## No linear fit of tau possible

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MBeining
Posts: 35
Joined: Thu Apr 03, 2014 8:18 am

### No linear fit of tau possible

Hey there,
I am quite new to NEURON and I have a (hopefully) very simple problem since I could reduce the core of it to its simple basis:
I have just one cylinder with simple passive properties and I inject a positive current for some time.
Actually, I should be able to measure tau from the voltage decay when current injection is over, either by:
1) Checking at which time V has decayed to 1/e
2) Get the slope of the (natural) logarithmic voltage plot. tau is 1/slope

The first solution works, even with more complex morphologies, at least the "experimental" tau is in the range of the theoretical tau = cm*Rm
However, I've read that the assumption with the 1/e decay is only true for a isopotential sphere. In cylinders it decays faster. Also, noise would be a problem.
Hence, I tried to use solution 2). However when I do the logarithmic plot, there is no linear slope part after current injection is gone! Not with complex morphologies and not with the simple cylinder.
What am I doing wrong?
I attached an image of the simple cylinder experiment. On the left, the voltage over time can be seen, on the right the (negative, but that does not matter) voltage is plotted logarithmically.
You can see the properties of the cylinder in the console as well as the IClamp parameters.
I should admit, that of course you might define some part of the logarithmic plot as linear, however the tau I would get from it, is not in the range of the theoretical tau.
By the way: When I do the slope thing with real data, i.e. averaged voltage traces, it actually works, you see a clearly linear part.

Hopefully, someone can help me. Thank you in advance! ted
Posts: 5810
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
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### Re: No linear fit of tau possible

By now you may have figured this out for yourself. If not, here's the hint.

The response of a cable to a current step that starts at t0 = 0 can be written as
Co + SUMMA Ci exp(-t/taui)
where Co is the steady state solution (the value that v approaches as t becomes very large), and the SUMMA stuff is a sum of an infinite series of decaying exponentials. You have to subtract the steady state in order to unmask the decaying exponentials.
MBeining
Posts: 35
Joined: Thu Apr 03, 2014 8:18 am

### Re: No linear fit of tau possible

I thought about substracting the offset, but never did it. Thanks for the hint!
Ok, this automatically means, linear fit does not work any more if more than one decaying exponential is influencing the voltage trace, as it might be in an active model..
ted
Posts: 5810
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: No linear fit of tau possible

A few comments, some theoretical, but most based on experimental evidence:
--In a passive model, the slowest time constant in the infinite sum is the membrane time constant.
--Most, if not all, neuron classes have multiple active currents, yet the literature is full of experimental evidence (e.g. a brief statement in the results section of an article on some other topic, or a plot of V vs. I that demonstrates linearity over a significant range of Vm even though the authors make no comment about it in the legend or body of the article) , or that many have a linear I-V relationship in the subthreshold region. In some cases linearity extends over several 10s of millivolts. In such a linear range, it may be possible to measure a phenomenological time constant that characterizes the low pass filtering that characterizes the effect of an injected current on local membrane potential.
--In clean patch clamp recordings from many classes of cells, using no chemical or pharmacological agents to block voltage-gated channels, the local response to a subthreshold injected current can be fit with a single time constant.
--Returning to the topic of linearity, many articles on h currents have demonstrated reciprocity despite the presence of significant sag. In at least some cases, reciprocity is evident in one or more published figures even though the authors made no comment about it. However, the authors of this particular article noted the phenomenon and recognized its significance:
Berger, T.; Larkum, M. E. & Lüscher, H. R.
High I(h) channel density in the distal apical dendrite of layer V pyramidal cells increases bidirectional attenuation of EPSPs.
Journal of Neurophysiology 85:855-868, 2001.