#77. How the Cerebellum May Adjust the Gains of Reflexes [Neuroscience]

 

NE

Red, theory; black, fact

The cerebellum is a part of the brain involved in ensuring accuracy in the rate, range, and force of movements and is well known for its regular matrix-like structure and the many theories it has spawned. I myself spent years working on one such theory in a basement, without much to show for it. The present theory occurred to me decades later on the way home from a conference on brain-mind relationships at which many stimulating posters were presented.

Background about the cerebellum

The sensory inputs to the cerebellum are the mossy fibers, which drive the granule cells of the cerebellar cortex, whose axons are the parallel fibers. The spatial arrangement of the parallel fibers suggests a bundle of raw spaghetti or the bristles of a paint brush. These synapse on Purkinje cells at synapses that are probably plastic and thus capable of storing information. The Purkinje cells are the output cells of the cerebellar cortex. Thus, the synaptic inputs to these cells are a kind of watershed at which stimulus data becomes response data. The granule-cell axons are T-shaped: one arm of the T goes medial (toward the midplane of the body) and the other arm goes lateral (the opposite). Both arms are called parallel fibers. Parallel fibers are noteworthy for not being myelinated; the progress of nerve impulses through them is steady and not by jumps. The parallel fibers thus resemble a tapped delay line, and Desmond and Moore seem to have [paywall] proposed this in 1988.

The space-time graph of one granule-cell impulse entering the parallel-fiber array is thus V-shaped, and the omnibus graph is a lattice, or trellis, of intersecting Vs.

The cerebellar cortex is also innervated by climbing fibers, which are the axons of neurons in the inferior olive of the brainstem. These carry motion error signals and play a teacher role, teaching the Purkinje cells to avoid the error in future. Many error signals over time install specifications for physical performances in the cerebellar cortex. The inferior olivary neurons are all electrically connected by gap junctions, which allows rhythmic waves of excitation to roll through the entire structure. The climbing fibers only fire on the crests of these waves. Thus, the spacetime view of the cortical activity features climbing fiber impulses that cluster into diagonal bands. I am not sure what this adds up to, but what would be cute?

A space-time theory

Cute would be to have the climbing fiber diagonals parallel to half of the parallel-fiber diagonals and partly coinciding with the half with the same slope. Two distinct motor programs could therefore be stored in the same cortex depending on the direction of travel of the olivary waves. This makes sense, because each action you make has to be undone later, but not necessarily at the same speed or force. The same region of cortex might therefore store an action and it’s recovery.

The delay-line theory, revisited

As the parallel-fiber impulses roll along, they pass various Purkinje cells in order. If the response of a given Purkinje cell to the parallel-fiber action potential is either to fire or not fire one action potential, then the timing of delivery of inhibition to the deep cerebellar neurons could be controlled very precisely by the delay-line effect. (The Purkinje cells are inhibitory.) The output of the cerebellum comes from relatively small structures called the deep cerebellar nuclei, and there is a great convergence of Purkinje-cell axons on them, which are individually connected by powerful multiple synapses. If the inhibition serves to curtail a burst of action potentials triggered by a mossy-fiber collateral, then the number of action potentials in the burst could be accurately controlled. Therefore, the gain of a single-impulse reflex loop passing through the deep cerebellar nucleus could be accurately controlled. Accuracy in gains would plausibly be observed as accuracy in the rate, range, and force of movements, thus explaining how the cerebellum contributes to the control of movement. (Accuracy in the ranges of ballistic motions may depend on the accuracy of a ratio of gains in the reflexes ending in agonist vs. antagonist muscles.)

Control of the learning process

If a Purkinje cell fires too soon, the burst in the deep cerebellar nucleus neuron will be curtailed too soon, and the gain of the reflex loop will therefore be too low. The firing of the Purkinje cell will also disinhibit a spot in the inferior olive due to inhibitory feedback from the deep nucleus to the olive. I conjecture that if a movement error is subsequently detected somewhere in the brain, this results in a burst of synaptic release of some monoamine modulator into the inferior olive, which potentiates the firing of any recently-disinhibited olivary cell. On the next repetition of the faulty reflex, that olivary cell reliably fires, causing long-term depression of concurrently active parallel fiber synapses. Thus, the erroneous Purkinje cell firing is not repeated. However, if the firing of some other Purkinje cell hits the sweet spot, this success is detected somewhere in the brain and relayed via monoamine inputs to the cerebellar cortex where the signal potentiates the recently-active parallel-fiber synapse responsible, making the postsynaptic Purkinje cell more likely to fire in the same context in future. Purkinje cell firings that are too late are of lesser concern, because their effect on the deep nucleus neuron is censored by prior inhibition. Such post-optimum firings occurring early in learning will be mistaken for the optimum and thus consolidated, but these consolidations can be allowed to accumulate randomly until the optimum is hit.

Photo by Robina Weermeijer on Unsplash