Size distribution of retrovirally marked lineages matches prediction from population measurements of cell cycle behavior

Authors

  • Li Cai,

    1. Department of Neuroscience and Cell Biology, UMDNJ-Robert Wood Johnson Medical School, Piscataway, New Jersey
    2. Physiology and Neurobiology Graduate Program, Rutgers University, and UMDNJ-Robert Wood Johnson Medical School, Piscataway, New Jersey
    Current affiliation:
    1. Dana-Farber Cancer Institute, Harvard Medical School, Boston, MA 02115.
    Search for more papers by this author
  • Nancy L. Hayes,

    1. Department of Neuroscience and Cell Biology, UMDNJ-Robert Wood Johnson Medical School, Piscataway, New Jersey
    Search for more papers by this author
  • Takao Takahashi,

    1. Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts
    2. Department of Pediatrics, Keio University School of Medicine, Tokyo, Japan
    Search for more papers by this author
  • Verne S. Caviness Jr.,

    1. Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts
    Search for more papers by this author
  • Richard S. Nowakowski

    Corresponding author
    1. Department of Neuroscience and Cell Biology, UMDNJ-Robert Wood Johnson Medical School, Piscataway, New Jersey
    2. Physiology and Neurobiology Graduate Program, Rutgers University, and UMDNJ-Robert Wood Johnson Medical School, Piscataway, New Jersey
    • Department of Neuroscience and Cell Biology, UMDNJ-Robert Wood Johnson Medical School, 675 Hoes Lane, Piscataway, NJ 08854
    Search for more papers by this author

Abstract

Mechanisms that regulate neuron production in the developing mouse neocortex were examined by using a retroviral lineage marking method to determine the sizes of the lineages remaining in the proliferating population of the ventricular zone during the period of neuron production. The distribution of clade sizes obtained experimentally in four different injection–survival paradigms (E11–E13, E11–E14, E11–E15, and E12–E15) from a total of over 500 labeled lineages was compared with that obtained from three models in which the average behavior of the proliferating population [i.e., the proportion of cells remaining in the proliferative population (P) vs. that exiting the proliferative population (Q)] was quantitatively related to lineage size distribution. In model 1, different proportions of asymmetric, symmetric terminal, and symmetric nonterminal cell divisions coexisted during the entire developmental period. In model 2, the developmental period was divided into two epochs: During the first, asymmetric and symmetric nonterminal cell divisions occurred, but, during the second, asymmetric and symmetric terminal cell divisions occurred. In model 3, the shifts in P and Q are accounted for by changes in the proportions of the two types of symmetric cell divisions without the inclusion of any asymmetric cell divisions. The results obtained from the retroviral experiments were well accounted for by model 1 but not by model 2 or 3. These findings demonstrate that: 1) asymmetric and both types of symmetric cell divisions coexist during the entire period of neuronogenesis in the mouse, 2) neuron production is regulated in the proliferative population by the independent decisions of the two daughter cells to reenter S phase, and 3) neurons are produced by both asymmetric and symmetric terminal cell divisions. In addition, the findings mean that cell death and/or tangential movements of cells in the proliferative population occur at only a low rate and that there are no proliferating lineages “reserved” to make particular laminae or cell types. © 2002 Wiley-Liss, Inc.

The number of neurons in the brain of the adult members of a single species is remarkably invariant from individual to individual (Blinkov and Glezer, 1968), including a relatively constant number of neurons in columns of neocortex sampled from different regions (Rockel et al., 1980). In theory, the ultimate determination of neuron number must be controlled primarily at the level of cell proliferation and secondarily at the level of cell death; however, the relative contributions of these two opposing processes remain unclear and controversial (Rakic, 1995a,b). In the neocortex, the production of neurons occurs in the ventricular zone (VZ), which contains a pseudostratified ventricular epithelium (PVE), i.e., a population of proliferating cells that is approximately coextensive with the cytoarchitectonically defined VZ (Boulder Committee, 1970; Takahashi et al., 1996b; Miyama et al., 1997), during a limited period of development, the neuronogenetic interval (NI), which in the mouse occurs between embryonic day 11 (E11) and E16, E0 being the day of conception (Nowakowski et al., 2002). Measurements of the cell cycle using cumulative labeling with bromodeoxyuridine (Nowakowski et al., 1989) show that, at the time of the production of the first neurons in the mouse neocortex, the total length of the cell cycle (Tc) is about 8 hr, with an S phase of about 3 hr, G2 + M of about 2 hr, and G1 of about 3 hr (Takahashi et al., 1995). As development proceeds, the cell cycle lengthens until, at the end of the period of neuron production, Tc reaches ∼18 hr; S and G2 + M remain approximately constant at 3–4 hr and 2 hr, respectively, so virtually all of the change in Tc is due to an increase in the length of G1 (TG1; Takahashi et al., 1995). As a result of the lengthening of the cell cycle, there are different numbers of cell cycles on each of the 6 days of production of neurons for the neocortex. On the first day of the NI (E11), the cell cycle starts at 8 hr and lengthens to over 10 hr; thus, there is time for approximately 2.5 cell cycles. On the sixth and last day of the NI (E16) the cell cycle is over 18 hr, and, thus, there is sufficient time to complete only just over one cell cycle. By integration under the linear fit to the Tc (see Fig. 5), we have determined that there is sufficient time for 11 cell cycles during the entire 6 day NI (Takahashi et al., 1995).

Figure 5.

