Lately I’ve been researching feedback controllers in the brain,
and I had this idea about how neurons could implement them.
Background: The purpose of a closed-loop controller (aka feedback controller) is to bring a measurable quantity (the sensory input) to some desired target value (the setpoint) by commanding a motor system. Inside of every feedback controller is a subtraction, when it compares the setpoint with the sensory input to determine which direction to go towards. A defining feature of closed loop controllers is the subtraction and how that’s implemented. There are many different ways that the brain could implement subtraction, and this post proposes yet another.
Hypothesis: Dendrites can implement a simple comparison operator based on the fact that inhibition can block excitatory NMDA-events from reaching the soma, but only if the inhibition is located between the soma and the NMDA-event. If the inhibition is further down the dendrite than the NMDA-event then it won’t block the NMDA-event.
Example: NMDA-Event does NOT reach soma:
vvv Inhibition
Soma O================================== Dendrite Tip
^^^ Excitation
Example: NMDA-Event DOES reach soma:
vvv Inhibition
Soma O================================== Dendrite Tip
^^^ Excitation
The dendrite is arranged like a number line, with each segment along its length detecting one number with both excitatory and inhibitory synapses. The excitatory synapses represent the setpoint and the inhibitory synapses represent the sensory feedback. In order to detect both positive and negative results, you need two cells with their number lines arranged in opposite directions.
I do not know how it could learn this arrangement of synapses.
I had an insight into how the inhibitory synapses could learn this:
Assume that the cell emitting an AP causes the animal to move. We can also assume that when the animal moves, it moves through a nice continuous and smooth space.
We can use these assumptions to learn which areas of the space are adjacent, and from there we can peice together a map of the whole space.
Learning Rule: When the neuron emitts an AP:
A) If there is no inhibition on the cell, pick a dendrite and learn the current sensory feedback on the most distal (furthest from the soma) segment possible.
B) If there is already an inhibited dendrite, then the region of the dendrite which is inhibited must move towards the soma over time. Learn new inhibitory synapses which are on the proximal (soma’s) side of the inhibited region of the dendrite as necessary. Unlearn distal synapses which stay active after you’ve moved beyond the position they encode.
How is that supposed to work, mechanistically? I suppose there could be a backprop to active inhibitory synapses, similar to how it works for excitatory, but does that actually happen?
I don’t know exactly how to implement these learning rules, but I think they can be implemented by local chemical reactions combined with the cytoskeletal transport systems [1] for communicating along the length of the dendrite.
It’s interesting conceptually. In my scheme patterns / clusters are “complemented”: each has positive core and negative contour. Both contribute to predictive value of the cluster, although in somewhat convoluted fashion. Normally, those positive and negative components are supposed to cancel-out, but they really represent different aspects of an object. If we consider a neuron as a centroid-based cluster of its synapses, then this semi-independently informative inhibition and excitation map to my contour and core.
But that requires some way to convert inhibitory input to excitatory, so it will contribute to AP?