Characterization of endothelial cell locomotion using a Markov chain model.

A Markov chain model was developed to characterize the two-dimensional locomotion of bovine pulmonary artery endothelial (BPAE) cells cultured with or without basic fibroblast growth factor (bFGF). This model provides a detailed description of the migration process by computing the following locomotory parameters: (i) the speed of cell locomotion; (ii) the expected duration of cell movement in any given direction; (iii) the probability distribution of turn angles that will decide the next direction of cell movement; (iv) the frequency of cell stops; and (v) the duration of cell stops. Eight directional states and a stationary state were used in our Markov analysis. From cell trajectory data, the transition probabilities among the various states and the waiting times for the directional and the stationary states were computed. The steady-state probabilities were also calculated to obtain the ultimate direction of cell motion and, thus, determine whether cell motion was random. Our results showed how the addition of bFGF enhanced the locomotory capability of BPAE cells. Cells cultured with 30 ng/mL bFGF had lower probability of moving to the stationary state than those cultured without bFGF. In addition, cells cultured with 30 ng/mL bFGF remained in the stationary state for shorter periods of time than cells cultured without bFGF. In both these cases, however, the transition probabilities from the stationary state to any directional state were uniformly distributed and were not affected by the presence of bFGF.