A: Diagram depicting the calculation of the size distribution of the PVE clades. For a retrovirally labeled founder cell at the beginning of G1 of cell cycle 1 (CC1), there are two possible fates, i.e, either to reenter the cell cycle and continue as a P cell (solid lines) or to exit the cell cycle and become a postproliferative, Q cell (dashed lines). Based on the average behavior of the population for the entire cortex, the AP-labeled founder cell will reenter S phase with probability P1, and, one cell cycle later, it will produce two daughter cells, which are at the beginning of G1 of CC2. For these two cells, there are also two possible fates as they proceed through G1, so there are three possible outcomes; i.e., both cells will continue to proliferate (with probability P12); one cell will continue to proliferate, and one will become postproliferative (with probability 2P1Q1); or both cells will become postproliferative and exit the cell cycle (with probability Q12). As a result, upon entry into S phase of the CC2, there will be P12 clades with two PVE cells and 2P1Q1 clades with one PVE cell. At each cell cycle, the process is repeated for each possible clade size by applying the binomial expansion iteratively, i.e., an expansion of (Pn + Qn)n, as shown in the bar graphs at right. The derivation of the P1, P2, P3, etc., used to calculate the solid lines in Figure 3 is described in B. Note that postproliferative cells leave the VZ within a few hours (Takahashi et al., 1996a) and, hence, for the most part, will not be detected in the VZ in this experiment. To illustrate, consider the relationship of the probable behavior of a single AP-labeled founder cell at the beginning of G1 to the size distribution of PVE clades. Such a founder cell will enter S phase and continue to proliferate with a probability P1 (subscript refers to integer CC1) to produce two daughter cells; each daughter cell will reenter S phase and continue to proliferate with a probability P2, etc., through Pn for the nth cell cycle. Thus, as the founder cell enters S phase during its first pass through the cell cycle, there will be only one possible size of the PVE clade, i.e., one cell (graph, top right column). As the two daughter cells enter S phase during the second cell cycle, there will be two possible sizes for the PVE clade (i.e., one or two cells) with a probability of occurrence of P1 · 2P2Q2, and P1 · P22, respectively (middle graph, right column). At the entry into S phase of the CC3, there will be one to four cells and, hence, one to four possible sizes of PVE clades with a respective probability of occurrence calculable from the clade size present at the previous cell cycle (CC2) using the binomial distribution (bottom histogram of right column). Iterative application of the binomial distribution produces the size distribution for each subsequent cell cycle. B: Because P is the only parameter necessary to calculate the probability of occurrence of any given size of PVE clade, changes in P with each passing cell cycle determine the PVE clade size distribution. P estimates from medial (Takahashi et al., 1996b) and lateral (Miyama et al., 1997) cortex were used. The changes in P used for the calculation of the distributions for model 1 (solid lines in Fig. 3) and model 2 (dashed lines in Fig. 3) are from measurements of the average behavior of P and Q in both the dorsomedial neocortex (dotted line in B; Takahashi et al., 1996b) and ventrolateral neocortex (dashed line in B; Miyama et al., 1997). The graph in B is shown with three separate abscissae; the uppermost is the conventional unit of time, i.e., embryonic days elapsed since conception. The lower two, labeled DM and VL, show the elapsed cell cycles during the E11–E15 develeopmental period for dorsomedial and ventrolateral neocortex, respectively (Takahashi et al., 1995; Miyama et al., 1997). Because the lineages are evenly distributed in the cortex (Fig. 2), the mean of the P values from both the DM and the VL (solid lines) were used. The mean numbers of cell cycles elapsed during the E11–E13, E11–E14, and E11–E15 experiments are approximately 4.5, 6.2, and 7.6 cell cycles, respectively. In considering an average delay of 1.5 cell cycles between the retroviral injection and the production of a single retrovirally labeled “founder cell” at the beginning of G1 (Cai et al., 1997b), approximately 3.0, 4.7, and 6.1 cell cycles, respectively, are available for lineage evolution.

Figure 3.

Frequency histogram of the PVE clades for the E11–E13 group (A), E11–E14 group (B), E11–E15 group (C), and E12–E14 group (D). The mean size of the PVE clades decreases with a longer survival time and with more cell cycles (3.0 cell cycles for E11–E13, 4.7 cell cycles for E11–E14, 6.1 cell cycles for E11–E15 and 2.8 cell cycle for E12–E14). There is also a shift toward smaller clade sizes. Each pie charts show the proportion of AP-labeled cells that reside in each clade size. The two curves in each histogram are the predicted size distributions calculated from independent data using model 1 (solid line) and model 2 (dashed line). A χ2 goodness of fit test shows that the distributions obtained from model 1 do not differ from the experimental data, whereas those obtained from model 2 are highly significantly different (P < 10–8). A separate calculation using a Pearson product moment correlation shows that the distribution obtained from model 1 accounts for 92.8–99.6% of the variation in clade size (Table I).

The output of neurons by the PVE is controlled, in principle, by a variety of factors, including the proportional representation of the three possible types of mitotic divisions: 1) symmetric nonterminal cell division (which produces two daughter cells that remain in the PVE and continue to proliferate), 2) symmetric terminal cell division (which produces two daughter cells that both migrate out of the PVE to become young neurons), and 3) asymmetric cell division (which produces one daughter cell that continues to proliferate and one that migrates out of the PVE). Changes in the proportions of these three types of mitotic divisions have been inferred from changes in the proportion of cells that enter vs. leave the cell cycle (Takahashi et al., 1996b; Miyama et al., 1997), from time-lapse cinematography (O'Rourke et al., 1992; Adams, 1996), from changes in the orientation of the mitotic apparatus (Smart, 1973; Chenn and McConnell, 1995; Adams, 1996), and from immunohistochemistry (Chenn and McConnell, 1995). It is not known, however, how such changes are effected within single lineages, nor how they may be distributed among lineages making various cortical cell types. For example, it has been suggested that there are specific populations “reserved” in the PVE to produce either specific cell types or cells that occupy specific laminae (Dehay et al., 1993; Kennedy and Dehay, 1993; Luskin et al., 1993). Because all of the cells in a given neighborhood of the PVE are proliferating (Takahashi et al., 1995, 1996b) with a similar cell cycle length (Cai et al., 1997a), in the absence of cell death such a “reserved population” would have a specific pattern of repeated symmetric nonterminal mitoses and would expand for several cell cycles to produce relatively large lineages of a specific and characteristic size (8, 16, 32, etc.) containing only proliferating cells. Similarly, lineages following other specific patterns of proliferation, e.g., repeated asymmetric divisions, would produce lineages of other specific characteristic sizes, e.g., a preponderance of even-sized or odd-sized lineages, etc. The alternative to such repeated patterns of mitosis type is the absence of pattern in the sequence of cell divisions within a lineage, in which case no specific and characteristic lineage size distribution would be produced. In general, the size distribution of lineages obtained during defined periods of development will reflect the dynamic changes in the proportions of these three types of cell divisions and will, thus, reveal any extant repeated patterns of mitosis. Note that the presence of cell death to any significant extent (cf. Blaschke et al., 1996; Thomaidou et al., 1997) would modify the specific and characteristic lineage sizes obtained but would do so in a predictable way.

