Dendritic morphology of pyramidal neurones of the visual cortex of the rat. IV: Electrical geometry

Features of the dendritic morphology of pyramidal neurones of the visual cortex of the rat that are relevant to the development of models of their passive electrical geometry were investigated. The sample of 39 neurones that was used came from layers 2/3 and 5. They had been recorded from and injected intracellularly with horseradish peroxidase (HRP) in vitro as part of a previous study (Larkman and Mason, J. Neurosci 10 :1407, 1990). These cells had been reconstructed and measured previously by light microscopy. The relationship between the diameters of parent and daughter dendrites during branching was examined. It was found that most dendrites did not closely obey the “3/2 branch power relationship” required for representation of the dendrites as single equivalent cylinders. Estimates of total neuronal membrane area ranged from 27,100 ± 7,900 μm 2 for layer 2/3 cells to 52,200 ± 11,800 μm 2 for thick layer 5 cells. Dendritic spines contributed approximately half the total membrane area. Both neuronal input resistance and the ratio of membrane time constant to input resistance were correlated with neuronal membrane area, as measured anatomically. The relative electrical lengths of the different dendrites of individual neurones were investigated, by using simple transformations to take account of the differences in diameter and spine density between dendritic segments. A novel “morphotonic” transformation is described that represents the purely morphological component of electrotonic length. Morphotonic lengths can be converted into electrotonic lengths by division by a “morphoelectric factor” ([R m /R i ] 1/2 ). This procedure has the advantage of separating the steps involving anatomical and electrical parameters. These transformations indicated that the dendrites of the apical terminal arbor were much longer electrically than the basal or apical oblique dendrites. In relative electrical terms, most apical oblique trees arose extremely close to the soma, and terminated at similar distances to the basals. These results indicate that the dendrites of these pyramidal cells cannot be represented as single equivalent cylinders. The electrotonic lengths of the dendrites were calculated by using the electrical parameters specific membrane capacitance (C m ), intracellular resistivity (R i ), and specific membrane resistivity (R m ). Conventional values were assumed for C m (1.0 μFcm −2 ) and R i (100 Ωcm), but three different R m values were used for each cell. Two of these were within the conventionally accepted range (10,000–20,000 ωcm 2 ), while the third value was an order of magnitude higher, in line with some recent evidence from modeling and whole‐cell recording studies. The high R m value yielded dendrites that were electrotonically very short, some 0,15 space constants for basal and oblique dendrites and 0.3–0.6 space constants for terminal arbor dendrites. The distribution of dendritic spines, as markers for the location of excitatory synaptic inputs, with electrotonic distance from the soma was estimated, for each R m value. With conventional R m values, 50% of each neurone's spines were within 0.23–0.33 space constants from the soma, depending on cell class. With high R m values, 50% of spines were within 0.08–0.10 space constants. Thus the majority of excitatory inputs to these cells appear to be located close to the soma in electrical terms. However, there is some evidence that R i may be higher than conventionally assumed, which would increase the electrotonic length of dendrites for a given R m . Further data are therefore required before adequate electrical models for these cells can be developed. © 1992 Wiley‐Liss, Inc.