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Volume 16, Number 19,
Issue of October 1, 1996
pp. 6183-6196
Copyright ©1996 Society for Neuroscience
The Leaving or Q Fraction of the Murine Cerebral Proliferative
Epithelium: A General Model of Neocortical Neuronogenesis
Takao Takahashi1, 2,
Richard S. Nowakowski3, and
Verne S. Caviness Jr.1
1 Department of Neurology, Massachusetts General
Hospital, Harvard Medical School, Boston, Massachusetts 02114, 2 Department of Pediatrics, Keio University School of
Medicine, Tokyo 160, Japan, and 3 Department of
Neuroscience and Cell Biology, University of Medicine and Dentistry of
New Jersey-Robert Wood Johnson Medical School, Piscataway, New Jersey
08854
 ABSTRACT
- INTRODUCTION
- MATERIALS AND METHODS
- RESULTS
- DISCUSSION
- FOOTNOTES
- REFERENCES
ABSTRACT 
Neurons of neocortical layers II-VI in the dorsomedial cortex of
the mouse arise in the pseudostratified ventricular epithelium (PVE)
through 11 cell cycles over the six embryonic days 11-17 (E11-E17).
The present experiments measure the proportion of daughter cells that
leave the cycle (quiescent or Q fraction or Q) during a single cell
cycle and the complementary proportion that continues to proliferate
(proliferative or P fraction or P; P = 1  Q). Q and P for
the PVE become 0.5 in the course of the eighth cycle, occurring on E14,
and Q rises to ~0.8 (and P falls to ~0.2) in the course of the 10th
cycle occurring on E16. This indicates that early in neuronogenesis,
neurons are produced relatively slowly and the PVE expands rapidly but
that the reverse happens in the final phase of neuronogenesis. The
present analysis completes a cycle of analyses that have determined the
four fundamental parameters of cell proliferation: growth fraction,
lengths of cell cycle, and phases Q and P. These parameters are the
basis of a coherent neuronogenetic model that characterizes patterns of
growth of the PVE and mathematically relates the size of the initial
proliferative population to the neuronal population of the adult
neocortex.
Key words:
neocortical neuronogenesis;
cell cycle;
proliferation;
mouse;
ventricular zone
INTRODUCTION
The neocortical histogenetic sequence is initiated
with generations of neurons (neuronogenesis) in the pseudostratified
ventricular epithelium (PVE) at the margin of the ventricular cavities
(Fig. 1) (His 1889 ; Schaper 1897; Sauer 1935; Sauer et
al., 1959; Fujita 1963; Stensaas and Stensaas, 1968; Hinds and Ruffett,
1971; Sidman and Rakic, 1982; Takahashi et al., 1993, 1995a). Within
the cortex, the earliest formed postmitotic neurons migrate to the
deepest cortical layers and progressively later-arising neurons migrate
past them to progressively more superficial layers (Sidman and Rakic,
1973; Caviness, 1982). Once neurons take up their final positions,
their numbers are reduced by histogenetic cell death (Finlay and
Slattery, 1983; Finlay and Pallas, 1989). Thus, the events of
neocortical histogenesis are extended in time and proceed in widely
separated zones that are greatly different in structure. Yet these
events are regulated coordinately to arrive at a neuronal density that
is approximately the same from region to region of the same brain and
in the brains of diverse mammalian species (Rockel et al., 1980;
Schüz and Palm, 1989; Finlay and Darlington, 1995; Caviness,
1995).
Fig. 1.
Schematic representation of the developmental
changes associated with the PVE in the neocortical cerebral wall during
the neuronogenetic interval. The PVE is approximately coextensive with
the ventricular zone (VZ) lying at the ventricular
margin. Young postmitotic neurons migrate across the intervening
cerebral wall (broken arrows) to the developing cortex
(CTX). The cells of the PVE undergo interkinetic
nuclear migration (curved arrows) in the course of the
cell cycle, which begins with the G1 phase and
progresses through S and G2 and is
completed with the M phase. Postmitotic cells either
exit the cell cycle (Q fraction,
Q1-Q11) or elongate through
G1 phase to reenter S phase (P fraction,
P1-P11). Before the onset of
neuronogenesis, the P fraction is 1.0, and the
Q fraction is 0. Q becomes >0 with the onset of
neuronogenesis (i.e., Q1 > 0) and eventually
reaches 1.0 at the end of the neuronogenetic interval, which
corresponds to 11 integer cell cycles
(CC1-CC11) in mouse. Reciprocally,
P follows a path from 1.0 to 0. The PVE gradually
increases in height, but over the final cycles it involutes and ceases
to exist with the termination of CC11. At the completion of
CC11, all postmitotic cells exit the VZ as
Q (Terminal Output).
[View Larger Version of this Image (36K GIF file)]
The present analysis is a pivotal link in a series of investigations
that are concerned with the regulation of neocortical neuron numbers
(Takahashi et al., 1992, 1993, 1994, 1995a,b). In previous studies, we
have determined that the length of the cell cycle
(TC) increases in the dorsomedial cerebral wall
of the mouse, and we have established that the neuronogenetic interval,
which extends from embryonic day 11 (E11) through early E17 in mice,
corresponds to approximately 11 cell cycles (Takahashi et al., 1995a).
We have also established that the growth fraction of the PVE remains at
1.0 throughout the course of neuronogenesis (Takahashi et al., 1995a).
These measures in themselves, however, are insufficient as a basis from
which to estimate the cellular productivity of the PVE. Missing are
measures of the proportion of daughter cells that ``elect'' either to
exit the cycle as terminally postmitotic neurons (the quiescent or Q
fraction of postmitotic cells or Q) or remain in the cycle (the
proliferative or P fraction of postmitotic cells or P), that is, to
replenish or even enlarge the proliferative pool (Fig. 1) (Takahashi et
al., 1993).
The specific objective of the experiments reported here is to determine
P and Q across the neuronogenetic interval. With those values, taken
together with cell cycle parameters determined earlier, we arrive at a
quantitative characterization of PVE proliferative behavior that we
refer to as a neocortical neuronogenetic model. This
neuronogenetic model will serve as an analytic tool for estimating
other parameters of histogenesis, such as the total number of neurons
to be formed and the rate that they will be formed over the course of
neocortical neuronogenesis. The model will also be used to make
specific predictions about the behavior of the proliferating cells and
their progeny, which will be amenable to experimental validation.