To estimate the frequency of occurrence of each of these distinct behaviors, we have studied individual lineages consisting of proliferating cells in the PVE in the developing neocortex at known numbers of cell cycles after infection with a retrovirus. We have examined, in contrast to most previously published experiments using this method (Price et al., 1987; Luskin et al., 1988, 1993; Walsh and Cepko, 1988, 1992; Williams et al., 1991; Mione et al., 1994, 1997; Lavdas et al., 1996), the resulting labeled lineages after short survivals, i.e., during the period when cell proliferation continues to occur, and have focused on the size of the proliferating population, i.e, the cells that remain in the PVE, rather than on the cells that migrate to the cortical plate. We have analyzed the results quantitatively in order to evaluate proportional contributions of cell production vs. other influences (Fig. 1). There are three influences (Fig. 1) that could act at each cell cycle to reduce the number of cells per lineage from the maximum that would be produced in a pure population of symmetric nonterminally dividing cells. First, some cells of the lineage could leave the cell cycle to migrate and become young neurons (Q cells; Q in Fig. 1). The proportion of cells that elects the Q fate increases monotonically during each of the 11 cell cycles of the 6-day-long NI (Takahashi et al., 1996b; Miyama et al., 1997); thus, at each cell cycle, a progressively increasing proportion of cells leaves the PVE. Second, some PVE cells could die (D in Fig. 1). Cell death could, in theory, occur at any time during development and has been well studied in the maturing neocortex during the postnatal period (Leuba et al., 1977; Finlay and Slattery, 1983; Heumann and Leuba, 1983; Crandall and Caviness, 1984; Finlay and Pallas, 1989; Verney et al., 2000). However, estimates of the magnitude of cell death occurring within the proliferative population and during the early period of cortical development vary greatly from <1.0% at any given time (Thomaidou et al., 1997) to over 70% of the progenitor cells (Blaschke et al., 1996). Thus, it remains unclear what role cell death in the proliferative population plays in the regulation of neuron number (Gilmore et al., 2000). Third, some PVE cells could move tangentially (T in Fig. 1), i.e., away from their sisters and cousins (Fishell et al., 1993; Tan and Breen, 1993; Walsh and Cepko, 1993). Such tangential movements would not affect the actual numbers of cells in the proliferative population but would affect the apparent number of cells identified in a lineage and would concomitantly increase the putative number of lineages identified. Previously, we have shown that retrovirally labeled PVE lineages reside in clusters (or clades) of varying size (Cai et al., 1997b). In addition, we have shown that there is a relative homogeneity of cell cycle length among the cells of the VZ (Cai et al., 1997a) and that the cells derived from a single precursor also seem to have a similarly homogeneous cell cycle (Cai et al., 1997a). This means that the average length of the cell cycle (Takahashi et al., 1995) can be used to determine how many cell cycles have elapsed between two time points; this is essential for understanding how retrovirally labeled lineage might evolve. We have exploited this principle to develop three models of the proliferative behavior of the cells of the VZ and to predict the size distribution of retrovirally labeled lineages. We have compared the experimentally determined distribution of retrovirally labeled clade sizes to the size distributions predicted by calculation from the three different models. The three models differ only with respect to their composition of types of cell division; i.e., they each have different ratios of asymmetric, symmetric nonterminal, and symmetric terminal cell divisions; however, all three models are based on the same P/Q values measured using double S-phase-labeling methods (Takahashi et al., 1996b; Miyama et al., 1997). The goodness of the fit of the experimentally determined distribution with the distributions obtained from the three models 1) provides evidence for the role of changes in P/Q in regulation of lineage size, 2) allows for an estimate of the amount of cell death and tangential movements in the PVE, and 3) allows a determination of the existence (or nonexistence) of populations that undergo a series of cell divisions with a repeated pattern.

Figure 1.

Diagram depicting the influences that could affect lineage size in a single cell cycle. For a cluster of cells present at the beginning of G1 (in this example, eight cells are shown), some cells could continue to proliferate (P), leave the proliferative population (Q), die (or lose the marker) in either the proliferative (D; VZ cell in gray with dashed lines) or the postproliferative (D; CP cell in gray with dashed lines) compartment, or move tangentially within the proliferative population (T). M, marginal zone; CP, cortical plate; IZ, intermediate zone; VZ, ventricular zone; V, lateral ventricle.

MATERIALS AND METHODS

Retrovirus Vectors

DAP retrovirus vector, a replication-incompetent retrovirus encoding human placental alkaline phosphatase (AP), was used and prepared according to a procedure modified from Cepko and colleagues (Fields-Berry et al., 1992; Cepko et al., 1995) and described in detail elsewhere (Cai et al., 1997b).

Animals and Surgical Procedures

Timed-pregnant CD-1 mice were purchased from Charles River Laboratories (Wilmington, MA) and maintained on a 12–12 hr (7:00 AM–7:00 PM) light-dark schedule. Pregnancies were timed from the day of detection of a vaginal plug (E0). By this convention, birth normally occurs on E19. On E11, pregnant mice were anesthetized with Avertin (0.02 ml/g body weight, i.p.) prior to undergoing a laparotomy. Approximately 0.5 μl of a solution containing DAP retrovirus vector (∼107 CFU/ml), polybrene (0.05 mg/ml), and fast green dye (0.025%) was pressure injected through the uterine walls directly into the lateral ventricles of individual fetuses. When injections were completed, the abdominal incision was closed, and the dam was kept warm until awake and normally active.

