Univ. of Illinois, Urbana-Champaign

Prof. Mark Nelson

2. Now we're going to simulate the response of the squid giant axon to a step current injection. The HH model for the squid giant axon is described by the following set of equations:

with the following parameter values:

Use the six subroutines from HW #3.1 above when evaluating the rate constants. Initialize the HH state variables at v=Vrest before starting the main simulation loop. Use Euler integration with an integration time step of 0.025 msec (Note: deltaT is a factor of 40 smaller than we used in our integrate-and-fire simulations in HW #2. This is necessary for numerical stability - more on this topic in the next homework assignment.) The structure of your simulation code should be something like the following:

initialize v to V_{rest.}

initialize m, n, &
h to their steady-state values at V_{rest.}

LOOP:

compute injection current for this time step.

get values of v, m, n, & h from previous time step.

use these values to compute
g_{Na}, g_{K}, dm/dt, dn/dt,

dh/dt, and dv/dt according to the ODEs given above.

update m, n, h, and v using the Euler method.

END LOOP

generate plots

(b) Now simulate the response to
strong depolarizing (I = +10.0 µA/cm2) and hyperpolarizing
(I = -10.0 µA/cm2) current pulses. Use a 25 msec
pulse duration (5 < t <= 30), and simulate 50 msec of the response
(0 < t <= 50). *What do you think causes the action potential at
the end of the hyperpolarizing pulse?*

Turn in your MATLAB code and response plots.