Finally, it will serve as a general formulation applicable to
neocortical histogenesis across mammalian species (Caviness et al.,
1995).
MATERIALS AND METHODS
Animals. CD1 mice were maintained on a 12 hr (7:00
A.M.-7:00 P.M.) light/dark cycle. Conception (E0) was ascertained by
plug-checks conducted at 9:00 A.M.
Experimental design. The experimental design is identical to
one used previously in analysis of proliferative behavior of small,
strictly specified cohorts of cells of the PVE (Takahashi et al.,
1994). Experiments were initiated at 7:00 A.M. on each of E12-E16,
inclusive, corresponding to the greater part but not the entire
neuronogenetic interval. Proliferating cells of the embryonic cerebral
wall are exposed sequentially, by intraperitoneal injection into
pregnant dams, to the S-phase marker tritiated thymidine
(3H-TdR; 5 µCi/gm body weight) and the thymidine analog
BUdR (50 µg/gm body weight; Sigma, St. Louis, MO). Two separate
tracer injection protocols make possible the experimental determination
of separate values for the number of Q and P cells
(NQ+P) (Fig. 2, Protocol 1) and
the number of Q cells (NQ) (Fig. 2,
Protocol 2) in a primary cohort of proliferative cells that exit S
phase in synchrony over a 2 hr interval (Takahashi et al., 1994) (for
details, see legend to Fig. 2). By using the two injection protocols in
two subsets of animals, NQ+P is determined from
Protocol 1 for one subset of animals and NQ
is determined from Protocol 2 for the second subset of animals. The Q
fraction itself can then be calculated as the ratio of
NQ to NQ+P, and the
P fraction is equal to 1 Q.
Fig. 2.
Labeling protocols for determining the number of
cells in the combined Q+P fractions (Protocol 1) and
those in the Q fraction (Protocol 2). Step
1, The embryos are exposed to tritiated thymidine
(3H-TdR) at 7:00 A.M. on each of E12-E16. The
3H-TdR labels the cells in S, as indicated
by the dots over the nuclei. Step 2, 2 hr
later at 9:00 A.M. the embryo is exposed to BUdR, which
again labels cells in S phase (gray-filled
nuclei). The sequence of 3H-TdR and BUdR exposures
results in three types of labeled cells: (1) cells that left
S for G2 during the 2 hr interinjection
interval, referred to as the 2 hr cohort of cells (*), will be
labeled only with 3H-TdR (dots in the
nucleus); (2) cells that entered S during the 2 hr
interinjection interval will be labeled only with BUdR
(gray-filled nuclei); and (3) cells that remained
in S during the interinjection interval
(gray-filled nuclei and black
dots). Embryos labeled in this way are then partitioned into
two subsets (Step 3). Step 3, Protocol 1
(left), Embryos receive no further exposure to BUdR. At
an interval after the initial BUdR exposure, which is longer than the
duration of the cell cycle minus the duration of S phase
(>TC-TS), both
the Q and P fraction cells of the 2 hr cohort will be labeled only with
3H-TdR. That is, the number of cells labeled only with
3H-TdR with Protocol 1 corresponds to the
number of cells of the cohort in the combined Q and P fractions
(NQ+P). Step 3, Protocol 2
(right), Embryos will receive a sequence of additional
exposures to BUdR (Step 3, right). At an interval
>TC-TS, the P
fraction cells of the 2 hr cohort will reenter S phase and become
labeled with BUdR, and thus are eliminated from the cohort. That is,
the number of cells labeled only with 3H-TdR with
Protocol 2 corresponds to the number of cells of the
cohort in the Q fraction
(NQ) .
[View Larger Version of this Image (22K GIF file)]
Embryos labeled by either of the two injection protocols were
removed by hysterotomy from dams anesthetized deeply by an
intraperitoneal injection of a mixture of ketamine (50 mg/kg body
weight) and xylazine (10 mg/kg). At E12-E14, the embryos were
decapitated, and the whole heads were fixed with 70% ethanol
overnight. E15 and E16 embryos were perfused via the left ventricle
with 70% ethanol. They were dehydrated and embedded in paraffin as
described previously (Takahashi et al., 1992, 1993, 1994).
Immunocytochemistry and autoradiography were performed on 4 µm
coronal sections as described previously (Takahashi et al., 1992, 1993,
1994).
Limits to the temporal window of the methods. The
study design and methods used here do not permit us to specify with
direct experiment measurements more accurately than did earlier
``time-of-origin experiments'' the time of initiation and termination
of the neuronogenetic interval that we considered to begin early on E11
and to continue until early on E17 (Takahashi et al., 1995a). Thus, we
made no attempt to determine with the present or earlier experiments
the precise moments when the first and last neurons arise from the
dorsomedial neocortical PVE. Furthermore, we made no attempt to measure
Q and P experimentally on E11 because there would have been so few
3H-TdR-only cells (with Q  0.1) that the results, in
our opinion, would have been unreliable. We also made no attempt in
these experiments to define Q and P through the early hours of E17
because Q would have reached 1.0, and P would have reached zero.
Indeed, the experimental design suitable for the analyses on E12-E16
could not have been repeated from 9:00 A.M. on E17. This is because the
PVE would have become exhausted as a pool of neuronal precursors before
completion of the required
TC-TS
interval.
Analysis. The analysis is undertaken in a standard coronal
sector of the dorsomedial cerebral wall (Takahashi et al., 1992, 1993).
The sector is 100 µm in its medial-lateral dimension and 4 µm
(corresponding to section thickness) in its rostral-caudal dimension.
The sector is divided in its radial dimension into bins 10 µm in
height, and the bins are numbered 1, 2, 3, and so on from the
ventricular margin (Takahashi et al., 1992, 1993). Cells labeled only
with 3H-TdR (distinguishable from background, typically
four or more grains per nucleus) were scored with respect to their bin
location in the cerebral wall.
Data were collected from the standard coronal sector from the brains of
16 embryos at each age: eight brains (four brains from each of two
separate litters treated by Protocol 1) were used to obtain
NP+Q, and eight brains (four brains from each of
two separate litters treated by Protocol 2) were used to obtain
NQ. The number of 3H-TdR-only
labeled cells was counted on six nonadjacent sections for each brain,
and then the average and SEM values for each set of eight embryos were
calculated to obtain NP+Q and
NQ for each day of the neuronogenetic interval
(Takahashi et al., 1994).
