## Homework 2 - Problem 1 Solution:

MATLAB SCRIPT: hw2p1.m ### Answer to question in part (b):

What is the minimum current that results in spike generation?

In this model, the minimum current injection level for spike generation is 0.5 nA. This value can be calculated by recalling that for constant current injection I, the steady-state voltage V_ss of the RC circuit is I*R. Spike generation occurs when V_ss >= V_thr, thus the threshold current is
I_thr = V_thr/R = (5 mV)/(10 MOhm) = 0.5 nA.

Why does the firing rate saturate for large currents?

In the model, the maximum firing rate is determined by the minimum number of integration time steps required to generate a spike, reset the voltage to zero following the spike, and prepare to generate the next spike. In this particular implementation, the minimal cycle time is two time steps (one to integrate & fire, one to reset). With an integration time step of 1 msec this implies that the minimum interval between spikes is 2 msec -- thus the maximal firing rate is 1/(.002 sec) = 500 Hz. If one changed the integration time step DT to a different value in this model, the maximal firing rate would also change. One enhancement to this simple integrate-and-fire model would be to add an explicit refractory period to limit the peak firing rate to a predetermined value (e.g., an absolute refractory period of 10 msec would limit the maximum firing rate to 100 Hz.) HOMEWORK home page