In joint research activites in this area, we focus on the central role of the glomeruli, the first synaptic way- stations for olfactory information in virtually all species with differentiated olfactory systems, and on the fact that glomerular function comprises several levels of description from the diffusion of extracellular potassium ions (possibly modulated by glial cells), thought the potentially nonlinear dynamics of the dendritic fields of interneurons, to an understanding of coding of odor information over the full array of glomeruli. Projects of the type that will be available to IGERT students are illustrated by several investigaions currently being pursued by students in the pilot program:
How do the glial borders that typically surround olfactory glomeruli influence information processig within and between the glomeruli? This question is being pursued by Anita Rado, a graduate student in Applied Mathematics. Her project takes as its basis a detailed cellular and electrophysiological knowledge of glomerular structure and function in the experimentally favorable insect Manduca sexta [6,7,8], a quantitative approach to accumulation of potassium ions in extracellular space during high levels of neural activity and the effects of that accumulation [1,5], and a mathematical approach to diffusion of small particles though media of low porosity that was first applied in non-neural systems [2].
To begin, Rado used the Hodgkin-Huxley formulation to calculate how rapidly potassium ions enter the extracellular space of a glomerulus. This value is related to spike activity in the sensory axons in response to an odor, which is monitored experimentally. The net increase in extracellular ionic concentration can be viewed, to a firse approximation, as a competion between that spike activity and extracellular diffusion [1]. The buildup of extracellular potassium ion concentration will reduce the magnitude of the potassium equilibrium potential, weakening the tendency of sensory axons to continue to spike and of target neurons to spike in response to the sensory input.
To explore how potassium ions will diffuse in the meandering extracellular space of the glomerulus, Rado quantified the shape of the extracullular space in (2-dimensional) electron micrographs from Tolbert's laboratory. Motivated by the geometrical considerations of El-Kareh et al. [2] and others [3,4], she estimated the effective diffusivity of potassium ions in 3-dimensional extracellular space by considering systems that are interconnected, isotropic, and homogeneous. She also estimated the ratio of effective to bulk diffusivities of extracellular potassium ions to be about equal to 2/3 of the volume fraction of glomerular neuropil occupied by extracullular space, a result similar to results obtained in studies of average magnetic permeability in mixed media.
Armed with this information, Rado is now asking: what role do the glial cells that form borders around glomeruli play in influencing the levels of extracellular potassium ion concentration? Little is know about the biophysical properties of the glia that surround the glomeruli in Manduce [6,7]. For the mathematical model, she supposed that the glia either: barrier to the diffusion of potassium ions. Each assumption predicts a distinctly different time course and global distribution of extracellular potassium ions, leading to qualitative effects that we intend to look for experimentally in the future, with the aid of potassium selective electrodes or by studying the diffusion of fluorescent dyes microinjected into glomeruli and monitored with video microscopy.
We also are interested in understanding the role played by the complex dendrites of interneurons and projection neurons in olfactory function. To this end, Aaron King, another graduate student in Applied Mathematics, working in Christensen's laboratory, has gathered coordinated stacks of optical sections from our laser scanning confocal microscope of the glomerular dendrites of neurons intrecellularly injected with a fluorescent label [8 - 11]. King has been working to reduce the images to numerical data in a form that is suitable for mathematical analysis. In addition to the importance for the present research activity, such procedures will be of more general value to the many other neuroscientists currently gathering confocal microscopic data.