The investigation of fluctuation scaling of stimuli in sensory systems.

Vemula, Sai1; Wong, Willy2,1;Norwich, Kenneth H.3

1. Institute of Biomaterials and Biomedical Engineering, University of Toronto; 2. Edward S. Rogers Sr. Department of Electrical & Computer Engineering, University ot Toronto; 3. Department of Physiology, University of Toronto

The study of perception involves the understanding of how information from the environment is conveyed to our senses, and how this information is processed by our sensory systems. The pathophysiology underlying sensory impairments (e.g. central auditory processing disorder or retinitis pigmentosa) can be viewed as deficits in information processing by our sensory organs. Developing mathematical models of sensation are critical for understanding and treating these impairments, as they can help uncover fundamental principles of the physiological systems. The entropic model of sensation, which incorporates the properties of information theory, aims to universally characterize sensory processing. Th entropic model of sensation posits that perception is a result of measuring the entropy (i.e. the uncertainty) of a stimulus being presented to us.  In other words, we gain information about our environment when we discern a specific quantity or type of stimulus from many possibilities.

In this model, sensory receptors can be regarded as drawing samples of stimuli from a larger population. For example, cilia on olfactory receptor neurons must sample odorant molecules in the nasal cavity, which is the first step of sensory transduction. Defining the relationship between the variance and mean of a stimulus presented to our senses is integral to the model. Is there a general theory that explains the relationship between the variance and mean of sensory stimuli? If this relationship is general, then it should be observed in all the senses.



Uncovering the relationship between the mean and variance of sensory stimuli involves the consideration of sensory transduction as a complex system founded in general principles. An example of such a complex system is the birth, death and immigration processes in population dynamics. Taylor’s Law, a power function relationship first discovered in ecological systems like this one, also manifests in many biological systems. Although there may be several mechanisms which can explicitly determine these processes, a general statistical model (a Poisson-gamma model) acts as an effective means to explain the clustering of individuals.

Tweedie distributions with specific parameters serve as a good candidate for defining the general theory underlying sensory stimuli, as they may explain the power function relationship between the variance and mean of all sensory stimuli. We consider the olfactory system as an example; a gamma distribution underlies the size of receptor site clusters on a single cilium and a Poisson distribution can explain how many cilia bind odorant molecules at these receptor sites. This compound Poisson-gamma model is a type of Tweedie distribution, which may be a reasonable model for all sensory modalities. We will demonstrate that this complex systems approach serves as a valuable framework for an investigation of the senses. 



If a general theory explains fluctuation scaling that is fundamental to neural responses in all sensory modalities, then a specific and vigorous search for mechanistic properties in each of the senses can be avoided. By characterizing the coupling of stimulus variation to sensory responses, we strengthen the entropic model of sensation. This principled approach empowers the development of prosthetics which aim to remove sensory impairments and restore perception.