*Geometry of the dendritic arbors*

The fusiform cell dendritic arbors were quantified by a series of
measurements inspired by the work of Blackstad et al.
(1984)^{}in the cat and described fully in METHODS.
The results serve as^{}a basis for comparison of the gerbil to the cat
and as a basis^{}for a subsequent quantitative examination of the
relationship^{}between physiology and anatomy. It is important to note
that Blackstad^{}et al. limited their consideration to the central third
of the^{}DCN and thus avoided effects due to the significant curvature^{}of
the nucleus at its edges. It was not possible to do likewise^{}in our
case due to the sample size limitations inherent to an^{}in vivo
intracellular survey of this^{}kind.

The anatomical properties of the apical arbors are summarized in Table
1. Estimates were made of the total
dendritic lengths^{}by summing the lengths of the individual segments
comprising each^{}three-dimensional (3-D) reconstruction. The mean apical
length^{}was 3,359 µm, which is very close to the mean value of 3,212 µm^{}reported by Blackstad et al. (1984) in the cat. The
width and^{}thickness measurements were obtained by rotating the arbor
about^{}its long axis to find the widest and narrowest projections,
respectively.^{}Both measures are smaller in the gerbil than in the cat,
although^{}the ratio, which reflects the degree of arbor planarity, is
approximately^{}the same in both cases (2.56 in the gerbil, roughly 3 in
the cat).^{}The mean height of the apical arbor, measured parallel to the^{}long axis, was 157 µm in the gerbil as compared with 267 µm in^{}the
cat.

Table 2 lists the anatomical properties
of the basal dendrites in this study. The mean total length was 1,925 µm, as compared^{}with 2,728 µm in the cat. The mean arbor width is
smaller in the^{}gerbil (314 µm) than in the cat (392 µm), but the
thickness is^{}larger (112 vs. 72 µm). The result is that the width to
thickness^{}ratio in the gerbil (3.07) is about half that in the cat
(5.70).^{}The mean basal arbor is 250 µm in height as compared with 389^{ }µm in the cat.

*Tonotopy*

A qualitative illustration of the tonotopic organization is
presented in Fig. 2*A,* in which
the 17 fusiform cells of this study^{}have been mapped onto a single DCN.
Only the basal dendrites have^{}been drawn because that is presumably
where fusiform cells receive^{}acoustic input (Smith and Rhode
1985). The dendrites are color^{}coded according to BF, as shown.
Figure 2*A* qualitatively suggests^{}that the gerbil DCN has a
substantial volume devoted to relative^{}low BFs. The orderly arrangement
of cells by BF is also apparent,^{}with the lowest BFs in the
rostral-most and ventrolateral-most^{}aspect of the nucleus.

Figure 2*A* shows that BF increases in both the dorsomedial
and caudal directions. This observation is quantified in Fig.
2*B*^{}where the BF is plotted as a function of the relative
*X*-positions^{}(ventrolateral-to-dorsomedial location) and the
relative *Z*-positions^{}(rostral-to-caudal location) of the
fusiform cell somata. The^{}straight line fits to these data indicate
that BF is indeed highly^{}correlated with these two^{}dimensions.

The tonotopic axis is described by the equation log(BF) = 1.45*Px* + 1.01*Pz* (*r* = 0.81, *P* < 0.001), obtained by performing multiple^{}linear
regression on log BF using both the relative *X*- and
*Z*-positions.^{}A tonotopic position was determined for each
neuron by projecting^{}its location onto this axis and computing the
distance from the^{}origin (*Px* = *Pz* = 0).
The resulting positions are plotted in Fig.^{}3 as a function of BF. For comparison,
the place-frequency map^{}for the gerbil cochlea is also plotted, where
position indicates^{}the relative distance from the base of the cochlea.
In general,^{}Fig. 3 shows that the spatial distribution of BFs in the
DCN closely^{}follows the distribution of characteristic frequencies
(CFs) along^{}the cochlea. For comparison, the place-frequency map
computed^{}for the cat DCN by Spirou et al. (1993) is also
plotted.

*Fusiform cell orientation varies with location*

Figure 4 summarizes a systematic
shift in the orientation of the long axis as a function of
rostral-caudal position. In the^{}rostral end of the nucleus, the apical
dendrites tend to be positioned^{}on the rostral side of the soma while
the basal dendrites extend^{}in the caudal direction. Near the center of
the DCN, the orientation^{}is roughly vertical (dorsal to ventral).
Toward the caudal pole,^{}fusiform cells have caudally directed apical
dendrites and rostrally^{}directed basal dendrites.

It would appear that this trend is a consequence of the shape of the
DCN itself. The DCN can be visualized as a series of^{}thin shells, with
the molecular layer wrapped around the fusiform^{}cell layer, which in
turn is wrapped around the deep layer. Thus^{}from any position within
the fusiform cell layer, the apical dendrites^{}radiate outward to fill
the molecular layer while the basal dendrites^{}converge inward to occupy
the deep layer. A similar finding was^{}reported by Rhode et al.
(1983), who further describe the cells^{}in the rostral end
having more numerous apical dendrites that^{}more frequently emerge
directly from the soma. Neither this study^{}nor the previous one finds
any obvious physiological sequellae^{}to this trend, which possibly is
simply a consequence of the overall^{}curvature of the^{}nucleus.

