Branching Morphogenesis: Exploring the Scaling Law and its Underlying Molecular Determinants

Dendrites, which serve as the antennae of neurons, are often highly branched so they can receive a large number of synaptic inputs, thereby supporting the high connectivity in the nervous system. The systematic narrowing of diameters in branched networks has tantalized physiologists and physicists since the discovery of da Vinci’s rule for trees: the sum of the cross-sectional areas of the daughter branches equals that of the mother branch. This can be written as d_1^p + d_2^p = d_m^p where d is the diameter and the exponent p = 2. In neurons, a scaling law with exponent 3/2, termed Rall's law, was proposed for diameter decrements in axons and dendrites. The challenge is that the finest dendritic processes are often beyond the diffraction limit and cannot be resolved using conventional approaches. I will describe recent progress in technology development and a new scaling law that was discovered due to the technical breakthrough. To gain mechanistic insight into the new scaling law, I combined multidisciplinary approaches including advanced imaging techniques and neurobiology for dissecting the molecular determinants underlying the scaling law. I will conclude by briefly discussing new opportunities and insights generated from this emergent field in biomedical engineering, physics, and neuroscience.