Shape dynamics and migration of branched cells on complex networks

Migratory and tissue resident cells exhibit highly branched morphologies to perform their function and to adapt to the microenvironment. Immune cells, for example, display transient branched shapes while exploring the surrounding tissues. In another example, to properly irrigate the tissues, blood vessels bifurcate thereby forcing the branching of cells moving on top or within the vessels. In both cases microenvironmental constraints force migrating cells to extend several highly dynamic protrusions. Here, we present a theoretical model for the shape dynamics and migration of cells that simultaneously span several junctions, which we validated by using micropatterns with an hexagonal array, and a neuronal network image analysis pipeline to monitor the macrophages and endothelial cell shapes and migration. In our model we describe how the actin retrograde flow controls branch extension, retraction and global cell polarization. We relate the noise in this flow to the residency times and trapping of the cell at the junctions of the network. In addition, we found that macrophages and endothelial cells display very different migration regimes on the network, with macrophages moving faster and having larger changes in cell length in comparison to endothelial cells. These results expose how cellular shapes and migration are intricately coupled inside complex geometries. ### Competing Interest Statement The authors have declared no competing interest.