Density Fluctuation in Brownian Motion and its Significance in Olfaction

Sensory perception might be defined, in part, as that activity whereby changes in the environment are detected. From this point of view, fluctuations in a stimulus are more important than the mean stimulus intensity. In this paper, we are concerned primarily with the chemical senses in which the stimulus consists of molecules undergoing random motion in a fluid. We extend Smoluchowski’s model of Brownian motion to include an analysis of the variance of observed density fluctuations (variance because we are concerned with changes rather than mean values). A computer simulation of Brownian motion in two dimensions was developed and run on the Cray supercomputer. It is shown that density fluctuations in the computer-simulated data fall within the constraints calculated from the analysis of variance, but that published experimental data deviate somewhat from the theoretical constraints. We then apply the computer simulations to show that successive density measurements by olfactory cells are probably highly correlated, which can produce an olfactory “illusion” during the early moments of the process of smelling. INTRODUCTION The sensory response to a stimulus can be measured physiologically by the frequency of action potentials in a sensory neuron (a nerve fiber issuing from a sensory receptor such as a light detector or taste bud), or psychophysically as the magnitude of a sensation (e.g., the brightness of a light or the perceived intensity of an odor). Usually, the sensory response is related to some mathematical function of the stimulus intensity, and various characteristic functions have been nominated [l]. However, sensory response diminishes and frequently vanishes when the stimulus is held constant, a process known as adaptation. A changing stimulus continues to be perceived, while a steady stimulus soon fades from the sensorium. Such considerations led to the formulation of a theory of sensation in which stimulus fluctuation, rather than stimulus magnitude, is the initiator of the sensory process [2]. When we consider these changes for the Address all correspondence to K. H. Norwich. This work has been supported by the Natural Science and Engineering Research Council of Canada. We are grateful to J. W. Ross at the Ontario Centre for Large Scale Computing at the University of Toronto for assistance rendered in performing the Cray simulations.