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In the article How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs, I read (p.11629)

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I have four questions concerning some formulations:

  1. What is "the membrane time constant" if this depends on the membrane resistance and capacitance which varies over the membrane? Maybe "local membrane time constant"? Or "mean membrane time constant"?

  2. What do the authors probably mean with "instantaneous postsynaptic currents"? Occurring at the same time all over the dendritic tree?

  3. What do they probably mean with "exponentially decaying synaptic currents"? The decaying of the PSPs while travelling down the dendritic tree?

  4. What's the relation between "synaptic decay time constant" and "membrane time constant"?

(Having digested the paragraph a bit more, another - probably more accurate - reading of "instantaneous" came to my mind: "starting and ending abruptly with the abrupt opening and closing of the ion channel".)

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  • $\begingroup$ I wouldn't suggest trying to understand this passage in terms of actual biology. This paragraph is the equivalent of the common physics trope "assume a uniform spherical cow" - they are simply describing some mathematical properties of a neuron given some assumptions. In many cases those assumptions may be very reasonable, but it doesn't make much sense to start from a uniform spherical cow and work backward into the actual shape of a cow. $\endgroup$ – Bryan Krause Sep 15 '17 at 16:08
  • $\begingroup$ I know what you mean. But the authors don't seem to be cowboys and they presumably know what they are talking about. And they obviously talk the language of actual biology (at least they use some of its vocabulary). $\endgroup$ – Hans-Peter Stricker Sep 15 '17 at 16:59
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Started writing a comment and realized it was an answer...

These guys are basically saying "take a uniform spherical neuron" the same way you would say in physics "take a uniform spherical cow." There isn't a dendrite mentioned in the whole paper.

By "the membrane time constant" they mean exactly that: one membrane time constant, effectively the somatic time constant. They aren't talking about dendritic trees: they are essentially saying assume a uniform spherical neuron that gets inputs on its soma.

Membrane time constant is associated with the rate of change of the membrane voltage; synaptic time constant is associated with the rate of change of the synaptic current (this is what they refer to when they talk about exponentially decaying synaptic currents). Real biological synaptic currents have a time course governed my neurotransmitter concentrations and the gating properties of postsynaptic receptors. Real biological postsynaptic potentials (voltages) are governed by both the time course of the synaptic current and the capacitive properties of the membrane (i.e., the membrane time constant).

Instead of considering synaptic time constants, you could simplify a synaptic event as an instantaneous current impulse: essentially the entire current all in one instant rather than over time. The presence of the membrane time constant helps with making this assumption somewhat reasonable, because the membrane time constant ends up filtering input currents anyways, whether they are impulses or have a synaptic time constant.

In a simulated environment, you can make computations simpler by just adding a little time to the membrane time constant to roughly simulate the effect of the membrane time constant + synaptic time constant. Again, this is for computational efficiency, like when you assume a cow is spherical, not for perfect biological accuracy.

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  • $\begingroup$ Can all of this really be true? Do these guys - who I really don't want to offend - really think of uniform spherical neurons? If so, they will have good reasons - which in turn I would like to learn about. $\endgroup$ – Hans-Peter Stricker Sep 15 '17 at 17:49
  • $\begingroup$ I agree and I also am irritated, that they don't mention dendrites. But what does this mean/imply...? $\endgroup$ – Hans-Peter Stricker Sep 15 '17 at 17:58
  • $\begingroup$ Well they are testing a fairly specific parameter in their paper, and they want to know what effect it has on a soma-centric measure. It's much more tractable to start with simple assumptions. I'd also suggest the Magee 2000 paper that I suggested you read on another answer - as that one shows, by the time you get to the soma, synaptic properties and active dendritic processes somewhat normalize the EPSPs. If that's true, then it doesn't much matter where on the dendrites they initially came in, at least not for the integrative properties of the soma. $\endgroup$ – Bryan Krause Sep 15 '17 at 22:05

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