Motor control is sometimes presented as the prototypical example of rate coding. That is, muscle contraction is determined by the firing rate of motoneurons, so ultimately the “output” of the nervous system follows a rate code. This is a very interesting example, precisely because it is actually not an example of coding, which I previously argued is a problematic concept.
I will briefly recapitulate what “neural coding” means and why it is a problematic concept. “Coding” means presenting some property of things in the world (the orientation of a bar, or an image) in another form (spikes, rates). That a neuron “codes” for something means nothing more than its activity co-varies with that thing. For example, pupillary diameter encodes the amount of light captured by the retina (because of the pupillary contraction reflex). Or blood flow in the primary visual cortex encodes local visual orientation (this is what is actually measured by intrinsic optical imaging). So coding is really about observations made by an external observer, it does not tell much about how the system works. It is a common source of confusion because when one speaks of neural coding, there is generally the implicit assumption that the nervous system “decodes it” somehow. But presumably the brain does not “read-out” blood flow to infer local visual orientation. The coding perspective leaves the interesting part (what is the “representation” for?) largely unspecified, which is the essence of the homunculus fallacy.
The control of muscles by motoneurons does not fit this framework, because each spike produced by a motoneuron has a causal impact on muscle contraction: its activity does not simply co-vary with muscle contraction, it causes it. So first of all, motor control is not an example of rate coding because it is not really an example of coding. But still, we might consider that it conforms to rate-based theories of neural computation. I examine this statement now.
I will now summarize a few facts about muscle control by motoneurons, which are found in neuroscience textbooks. First of all, a motoneuron controls a number of muscle fibers and one fiber is contacted by a single motoneuron (I will only discuss α motoneurons here). There is indeed a clear correlation between muscle force and firing rate of the motoneurons. In fact, each single action potential produces a “muscle twitch”, i.e., the force increases for some time. There is also some amount of temporal summation, in the same way as temporal summation of postsynaptic potentials, so there is a direct relationship between the number of spikes produced by the motoneurons and muscle force.
Up to this point, it seems fair to say that firing rate is what determines muscle force. But what do we mean by that exactly? If we look at muscle tension as a function of a time, resulting from a spike train produced by a motoneuron, what we see is a time-varying function that is determined by the timing of every spike. The rate-based view would be that the precise timing of spikes does not make a significant difference to that function. But it does make a difference, although perhaps small: for example, the variability of muscle tension is not the same if the spike train is regular (small variability) or if it is random, e.g. Poisson (larger variability). Now this gets interesting: during stationary muscle contraction (no movement), those motoneurons generate constant muscle tension and they fire regularly, unlike cortical neurons (for example). Two remarks: 1) this does not at all conform to standard rate-based theory where rate is the intensity of a Poisson process (little stochasticity); 2) regularly firing is exactly what motoneurons should be doing to minimize variability in muscle tension. This latter remark is particularly significant. It means that, beyond the average firing rate, spikes occur at a precise timing that minimizes tension variability, and so spikes do matter. Thus motor control rather seems to support spike-based theories.