## 3 Results
### Gray Level Information Entropy (GLIE) Is Sensitive to the Motion of Intracellular Particles
The \(SA\) parameter relates to the general dynamics in the measured system. As expected according to these relations, we observe higher parameter values obtained in active cells that produce significant amount of mechanical work in comparison to cells after ATP depletion, in which no mechanical work is produced. We observe significant correlations between SICS-based parameters and their corresponding GLIE-based parameters (Figure 7). These correlations establish the ability of GLIE-based parameters to  
Figure 6: A comparison of average GLIE and SICS fluctuations analysis results in Jurkat cells (n = 34) before and after ATP depletion. Average power-fit and ASD parameters results in the cells before and after ATP depletion following SICS fluctuation analysis (**a**) or GLIE fluctuation analysis (**b**). Error bars in panels **a,b** are SEM, and \(p\)-values are presented in the corresponding panels. characterize aspects of intracellular dynamics. Based on t-statistics (Figure 7d), GLIE-based parameters seem to provide a significantly higher discrimination power between conditions of normal cellular activity and ATP depletion. Figure 7: Correlation between the power fit and ASD parameters calculated by SICS analysis and the corresponding parameters that were calculated by GLIE analysis in active Jurkat cell (n = 34). The correlation between \(b\) parameter results (**a**) or _Sum of Squared estimate of Errors (SSE)_ parameter results (**b**) or _Sum of Amplitudes (SA)_ parameter results (**c**) following SICS analysis and the same parameters results following GLIE analysis in the Jurkat cells. (**d**) A comparison of t-statistic values for the difference in results in cells before and after ATP depletion that were obtained for each parameter and each method of analysis (SICS vs. GLIE analysis). Corresponding parameters (such as \(b\) of SICS analysis versus \(b\) of GLIE analysis) are compared and the \(p\)-value for the significance of the difference in t-statistic results between the two methods of analysis is also presented (\(p\) = 0.02). In panels **a–c** the R-values of each correlation and \(p\)-values for the significance of that correlation are presented. The advantage of GLIE-based parameters in the detection of intracellular dynamics due to mechanical work may stem from the intracellular medium becoming more homogenous under such conditions [6]. This is reflected by the average GLIE values that are lower in these cells (Figure 8). Due to the fact that GLIE is a logarithmic function, lower average GLIE values make GLIE fluctuations more pronounced (Figure 3). Hence, the combined effect of an increase in intracellular motion and an increase in intracellular homogeneity enables the resultant high GLIE fluctuations. This increases the sensitivity of our approach to intracellular mechanical work and related dynamics (Figure 7d). The \(a\) parameter (which relates to \(K_{\alpha}\)) is expected to be higher in active cells, as compared to ATP-depleted cells [4; 6]. Therefore, the relatively lower \(a\) parameter results in active cells found by our SICS analysis (Figure 6a) needs further consideration. These unexpected lower \(a\) parameter values are probably due to artifactual lowering of this parameter as a result of a significant degree of mismatch between the ASD values and their adjusted power fit under this condition. We further discuss this subject in the Supplementary Materials. When using GLIE-based fluctuation analysis, this issue is resolved due to the lower average GLIE values in the normal active cells (Figure 8). Higher homogeneity in active cells causes a further increase in \(a\) values. This increase compensates for the artifactual lowering of \(a\) values through the power fit. As a result, when using GLIE fluctuation analysis, \(a\) values are higher in cells before ATP depletion than after ATP depletion.