Tissue Processing and Histochemistry

Two, three, or four days after the intraventricular injections, dams were deeply anesthetized with 4% chloral hydrate, and fetuses were removed by hysterotomy. Fetal heads were submerged in fixative overnight at 4°C, and then the brains were removed and transferred to 30% sucrose in phosphate-buffered saline (PBS) until they sank. Four fetal brains from to dams were used for each of the E11–E13, E11–E15, and E12–E14 groups and seven fetal brains from four dams for the E11–E14 group. Brains were sectioned on a cryostat at 30, 35, or 40 μm. Sections were mounted on slides and processed for AP activity (Fields-Berry et al., 1992). Labeled cells were detected by microscopic examination; cell morphology and position were recorded by photography and camera lucida drawings.

Lineage Analysis

A retrovirally marked lineage was defined as an isolated cluster of AP-labeled cells separated from any other labeled cells by at least 150 μm in the tangential plane (i.e., parallel to the pia). This distance was derived from the 95% confidence interval of a “random walk” computer simulation (Cai et al., 1997b) based on the movements of cells in the VZ (Fishell et al., 1993) for the longest survival time used in these experiments. In practice, most labeled cells of a lineage (i.e, well over 95%) were confined to an even smaller diameter (<50 μm).

Nomenclature

PVE cells were defined based on their position. Thus, AP-labeled cells occupying the VZ were classified as PVE cells and were analyzed for this study. Cells occupying the subventricular zone (SVZ), intermediate zone, marginal zone, subplate, or ventricular zone were not considered. The border of the VZ with the SVZ was determined on cytoarchitectonic grounds, the principle cue being the orientation of the nuclei. Each cluster of AP-labeled VZ cells is called a PVE clade to emphasize that the cells in the cluster are proliferative members of a single lineage, but the precise lineage relationships among the constituent cells of each cluster (i.e., sisters, first cousins, etc.) are not known (Cai et al., 1997b).

Age of Lineages in Each Experimental Group

In mouse, 100% of the VZ cells are proliferating (Takahashi et al., 1995); the range of the cell cycle lengths is small, i.e., about ±8% of the mean cell cycle time (Cai et al., 1997a); and lineage-related cells form clusters in the PVE (Cai et al., 1997b). Thus, AP-labeled VZ cells had proliferated continuously from the time of retroviral infection to the time of sacrifice, and the number of cell cycles elapsed for each PVE clade is a function of survival time. Previously, we estimated that the average age of a PVE clade is the total number of cell cycles elapsed during the experimental period minus an average delay of approximately 1.5 cell cycles corresponding to the interval required for insertion and expression of the transgene (Cai et al., 1997b). Thus, for the E11 experimental group, the cells in the PVE clades recovered on E13, E14, and E15 have passed through approximately 3.0, 4.7, and 6.1 cell cycles, respectively; for the E12–E14 group, the cells in the PVE clades have passed through approximately 2.8 cell cycles (see Fig. 3).

Reconstruction of the Fetal Brain

Reconstructions of the hemispheres of the fetal mouse brains were made from drawings of serial sections. The drawings were registered by using anatomical landmarks, and the AP-labeled PVE clades from both hemispheres were mapped onto a lateral view of the neocortex (Fig. 2a–c).

Figure 2.

PVE clade distribution across the surface of the neocortex of the fetal mouse brain (a–c) and examples of AP-labeled PVE clades (d–i) after injections of DAP retrovirus were on E11, with sacrifice on E13, E14, or E15. Reconstructions of the right hemisphere of one hemisphere from each of the three experimental groups: E11–E13 (a), E11–E14 (b), and E11–E15 (c) are shown as viewed from the lateral side (rostral is to the right, caudal is to the left, dorsal is upward, and ventral is downward). AP-labeled PVE clades (dots) from both hemispheres were projected onto the surface and are evenly distributed and widely spaced across the entire neocortex. d,g: Examples of AP-labeled PVE clades from the E11–E13 experimental group. The clade shown in d contains two PVE cells in the outer half of the ventricular zone (VZ); the two cells were located within a distance of about 20 μm. The clade shown in g contains only one PVE cell in the outer half of the VZ. e,h: Examples of AP-labeled PVE clades from the E11–E14 experimental group. The clade shown in e contains one PVE cell in the middle of the VZ; the clade shown in h contains eight PVE cells at the ventricular surface. f,i: Examples of AP-labeled PVE clades from the E11–E15 experimental group. The clade shown in f contains two PVE cells aligned radially at the ventricular surface. The clade shown in i contains three closely apposed PVE cells in the middle of the VZ. Scale bar = 300 μm in c (for a–c); 20 μm in i (for d–i).

Mathematical Modeling

Calculations for the mathematical models presented were performed using Excel (Microsoft) or Mathcad (Mathsoft).

