Mice
As illustrated in fig. 6.1, strains of mice were chosen primarily to
represent the two major modes in ganglion cell number. Three standard inbred
strains were selected from the low mode (C57BL/6J, A/J, and LP/J) and four
standard inbred strains were selected from the high mode (BALB/cJ, C3H/HeSnJ,
CE/J, and DBA/2J). All of these strains were obtained from the Jackson
Laboratory, (Bar Harbor, ME). In addition, I selected two strains—CAST/Ei
and BXD32—that have exceptionally low and high ganglion cell numbers,
respectively. BXD32 was obtained from Dr. Benjamin Taylor at the Jackson
Laboratory. CAST/Ei is an inbred strain derived from M. musculus castaneus
that I obtained from Dr. Eva Eicher at the Jackson Laboratory. Finally, I
studied an outbred sample of Mus caroli that I refer to as CARL/ChGo, a
strain that falls into the low ganglion cell mode. CARL/ChGo is a partially
inbred strain of M. caroli given to us by Dr. Dan Goldowitz at the
University of Tennessee. Both CARL/ChGo and CAST/Ei are representatives of
wild species endemic to Southeast Asia. All mice were mated at the
University of Tennessee mouse colony to produce neonates. The day of birth
was designated postnatal day zero (P0).
Figure 6.1. Bimodal distribution
of adult ganglion cell averages for 60 inbred strains. The strains
include 38 recombinant inbred strains and 17 standard inbred strains listed
in Chapter 4, and 5 additional strains. A Gaussian probability distribution
was computed for each strain and summed to obtain a probability density plot
(see Chapter 2, (Williams et al., 1996). The figure shows that most strains
fall into two main modes. The Gaussian function drawn in the background has
a mean of 60.6 ± 6.3 (x1000), the average and SD of the 60 strains. The
arrows designate the strain averages for the ten strains examined in this
study.
Tissue fixation
The neonates were anesthetized by placing them on ice for several
minutes. Neonates were then perfused transcardially with 0.1 M phosphate
buffered saline (0.9%), followed by fixative (2.5% glutaraldehyde and 2.0%
paraformaldehyde in 0.1 M phosphate buffer). Midorbital segments of optic
nerves were dissected from the neonates, osmicated, and embedded in Spurr’s
resin. Nerves were thin-sectioned, placed on formvar-coated grids, and
stained with lead citrate and uranyl acetate.
Estimating ganglion cell number
I estimated ganglion cell numbers by counting axons in P0 optic nerve
cross-sections. Axons were counted as described in Chapter 4, Methods
section, with the following exceptions. Nerves were photographed in a grid
pattern at ~X30,000 using a JEOL EX2000II
electron microscope. Unmyelinated axons were easily identified and counted
(Fig. 6.2)
Figure 6.2. Cross-section of a
neonatal optic nerve. Magnification is 15,000. The scale bar in the
bottom left corner represents 1 µm. Axons at this stage have relatively
uniform diameters, with a mean fiber diameter of ~ 0.4 µm. Axons can be
recognized unambiguously in well fixed tissue. The two structures marked by
arrows are astrocyte processes and were not counted.
I counted necrotic axons in neonatal optic nerves from two strains
belonging to the high mode and two strains belonging to the low mode. I did
this by systematically scanning the entire optic nerve cross-section for
necrotic axons at X15,000. The criteria for
distinguishing necrotic axons are those described in Williams et al.,
(1986). I also searched for growth cones in the sample of photographs used
for counting axons and by scanning several optic nerves at high
magnification (>X40,000).