This basic analytic method was modified slightly to deal with the
differential distributions and proliferative behaviors of the PVE and
the secondary proliferative populations (SPP) at different times of
development. Thus, the PVE is approximately co-extensive with the
ventricular zone (VZ) during the entire neuronogenetic interval, but
the distribution of the SPP changes markedly (Takahashi et al.,
1995a,b). The SPP is first detectable on E13 as a few rare
abventricular mitotic figures at the border between the VZ and the
primitive plexiform zone (PPZ). Thus, the measurements of
NQ+P and NQ obtained
on E12 and E13 in essence are direct measurements of the behavior of
the PVE cells. The SPP then enlarges rapidly and populates the entire
subventricular (SVZ)-intermediate (IZ) zone continuum after these two
strata emerge in the dorsomedial cerebral wall in the course of E14
(Takahashi et al., 1995a,b). Concurrently the SPP increases
substantially as a proportion of the total proliferative population of
the cerebral wall. By E14 the PVE comprises ~89% and the SPP 11% of
the total proliferative population of the dorsomedial cerebral wall,
and by E16 these proportions are 65% and 35% (Table 4, column 3)
(Takahashi et al., 1995b)).
Table 4.
Values for Q and P for the PVE and for the SPP E14-E16
| (1) Age |
(2) Proliferative
population |
(3) % of total proliferative
population |
(4) |
(5) NP+Q |
(6) NP |
(7) P |
(8) Q
|
|
|
PVE |
89 |
|
17.30 |
10.8-11.3 |
0.62-0.66 |
0.34-0.38
|
| E14 |
SPP |
11 |
19.40 |
2.10 |
1.54-2.10 |
0.73-1.0 |
0-0.27
|
|
PVE |
86 |
|
15.66 |
5.19 |
0.33 |
0.67
|
| E15 |
SPP |
14 |
18.21 |
2.55 |
2.29 |
0.90 |
0.10
|
|
PVE |
65 |
|
12.14 |
2.59 |
0.21 |
0.79
|
| E16 |
SPP |
35 |
18.68 |
6.54 |
5.93 |
0.91 |
0.09 |
|
|
The PVE and the SPP as fractions of the total proliferative
population (column 3) have been determined previously (Takahashi et
al., 1995b). The total numbers of cell in the 2 hr cohort, including
those in the P and Q fractions (NP+Q, column 4),
are assigned to either the PVE or the SPP and entered in column 5. These values are derived as the products of the values in columns 3 and
4. The number of cells of the P fraction (NP)
are determined separately for the PVE and SPP and are entered in column
6. For the derivation of these values, see P and Q fractions of the PVE
and of the SPP in Results. The P fraction (column 7) is the values in
column 6 divided by those in column 5; the Q fraction (column 8) is the
complement of the P fraction (1.0 minus the values in column 7; i.e.,
1 P).
|
|
The difficulty for the present analysis is that from E14 to E16, cells
of the PVE and SPP intermingle with each other at the interface of VZ
and SVZ (Takahashi et al., 1993, 1995a,b), and in this small portion of
the developing cerebral wall the two populations cannot be separated by
cytoarchitectonic criteria. For this reason, after E14 separate
measures of the values of P and Q for the PVE and for the SPP were
obtained by following a strategy that will be described in detail in
Results.
RESULTS
The dorsomedial cerebral wall is ~50 µm in thickness at the
initiation of these experiments on E12 (Fig. 3). The
thickness increases nearly eightfold to ~400 µm at the time that
the experiments are completed on E16 (Takahashi et al., 1995a). Before
E14 the VZ is ~80-90% of the thickness of the cerebral wall, with
only a narrow PPZ interposed between VZ and pia. Late on E14 several
histogenetic transitions occur essentially simultaneously. First, the
cortical strata, including molecular layer, cortical plate, and
subplate, emerge at the surface of the cerebral wall. Second, the IZ
intervenes between cortical strata and VZ. Third, the SVZ becomes
distinguishable in the depths of the IZ at its interface with the
VZ.
Fig. 3.
Growth of strata of the murine dorsomedial
cerebral wall during the neuronogenetic interval E11-E17 (modified
from Takahashi et al., 1995a). The height of each stratum was
obtained by direct measurement in histological sections. The
ventricular surface is at 0 on the y-axis. The upper
border of the ventricular zone (VZ) is indicated by
closed circles, the pial surface by X,
the subventricular zone and intermediate zone (SVZ, IZ)
border by open circles, the border between
IZ and the developing cortex (CTX)
by closed squares, and the border between
CTX and the molecular layer (ML) by
closed triangles. The contours tracing progressive
growth of strata were made initially by a least-squares fit to a
fourth-order curve and then smoothed by eye. Through early E14, the
cerebral wall has only two strata, the primitive plexiform zone
(PPZ) and the VZ. The VZ approaches maximum height by
E15, which then declines ~50% by the end of E16 as it involutes. The
cortical strata (ML + CTX), by contrast, increase progressively in
height. The period of most rapid growth of the IZ is completed early on
E14.
[View Larger Version of this Image (17K GIF file)]
The PVE, although approximately co-extensive with the VZ, must be
distinguished as a specific proliferative population from the VZ, which
is an architectonically defined stratum (Takahashi et al., 1992). The
VZ includes three separate populations: proliferative PVE cells (i.e.,
P fraction), Q fraction cells of the PVE exiting through the VZ, and
the cells of the SPP. The importance of this distinction is that in the
outer region of the VZ, the SPP overlaps with the PVE (Takahashi et
al., 1993, 1995a).
P and Q fractions of the overall proliferative population (PVE
+ SPP)
From the microscopic perspective, the cells
labeled only with 3H-TdR define the P+Q and Q-only
populations, depending on the experiment. For data analysis at each of
E12-E16, sections similar to the ones shown in Figure 4
were used to obtain the distribution of P+Q cells and of Q cells only,
which were mapped with respect to depth in the cerebral wall (per 10 µm bin; see Materials and Methods). The distribution of P cells was
obtained by taking the difference between the number of P+Q cells and
the number of Q cells on a bin-by-bin basis (Figs. 5, 6)
(Takahashi et al., 1994). The quantitative distributions that were
obtained confirm the impression derived from sections shown in Figure 4
that the cells of the P+Q fractions are distributed widely from the
ventricular surface throughout the IZ. As expected from our choice of
survival times (Table 2), none of the P+Q fraction cells
was observed to be in mitosis.
