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Neuron, Vol. 47, 281293, July 21, 2005, Copyright 2005 by Elsevier Inc. DOI 10.1016/j.neuron.2005.05.031 Do Motoneurons Encode the
 

Summary: Neuron, Vol. 47, 281293, July 21, 2005, Copyright 2005 by Elsevier Inc. DOI 10.1016/j.neuron.2005.05.031
Do Motoneurons Encode the
Noncommutativity of Ocular Rotations?
Fatema F. Ghasia and Dora E. Angelaki* (Haslwanter, 1995, 2002; Tweed and Vilis, 1987, 1990).
Thus, when eye movements are made from eccentricDepartment of Neurobiology
positions, the angular velocity axis of the eye does notWashington University School of Medicine
remain confined to Listing's plane but deviates in theSt. Louis, Missouri 63110
same direction as gaze by approximately half as much
(half-angle rule; Figure 1A; see also Tweed and Vilis,
1987, 1990).Summary
How this torsional eye velocity, which is necessary to
keep eye position in Listing's plane, is generated in theAs we look around, the orientation of our eyes de-
absence of relevant sensory drive has been in the cen-pends on the order of the rotations that are carried
ter of the controversy. Tweed and Vilis (1987, 1990)out, a mathematical feature of rotatory motions known
were the first to address this problem in modern timesas noncommutativity. Theorists and experimentalists
(see also von Helmholtz, 1867; Westheimer, 1957). Un-continue to debate how biological systems deal with
der the prevailing assumption of the late 1980s that thethis property when generating kinematically appropri-
muscle pulling directions remain independent of eyeate movements. Some believe that this is always done
position, Tweed and Vilis proposed that nonlinear (i.e.,by neural commands to a simplified eye plant. Others
multiplicative) mathematical operations exist within thehave postulated that noncommutativity is implemented

  

Source: Angelaki, Dora - Department of Anatomy and Neurobiology, Washington University in St. Louis

 

Collections: Biology and Medicine