I was lucky enough to do some programming work, very many years ago, in the 1990s, in the laboratory of Ralph Siegel (https://en.wikipedia.org/wiki/Ralph_Siegel_(scientist)), who among other things worked on this type of worm connectome models. He used the Hodgkin-Huxley equations to simulate neuron responses on the connectome. The Hodkin-Huxley model, as someone explained to me, is kind of like modeling a human leg as three rigid blocks connected by hinges - it's enough to be useful in many models, but of course it's not a full description. Also, it may not the right model for worm neurons, because worm neurons are non-spiking, and the HH equations describe neurons that produce trains of spikes; they exist in more complicated nervous systems. The HH equations are used in simulations because it's the mathematical model we have, and it seems that they're still used by the OpenWorm project. (I am not very sure about properties of worm neurons, I heard about this a long time ago and the information may be out of date).
I think it's great that this work is still going on, it may produce insights about functioning of nervous systems. But the difficulties are fierce, and we're making very slow and difficult progress in an immense unknown area.
This is the first time I read that. That's fascinating. So they are very different then compared to what we have in humans? How do they work? Where can I read about this?
They aren't too different from human neurons. Non-spiking neurons also use nonlinear membrane dynamics to integrate inputs into a signal encoded by the voltage across the membrane. The cell then outputs a neurotransmitter in response to its voltage. In the case of a spiking cell and a spike dependent synapse, synaptic release is thought to be all or nothing. While in graded synapses, synaptic release is a more linear (modeled as a less steep sigmoid) function of voltage. Spiking cells can also have graded synapses (at least in crustaceans, I don't really know about vertebrates).
The idea is that spiking is one way to have a more robust signal over long distances: Crustaceans often have nonspiking local interneurons and spiking projection neurons and motor neurons. The problem of fast, reliable electrical signal transduction over long distances is also solved by having more insulation (particularly in vertebrates) or having thicker cables (particularly in invertebrates).
Humans also have non-spiking neurons with graded synapses in the retina.
I am not the best person to ask, since it's not my field. I heard this from the neuroscientists that I worked with. My understanding is that there are spiking and non-spiking neurons in most nervous systems, including human, but most of the ones in ours are spiking. The earliest-evolved animals, such as nematodes, do not have spiking neurons, or myelin, or some of the ion channels in neuron membranes that more evolved neurons have. Their neurons still have axons and dendrites, but the signals propagate much more slowly and in different ways. I am not sure how well they are understood.
As I said, this is possibly out-of-date information. If there is someone here from the neuroscience field, they can probably make a better comment.
Not all the cells of the nervous system produce the type of spike that define the scope of the spiking neuron models. For example, cochlear hair cells, retinal receptor cells, and retinal bipolar cells do not spike.
Ralph's main work was on neural impulses in the visual cortex, and on measurements of various potentials in the living brain. He published a memoir called "Another Day in the Monkey's Brain". I believe he had potential medical applications in mind, but I don't think anything that was close by. Unfortunately, he died of an illness in 2011.
I think it's great that this work is still going on, it may produce insights about functioning of nervous systems. But the difficulties are fierce, and we're making very slow and difficult progress in an immense unknown area.