Week 1.4 - Biophysical Neuronal Models

Question 1

What does this equation represent?

Answer 1

This is the Nernst equation. It describes the equilibrium potential of a single ion type. (e.g. Na+, K+)

Remember that the [square brackets] represent concentration and R, T, z and F are all constants

Question 2

What do we mean by stating that the cell membrane is

“Semi-permeable”

Answer 2

It means that not everything can pass or diffuse across the lipid membrane.

That is why there are channel proteins embedded in the cell.

Question 3

Nature likes to be in balance, or equilibrium. What are the 2 factors that determine how fast V returns to V_rest?

Answer 3

Membrane capacitance (C_m)

& Leak Resistance (R_leak)

_{Their product is tau, which is the time it takes for an ion channel to open.}

Question 4

What are leak channels?

Answer 4

Leak channels are passive ion channels. They randomly open and close.

Question 5

What is conductance? And how is it related to resistance?

Answer 5

Conductance (g) expresses how easy it is for the ions to flow through the cell membrane.

It is the reciprocal of resistance. That is,

g = 1/R

Question 6

How can we model the process of V tending to V_rest ?

Answer 6

With an ordinary differential equation

Question 7

What is the driving force when a cell is at equilibrium?

Answer 7

0

( V = Vrest )

Question 8

What do gating variables represent? And how?

Answer 8

The state of an active ion channel. They express the proportion of open and closed channel at a point in time.

So they have values between [0,1].

Question 9

The conductance of an ion type is a function of …

Answer 9

Its maximum conductance and respective gating variables.

For example for Na+ we have;

Question 10

What does this remind you of?

(Hint: giant squid axon)

Answer 10

Hodgkin and Huxley where the first to mathematically formulate action potentials and its mechanics.

This lead to the establishment of the field of Computational Neuroscience, and their model is one of the most accepted ones in the field.

Question 11

Why does capacitance (C_m ) affect the rate of change of membrane potential (V)?

Answer 11

Recall that the definition of capacitance is how well the membrane can store charge. As the capacitance increases, more current is stored in the membrane and thus taken out of the circuit.

You can think of it as friction in Physics.