<p>Longer axons would mean longer delays between the time a cell fires an action potential/reaches threshold and the time that synapses from that cell are activated: neurotransmitter released, postsynaptic voltage changes.</p>
<p>The model you link to doesn't bother to model these delays, so there's no way to make them longer within the framework of this model. It does have a time constant that smooths voltage changes, but the changes begin instantaneously. You could possibly introduce a delay such that you look at past values of &quot;r&quot;, but you'd have to start with some baseline delay: you can't model something &quot;twice as long&quot; by multiplying zero by 2.</p>
<p>In a real brain, conduction delays are quite short within the brain itself, and &quot;fixed&quot; costs of synaptic transmission are comparatively large: vesicle fusion, neurotransmitter diffusion and binding to post-synaptic receptors, and voltage changes governed by post-synaptic membrane capacitance all influence the speed of transmission; the latter (membrane capacitance) is arguably the slowest, so the model you link to only bothers with that step. Conduction delays begin to be more appreciable when considering communication with the periphery: muscles, sensory neurons. Additionally, conduction velocity is proportional to diameter, so in a larger brain some differences in conduction velocity can be accounted for by making axons larger as they get longer. This variation can also be seen in a single brain, e.g.:</p>
<p><em>Chomiak, T., Peters, S., &amp; Hu, B. (2008). Functional architecture and spike timing properties of corticofugal projections from rat ventral temporal cortex. Journal of neurophysiology, 100(1), 327-335.</em></p>
<blockquote>
<p>for those axonal projections on the ipsilateral side, the speeds of axonal conduction appear to be tuned to their length. As such, spike delivery becomes nearly isochronic along these pathways regardless of projection distance</p>
</blockquote>
<p>This paper finds that axons from a certain class of neurons have a diameter that depends on their projection target: neurons with a longer projection have a larger axon, such that signals from those neurons have about the same delay to their targets regardless of distance.</p>
<p>I certainly don't mean to argue that it's unimportant to consider brain size and conduction velocities in the experiment/model you propose, but just wanted to give some reasoning as to why you're likely to find simplified models that do not bother with these concerns for brain networks.</p>

CC BY-SA 4.0
2022-10-12T14:02:59.183Z
2022-10-12T14:10:01.260Z
2022-10-12T14:10:01.260Z
Bryan Krause
<p>I am studying the model presented in <a href="https://www.pnas.org/doi/10.1073/pnas.1905926116" rel="nofollow noreferrer">&quot;Simple framework for constructing functional spiking recurrent neural networks&quot;</a> but I am also interested in general answers or answers applicable to other models.</p>
<p>Let's say I have a brain A and a brain B with the same connectivity but in brain A axons are twice as long. Which parameter of the recurrent neural network should I change and how?</p>
<p>I come from a machine learning background so never thought of this question, but I imagine it should matter for neuroscience comparative studies with brains that vary significantly in size.</p>

CC BY-SA 4.0
2022-10-12T13:15:29.497Z
Welcome. What do you mean with '*synapses twice as long*'? And why would a brain be twice as big when its synapses are twice their size? Most of the cells in a brain are glial cells that lack synapses. Furthermore, there are fluid-filled cavities in a brain too that have a volume regardless synapse size.
AliceD
CC BY-SA 4.0
2022-10-12T13:34:46.290Z
I agree, twice as long synapses does not mean twice brain size. I realize I should have said "axonal length" instead of "synapse length", I will edit. By axonal length  I refer to  the length of the path connecting two neurons
blindeyes
CC BY-SA 4.0
2022-10-14T07:54:43.947Z
Why do you want to test the effect of varying the axonal length? Based on the kind of models you use, perhaps you are more interested in varying the number of connections in a "path" that links two neurons, i.e. the number of layers.
vkehayas
<neuroscience>
How can you set the axonal length in a recurrent neural network?
blindeyes
# How can you set the axonal length in a recurrent neural network?

(Asked by: username_0 on 2022-10-12)

I am studying the model presented in ["Simple framework for constructing functional spiking recurrent neural networks"](https://www.pnas.org/doi/10.1073/pnas.1905926116) but I am also interested in general answers or answers applicable to other models.

Let's say I have a brain A and a brain B with the same connectivity but in brain A axons are twice as long. Which parameter of the recurrent neural network should I change and how?

I come from a machine learning background so never thought of this question, but I imagine it should matter for neuroscience comparative studies with brains that vary significantly in size.

**Tags:** neuroscience

> **Comments:**
> **username_1**: Welcome. What do you mean with '*synapses twice as long*'? And why would a brain be twice as big when its synapses are twice their size? Most of the cells in a brain are glial cells that lack synapses. Furthermore, there are fluid-filled cavities in a brain too that have a volume regardless synapse size.  
> **username_0**: I agree, twice as long synapses does not mean twice brain size. I realize I should have said "axonal length" instead of "synapse length", I will edit. By axonal length  I refer to  the length of the path connecting two neurons  
> **username_2**: Why do you want to test the effect of varying the axonal length? Based on the kind of models you use, perhaps you are more interested in varying the number of connections in a "path" that links two neurons, i.e. the number of layers.  

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## 1 answers

### Answer by username_3 on 2022-10-12. Score: 1

Longer axons would mean longer delays between the time a cell fires an action potential/reaches threshold and the time that synapses from that cell are activated: neurotransmitter released, postsynaptic voltage changes.

The model you link to doesn't bother to model these delays, so there's no way to make them longer within the framework of this model. It does have a time constant that smooths voltage changes, but the changes begin instantaneously. You could possibly introduce a delay such that you look at past values of "r", but you'd have to start with some baseline delay: you can't model something "twice as long" by multiplying zero by 2.

In a real brain, conduction delays are quite short within the brain itself, and "fixed" costs of synaptic transmission are comparatively large: vesicle fusion, neurotransmitter diffusion and binding to post-synaptic receptors, and voltage changes governed by post-synaptic membrane capacitance all influence the speed of transmission; the latter (membrane capacitance) is arguably the slowest, so the model you link to only bothers with that step. Conduction delays begin to be more appreciable when considering communication with the periphery: muscles, sensory neurons. Additionally, conduction velocity is proportional to diameter, so in a larger brain some differences in conduction velocity can be accounted for by making axons larger as they get longer. This variation can also be seen in a single brain, e.g.:

*Chomiak, T., Peters, S., & Hu, B. (2008). Functional architecture and spike timing properties of corticofugal projections from rat ventral temporal cortex. Journal of neurophysiology, 100(1), 327-335.*

> for those axonal projections on the ipsilateral side, the speeds of axonal conduction appear to be tuned to their length. As such, spike delivery becomes nearly isochronic along these pathways regardless of projection distance

This paper finds that axons from a certain class of neurons have a diameter that depends on their projection target: neurons with a longer projection have a larger axon, such that signals from those neurons have about the same delay to their targets regardless of distance.

I certainly don't mean to argue that it's unimportant to consider brain size and conduction velocities in the experiment/model you propose, but just wanted to give some reasoning as to why you're likely to find simplified models that do not bother with these concerns for brain networks.


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