Modeling of the axon membrane skeleton structure and implications for its mechanical properties

<div><p>Super-resolution microscopy recently revealed that, unlike the soma and dendrites, the axon membrane skeleton is structured as a series of actin rings connected by spectrin filaments that are held under tension. Currently, the structure-function relationship of the axonal structure is unclear. Here, we used atomic force microscopy (AFM) to show that the stiffness of the axon plasma membrane is significantly higher than the stiffnesses of dendrites and somata. To examine whether the structure of the axon plasma membrane determines its overall stiffness, we introduced a coarse-grain molecular dynamics model of the axon membrane skeleton that reproduces the structure identified by super-resolution microscopy. Our proposed computational model accurately simulates the median value of the Young’s modulus of the axon plasma membrane determined by atomic force microscopy. It also predicts that because the spectrin filaments are under entropic tension, the thermal random motion of the voltage-gated sodium channels (Na_v), which are bound to ankyrin particles, a critical axonal protein, is reduced compared to the thermal motion when spectrin filaments are held at equilibrium. Lastly, our model predicts that because spectrin filaments are under tension, any axonal injuries that lacerate spectrin filaments will likely lead to a permanent disruption of the membrane skeleton due to the inability of spectrin filaments to spontaneously form their initial under-tension configuration.</p></div

Young's moduli of rat hippocampal neuronal subcompartments determined by AFM.

<p>Histograms of Young’s moduli of rat hippocampal (A) soma, (B) dendrites, (C) axons, and (D) axons treated with 20μm Latrunculin B. The median Young's modulus of the soma is 0.7 ± 0.2 <i>kPa</i> (A), of dendrites is 2.5 ± 0.7 <i>kPa</i> (B). For the axon plasma membrane, the median Young’s modulus is 4.6 ± 1.5 <i>kPa</i> (C). When axons were treated with Latrunculin B (20μm, 1 hour) the median value of the axon plasma membrane Young’s modulus was reduced to 2.2 ± 0.6 <i>kPa</i>. Number of samples (N = 2), total number of tested neurons (n = 8). N = 1 and n = 6 for axon + Latrunculin B. (E) Box-whisker plots of mean Young's moduli of the soma, dendrites, axon, and axon treated with Latrunculin B. *** indicates statistical significance of <i>p</i> < 0.001 (Kruskal-Wallis test).</p

Axon membrane skeleton model.

<p>(A) Illustration of the axon membrane skeleton based on super-resolution microscopy results [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005407#pcbi.1005407.ref003" target="_blank">3</a>] exhibiting actin rings connected by spectrin tetramers. Ankyrin associated Na_v channels anchor the lipid bilayer to the membrane skeleton. Adducin has also been observed to colocalize with the actin rings possibly capping actin filaments. (B) A coarse-grain membrane skeleton dynamics model comprising representation of actin rings, spectrin filaments, and ankyrin. The insert shows the dimensions of the considered particles. (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005407#pcbi.1005407.s003" target="_blank">S2 Fig</a>)</p

Laceration of spectrin filaments.

<p>(A) Axon membrane skeleton with severed spectrin filaments in the marked area between two consecutive rings. (B) None of the severed spectrin filaments (blue color) were reconnected to their initial junction points.</p

Membrane skeleton dynamics simulations.

<p>(A) The membrane skeleton was equilibrated at a distance of approximately 185 <i>nm</i> between actin rings while the trajectory of ankyrin particles (insert) was recorded for 10×10⁶ time steps every 10⁵ time steps. (B) The skeleton was equilibrated at a distance of approximately 110 <i>nm</i> between actin rings while the trajectory of ankyrin particles (insert) was recorded for 10×10⁶ 10⁵ time steps. (C, D) Normalized probability distribution of the ratio <i>d</i>(<i>z</i>)/<i>L</i>_<i>c</i>, where <i>d</i>(<i>z</i>) is the deviation of an ankyrin point from its mean position during its thermal motion along the z-direction and <i>L</i>_<i>c</i> is the mean distance between two consecutive ankyrin points along the z-direction when the spectrin is under tension <i>L</i>_<i>c</i> = 185.78 <i>nm</i> (C) and when the spectrin is almost at equilibrium <i>L</i>_<i>c</i> = 112.32 <i>nm</i> (D). The longitudinal and circumferential separations of the trajectories of neighboring ankyrin particles, and consequently of the corresponding Na_v channels, are well-defined in (A) but not in (B).</p