Modeling mitochondrial dynamics during in vivo axonal elongation.

Many models of axonal elongation are based on the assumption that the rate of lengthening is driven by the production of cellular materials in the soma. These models make specific predictions about transport and concentration gradients of proteins both over time and along the length of the axon. In vivo, it is well accepted that for a particular neuron the length and rate of growth are controlled by the body size and rate of growth of the animal. In terms of modeling axonal elongation this radically changes the relationships between key variables. It raises fundamental questions. For example, during in vivo lengthening is the production of material constant or does it change over time? What is the density profile of material along the nerve during in vivo elongation? Does density change over time or vary along the nerve? To answer these questions we measured the length, mitochondrial density, and estimated the half-life of mitochondria in the axons of the medial segmental nerves of 1st, 2nd, and 3rd instar Drosophila larvae. The nerves were found to linearly increase in length at an average rate of 9.24 microm h(-1) over the 96 h period of larval life. Further, mitochondrial density increases over this period at an average rate of 4.49x10(-3) (mitochondria microm(-1))h(-1). Mitochondria in the nerves had a half-life of 35.2h. To account for the distribution of the mitochondria we observe, we derived a mathematical model which suggests that cellular production of mitochondria increases quadratically over time and that a homeostatic mechanism maintains a constant density of mitochondria along the nerve. These data suggest a complex relationship between axonal length and mass production and that the neuron may have an "axonal length sensor."