### Voltage dependent tau1 and tau2 in k3.mod

Strategy:
Start from the previous session and simultaneously fit the 109mV and 32mV curves allowing all four parameters governing the time constants to vary.

The completed exercise can be run by executing the k3taufit2.hoc file.

1) Start from your own previous session or start with the solution to the previous exercise: k3taufit1.hoc

2) Mark both "109" and "32" generators for use.

3) Pop up the parameter and domain panels and mark tk1 and tk2 for optimization (all four parameters marked) and give starting values for tk1 and tk2 different from 0 (e.g. 1)

I generally like to use log scaling since optimization often proceeds much faster. However in this case it is not clear whether tk1 and tk2 should be positive or negative. Actually, it is clear with a bit of thought. The overall time constant gets smaller as voltage increases. Although the fact that our model has two time constants somewhat muddies the waters. So start with unbounded limits for those parameters. When it is clear what sign they are, and if the fit is slow, we can restrict to that half of the number line and try log scaling. In the domain panel, double clicking on a parameter line pops up a string editor in which you enter three numbers separated by spaces. In our case enter:

    0 -1e6 1e6

The first number must be 1 or 0 and refers to log or linear scaling. The remaining two numbers are the low and high limits.

3) Pop up an Optimizer panel and optimize for a while. Press Stop if it does not seem to converge, enter a more reasonable starting value for any parameter that seems to be far out of range and restart.

4) If you are not using the best steady state values open the k3ssfit.ses file and optimize for the steady state (the default values in the k3.mod file are approximate versions of the best values). But remember that the steady state fit leaves v_init at 109 so use the RunControl panel to put it back to the default of 0 before doing time course fits.

5) Add a few more conductance curves to the multiple run fitter. (Use the Generators/CloneGenerator) You can get the data by loading hh508.hoc. Don't bother to optimize them all. Perhaps just add the "63mV" curve to the total error value. Each needs a phenomenological delay via the SEClamp[0].dur1 protocol constant if it is to be seriously fit. Just check the quality of the model at other voltage values finding the appropriate delay for each.

6) You can see what I came up with by running k3taufit2.hoc, selecting Generators/ViewAllGraphs and then Generators/RunAll

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