We propose a framework for tracking arbitrary complex cell boundary movements, relying on a unique definition of protrusion and retraction as the pathlength a virtual edge marker traverses when moving continuously perpendicular to the cell boundary. We introduce the level set method as a numerical scheme to reconstruct continuous boundary movement in timelapse image sequences with finite time sampling. For moderately complex movements, we describe a numerically less expensive method that satisfactorily approximates the definition. Densely sampled protrusion and retraction rates were accumulated in space-time charts revealing distinct morphodynamic states. Applying this technique to the profiling of epithelial cell protrusion we identified three different states. In the I-state, long cell edge sectors are synchronized in cycles of protrusion and retraction. In the V-state random bursts of protrusion initiate protrusion waves propagating transversally in both directions. Cells switch between both states dependent on the Rac1 activation level. Furthermore, the persistence of transversal waves in the V-state depends on Arp2/3 concentration. Inhibition of PAK shifts cells into a l-state where continuous protrusion is occasionally interrupted by self-propagating ruf.es. Our data support a model where activation of Rac1 mediates the propagation of protrusion waves, whose persistence depends on the relative abundance of activated Arp2/3 and polymerizable G-actin.
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