Difference between revisions of "Threshold"

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(New page: Tuesdays lecture has been postponed for today due to a projector malfunction. == Equilibrium Potentials == Recall the equation for the membrane potential in the Hodgkin-Huxley model: <m...)
 
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Tuesdays lecture has been postponed for today due to a projector malfunction.
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Tuesday's lecture has been postponed for today due to a projector malfunction.
  
 
== Equilibrium Potentials ==
 
== Equilibrium Potentials ==

Revision as of 18:52, 19 February 2009

Tuesday's lecture has been postponed for today due to a projector malfunction.

Equilibrium Potentials

Recall the equation for the membrane potential in the Hodgkin-Huxley model:

C \frac{dV}{dt} = I(t) - g_L (V(t) - E_L) - g_{Na} m^3(t) h(t) (V(t) - E_{Na}) - g_K n^4(t) (V(t) - E_K)

You can find the equilibrium potential for given channel conductances. Set the injected current to zero I = 0. Then fix and absorb the gating variables and maximal conductances (g_L, g_{Na}, g_{K}) into single conductance variables (G_L, G_{Na}, G_{K}) .

For example

G_{K} = g_K n^4

Then the differential equation for the membrane is

C \frac{dV}{dt} = - G_L (V - E_L) - G_{Na} (V - E_{Na}) - G_K (V - E_K)

The equilibrium potential is the value of V such that \frac{dV}{dt} is zero. You can plug in \frac{dV}{dt} = 0 and solve for V_{equilibrium}.

V_{equilibrium} = \frac{G_L E_L + G_{Na} E_{Na} + G_K E_K}{G_L + G_{Na} + G_K}

The equilibrium potential is the weighted average of the reversal potentials -- weighted by the corresponding conductances. Note that the weights add to one.

Now we can talk about the homework due Monday night.

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