State and Parameter Discontinuities

Physical System

Transient voltage clamp to assess action potential stability.

Model

Force a discontinuous change in potential during an Action Potential

Simulation

To work properly with variable time step methods, models that change states and/or parameters discontinuously during a simulation must notify NEURON when such events take place. This exercise illustrates the kinds of problems that occur when a model is changed without reinitializing the variable step integrator.

1. Start with a current pulse stimulated HH patch. We recommend that you try creating this yourself with a brief current pulse at t = 0.1, either in Python or with the GUI tools. Our Python solution is hh_patch.py.

   
   

2. Discontinuously change the voltage by +20 mV via
   

   def change():
       print('change at %g' % h.t)
       soma.v += 20
   
   def setup_discontinuities():
       h.cvode.event(2, change)
   
   fih = h.FInitializeHandler(setup_discontinuities)
   

   Note the difference between the fixed and variable step methods.

   
   

3. Replace the change() function with the following and try again:
   

   def change():
       print('change at %g' % h.t)
       soma.v += 20
       h.cvode.re_init()

   
   

4. What happens if you discontinuously change a parameter such as gnabar_hh during the interval 2-3 ms without notifying the variable time step method?
   

   def change(action):
       print('change at %g: %s' % (h.t, action))
       if action == 'raise':
           soma(0.5).hh.gnabar *= 2
       else:
           soma(0.5).hh.gnabar /= 2
       # h.cvode.re_init()   # should be here for cvode, but see below
   
   def setup_discontinuities():
       h.cvode.event(2, (change, 'raise'))
       h.cvode.event(3, (change, 'lower'))
   
   fih = h.FInitializeHandler(setup_discontinuities)

   It will be helpful to use the Crank-Nicholson fixed step method and compare the variable step method with and without the cvode.re_init(). Zoom in around the discontinuity at 2 ms.