Table 1.
Abbreviations used
| CC1-11 |
Integer
cell cycles 1-11 |
| CTX |
Neocortex |
| IZ |
Intermediate zone
|
| ML |
Molecular layer |
| NQ |
Number of Q
fraction cells |
| NQ+P |
Number of Q and P
fraction cells |
| P |
P fraction |
| PPZ |
Primordial plexiform zone
|
| PVE |
Pseudostratified ventricular epithelium |
| Q |
Q fraction
|
| SPP |
Secondary proliferative population |
| SVZ |
Subventricular
zone |
| TC |
Length of cell cycle
|
| TS |
Length of S phase
|
| VZ |
Ventricular zone |
|
Fig. 4.
A, C, Representative
micrographs of preparations labeled according to Protocol 1 in Figure
2; B, D, those labeled according to Protocol 2 in Figure
2. These micrographs show comparative distributions of cells of the
combined Q + P (A, C) and Q fractions (B,
D) in the 2 hr cohort at E12 (A, B) and E15
(C, D). At E12, the micrograph includes the full height
of the cerebral wall. The pial surface is indicated by a dashed
line, and the border between the VZ and SVZ zones is indicated
by asterisks. At E15, the micrograph includes only the
VZ and the adjacent SVZ and IZ. Cells marked only by 3H-TdR
are recognized as accumulations of silver grains over the cell nucleus
(arrowheads). Cells labeled with BUdR or BUdR and
3H-TdR have darkly stained nuclei. Scale bar (shown in
A): 20 µm.
[View Larger Version of this Image (115K GIF file)]
Fig. 5.
The distributions of cells of the P, Q, and
P+Q fractions on E12 and E13. The analysis is undertaken in a coronal
sector of the dorsomedial cerebral wall that is 100 µm in its
medial-lateral dimension and 4 µm (corresponding to section
thickness) in its rostral-caudal dimension. The sector is divided in
its radial dimension into bins (x-axis) 10 µm in
height and numbered 1, 2, 3, and so on from the ventricular margin
(Takahashi et al., 1992, 1993). The number of cells in the Q
(NQ) and P+Q fractions
(NP+Q) for each bin
(y-axis) are determined according to the method
illustrated and described in Figure 2. The values for P fraction cells
(NP) are estimated as
NP+Q NQ. On E12 and
E13, the dorsomedial cerebral wall is formed of only two strata, the VZ
and the PPZ (see Fig. 3). Error bars represent SEM.
[View Larger Version of this Image (20K GIF file)]
Fig. 6.
The distributions of cells of the P, Q, and P+Q
fractions on E14-E16. See legend to Figure 5 for details. On E14-E16,
the dorsomedial cerebral wall is formed of the VZ, the IZ, and the
developing cortex (CTX; see Fig. 3). The bins 10 µm in
height (see legend to Fig. 5) are the x-axis. Error bars
represent SEM.
[View Larger Version of this Image (24K GIF file)]
Table 2.
Summary of PVE cell cycle phase durations (hours) and
experimental intervals
| Embryonic
days |
TC-TS |
TC |
Experimental
interval (after initial BUdR) |
|
| E12 |
5.3 |
10.2 |
6.5
|
| E13 |
7.5 |
11.4 |
9.5 |
| E14 |
11.3 |
15.1 |
12.5
|
| E15 |
13.8 |
17.5 |
15 |
| E16 |
14.4 |
18.4 |
17 |
|
|
TC, Length of cell cycle;
TS, length of S phase.
TC-TS and
TC have been established previously (Takahashi
et al., 1995a). For the present experiments, the duration of survival
after the initial (or only) injection of BUdR was greater than
TC-TS but shorter
than would be required for the P fraction to complete a second M phase,
i.e., shorter than TC.
|
|
For each age, the total number of cells in the entire cohort (i.e.,
NP+Q for PVE and SPP collectively) and the total
number of cells in the Q fraction only (NQ) are
shown in Table 3 (columns 2 and 3, respectively). The Q
fraction for the overall proliferative population (PVE + SPP
collectively), i.e., the fraction of cells exiting the cell cycle, for
each embryonic date from E12 through E16, is
NQ/NP+Q. Q increases from
0.11 on E12 to ~0.6 on E15 and E16 (Table 3, column 4). The P
fraction, 1 Q (Table 3, column 5), decreases from just under
0.9 on E12 to ~0.4 on E15 and E16.
Table 3.
Estimate of Q and P for the entire proliferative population
(PVE + SPP)
| (1) Embryonic
days |
(2) NP+Q |
(3) NQ |
(4) Q |
(5) P
|
|
| E12 |
17.23 |
1.94 |
0.11 |
0.89
|
| E13 |
25.90 |
4.96 |
0.19 |
0.81
|
| E14 |
19.40 |
6.52 |
0.34 |
0.66
|
| E15 |
18.21 |
10.73 |
0.59 |
0.41
|
| E16 |
18.68 |
10.60 |
0.54 |
0.46 |
|
|
The total number of cells in the 2 hr synchronous cohort,
including those in the P and Q fractions (NP+Q)
estimated by labeling protocol 1 in Figure 2 and the number of cells in
the Q fraction alone (NQ) estimated by labeling
protocol 2 are entered, for each of E12-E16, in columns 2 and 3, respectively. The Q fraction (=
NQ/NP+Q, values in
column 3 divided by those in column 2) and the P fraction (= 1 Q) are entered in columns 4 and 5, respectively.
|
|
P and Q fractions of the PVE and the SPP
As mentioned briefly in Materials and Methods, developmental
changes in the magnitude and distribution of the SPP require that early
and late periods be treated differently. On E12 and E13, the entire
proliferative population is PVE. Thus, NP+Q and
NQ for the SPP are 0 on both E12 and E13. For
this reason the values for Q and P estimated for the overall population
may be taken to be the values of Q and P for the PVE on these two dates
(Table 3, columns 4 and 5). Over the interval E14-E16, however, the
SPP increases from ~11% to 35% of the total proliferative
population (Table 4, column 3) (Takahashi et al.,
1995b). For this later interval, Q and P must be estimated separately
for the PVE and the SPP. These estimates require two steps, each of
which depends on (1) our previous determinations of the sizes of PVE
and SPP as fractions of the total proliferative population (Takahashi
et al., 1994, 1995b) and (2) the patterns of distribution of PVE and
SPP within the cerebral wall.
