## 3 Results
### Gray Level Information Entropy (GLIE) Is Sensitive to the Motion of Intracellular Particles
Thus, most of the translocations of the intracellular particle under ATP-depletion conditions are much smaller than the adjacent pixel length of 0.16 \(\upmu\)m. The translocations become more comparable to the pixel size when considering a normal active cell. Figure 2: An example of a particle motion captured by five pixels in a non-homogenous intracellular medium. Parameters that match live cells experiments are presented: The pixel’s length is 0.16 \(\upmu\)m, and the diffusion coefficient of the vesicle is between 0.001 and 0.012 \(\upmu\)m\({}^{2}\)/s\({}^{\alpha}\) (depending on the presence or absence of intracellular ATP), and accordingly the SD of length of translocations for a single time lag is between 0.03 and 0.07 \(\upmu\)m. (**a**) The particle is located in the center and covers the length of the three central pixels. Accordingly, the five pixels present three gray levels and information entropy of 3.73. (**b**) The particle moves a length of 0.5 pixel to the right. In that situation, it fully covers the length of two pixels, partially covers the length of two pixels and does not cover one pixel. Accordingly, the five pixels present four gray levels and information entropy of 5.74. (**c**) The particle conducts a large non-equilibrium translocation to the right. In that situation, it partially covers the last pixel. In that case, the five pixels present five different gray levels and information entropy of 8.05. The heterogeneity of the intracellular particle surrounding is expected to affect the relative information entropy in pixels that capture the particle vs. pixels that capture only the surrounding. Pixels that capture the particle will tend to have more homogenous intensity readouts and thus a relatively lower \(E\) values (Figure 2a). We can consider three principle locations of the intracellular particle. First, the particle is located at the center of five capturing pixels (Figure 2a). This yields three different gray levels, and \(E=3.73\). Second, the particle moves about 0.5 pixel-length from the center (Figure 2b). The related five pixels produce four different gray levels, and \(E=5.74\). Third, the particle is undergoing a large non-equilibrium translocation and is now almost out of the range of the related pixels (Figure 2c). The five capturing pixels now yield five different gray levels, and \(E=8.05\). Following this example, the particle motion could translate to corresponding changes in the information entropy values at the relevant pixels. For employing this technique to study the motion of intracellular particles, it is important to choose the appropriate number of capturing pixels according to the particle size and motion in order to generate maximal fluctuations in \(E\). As an example, increasing the number of capturing pixels from five to seven in the example of Figure 2 yields fluctuations in \(E\) between 8.63 and 13.62. This range represents possible changes of up to 58% in \(E\), and is relatively smaller than the corresponding range for five capturing pixels (of 116%). Increasing the number of capturing pixels will further decrease the relative fluctuation range of \(E\). A moving particle may create a change in the gray levels of its capturing pixels when it either protrudes into a neighboring pixel or withdraws from a capturing pixel (see example in the Figure 2b). This change is maximal when the particle moves to cover about 50% of a pixel. If the moving particle covers less than 50% of a pixel due to a small movement (and accordingly, more than 50% of the pixel on the opposite side), the gray levels and information entropy associated with those pixels are less likely to change. Given that, we can estimate the probability of that particle to translocate to a distance around half a pixel.