Mechanical Properties of Axons

The mechanical response of PC12 neurites under tension is investigated using a microneedle technique. Elastic response, viscoelastic relaxation, and active contraction are observed. The mechanical model proposed by Dennerll et al. [J. Cell Biol. 109, 3073 (1989).], which involves three mechanical devices—a stiff spring $\kappa$ coupled with a Voigt element that includes a less stiff spring $k$ and a dashpot $\gamma$—has been improved by adding a new element to describe the main features of the contraction of axons. This element, which represents the action of molecular motors, acts in parallel with viscous forces defining a global tension response of axons $T$ against elongation rates ${\dot{\delta }}_k$. Under certain conditions, axons show a transition from a viscoelastic elongation to active contraction, suggesting the presence of a negative elongation rate sensitivity in the curve $T$ vs ${\dot{\delta }}_k$.

Figure 1

(a) An axon with the needle in contact (bright spot). (b) Initial deformation caused by moving the motor at $25\mu \mathrm{m}/\mathrm{s}$ for 1 s [with the negative of image (a) added as reference]. (c) Subsequent evolution of the axon needle.

Figure 2

(a) The axon and needle deflections and involved variables for an elastic deformation. (b) Variables for a viscoelastic mechanical response. (c) Classical model for axons proposed in Ref. 8. (d) Model including motors action.

Figure 3

(a) Force experienced by different axons as a function of $\theta$ during deformations at $25\mu \mathrm{m}/\mathrm{s}$ for 1 s. The slope at $\theta =0$ relates to $T_0$ and the nonlinear term in $\theta$ to $\kappa$. (b) $\kappa$ for different neurites shows a roughly linear trend with $A/L_x$.

Figure 4

(a) Viscoelastic relaxation that follows the initial elastic response in different neurites. The relaxation times are about 10 s. (b) Active behavior which results in a transition from a fast viscoelastic elongation to a slow contraction is observed in some cases. (c) $\gamma$ as a function of cross-sectional area. (d) Schematic of the viscous and motor responses of an axon as a function of the ${\dot{\delta }}_k$. (e) In order to measure $\gamma$, ${\dot{\delta }}_k>v$. Thus, the initial slope of the $\delta l\mathrm{\text{−}}t$ curve depends only on $\gamma$ and the external force. (f) The elastic energy stored in the spring $k_{\mathrm{mot}}$ is dissipated when motors detach from the filaments.

Figure 5

Phase diagram defined by $\gamma$ and $T_a/v$, passive (○) or active (□) behavior. Insets: active force plus viscous drag.