A model for stretch growth of neurons

In the first phase of axon growth, axons sprout from neuron bodies and are extended by the pull of the migrating growth cones towards their targets. Thereafter, once the target is reached, a lesser known second phase of axon growth ensues as the mechanical forces from the growth of the animal induce extension of the integrated axons in the process of forming tracts and nerves. Although there are several microscopic physics based models of the first phase of axon growth, to date, there are no models of the very different second phase. Here we propose a mathematical model for stretch growth of axon tracts in which the rate of production of proteins required for growth is dependent on the membrane tension. We assume that growth occurs all along the axon, and are able to predict the increase in axon cross-sectional area after they are rapidly stretched and held at a constant length for several hours. We show that there is a length dependent maximum stretching rate that an axon can sustain without disconnection in steady state when the axon length is primarily increased near the cell body. Our results could inform better design of stretch growth protocols to create transplantable axon tracts to repair the nervous system.