The resistor-capacitor network model we developed in Lecture (see figure below where it is shown only for the myelinated case) for the transmission of signals in nerve axons can actually be applied to both unmyelinated and myelinated nerve cells to estimate the propagation speed of a nerve impulse. In the unmyelinated case the 6-7 nm thick plasma membrane (the lipid bilayer) acts both as a (very thin) dielectric layer forming a capacitor between the inside of the axon and the outside, and as an insulating (high resistance) boundary between the inside and outside of the axon. The myelination does the same thing but now the dielectric/insulating layer layer is MUCH thicker, typically 2 um instead of 6 nm. Unmyelinated AX Plasma membrane - high resistivity, but thin Axoplasm: conducting medium Myelinated Axoplasm resistance V(t) 3 Membrane (myelin) resistance Membrane (myelin) capacitance Consider a single short segment of a nerve axon of length Ax, as shown below, where the outer cylindrical insulating layer can be either the plasma membrane of an unmyelinated fiber or the combination of the plasma membrane plus myelin layer for the myelinated case. AX AX K, Pm K, Pm Ra a a Ra Pa Pa Cm- 3Rm's m 7 Rm Myelinated Unmyelinated(a) Take the axon to be a cylinder of radius a with electrical resistivity pa (i.e. think of it as a long cylindrical resistor) calculate the resistance Ha for currents traveling along a length A15 of the axon. Note that since pa is much less than the membrane (or myelin) resistivity pm (see below)1 you can assume for this calculation that the current stays inside the axon. (1.)) Calculate the capacitance Cm of the segment between the interior of the axon (axoplasm) and the conducting medium outside the nerve cell. The insulating layer has dielectric con- stant a. You may consider the thicknt'rss of the insulating layt'3r to be thinner than the radius of the axon. i.e.. t