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Cell migration plays essential roles in development, wound healing, diseases, and in the maintenance of a complex body. Experiments in collective cell migration generally measure quantities such as cell displacement and velocity. The observed short-time diffusion regime for mean square displacement in single-cell migration experiments on flat surfaces calls into question the definition of cell velocity and the measurement protocol. Theoretical results in stochastic modeling for single-cell migration have shown that this fast diffusive regime is explained by a white noise acting on displacement on the direction perpendicular to the migrating cell polarization axis (not on velocity). The prediction is that only the component of velocity parallel to the polarization axis is a well-defined quantity, with a robust measurement protocol. Here, we ask whether we can find a definition of a migrating-cell polarization that is able to predict the cell's subsequent displacement, based on measurements of its shape. Supported by experimental evidence that cell nucleus lags behind the cell center of mass in a migrating cell, we propose a robust parametrization for cell migration where the distance between cell nucleus and the cell's center of mass defines cell shape polarization. We tested the proposed methods by applying to a simulation model for three-dimensional cells performed in the CompuCell3D environment, previously shown to reproduce biological cells kinematics migrating on a flat surface. • Proposition of a polarization vector based on its correlation with cell displacement. • The proposition can be easily applied to experimental results. • The polarization definition quality depends on the time interval used to measure cell displacement. • The polarization vector is a good predictor for cell displacement provided it is not small. • The cell velocity is well defined only when measured parallel to the polarization vector. [ABSTRACT FROM AUTHOR]

Cell crawling has usually been characterized by a diffusion constant D and instantaneous velocity 〈 | v → | 2 〉. However, experimentally 〈 | v → | 2 〉 diverges. A three regime (diffusive-ballistic-diffusive) modified Fürth equation parameterized by D , the dimensionless excess diffusion coefficient S and the persistence time P is compatible with experiment. S allows comparison of trajectories across experiments and sets limits on the intervals and duration of experiments required to assess cell movement. Cell trajectories in a variety of published experiments are consistent with longitudinal Langevin dynamics and a transverse Wiener process with S ∼ 1 + c o n s t a n t ∗ D − 1 . • Experimental data show quasi-diffusive behavior for very small-time intervals. • Diffusive behavior cannot be attributed to image acquisition segmentation errors. • Instantaneous velocity is not well-defined when small-time scale regime is present. • Velocity autocorrelation function differs from Langevin behavior at small-time scale. • Small-time scale depends on the cell type and/or experimental setup. [ABSTRACT FROM AUTHOR]