Preprint available

[Kechen Zhang]

The following paper is available in PostScript form:

Journal of Neuroscience, in press 

A theory of geometric constraints on neural activity for natural
three-dimensional movement

Kechen Zhang and Terrence J. Sejnowski 

Howard Hughes Medical Institute, The Salk Institute, and
University of California, San Diego

Abstract:  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 non-rigid
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.

http://www.cnl.salk.edu/~zhang/objectwfigs.ps.Z

31 pages, compressed PostScript file about 2.0 Mb (7.7 Mb uncompressed)