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

## Homework 2 - Problem 1

 1. Transform your RC model from HW #1.2 into an integrate-and-fire (IAF) neuron model by adding a voltage threshold. Whenever the voltage crosses the threshold, set the voltage on that time step to +70 mV to represent the generation of an action potential, and then reset the voltage to 0 mV on the next time step to represent the repolarization phase of the action potential.

 (a) Using the following parameters: R=10 MOhm, C=1 nF, Vthr=5 mV, Vspk=70 mV, and a time step of 1 ms, simulate the response of the integrate-and-fire model using Euler integration. Generate a representative plot of the membrane voltage as a function of time for a step current injection with I=1 nA for 10 <= t < 60 ms and I=0 otherwise. Your graph should look similar to the attached plot.

 (b) Now examine the behavior of this model as you change the magnitude of the injection current. Compute a firing rate (spikes per second) by dividing the number of spikes by the duration of the stimulus. Generate a plot of "firing frequency vs. injected current" for currents from 0 to 10 nA. You'll need to determine a set of current injection values to use (make the spacing fine enough to map out the threshold transition). For each injection level, have your program count the number of spikes in a 1-second window to determine the firing rate (spikes/s). Your graph should look similar to the attached plot. What is the minimum current that results in spike generation? Why does the firing rate saturate for large injection currents?

VIEW SOLUTION

 (c) EXTRA CREDIT: Repeat part (b), but now add random gaussian noise to the injected current. Use Inoise=2*randn(size(t)) to generate a vector of noise values with a standard deviation of 2 nA. Graphically overlay a plot of firing-frequency versus injected-current on top of the noise-free case (use a different linestyle). With 2 nA of noise, what is the minimum current that results in spike generation? VIEW SOLUTION