## 3 Results
### Gray Level Information Entropy (GLIE) Is Sensitive to the Motion of Intracellular Particles
The GLIE fluctuation analysis is further demonstrated in Figure 5a-d. The \(50\times 50\) pixels ROI of each cell was further divided into 100 units of \(5\times 5\) pixels (Figure 5b), in accordance with the conclusions in the previous section. In each \(5\times 5\) unit, GLIE values were calculated for each of the 200 time points (Figure 5d). Next, the 200 time-dependent GLIE results of each unit of \(5\times 5\) pixels were analyzed by DFT. Averaged amplitudes of all 100 (\(5\times 5\) pixels) units for each frequency were determined to define the ASD results of that cell regarding GLIE fluctuations. The average ASD results from the GLIE analysis of all the cells under each condition (before and after ATP depletion) are presented in Figure 4c. Figure 4: GLIE and spatial image correlation spectroscopy (SICS) fluctuations in Jurkat cells (n = 34) before and after ATP depletion. (**a**) An example of a Jurkat cell with the ROI of \(50\times 50\) pixels in its center. Serial 200 images in a time lag of 0.2 s were acquired for each cell. In that region of interest (ROI), SICS and GLIE values for each image were calculated as explained in the Material and Methods section. Average amplitudes of discrete Fourier transform (DFT), of SICS (**b**) or of GLIE (**c**) time-dependent fluctuations (Amplitude Spectral Density (ASD)) in the group of cells are plotted before and after ATP depletion. Power-fit R-values for each condition are presented. Error bars in panels **b,c** are SEM. The ASD results (Figure 4b,c) show that the amplitudes of SICS and GLIE fluctuations have similar patterns and are both higher in normal active cells, as compared to these cells after ATP depletion. The compatibility of power-fit regressions to these ASD patterns is high according to the R-values presented in Figure 4b,c. These high compatibilities of power-fit formulas to the ASD results are not surprising, since multiple analytical models of Brownian and anomalous diffusion were found to match the general formula: _Amplitude_\((f,\infty)=\frac{\sqrt{D}}{f^{0.56}}\), where \(f\) represents the frequency, \(\beta\) represents the power of diffusion and \(D\) represents a constant that relates to \(K_{\alpha}\)[19; 20; 21]. The power-fit (_Amplitude_\(=\frac{a}{Frequency^{b}}\)) parameters \(a\), \(b\) and _Sum of Squared estimate of Errors_ (_SSE_), as well as the parameter _Sum of Amplitudes_ (_SA_), were defined and calculated in each analysis (SICS fluctuations or GLIE fluctuations) for each cell and each condition (Figure 6). Apart from the \(a\) parameters in the SICS fluctuation analysis, all other parameters were significantly higher in live cells before ATP depletion, as compared to the values in the same cells after ATP depletion. Figure 5: Capturing and analyzing GLIE fluctuations in an imaged cell. (**a**) An example of a Jurkat cell with the ROI of \(50\times 50\) pixels in its center. Serial 200 images in a time lag of 0.2 s were acquired for each cell. (**b**) The ROI of \(50\times 50\) pixels was divided to a 100 units of \(5\times 5\) pixels. (**c**) An example of distribution of gray levels in a unit of \(5\times 5\) pixels. (**d**) GLIE calculations according to the information entropy function in that \(5\times 5\) pixels unit for each time point out of the 200 serial acquisitions. As previously suggested, PSD or ASD analyses can serve for characterizing intracellular dynamics, and relate to the Mean Squared Displacement (\(MSD\)) equation; \(MSD=K_{\alpha}\Delta t^{\alpha}\), where \(K_{\alpha}\) represents the diffusion coefficient, \(\Delta t\) represents the time lag and \(\alpha\) represents the power of diffusion [20]. Specifically, the \(a\) parameter is related to \(K_{\alpha}\)--the diffusion coefficient; the \(b\) parameter is related to \(\alpha\)--the power of the diffusion. Like \(\alpha\), the parameter \(b\) also increases by introducing mechanical work to the cell and a break in ergodicity. The \(SSE\) parameter also increases by adding mechanical work and a break in ergodicity.