RESULTS

The retroviral injections were made directly into the lateral ventricles of the developing mouse brain at E11 (Cai et al., 1997b), i.e., near the onset of neuronogenesis, when only PVE cells are present (Takahashi et al., 1995), or 1 day later, on E12. When the embryos were harvested at E13, E14, and E15, isolated or clustered AP-labeled cells were found to be relatively uniformly distributed throughout the tangential dimensions of the neocortical portion of the cerebral wall (Fig. 2a–c). The labeled cells included both proliferative cells still within the PVE and postproliferative cells within the intermediate zone or in the emerging cortical strata near the surface of the cerebrum. For this study, we analyzed only the AP-labeled cells that were in the PVE, as identified by their location in the VZ. The majority of AP-labeled cells was confined to clusters with a tangential extent of <50 μm (Fig. 2d–i). In addition, for cells in the VZ, the AP-labeled clusters were confined to a single level of the VZ (Cai et al., 1997b), and most cells were touching (Fig. 2d–i). Hence, decisions about lineage relationships of P cells could be made unambiguously (Cai et al., 1997b). In contrast, the nonproliferating cells belonging to a lineage, i.e., those that exit the cell cycle (the postproliferative cells, or Q fraction), may not be completely identifiable because of the complexities introduced by cell death, tangential migration, and possible loss of retroviral marker (Fig. 1) associated with the diaspora of postproliferative cells (Walsh and Cepko, 1992; Golden et al., 1995; O'Rourke et al., 1995; Reid et al., 1995; Blaschke et al., 1996; Thomaidou et al., 1997). However, these postproliferative cells leave the VZ within a few hours after their last mitosis (Takahashi et al., 1996a) and, therefore, were not included in this analysis.

Number and Size Distribution of Retrovirally Labeled Lineages

In total 505 AP-labeled lineages were identified, of which 351 lineages contained PVE cells and were further analyzed (Table I). For the retroviral infections at either E11 or E12, the AP-labeled PVE clades vary substantially in size (histograms in Fig. 3), and, for all survival periods, the size distribution is unimodal, with no apparent preference for either even or odd sizes. For a 2 day survival after retroviral injection at E11 (i.e., until E13), there is a high frequency (45.6%) of small (i.e., one or two cells) PVE clades, and, strikingly, with progressively longer survival times, there is a progressive shift toward smaller clades; i.e., between E13 and E15, one and two cell PVE clades increase to about 74.5% of the total. This shift is accompanied by a decrease in the mean size from 3.15 cells/clade at E13 to 2.02 cells/clade at E15 (Fig. 3, Table I). Very large PVE clades (i.e., containing more than seven cells) were rarely seen, accounting for ∼3.4% (12 of 351) of the PVE clades that had existed for three to seven cell cycles. Note that, although most of the clades contain only one or two cells, the proportion of cells in large PVE clades (i.e., containing five or more cells) decreases from 38% at E13 to 17% at E15 (pie charts in Fig. 3).

Table I. Experimental Results Compared With Model 1*
Experimental resultsModel 1
Experimental groupsAP-labeled lineagesCellsPVE cladesPVE cellsMean PVE clade sizePredicted Mean PVE clade sizeAdjusted R2 and P
  • *

    In the first six columns, the numbers of AP-labeled lineages, cells, PVE clades, and PVE cells are shown for each experimental group and used to calculate the mean size of the PVE clades. A Pearson product moment correlation test determined the proportion of variance (adjusted R2) in the experimental data (bars in Fig. 3) accounted for by the calculated data from model 1 (solid curves in Fig. 3) and the level of statistical significance of each fit (P).

E11–E1390359682143.153.060.928 (P < 10−8)
E11–E142599661734982.882.890.995 (P < 10−17)
E11–E155725347952.022.030.996 (P < 10−17)
E12–E1499242631342.132.130.970 (P < 10−6)
Totals5051,870351941

Development of the Three Models

On first impression, the observation that PVE clades become progressively smaller over time (Fig. 3) is counterintuitive; it would seem that, with lengthened survival time, i.e., as the cells pass through more cell cycles, PVE clades should become progressively larger. Why is this not the case? Also, do changes in PVE clade size reflect the decision to exit the cell cycle (Q in Fig. 1), or do the changes reflect the consequences of cell death (D in Fig. 1) and/or tangential movements within the PVE (T in Fig. 1)? To answer these questions and to distinguish among these possibilities, we developed three models (Fig. 4) of neuronogenesis based on the progressive change of P and Q with successive cell cycles using 3H-thymidine and bromodeoxyuridine double labeling (Takahashi et al., 1996b; Miyama et al., 1997), which, therefore, reflect the changes in the average behavior of the population. In contrast, retroviral methods reflect the behavior of individual members of the population integrated over the life span of the retrovirally labeled lineage. How is the average behavior of the population related to the behavior of its members? In principle, the average behavior of the population (as reflected in P and Q) should be sufficient to predict the range of behaviors of the retrovirally labeled lineage. Thus, to make a quantitative link between these experimental approaches, we developed three models that define three different ways of relating the specific values of P and Q to the frequency of symmetric terminal, symmetric nonterminal, and asymmetric cell division. Each of these three models has a different underlying assumption about the proportional mixture of the three modes of cell division at each pass through the cell cycle (Fig. 4). We then used these three models to make unbiased estimates of PVE clade size distributions for each of the four survival periods after retroviral transfection (Fig. 3).

Figure 4.

Diagrams of the proportions of the changes in the proportions of symmetric nonterminal (S/NT), symmetric terminal (S/T), and asymmetric (A) cell divisions as a function of changes in P (abscissa) during the neuronogenetic interval. At any given time, the sum of the proportions of the three types of cell divisions adds up to 1.0 (ordinate). The changes shown are the changes in the three types of cell divisions for the three different models developed for this study. For a detailed explanation of the assumptions of each model, see the text.

Model 1.

In model 1 it is assumed that all three types of cell divisions are present at each cell cycle during the entire developmental period (Fig. 4A). If the proliferative fate of the two daughter cells is determined independently during G1, then some daughter cells would elect a P fate and others a Q fate. If both daughter cells elect a P fate, then the cell division would be a symmetric nonterminal one; if both elect a Q fate then, the cell division would be a symmetric terminal one; if one daughter elects a P fate and the other a Q fate, then the cell division would be asymmetric. In other words, at each cell division, there would be a mixture of all three types of cell divisions, and the proportion of each is given by the expansion of the binomial (P + Q)2 or P2 + 2PQ + Q2. Thus, the proportional mixture of the three types of cell divisions changes systematically during the NI as P and Q change. In model 1, the peak in the proportion of asymmetric divisions reaching 50% at P = Q = 0.5 (Fig. 4A). By using the binomial expansion, one gets (0.5)2 + 2(0.5)(0.5) + (0.5)2 or 0.25 + 0.50 + 0.25. In other words, 25% of the mitoses should be symmetric nonterminal, 50% should be asymmetric, and 25% should be symmetric terminal. As an additional specific example, consider a time at which P = 0.7 and Q = 0.3; by using the binomial expansion, one gets (0.7)2 + 2(0.7)(0.3) + (0.3)2 or 0.49 + 0.42 + 0.09. Thus, 49% of the mitoses should be symmetric nonterminal, 42% should be asymmetric, and 9% should be symmetric terminal.

