  In color vision, the quantitative rules for mixing lights to make a target
color are well understood. By contrast, the rules for mixing odorants to make a
target odor remain elusive. A solution to this problem in vision relied on
characterizing receptor responses to different wavelengths of light and
subsequently relating these responses to perception. In olfaction,
experimentally measuring receptor responses to a representative set of complex
mixtures is intractable due to the vast number of possibilities. To meet this
challenge, we develop a biophysical model that predicts mammalian receptor
responses to complex mixtures using responses to single odorants. The dominant
nonlinearity in our model is competitive binding (CB): only one odorant
molecule can attach to a receptor binding site at a time. This simple framework
predicts receptor responses to mixtures of up to twelve monomolecular odorants
to within 15\% of experimental observations and provides a powerful method for
leveraging limited experimental data. Simple extensions of our model describe
phenomena such as synergy, overshadowing, and inhibition. We demonstrate that
the presence of such interactions can be identified via systematic deviations
from the competitive binding model.
