Adaptation of olfactory receptor abundances for efficient coding

Olfactory receptor usage is highly non-uniform, with some receptor types being orders of magnitude more abundant than others. We propose an explanation for this striking fact: the receptor distribution is tuned to maximally represent information about the olfactory environment in a little-studied regime of efficient coding that is sensitive to the global context of correlated sensor responses. This model predicts further that in mammals, where olfactory sensory neurons are replaced regularly, receptor abundances should continuously adapt to odor statistics. Indeed, experiments have found such changes in response to olfactory experience. These changes are mysteriously context-dependent, with increased exposure to odorants leading variously to increased, decreased or unchanged abundances of activated receptors. We show that efficient coding theory predicts precisely such a context-dependence when sensors are correlated. Finally, we demonstrate simple dynamical rules for neural birth and death processes that might provide a mechanism for receptor abundances to adapt optimally.