Mathematical models of ionic diffusion in olfactory glomeruli

Abstract

Many vertebrate and invertebrate olfactory systems are similar in the organization of their synaptic neuropil into glomeruli, structures surrounded by an incomplete layer of glial processes. Within glomeruli, the axons of olfactory receptor neurons synapse with the dendrites of their target brain neurons. Glomeruli are likely to be odor specific in that each glomerulus processes information from a subset of axons about a particular chemical feature of odorant molecules. Therefore, a large proportion of the neurons within a glomerulus may be excited simultaneously in response to a particular odor. The resulting release of potassium ions from neurons may be sufficient to cause a substantial increase in the extracellular concentration of potassium ions and thus affect the excitability of neighboring neurons. The goal of this study is to develop theoretical models for the diffusion of potassium ions in the extracellular space, and to predict how the glial border affects the spread of potassium ions following the activation of olfactory sensory neurons. Observations of the morphology of the interior and border of the glomerulus were used to estimate the porosity and effective diffusivity of these regions, and the size of the "mouth" region where there is no glial covering. Potassium was assumed to be released into the extracellular space during an initial 0.5 seconds. The time-dependent diffusion equation was solved in spherical coordinates using a finite-difference method. The results indicated that the glial envelope forms a partial barrier to the diffusion of potassium ions, and greatly reduces the spread of potassium ions to neighboring glomeruli following release. According to the model, the decline in potassium concentration within the glomerulus due to the leakage from the mouth and glial boundaries is relatively slow, taking more than 10 seconds to approach its resting level. These findings support the hypothesis that the characteristic distribution of glial cells around glomeruli could play a significant role in olfactory information processing.