# Threshold

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.

And the homework due Wednesday night.

Today's Lab is the Threshold Tutorial.

• Homework: Go through the threshold tutorial, put three observations into PowerPoint and send to me.

## Next Week

I will introduce the code that we will use for the project. The homework assigned next Tuesday will be part "getting acquainted" with the code and part "review" of the tutorials.