Figure 8. Stimuli on the channels due to a step.

(A) Indentation profile for a step stimulus. (B) The diagonal components of the strain tensor ${\epsilon }_{i\mathrm{}j}$vs the longitudinal position along the cylinder. The overlap of those components (color) and the eigenvalues of ${\epsilon }_{i\mathrm{}j}$ (black) show that the tensor is essentially diagonal, which leads to the conservation of angles under deformation discussed in the main text. (C) The two components (green and blue curves) tangential to the neural membrane of the force acting upon on a channel (computed using Equations (5), (9)) for the stimulus in panel A. The panels refer to the different directions of the elastic filament (the first two are tangential and the third orthogonal to the neural membrane). (D) Gating probability for an individual symmetric or directional channel, as produced by the two tangential extensions in panel C. Parameters are: $y\mathrm{=}\mathrm{1}\mathrm{}\mu \mathrm{}m$, $\theta \mathrm{=}\mathrm{0}$, $\text{𝑣}\mathrm{=}\cos \mathrm{}\mathrm{(}\pi \mathrm{/}\mathrm{3}\mathrm{)}\mathrm{}{\widehat{\mathbf{𝐰}}}_{\mathrm{1}}\mathrm{-}\sin \mathrm{}\mathrm{(}\pi \mathrm{/}\mathrm{3}\mathrm{)}\mathrm{}{\widehat{\mathbf{𝐰}}}_{\mathrm{2}}$. The sketch on the right illustrates that directional channels respond only to stimuli properly aligned with respect to their preferential direction while symmetric channels respond isotropically.