Results
The retinal ganglion cell population at birth ranged from 131,000 to
224,000 (Table 6.1). The mean for all 46 cases is 182,500 ± 4,400 SE. This
value is almost three times higher than the average for an equally diverse
sample of adult mice (see Chapter 4, (Williams et al., 1996)). I counted an
average of five neonates per strain. The coefficient of variation within
strains averaged 8.2%—only slightly higher than the 7.2% value obtained for
adult mice (see Chapter 4, (Williams et al., 1996)). The small increase is
probably due to the technical difficulty of counting axons before they are
myelinated. Given the anticipated variation in the stage of maturation of
sets of neonatal mice sacrificed at birth, this CV is low and suggests that
the ganglion cell population within a strain is comparatively stable at this
stage of development. The average coefficient of error (the standard error
divided by the sample mean) averaged 4.5% in neonates and 2.5% in adults.
These values provide an assessment of the reliability of adult and
neonatal ganglion cell counts.
Table 6.1.Ganglion cell number and percentage
cell loss
Strain |
Phenotype |
Adult mean ± SE |
n |
P0 mean ± SE |
n |
Absolute Cell Loss |
Percent Loss |
BXD32 |
very high |
75,800 ± 1,900 |
11 |
199,500 ± 5,500 |
6 |
123,700 |
62% |
C3H/HeSnJ |
high |
67,800 ± 1,400 |
3 |
224,000 ± 8,100 |
5 |
156,200 |
70% |
CE/J |
high |
63,600 ± 2,400 |
5 |
207,000 ± 8,900 |
3 |
143,400 |
69% |
BALB/cJ |
high |
63,400 ± 2,200 |
8 |
180,800 ± 7,700 |
4 |
117,400 |
65% |
DBA/2J |
high |
63,400 ± 1,100 |
13 |
202,100 ± 7,900 |
4 |
138,700 |
69% |
C57BL/6J |
low |
55,500 ± 1,300 |
13 |
185,700 ± 6,400 |
7 |
130,200 |
70% |
LP/J |
low |
52,200 ± 1,900 |
8 |
171,400 ± 8,000 |
5 |
119,200 |
70% |
CARL/ChGo |
low |
51,300 ± 2,200 |
11 |
131,200 ± 5,500 |
3 |
79,900 |
61% |
A/J |
low |
50,600 ± 1,300 |
8 |
155,600 ± 6,000 |
6 |
105,000 |
67% |
CAST/Ei |
very low |
45,000 ± 1,000 |
12 |
146,600 ± 6,600 |
3 |
101,600 |
69% |
Cell Production
If strain differences in adult ganglion cell numbers result from
differences in the number of neurons that are generated, then at birth each
strain should have a population that is approximately three-fold higher than
its adult mean. The slope of the regression should be close to 1:3 and the
correlation should be high. This is almost exactly what I found. The slope
of a free regression for the ten strains is 0.26 ± 0.07 (Fig. 6.3). Forcing
the regression line through the origin produces the expected slope of 1:3
with an excellent fit (inset to Fig. 6.3). The positive y-intercept (11,600
adult cells) in the free regression may result from sampling error,
non-linearity of cell death, or may indicate a basal level of cell
production. The correlation coefficient of the free regression in Fig. 6.3
is 0.81, and the corresponding coefficient of determination (r^{2})
is 0.66. Thus, two-thirds of the variance in adult cell number can be
readily explained by strain differences in cell
genesis.
Figure 6.3. Regression of P0 and adult
ganglion cell number averages for ten strains. The error bars represent
one standard error. The thin regression line includes all strains and the
coefficient of determination for these data is 0.66, whereas the dark
regression line excludes strains CAST/Ei and BXD32 and the coefficient of
determination is 0.77. The inset plots the same data but with the regression
line forced through the origin. A regression through the origin is expected
because when cell production is zero adult cell number must be zero.
I was particularly interested in understanding the process that produces
bimodality in adult strain averages and for this reason I also restricted
the analysis to the eight strains belonging to high and low modes (Fig. 6.3,
bold line). The coefficient of determination for this subset of points is
0.77, indicating that the bimodality is generated primarily by differences
in ganglion cell production. The remaining "unexplained" variance must
result from strain differences in the severity of cell death, developmental
noise, and technical error.
