## Reciprocity?

Bill Connelly
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### Reciprocity?

Am I right in thinking that a section of dendrite between points A and B is reciprocal if injection a X pA of current at location A creates Y mV of deflection at location B AND injection of X pas of current at location B creates Y mV of deflection at location A?

And if the connection between a dendritic site and a somatic site is reciprocal, what does that mean for the physical/electrical properties of your typical tapering dendrite?
Keivan
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### Re: Reciprocity?

if the connection between a dendritic site and a somatic site is reciprocal, what does that mean for the physical/electrical properties of your typical tapering dendrite?
I think It depends on many different factors, from theoretical point of view:
1) the the homogeneity of the passive properties of the dendrites.
2) active properties of dendrites (ion channels)
3) frequency of the input
4) morphology of dendrites
to my knowledge, this is not happening in the CA1 and layer 5 cortical pyramidal neurons in reality.
there are lots of information in this regard. I refer you the book "Neuroscience - A Mathematical Primer" for a detailed mathematical information about this. for a simplified and easy to understand information you can see the book "From Computer to Brain - Foundations of Computational Neuroscience".

on the other hand from the practical point of view in one of the articles I have seen they could not measure this experimentally, because there is a significant difference between a dendritic patch electrode and a somatic one, considering the series resistance of the device and the resultant series error or space clamp artifact.
ted
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### Re: Reciprocity?

Bill Connelly wrote:Am I right in thinking that a section of dendrite between points A and B is reciprocal if injection a X pA of current at location A creates Y mV of deflection at location B AND injection of X pas of current at location B creates Y mV of deflection at location A?
A two port system has the property of reciprocity if application of a current I to one port elicits the same potential V at the other port, even if the "current injection" and "voltage observation" ports are swapped. So the answer to your question is "yes."
And if the connection between a dendritic site and a somatic site is reciprocal, what does that mean for the physical/electrical properties of your typical tapering dendrite?
Not much except that (1) it happens and (2) it's always a surprise when it happens.
Keivan wrote:to my knowledge, this is not happening in the CA1 and layer 5 cortical pyramidal neurons in reality.
Quite the contrary. Fairly striking examples of reciprocity are presented in Fig. 9 A and B of
Magee, J.C.
Dendritic hyperpolarization-activated currents modify the integrative properties of hippocampal CA1 nyramidal neurons
J. Neurosci. 18: 7613 - 7624, 1998
which is obtainable for free from the journal's WWW site. The figure shows membrane potential recorded in a CA1 pyramidal cell patched at the soma and apical dendrite. Current steps were injected at one site, and observed at the other. Note that the membrane potential traces overlie each other almost exactly, regardless of where the current was injected, even though there was a prominent sag in all responses (compare "I inject to dend / propagated" with "I inject to soma / propagated"). Adding cesium to the bath eliminated the sag, but the traces were still nearly identical. An impressive demonstration of reciprocity in at least a portion of the apical dendritic tree of a cell whose membrane was full of voltage-gated, time-dependent currents, including a fairly large h current. The injected currents were large enough to elicit 10 - 15 mV changes of membrane potential at the injection and "remote" sites--fairly substantial perturbations.

The paper makes no mention of reciprocity. It might be worth asking Jeff if he noticed it, and if he did, whether reciprocity was also found in other cells. Or, if he didn't, whether he can easily dig up the data from those old experiments to take another look . . .

I wouldn't be surprised if others have done similar experiments and gotten similar results (but may not have recognized them for what they were, or what they imply). Certainly there are lots of papers that present IV curves obtained by injecting and recording current at the same site--almost always the soma--under control conditions (no drugs or ionic manipulations), in which the slope is nearly linear over membrane potential ranges that span 10-20 mV or more. This suggests that, except in the near vicinity of spike threshold, neurons are operating in a more or less linear manner, and that reciprocity is quite common if not the rule.

Experimentalists and theoreticians who work on a systems level find it convenient to treat cells as essentially linear integrators of synaptic inputs, but those who work at the cellular level tend to focus on the complexities of ion channels and their nonuniform distribution over the cell surface. It might be expected that papers by the latter would seem to ignore accidentally revealed linearities.
Keivan
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### Re: Reciprocity?

First of all I have some quotation for you Ted.
As I have repeatedly discovered in my career, the informal lunch-seminar approach to science is hard to substitute with formal lectures or the reading of dense scientific papers. Seminars are tailored for an average group of people with the naive assumption that the audience retains all the details and follows and accepts the fundamental logic of the lecturer. In contrast, the essence of lunch conversations is to question the fundamental logic, a quest for clarification and simplification, a search for explanations and answers without a rigid agenda, where the focus is not on covering large chunks of material but on fully understanding even the smallest details.
Rhythms of the Brain - György Buzsáki
Dendritic hyperpolarization-activated currents modify the integrative properties of hippocampal CA1 nyramidal neurons
to be honest, although I read that article recently, I was completely forgotten about that. because, recent works of "Poirazi 2003" had a great impact on me. they show that the dendritic trees of CA1 act non-linearly so that we can model it with a two layer artificial neural network.

