Hi Jack. Assuming I've understood your question correctly, I think the simple answer is: no, the 'signal' is not diluted by the number of synaptic connections formed by the presynaptic neuron.

Remember that action potentials are regenerative, all-or-none events. Therefore, even in a neuron with a highly branched axon and many presynaptic terminals, the AP will invade all terminals equally, with no attenuation. Each individual presynaptic terminal is effectively indifferent to how many neighbours it shares an axon with.

Of course, the 'strength' of synaptic transmission at each individual synapse / release site can vary considerably, but this is determined by the properties intrinsic to the individual synapse (e.g. release probability / quantal content / postsynaptic receptor number / etc) and is not affected by the number of synapses formed by a particular axon.

Hope this helps.

Cheers,

Patrick.

Dear Jack,

What would "dilute the signal" mean? By signal, do you mean postsynaptic EPSP? By dilute, do you mean change the size/shape of the EPSP, or probability of the EPSP happening at all? I think if you get more specific about these details, it may help you find any relevant articles.

You could look for literature on action potential propagation at axonal branch points. I believe there is work looking at the reliability of transmission when branching.

Also, consider that the connection from one neuron to a second neuron usually is mediated by multiple synapses; ~5 in the case of L5 pyramidal neurons onto each other; see (Markram et al 1997) attached. And that individual synapses have variable reliability of transmission.

Good luck,

Ben.

Article Physiology and anatomy of synaptic connections between thick...

@Benjamin A Suter ·

Thank your reply. I do indeed mean the Excitatory postsynaptic potential. I will explain further.

Consider some neuron x1, it has has excitatory synapses to neurons y1,y2,y3.

We also have an identical neuron, x2. However, it has identical excitatory synapses  only to neurons y1 and y2.

Is EPSP felt by neuron y1 from neuron x1 less than the EPSP felt from x2 due to the difference in the number of synapses?   If so by how much?

In other words, does the number of outgoing synapses of a presynaptic neuron dilute the the EPSP felt by the post synaptic neurons?

Perhaps it is a naive question. However, the reason I ask is from a neural modeling perspective. Most neural models assume that it does not dilute the signal, however, I suspect it does!  

Many thanks,

Jack

Hi Jack,

A "unitary EPSP" (uEPSP) is the EPSP evoked by a single pre-synaptic neuron, which often is mediated by multiple (e.g. 5) synapses (these can be distributed across different dendrites of the post-synaptic neuron). 

Synaptic strength (and kinetics, plasticity, etc) vary greatly depending on the types and locations of pre-synaptic and post-synaptic neurons. But there is variability in the uEPSP even for a specific type of synaptic connection - by "type" I mean roughly a connection between two known cell types, for example from a L2/3 pyramidal onto a nearby L5 pyramidal; or from a thalamic neuron onto a L4 neuron.

So in the example of the uEPSP between two L5 pyramidal neurons, nicely described in the paper I referenced above, they report a range of uEPSP amplitudes: "0.15 to 5.5 mV in different connections with a mean of 1.3 +/- 1.1 mV" (and they also give kinetics). In a small subset of the experiments they were able to count the # of synaptic contacts, i.e. how many synapses make up each unitary connection: the range was 4 to 8, with an average of 5.5 +/- 1.1 contacts.

So in the context of your question, you might think "aha, perhaps the weaker uEPSPs of ~0.15 mV had only 4 contacts, and the 5.5 mV uEPSPS had 8 contacts". However, the abstract also states: "Peak amplitudes of unitary EPSPs fluctuated randomly from trial to trial. The coefficient of variation (c.v.) of the unitary EPSP amplitudes ranged from 0.13 to 2.8 in different synaptic connections (mean, 0.52; median, 0.41)." Just reading the abstract alone will give you this, and much more data - I highly recommend reading the whole paper, it's very nice, and fairly easy to follow.

Okay, so we've seen that even in a well-defined type of connection (between nearby L5 pyramidal neurons) the uEPSP varies across different connections, and even across multiple trials in a single connection. And we've seen that the # of synaptic contacts that mediate a single uEPSP varies across connections. This was all for a unitary connection, one neuron onto another neuron. In the context of your question, I hope this helps you to understand some of the underlying experimental facts.

