Adaptive Control and Learned Sensory Derivatives

November 3, 2009

One popular method for modeling motor control systems is as an adaptive controller.  The brain learns, through progressive experiences, the correct sequence of output signals to yield a set of muscle contractions which will result in the desired action. Such a description is still highly nebulous, but it provides an established and already well-developed mathematical and conceptual framework. The fleshing out of the details* in relation to the underlying biological system provides a test for the applicability of adaptive control theory to biological motor control, as well as helping to guide the exploration of the otherwise overwhelmingly complicated field of cognitive control.

In a given control system, the variables that relate control signals and the resultant system performance are referred to as sensitivity derivatives. In a highly readable paper, M. N. Abdelghani, T. P. Lillicrap, and D. B. Tweed argue that sensory derivatives are not innate properties of human motor control systems, but are instead learned qualities1. They propose a novel, elegant, and biologically feasible mechanism for learning sensitivity derivatives which is well worth a look for anyone interested in adaptive control models for biological systems.

Rather than get too involved in the details of specific control architectures, however, I would like to look more closely at the question of learned versus innate sensitivity derivatives. The primary evidence for a learned sensitivity derivative is the ability of a motor system to recover from a reversal in the sign (or a change from zero**) of the effect of control signals and system response. For example, if the nerve fibres providing innervation to the extensor and flexor muscles in a limb are surgically reversed, a system relying on an innately known relationship between motor output and resultant muscle response (with learning focused solely on the correct magnitude of desired muscle flexion) would be unable to recover. Conversely, a system capable of learning sensitivity derivatives would be able to eventually recover after an appropriate learning period.

What is absolutely fascinating is the variation of recovery across species. Unfortunately, the systematic experimental protocols to test the recovery of various re-wirings of the nervous system are rather brutal seeming, and thus I was not able to find a lot of recent examples. The zoologist R. W. Sperry not only engaged in a number of such experiments during the 1940s, he also produced a lengthy article reviewing similar studies throughout the preceding decades2. I was unfortunately unable to find a non-mammalian study including transposition of nerve fibres in the limbs, but Sperry did perform an experiment in which he rotated the retinas of a group of salamanders. They never adapted to the altered state, and their visuomotor coordination remained permanently impaired3. In mammals, Sperry notes that recovery of coordination almost always occurs in humans and usually occurs in dogs and cats2. The recovery of cats has been verified in a more modern experiment4, as well as in monkeys5. Surprisingly, however, rats showed a complete lack of recovery following transposition of extensor and flexor nerves in their forelimbs6.

Considering the ubiquity of rodents as model organisms in neuroscience, this is a somewhat disconcerting functional difference. It is unclear whether the inability of rodents to recover is due to proteomic differences at the level of the synapse or larger-scale organizational differences (obviously, since we are not entirely sure how we perform motor learning and neuronal adaption in either humans or rodents), but it is an important difference that should remain in the back of a neuroscientist’s mind.

The question of learned versus innate sensory derivatives fascinates me, however, for somewhat less practical reasons. Recovery from the surgical transposition of nerves, after all, was not exactly a selective factor in vertebrate evolutionary history. Due to the fact that it is not something that is found in all vertebrate species, the ability to explicitly learn sensory derivatives is clearly an evolutionary development in neuronal architecture rather than simply the manner in which motor control initially evolved. Given the propensity for biological systems to re-use existing architectures with minor tweaks, it is possible that the expansion of motor repertoires provided by the development of a control network capable of modifying sensitivity derivatives (like implicit supervision) did not end there, but actually opened up the possibility for an entire host of more complicated and nuanced behaviours.

*No pun intended.
**A fascinating example of this sort of recovery is a surgical treatment for facial palsy using hypoglossal nerve transposition. With facial palsy resulting from damage to the facial nerve, surgeons are able to cut the facial nerve and attach in its place part of the hypoglossal nerve that formerly innervated the tongue. Although patients initially move their face whenever they try to move their tongues, they are eventually able to recover independent control of both face and tongue.
1 Abdelghani, M. N., T. P. Lillicrap, and D. B. Tweed. 2008. Sensitivity derivatives for flexible sensorimotor learning. Neural Computation, 20:2085-2111.
2 Sperry, R. W. 1945. The problem of central nervous reorganization after nerve regeneration and muscle transposition. The Quarterly Review of Biology, 20:311-369.
3Sperry, R. W. 1943. Effect of 180 degree rotation of the retinal field on visuomotor
coordination. Journal of Experimental Zoology, 92:263-279.
4Yumiya, H., K. D. Larsen, and H. Asanuma. 1979. Motor readjustment and input-output
relationship of motor cortex following crossconnection of forearm muscles in cats. Brain Research, 177:566-70.
5Brinkman, Cobie, R. Porter, and Julie Norman. 1983. Plasticity of motor behavior in monkeys with crossed forelimb nerves. Science, 220:438-440.
6Sperry, R. W. 1942. Transplantation of motor nerves and muscles in the forelimb of the rat. Journal of Comparative Neurology, 76:283-321.