I have some other quotation
A passive cable structure with current or voltage inputs is a linear system, that is, if you double the input, the output should also double, if you multiply the input by –1, you should get –1 times the output. The response to two stimuli is given by the sum of the responses to the individual stimuli.
Linear scaling tests should always be performed before using electrophysiological data for passive cable modeling, but rarely are.
Conductance inputs however do not behave linearly in a passive system, a fact often forgotten by inexperienced modellers.
If you simulate a synaptic conductance, then double it, you won’t get twice the response, because of a reduced driving voltage, and because of the local increase in net membrane conductance. The responses to very small conductances, however, can scale approximately linearly, if these effects are negligible.
Computational Neuroscience - Realistic Modeling for Experimentalists
chpter 8 - Passive Cable Modeling — A Practical Introduction - by Guy Major
8.6.1 FITTING A PASSIVE CABLE MODEL TO ACTIVE DATA
ted
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### Re: Reciprocity?

In the interests of clarity, I should point out that the discussion risks entering the realm of "apples vs. oranges." Cells don't always stay in the linear range, nor do they always operate outside that range. But they are in the linear range most of the time. The statement
except in the near vicinity of spike threshold, neurons are operating in a more or less linear manner
is supported by a large body of data. In addition to the evidence memtioned in my previous post, many papers have shown that excitatory synaptic inputs summate linearly as long as they are subthreshold and are separated sufficiently by time and/or space to not drive membrane potential near threshold or interfere with each other's driving force.

The evidence from in vivo recordings is that most cells, under most conditions, receive lots of synaptic input all the time, but fire spikes only occasionally. So most of the time, membrane potential is not hovering near spike threshold (or random fluctuations would cause higher baseline firing rates). Consequently, most cells are quite subthreshold most of the time, and likely to be in a potential range where they act as a more or less linear integrators.

The model of Poirazi et al. is hardly a refutation of empirical fact. Of course the model demonstrated and exploited dendritic nonlinearities--that was by design, and hardly a surprise, because it was constructed to be used for "proof of concept" and "exploration of consequences." The model would have been pointless and useless if it did not have a high degree of dendritic nonlinearity. "Proof of concept" and "exploration of consequences" are perfectly valid reasons for building and using a model, but successful use of a model for "proof of concept" does not establish that everything (or anything) in the real world works in the same way that the model does.

Regarding the quote from Guy Major, unitary excitatory synaptic events (events elicited by the spiking of one presynaptic axon) produce conductance changes so small that the peak amplitude of the local response is only a tiny fraction of the driving force, regardless of where on the cell the synapse is attached. Since in vivo spontaneous firing rates tend to be low, it follows that temporal summation rarely departs significantly from linearity--except under experimental conditions where axons are forced to fire at high rates, or the occasional behavioral circumstance in which high rates may occur naturally.

Bottom line: theory is good, but experimental evidence trumps theory. Most of the time cells are quite subthreshold, in which case linearity seems a reasonable first approximation--subject to experimental verification--except when they are close to or above threshold, in which case linearity seems not a good appriximation--subject to experimental verification.
Keivan
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### Re: Reciprocity?

ted wrote:Fairly striking examples of reciprocity are presented in Fig. 9 A and B of Magee, J.C. Dendritic hyperpolarization-activated currents modify the integrative properties of hippocampal CA1 nyramidal neurons J. Neurosci. 18: 7613 - 7624, 1998
This example shows the reciprocity of Dendrites in response to constant current injection.
do you aware of an example of reciprocity of Post Synaptic Potentials in CA1?
ted
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### Re: Reciprocity?

You mean "has anyone demonstrated reciprocity by injecting a synaptic current waveform"? Not to my knowledge, but it sounds doable. Maybe worth writing up a small proposal and leveraging it into a summer at Woods Hole.
Keivan
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### Re: Reciprocity?

when I was reading my new book "Computational Modeling Methods for Neuroscientists" I found a piece of information about reciprocity in it.
Passive systems exhibit a nonintuitive symmetry in voltage responses called reciprocity (see discussion in Major et al., 1993). The voltage response at the soma to current injection at a dendritic location will equal the voltage response at this dendritic location following the same current injection at the soma. It should be noted that the voltage responses at the injection sites and the degree of voltage attenuation between the injection site and the recording site may be drastically different, but the responses at the recording sites will be identical (e.g., figure 1 of Roth and Hausser, 2001). Checking for reciprocity is a good way to determine if a dendritic tree is passive or if blockers have been successful at making it so.
Major93 [Solutions for transients in arbitrarily branching cables: II. Voltage clamp theory.]
Roth01 [Compartmental models of rat cerebellar Purkinje cells based on simultaneous somatic and dendritic patch-clamp recordings.]
ted
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### Re: Reciprocity?

Checking for reciprocity is a good way to determine if a dendritic tree is passive or if blockers have been successful at making it so.
Except when it isn't, as demonstrated by published figures of recordings from active trees operating in the subthreshold region.
Keivan
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### Re: Reciprocity?

explain more, please. I don't get what you mean.
ted