Model 2.

In model 2 it is assumed that the symmetric nonterminal and symmetric terminal types of cell divisions do not coexist. During early neocortical development, the mode of cell division is limited to symmetric nonterminal and asymmetric cell divisions, and the changes in P and Q are due to changes in the mixture of these two types of cell divisions. The proportion of each is derived from the value of Q, because Q cells would be made only by the asymmetric cell divisions; 2Q asymmetric divisions and 1 – 2Q symmetric nonterminal cell divisions would be needed. This would apply only when Q ≤ 0.5, at which time it predicts that 100% of the mitotic divisions would be asymmetric. Later in development, when Q > 0.5, symmetric nonterminal cell divisions would be replaced by symmetric terminal divisions, and the proportion of asymmetric cell divisions would fall below 100% (Fig. 4). [This is the model suggested implicitly by Chenn and colleagues (Chenn and McConnell, 1995; Chenn et al., 1998).] As a specific example, for P = 0.7 and Q = 0.3, there would be a mixture of 60% asymmetric cell divisions and 40% symmetric nonterminal.

Model 3.

In model 3, it is assumed that the PVE cells divide only symmetrically, selecting either a nonterminal or a terminal mode. Here the proportion of each is simply equal to P and Q, respectively, and the proportion of symmetric terminal increases as development progresses. As a specific example, for P = 0.7 and Q = 0.3, there would be 70% symmetric nonterminal and 30% symmetric terminal.

Calculation of the Size Distribution of the PVE Clades

The three models serve as a set of “null hypotheses” and also as constraints to allow a frequency histogram of PVE clade sizes to be calculated using the binomial distribution for each cell cycle of the life span of the PVE clade (Fig. 5). There were three key assumptions made for these calculations: 1) at each cell division, the P/Q decision made by each daughter cell is made according to the assumptions of one of the three models as described above; e.g., for model 1, the P/Q assignment for each daughter is made independently of its sister cell's P/Q decision, etc.; 2) at each pass through the cell cycle, the P/Q decisions are “remade”; i.e., there is no pattern of cell division within the lineages; and 3) neither cell death nor tangential movements occurs at a magnitude sufficient to effect local net differences in the size of the clades. Using these calculations, the three models can be distinguished by comparing the number of P cells remaining in the PVE after a known number of cell cycles. In Figure 3, we show the calculated size distributions of PVE clades that would be produced by model 1 (solid lines) and model 2 (dashed lines) during each of the survival periods using the values for P derived from previous experiments (Fig. 5). Model 3 is not shown because the calculations revealed that a population behaving as model 3 specifies would contain only even-sized clades, which is not similar to any of the experimentally obtained distributions. Visual inspection of the calculated distributions for all four injection survival time periods for both model 1 and model 2 (Fig. 3) shows that the intuitive expectation that PVE clade size should increase is incorrect, and a decreasing PVE clade size should be expected. A comparison of the goodness of fit for all four time periods and for both models shows that the distribution from the model 1 calculations does not differ from the experimental data (χ2, P > 0.4), whereas the model 2 calculations are significantly different from the data (χ2, P < 10–8). Thus, the predictions from model 1 account for the experimental data significantly better than do the predictions from model 2. In addition, the calculated mean sizes (Table I) of the PVE clades for all four survival periods are indistinguishable from the experimental data (bars in Fig. 3), and the overall distribution accounts for between 92.8% and 99.6% of the experimental variance (Table I). Finally, for model 1, simulating cell death in the PVE population by decreasing P produces an optimal fit (but not statistically better) to the experimental data if cell death is ∼0.8% per cell cycle; simulation of larger amounts of cell death in the PVE decreases the goodness of fit of the prediction. The addition of simulated cell death to the model 2 calculations further decreases the goodness of fit.

Quantitative Considerations Regarding Cell Death in the Proliferative Population

Cell death in the proliferative population will affect both clade size as measured in the experiments performed here and P/Q measurements using double S-phase markers. Thus, cell death in the proliferating population will affect the calculations for the three models presented. For this reason, we have performed the following quantitative explanation of how population measurements of Q and P (Takahashi et al., 1996b; Miyama et al., 1997) and clade size distributions would differ quantitatively were there significant amounts of cell death in the PVE. (For these purposes, cell death and loss of label are equivalent.)

First, for the population method, Q and P are estimated from the ratio of Q cells that have exited the PVE during a defined portion of a cell cycle to the total number of proliferating cells (i.e., Q + P). Mathematically, this is

equation image(1)

where NQ and NP + Q are the numbers of Q cells and P + Q cells detected, respectively. (Note that tangential movements of cells does not affect this measurement, because there would be a balance of cells entering and leaving the measured area.) However, were some cells in the PVE to die during the experimental interval (i.e., approximately one cell cycle), then the true Q would be

equation image(2)

where ND is the number of labeled PVE cells that died (or otherwise disappeared from the PVE) during the experiment. Because the cells that die would be invisible to the experiment, the results obtained would be

equation image(3)

and would be larger than the true value of Q. For example, if there is no cell death and NQ is 20 cells and NP is 80 cells, then, according to equation 1, Q = 20/(80 + 20) = 0.2 for that cell cycle, and P = 1 – Q = 0.8. If, however, an additional 20 cells died during the experiment and, hence, went undetected, the measured Qpop would still be 0.2 (according to equation 3), and estimated Ppop would be 1 – Qpop or 0.8, but the true Q would be Q = 20/(80 + 20 + 20) = 0.167 (according to equation 2), the true P would be P = 80/(80 + 20 + 20) = 0.667, and D would be D = 20/(80 + 20 + 20) = 0.167, i.e., P + Q + D = 1. In other words, the experimentally determined Ppop would overestimate the true P (0.8 vs. 0.667). In general, the existence of cell death in the PVE would consistently overestimate P:

equation image(4)

