A mathematical model of chemoreception for odours and taste

We propose a mathematical model based on the occupation theory and on the hypothesis that, for a given stimulus, there exist two kinds of receptors. The receptors of the first kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active depolarizing form (this scheme was already used by Del Castillo & Katz, 1957). In the same way, the receptors of the second kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active hyperpolarizing form. The response is assumed to be proportional to the difference between the fraction of the active depolarizing compound and that of the active hyperpolarizing compound. The present paper deals only with the time course of the intensity of the response: in the first part, when a continuous flow of stimulus is applied and in the second part, when this continuous flow is removed. It does not deal with the quality and the discrimination of odours. The proposed mathematical model accounts for the depolarizing responses (which are the most frequent ones), the hyperpolarizing responses, the mixed responses reported by Patte et al. (1989), the off-responses reported by Takagi & Shibuya (1959) and for their variability, and the latent period in the olfactory response (Ottoson, 1974).