Transcript Slide 1

Post-Synaptic
Potentials
1. Membrane Resistance
2. Membrane Capacitance
3. Internal (axial) Resistance
Rin = Rm/4πa2
Where Rm is specific membrane resistance in Ω cm2 and a
is the radius of the neuron.
Cin = Cm(4πa)2
Where Cm is specific membrane resistance (~1uF/cm2) and a
is the radius of the neuron.
Time constant (Ƭ)
ΔVm(t) = ImRin(1 – e-t/ Ƭ)
Let t = Ƭ, then
ΔVm(t) = ImRin(1 – e-1)
= ImRin(1-1/e)
= ImRin(1-.37)
= ImRin(.63)
Note that the time
constant of the
membrane is a function
of both membrane
resistance and
membrane capacitance
Assume all resistors in the above circuit diagram are 10Ω.
Resistances in SERIES summate, so the axial resistance
between the two arrows is 10 + 10 + 10 +10 + 10 = 50Ω.
Recall that conductance is the reciprocal of resistance, so the
conductance of each resistor is 0.1.
Conductances in PARALLEL summate, so the total
membrane resistance is the reciprocal of the sum of the
conductances, or 1 /(.1 + .1 + .1 + .1 + .1 + .1) = 1/.6 = 1.67Ω
Length Constants
A length constant (λ) = rm/ra
where rm and ra are membrane and axial resistances of a 1cm length of a neural process
Axial resistance: ra = ρ/πa2
where ρ is the specific resistance of the cytoplasm
Membrane resistance: rm = Rm/2πa
So, λ =
Rm/2πa =
ρ/πa2
Rm
ρ
x
a
2
ΔV(x) = ΔV0e-x/λ
Let x = λ, then
ΔV(x) = ΔV0e-1
=ΔV0(.37)
Note that the length
constant does not have
a capacitive component.
That is, it is a steady-state
property of the membrane