A mathematical method for the 3D analysis of rotating deformable systems applied on lumen‐forming MDCK cell aggregates

Cell motility contributes to the formation of organs and tissues, into which multiple cells self‐organize. However such mammalian cellular motilities are not characterized in a quantitative manner and the systemic consequences are thus unknown. A mathematical tool to decipher cell motility, accounting for changes in cell shape, within a three‐dimensional (3D) cell system was missing. We report here such a tool, usable on segmented images reporting the outline of clusters (cells) and allowing the time‐resolved 3D analysis of circular motility of these as parts of a system (cell aggregate). Our method can analyze circular motility in sub‐cellular, cellular, multi‐cellular, and also non‐cellular systems for which time‐resolved segmented cluster outlines are available. To exemplify, we characterized the circular motility of lumen‐initiating MDCK cell aggregates, embedded in extracellular matrix. We show that the organization of the major surrounding matrix fibers was not significantly affected during this cohort rotation. Using our developed tool, we discovered two classes of circular motion, rotation and random walk, organized in three behavior patterns during lumen initiation. As rotational movements were more rapid than random walk and as both could continue during lumen initiation, we conclude that neither the class nor the rate of motion regulates lumen initiation. We thus reveal a high degree of plasticity during a developmentally critical cell polarization step, indicating that lumen initiation is a robust process. However, motility rates decreased with increasing cell number, previously shown to correlate with epithelial polarization, suggesting that migratory polarization is converted into epithelial polarization during aggregate development. © 2010 Wiley‐Liss, Inc.