Efficient simulations of tubulin-driven axonal growth

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites-axons and dendrites-to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Single-cell branching morphogenesis in the Drosophila trachea

The terminal cells of the tracheal epithelium in Drosophila melanogaster are one of the few known cell types that undergo subcellular morphogenesis to achieve a stable, branched shape. During the animal's larval stages, the cells repeatedly sprout new cytoplasmic processes. These grow very long, wrapping around target tissues to which the terminal cells adhere, and are hollowed by a gas-filled subcellular tube for oxygen delivery. Our understanding of this ramification process remains rudimentary. This review aims to provide a comprehensive summary of studies on terminal cells to date, and attempts to extrapolate how terminal branches might be formed based on the known genetic and molecular components. Next to this cell-intrinsic branching mechanism, we examine the extrinsic regulation of terminal branching by the target tissue and the animal's environment. Finally, we assess the degree of similarity between the patterns established by the branching programs of terminal cells and other branched cells and tissues from a mathematical and conceptual point of view.