What the odor is not: Estimation by elimination

The olfactory system is thought to encode vast numbers of odors combinatorially in the responses of a much smaller number of broadly sensitive receptors. Here, we propose a method for decoding such a distributed representation. The main idea is that it is much easier to identify what the odor is not, rather than what the odor is. This is because a typical receptor binds to many odorants; so a response below threshold signals the absence of all such odorants. We demonstrate that, for biologically realistic numbers of receptors, response functions, and odor mixture complexity, this remarkably simple method of elimination turns an underdetermined decoding problem into an overdetermined one, allowing accurate determination of the odorants in a mixture and their concentrations. We give a simple neural network realization of our algorithm which resembles the known circuit architecture of the piriform cortex.