Moving on to many-to-many connections, which is what your question is about: the same paper reports a connection probability of 0.1 in this population. That alone won't be enough information to address your question directly. Keep in mind that these neurons (L5 thick-tufted pyramidal) in most cases send axon collaterals to dozens of brain regions (including striatum, thalamus, brain stem, spinal cord) in addition to the local connections studied by (Markram et al, 1997). Therefore counting the # of post-synaptic targets for a single neuron, and repeating this for many similar neurons, in order to correlate the strength of their uEPSPs as a function of # of targets (which is your "dilution" hypothesis), seems to be experimentally very difficult.

So ... long story short:

There already is quite a bit of variability even for one-to-one connections. The trial-to-trial variability happens without the pre-synaptic neuron changing the # of connections it makes. The variability across connections, however, could in theory reflect the "dilution" that you describe, but I'm not aware of any studies that have directly obtained the data needed to answer your question with certainty. However, based on the known mechanisms of action potential propagation and synaptic transmission, I do not think the "dilution" that you propose is likely. To dig into this deeper, I previously suggested you could read the literature on AP propagation failures at axonal branch points - and maybe make some predictions from there.

Note: I am not aware of a reliable method for counting the # of outgoing (target) connections made by a single neuron (except perhaps in a few specialized cases with very few and easily traced axons, such as mossy fibers). There is some hope on the horizon, though: new methods to fluorescently label a single neuron and then image the entire brain would allow for a structural counting of axon boutons (though these don't necessarily correspond to functional synaptic contacts); combine this with some prior, in vivo measurement of synaptic strength from this single neuron to its partners, and you'd have yourself a very interesting study :)

Many thanks for your in depth answer, it is very useful! I assumed this was and easily answerable question, but as you astutely point out, experimentally it is extremely challenging.

I asked because  most neural models say the activation of a neuron is the weighted sum of it's inputs. However if this dilution does take place, then the signal from an input should perhaps be divided by the out-degree of that input. I was just curious to see if there is any research which validates or nullifies this idea.

Cheers,

Jack 

Hi Jack. Assuming I've understood your question correctly, I think the simple answer is: no, the 'signal' is not diluted by the number of synaptic connections formed by the presynaptic neuron.

Remember that action potentials are regenerative, all-or-none events. Therefore, even in a neuron with a highly branched axon and many presynaptic terminals, the AP will invade all terminals equally, with no attenuation. Each individual presynaptic terminal is effectively indifferent to how many neighbours it shares an axon with.

Of course, the 'strength' of synaptic transmission at each individual synapse / release site can vary considerably, but this is determined by the properties intrinsic to the individual synapse (e.g. release probability / quantal content / postsynaptic receptor number / etc) and is not affected by the number of synapses formed by a particular axon.

Hope this helps.

Cheers,

Patrick.

Hey Patrick, many thanks for your answer. I understand the characteristics  of each synapse can vary drastically, and this of course changes the uEPSP of the post synaptic neuron. However I still find it very counter intuitive that the action potential received by the out going synapses is not diluted by the number of outgoing synapses of the post synaptic neuron. Let me explain:

Consider a neuron with an infinite number out going synapses, it receives a finite stimulation, perhaps from an external source or from a pre synaptic neuron. It spikes and then sends its action potential to each of the infinite outgoing synapses. If the signal is not diluted, then a infinite amount of change has occurred from a finite source, which violates the conservation of energy. Thus the action potential must be diluted some how, meaning he number of synapses formed by a particular axon, does effect the uEPSP of the post synaptic neurons. 

I am not sure what the mechanism is which `dilutes` the signal, perhaps the depletion of ions or neurotransmitters? However, in practical terms, maybe there is an abundance of ions and neurotransmitters, thus the dilution is neglable as the number of out going synapses never gets so large as to deplete them. 

Cheers,

Jack

Hi, Jack-

Patrick has this right. It may seem counter-intuitive if you think of the axon like a wire carrying current from a battery, but the action potential is not due to a source of energy that is being distributed across space. Instead, the action potential is a local change in electrical potential (due to differences ion concentrations) across the cell membrane, which is propagated along the axon. When the electrical potential difference across the membrane (Vm) reaches the threshold for the voltage-gated Na channel, this channel opens and allows Na ions to flow into the cell, resulting in a massive (relatively) change in the Vm. This causes the next set of voltage-gated Na channels to open, and this continues down the length of the axon. So, the source of the action potential isn't at the soma or axon hillock, it is local. Therefore, there is no violation of the principle of conservation of energy. Since the differences in ion concentration inside and outside the cell are pretty constant throughout the entire cellular environment (and kept this way thanks to those hard-working glial cells), the potential energy for this process is equal and equally available along every one of the axon's branches, no matter how many of them there are. And since the number of ions that actually move across the membrane is infinitesimally small compared to the concentration difference, it is not in danger of being depleted (just keep those Na/K co-transporters going...). I hope this helps.