This statistical analysis is complicated by two factors. First, the
parameters plotted in Fig. 6.3 are dependent—total cell production cannot be
less than the adult population. Second, the distribution of adult values is
far from normal (Fig. 6.1). Conventional statistical estimates are therefore
difficult to interpret. To address these problems I carried out Monte Carlo
simulations to test cell production and cell death models using seed
parameters taken from the adult distribution (Fig. 6.4). I subtracted the
adult population from the neonatal population to insure independence between
the parameters (Fig. 6.4A). Figures 6.4B and 6.4C show the outcomes of two
typical Monte Carlo simulations in which I plotted adult cell number against
the number of lost cells. The first model (Fig. 6.4B) assumes that all
differences in adult cell number are caused by matched differences in cell
production and that cell death is strictly proportional to cell production.
The second model (Fig. 6.4C) assumes that all differences among adult
strains are caused by variation in the severity of cell death and that at
birth all strains have roughly the same cell population (~180,400 ± 18,400
cells). In the cell production simulation (Fig. 6.4B), the regression slope
is +1.2, whereas in the cell death simulation (4C) the slope is –1.1. My
actual data set (Fig. 6.4A) with its slope of +1.5 strongly supports a cell
production model.
Figure 6.4. Regression of numbers of cells that are lost (number
at P0 minus the number at maturity) and adult ganglion cell number from our
data.(4A), and two alternative Monte Carlo simulations (B and C). The
first model (B) assumes that all differences in ganglion cell number are
caused by cell production differences, whereas the second model (C) assumes
that all differences are caused by variation in the severity cell death.
Monte Carlo data sets consisted of 200 numbers randomly selected from normal
distributions. In both models, high and low adult ganglion cell groups, (n
= 100 each), were selected from two normal distributions with seed
parameters (mean and standard deviation) from the 5 high (66,800± 5,400) and
5 low (50,920 ± 3,800) strains that I studied. In the production model (B),
means were obtained from two normal distributions with seed parameters (mean
and standard deviation) from the 5 high (202,680 ± 15,500) and 5 low
(158,100 ± 21,200) strains. In the case of the cell death model (C), where
no production differences are assumed, the neonatal means were obtained from
a single distribution, with a mean and standard deviation of all 10 strains
combined (180,390 ± 18,400). The slope obtained with our real data is +1.5
(A), while the cell production (B) and cell death (C) models are +1.2 and
–1.1, respectively. The positive slope from our data is close to that of the
simulated cell production model, demonstrating that differences in adult
ganglion cell number is predominantly due to differences in cell production.
In used Model I linear least-square regression for this analysis because the
measurement error term is without bias. Adult ganglion cell number was
subtracted from P0 ganglion cell number to make the y-axis formally
independent of adult ganglion cell number plotted on the x-axis.
The 10 inbred strains were divided into high (BALB/cJ, C3H/HeSnJ, CE/J,
BXD32, and DBA/2J) and low groups (C57BL/6J, A/J, CAST/Ei, CARL/ChGo, and
LP/J). Mean adult ganglion cell numbers for these groups are 66,800 ± 2,700
and 50,900 ± 1,900, respectively. There are highly significant differences
in ganglion cell production between these groups, with means of 202,700 ±
7,800 and 158,100 ± 10,600, respectively (t test, p < 0.001).
In contrast, there is no significant difference in the percentage of
ganglion cell loss between high and low groups, with mean percentage cell
loss relative to neonatal values of 66.9% and 67.5%, respectively (p
= 0.42).
Nnc1 was mapped using recombinant inbred strains generated from the
parental strains, DBA/2J and C57BL/6J. For this reason a comparison between
these two strains is especially germane in discovering how Nnc1
modulates ganglion cell number. The severity of percentage cell death was
closely matched between DBA/2J and C57BL/6J—69% and 70%, respectively. In
contrast, DBA/2J produces ~16,400 more cells than C57BL/6J. This result,
together with our previous finding of additive gene action (see Chapter 5,
and , indicates that the substitution of a single allele at Nnc1 is
associated with a production difference of approximately 8,000 cells.