Next, from the perspective of the retrovirally measured PVE clade size distribution, the effects of cell death (or loss of label) are different. This is because the PVE clade size distribution “sees” only the P cells, because both Q cells and D cells would disappear from the assay. Hence, the P seen by the retrovirally labeled clade size distribution is the true P (i.e., one of a set of values; see Fig. 5) and is given by the simple expression

equation image(5)

where Q and D are the true values of Q and D, respectively, i.e., the only two possible non-P fates. The relationship between Pclade (i.e., the true P) and Ppop is trivial if there is no cell death in the PVE, because D and ND are zero, and P = Ppop from equation 4. However, if there is cell death in the PVE, then the relationship between Ppop and P is given by equation 4. In particular, this means that, if there exists significant cell death in the PVE, then the measured Ppop would be larger than the true P and would predict larger clades than should be obtained; i.e., the solid curve in Figure 3 would be shifted to the right.

Finally, the effects of tangential movements of cells on Pclade have to be considered. Each time when a proliferating cell moves tangentially away from the other members of its lineage, it would establish a new clade elsewhere in the PVE, leaving the original clade with one fewer cell and a “new” clade with one cell. The effect of this process on clade size distribution would depend on the time taken for the lateral movement, i.e., how many cell cycles elapse after retroviral integration and before sacrifice. If the tangential movements occur soon after retroviral integration, then there would be a general reduction in clade size. However, if tangential movements occur shortly before sacrifice, then the clade size distribution would show a marked increase in clades of one or two cells. Thus, a prediction made from population methods can match the clade size distribution obtained with retroviral methods if 1) cell death, loss of label, and tangential movements of cells in the PVE are all minimal (i.e., close to 0) or 2) the clade-size-enhancing effects of cell death (and loss of label) are exactly matched by the clade-size-reducing effects of tangential movements at all survival times. Because we used four different injection-survival time periods for the retroviral experiments reported here, and because all four time periods are fit equally well by the model 1 calcuations, it seems most likely that cell death, loss of label, and tangential movements of the PVE cells are all close to zero for the period extending from the time of the initial exposure to the retrovirus, i.e., E11, through the end of the time period sampled, i.e., E15, which covers almost all of the NI of the mouse.

DISCUSSION

Traditionally, the problem of neuron number regulation in the CNS has been explored through dichotomous approaches. One approach has been to study the development of the neocortex using methods that reflect the average behavior of the population. This approach has been used to determine changes in the average length of the cell cycle (Takahashi et al., 1995), the proportion of cells that enter vs. leave the cell cycle for each of the mitotic divisions (Takahashi et al., 1996b; Miyama et al., 1997), the proportion of the population that dies (Thomaidou et al., 1997), etc. The second approach has been to study the individual members of the population using cell lineage tracing methods (Price et al., 1987; Cepko, 1988), time-lapse cinematography (Fishell et al., 1993; Chenn and McConnell, 1995), or other methods (Fishell et al., 1993) that identify single proliferating cells and their progeny. Here we present a third approach to this problem by combining data obtained from population methods and lineage tracing methods. Thus, we have performed retroviral experiments that reflect the Q/P decisions made by individual members of the proliferative population (and their progeny) integrated over several cell cycles and combined these results with data from population studies in which estimates of P and Q were made that reflect the average reentry vs. exit decisions made by a population of PVE cells at each of several single cell cycles during the NI. This novel combined approach provides a method for dealing with the dynamic changes of the proliferative populations of the developing brain over the course of several cell cycles.

Our results show that during a developmental period from E11 through E15, which comprises approximately 7 of the 11 cell cycles during which cortical neurons are produced (Takahashi et al., 1995, 1996b), the number of proliferating cells per retrovirally labeled clade varies greatly. We then developed three models that are consistent with the previous population studies (Takahashi et al., 1996b; Miyama et al., 1997) and then evaluated each model by comparing predictions from the model with the experimentally determined numbers of retrovirally labeled cells that remain in the VZ after known survival periods. Among the three models evaluated, only model 1 accurately accounted both for the broad variation in cell number per VZ clade and for the proportional representation of each clade size. Thus, the distribution from model 1 shows that the variation in clade size is almost completely accounted for by changes in P and Q, i.e., in the proportions of cells remaining in vs. leaving the PVE, as determined by population studies using double labeling with S-phase markers (Takahashi et al., 1996b; Miyama et al., 1997). Because the three models used represent, in a sense, three different sets of null hypotheses about the behavior of the proliferating population in the VZ, the goodness of fit of the prediction (i.e., ∼93–99% of the variance), including the facts that there are no large PVE clades (i.e., 8, 16, or 32 cells), that neither even-sized nor odd-sized clades predominated in the distribution, and that no more one-cell clades were found than were predicted by P/Q changes, affirms the following properties of the proliferative population of the VZ in the developing mouse neocortex.

