Statistical Analysis of Cellular Directional Movement: Application for Research of Single Cell Movement

Abstract

Cell movement plays a fundamental role in physiological collective phenomena including angiogenesis. In early studies, it has been mainly discussed whether cell movement may be considered as the so-called random walk (Brownian motion) in two dimensions or not. Due to Einstein’s theory for Brownian motion, the mean squared displacement (MSD), which is estimated from experimental data, is endorsed as a criterion for the motility to be random walk; the MSD of a random walker is proportional to time, whereas that of those with a constant velocity is to the square of time. The two cases above are called diffusive and ballistic, respectively, and the other cases are anomaly. Recent studies, based on experimental data measured with a high degree of accuracy, tend to conclude that cells move with a directional persistency. As a consequence, one considers that a persistent random walk will model cell movement well, where the MSD includes a persistency parameter of time to cross over from the persistent regime to the random one. The persistence time may show a global property of cell movement. In this chapter, we explain the key words mentioned above and statistical methods for analysis of cell movement.