The first step is a partition of NP+Q of
the overall proliferative population into its PVE and SPP components by
taking the product of NP+Q of the overall
proliferative population (Table 4, column 4) and the fractional
contribution of PVE and SPP, respectively (Table 4, column 3). For
example, at E14 NP+Q is 19.40 cells, of which
89% (17.30 cells) is apportioned to the PVE and 11% (2.10 cells) is
apportioned to the SPP (Table 4, column 5).
The second step is determination of NP for
the PVE and for the SPP. On E15 and E16, the P fractions are
distributed bimodally with one distribution entirely within the VZ and
the other distribution in the SVZ and IZ (Fig.
6B,C). On these two dates the P
fraction cells can be counted separately for the VZ and the SVZ-IZ.
Those of the VZ are assigned by definition to the PVE, whereas those of
the SVZ-IZ are assigned by definition to the SPP (Table 4, column 6).
The P fraction for PVE and for SPP for each of E15 and E16 is then
derived as NP divided by
NP+Q (Table 4, column 7); the Q fraction is
derived as 1 P (Table 4, column 8).
On E14, however, the separation of P fraction cells belonging to the
PVE and SPP is incomplete, with a small but continuous distribution of
the P fraction spanning VZ and SVZ-IZ (Fig. 6A). For
this reason, a range of plausible estimates for
NP of the PVE and SPP was made as described
previously (Takahashi et al., 1994). Briefly, the range is determined
by moving imaginary ``dividing lines'' between bins where the P
fraction cells are assigned either totally to the SPP or totally to the
PVE. The minimum plausible estimate for P of 0.62 for the PVE was
obtained when the dividing line between PVE and SPP was taken to lie
between bins 6 and 7. The maximum estimate of 0.66 was obtained when
the line was set between bins 7 and 8 (Table 4, column 7); the Q
fraction is derived as 1 P (Table 4, column 8).
Progression of Q over the neuronogenetic interval
The Q fraction for the PVE, determined by the series of
experiments, follows a monotonic ascent through the interval E12-E16
(Fig. 7). The values for the SPP (Table 4, columns 7 and
8) are indistinguishable from those obtained previously by a totally
different method [and discussed in an earlier report (Takahashi et
al., 1995b)] and will not be considered further here, where the focus
is on values for the PVE.
Fig. 7.
The progression of Q during the neuronogenetic
interval of the dorsomedial cerebral PVE. A,
Experimentally determined values for Q for E12-E16 are positioned by
solid circles. Open circles at 0 on E11
and at 1.0 on E17 mark the approximate time of initiation and
termination of the neuronogenetic interval as estimated from
autoradiographic cell birth date experiments (Caviness, 1982).
B, The curvilinear ascending progression of Q is plotted
with respect to both E11 and E17 and the elapsed integer cell cycles
that comprise the neuronogenetic interval. Two fits are shown in
B, both incorporating the experimentally determined
values of Q plotted for E12-E16 in A (i.e., the
solid circles in A). For the solid
line plot, a least-squares curvilinear fit was made to the
experimentally determined data plus the initial 0 and terminal 1.0 values of Q for E11 and E17, respectively. For the dashed line
plot, a least-squares curvilinear fit was made to the
experimentally determined data without considering the initial 0.0 and
terminal 1.0 values of Q. Note that the two fits are essentially
identical, indicating that the estimates of Q = 0 and Q = 1.0 at E11 and E17, respectively, must be quite close to the actual
values.
[View Larger Version of this Image (14K GIF file)]
The onset of the neuronogenetic interval is by definition the moment
when Q first becomes nonzero and P becomes <1.0. Correspondingly, the
termination of the neuronogenetic interval is by definition the moment
when Q reaches 1.0 and P becomes zero (Fig. 1). In our previous
analyses, concerned principally with the progression in the length of
the cell cycle and its phases across the neuronogenetic interval, we
specified the time of initiation and termination of neuronogenesis only
approximately as occurring at 9:00 A.M. on E11 and at 9:00 A.M. on E17,
respectively (Caviness, 1982; Takahashi et al., 1995a). Here we are
able to estimate the moment of initiation and termination somewhat more
accurately through recourse to the progression of Q and P. For this
more accurate estimate, we construct a best fit curve to the values of
Q obtained experimentally on E12-E16. We extrapolate to an initial
value for Q of zero, i.e., the x-intercept of the curve,
which is found to correspond to late on E10, a starting point
consistent with observations of the time of origin of neurons destined
for layer I and the subplate (Wood et al., 1992). At the other end of
the curve we extrapolate to a terminal value for Q of 1.0, which occurs
early on E17. This revised estimate of the time of initiation and
termination of the neuronogenetic interval, like our earlier
approximation, provides for a neuronogenetic interval of approximately
11 integer cell cycles (precisely, 10.8 cycles). For convenience, we
refer to each cell cycle using an abbreviation,
CCn, in which the subscript n
designates the integer cell cycle number (Fig. 1).
At least to the resolution of our methods, the progression of Q (and
the complementary descent of P) seems not to pause at the 0.5 or
steady-state point. Rather Q continues to increase as a function of
time (i.e., Embryonic Days, Fig. 7A) or of
integer cell cycle number (Fig. 7B) over the entire course
of the neuronogenetic interval. During the middle 2 d of the
neuronogenetic interval (i.e., E13 and E14), from CC5
through CC8, Q ascends and P descends rapidly, reaching the
steady-state level of 0.5, which is the critical turning point in the
overall process of waxing and then waning of the proliferative capacity
of the PVE, as will be discussed in more detail below. This critical
turning point is reached after ~60% of the neuronogenetic interval,
or 70% of the integer cell cycles (i.e., in the course of
CC8), has been completed (Fig. 7B).
