Olfactory receptor neuron stimulated with Markov process

Abstract

Excitable membrane of olfactory receptor neuron (ORN) is populated with large number of identical receptor proteins (R) able to bind/release odor (O) molecules. Affinity between R and O depends on the odor presented, and this is the very first mechanism enabling olfactory selectivity. Our aim is to compare the R selectivity, expressed in terms of affinity, with that of ORN, expressed in terms of its firing rate. For this purpose we model the number of R bound with O at time t, n(t), as a Markov stochastic process. With each bound R, as it is observed for insects, we associate an open channel having conductance 0.015 nS, which injects a depolarizing current through the membrane (see a figure above). The ORN's membrane voltage is governed by the leaky integrate-and-fire neuronal model, see an equation below:

c_M * dV(t)/dt = -g_l * (V(t) - V_rest) - n(t) * g_R * (V(t) - V_e),

where V(t) is the membrane voltage; V_rest is the resting voltage; c_M is the total capacity of ORN's membrane; g_l is the total leakage through it; V_e is the reversal potential for current through an open R; n(t) is the fluctuating number of open channels at moment t due to odor molecules bound with R; g_R is the conductance of a single open channel. The total number of R per ORN is N = 2.5 * 10^6 (the number observed for moth). By means of numerical simulation of the Markov process n(t) and the aforementioned equation we conclude that the ORN selectivity can be much better than that of its receptor proteins R. The effect of the selectivity gain is better pronounced if odors are presented at low concentration.