Central pattern generators

A walking leg swings forward and pushes back, and each phase of the cycle stretches some muscles and loads or unloads the foot. The obvious design is a chain of reflexes, each phase’s sensory consequences triggering the next. A central pattern generator is the alternative: a circuit in the spinal cord or a ganglion that makes the alternation itself, from an input with no rhythm in it, and leaves the senses to adjust the result. To an engineer it is an oscillator with a control input.

An arrhythmic stimulus, a rhythmic answer

Thomas Graham Brown did the experiment in Sherrington’s own laboratory in Liverpool and published it in 1911. In decerebrate cats he deafferented both hind legs and silenced every muscle but an ankle flexor and an ankle extensor. Then he cut the spinal cord at about the twelfth thoracic segment — a stimulus with no rhythm in it — and the two muscles answered by contracting in alternation, scarcely differently from muscles whose sensory nerves were intact. The phasing, he concluded, was set in the cord.

His mechanism was two antagonistic centres inhibiting each other: the active one fatigues, the inhibited one rebounds past the point of balance, and the cycle repeats. By 1914 he was calling them half-centres. Calabrese and Marder, in a 2026 history, call the 1911 paper the first definitive demonstration of a central pattern generator for a non-automatic rhythm, but it changed very little. Sherrington explained it away, and the reflex chain held through the 1950s.

The tipping point, in their account, was Donald Wilson’s 1961 paper on locust flight. With the timed sensory input from the wings removed, stimulating the nerve cord or blowing a steady wind on the head still produced a pattern resembling flight, only considerably slower. Wilson reached Graham Brown’s conclusion — the coordination is central, and feedback adjusts its frequency and details — without citing him.

Two ways to keep time

Graham Brown’s pair survives as the half-centre oscillator: two neurons, or two pools, that do not burst on their own but alternate when each inhibits the other. Two inhibitions in a loop make positive feedback, so the pair latches with one side on — a two-entrant version of the winner-take-all that lateral inhibition becomes when pushed hard. It oscillates when something slow undermines the winner: its firing adapts until it releases the other side, or the loser escapes through its own membrane currents, often firing on rebound as the inhibition lifts. An engineer would draw an astable multivibrator, two cross-coupled stages each holding the other off until a timing capacitor recharges. Reciprocal inhibition is a core feature of almost every pattern generator whose wiring is known.

The other way is a pacemaker, a neuron whose own voltage-dependent conductances — the kind the Hodgkin–Huxley model describes — make it burst unprompted and drag its followers along. The stomatogastric ganglion of crabs and lobsters, among the best-understood cases, has both. Its 26–30 identified neurons drive the stomach: a pyloric rhythm with a period of about a second, continuous and paced by a bursting interneuron, and an episodic gastric mill rhythm of 10–20 seconds built on reciprocal inhibition. The wiring is known, yet modulatory neurons carrying different mixtures of transmitters call different rhythms out of the same cells.

One drive signal, two gaits

The arrangement that emerged is a hierarchy — a command from above, a generator in the cord, the senses grading each step — and its top layer needs little. Shik, Severin and Orlovsky found in 1966 that stimulating a small region of a decerebrate cat’s midbrain, now called the mesencephalic locomotor region, made it walk, faster as the current rose; in many such experiments the gait changed too, from walk to trot to gallop. In a salamander a few microamps there produce stepping, and a little more, swimming (Cabelguen and colleagues, 2003). The stimulus carries no step timing; its strength picks the gait.

Ijspeert, Crespi, Ryczko and Cabelguen built that into a robot salamander in 2007. Its ten motors — six in the spine, four turning the legs — took their set-points from 20 coupled oscillators, a double chain of 16 along the body as in the lamprey and one per leg, whose phases obey

$$\dot{\theta}_i = 2\pi\nu_i + \sum_j r_j \, w_{ij} \sin\left(\theta_j - \theta_i - \phi_{ij}\right)$$

Here $\theta_i$ is the phase of oscillator $i$, $\nu_i$ its intrinsic frequency, $r_j$ the amplitude of oscillator $j$, $w_{ij}$ the coupling strength and $\phi_{ij}$ the phase lag the coupling tends to impose. One drive sets every intrinsic frequency and amplitude, which rise with it between two thresholds and are zero outside them. The leg oscillators run slower than the body’s and shut off above a drive of 3, where the body’s continue to 5, and they pull on the spine three times as hard as its segments pull on each other. At low drive the legs win and bend the body into a walking salamander’s standing S-wave. Above 3 their amplitude falls to zero, so through the $r_j$ in the coupling term they vanish from the spine’s equations, and its own phase lags send a travelling wave from head to tail.

What crossed was an architecture, not a circuit. Two slow commands, a drive for each side whose difference steers, become ten coordinated joint trajectories, and because the pattern is a limit cycle the oscillators return to it after a disturbance. The authors offered it because robots with many joints had no well-established method of locomotion control; Ijspeert’s 2008 review defines a pattern generator by that property: coordinated, high-dimensional rhythmic output from simple, low-dimensional input. Even the layering crossed, with a PD position loop on each motor where the animal has reflexes.

What the pure story leaves out

Graham Brown never claimed the cord could walk unaided. A central mechanism alone might carry an animal across perfectly even ground, he wrote, but would rule out “the fine stalking of a cat over rough ground”, where each step must be graded. Later measurements gave feedback a bigger job than grading.

In the locust, removing the four stretch receptors at the wing hinges roughly halved the wingbeat frequency, while disturbing their timing left the frequency normal (Wilson and Gettrup, 1963): to the oscillator they are a bias, not a clock. Pearson and Wolf (1987) found the deafferented pattern distinctly different in shape too, the interval from depressor to elevator activity growing from about 20 ms to 50–90 ms. In walking cats, a leg held still and drawn slowly backwards lifts into swing at about the hip angle where swing normally begins (Grillner and Rossignol, 1978), and swing waits while the ankle extensors are loaded: more than about 4 kg on them suppressed the flexor burst altogether (Duysens and Pearson, 1980). The generator proposes the next phase, and the leg’s sensors decide when it may start. And the cat’s spinal half-centres, Calabrese and Marder note, have yet to be pinned down.

The 2007 robot’s oscillators took no sensory input, only the drive. Its gait was easy to command; fitting it to the ground is the part Graham Brown left to the senses.