How to access and plot derivatives of variables?
How to access and plot derivatives of variables?
I am using the phase plane plot tool in NEURON GUI. I find if I want to plot dV/dt ~ V, I can plot total current of that segment versus V. However, is there a variable which I can access from hoc that is exactly this dV/dt value? If that is possible, it would be much easier for me to plot also, say, dg/dt value.
Otherwise I would have to record the vectors down and make difference of the vectors, which might be troublesome especially when I am using variable step integration in my simulation.
Otherwise I would have to record the vectors down and make difference of the vectors, which might be troublesome especially when I am using variable step integration in my simulation.

 Site Admin
 Posts: 5704
 Joined: Wed May 18, 2005 4:50 pm
 Location: Yale University School of Medicine
 Contact:
Re: How to access and plot derivatives of variables?
You are of course referring to total ionic current, not total membrane current.eacheon wrote:I am using the phase plane plot tool in NEURON GUI. I find if I want to plot dV/dt ~ V, I can plot total current of that segment versus V.
Numerical integration always produces approximate results. The best one can get is resultsHowever, is there a variable which I can access from hoc that is exactly this dV/dt value?
that are internally consistent and within an acceptable error tolerance.
NEURON's default integrator is implicit Euler, which has first order accuracy. Greater
precision is achievable by setting secondorder = 2, which gives second order accurate
results for voltage and currentsbut at different times in the course of the simulation!
That is, v is 2nd order correct at times n*dt, and i is 2nd order correct at n*dt  dt/2
(see
http://www.neuron.yale.edu/neuron/stati ... econdorder
). If you must have both correct to the highest precision at the same time, use adaptive
integration (aka cvode).
Not at all. UseOtherwise I would have to record the vectors down and make difference of the vectors, which might be troublesome especially when I am using variable step integration in my simulation.
vdest.record(&var, DT)
where DT is your desired sampling interval, and NEURON will generate the solution wth
adaptive integration but forcing the integrator to stop at integer multiples of DT to calculate
and record the variable to your vector. So you have evenly spaced samples, and can
readily use the Vector class's deriv() method to calculate your derivative.
The only caveat is to use cvode.record rather than vector.record() if you are using local
variable time step integration.
Re: How to access and plot derivatives of variables?
Exactly.ted wrote: You are of course referring to total ionic current, not total membrane current.
Thanks for the very patient and detailed answer on this. I've read similar notes provided by you on this forum in two or three other threads.ted wrote: Numerical integration always produces approximate results. The best one can get is results
that are internally consistent and within an acceptable error tolerance.
NEURON's default integrator is implicit Euler, which has first order accuracy. Greater
precision is achievable by setting secondorder = 2, which gives second order accurate
results for voltage and currentsbut at different times in the course of the simulation!
That is, v is 2nd order correct at times n*dt, and i is 2nd order correct at n*dt  dt/2
(see
http://www.neuron.yale.edu/neuron/stati ... econdorder
). If you must have both correct to the highest precision at the same time, use adaptive
integration (aka cvode).
So you are saying there's no way I can access the dg/dt values directly from hoc? It is a pity since anyway NEURON's integrator knows these values at a first hand.
Thanks for this nice tip! I will do as you suggested. This way I may actually directly using the "phase plane" tools to plot those in NEURON...ted wrote: Not at all. Use
vdest.record(&var, DT)
where DT is your desired sampling interval, and NEURON will generate the solution wth
adaptive integration but forcing the integrator to stop at integer multiples of DT to calculate
and record the variable to your vector. So you have evenly spaced samples, and can
readily use the Vector class's deriv() method to calculate your derivative.
The only caveat is to use cvode.record rather than vector.record() if you are using local
variable time step integration.

 Site Admin
 Posts: 5704
 Joined: Wed May 18, 2005 4:50 pm
 Location: Yale University School of Medicine
 Contact:
Re: How to access and plot derivatives of variables?
Correct. Whether dg/dt is even computed internally depends on howSo you are saying there's no way I can access the dg/dt values directly from hoc?
the channel's properties have been specified, and on which integrator
is being used.
You will have to plot your own phase plane using the Vector class'sI will do as you suggested. This way I may actually directly using the "phase plane" tools to plot those in NEURON...
plot() method, with the syntax vec.plot(graphobj, x_vec) (see
https://www.neuron.yale.edu/neuron/stat ... .html#plot
), not with the phase plane graph created by
NEURON Main Menu / Graph / Phase Plane
Re: How to access and plot derivatives of variables?
Ted, I might miss something here. Shouldn't I be plotting i_cap versus v as the dV/dt ~ V phase plot? And I am thinking i_cap (for a segment in a section) almost always does not equal to total ionic current (for that segment), am I right, or I am missing some serious thing here?eacheon wrote:Exactly.ted wrote: You are of course referring to total ionic current, not total membrane current.

