My initial sense is that PCT demos do not necessarily need to implement bidirectional control in the same manner as neural tissue in the brain. We are talking about models of control, and the equations that implement PCT comparators in those models can already go positive or negative. The math takes care of it. It doesn’t need a neurochemical implementation.
However, in the brain, neurophysiology certainly does count. As Rick rightly notes, B:CP’s working assumption is that control loop signals in the brain are carried by the rate of firing itself. And neural action potentials cannot go negative. The most an inhibitory signal can do is to reduce an excitatory signal to zero. The analogy that works for me is that you cannot push on a rope, only pull.
I made the claim in “How the brain gets a roaring campfire: Thalamus through a PCT microscope” (one of the online chapters in The Interdisciplinary Handbook of Perceptual Control Theory: Living Control Systems IV) that thalamic relay cells can function as PCT Comparators. There appears to be Reference input ‘from above’ (specifically, layer 6 neurons in the neocortex), which arrive in thalamic relay nuclei at the same locale as Perceptual input ‘from below’. The standard way that the Reference input is routed is through the thalamic reticular formation, which receives an excitatory signal and sends out an inhibitory signal, down to the thalamic relay neuron. In other words, it reverses the sign of the Reference signal!
So the ‘thalamic comparator’ there now has the equivalent of (p - r), which in the context of control loop equations will tend to decrease subsequent values of p until they approximate the value of r. That is to say, ‘Give me less of p.’ But we also need a way to increase values of p that are too low, i.e., ‘Give me more of p.’ In other words, we need a parallel mechanism providing (r - p ). The thalamus seems to have a way to do that as well.
The mechanism performing this function is called a Dendritic Triad, which essentially reverses the sign of the incoming Perceptual signal! There are fast-acting and slow-acting synapses in the brain. A regular (excitatory) perceptual signal can use the fast form to both excite a relay neuron and excite a nearby (inhibitory) interneuron, which essentially cancels out that perceptual signal. At the same time, the perceptual signal uses the slow-acting form of synapse to pass along an inhibitory version of itself, through the self-same interneuron. These actions typically happen on distal dendrites far from the relay neuron’s cell body.
The descending Reference input also has an alternate route to get to the thalamic relay cell, (without passing through the thalamic reticular formation.) Those neocortical layer-6 cells also make direct connections to the relay cells in the thalamus, specifically onto their distal dendrites. So here we have an excitatory version of the Reference, lining up with an inhibitory version of the Perception, i.e., (r - p).
There are two pieces of important evidence here. These excitatory Reference signals arrive at relay cells that are nearby to the relay cells receiving the inhibitory version of the Reference signals (routed through the thalamic reticular formation). So it looks like adjoining mechanisms, one providing (p - r), & the other providing (r - p). The evidence coming from below is that the Dendritic Triad form of inhibitory signal onto thalamic relay cells seems to be half as common as the regular form of inhibition (doing other things) through interneurons in the thalamus. In other words, that is just the proportion we would expect, if every PCT Comparator there is actually enacted by two mechanisms operating in parallel, but with opposite signs.
There are various other neurophysiological details, in terms of how the synapses actually work. But the gist of it is given above. Again, I don’t necessarily think PCT models have to go into this level of detail, because the implementing language of our models is math, not neurochemistry.
All the best,