Sparse incomplete representations: a potential role of olfactory granule cells.

Mitral/tufted cells of the olfactory bulb receive odorant information from receptor neurons and transmit this information to the cortex. Studies in awake behaving animals have found that sustained responses of mitral cells to odorants are rare, suggesting sparse combinatorial representation of the odorants. Careful alignment of mitral cell firing with the phase of the respiration cycle revealed brief transient activity in the larger population of mitral cells, which respond to odorants during a small fraction of the respiration cycle. Responses of these cells are therefore temporally sparse. Here, we propose a mathematical model for the olfactory bulb network that can reproduce both combinatorially and temporally sparse mitral cell codes. We argue that sparse codes emerge as a result of the balance between mitral cells' excitatory inputs and inhibition provided by the granule cells. Our model suggests functional significance for the dendrodendritic synapses mediating interactions between mitral and granule cells.