OK, I've skimmed through Hercules Rockefeller's links and found that most specialists seem to lean somewhat in favour of a broad similarity between neurons across the vertebrate-invertebrate division line.
However, there doesn't seem to be anything like a scientific position on this yet. Further, neurons have evolved and there may be different points along this long evolution where neural-like cells have acquired the various structural characteristics that give our neurons their functional value. Thus, there is no doubt that at least some species must have, or must have had, neural cells with some functional differences compared to our own neurons.
There are also suggestions that the main difference is the number of neurons and the organisation of these neurons into a functional whole rather than functional differences between the neurons themselves, with the suggestion that the same neuron is probably capable of functionally different roles depending on where it happens to be located within the whole system of neurons, and therefore what connections it has with other neurons.
I put a selection of what I found that give some light on the subject. None of these people provide anything like a direct answer to my question, but there is definitely a broad direction of travel, at least for now.
To think about this problem, we can think of limbs and how different species incarnate the different solutions to the problem of using extensions to the body to perform some activities on behalf of the organism as a whole. Although these solutions can be structurally very different from one species to the next, the functionality can be remarkably similar.
It should be noted that the brain has local areas which themselves have functionally different roles, for example memory, perception or language. Yet, the neurons are probably essentially of the same model across the brain, each neuron only developing in situ a specific set of characteristics according to the area where it is located.
See in particular the last paragraph.
In any case, there seems to be still an awful lot to be discovered about our neurons although it is probably going much faster today.
EB
Vertebrate versus invertebrate neural circuits
https://www.sciencedirect.com/science/article/pii/S0960982213006349
Eve Marder
Brandeis University, Waltham, USA
Many years ago, invertebrate circuits were often called ‘simple”. Today we know that small circuits are quite complex and show dynamics that reveal many fundamental principles of circuit function. These principles provide a library of circuit mechanisms that are almost certainly used in all large brains. Indeed, any mechanism found first in small nervous systems (for example, bursting neurons, widespread neuromodulation, electrical coupling) eventually has been revealed in larger brains. To me, the essential question is how special features arise in large networks precisely because of their size, despite the fact that many explanations of how large circuits work resort to describing them as if they were small circuits.
Sten Grillner
Karolinska Institute, Stockholm, Sweden
The general features of the control systems for motion (sensory and network level) are similar in invertebrates and vertebrates. Moreover, recent evidence suggests that more advanced invertebrates (protostomes) and vertebrates have a common design of forebrain circuits. At the microcircuit level, a variety of invertebrate systems have contributed importantly, notably the stomatogastric system. Vertebrate circuits tend to be more complex with larger numbers of interacting nerve cells. On the other hand, vertebrate cells are simpler to analyze, since the cell body is located between the dendrites and the axonal spike initiating zone. In contrast, invertebrate neurons have their processes located in a dense neuropil in the central parts of the ganglia, and signals from dendrites and axons are transmitted passively to the unipolar cell body.
Alexander Borst
Max-Planck-Institute of Neurobiology, Martinsried, Germany
Clear structural similarities exist in peripheral processing stages of vertebrate and invertebrate nervous systems — for example, between the nicely layered optic lobe of insects and the vertebrate retina, or the glomerular organization of the insect antennal lobe and the olfactory bulb of vertebrates. These similarities apply to functions as well. Telling examples are the convergence of spatially distributed olfactory receptors with the same odor response spectrum in single glomeruli in the olfactory system or the splitting of photoreceptor input into parallel ON- and OFF-processing channels in the early visual system of both animal groups. To what extent the actual circuits performing a particular computation are similar remains to be seen. Given the current intense investigations in both the retina and the fly optic lobe, the circuit for local motion detection might be the first case where this question can soon be answered.
Ralph Greenspan
Kavli Institute for Brain and Mind, San Diego, USA
They are likely transferable in several respects: first, the functional and computational strategies in invertebrates, where they are more easily discernible, are likely to be found in vertebrates; second, the embryonic gene expression patterns designating brain structures and substructures show a high level of conservation; and third, there is emerging evidence that adult brain structures sharing embryonic gene expression patterns carry out similar tasks and use the same intercellular signaling systems. Examples of the latter are the correspondence between the insect pars intercerebralis and the hypothalamus, and between the insect central complex and the basal ganglia, despite the lack of any anatomical similarities.
William Kristan
University of California, San Diego, USA
The brains of many animals differ in their details: ionic channels, neurotransmitters, neuronal interconnections vary, even between rats and mice. General functional principles, however, are overwhelmingly similar: central pattern generators, lateral inhibition, gain control, balanced excitation and inhibition; the list of generalities across phyla is both extensive and will expand as more circuits are investigated. Finding the mechanisms underlying these principles is more tractable — and more convincing — using a nervous system that is simple enough to be able to both record the activity of many of its neurons during behavior and modify that behavior by stimulating single neurons. Yes, I want to know how human brain circuits work; that’s why I study the leech nervous system!
Dmitri “Mitya” Chklovskii
Janelia Farm Research Campus, HHMI, Virginia, USA
Because both vertebrates and invertebrates often live in the same environment and have similar behavior objectives, the functional requirements on their neural circuits are similar. For example, the statistics of natural visual scenes are reflected in the properties of receptive fields of neurons in the early visual systems: spatial receptive fields are center-surround and temporal receptive fields are biphasic as predicted by efficient coding/predictive coding theories. However, similar functional properties may be achieved by different mechanisms. It would be very interesting to see, by combining connectomes with the results of genetic, physiological, and behavioral experiments, how similar these mechanisms actually are. Both similarities and differences will inform our theoretical understanding of brain function.
https://www.nap.edu/read/13462/chapter/3#4
Surprisingly, the genome of the Poriferan demosponge, Amphimedon queenslandica, contains an almost complete set of genes homologous to those found in mammalian synapses (Fig. 1.1A), although the organism does not assemble any structure morphologically resembling a synapse (Sakarya et al., 2007; Srivastava et al., 2010).