A method for mapping response fields and determining intrinsic reference frames of single-unit activity: Applied to 3D head-unrestrained gaze shifts

Natural movements towards a target show metric variations between trials. When movements combine contributions from multiple body-parts, such as head-unrestrained gaze shifts involving both eye and head rotation, the individual body-part movements may vary even more than the overall movement. The goal of this investigation was to develop a general method for both mapping sensory or motor response fields of neurons and determining their intrinsic reference frames, where these movement variations are actually utilized rather than avoided. We used head-unrestrained gaze shifts, three-dimensional (3D) geometry, and naturalistic distributions of eye and head orientation to explore the theoretical relationship between the intrinsic reference frame of a sensorimotor neuron's response field and the coherence of the activity when this response field is fitted non-parametrically using different kernel bandwidths in different reference frames. We measure how well the regression surface predicts unfitted data using the PREdictive Sum-of-Squares (PRESS) statistic. The reference frame with the smallest PRESS statistic was categorized as the intrinsic reference frame if the PRESS statistic was significantly larger in other reference frames. We show that the method works best when targets are at regularly spaced positions within the response field's active region, and that the method identifies the best kernel bandwidth for response field estimation. We describe how gain-field effects may be dealt with, and how to test neurons within a population that fall on a continuum between specific reference frames. This method may be applied to any spatially coherent single-unit activity related to sensation and/or movement during naturally varying behaviors.