Hi, Henry --
Hi Bill,
It's probably not realistic to derive a general transfer function for
a neuron, because different types of neurons differ mainly in the
receptors and channels they express and, as a consequence, cannot
possibly have the same transfer function.
BP: Probably I'm asking too much -- yes, it's difficult to get measurements in vivo, especially the subtle kind I suspect that we need to measure: processes in the dendrites due to diffusion and mutual interactions of inputs. There could be input functions at the level of biochemistry that define what patterns the cell can detect, as Randy's model suggests but at a finer level of detail in a single neuron.
I wasn't proposing to find "the" transfer function for "the" neuron: just one will do for starters. I just want to see how it looks -- time lags, integration lags, amplification, differentiation, and so on. I'd like to have a more realistic version of the arrangements I described very sketchily in B:CP, chapter 3. It would be nice to show how those circuits would work with realistic neural models. Is my concept of a neural time-integrator feasible? And if not, is there another arrangement that would create the same effect? I've seen recordings of neural responses that show a very slow decay of impulse frequency after cessation of an input signal, the time constant being many seconds. I wish I had been scholar enough to write down the references, all those years ago. At least I know that can be done with neurons.
Actually, we don't necessarily need to do these measurements in vitro. Instead of experimentally manipulating the input signals, we could just take whatever signals show up in a working system, and record them. The question would be whether it is possible to record the action potentials at input and output without interfering with normal operation. Maybe one of those techniques using fluorescent dyes?
HY: And even if you can get such a function for a particular neuronal type, say the pyramidal neuron in the cortex, still it's not clear what you can do with it, because it's not known what this neuron is doing--i.e. which function it may correspond to in a control system.
BP: Leave that to me and don't worry. I'll figure out something. Give me a nice model of a pyramidal cell and I'll sit and watch it run for a few hours, tinkering with it, and something will come to me. That's the part I'm good at because I trust my reorganizing system, and I understand circuitry. The question is, what sorts of things could a cell like this do? Or two cells like this, or a dozen, properly interconnected? And when I figure that out I can send my circuit model to Randy and you, and ask "Have you ever seen anything like this in a real nervous system?". Remember how we got onto the phase splitter idea -- you told me of a strange organization that keeps showing up, and I recognized it. We ought to be able to make something out of that kind of division of labor.
HY: Besides, this type of
measurement is largely impossible in vivo or in vitro. You have to
preserve all the inputs to the cell and stimulate those inputs. It's
possible perhaps in cell culture, but then the connectivity is not at
all similar to real connectivity. One day it may be possible to do it
at the Calyx of Held
BP: Now, now, Henry, stop showing off. I had to look that one up.
HY: or the neuromuscular junction, but it will
require extremely sophisticated technology which we currently don't
have.
BP: Either that, or something very clever. For example, we can deduce the muscle force resulting from a certain level of motor signals from the spinal cord by measuring the second derivatives of joint angles, if we know the mechanical advantages and the moments of inertia of the moving parts. We don't actually need to get in there with probes at the level of the neuromuscular junction. A little physics can help a lot.
HY: So this bottom-up approach is not feasible. If you really
wanted to do this sort of thing, you might as well accept the standard
neuron using the channels and receptors commonly found in neurons
(which NEURON should offer) and see what happens when you play with
that. Now a lot of people have done that, but it's difficult to
evaluate this large literature.
BP: Who knows, you may be right. On the other hand, maybe I can do it anyway. We'll never know unless I try, or somebody does. Actually, I was thinking of doing exactly what you say with Neuron -- build some models and see what happens. You already know that this is how I like to work. If I get lucky we will all be happy.
HY: I'm inclined to think that the "ideal neuron" that is often used in
modeling is good enough for your purposes. But I don't recommend the
bottom-up approach.
BP: In that case, you should avoid using it. I, on the other hand, like to start in the middle and work both ways, which does sometimes work. Fortunately, I have no academic reputation to protect, and can take chances.
Best,
Bill