The Terence

We are often told that there are many different sorts of neurons, doing all sorts of different things; a regular menagerie of them. So I thought it was time to try my hand at making one up and I have named him Terence.

By some chemical means or another, Terence maintains an internal stack, which I number from the left S1, S2, … SN where N is some number between 5 and 10, numbers which have no particular significance, but which serve to set the scene. A stack element may be set or unset. Each stack element is associated with a chemical, probably some tricky organic chemical like 5-hydroxytryptamine, so we have the array C1, C2, … CN, and in order to maintain coherence, adjacent chemicals must be distinct. It may well be that no one chemical appears in the array more than once.

At any particular time, Terence’s state is some number between 0 and N. In the case that state is zero, none of the stack elements are set. In the case that state is M, where M is in the range [1..N-1], then all the stack elements in the range [1..M] are set and all the stack elements [M+1..N] are unset. In the case that M is N, then all the stack elements are set.

There is a decay counter which counts the number of milliseconds for which Terence has been in his current state. Some kind of neural clock.

If M is positive, in the absence of any external events, stack element M will decay to unset after some number of milliseconds, a number which might be a global constant or which might depend on M, and the decay counter is set back to zero. After some further number of milliseconds, stack element M-1 will decay to unset and so on, until the entire stack is unset and the state is zero.

We call all the neurons which connect presynaptically to Terence, his neighbours. The firing of these neighbours are our external events. The firing of some of these neighbours involves the release of one of the chemicals mentioned above into their synaptic gaps.

Firing

In the case that the state is N, and the chemical is CN, then Terence will fire again and the decay counter will be set back to zero.

In the case that the state is N-1, and the chemical is CN, then stack element N will be set, Terence will fire and the decay counter will be set to zero.

Other promotion

In the case that the state is M less than N-1 and the chemical is CM+1 (C(M+1) might have been less ambiguous, but is more tiresome to type), then stack element M+1 will be set, the state will be set to M+1 and the decay counter will be set to zero.

Maintenance

In the case that the state is M less than N and the chemical is CM, then the decay counter will be set back to zero.

Demotion

In the case that the state is M less than or equal to N and the chemical is CK for some K less than M, and the stack elements for [K+1.. M] are unset and the decay counter will be set to zero.

In this way, Terence’s firing is testimony to a certain, very particular firing history of his neighbours.

A variation would be to say that once the state is N, Terence is prepped or enabled and sufficient firing of non-chemical neighbours, will fire him. That is to say we add up the corresponding synaptic weights and if there are enough of them in unit time, then Terence fires, in the normal way of neural networks on computers, for which the jargon might be the integrate and fire of reference 1.

Note that for M less than N, it would be difficult to cheat by injecting chemical M into synaptic gaps from the outside. Given the rules for the stack, one would need to be unrealistically precise about the dose and the timing, and the neuron would be stuck at or below state M. But if M were equal to N and the chemical N only occurred in that top place in the stack, then flooding the gaps with chemical N would promote or amplify Terence’s firing in the case that he was more or less prepped otherwise.

Which also gives us a couple of simple mechanisms for inhibiting Terence, one endogenous, one exogenous.

Terence’s little sister

A variation would be to downgrade Terence’s stack to a set, a set to which a logical AND was applied. Each member of the set would be set and unset roughly along the lines suggested above, but with the only unsetting being down to decay. Little sister would be prepped when all the states were set and would carry on firing when poked until there was a long enough pause in the firing for one of the states to decay.

Conclusions

It would be easy to go on elaborating Terence and his family, to make the history and the firing even more particular. But a first job is to think about what on earth Terence might be for – or even his little sister, which would be easier. Easier still, how the function Terence implements might usefully be incorporated into a computer program of the ordinary sort.

And maybe I should try reading reference 1, heavy going though it might be.

References

Reference 1: https://en.wikipedia.org/wiki/Biological_neuron_model.