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Zigzag Turning Preference of Freely Crawling Cells

Figure 4

Long-range directional persistence and zigzag turns of the crawling trajectories of a mathematical model cell.

A) Mean square displacements vs. time for (red), (blue), (violet), and (green). The cyan and black dotted lines have a slope of 1 and 2, respectively. B) Close-up view of the green highlighted segment in Fig. 3 (). Some snapshot images of the crawling cell are superimposed on the trajectory. The red (blue) boundary is the moving front (trailing edge) where (). The inset plots the instantaneous local curvature along the centroid trajectory. Local maxima and minima are marked by red dots, which correspond to the turning points (black dots) along the centroid trajectory. C) Return map of the turning angle (). The zigzag preference . D) Auto-correlation function of the sequence of turning angles (). The blue dotted line is an exponential function fit with a decay time constant of 0.705. E) Auto-correlation functions of the instantaneous direction of movement for (red), (blue), (violet), and (green). F) Two time constants obtained by fitting cos to . The error bars represent the standard deviation based on 10 different trajectories obtained with a different initial condition.

Figure 4

doi: https://doi.org/10.1371/journal.pone.0020255.g004