The critical turning point of the progression of Q above 0.5 and P
below 0.5 marks the beginning of the involution of the PVE. The reason
for this is simply because if p < 0.5, then fewer
cells reenter S phase than have left it, with the necessary
consequence that the PVE becomes smaller with each cell cycle. The
smaller the value of P (and the larger the value of Q), the more rapid
the involution. At the latest developmental age measured, E16, Q is
~0.8 and P is ~0.2. The consequence of this is that in the course
of a cell cycle the PVE would be reduced in size by 40-60% (2 × P = 2 × 0.2 = 0.4; see legend to Fig. 8
for explanation) of its size at the beginning of the cycle. By
extrapolation we have determined that during the 24 hr subsequent to
E16 (i.e., just over one cell cycle), Q continues to rise toward 1.0, and P continues to fall toward zero. Appropriately, the height of the
VZ declines precipitously through E16 and early E17 (Fig. 3).
Fig. 8.
Growth of cortical strata and PVE occurring in the
course of the first three integer cell cycles. Growth of the cortical
strata reflects the fate and contributions of the Q fraction
(broken arrows), whereas the expansion and growth of the
PVE reflects the fate of the P fraction (thick arrows).
For this illustration, a ``unit'' population of PVE at the beginning
of the first cell cycle (CC1, founder
population) is shown as a cube with a volume of 1. The
events occurring during each cell cycle are enclosed in
brackets. At the conclusion of
CC1, the postmitotic population is partitioned
according to its Q and P fates. Cells with Q fate exit the VZ and
migrate to the cortex (dashed arrows). Cells of P fate
remain in the PVE (thick arrow), now corresponding to a
volume of P1, and will form the proliferative
population for CC2. During
CC2, the premitotic population (size now = P1) will double in size (=
P1*2, shown as two separate
blocks). Again, a proportion of cells equal to Q2
for CC2 exit the VZ so that the exiting
population will be (P1*2)*Q2,
i.e., the volume of the PVE at the beginning of CC2 × Q
for CC2. As the population exits, the size of the
population that will progress to CC3 will be
(P1*2)*P2, where P2
is P for CC2. The cumulative output from CC1
and CC2 will be the sum of the output of the two cycles,
that is, Q1 + (P1*2)*Q2. The same process repeats
itself during the third cell cycle (CC3): the
size of the population that will progress to CC4
will be
[{(P1*2)*P2}*2]*P3
and the cumulative output will be Q1 + (P1*2)*Q2 + [{(P1*2)*P2}*2]*Q3.
Note that this is a highly schematic representation that describes the
behavior of a unit of PVE in which proliferative activity is perfectly
synchronized.
[View Larger Version of this Image (30K GIF file)]
DISCUSSION
Neocortical neuronogenetic model
Elementary parameters
Four parameters govern the growth and output of a founder
proliferative population. These are (1) the growth fraction, i.e., the
proportion of PVE cells that is proliferating [determined previously
to be essentially 1.0 (Takahashi et al., 1995a)]; (2) the number of
integer cell cycles comprising the neuronogenetic interval
[approximately 11 for the PVE) (Takahashi et al., 1995a)]; and (3) Q
and (4) P at each integer cell cycle. Cell death, if substantial in the
PVE, would obviously also affect both growth and output. We will return
to this consideration in a subsequent section.
Growth of the PVE
Growth of the PVE can be calculated for an arbitrarily sized
founder ``unit'' (Fig. 8). The unit can be either the
average single cell or, because cell density in the PVE is
constant (Takahashi et al., 1993, 1995a), a unit volume of the PVE
present at the beginning of G1 of CC1. Before the outset of
neuronogenesis (Q = 0 and P = 1), the PVE would double in
cell number and volume with each cell cycle.
Once Q becomes nonzero, the PVE will grow by a factor equal to twice
the P for each integer cell cycle (see legend to Fig. 8 for details).
Cycle-to-cycle growth is multiplicative, so that the size of the PVE
(PVEN) derived from a unit founder population
over the course of N cell cycles is:
|
(1)
|
where Pn is the P fraction of cell cycle
n. ( is a mathematical symbol that means take the product
of the elements in a series.) The founder unit of the PVE will increase
until Pn becomes 0.5, that is, over the first
eight cell cycles. It reaches its maximum size after an increase of
>55 times its initial size (Fig. 9).
Growth must be accommodated principally by tangential expansion of the
epithelium, because our data show that the radial expansion of the
epithelium is limited to a 2.7-fold increase (30 µm on E11 to 80 µm
on early E15) (Fig. 3). Radial rather than tangential contraction will
be the consequence of the rapid reduction in the number of
proliferative cells after P declines below 0.5.
Fig. 9.
Expansion and involution of a founder PVE
population and cell output over the course of the neuronogenetic
interval. The volume of the PVE (Volume of PVE), the
cell output from a single cell cycle (PVE Output), and
the cumulative cell output (Cumulative Output) are
calculated from Equations 1 and 2 in the Discussion. The values are
plotted with respect to both the elapsed cell cycles,
CC1-CC11, and embryonic days on the
abscissa. At the beginning of the neuronogenetic interval,
where 0 cell cycles have elapsed (i.e., the
beginning of CC1) at 9:00 A.M. on E11, the PVE
volume is set at the arbitrary unit value of 1.0, and cell output at
this point is by definition 0. The vertical dashed line
divides the neuronogenetic interval with respect to where Q and P reach
the critical turning point of 0.5. To the left of the
vertical dashed line, Q < 0.5 and the PVE is
expanding; to the right of the vertical dashed
line, Q > 0.5 and the PVE is involuting. The PVE size
reaches its maximum value at this point, and cell output/cycle is
maximum beyond this point. The P fraction cells of
CC11 will divide to produce two daughter cells,
all of which (Q = 1.0) will exit the cell cycle as the terminal
output (TO on the abscissa). The contribution of Q from
the first half of the 11 cell cycles (CC1-6) is
only ~6%, whereas that of the last two cycles
(CC10-11) and the terminal output is ~50% of
the total neuronal population of the cortex at the end of the
neuronogenetic interval. Our previous estimate of the cumulative output
throughout the full neuronogenetic interval (Caviness et al., 1995) was
approximately twice that represented here. This is because the unit
founder population was considered to be the population of the cell
cycle preceding CC1 for the previous estimate
but was considered to be the population at the beginning of G1 of
CC1 in this plot.
