  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.
