in-situ calibration is conducted using the feedback-tracking technique, LI experiments are destabilized when the laser propagates through highly heterogenous regions in cells such as cell-cell and cytoplasm-nucleus boundaries. Therefore, probe particles that are located in relatively homogeneous regions in between nucleus and cell-cell boundaries were chosen for LI experiments in prior study [15] and also in this study. Refractive indices of cells \(n\) were changed by controlling the cell volume \(v\) by adding sucrose to the culture media. By assuming that the total amount of solid contents in cells was kept constant, and that the mean refractive index of cells is \(n=1.38\)[9; 25; 26; 27; 28; 29; 30] for isotonic cytoplasm and \(n=1.33\) for \(v\rightarrow\infty\), the refractive index in the cells was estimated by the mixing rule based on the Lorenz-Lorenz relation [36]. As shown in Figure 5a, normalized LI sensitivities \(A\) in cells are systematically higher than the theoretical predictions for both melamine and silica particles. Laser aberrations owing to the heterogeneity in cells would reduce sensitivities, rather than increase. A part of the reason for this may be the amplification of the laser diffraction at the cell-culture interface. As shown in Figure 5b, the laser deflection is amplified by -5% at the cell (\(n\sim 1.38\))-media (\(n\sim 1.33\)) interface after it is refracted by the probe. Since this deflection at the boundary does not occur in experiments in the reference material (40% aqueous glycerol), this amplification effect may explain the slightly higher sensitivity of melamine particle in living cells than that in glycerol solutions. However, errors measured in silica particles are elusive. This is seen more clearly in Figure 5c, in which \(A/R(n_{40},\,n_{\mathrm{P}})/(n_{\mathrm{P}}-n)\sim f(n,n_{\mathrm{P}})/(n_{ \mathrm{P}}-n)\) obtained in cells and aqueous glycerol are plotted. The dispersions as well as the systematic deviations from theoretical predictions (which is almost constant in this plot) are remarkably large for silica particles, especially when the cell refractive index is similar to \(n_{\mathrm{P}}\).