It has been experimentally reported that chemotactic cells exhibit cellular memory, that is, a tendency to maintain the migration direction despite changes in the chemoattractant gradient. In this study, we analyzed a phenomenological model assuming the presence of cellular inertia, as well as a response time in motility, resulting in the reproduction of the cellular memory observed in the previous experiments. According to the analysis, the cellular motion is described by the superposition of multiple oscillative functions induced by the multiplication of the oscillative polarity and motility. The cellular intertia generates cellular memory by regulating phase differences between those oscillative functions. By applying the theory to the experimental data, the cellular inertia was estimated at m= 3 - 6 min. In addition, physiological parameters, such as response time in motility and intracellular processing speed, were also evaluated. The agreement between the experiemental data and theory suggests the possibility of the presence of the response time in motility, which has never been biologically verified and should be explored in the future.
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