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: The impulse response is the 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: (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.)  HOMEWORK home page