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. 2017 Jan 18;6:e20172. doi: 10.7554/eLife.20172

Figure 4. Simulation of axon shape with varying mechanical properties.

(A) Representative images derived from simulations based on a discrete elastic rod or DER model (Methods, Appendix) using the following parameters: B = 5⋅10−24 N m2, G = 1.35 kPa and the value of for tension as indicated in each panel. In this example, tension decreases from top to bottom: (i) Stiff and twisted neuron remains straight. (ii) A slight decrease in tension causes local bends and spiraling. (iii) Further reduction in tension leads to the transfer of torsional energy into bending of the rod and the formation of local coils. (iv) Further reduction in tension causes the coils in the model neuron to rotate, leading to plectonemes spaced at regular intervals. (B) Parameter space plot of a simulated neuron subjected to low torque (top, shear modulus, G = 0.33 kPa) or higher torque (bottom G = 1.35 kPa) and varying axial stiffness and bending stiffness. For panels (B–D), vertex color shows the number of coils predicted for pair of values for tensile modulus and bending rigidity, according to the scale to the right of each plot. Gray areas indicate conditions with no coils; beige areas indicate conditions with at least one coil; green line indicates the boundary between the two shape phases. (C) Parameter space plot of a simulated neuron under low (top, 1 kPa) and high tension (bottom, 6 kPa) and varying shear modulus and bending stiffness. (D) Parameter space plot of a simulated neuron with low (top, 1.25⋅10−24 Nm2) and high bending stiffness (bottom, 7.5⋅10−24 Nm2) and varying shear and elastic moduli. Bending stiffness was calculated according to B=EI, with I as the second moment of inertia. (E) Comparison of the morphology of an TRN in ptl-1(ok621); unc-70(e524) double mutant animals with a simulation result of our DER model with the following parameters: bending stiffness = 7.5⋅10−24 Nm2; shear modulus = 8 kPa; axial stiffness = 1 kPa. Scale = 10 µm.

DOI: http://dx.doi.org/10.7554/eLife.20172.024

Figure 4.

Figure 4—figure supplement 1. Atomic force microscopy on axons of isolated TRNs.

Figure 4—figure supplement 1.

(A) Schematic representation of the atomic force microscopy assay and contact geometry, following Puttok and Thwaite (Puttock and Thwaite, 1969). (B) Indentation was modeled as a sphere-cylinder contact, with a 60 nm nominal tip diameter of the conical indenter and 100 nm radius for the TRN as determined from TEM images. (C) Representative AFM force-indentation curve taken on TRN axon in vitro. TRNs were identified in the mixed cultures by the expression of GFP. The thick line is a fit of the data with a Hertz contact model of a sphere and a cylinder.
DOI: http://dx.doi.org/10.7554/eLife.20172.025
Figure 4—figure supplement 2. Elastic moduli of axons of touch receptor neurons in vitro.

Figure 4—figure supplement 2.

(A) Elastic (Young’s) modulus for control neurons, neurons treated with 1 µM of the actin depolymerizing drug Latrunculin A, and unc-70(e524) mutant neurons. (B) Elastic (Young’s) modulus for control neurons, ptl-1(ok621), mec-7(wy116) and unc-70(e524);ptl-1(ok621) double mutant neurons. Numbers on each bar indicate the number of axons tested for each genotype or condition.
DOI: http://dx.doi.org/10.7554/eLife.20172.026
Figure 4—figure supplement 3. The distance between plectonemes in mutant and simulated axons.

Figure 4—figure supplement 3.

Plectoneme spacing in ptl-1(ok621);unc-70(e524) double mutants (n = 13 animals and 121 plectonemes) and DER simulations with the following parameters: G = 2333 Pa, k = 1 kPa and B = 7.5∙10−24 N m2.
DOI: http://dx.doi.org/10.7554/eLife.20172.027