As we look around, the orientation of our eyes depends on the order of the rotations that are carried out, a mathematical feature of rotatory motions known as noncommutativity. Theorists and experimentalists continue to debate how biological systems deal with this property when generating kinematically appropriate movements. Some believe that this is always done by neural commands to a simplified eye plant. Others have postulated that noncommutativity is implemented solely by the mechanical properties of the eyeball. Here we directly examined what the brain tells the muscles, by recording motoneuron activities as monkeys made eye movements. We found that vertical recti and superior/inferior oblique motoneurons, which drive sensory-generated torsional eye movements, do not modulate their firing rates according to the noncommutative-driven torsion during pursuit. We conclude that part of the solution for kinematically appropriate eye movements is found in the mechanical properties of the eyeball, although neural computations remain necessary and become increasingly important during head movements.
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