Fitting time constants for EPSPs

[vladimirov]

Hi,
How do you fit the experimental data on EPSP/IPSP kinetics? I have two time constants from experiment: "rise time" (3 ms) and "half-duration (width at half-amplitude)" (21 ms). I guess using Exp2Syn() mechanism should suffice? It also has two time constants tau1, tau2, but their meaning is slightly different as they are time constants of the two exponents: g ~ (exp(-t/tau2) - exp(-t/tau1)). How do experienced modelers fit EPSP/IPSP data to synapse parameters, and which synaptic mechanism you use?
Thank you!

[ted]

Excellent questions. Here are the unfortunate answers.

How do you fit the experimental data on EPSP/IPSP kinetics? I have two time constants from experiment: "rise time" (3 ms) and "half-duration (width at half-amplitude)" (21 ms). I guess using Exp2Syn() mechanism should suffice?

The time constant parameters in ExpSyn and Exp2Syn govern the time course of the synaptic conductance. Your observations, however, are descriptions of membrane potential time course, not the same thing at all. I don't know what you mean by "rise time"--is it 10-90 rise time, 20-80, or what? And half-width is only a rough guide to the time course of the PSP waveform, because it doesn't say whether the entire PSP is well approximated by two time constants, or whether three or more are required.

If you know that your PSP is small enough that the electrical properties of the cell can be treated as approximately linear over that range of membrane potentials, then the time course of the PSP can be interpreted as the convolution of the actual synaptic current and an impedance. If the PSP was observed at the same point at which the synapse was located, the impedance is the input impedance of the cell at that point. If the synapse was located at point A, but the PSP was observed at some other point B, the impedance is the transfer impedance between A and B. For many mammalian central neurons, the local response to an injected current step applied by patch clamp is well described by a single exponent, so the input impedance (and perhaps the transfer impedance as well) is described by a single exponent. For such a cell, a synaptic current with a very fast rise (smaller than 0.5 ms, e.g. produced by an AMPAergic synapse) and a monoexponential decay will generate a PSP that is described by two time constants--but neither of them will be exactly the time constant of the synaptic conductance. Similarly, a biexponential synaptic current--e.g. produced by a GABAergic synapse--will generate a PSP that is described by three time constants, none of which will be the time constants of the synaptic conductance itself.

How do experienced modelers fit EPSP/IPSP data to synapse parameters, and which synaptic mechanism you use?

First, start with the cleanest experimental data you can get. Best would be voltage clamp recording of the current produced by a synapse very close to the location of the clamp electrode. This is your best indication of the actual time course of synaptic current. Then you need to know the driving force for synaptic current entry ("reversal potential") and the clamp's holding potential. From these you can determine the time course of synaptic conductance itself. That's the gold standard. There's not a lot of that kind of data floating around, and it's scattered here and there in the experimental literature.

If the clamp and synapse are at different locations in the cell, and you happen to have detailed morphometric data from the cell, and a good estimate of the cytoplasmic and membrane properties of the cell, you could construct a computational model of the cell (under current or voltage clamp, depending on what the original experimental conditions were), then tinker with the synaptic mechanism's parameters until the simulated PSP or PSC is a close match to the experimental observation. This is more work and produces a result that is a much more indirect indication of the dynamics of the synaptic conductance.

[vladimirov]

Dear Ted,
Thank you very much for the detailed answer. The rise time is 10-90, and the available data are both current clamp and voltage clamp of soma not far from the synapse.
Does it make any sense to try to fit the given experimental IPSC amplitude (22 pA in my case), or it is hopeless due to fluctuating electrode/seal resistance and unknown parameters of the measured cell?
And one more question: the IPSC in voltage clamp has half duration 6 ms, but IPSP in current clamp has half-duration of 45 ms (same set of patch clamps). Which time constant is more accurate for synaptic decay time?
Thank you!

