## Explain the difference between activation and inactivation gate. Include a sketch as appropriate.

### computer science

##### Description

1. Explain the difference between activation and inactivation gate. Include a sketch as appropriate.

2. Define the leak current and explain the origin of its name.

3. Sketch the kinetic model of the delayed-rectified potassium channel studied in class. Make sure to label appropriately the transition rates and to define the quantities in the sketch.

4. An ion channel comprises 5 independent subunits, 3 activation gates and 2 inactivation gates. How many gates must be open for the channel to be open? Explain.

5. Sketch the equivalent circuit of the Hodgkin-Huxley model. Make sure to label correctly every element of the circuit and write down the corresponding differential equation for the membrane potential V .

6. Is the Hodgkin-Huxley model a deterministic or stochastic model? Explain.

7. Describe all relevant phases of an action potential. 8. What is the order of magnitude of the range of change in membrane voltage during an action potential?

9. True or false: “the ion pumps are responsible for the repolarization of the membrane after an action potential”. Justify your answer.

10. Describe the boundary conditions for the leaky integrate-and-fire (LIF) neuron model and explain why boundary conditions are required in this model.

11. Does the LIF model neuron have a threshold for spike emission? Is this threshold un unstable equilibrium of the membrane potential dynamics?

12. Describe the type of bifurcation taking place in the quadratic integrate-and-fire model neuron.

13. We have seen that the QIF model neuron can generate the upstroke of a spike but not its downstroke. Is it possible to write down a more complex 1D non-linear ODE that generates both the upstroke and the downstroke of the action potential? Why or why not?

14. Is the f − I curve of the LIF neuron continuous or discontinuous at the rheobase current? Can you think of a way in which your answer could be linked to a bifurcation at rheobase in this model? (Hint: how does the input current modify the V˙ − V plot of this model? Include the boundary conditions.)