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

¹ Michigan State University

^* To whom correspondence should be addressed. E-mail: kmiller{at}msu.edu.

Submitted on July 18, 2007
Revised on August 14, 2007
Accepted on 4 December 2007

	Abstract

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, 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 (3.6 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.

Key Words: axonal transport, cytoskeleton, friction, substrate, tension, viscosity