## A zoo of models that were discussed in class

These are mostly XPP files, but you should be able to extract the
parameters if you want to try them in some other simulator or write
your own C code. Note that in some cases, Euler's method will ream you
pretty badly if you use it unless you use a real small step.
- The Morris-Lecar discussed in class
- The LIF model in MatLab
- The LIF model in XPP
- The LIF model with refractory period in XPP
- The Morris-Lecar equations with a fast
calcium channel and a delayed-rectifier. The simulation consists of a
current pulse on top of a fixed current:

i(t) = I_{0} + I_{p} Heav(t-t_{on})
Heav(t_{off}-t)

- The famed Hodgkin-Huxley equations with the
same sort of current protocol. Try eliciting anodal break excitation
by hyperpolarizing with a current of -5 muA/cm2 for 10 msec. Try a
step depolarizing current of 10 muA/cm2 for 50 msec. Find an applied
current,
** I**_{0} such that the membrane has both a
stable rest state and a stable oscillation. Try **I**_{0}
around 7 or 8 muA/cm2.
- The Connor-Stevens model which has an A-type
potassium current in addition to the usual potassium current. Here it
is set up so that it is strongly hyperpolarized to activate the
A-current and then a step current is applied to see the delay to
spiking. Does this model exhibit anodal break excitation? is it ever bistable?
- The Traub spiking model which has the same
channels as HH but with different kinetics so that it spikes very
quickly with short-lasting spikes. Verify that it can fire at
arbitrarily low firing rates and does not display anodal break
excitation. Show that it is not bistable.
- The Wang-Buszaki model for an inhibitory
interneuron. It is similar to the Traub neuron but not as stiff. It
has transient sodium, leak, and a delayed rectifier. The sodium
activation is treated as instantaneous.
- The Golomb-Amitai cortical neuron. This has
the usual fast spiking current as well as an M-type slow potassium
current for spike frequency adaptation, an A-type potassium current,
and a persistent sodium current. This is set up for 1 second of
simulation time with a 250 msec applied current step of 2
muA/cm2. This illustrates strong spike frequency adaptation. Note the
prolonged hyperpolarization.