First, the decision made by each of the two daughter cells to remain in the proliferative pool (P) or to leave the pool (Q) is independent of the decision made by the other daughter cell (Fig. 5A), and this decision is made anew at each cell cycle. These characteristics are reflected in the fidelity with which P, a population parameter, predicts the frequency distribution of PVE clade size over a succession of several cell cycles (Fig. 5A) and in the unimodal distribution of the observed and calculated PVE clades (Fig. 3). The independence of fate at each cell cycle is explicit in the iterative application of the binomial distribution (Figs. 4A, 5A) that is the basis of model 1. The biological significance of this is that it indicates that all three types of cell divisions, symmetric terminal, symmetric nonterminal, and asymmetric, coexist at all stages of development of the ventricular zone (Fig. 1A). Our data show clearly that the coexistence of all three types of cell divisions is necessary to account for the portion of the total lineage that remains in the PVE. It seems reasonable, therefore, that the converse is also true, i.e., that timing and rate of production of neurons of the cortex depend on the coexistence of all three types of cell divisions. This means that both asymmetric and symmetric terminal cell divisions in the PVE produce neurons. Note that, because at each cell cycle P decreases and Q increases (Fig. 5B; Takahashi et al., 1996b; Miyama et al., 1997), the proportional contributions of the three types of cell divisions change during the NI (Fig. 4A). Overall, this view is consistent with previous retroviral studies from which the existence of both asymmetric and symmetric terminal divisions producing neurons can be inferred from the number and spatial distribution of the labeled cells (Parnavelas et al., 1991; Kornack and Rakic, 1995a; Mione et al., 1997). For example, a recent scheme suggesting that radially oriented VZ cells divide through a “series of asymmetric … cell divisions” (Noctor et al., 2002) does not exclude the possibility that some radial cells will divide symmetrically to produce two radial cells and that some radial cells will divide to produce two cells that leave the VZ. Indeed, in the figures from a time-lapse cinematographic analysis of the VZ (Miyata et al., 2001), both symmetric terminal (i.e., producing two neurons) and symmetric nonterminal (i.e., producing two VZ cells) cell divisions seem to occur. [Note that the symmetric division of VZ cells to produce neurons differs from the suggestion that SVZ cells may produce neurons from symmetric divisions (Ishii et al., 2000).]

Second, the independence of fate, the unimodal distribution of the PVE clade size, and the absence of large clades specifically indicate that there is no significant number of progenitor cells that are “reserved” to produce specific classes of neurons (Luskin et al., 1993) or designated to a specific cortical layer (McConnell and Kaznowski, 1991; Chenn and McConnell, 1995; Kornack and Rakic, 1995b; Frantz and McConnell, 1996). Such very large PVE clades (e.g., 8, 16, 32 cells, etc.) might have been formed if an AP-labeled proliferating cell had divided symmetrically for several cell cycles. In addition, other specific repeated patterns of mitosis, e.g., a non-random mixture of symmetric divisions with asymmetric divisions, would produce a distinctly bimodal size distribution of PVE clades with a significant incidence of large clades or a predominance of even-sized (e.g., model 3) or odd-sized clades. We conclude that such “reserved” populations either are rare or do not exist and that, if they exist, they are neither a major histogenetic mechanism for the construction of cortical laminae nor necessary for the production of substantial numbers of particular neuronal classes.

Third, one of the assumptions underlying the calculations made for model 1 is that, at each cell cycle, cell death (and/or the disappearance of the retroviral label; Blaschke et al., 1996; Thomaidou et al., 1997) and tangential migration of the proliferating cells (Fishell et al., 1993; Tan and Breen, 1993; Walsh and Cepko, 1993; Reid et al., 1995) in the PVE affect only a small fraction of the PVE cells. Cell death in the PVE would affect the set of Ps used for the calculations (Fig. 4B) and the clade size histograms differently, leading to the prediction of larger clones than we obtained. Although the tangential migration of PVE cells could, in theory, balance out the effects of cell death, the fact that we used four separate injection-survival intervals effectively eliminates this possibility, because the timing of the tangential migration of PVE cells needed to achieve this balance for one survival time would not do so at the other three injection-survival intervals. In addition, there is no qualitative evidence of tangential movements of cells within the PVE in our material (see also Cai et al., 1997b). In other words, the simplest explanation is that cell death (or disappearance of label) is small; i.e., D = 0. Indeed, our mathematical analysis indicates that the inclusion of a small amount of cell death (∼0.8% per cell cycle) in the simulations improves the fit to the actual data (albeit not significantly), but including larger amounts degrades the fit. This estimate confirms the measurements (<1.8% per cell cycle) of Thomaidou et al. (1997) and indicates that the much larger estimates of 50–70% cell death (Blaschke et al., 1996, 1998) are too high (see also Gilmore et al., 2000). Also, the inclusion of large amounts of cell death does not improve the fit of any of the models to the experimental data.

In conclusion, this combined approach indicates that the total number of neurons made for a region of the brain is controlled tightly during the proliferative phase of development by mechanisms operating at each cell cycle over the course of the NI and that the control is largely by way of a determination of the decision of each proliferative cell to reenter S phase. Specifically, at the beginning of each cell cycle (e.g., presumably sometime during G1), each of the two daughter cells resulting from a single mitosis decides independently whether it will reenter the cell cycle or exit the proliferative population. These results indicate that lineages containing specific repeated patterns of mitotic divisions (Qian et al., 1998; Shen et al., 1998) do not occur to any significant extent in the developing neocortical PVE in vivo. Thus, cell class (Luskin et al., 1993; Mione et al., 1997) and laminar fate (McConnell and Kaznowski, 1991; Frantz and McConnell, 1996) cannot be a consequence of restrictions in cell lineage, at least in terms of any patterns of cell division. These characteristics of the cells of a region must be determined by other factors, such as local cellular interactions (Harris and Messersmith, 1992), diffusible factors (Yamada et al., 1993), and so on, which could occur at any time during a cell's life history, including during the proliferative phase (McConnell and Kaznowski, 1991). Most importantly, these results indicate that neuron production in the VZ during a substantial period of the time when neocortical neurons are being born occurs both from asymmetric and symmetric terminal cell divisions.

Acknowledgements

This study was supported by NIH grants MH63957 (to N.L.H.) and NS12005 (to V.S.C.), NASA grant NAG2-1367 (to R.S.N.), grant 12B-2 for Nervous and Mental Disorders from the Japanese Ministry of Health Labour and Welfare (to T.T.), and the Pharmacia Fund for Growth and Development Research.

Ancillary