Application of Statistical Thermodynamics to the Olfaction Mechanism

Abstract

The application of the grand canonical ensemble in statistical thermodynamics to the stimulus adsorption on the olfactory receptor sites, assuming some simplifying hypotheses, leads us to an expression of the olfactory response R, which is a function of various physico-chemical parameters involved in the olfaction mechanism, e.g. the stimulus concentration, the saturated vapor pressure, the power law exponent and the partition coefficient. This expression of R is in agreement with the olfactory response of the Hill model, but is more explicit. Stevens' law and the olfactory threshold expression are easily deduced from R. The expression of the threshold we established from R enabled us to explain some empirical relations in the literature between the parameters quoted above. The use of the grand canonical ensemble with the chemical potential notion gave us an interpretation of Stevens' law and a better understanding of the role of some parameters involved in the olfaction mechanism, such as saturated vapor pressure and power law exponent.

On the use of the Hill’s model as local isotherm in the interpretation of the behaviour of the adsorption energy distributions

“…This model is established by applying grand canonical ensemble in a statistical physics approach [16]. To treat such adsorption problem with a statistical physics, some assumptions are made [16,17].…”

“…For this reason, we define the state of occupation N i and it is assumed that any given receptor site can either be empty or occupied, and consequently N i takes the value 0 or 1. The grand canonical partition function in this case, for only one site, has the form [16]:…”

“…Where β is the Boltzmann factor, and for N m identical receptor sites, the total grand canonical partition function is [16,17]:…”

“…This parameter represents the energetic density of the spatial density of the effectively occupied sites. The Hill isotherm, which is established by applying the grand canonical ensemble in a statistical physics approach [15,16], is used as a local isotherm. The advantage to apply this model is to give a physical meaning to the parameters involved in the model and then to give new interpretations of the adsorption process at molecular level.…”

Posterior evaluation of odour intensity in gas chromatography–olfactometry: comparison of methods for calculation of panel intensity and their consequences

“…The relationship in fact follows an exponential, two-parameter growth function ( Figure 5; R 2 = 0.96, F = 266.6, p < 0.0001; geometric mean). The resemblance of olfactory mechanisms with gas-solid adsorption mechanisms has already been discussed, [43][44][45][46] considering olfactory tract mucus to behave like an ideal solution or even assuming direct, 'dry' adsorption of the volatile compound from air onto the olfactory receptor. Under these conditions, the Stevens exponent depends on the adsorptive affinity of the olfactory receptor for a volatile compound (Henry's law).…”