This month, I discuss a thesis that addresses theoretical questions about the morphology of neurons (1). It tries to understand why neurons of higher invertebrates have a different morphology than those of vertebrates. Another paper (2) asks the following question: what would happen if the sodium channels did not accumulate in the initial segment? The authors use a computational model and a genetic approach. Finally, one paper (3) introduces a much needed framework to compare models of binaural hearing.
This is a PhD thesis in theoretical neurophysiology. It addresses several topics, but I will only discuss the part about the morphology of neurons. The thesis addresses the following question: why is the soma of higher invertebrates externalized, that is, with a unipolar morphology (dendrite and axon forming a single process, with the soma attached by a stem). The core of the work was published as a separate paper (Hesse and Schreiber, 2015), but the thesis contains a more in-depth discussion, in particular some comparative biology. The approach is to look at electrical transmission from dendrite to axon, and the theoretical argument is the following. If the soma is on the path between dendrite and axon, then there is an attenuation due to a passive current proportional to the surface of the soma. If the soma is externalized through a long stem, then the leak is proportional to the surface of a characteristic length of neurite, which varies with its diameter. Thus, for a large soma, it is more advantageous to externalize the soma; for a small soma, it is better if it is centralized. More precisely, soma area is proportional to d_soma^2 and stem characteristic area is proportional to d_stem^3/2, and it is the ratio of these two numbers that determines whether the soma should be externalized or not (the paper mentions the ratio d_soma^2/d_stem, because the characteristic length is inserted in the critical value rather than in the ratio). The empirical data shows the expected trend. The thesis discusses other aspects that are not electrical.
One critical question in the theory is the relation between stem diameter and soma diameter. A simple idea proposed in the thesis is that the soma produces proteins at a rate proportional to its volume d_soma^3, and those proteins must flow through a section of area d_stem^2, so the diameter of the stem should scale as d_soma^3/2. This is actually roughly consistent with the data shown in table S1 of the paper (although this interesting empirical fit does not appear in the paper or thesis).
If we then look at what was defined as the “soma-to-neurite” ratio in the paper, which is d_soma^2/d_stem, then we find that it should scale as d_soma^1/2: so, larger somas should be externalized. However, if we look at the more relevant ratio, which is soma area over area of a characteristic length of stem, then we actually find d_soma^(-1/8), and we obtain the opposite conclusion. Thus, the theory would actually predict that larger somas should not be externalized; in other words, it is not so clear that the size of the soma explains its externalization.
The thesis also has an interesting discussion of other scaling relations in neuronal morphology.
2. Lazarov E, Dannemeyer M, Feulner B, Enderlein J, Gutnick MJ, Wolf F, Neef Z (2017). Axonal spike initiation can be maintained with low axonal Na channel density, but temporal precision of spiking is lost. (Comment on PubPeer)
This study looks at the effect on spike initiation of a genetic mutation that specifically impacts an AIS-specific protein (beta-IV spectrin). That mutation seems to affect the density of Nav channels at the AIS, which becomes close to the somatic density (with the caveat that this observation is based on immunochemistry, and it is not so obvious to precisely compare the axonal and somatic fluorescence signals quantitatively). Electrophysiologically, the consequences are: higher threshold, lower onset rapidness, lower spiking precision, poorer high-frequency tracking properties.
The authors insist on the fact that the results show that a high density of Nav channels is not necessary for axonal initiation of spikes. Indeed the mutant cells generally show a biphasic phase plot characteristic of axonal initiation. They found the same thing in a biophysical model (from Hallermann et al. 2012), where Nav density is modified to be the same in AIS and soma. This, however, is not particularly surprising since Nav channels have a lower activation voltage in the AIS than in the soma (both in the model and in empirical observations). The authors cite an old paper (Moore 1983) that proposes another potential reason why spikes initiate in the axon, which is interesting: if the soma and AIS have the same Nav channel density, spikes would still initiate in the AIS because less current leaks in the direction of the axon than towards the dendrite (both resistance and capacitance). This, however, is only true if there are no dendritic Nav channels, but the model used here actually has the same Nav density in the soma and dendrites, so the reason why spikes initiate in the AIS in this case is because of lower activation voltage of axonal channels.
3. Dietz M, Lestang JH, Majdak P, Stern RM, Marquardt T, Ewert SD, Hartmann WM, Goodman DFM (2017). A framework for testing and comparing binaural models. (Comment on PubPeer)
This paper introduces an open computational framework (on github) to test binaural models on empirical data. This is a very valuable initiative as many models have been developed but it is very difficult currently to compare them, in particular because they are written with different languages. The idea of the framework is to use a file-based approach: the model is expected to read a stereo wave file and output a response (which can be a decision or spike trains, for example). The rest is handled by the framework. The code seems to be in its infancy and there are not many data sets, but hopefully this will grow. I would like in particular to see more ecological sets, eg with natural binaural signals and an absolute localization task.
There is also a valuable review of binaural models. I have a few remarks on some points of the review. In the open questions, it is written that there are binaural neurons that respond at non-zero ITDs and that this is challenging to some models. I believe the authors meant that there are more neurons that respond at non-zero ITDs than at zero ITDs; in all models, there are neurons that respond at non-zero ITDs. When introducing hemispheric rate difference models, the authors cite van Bergeijk (1962) and von Békésy (1930); these two citations are indeed always cited in this context. But it is actually wrong, because those models are quite different from the hemispheric model. One similarity is that the number of active neurons is counted (instead of picking the most active one), but this is done on top of a delay-line model, with heterogeneous delays covering the physiological range – so in reality quite close to the Jeffress model. The discussion of the interaural group delay seems to have missed our work on this topic: 1) Bénichoux V, Rébillat M, Brette R (2016). On the variation of interaural time differences with frequency, where we explain how this produces an additional cue for realistic binaural signals, and most importantly 2) Bénichoux V, Fontaine B, Karino S, Franken TP, Joris PX, Brette R (2015). Neural tuning matches frequency-dependent time differences between the ears, where we explain how coincidence detection between mismatched places on the two cochleae produces selectivity for a specic interaural group delay (or envelope ITD).
I am looking forward to seeing more data integrated into this framework.