[View Larger Version of this Image (24K GIF file)]
Neuronal output
The cumulative output of a one-unit size founder population
through N cell cycles (OUTN) is the
sum of the output from CC1 (= Q1) and those
from each of CC2-CCn or:
|
(2)
|
where Qn is the Q fraction of
CCn and PVEn  1 is
the size of the PVE at the beginning of the preceding cell cycle (=
CCn 1; see legend to Fig. 8 for
explanation). As the final cell cycle is completed (i.e., at the end of
CC11), all of the P fraction cells from CC11
will divide into two daughter cells giving rise to 2 × PVE11 cells. These will exit the VZ as the terminal output
(Fig. 1). Thus, the average founder cell will give rise to
OUT11 + 2 × PVE11 or approximately 140 cells over the full neuronogenetic interval (Fig. 9). Taken together,
Equations 1 and 2 describe the neuronogenetic model and an entire
dynamic process, including growth and involution of the PVE and the
fractional contribution of each of the 11 cell cycles to the
postmigratory neuronal population of the cortex (presented graphically
in Fig. 10).
Fig. 10.
Graphic representation of the entire set of
dynamic events of the PVE. This schema shows the growth
and involution of the PVE and the output of the PVE at each of the 11 cell cycles comprising the neuronogenetic interval. The fractional
contribution of the PVE output to the postmigratory neuronal population
of the cortical plate is also shown. The PVE continues to enlarge as
long as p > 0.5, that is, through
CC8. Thereafter, in the course of
CC9-11, the PVE becomes progressively smaller
and eventually is replaced by the ependyma, which will line the
ventricle in the adult animal. The contribution of Q to the
Cortical Strata is minimal initially but increases with
successive integer cycles and is maximum with
CC10. The relative contribution of the final
cycle, CC11, and the terminal output
(TO) to the neuronal population of the cortex lessens
with exhaustion of the PVE. Note that the schema ignores the
consequences of cell death on the final proportions of neurons to arise
from the successive integer cycles.
[View Larger Version of this Image (51K GIF file)]
Cell death
This simple neuronogenetic model does not provide for cell death
in the proliferative population. Estimates based on pyknotic or
necrotic cells by light and electron microscopy (Stensaas and Stensaas,
1968; Hinds and Ruffett, 1971; Nowakowski and Rakic, 1981; Gressens et
al., 1991; Takahashi et al., 1992; Reznikov and van der Kooy, 1995)
have varied from 0% to a few percent. A recent estimate, on the basis
of staining with ISEL+, places cell death in the VZ at 50-70%
(Blaschke et al., 1996). This high rate of cell death would preclude
growth of the PVE and also an acceleration in the output of neurons
from the PVE over the course of the neuronogenetic interval. That both
phenomena occur is incontrovertible (Rakic, 1974; Luskin and Shatz,
1985; Bayer and Altman, 1991). Because 100% of PVE cells are
proliferating (Waechter and Jaensch, 1972; Takahashi et al., 1993,
1995a), the suggested clearance time of dead cells of 24-48 hr implies
that dying cells synthesize DNA, execute multiple cell cycles, and also
undergo interkinetic nuclear migration. Thus the meaning of the
ISEL+-labeled cells is unclear, and the actual rate of cell death
within the PVE must be viewed, for the present, as unknown but probably
small. Whatever the true rate, if the clearance time of dying cells is
short compared with Tc and involves only the Q
fraction, cell death would reduce output but not growth of the PVE. If
it involves the P fraction, the estimate of the rate of growth of the
PVE (Eq. 1) would require a corresponding reduction in the factor P.
Proliferative fates: symmetric and asymmetric cell divisions
With respect to proliferative fate, a cell division may be
``symmetric,'' where both daughter cells are either Q or P, or it may
be ``asymmetric,'' with one daughter cell Q and one P (Rakic, 1988).
In the neuronogenetic model, at any given time during the
neuronogenetic interval the relative proportions of the three types of
cell division would be given by the binomial theorem and determined by
the Q and P (Fig. 11). Observations consistent with the
predictions of our model have been made by Chenn and McConnell (1995),
who suggested that when the plane of separation of daughter cells is
parallel to the ventricular surface (horizontal division), the daughter
cells will have opposite (P+Q) proliferative fates, and when the plane
of separation of daughter cells is orthogonal to the ventricular
surface (vertical division), the daughter cells will have the same (P+P
or Q+Q) proliferative fates. Early in the neuronogenetic interval of
the ferret (Chenn and McConnell, 1995), the proportion of vertical
divisions is ~80% and that of horizontal divisions is ~20%;
later, the proportions are changed, in a direction consistent with the
neuronogenetic model, to ~50% and 30%, respectively.
Fig. 11.
P and Q in relation to proliferative fate. The
upper bar of the double abscissa marks the elapsed
integer cell cycles CC1-11 of the dorsomedial murine
cerebral PVE; the lower bar of the abscissa marks the
elapse of time in Embryonic Days. The ordinate provides
a calculation, on the basis of the data shown in Figure 7 and the
binomial theorem, for the proportion of total mitotic divisions at each
integer cycle that will give rise only to P cells (P+P symmetric
proliferative fate), only to Q cells (Q+Q symmetric
proliferative fate), or to P + Q cells (P+Q asymmetric
proliferative fate). For example, if Q = 0.3 and P = 0.7, there will be Q2 = (0.3)2 = 0.09 and
P2 = (0.7)2 = 0.49 symmetric divisions and
2 × P × Q = 2 × 0.3 × 0.7 = 0.42 asymmetric divisions. All three types of mitoses could exist at all
times, but the sum of their proportions will be equal to 1.0. Early in
the neuronogenetic period, the P+P symmetric cell divisions should
predominate. Late in the neuronogenetic interval, the Q+Q symmetric
cell divisions should predominate. The proportion of asymmetric cell
divisions should reach its maximum when P = Q = 0.5, i.e., at
approximately CC8, at which time the proportion of Q+Q- and
P+P-type symmetric cell divisions should be equal.
