Cable Theory Lecture

how long a signal decays is given by

cable theory

Cable theory equation

lamina

space constant

tau

time constant

to see how voltage changes over the course of the time is given by

what happens as we move lamina on a current clamp

as we increase lamine our initial voltage decreases by a factor of e. This occurs in a bidrectional fashion across the axon

ri

axial resistance (ohm/cm)

rm

membrane resistance (ohm times cm)

Cm

membrane capacitance (F/cm²)

assumptions in cable theory

membrane parameters, ri, rm, and cm are linear and uniform and constant on all parts of the neuron and are not dependent on membrane potential

ro= 0

passive properties

leak channels

active properities

voltage channels

length constant is

square root of rm/ ri

increase of rm

increases length constant, and voltage travels farther

increase in ri

length constant decreases and voltage doesnt travel as far

R input in an axon

sqrt rm ri / 2

rm

ri

the resistance of an axon can also be given in terms of resistivity

true

what is resistivity

explains how strong things opposes an electric current

membrane resistance in terms of resistivity

rm= Rm/C = Rm/2pia

rm large axon vs rm small axon

rm (large axon) < rm (small axon)

more area= more charge carriers= more conductance = lower resistance

space constant as a function of geometry

uses the resistivities instead

rm in terms of geometry

ri in terms of geometry

bigger radius

voltage decays less

smaller radius

voltage decays more

tau is defined where

when lamina is equal to 1

how does tau change at different points in the axon

it’s one space constant away

time constant is

independent of axon diameter

action potential propagation

dependent on length constant and time constant

length constant

greater is equal to faster velocity

time constant

smaller time constant= faster velocity

length constant is the

only variable that increases with axon diameter

the time constant remains constant!!

myelination

oligodendrocytes and schwann

schwann

PNS

oligodendrocytes

CNS

tau , Ri, and myleination

Ri does not change but Tau does because of Cm. There is a reduction in Cm

lower Cm

lower charge or lower capacitance

does Rm change in myelination

no

myelination and AP

time constant= has a large decrease

space constant= small increase