A simple active fluid model unites cytokinesis, cell crawling, and axonal outgrowth.

While the structural organization and molecular biology of neurons are well characterized, the physical process of axonal elongation remains elusive. The classic view posited elongation occurs through the deposition of cytoskeletal elements in the growth cone at the tip of a stationary array of microtubules. Yet, recent studies reveal axonal microtubules and docked organelles flow forward in bulk in the elongating axons of , chick sensory, rat hippocampal, and neurons. Noting that the morphology, molecular components, and subcellular flow patterns of growth cones strongly resemble the leading edge of migrating cells and the polar regions of dividing cells, our working hypothesis is that axonal elongation utilizes the same physical mechanisms that drive cell crawling and cell division. As a test of that hypothesis, here we take experimental data sets of sub-cellular flow patterns in cells undergoing cytokinesis, mesenchymal migration, amoeboid migration, neuronal migration, and axonal elongation. We then apply active fluid theory to develop a biophysical model that describes the different sub-cellular flow profiles across these forms of motility and how this generates cell motility under low Reynolds numbers. The modeling suggests that mechanisms for generating motion are shared across these processes, and differences arise through modifications of sub-cellular adhesion patterns and the profiles of internal force generation. Collectively, this work suggests that ameboid and mesenchymal cell crawling may have arisen from processes that first developed to support cell division, that growth cone motility and cell crawling are closely related, and that neuronal migration and axonal elongation are fundamentally similar, differing primarily in the motion and strength of adhesion under the cell body.