[View Larger Version of this Image (50K GIF file)]
Lineage continuity
Neocortical histogenesis requires lineage continuity from founder
population throughout the neuronogenetic interval. Paradoxically, the
majority of lineages traced by viral insertion of the Xgal
reporter gene becomes extinct after a single mitosis or within two to
four cycles of viral genome insertion. Clone size is small, and only
rarely are marked cells among the last formed in upper layers III and
II.
The neuronogenetic model provides insight into these lineage
experiments. The cumulative probability of extinction of a lineage
originating from a single founder cell, i.e., the probability that at
any time all of its descendants would leave the PVE, in
CC1 is only ~4% over the first 11 cell cycles
(CC1-11) of the neuronogenetic interval (Fig.
12A; for calculations and details,
see the legend to Fig. 12A). The probability of
extinction of a polyclonal set of founder cells decreases exponentially
as the number of cells included in the founder polyclone is increased
(Fig. 12A). For example, the probability of
extinction before CC11 of a two-cell founder polyclone is
0.16%, but of a seven-cell founder polyclone it is 1010.
This low probability of extinction virtually guarantees that one small
area of the PVE will contribute to the entire thickness of the
overlying cortex.
Fig. 12.
Lineage continuity. A, The
Probability of Extinction of a hypothetical
monoclonal lineage derived from a single PVE founder cell (open
circles) is plotted through CC11 of the
neuronogenetic interval. The founder cell is presumed to be at the
beginning of G1 at the beginning of CC1. The probability
that such a lineage will become extinct by CC11 is 0.04 (arrow with dashed line), which means
that it has a 96% chance of continuing to exist over the entire
neuronogenetic interval and thus to contribute to each of cortical
layers VI through II. The cumulative probabilities of extinction of
hypothetical polyclonal lineages of two, three, or seven cells barely
rise above 0 by CC11. Thus, such polyclonal lineages would
have virtually a 100% chance of sustaining histogenesis of cortical
layers VI-II. B, The cumulative probabilities of
extinction of hypothetical monoclonal lineages arising from single
founder cells present at the beginning of G1 at the beginning of each
of the integer cell cycles of the neuronogenetic interval. The
probability of lineage extinction mounts rapidly with initiation at
each successive integer cycle. The lowest probability of extinction is
associated with a monoclonal lineage initiated at
CC1 (open circle plot in
A), but a lineage initiated at
CC4 will have a cumulative probability of
extinction of ~0.57 through CC11
(arrowhead). These extinction probabilities become quite
high even before the final three cell cycles of the
neuronogenetic interval, after which a substantial proportion of the
neurons of the cortex are still to be produced (Figs. 9, 10). The
darker lines represent lineages of the sort initiated in
retroviral studies (for details, see the text).
[View Larger Version of this Image (24K GIF file)]
Where the lineage is considered to be initiated later than at the
onset of CC1, the apparent probability of extinction is
much greater. For lineages initiated at CC2 with a single
founder cell, the extinction probability by CC11 is ~15%
and 57% for initiation at CC4. A family of curves
reflecting a dramatically increasing probability of extinction
associated with ``delay'' in lineage initiation from the actual start
of neuronogenesis is shown in Figure 12B. By way of
illustration, consider the experiments of Walsh and Cepko (1988, 1993)
in rat, which were initiated with retroviral injections at E17 and E14
corresponding approximately to E15 and E12 in mouse, respectively.
Allowing a couple of cell cycles after injection before the insertion
of the Xgal gene into a single founder cell (Cepko, 1988),
we estimate that Xgal-marked lineage founder cells would
appear, at the earliest, at CC9 and CC5,
respectively. The mounting probability of extinction with successive
cell cycles for such lineages is indicated by the darker lines in
Figure 12B.
Similar considerations also clarify the prominence of ``one-cell
clones'' and the generally small sizes of the ``clones'' observed
with retroviral experiments (Luskin et al., 1988; Price and Thurlow,
1988; Walsh and Cepko, 1988; Austin and Cepko, 1990; Walsh and Cepko,
1990; Parnavelas et al., 1991; Walsh and Cepko, 1992, 1993; Mione et
al., 1994). Because only one daughter cell carries the reporter gene at
the first cell division after gene insertion, the probability that this
cell will leave the cycle with apparent lineage extinction is Q. For
example, Q is ~0.42 at CC7; this means that ~42% of
the clones marked by a reporter gene at this cell cycle would have only
one cell. Even if the daughter cell carrying the reporter gene at
CC7 is P, the rapid increase in Q after CC7
dictates that the average lineage will rapidly become extinct (Fig.
12B). Thus, the average multicellular clone size will
be small. Large clones reflecting lineage continuity over more than two
to three integer cell cycles have been achieved only when the
experiments have been initiated early enough to allow insertion at an
earlier integer cell cycle (Austin and Cepko, 1990; Mione et al., 1994;
Reid et al., 1995). Thus, the important conclusion is that the low
values of Q and high values of P over the first several cell cycles of
the neuronogenetic interval and the resultant expansion of the PVE and
the founder-cell population are critical to the production of a ``full
thickness'' neocortex.
The proliferative model and neocortical histogenesis: a
look ahead
The fundamental parameters of cell proliferation measured by
these investigations have lead to a quantitative neuronogenetic model
characterizing patterns of growth of the PVE and neuronal production.
Elsewhere (Caviness et al., 1995) the neuronogenetic model has been
used to ``explain'' the expansion of neocortex in primates. The
parameters P and Q provide clarifying links to mitotic spindle
behavior, the continuity of proliferative lineages, and the relatively
small size of retrovirally labeled clones. Thus, the neuronogenetic
model provides a method for generating experimentally verifiable
quantitative hypotheses about cortical development and is
applicable to the interpretation of data collected with other methods.
FOOTNOTES
Received April 4, 1996; revised June 5, 1996; accepted July 12, 1996.
This work was supported by National Institutes of Health Grants NS12005
and NS28061 and National Aeronautics and Space Administration Grant
NAG2-950. T.T. was supported by a Fellowship of The Medical Foundation,
Inc., Charles A. King Trust, Boston, MA. Valuable discussions with
Pradeep Bhide and Sahoko Miyama are gratefully acknowledged.
Correspondence should be addressed to Dr. Takao Takahashi, Department
of Neurology, Massachusetts General Hospital, 25 Fruit Street, Boston,
MA 02114.
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