Comparative Electrotonic Analysis of Three Classes of Rat Hippocampal Neurons

We present a comparative analysis of electrotonus in the three classes of principal neurons in rat hippocampus: pyramidal cells of the CA1 and CA3c fields of the hippocampus proper, and granule cells of the dentate gyrus. This analysis used the electrotonic transform, which combines anatomic and biophysical data to map neuronal anatomy into electrotonic space, where physical distance between points is replaced by the logarithm of voltage attenuation (log A). The transforms were rendered as "neuromorphic figures" by redraing the cell with branch lengths proportional to log A along each branch. We also used plots of log A versus anatomic distance from the soma; these reveal features that are otherwise less apparent and facilitate comparisons between dendritic fields of different cells. Transforms were always larger for voltage spreading toward the soma (V_in) than away from it (V_out). Most of the electrotonic length in V_out transforms was along proximal large diameter branches where signal loss for somatofugal voltage spread is greatest. In V_in transforms, more of the length was in thin distal branches, indicating a steep voltage gradient for signals propagating toward the soma. All transforms lengthened substantially with increasing frequency. CA1 neurons were electrotonically significantly larger than CA3c neurons. Their V_out transforms displayed one primary apical dendrite, which bifurcated in some cases, whereas CA3c cell transforms exhibited multiple apical branches. In both cell classes, basilar dendrite V_out transforms were small, indicating that somatic potentials reached their distal ends with little attenuation. However, for somatopetal voltage spread, attenuation along the basilar and apical dendrites was comparable, so the V_in transforms of these dendritic fields were nearly equal in extent. Granule cells were physically and electrotonically most compact. Their V_out transforms at 0 Hz were very small, indicating near isopotentiality at DC and low frequencies. These transforms resembled those of the basilar dendrites of CA1 and CA3c pyramidal cells. This raises the possibility of similar functional or computational roles for these dendritic fields. Interpreting the anatomic distribution of thorny excrescences on CA3 pyramidal neurons with this approach indicates that synaptic currents generated by some mossy fiber inputs may be recorded accurately by a somatic patch clamp, providing that strict criteria on their time course are satisfied. Similar accuracy may not be achievable in somatic recordings of Schaffer collateral synapses onto CA1 pyramidal cells in light of the anatomic and biophysical properties of these neurons and the spatial distribution of synapses.

Figure 3

Left: Two-dimensional projection of the anatomy of a CA1 pyramidal neuron (cell 524). Right: neuromorphic renderings of the electrotonic transforms of this cell computed at DC (0 Hz} and 40 Hz for somatofugal (V_out, upper) and somatopetal (V_in, lower) signal flow. The primary apical dendrite dominates the V_out transforms, while the basilar and terminal branches appear much smaller. In the V_in transforms the basilars and terminal branches are the most prominent features.

Figure 4

Plots of the logarithm of attenuation at DC as a function of physical distance from the soma (log A vs. x) for the V_out (left) and V_in (right) transforms of the CA1 neuron of Fig. 3. Positive distances along the x axis correspond to the apical dendrites, and the basilars are shown at negative distances. For V_out, the primary apical dendrite stands out as a diagonal that gives rise to many tributaries that are almost horizontal (the nearly isopotential terminal branches). In the V_in transform these branches are much steeper than the primary apical because of the rapid attenuation of voltage along their length.

Figure 5

Left: Two-dimensional projection of the anatomy of a CA1 pyramidal neuron (cell 503). Right: V_out (upper) and V_in (lower) neuromorphic figures at DC and 40 Hz. The primary apical dendrite bifurcates close to the cell body, giving rise to a pair of branches that dominate the V_out transforms. The basilar and terminal branches, nearly inconspicuous in the V_out transforms, are the most noticeable aspects of the V_in transforms.

Figure 6

Log A vs. x plots at DC for the V_out and V_in transforms of the CA1 neuron in Fig. 5. For V_out, the steep diagonals of the twinned primary apical dendrites are quite distinct from their nearly horizontal daughter branches. As in Fig. 4, the terminal branches are much steeper in the V_in plot because of the more rapid decline of voltage with distance for voltage spread toward the soma.

Figure 7

Left: Two dimensional anatomic projection of a CA3c pyramidal neuron (cell 701). Right: V_out and V_in neuromorphic figures at DC and 40 Hz. This cell has several roughly equivalent apical dendritic branches instead of a single primary apical dendrite. As in the CA1 cells of Figs. 3 and 5, however, the basilar and terminal branches of this cell are very small in the V_out transforms yet quite prominent in the V_in transforms.

Figure 8

Log A vs. x plots at DC for the V_out and V_in transforms of the CA3c neuron in Fig. 7. The four steep diagonals correspond to the cluster of proximal apical branches in Fig. 7. The slopes of the terminal branches and basilar dendrites depend on the direction of signal propagation, as in Figs. 4 and 6.

Figure 9

Left: Two-dimensional anatomic projection of a granule cell (cell 964). Right: V_out and V_in neuromorphic figures at DC and 40 Hz. Granule cells are electrotonically more compact than either CA1 or CA3 neurons. The dendritic branches have nearly identical electrotonic lengths.

Figure 10

Log A vs. x plots at DC for the V_out and V_in transforms of the granule cell in Fig. 9. As in pyramidal cells, terminal branches are nearly horizontal in the V_out figure because of their sealed--end terminations. The V_in figure displays much greater attenuation for potential spread from the dendrites toward the soma.

Figure 11

Left: Two-dimensional anatomical projection of a granule cell (cell 950). The soma of this neuron lies in a deeper layer of the dentate gyrus than the cell displayed in Figs. 9 and 10. It has a short apical branch that gives rise to the remainder of the dendritic tree. Right: V_out and V_in neuromorphic figures at DC and 40 Hz. The short initial apical segment accounts for about one-third of the electrotonic extent of the cell for somatofugal voltage transfer

Figure 12

Log A vs. x plots at DC for the V_out and V_in transforms of the granule cell in Fig. 11. The initial apical segment is nearly vertical in the V_out plot because of the steep spatial gradient of voltage spreading from the soma to the dendrites. This segment is nearly horizontal in the V_in plot because it is almost isopotential along its length for voltage spreading from the dendrites to the soma.

Figure 13

Maximum anatomical and electrotonic measures of the dendrites of granule cells and the apical dendrites of CA1and CA3c pyramidal cells. A. The values of x^max. B and C: L^max_out for DC and 40 Hz. D and E: L^max_in for DC and 40 Hz. Obvious differences between cell classes in these plots turned out to be statistically significant (Table 1). See text for details.

Figure 14

Maximum anatomic and electrotonic measures of the dendrites of granule cells and the basilar dendrites of CAl and CA3c pyramidal cells. A: The values of x^max. B and C: L^max_out for DC and 40 Hz. D and E: L^max_in for DC and 40 Hz. Obvious differences between cell classes in these plots turned out to be statistically significant (Table 1). See text for details.

Figure 15

Side by side comparison of the log A vs. x plots at DC for V_out in a CA1 neuron (cell 503) and a granule cell (cell 964). The range of attenuations and their variation with distance are very similar. This suggests possible functional parallels between dendritic fields in these cell classes

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