Today we cover oscillations emerging with zero frequency in the Morris-Lecar model as well as another form of bi- and tri-stability, which can occur in the Morris-Lecar model as we make the kinetics of the potassium current faster.

Here are two sets of original data that I recorded in my lab on Friday November 4, 2005. I recorded these two cells separately and I applied current (i.e., I_app) to cause the emergence of spiking (i.e., limit cycle oscillations). In one example I raised I_app and then lowered it back down until spiking ceased. In the other I simply kept increasing I_app.

I have saved the data in ascii text format (3 columns of text data), where column 1 contains time (in ms), column 2 contains voltage (in mV), and column 3 contains I_app (in pA). The columns are separated by blank spaces. Any plotting/graphing program will be able in import these data. Here are the two sets: Data_A and Data_B.

Your assignment is to download these data, load them into your favorite graphing/plotting program, and then analyze the data, and thus come up with an explanation (for each dataset) as to which mechanism gives rise to oscillations: either the Hopf bifurcation or the saddle-node-on-an-invariant-circle (SNIC) bifurcation. Explain and justify your analysis using arguments about oscillatory frequency, evidence for/against bistability, and in both cases draw (or plot) a bifurcation diagram to accompany your written explanation. You must hand in a plot of the original data in a time series format, i.e., plot V_m and I_app vs time.