Local and global measures of shape dynamics

The shape and motion of cells can yield significant insights into the internal operation of a cell. We present a simple, yet versatile, framework that provides multiple metrics of cell shape and cell shape dynamics. Analysis of migrating Dictyostelium discoideum cells shows that global and local metrics highlight distinct cellular processes. For example, a global measure of shape shows rhythmic oscillations suggestive of contractions, whereas a local measure of shape shows wave-like dynamics indicative of protrusions. From a local measure of dynamic shape, or boundary motion, we extract the times and locations of protrusions and retractions. We find that protrusions zigzag, while retractions remain roughly stationary along the boundary. We do not observe any temporal relationship between protrusions and retractions. Our analysis framework also provides metrics of the boundary as whole. For example, as the cell speed increases, we find that the cell shape becomes more elongated. We also observe that while extensions and retractions have similar areas, their shapes differ.