Neuro 317 Methods in Computational Neurobiology
Univ. of Illinois, Urbana-Champaign
Prof. Mark Nelson

Homework 4 - Problem 1

1. In this problem you will simulate conductance changes at a single synapse, in response to a train of uniformly spaced input spikes. The conductance change is described by:
equations

The impulse response is the alpha function:

alpha function

Write a MATLAB program that uses the two first-order differential equations to simulate conductance changes in response to a train of uniformly spaced  input spikes. Model the spike input as:

spike input representation

(a) Simulate the following four cases and turn in plots of conductance vs. time.
Use Tmax = 500 msec, dt =1 msec, and gpeak=0.1 uS.

input spike interval (ms)
synaptic time constant (ms)
50
10
50
50
10
10
10
50

Your output should look similar to the following graph.

 
EXTRA CREDIT:
(b) Demonstrate mathematically that the two first-order differential equations are equivalent to the single second-order differential equation at the top of the page.

(c) Demonstrate mathematically that the peak of the alpha function occurs when t = tau. (HINT: show that the first derivative goes to zero and that the second derivative is negative at that point.)

  Matlab graph

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