Insights into the Cell Shape Dynamics of Migrating \textit{Dictyostelium discoideum}

Dynamic cell shape is a highly visible manifestation of the interaction between the internal biochemical state of a cell and its external environment. We analyzed the dynamic cell shape of migrating cells using the model system Dictyostelium discoideum. Applying a snake algorithm to experimental movies, we extracted cell boundaries in each frame and followed local boundary motion over long time intervals. Using a local motion measure that corresponds to protrusive/retractive activity, we found that protrusions are intermittent and zig-zag, whereas retractions are more sustained and straight. Correlations of this local motion measure reveal that protrusions appear more localized than retractions. Using a local shape measure, curvature, we also found that small peaks in boundary curvature tend to originate at the front of cells and propagate backwards. We will review the possible cytoskeletal origin of these mechanical waves.