 Site Admin
 Posts: 5704
 Joined: Wed May 18, 2005 4:50 pm
 Location: Yale University School of Medicine
 Contact:
Re: How to access and plot derivatives of variables?
It looks like we were both missing something. dV/dt = membrane capacitiveeacheon wrote:Ted, I might miss something here. Shouldn't I be plotting i_cap versus v as the dV/dt ~ V phase plot?
current divided by membrane capacitance. Total membrane current is the
sum of ionic and capacitive components, so in a model that has only one
compartment, dV/dt =  ionic membrane current divided by membrane
capacitance. But in a model with more than one compartment, there are
axial currents that destroy this nice relationship, i.e. as you put it
So the strategy that works with all models is to compute dV/dt numerically.i_cap (for a segment in a section) almost always does not equal to total ionic current (for that segment)
The deep question is: what sense can one make out of a phase plane plot
in a model that has multiple compartments?

 Site Admin
 Posts: 5704
 Joined: Wed May 18, 2005 4:50 pm
 Location: Yale University School of Medicine
 Contact:
Re: How to access and plot derivatives of variables?
I seem to have sowed confusion. These statements are true:
i_cap(x)/(area(x)*cm(x)) at any internal node
should be equal to dv/dt at that node. Numerical differentiation of v is not necessary.
But the range variable i_cap _is_ the current through the membrane capacitance, so the ratiodV/dt = membrane capacitive
current divided by membrane capacitance. Total membrane current is the
sum of ionic and capacitive components, so in a model that has only one
compartment, dV/dt =  ionic membrane current divided by membrane
capacitance. But in a model with more than one compartment, there are
axial currents that destroy this nice relationship, i.e. as you put iti_cap (for a segment in a section) almost always does not equal to total ionic current (for that segment)
i_cap(x)/(area(x)*cm(x)) at any internal node
should be equal to dv/dt at that node. Numerical differentiation of v is not necessary.
Re: How to access and plot derivatives of variables?
I am still not 100% sure what icap is. I made a test with a singlecompartment model where I compared icap with the negative sum of all ionic currents plus the injected current and found that there where differences between those two which reduced with increasing step size. This suggests that icap is not just
Is this true?
If not, why is it not equal to the sum of the currents?
Is there a variable in NEURON from which I can directly access dV/dt before integration of V?
but is computed by numerical differentiation of the integrated membrane potential V times the cells capacitance.the current through the membrane capacitance
Is this true?
If not, why is it not equal to the sum of the currents?
Is there a variable in NEURON from which I can directly access dV/dt before integration of V?

 Site Admin
 Posts: 5704
 Joined: Wed May 18, 2005 4:50 pm
 Location: Yale University School of Medicine
 Contact:
Re: How to access and plot derivatives of variables?
Not at all. If the model is passive and is subjected to a tonic (static, unchanging) stimulus, that is exactly what should happen with implicit Euler. It has no implications for how i_cap is computed.cafischer wrote:I am still not 100% sure what icap is. I made a test with a singlecompartment model where I compared icap with the negative sum of all ionic currents plus the injected current and found that there where differences between those two which reduced with increasing step size. This suggests that icap is not justbut is computed by numerical differentiation of the integrated membrane potential V times the cells capacitance.the current through the membrane capacitance
Is this true?
Re: How to access and plot derivatives of variables?
The fixed step method implementation does not expose the derivatives of the states. But they are available with the variable step integrators. You need to consider
http://neuron.yale.edu/neuron/static/ne ... de.dstates
also helpful in this context is
http://neuron.yale.edu/neuron/static/ne ... .statename
http://neuron.yale.edu/neuron/static/ne ... de.dstates
also helpful in this context is
http://neuron.yale.edu/neuron/static/ne ... .statename