Whether the axonal framework is stationary or moves is a central debate in cell biology. To better understand this problem, we developed a mathematical model that incorporates force generation at the growth cone, the viscoelastic properties of the axon, and adhesions between the axon and substrate. Using force-calibrated needles to apply and measure forces at the growth cone, we used docked mitochondria as markers to monitor movement of the axonal framework. We found coherent axonal transport that decreased away from the growth cone. Based on the velocity profiles of movement and the force applied at the growth cone, and by varying the attachment of the axonal shaft to the coverslip, we estimate values for the axial viscosity of the axon (3 x 10(6) +/- 2.4 x 10(6) Pa.s) and the friction coefficient for laminin/polyornithine-based adhesions along the axon (9.6 x 10(3) +/- 7.5 x 10(3) Pa.s). Our model suggests that whether axons elongate by tip growth or stretching depends on the level of force generation at the growth cone, the viscosity of the axon, and the level of adhesions along the axon.

Forces are important for neuronal outgrowth during the initial wiring of the nervous system and after trauma, yet subcellular force generation over the microtubule-rich region at the rear of the growth cone and along the axon has never, to our knowledge, been directly measured. Because previous studies have indicated microtubule polymerization and the microtubule-associated proteins Kinesin-1 and dynein all generate forces that push microtubules forward, a major question is whether the net forces in these regions are contractile or expansive. A challenge in addressing this is that measuring local subcellular force generation is difficult. Here we develop an analytical mathematical model that describes the relationship between unequal subcellular forces arranged in series within the neuron and the net overall tension measured externally. Using force-calibrated towing needles to measure and apply forces, in combination with docked mitochondria to monitor subcellular strain, we then directly measure force generation over the rear of the growth cone and along the axon of chick sensory neurons. We find the rear of the growth cone generates 2.0 nN of contractile force, the axon generates 0.6 nN of contractile force, and that the net overall tension generated by the neuron is 1.3 nN. This work suggests that the forward bulk flow of the cytoskeletal framework that occurs during axonal elongation and growth-cone pauses arises because strong contractile forces in the rear of the growth cone pull material forward.

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Axonal stretching is linked to rapid rates of axonal elongation. Yet the impact of stretching on elongation and slow axonal transport is unclear. Here, we develop a mathematical model of slow axonal transport that incorporates the rate of axonal elongation, protein half-life, protein density, adhesion strength, and axonal viscosity to quantify the effects of axonal stretching. We find that under conditions where the axon (or nerve) is free of a substrate and lengthens at rapid rates (>4 mm day⁻¹), stretching can account for almost 50% of total anterograde axonal transport. These results suggest that it is possible to accelerate elongation and transport simultaneously by increasing either the axon's susceptibility to stretching or the forces that induce stretching. To our knowledge, this work is the first to incorporate the effects of stretching in a model of slow axonal transport. It has relevance to our understanding of neurite outgrowth during development and peripheral nerve regeneration after trauma, and hence to the development of treatments for spinal cord injury.

BackgroundAs we age, the speed of axonal regeneration declines. At the biophysical level, why this occurs is not well understood.ResultsTo investigate we first measured the rate of axonal elongation of sensory neurons cultured from neonatal and adult rats. We found that neonatal axons grew 40% faster than adult axons (11.5 µm/hour vs. 8.2 µm/hour). To determine how the mechanical properties of axons change during maturation, we used force calibrated towing needles to measure the viscosity (stiffness) and strength of substrate adhesion of neonatal and adult sensory axons. We found no significant difference in the strength of adhesions, but did find that adult axons were 3 times intrinsically stiffer than neonatal axons.ConclusionsTaken together, our results suggest decreasing axonal stiffness may be part of an effective strategy to accelerate the regeneration of axons in the adult peripheral nervous system.

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