Osmotically Driven Shape Transformations in Axons

We report a cylindrical-peristaltic shape transformation in axons exposed to a controlled osmotic perturbation. The peristaltic shape relaxes and the axon recovers its original geometry within minutes. We show that the shape instability depends critically on the swelling rate and that volume and membrane area regulation are responsible for the shape relaxation. We propose that volume regulation occurs via leakage of ions driven by elastic pressure, and analyze the peristaltic shape dynamics taking into account the internal structure of the axon. The results obtained provide a framework for understanding peristaltic shape dynamics in nerve fibers occurring in vivo.

Figure 1

(a) Osmotically induced shape instability in chick-embryo neurons. (b) Image sequence showing the growth and relaxation of the instability in a PC12 neurite.

Figure 2

Evolution of the normalized volume $\tilde{V}$ and area $\tilde{A}$ of a neurite with $R_0=0.5\mu \mathrm{m}$ at 33 °C. The ratio $\sqrt{\tilde{V}}/\tilde{A}$ (dotted line) reflects any deviations from the cylindrical geometry. The inset shows the volume and shape responses when the concentration is switched in the sequence ${\varphi }_0\stackrel{0\mathrm{s}}{\to }0.5{\varphi }_0\stackrel{370\mathrm{s}}{\to }{\varphi }_0$. The initial slow swelling is due to a nonsteplike change in concentration, as revealed by using an absorbing dye. Note: the shape remains cylindrical for the $0.5{\varphi }_0\to {\varphi }_0$ shock.

Figure 3

Comparison between volume evolutions obtained experimentally and from the analysis. (a) For ${\varphi }_0\to 0.7{\varphi }_0$ shock. $\tilde{K}=0.025{\Pi }^0$, $P_a=0.06{\Pi }^0$, ${\tau }_w=22\mathrm{s}$, and ${\tau }_{\mathrm{ion}}=70\mathrm{s}$ for 25 °C. $\tilde{K}=0.03{\Pi }^0$, $P_a=0.09{\Pi }^0$, ${\tau }_w=18\mathrm{s}$, and ${\tau }_{\mathrm{ion}}=60\mathrm{s}$ for 36° C. (b) For $0.5{\varphi }_0\to {\varphi }_0$, using $\tilde{K}=1.5{\Pi }^0$, $P_a=0$, ${\tau }_w=34\mathrm{s}$, and ${\tau }_{\mathrm{ion}}=24$. The neurite is densely filled with cytoskeleton and organelles that have to be compressed close to their “dead volume” for $V<V_0$, giving a higher effective value of $K$ for (b).

Figure 4

(a) Theoretical plot for the fastest growing wave number with tension and histogram of observed wave numbers. (b) Variation of $\lambda$ with $R_0$ at 25 °C for ${\varphi }_0\to 0.67{\varphi }_0$. The scatter in the data is due to natural variations between cells.