A model of partial reference frame transforms through pooling of gain-modulated responses

In multimodal integration and sensorimotor transformation areas of the posterior parietal cortex (PPC), neural responses often appear encoded in spatial reference frames that are intermediate to the intrinsic sensory reference frames, for example, eye-centered for visual or head-centered for auditory stimulation. Many sensory responses in these areas are also modulated by direction of gaze. We demonstrate that certain types of mixed-frame responses can be generated by pooling gain-modulated responses--similar to how complex cells in the visual cortex are thought to pool the responses of simple cells. The proposed model simulates 2 types of mixed-frame responses observed in the PPC: in particular, sensory responses that shift differentially with gaze in horizontal and vertical dimensions and sensory responses that shift differentially for different start and end points along a single dimension of gaze. We distinguish these 2 types of mixed-frame responses from a third type in which sensory responses shift a partial yet approximately equal amount with each gaze shift. We argue that the empirical data on mixed-frame responses may be caused by multiple mechanisms, and we adapt existing reference-frame measures to distinguish between the different types. Finally, we discuss how mixed-frame responses may be revealing of the local organization of presynaptic responses.