*Spontaneous rate depends on basal dendrite orientation*

The spontaneous discharge rates of the fusiform cells in this
sample range from 0 to 54 spikes/s. These can be separated into^{}a low
SR group (rate <2.5 spikes/s, 8/17 cells) and a high SR^{}group (rate
>7.5 spikes/s, 9/17 cells). The creation of two SR^{}categories may, in
fact, represent an artificial division of a^{}continuously distributed
property, but is useful here as a convenient^{}means of visualizing a
related anatomical trend. Specifically,^{}there is a correlation between
spontaneous rate group and the^{}disposition of the basal dendrites, as
depicted in Fig. 5. The^{}basal dendrites
of the low SR cells (*top row*) are primarily directed^{}caudally away from the soma. The high SR cells (*bottom row*)
tend^{}also to have branches oriented in the rostral direction, giving^{}the distribution of the basal dendrites a more symmetrical appearance.

These observations were put on a more quantitative basis by computing
the centroid of each basal arbor with respect to the^{}soma. The trend is
specifically captured by the rostral-caudal^{}component,
*Z*_{C}, as shown in Fig. 5. Note that the
value of *Z*_{C} is^{}positive for positions
caudal to the soma. For every low SR cell^{}(*Z*_{C} 63.2 µm), the basal arbor
centroid is caudal to that of^{}every high SR cell
(*Z*_{C} 48.8 µm). No correlation was
found between^{}the absolute position of the basal arbor centroid and
spontaneous^{}activity.

The nine cells shown in Fig. 5 come from the same general region of the
DCN, reflected by the similarity of their best frequencies.^{}This is an
important consideration when examining the arrangement^{}of the basal
dendrites, because as described above, the orientation^{}of the fusiform
cell long axis changes as a function of position^{}(Fig. 4).

*Input resistance is a function of total apical dendritic length*

Figure 6 shows that fusiform cell
input resistance is correlated with apical dendritic length, but not
with basal dendritic^{}length. The best line fit to the apical length was
computed after^{}removing the two points indicated by triangles in Fig.
6*A*. The^{}correlation with apical length is negative, so that
larger lengths^{}correspond to smaller resistances. This is consistent
with a passive^{}model in which membrane conductance is proportional to
surface^{}area, insofar as dendritic surface area is proportional to
total^{}length. Input resistance was not correlated with the sum of the^{}apical and basal lengths (*r* = 0.06). The presence of
spines,^{}however, greatly increases the surface area per unit length of^{}the apical dendrite and so a simple sum of total lengths probably^{}understates the contribution of the apical dendrite to the
overall^{}passive membrane conductance. We did not consider the effects^{}of surface area more directly because of difficulties estimating^{}it
that arose from inconsistencies in the quality of spine labeling.

*Regularity histogram shape depends on orientation of apical
arbor*

Regularity histogram shapes were quantified using three slope
measurements as described in the companion paper. Briefly, the^{}transient slope, *m*_{T}, most closely
follows the classification scheme^{}of Gdowski (1995). It
is particularly sensitive to the change^{}in interspike interval over the
initial 5-10 ms of response and^{}since nearly all of the cells in this
study had decreasing intervals^{}over this range, regardless of their
subsequent behavior, the^{}transient slope was not necessarily an
effective means of characterizing^{}rate trends over the entire stimulus
duration. To better capture^{}these rate trends, the slope measurements
*m*_{1} and
*m*_{2} were computed^{}by performing a
two-line fit to the interspike interval data after^{}omitting the
first^{}bin.

Figure 7 shows that for the 10 fusiform
cells with BFs less than 2 kHz, the slope
*m*_{1} is correlated with the orientation
of^{}the apical dendrites. The angle _{apical}
corresponds to the rotation^{}required to find the narrowest dendritic
profile after making^{}the long axis of the arbor vertical. A value of
zero corresponds^{}to an arbor oriented perpendicular to the coronal
plane. The apical^{}dendrites in Fig. 7 are drawn looking down on their
tops, such^{}that their long axes project out of the page. The values of
*m*_{1}^{}have been divided into three
groups: high, medium, and low, indicated^{}in Fig. 7 by circles,
triangles, and squares, respectively. The^{}data indicate that the
fusiform cells with apical arbors oriented^{}most nearly perpendicular to
the coronal plane have the most positive^{}*m*_{1} values (circles), while those
oriented closest to parallel^{}to the coronal plane have the most
negative *m*_{1} values (squares).

*Correlation of cell properties with location*

An effort was made to identify fusiform cell characteristics that
vary systematically with location. To do this, a wide variety^{}of
physiological response metrics (see companion paper) were
systematically^{}correlated with the normalized *X*-,
*Y*-, and *Z*-position measurements^{}(see
METHODS).

Two statistically significant trends were identified, roughly
orthogonal to the tonotopic axis. The relative noise index decreased^{}in
the *X*-direction (ventrolateral to dorsomedial), meaning that^{}the responses to noise became progressively weaker in this direction^{}(Fig. 8*A*). A gradient in
wideband inhibitory strength is sufficient^{}to account for this
observation, as detailed in the DISCUSSION.^{}The second
trend was that input resistance also tended to decrease^{}in the
*X*-direction (Fig. 8*B*). This is consistent with
the fact^{}that total apical dendritic length increases in the same
direction^{}(Fig. 8*C*), since the inverse relationship between
these two properties^{}has already been described.

Aside from tonotopy, the only statistically significant spatial trends
were found in the *X*-direction. Since neither trend^{}was
accompanied by a significant dependence on *Z*-position, it^{}was not possible to compute an axis trajectory for quantitative^{}comparison with the tonotopic axis computed above. It can, however,^{}be
said that while best frequency is strongly correlated with^{}both
*X*- and *Z*-position, input resistance and relative
noise response^{}are strongly correlated only with *X*-position.
So, although these^{}results cannot resolve the issue of an orthogonal
axis per se,^{}there is at least a qualitative suggestion that the
spatial gradients^{}of these two properties are not parallel with the
frequency^{}axis.