Statistical characterization of cell motility

Both in their natural tissue environment and in the artifical environment of the tissue culture dish, animal tissue cells can exhibit a highly migratory behavior. Responding to proteins and other signals in their surrounding, cells continously remodel their cytoskeleton and energize a host of molecular motors. The resulting forces alter the cell shape as well as "pull" the cell body forward. Thus, cell displacements are a high-level manifestation of a vast array of molecular processes, much like automobile displacements are resulted by a (probably less complex) underlying machinery.

To characterize the complexity of cell behavior, quantiative measures are to be extracted from the time-lapse images. Most of these quantities characterize the cellular trajectories, and thus completely ignore the complexity associated with changing cell shape. The trajectories are provided by a tracking procedure, which identifies the same cells on a number of consecutive images. Related software is downloadable from here.

Once the spatio-temporal coordinates of cell positions are known, various statistical quantities can be derived.

  • Cell velocity distribution gives the empirical distribution of cell displacements during a suitably short period of time. Most tissue cells exhibit saltatory motion, that is irregularly alternating active and passive periods of movements. This wide spectrum of locomotory activity is reflected in a non-gaussian distribution of velocities, which is often found to be well approximated by an exponential distribution. (Related papers: Czirok et al 1998, Hegedus et al 2000)

  • Time-averaged cell displacements systematically characterize the long-term behavior of cellular motion. While velocities are calculated from the distance between cell positions at the beginning and at the end of one-hour-long time periods, this comparision can be made for an arbitrary long time window. Thus, average (over time and population) cell displacements are calculated for a range of time periods, thereby eliminating the choice of a particular time interval length for velocity calculations. (Related papers:Mehes et al 2002, Hegedus et al 2004)

  • Diffusion index: Beside a simple a natural way to compare the motility of cell populations, the average displacement as a function of elapsed time can also be very informative on the type of motion: for a highly persistent, linear motion with a steady velocity the average displacement is proportional with the elapsed time. In contrast, for a mathematical random walk, where each step is an independent random variable, the displacement grows with the square root of time. For  a boundend motion (when a cell can not leave a certain area), the displacement saturates to a constant value for long time intervals. Therefore, the functional form of the average displacement vs time curve yields information on the persistence of cell motility. (Related papers:Mehes et al 2002, Mehes et al 2004)