(Not a specialist here) Several questions touch the voltage propagation along an unmyelinated axon, but I'd like to focus on the following.

How fast does the voltage of a sub-threshold perturbation propagate? More specifically, as in the picture, consider two positions $x_0$ and $x_1$ along an unmyelinated axon. At time $t_0$, a current step is injected at $x_0$. My understanding is that, at every position $x$ the voltage will charge up with a characteristic time given by the (local) RC value, up to a value that will build, in space, an exponentially decaying profile, with characteristic length given by the resistances of the system.

At position $x_0$ the charging starts at time $t_0$, and at position $x_1$ it starts at time $t_1$.

How much is $t_1$? Is $t_1=t_0$, as suggested here, and probably by cable theory? Does the voltage propagate at, or close to, the speed of light? Doesn't diffusion of ions enter into the picture at all?

And, importantly, can you give me references where I can learn more about this aspect?

voltage along unmyelinated axon



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