Biomathematics Seminar: Mathematical equivalence between branched and unbranched dendritic structures.
17 March 2009 14:15 in Kinsgley Barrett Lecture Theatre (CLC407)
The observed complexity and variety of dendritic geometries raises important questions concerning the role played by dendritic morphology in neuronal signal processing. Cajal recognised this diversity of shape over 100 years ago, assumed that it had purpose, and lamented that he was unable to discern this purpose. Much of our present insight into the properties of dendritic trees has been obtained through the development and application of dendritic models based on cable theory. The complexity of a biophysical dendrite resides, in part, in its intricate branched structure. However, when cable theory is extended to a model of a branched dendrite, the resulting mathematical complexity often precludes exact mathematical analyses from which general truths can be derived. In this talk I shall describe how large classes of nerve cells with arbitrarily branched dendrites can be reduced to a canonical nerve cell with a single dendrite, called the equivalent cable, which is unbranched and functionally equivalent to the original nerve cell. The equivalent cable describes how configurations of input on the nerve cell affect the biological function of the cell in the respect of its ability to generate propagated action potentials.
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