Cheers,

-KI

Hi Jack. I'm afraid the consideration of infinite synapses and energy conservation might be a bit beyond my limited understanding of physics. However, under 'normal operation' I think it's fair to say that biological organisms (and their brains) are finite, open systems, and energy demands are usually easily met from external sources (i.e. food). Of course, it is possible that under pathological conditions (or perhaps in hypothetical infinite conditions) things can go awry, and the electrochemical gradients upon which action potentials depend might indeed break down / become depleted.

However, under normal conditions, action potentials do not attenuate or become diluted, no matter how highly branched the axon might be, or how many presynaptic terminals it has. The all-or-none nature of APs is one of their key characteristics, making their occurrence in a patch of axonal membrane effectively binary: an AP either happens or it doesn't. Furthermore, an AP occurring locally in one patch of membrane is always enough to trigger an AP in the adjacent patch of membrane, causing the AP to propagate along the axon (unless some sort of abnormal condition is present, such as a block of voltage-gated Na channels).

So if you consider an AP propagating along an axon, and it reaches a branch point where the axon splits into two... The AP waveform is not halved in each axonal branch... The amplitude of the AP in each branch will be (more-or-less) the same (and the same as it was before reaching the branch point). This is because APs are regenerated locally, in each local patch of membrane (i.e. you don't start with a certain amount of energy at the axon initial segment, which then needs to be distributed amongst the entire axonal arbour / presynaptic terminals). You can imagine each local patch of axonal membrane as containing its own energy store, ready to produce an AP upon receiving the appropriate (depolarising) stimulus.

In brief: APs do not become diluted or attenuated (unlike electrotonic potentials), because they are periodically regenerated. The AP occurring in one branch of an axon doesn't 'know', or 'care about', the AP occurring in another branch.

Hope this helps?

Cheers,

Patrick.

Hey Kurt,

Thank you! That clears things up for me. So in summary the limiting factor is the number of ions. However they are in no danger of being depleted due to:

1) The vast number of ions 

2) The relatively few number of ions required to create a sufficient change in Vm.

3) The speed at which ions are recycled.

Thus, the length of axon and number of synapses can be very very large without having any 'dilution'  effect on the action potential. 

I hope it wasn't too stupid a question.

Cheers,

Jack

@Patrick, 

Thank you! It does help. I was just wondering if models might need to consider this dilution effect, but as yourself and others have pointed out, the circumstances would have to be so extreme, that it would very likely never happen, thus it is not worth considering. 

thank you again for your answers,

Jack

There is no 'dilution' of action potentials because of their regenerative nature. Multiple synapses from a single axon are common, and this the basis of divergence. However, nerve conductance can fail at branching points (bifurcations), see: Parnas I, Segev I. A mathematical model for conduction of action potentials along bifurcating axons. J Physiol. 1979 Oct;295:323-43

Dear Jack,

Many people already emphasized that if the neurons X1 and X2, having outputs to Y1 Y2 and Y3 or Y1 and Y2, respectively, produce a single action potential, they will produce equal output signals in each of their axonal branches (equal input signals to neurons Y1, Y2, and Y3), because of the all-or-none principle, applicable for action potentials.

I'd like, however, give an additional point here. A question arises if the neurons X1 and X2 would themselves produce equal responses at their own inputs if they are equally stimulated. Let's assume that the neurons X1 and X2 have an equal input from the neuron Z (the same amount of neurotransmitter release, the same number of postsynaptic receptors and channels). Because of their different geometry, the two neurons may have different resistance of their extrasynaptic membrane which would result in a different amplitude of the postsynaptic potentials at their input (it's just the Ohm's law). Therefore, the two neurons would have different excitability and different discharge rate. This means that the two neurons are not equivalent for the information transfer. The neuron with the higher excitability and discharge rate will produce greater input to the Y neurons, because of the more effective temporal summation of PSPs  in the Y cell postsynaptic membrane. A popular example demonstrating the above described events are the motor neurons of different size. The smaller motor neurons possess higher excitability, because of their greater input resistance, and the smaller motor units are first recruited in the process of regulation of muscle strength (the size principle)

Dear Petia, size is something I did not consider, many thanks for your explanation and apt example!

Cheers,

Jack