Project Title: Multiscale Modeling of the Neural Subcircuits in the Outer-Plexiform Layer of the Retina
PIs: S. Baer, S. Crook, C. Gardner, C. Ringhofer

Sponsor: NSF, 2008-2011

Awardee: Arizona State University
Award Number: 0718308

Students: Shaojie Chang

The retina is part of the central nervous system and an ideal region for studying information processing in the brain. It is accessible, well documented, and the subject of research spanning the clinical, experimental, and theoretical sciences. Image processing begins in the outer-plexiform layer (OPL) of the retina, where bipolar, horizontal, and photoreceptor cells interact. In this first layer of the visual pathway, knowledge of synaptic feedback mechanisms allows for the formulation of computational models that encapsulate essential phenomenology. From the biologist’s perspective, mathematical modeling allows one to disassociate the functional effects of various circuitry elements, similar to performing experiments with selective pharmacological agents, except that not all the agents one might like actually exist. From a mathematician’s perspective, the availability of electrophysiological, anatomical, and molecular data provides a rare opportunity for the construction of complex multiscale models for the system. The primary goal of this research proposal is to mathematically model, in detail, the subcircuits of the OPL, capturing the spatiotemporal dynamics on two spatial scales–that of an individual synapse and of the receptive field. The biological merit of this proposal is to use the models to gain insight into two competing hypotheses for explaining synaptic feedback effects in the OPL. Simply put, are the feedback effects in the cone photoreceptor’s synapse driven by electrical (ephaptic) or chemical (GABA)

mechanisms, or both? This collaborative research effort brings together experts in mathematical and computational neuroscience (Drs. Baer and Crook) with experts in computational and numerical analysis (Drs. Gardner and Ringhofer). The research group will consult with Dr. Ralph Nelson (Head of Neural Circuitry Unit, NINDS, NIH). The specific objectives of this project are to: 1) test the validity of the GABA vs ephaptic feedback hypotheses by comparing simulations of a proposed two-cell differential equation model with experimental data for the enhancement effect in cat horizontal cells, 2) formulate and analyze a partial differential equation system that includes the horizontal cell syncytium and its numerous processes into cone pedicles, and compare simulation results with spatial enhancement data for slit and square test regions, 3) formulate and analyze, using modern computational methods, a drift-diffusion model of the synaptic cleft within a cone pedicle to explore field effects in the intersynaptic space, and 4) develop a multiscale system of partial differential equations that combines the drift-diffusion model for the synapse with the continuum formulation at the receptive field level.

Broader Impacts: New insights into the function of retinal circuitry obtained through this project will impact research in bioengineering, biology, image processing, visual psychophysics, and pharmacology. The multiscale modeling and numerical techniques resulting from this research will

impact other areas of applied mathematics and engineering. The proposed project will generate problems that are accessible to graduate and undergraduate students and will provide excellent opportunities for multidisciplinary training that builds analytical and computational skills for solving

complex biological problems. The Mathematical and Theoretical Biology Institute has recruited many minority students pursuing research in mathematical biology to the Department of Mathematics and Statistics at ASU, and the participation of Dr. Zela at the University of Advancing

Technology (consultant) provides a new and exciting opportunity for outreach to additional students who would not traditionally be involved in research. All published models will be made available through appropriate databases or websites, making it possible for other researchers to reproduce the proposed studies, and new results with relevance to retina function will be submitted to WEBVISION, a website dedicated to the organization of the retina and visual system. Dr. Nelson (consultant) is one of the editors of this website.