Standard models

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) = I₀ + 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, I₀ such that the membrane has both a stable rest state and a stable oscillation. Try I₀ 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.