[From Bill Powers (2011.01.31.1147 MST)]
In a conversation with Henry Yin, the subject of multiple channels for
signals in neural control systems came up. I realized that this subject
will be of interest in several contexts, from Martin Taylor’s work with
information theory to modeling efforts and neuroscience
investigations.
In the attached paper, the authors say
**With the goal of reducing the computational burden, we downsized the
total number of fibers in our model by a factor of 25 (resulting in 5654
fibers distributed among 1/5 of the normal number of MUs each with 1/5 of
the normal innervation ratio ;see below).**MU means Motor Unit, a set of 3 to 50 muscle fibers all acting to
stretch the same Golgi Tendon Organ (GTO). In their reduced model they
show 25 GTOs, suggesting that altogether there would be 125 of them. From
each GTO arises an axon that returns negative feedback to one spinal
motor neuron, if I am reading correctly.
The first point of interest to us is that the perceptual signal for this
first-order intensity control system (actually controlling angular
acceleration or torque about a joint) consists of over 100 axons, each
neuron sensing the same force applied by the muscle to its attachment
(sensing by streching the GTO and thus compressing transverse sensory
endings). Therefore measuring the neural signal in only one of these
axons will give a very exaggerated picture of the noise level relative to
the signal in the control system’s input function.
I have no idea whether each sensory axon affects the same spinal motor
neuron, but I suspect that different axons affect different motor
neurons, each motor neuron sending an axon to the same muscle. Where the
axon nears the muscle, it appears to be common that the axon will
split into multiple paths, innervating some number of motor fibers in the
same muscle. In a gastrocnemius muscle (calf muscle) in a cat, there are
1000 to 2000 muscle fibers, so several hundred spinal motor neurons would
seem to carry one error signal from the motor neuron (which is the
comparator) to the muscle.
We thus have, apparently, a control system in which every component and
signal is really a collection of 100 or more components and signals that
operate in parallel and redundantly. Together, they control the force
applied by the whole muscle to its attachments at the bones. To measure
the actual perceptual signal and error signal, we would have to detect
the signals in a large number, 100 or more, axons for each signal, and
average the spike rate over the whole set.
Curves are given showing “recruitment” effects; the overall
relationship between summed impulse rates and tension is a smooth curve,
in some cases with a large relatively linear portion. The noise in these
summed signals is very small relative to the signal magnitude.
Something similar would seem to be involved in the reference signals that
reach the spinal motor cells – these signals must be multiple, or the
pathways must arborize into multiple pathways, or both. This suggests
that we can expect similar redundancies at the sources of the reference
signals, and perhaps everywhere else in the brain.
If this degree of redundancy is found everywhere in the brain, then the
task of finding neural correlates of the signals and functions in our PCT
models will become very much more difficult. Simply to measure a signal
magnitude, it will be necessary to measure a large number of channels
carrying redundant signals and average them together. Doing this in a
non-invasive way may be impossible, so we will never see an intact
control system in normal working condition by direct study with
electrodes. The best we could hope to do under those circumstances would
be to do behavioral studies and match models to overall observed
behavior, and then use the model as a guide for finding what
verifications of the connections are possible. The degree of quantitative
verification will be limited by the fact that a single axon will give
only a very noisy indication of the “ensemble” signal (as they
call the redundant sets). If signals can be measured only in a few
redundant axons, the noise level will limit the accuracy of the electrode
measurements. The models would then best be verified by comparing them
with behavior, not with neural structures. The neural data will be useful
only for telling us whether a model is drastically wrong.
Another implication of brain-wide redundancy of this kind would be that
the brain contains very many fewer independent units of organization than
there are individual neurons. All the combinatorial calculations
indidicating that the number of brain states approaches the number of
elementary particles in the universe would be called into question.
Brains may not be anywhere near as complex as the enthusiastic estimates
of the past have made them. We might even hope to understand them, to
some degree.
Clearly, all these comments have to be taken as very preliminary; a large
literature search – and perhaps some real research – will be necessary
to fill in all the missing details.
Best,
Bill P.
Mileusnic&Loeb09JNeuralEng.pdf (1.95 MB)