Cell Death
With the exception of strains BXD32, CARL/ChGo, and BALB/cJ, the average
percentage of cell death among strains is relatively uniform—69% ± 1.2%
(Table 6.1). While the percentage of cell death is relatively uniform, the
absolute magnitude of ganglion cell death is variable among strains and is
highly correlated with production values (Table 6.1). There are some notable
exceptions to this generality. The percent cell death in BXD32 and CARL/ChGo
is significantly lower than in other strains (t test, p < 0.05, with
Bonferonni correction). Estimates of ganglion cell production are similar in
BALB/cJ and C57BL/6J, yet these strains have adult populations that differ
by about 8,000 cells (Table 6.1). A slight reduction in the severity of cell
death in BALB/cJ (65% loss) appears to account for this strain’s relatively
high cell number at maturity. In this instance, the marked strain difference
in adult population size results primarily from variation in the severity of
cell death. Differences in cell death can also compensate for differences in
cell production. For example, CARL/ChGo produces an average of 131,000
ganglion cells—20,000 to 40,000 fewer cells than A/J and LP/J,
respectively—yet all three strains have very closely matched adult
populations (Table 6.1.).
Necrotic axons and growth cones
The validity of our quantitative analysis depends on the assurance with
which I can estimate total ganglion cell production in mice. If much cell
loss occurs before birth or much cell addition occurs after birth, then
production estimates based on axon counts in the optic nerve at P0 will be
too low. To rule out the possibility that significant cell death occurs
prenatally, I counted necrotic axons in neonatal optic nerves from strains
belonging to the high and low modes using criteria described by Williams and
colleagues (1986). Necrotic axons are relatively easy to see, and it was
practical to count all sites of necrosis in a single optic nerve
cross-section. Necrotic axons at P0 make up 0.02% and 0.05% of the fiber
population in cases selected from the low strains, A/J and C57BL/6J,
respectively, whereas they make up 0.07% and 0.09% of the population in
cases selected from the high strains, BXD32 and C3H/HeSnJ, respectively. The
fact that a somewhat higher incidence of necrosis was noted in nerves taken
from the high strains makes it very unlikely that variation in early axon
loss accounts for differences between adult values. Growth cones were
exceeding rare in all material and fewer than 5 profiles among all cases met
even a relatively lax criteria for these structures
(Colello and Guillery, 1992; Williams et al., 1986).
Specificity of strain differences
Do strain differences in retinal ganglion cell number correspond to
differences in total brain weight or are differences among strains specific
to the ganglion cell population? The correlation of ganglion cell number and
brain weight across individual mice is 0.37, but when strain averages are
used the correlation rises to 0.75. This suggests that about half the
variance in neonatal ganglion cell number can be explained directly or
indirectly by differences in brain weight. As assessed by quantitative DNA
analysis, brain weight differences among neonatal mice are primarily due to
differences in total cell number (Zamenhof and van Marthens, 1978). Thus,
mechanisms modulating ganglion cell number may have common effects on cell
number in the other parts of the CNS. Alternatively, the correlation between
ganglion cell number and brain weight could suggest that variation of
ganglion cell number is the result of differences occurring very early in a
neural progenitor pool, perhaps during neurulation. The correlation between
strain averages of adult brain weight and ganglion cell number for the same
strains is only 0.51. Given the wide confidence intervals of correlations
computed with low numbers of cases, the difference between the adult and
neonatal correlations (0.51 and 0.75, respectively) may be due to sampling
error. However, it is also conceivable that strain variation in cell death
decreases an initially high correlation between brain weight and retinal
ganglion cell number. In any case, the cellular specificity of the strain
differences is likely to be low, and I expect differences in numerous other
neuronal cell populations to be closely matched with the differences I find
in ganglion cell number.
