# Optimization of Optical Trapping and Laser Interferometry in Biological Cells
## 5 Conclusions  
In this study, we investigated the way to optimize OT and LI experiments in biological cells. Using cultured cells and in vitro homogeneous samples, positional sensitivities of LI experiments were measured for various conditions and compared to theoretical predictions. The dependence of the LI sensitivity on the refractive indices of in vitro samples (aqueous glycerol) and probe particles (silica, latex, melamine) conformed to geometrical optics and Rayleigh scattering theory. In living cells, LI sensitivities were measured while the relative location (\(x,y,z\)) of a probe to the laser focus is maintained with the feedback-tracking technique. Regardless of the precise measurements with the feedback control, results in living cells showed greater systematic and random errors, especially when silica particles were used as a probe. Our investigations indicate that the in-situ calibrations of the positional sensitivity are a prerequisite for LI experiments in living cells because the cell interior is heterogeneous in space and the heterogeneity fluctuates with time.  
The feedback-tracking technique was necessary for LI experiments and in-situ calibrations in living cells, not only because probes readily go out of the laser focus during the experimental period of time, owing to vigorous cytoplasmic fluctuations. As we showed in this study, even if the probe is maintained around the focus of the laser, the LI sensitivity still depends on the slight deviations from the laser focus. Therefore, the offsets between the probe particle and the laser focus must be maintained with small tolerance for the precise OT and LI in living cells. We report that the LI sensitivity was stable in a narrow range \(-0.15\upmu\)m \(<\)\(x\), \(y\)\(<\) 0.15 \(\upmu\)m) for probe offsets in radial directions. For offset in the direction of the optical axis, it was found that the LI sensitivity at \(z=0\) is significantly reduced. The sensitivity is both higher and more stable when the probe is located above  
Figure 9: Height dependence of LI sensitivity in HeLa cells. Red circles show experimental results. The focus of microscope image was changed at \(z\) = 1.5 \(\upmu\)m by moving the CCD camera position because of the reason explained in Figure 7b and in the corresponding text. Open diamonds show numerical results based on Lorenz-Mie theory. Solid curve indicates the eye guide generated by the Smoothing Spline interpolation ([PERSON], Wavemetrics, Lake Oswego, OR, USA). Error bars represent standard deviations of the mean in \(z\) \(\leq\) 1.4 \(\upmu\)m (N = 3).  
the laser focus (\(z\sim 0.6\)\(\upmu\)m). However, the stable feedback tracking was not possible at the position. For conducting feedback tracking in the \(z\) direction, we measured the \(z\) position of the probe particle by analyzing the microscope image. Since the high-magnification and high-NA objective lens was used for OT and LI, the probe image was already significantly defocused at \(z\sim 0.6\)\(\upmu\)m. The feedback tracking was then destabilized since the \(z\) position could not be precisely estimated. In this study, the feedback stability and the LI sensitivity was optimized simultaneously by shifting the focus of the microscope image by moving the camera position and by conducting extra tuning in the \(z\) estimation procedure. We believe that the achieved precision and stability of LI experiments are unprecedented in living cells, and thus will open the door to novel micromechanical investigations of living cell interiors.  
Conceptualization, D.M.; formal analysis, Y.S. and M.I.; investigation, Y.S. and M.I.; writing--original draft preparation, D.M.; writing--review and editing, Y.S. and D.M.; supervision, D.M.; funding acquisition, D.M. All authors have read and agreed to the published version of the manuscript. This work was supported by JSPS KAKENHI Grant Number JP18H01189, JP25103011, JP15H03710 (to DM). The authors declare no conflict of interest.