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Fitting the dV/dt vs V plot

Posted: Mon Mar 10, 2008 5:24 pm
by patoorio

I'm trying to reprouce the shape of an action potential, and in order to make a better fit I want to fit the dV/dt vs V phase plot, in addition to (or instead of) the common V vs t plot.
If I understood well this thread, I can easily obtain dV/dt by plotting i_cap (capacitative membrane current) as long as I am dealing with a single compartment, which is my case. In fact, I can do a very nice phase plane plot of my simulated action potentials. But I can not see how to creat a Fitness Generator with it.
What kind of Generator should I use? specially, I don't know how to specify a fitness generator in which the x variable is not time.

Thanks in advance for your answers!!

Posted: Tue Mar 11, 2008 1:41 pm
by ted
Actually dV/dt is equal to i_cap, regardless of fhe number of compartments. Total ionic
current in a compartment is equal to -i_cap only if there is one compartment. I apoloogize
If my comments in the referenced thread were confused or induced confusion in others.
fit the dV/dt vs V phase plot
An interesting idea. First question is: does it make sense for your particular application?
That is, do you really want the error function, that you are minimizing, to be one that
emphasizes those regions of the trajectory in which dV/dt and V are both large? i.e. in
which V changing rapidly and far from rest. It will allow greater error near the depolarized
and hyperpolarized extrema (may not matter much), but the biggest degradation of fit will
be in the near-threshold region, where V is near rest and changing slowly. That sounds like
a bad idea, since this is where the cell is "thinking" about whether or not to spike.
I can do a very nice phase plane plot of my simulated action potentials. But I can not see how to creat a Fitness Generator with it.
You can't. The x axis of the fitness generator has to be a monotonically increasing
independent variable. Neither v nor dv/dt would be an independent variable, nor would they
be monotonically increasing.

You _could_ abandon the MRF altogether, and just use praxis through hoc code. You'd
have to define an objective function to be minimized (e.g. the area between the "ideal"
phase plot and the actual trajectory), being careful to scale both axes to achieve the
desired weighting of amplitude and velocity.

If you prefer to stick with the MRF, set up two fitness generators: both would have t as
the independent variable, but the dependent variable would be v in one, and dv/dt in the

Posted: Thu Mar 13, 2008 11:43 am
by ted
A slight variation on the theme I proposed:
convert the sequence of points from cartesian (v, dv/dt, t) to polar coordinates (r, theta, t),
relative to a well-chosen* "center" in the (v, dv/dt) plane. Then use the MRF to fit the model
to the time courses of r and theta.

*--somewhere in the middle of the spike's loop in the v, dv/dt plane--maybe halfway between
the x & y axis extrema, or maybe a "weighted" center (i.e. the mean values of v and dv/dt
in the course of a spike).

Posted: Mon Mar 17, 2008 4:42 pm
by patoorio
Very interesting suggestion, specially the one about the polar coordinates. I will try it and see what happens.

Thank you!!

Posted: Mon Mar 17, 2008 8:18 pm
by ted
It would be quite interesting if it works. Also interesting if it doesn't (in which case it would
be even more interesting to know why it failed).