## 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.)

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