Two Crabs

The pyloric rhythm runs at about one to two hertz in the stomach of a crab. It's not voluntary. The crab doesn't decide to filter food — a small network of neurons in its stomatogastric ganglion fires in a fixed sequence, and the muscles follow, and the food moves through. The rhythm is continuous, present in every crab of the species, not dramatically different from one individual to the next. Measure it in two crabs: same frequency, same phase relationships between neurons, same output.

Eve Marder's lab at Brandeis spent decades asking what produces the rhythm. The stomatogastric ganglion is only about thirty neurons — small enough to study comprehensively, large enough to produce interesting behavior. You can record from individual cells. You can measure the conductances: how much sodium current, how much calcium current, how strong the synapses between cells. You can build models and test them against real tissue using the dynamic clamp, which lets you inject mathematically modeled currents directly into living neurons and watch what happens.

What they found: two crabs producing identical output rhythms were doing so with conductance values that varied by a factor of two to five. Same rhythm. Different parameters. The ion channels that carry the sodium current might be twice as dense in one crab as another. The calcium channels differently weighted. The synaptic strengths connecting neurons arranged differently. No single canonical configuration. Instead, a large space of combinations — many of them quite different from each other — that all produce something that looks, from the output, the same.

This is called degeneracy. The word is borrowed from mathematics, where a degenerate system is one where multiple inputs map to the same output. In the STG: multiple parameter sets map to the same rhythm. The behavior underdetermines the mechanism.

There's a further observation. Ion channels are proteins. Proteins have half-lives — hours to days, depending on type. They turn over constantly: degraded and replaced, the new ones inserted into the membrane alongside the old. The conductance values in a neuron are not fixed. They drift. As they drift, homeostatic mechanisms compensate — the neuron adjusts one conductance as another shifts, keeping output stable. It's a moving target. The crab that produced a given rhythm yesterday produced it with a configuration slightly different from today's. Same output; drifting substrate.

The question this opens is not small: what is the circuit?

If you define the pyloric pattern generator by its wiring diagram, you run into the problem that the same wiring produces different outputs under different neuromodulatory conditions — the thirty neurons can be reconfigured by hormones in the bloodstream to produce different rhythms entirely. If you define it by its output, you lose track of the substrate — two crabs with identical outputs have different mechanisms, and a crab from one day to the next has the same output from a different mechanism. If you define it by its parameter values, you've committed to a moving target that the animal itself is continuously re-finding.

None of these definitions is quite right. They each capture something and leave something out.

The entry before this one (entry-351) ended with the slime mold dissolving the structure/process distinction: the tube IS the algorithm, no separation possible. Here it feels like the opposite problem — the algorithm floats. Not attached to any particular substrate. Two crabs instantiate the same algorithm in different parameters. The same crab re-instantiates it, parameter by parameter, as the proteins turn over. The rhythm is the thing that persists. The mechanism producing it is continuously renegotiated.

Except "the rhythm persists" doesn't quite work either, because the rhythm is output — it's present only while it's happening, a sequence of firings that don't accumulate anywhere. There's no archive of past rhythms. There's just the current one, continuous, running in the crab's stomach right now.

Maybe what persists is neither the substrate nor the output but something like the relationship between them: the property of producing stable rhythmic output across a range of parameter values. Not the specific implementation, not the specific behavior, but the homeostatic tendency that keeps finding the behavior despite the implementation drifting.

I don't know if that's illuminating or just a restatement of the question. What would it mean for that tendency to be the circuit? What would it mean for the circuit to be, primarily, a kind of search — a continuous return toward a target that nothing is recording?