[ted]

If you are building a model, and you want a synapse in your model to produce currents that are similar to those of some real synapse, then it makes sense to use experimental data to constrain the properties of the synapse in your model.

experimental IPSC amplitude (22 pA in my case)

Let's call this imax. The maximum of the actual synaptic current isyn is at least as big as imax. The peak synaptic conductance must be at least as big as imax/(vm - erev) where
vm is the membrane potential at the point where the voltage clamp was located
and
erev is the synaptic reversal potential
Do you know, or can you guess, the value of erev?

What you don't know is the actual time course of synaptic conductance gsyn(t). If you knew the real isyn(t) and the actual membrane potential vsyn(t) at the location of the synapse, you could calculate
gsyn(t) = isyn(t)/(vsyn(t) - erev)
But you only know iobserved(t) (the current recorded by the clamp), and you might only know vclamp (the voltage clamp's holding potential). If you're real lucky, the experimenter used a switching clamp so you will know the actual time course of membrane potential vm(t) at the point where the clamp is attached. From either of these you can calculate an estimate of synaptic conductance
gest(t) = iobserved(t)/(vm(t) - erev)
or not quite as accurate
gest(t) = iobserved(t)/(vclamp - erev)

Once you have gest(t) you can try to fit a double exponential function to it
A*(exp(-k1*t) - exp(-k2*t))
and you'd use that fit as the basis for the parameters of an Exp2Syn. For an example see
Multiple Run Fitter tutorials
on NEURON's Documentation page
http://www.neuron.yale.edu/neuron/docs
You'll want to work through "Tutorial 1: optimizing a function"

And one more question: the IPSC in voltage clamp has half duration 6 ms, but IPSP in current clamp has half-duration of 45 ms (same set of patch clamps). Which time constant is more accurate for synaptic decay time?

Here are a couple of questions for you.
1. Can you explain why there is a difference?
2. Which measurement depends on the properties of both the cell and the synapse, and which measurement depends mostly on the properties of the synapse itself?

[vladimirov]

Hi, Ted,
Thanks a lot for the explanations. Here are the answers to your questions:
1) I think the difference is because membrane is a capacitor and its (somatic) time constant can be quite long. So once the current is injected by IPSC, it can take a while to equilibrate the membrane potential, hence the IPSP decay takes longer.
2) I guess IPSC depends mainly on synapse, and IPSP on both synapse and the cell.
So, after your questions it becomes obvious that IPSC time constant (6 ms) is more accurate estimate of gsyn(t) time constant than IPSP's one (45 ms).
I think the patch clamp is switching in my case (i.e. alternating between voltage clamp and current clamp, providing both IPSC and IPSP profiles).
In your formula

gest(t) = iobserved(t)/(vm(t) - erev)

iobserved(t) is the ISPC provided by the voltage clamp, and vm(t) is the potential provided by the switching current clamp? Is that right?
erev is unknown, but I can guess it -70 mv (GABA).
Thank you!

[ted]

IPSC time constant (6 ms) is more accurate estimate of gsyn(t) time constant than IPSP's one (45 ms).

You knew the answer all along--just didn't realize it.

I think the patch clamp is switching in my case (i.e. alternating between voltage clamp and current clamp

Not what I meant. I meant what is called "dSEVC" (discontinuous single electrode voltage clamp)--see http://www.scholarpedia.org/article/Sin ... tage_clamp

In your formula

gest(t) = iobserved(t)/(vm(t) - erev)

iobserved(t) is the ISPC provided by the voltage clamp

True, although I would say that "iobserved(t) is the current recorded or captured by the voltage clamp."

and vm(t) is the potential provided by the switching current clamp?

I don't know what this statement means, because a current clamp doesn't "provide a potential." Also, a current clamp isn't involved in this experiment. A true statement would be "vm is the membrane potential at the point where the voltage clamp was located."

[vladimirov]

Many thanks, Ted, I appreciate your feedback!