Baer Using theory and experiment, the investigator and his colleague study the integration of multiple electrical inputs into excitable neuronal structures. A new cable theory, developed by Baer and Rinzel (1991) to study large populations of dendritic spines, is adapted to fit the reality of a particular biological system: the multiterminally innervated muscle fiber of the insect Manduca. The mathematics involves the formulation and analysis of reaction diffusion models for multiple populations of spines, to model the amplitude and timecourse of potentials arising in cylindrical structures (dendrite or muscle fiber) receiving synchronous input from multiple clusters of synapses. Important biological properties considered are the amplitude of the quantal currents, shape of the postsynaptic process, the inherent uncertainty of an input actually occurring (probability of release), and the precise distribution of voltage gated channels. Theory is related to experimental data and drives new experiments. The functions of all excitable cells, both nerve and muscle, are regulated with precision by transmembrane potentials. This project is an interdisciplinary collaboration between a mathematician and a neurobiologist to study, using experiments and mathematical modeling, the spatial and temporal distribution of electrical potentials in complex neuronal structures. A mathematical model is developed to simulate amplitude and timecourse of potentials arising in cylindrical structures (dendrite or muscle fiber) receiving synchronous input from multiple clusters of synapses. The investigators use multiterminally innervated muscle fibers to test the predictions of the model, and conversely use the model to augment their understanding of synaptic physiology. The multiterminally innervated muscle fiber allows an unusual array of experimental and morphometric measurements, and has the added advantage of being the topological equivalent of a dendrite having clust ers of input spines. Consequently, both the conclusions of the simulations and the methodology being developed have broad applications to central nervous system structures.
