Mini-Tutorial on Voltage Clamp Circuitry Tuning

The GENESIS Scripts/squid simulation, by Mark Nelson, uses simulated voltage clamp circuitry constructed from a combination of the RC, diffamp and PID objects. Further information is given in the documention for these objects, and for PID in particular. The GENESIS commands to implement this are in the file squid_electronics.g. Neurokit also provides a voltage clamp for any compartment, although the code (in xout_funcs.g) is more complicated and will be harder to follow. Scripts/vclamp has a demonstration of how to use Neurokit to do a series of voltage clamp experiments.

When this circuitry is used on small cells with the default values, integration errors may occur during the nearly instantaneous change of the membrane potential as it attempts to follow changes in the clamp command voltage. These notes, which were provided by Mark Nelson, suggest strategies for "tuning" the circuitry parameters to achieve a balance of the quality of the voltage clamp against the size of the integration time step.

Notes on Vclamp problems and PID controller tuning

Here are a few things to be aware of when setting up voltage clamp circuitry ala the Squid model:

1. diffamp elements and the PID element have a "saturation" field that limits the absolute magnitude of their output. Unfortunately this field defaults to 0, which isn't very useful. Be sure to set it to some large value (in the squid scripts it's set to 999, but you may have to use a larger value if you're using some other set of units).
2. The tuning of the PID (proportional-integral-derivative) controller involves balancing the quality of the voltage clamp against the size of the integration time step. Basically, higher gain gives a better clamp, but requires a smaller integration time step to avoid numerical instability. (For more info on PID controllers see: Franklin, Powel, Emami-Naeini (1986) "Feedback Control of Dynamic Systems", Addison-Wesley,

   pp. 99-106) I'll outline a strategy for tuning the controller below.

3. the abrupt step change in voltage at the beginning of the clamp can also give rise to numerical instabilities, hence the need to lowpass filter the command signal with an "RC" element.

Here's the strategy I suggest for tuning the voltage clamp circuitry:

1. decide what rise time you are willing to accept on the leading edge of the step and set the time constant of the "lowpass" element accordingly (watch out for units - the value "0.1" in the squid script is in units of msec. If your simulation uses units of seconds, you'd want "0.0001" for a 100 usec time constant.)
2. set the integration time step, DT, to be 4-5 times smaller than the lowpass time constant.
3. set the PID integration time constant, tau_i, equal to the integration

   time step DT

4. set the PID derivative time constant, tau_d, equal to DT/4
5. empirically determine the value of PID gain where things go unstable and set the gain just below that point

The three plots below show the Squid tutorial voltage clamp with the lowpass time RC time constant set to 0.003, 0.03, and 0.3 msec. Note that with the slowest (largest) time constant, Vm follows the command voltage well, but the rise time is slow. With RC = 0.003, there is more overshoot than with 0.03.

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