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

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 v ariables 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 ra tes of sensory and motor neurons during natural movements with low degrees of freedom, such as a limb movement and rigid object motion. When applied t o nonrigid reaching arm movements, the linear theory accounts for cosine di rectional tuning with linear speed modulation, predicts a curl-free spatial distribution of preferred directions, and also explains why the instantane ous 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 p referred translational direction and a preferred relation axis in space, bo th with cosine tuning functions modulated multiplicatively by speed and ang ular speed, respectively, Some known tuning properties of motion-sensitive neurons follow as special cases. Acceleration tuning and nonlinear speed mo dulation are considered in an extension of the linear theory. This general approach provides a principled method to derive mechanism-insensitive neuro nal properties by exploiting the inherently low dimensionality of natural m ovements.