Exploring the computational capabilities of single neurons by continuous cable modelling.
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Biomedical subjects
A K Schierwagen
Publications and source records attributed to A K Schierwagen.
Growth, structure and dynamics of real neurons: model studies and experimental results.
One of the most striking features of vertebrate neurons is the immense diversity of their dendritic branching patterns, bearing witness to the range of operations subserved by dendritic membranes. The paper deals with three questions which naturally arise in this context: 1) What kind of growth process leads to a particular branching pattern? 2) How can we quantify such patterns? 3) Is it possible to derive a functional characterization related to the dendritic pattern so quantified? Probabilistic growth models were tested against morphological data derived from experiments with mammalian sensory-motor neurons, and their fractal dimensions were determined. The functionality of the dendritic neuron types was evaluated by electrotonic modelling of the synaptic transfer properties. The results support the hypothesis that a close relationship between dendritic pattern and neuron function might exist. The nonlinear properties of neuronal membranes represent the other determinant of neuron function. Using the Hodgkin-Huxley model for description, the functional role of the repolarizing ionic currents in the periodic activity of nerve membranes was analyzed. New models have been developed which allow the analytical treatment of both passive membrane voltage changes in neurons with branching dendrites and nerve impulse propagation in non-uniform axons.
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A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree.
A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree extending Rall's equivalent cylinder model is presented. It is obtained from a combination of cable theory with the continuum approach. Replacing the fine structure of the branching dendrites by an equivalent, conductive medium characterized by averaged electrical parameters, the one-dimensional cable equations with spatially varying parameters are derived. While these equations can be solved in general only numerically, we were able to formulate a general branching condition (comprising Rall's 3/2 power relationship as a special case) under which analytical solutions can be deduced from those of the equivalent cylinder model. This model allows dendritic trees with a greater variety of branching patterns than before to be analytically treated.
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