The Leaving or Q Fraction of the Murine Cerebral Proliferative Epithelium: A General Model of Neocortical Neuronogenesis

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 4were 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 4that 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.

For each age, the total number of cells in the entire cohort (i.e.,N_P+Q for PVE and SPP collectively) and the total number of cells in the Q fraction only (N_Q) 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, isN_Q/N_P+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.

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, N_P+Q andN_Q 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 N_P+Q of the overall proliferative population into its PVE and SPP components by taking the product of N_P+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 N_P+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 N_P 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 N_P divided byN_P+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 forN_P 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.

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, CC_n, in which the subscript ndesignates 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 CC₅through 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. 8for 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).

Neocortical neuronogenetic model

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 T_c 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.

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 Xgalreporter 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 (CC_1–11) 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 10⁻¹⁰. This low probability of extinction virtually guarantees that one small area of the PVE will contribute to the entire thickness of the overlying cortex.

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 CC₇dictates 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 verifiablequantitative hypotheses about cortical development and is applicable to the interpretation of data collected with other methods.