Discussion
The analysis demonstrates that most of the variation in adult ganglion
cell number among strains of mice can be traced to differences in cell
production. Allelic variants at the Nnc1 locus on Chr 11 generate the
pronounced bimodality in ganglion cell population size by modulating
ganglion cell production.
Generation and death of retinal ganglion cells Generation of retinal
ganglion cells in mice begins on E11 and lasts until just before birth (Dräger,
1985). There is a short delay between neurogenesis and the time at which
ganglion cell axons extend into the optic nerve (Colello and Guillery,
1992). This delay could deflate estimates of total cell production. However,
very few ganglion cells are produced after E18 and as anticipated from the
work of Colello and Guillery (1992), I did not find growth cones in neonatal
optic nerves. It is therefore unlikely that the estimates of total
production are biased downward by late ganglion cell generation.
In contrast, ganglion cell death begins at, or just before, birth, peaks
between postnatal days 4–6, and is essentially complete by P12 (Linden and
Pinto, 1985). At the peak of cell loss, between 5,000 and 10,000 ganglion
cells are eliminated per (Williams et al., 1990). However, fewer than 2,000
cells are lost on the day of birth in mice, consistent with my observation
of very few necrotic axons—less than 300 per nerve. At this rate it is
improbable that more than a total of 10,000 ganglion cells are lost
prenatally. In chickens there is as much as a three day delay between the
onset of ganglion cell degeneration in the retina and the elimination of
axons in the optic nerve (Rager et al., 1978). If there is a similar delay
in mice then axon counts should preserve our production estimates.
Nonetheless, the estimates of total production maybe biased downward
slightly by the early loss of ganglion cell axons. However, the magnitude of
this error is sufficiently small (~10,000 cells) that I did not think this
loss warranted correction.
Variation in retinal ganglion cell death
The severity of cell death is close to 68–70% in most strains of mice.
However, there are three exceptional strains with less severe loss. Three to
nine percent fewer cells are lost in BXD32, CARL/ChGo, and BALB/cJ. BXD32 is
particularly interesting because it has the highest adult population (75,800
± 1,900) among the 60 strains I have now examined. Yet at birth BXD32 has an
unexceptional number—199,500—that is lower than three other strains.
Clearly, one or more genes controlling rates of ganglion cell death are
responsible for the high adult cell number in this strain. It would be
feasible to map a cell death gene by crossing BXD32 to a strain with similar
ganglion cell production but higher cell death.
Variation in the severity of cell death may result from differences in
titers of neurotrophic factors. The neurotrophins—BDNF and
neurotrophin-3/4—have been found to increase survival of retinal ganglion
cells in chicken and rat (Ma et al., 1998; Rosa et al., 1993). Neuregulin,
found on the cell surface and as a secreted protein, can also increase
survival of neonatal rat retinal ganglion cells in culture (Bermingham-McDonogh
et al., 1996). Differences in the concentration or expression time of these
neurotrophic factors, their receptors, or components within their signaling
pathways could produce variation in the severity of naturally occurring
ganglion cell death.
Nnc1 controls cell production
Approximately 77% of the variation among adult strains result from
differences in the production of ganglion cells. The percentage of cell
death in high and low groups does not differ significantly (66.9% and 67.5%,
respectively). I conclude that variation in adult ganglion cell number among
inbred mouse strains results predominantly from differences in cell
production. Comparison of our data with the Monte Carlo simulations (Fig.
6.4) corroborates this conclusion. A major motivation for undertaking the
present study was to determine how and when allelic variants at Nnc1
influence the size of the ganglion cell population. Collectively, the
results strongly indicate that Nnc1 modulates ganglion cell number by
influencing cell production, and because ganglion cell production occurs
before birth, this result provides a time frame for the action of Nnc1.
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