Analysis of cell locomotion

Abstract

The methods of statistical physics have been applied to the analysis of cell movement. Human polymorphonuclear leukocytes were exposed to different surfaces possessing parallel oriented physical stuctures (scratched glass surface, machine drilled aluminium surface, optical grid and stretched polyethylene foil) and cell migration was observed using time-lapse photography.

We demonstrate that in cell migration along physical structures, referred to as contact guidance, two subgroups can be distinguished: 1) The nematic type where the cell size is large in relation to the grid distance of the undulate surface. 2) The smectic type where the cell size is small in relation to the grid distance of the substrate.

Nematic contact guidance is characterized by an anisotropic random walk. In all substrates investigated the diffusion process parallel to the lines was faster than the diffusion process perpendicular to them. The angular dependent diffusion coefficient was described by an ellipse. Deviation from a circle defined an apolar order parameter, whose value was about 0.3. The amount of information which the cells collected from, the undulate surface was very low, between 0.1 and 0.2 bits. We demonstrate that cells do not recognize all the details of their surroundings and that their migration can be compared to the “groping around” of a short sighted man. The blurred environment can be described by a mean field whose strength is proportional to the aploar order parameter. It is argued that the anisotropic surface tension is the basic source for nematic contact guidance.

Smectic contact guidance is characterized by an anisotropic random walk and is quantified by a density order paramter which is 0.28 in the case of the scratched glass surface of a Neubauer counting chamber. The information which the cells collect from their environment is very low (0.03 bits). The lines seen by the cell can be described by a mean field whose strength is proportional to the density oder parameter.

Finally, we demonstrate that the locomotion of granulocytes is governed by an internal clock and internal programs. After migrating for a certain time (32 s) in a particular direction, a new direction of locomotion is determined by an internal program. The cell decides basically between left or right, thereby preferring a turn angle such that the cell migrates either parallel or perpendicular to the lines. the angles are nearly equally probable but the cell moves, in the case of nematic guidance, with different velocities in the +or-direction. The cell also has directional memories with characteristic times of 32 s and greater than 100 s.