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A Physical Model of Axonal Elongation: Force, Viscosity, and Adhesions Govern the Mode of Outgrowth

Matthew O'Toole ^*, Phillip Lamoureux  and Kyle E. Miller 

^* Department of Mathematics and Department of Zoology, Michigan State University, East Lansing, Michigan

Correspondence: Address reprint requests to Kyle E. Miller, Dept. of Zoology, 336 Natural Sciences Bldg., Michigan State University, East Lansing, MI 48824-1115. Tel.: 517-353-9283; E-mail: kmiller{at}msu.edu.

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 10⁶ ± 2.4 x 10⁶ Pa·s) and the friction coefficient for laminin/polyornithine-based adhesions along the axon (9.6 x 10³ ± 7.5 x 10³ 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.