In both vertebrates and invertebrates, clusters of neurons fire rhythmically to generate the basic pattern for regular movements such as walking, swimming and gut peristalsis. These central pattern generators, or CPGs, need neither sensory input nor higher brain function to produce a more-or-less appropriate rhythm at some baseline frequency. But even though they can operate in isolation, they're also strongly affected by the senses. The walking CPG, for example, can reset its rhythm if one leg catches on something as it swings.

Sensory feedback on CPGs isn't limited to dealing with simple perturbations. It can also help make movements more efficient by taking advantage of mechanical resonance. For example, when a leg swings during walking, it's like a pendulum. And, like a pendulum, it has a natural frequency that it prefers'. Pushing it to swing faster or slower than this frequency takes more energy. If a CPG's baseline frequency and the body's mechanical resonant frequency aren't too far apart, often the CPG will burst at the resonant frequency, which helps conserve energy.

But what types of sensory input does a CPG need to achieve this resonance tuning?' To probe this question, Carrie Williams and Stephen DeWeerth of the Georgia Institute of Technology started with a simple mathematical model of a CPG called a half-centre oscillator', two neurons that are linked so that they fire alternately. Then they linked the neurons to a mathematical model of a classic mechanically resonant system: a pendulum whose swinging is gradually damped out with friction. Each neuron controlled muscles' that pushed the pendulum in opposite directions.

Then they tried four different types of feedback from the pendulum to the CPG. The first two were negative feedback - swinging to the left either inhibited the left-side neuron or excited the right side. Either way would tend to stop the pendulum and push it back the other way. The other two ways were positive feedback - swinging to the left now excited the left-side neuron or inhibited the right. These feedback modes would tend to enhance a swing in one direction.

Even though positive feedback loops cause many systems to spiral out of control, in Williams and DeWeerth's model both positive and negative feedback loops settled at the resonant frequency. Negative feedback can speed up the system when the resonant frequency is higher than the CPG's baseline. The stronger the sensory input, the wider the range of resonant frequencies the CPG can use. By contrast, positive feedback slows the system down, but only if the input has just the right strength. With a weak input, the CPG just runs along at its own frequency. With a strong input, the positive feedback causes the system to oscillate unstably. Somewhere in the middle, though, the CPG slows down nicely to a resonant frequency below its baseline.

The researchers' results point towards a way for experimentalists to differentiate between positive and negative feedback. In the model, negative feedback could only speed the CPG up. So if the CPG runs slower without any sensory input at all, as the CPGs in most vertebrates do, then at least some of the feedback is probably negative. By contrast, if the CPG runs faster in isolation, or, better yet, behaves strangely with very high amplitude inputs,then positive feedback probably plays a role.

Williams, C. A. and DeWeerth, S. P. (
2007
). A comparison of resonance tuning with positive versus negative sensory feedback.
Biol. Cybern.
96
,
603
-614.