Passive Dendritic Trees
Passive Dendritic Trees
The previous chapter dealt with the solution of the cable equation in response to current pulses and steps within a single unbranched cable. However, real nerve cells possess highly branched and extended dendritic trees with quite distinct morphologies. Figure 3.1 illustrates the fantastic variety of dendritic trees found throughout the animal kingdom, ranging from neurons in the locust to human brain cells and cells from many different parts of the nervous system. Some of these cells are spatially compact, such as retinal amacrine cells, which are barely one-fifth of a millimeter across, while some cells have immense dendritic trees, such as α motoneurones in the spinal cord extending across several millimeters. Yet, in all cases, neurons are very tightly packed: in vertebrates, peak density appears to be reached in the granule cell layer of the human cerebellum with around 5 million cells per cubic millimeter (Braitenberg and Atwood, 1958) while the packing density of the cells filling the 0.25 mm3 nervous system of the housefly Musca domestica is around 1.2 million cells per cubic millimeter (Strausfeld, 1976). The dendritic arbor of some cell types encompasses a spherical volume, such as for thalamic relay cells, while other cells, such as the cerebellar Purkinje cell, fill a thin slablike volume with a width less than one-tenth of their extent. Different cell types do not appear at random in the brain but are unique to specific parts of the brain. By far the majority of excitatory cells in the cortex are the pyramidal cells. Yet even within this class, considerable diversity exists. But why this diversity of shapes? To what extent do these quite distinct dendritic architectures reflect differences in their roles in information processing and computation? What influence does the dendritic morphology have on the electrical properties of the cell, or, in other words, what is the relationship between the morphological structure of a cell and its electrical function? One of the few cases where a quantitative relationship between form and some aspect of neuronal function has been established is the retinal neurons.
Keywords: Axons, Boundary conditions, Cable equation, Dendritic delay, Electrotonic distance, Finite cable, GENESIS (software), Hyperpolarization, Impedance matching, Leak conductance, Membrane capacitance
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