The Journal of Neuroscience, April 15, 1999, 19(8):3122-3145
A Theory of Geometric Constraints on Neural Activity
for Natural Three-Dimensional Movement
Kechen
Zhang1 and
Terrence J.
Sejnowski1, 2
1 Howard Hughes Medical Institute, Computational
Neurobiology Laboratory, The Salk Institute for Biological Studies,
La Jolla, California 92037, and 2 Department of Biology,
University of California, San Diego, La Jolla, California 92093
Although the orientation of an arm in space or the static view of
an object may be represented by a population of neurons in complex
ways, how these variables change with movement often follows simple
linear rules, reflecting the underlying geometric constraints in the
physical world. A theoretical analysis is presented for how such
constraints affect the average firing rates of sensory and motor
neurons during natural movements with low degrees of freedom, such as a
limb movement and rigid object motion. When applied to nonrigid
reaching arm movements, the linear theory accounts for cosine
directional tuning with linear speed modulation, predicts a curl-free
spatial distribution of preferred directions, and also explains why the
instantaneous motion of the hand can be recovered from the neural
population activity. For three-dimensional motion of a rigid object,
the theory predicts that, to a first approximation, the response of a
sensory neuron should have a preferred translational direction and a
preferred rotation axis in space, both with cosine tuning functions
modulated multiplicatively by speed and angular speed, respectively.
Some known tuning properties of motion-sensitive neurons follow as
special cases. Acceleration tuning and nonlinear speed modulation are
considered in an extension of the linear theory. This general approach
provides a principled method to derive mechanism-insensitive neuronal
properties by exploiting the inherently low dimensionality of natural movements.
Key words:
3-D object; cortical representation; visual cortex; tuning curve; motor system; reaching movement; speed modulation; potential function; gradient field; zero curl
Copyright © 1999 Society for Neuroscience 0270-6474/99/1983122-24$05.00/0
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