movement patterns. Second, the end position of the apical-to- basal migration varies signiﬁcantly from nucleus to nucleus. This suggests that the conditions of the model are essentially consistent with the in vivo situation. We used this computational model to identify conditions that signiﬁcantly inﬂuence apical-to-basal migration by ex- ecuting models with varying parameters. We found that changes in cell-cycle length had major effects on the velocity of apical-to-basal movement (Figure 7Ca). To further evaluate the validity of the computational model, we tested this prediction in brain tissue. The cell cycle of neural progenitors, particularly the duration of the G1-phase, becomes progres- sively longer as development progresses (Takahashi et al, 1995). Thus, the effect of cell-cycle length can be tested in vivo by comparing two different developmental stages. To compare results from the computational model with in vivo results using the same criteria, we designed in silico experiments to label the S-phase nuclei and measure the distance the nuclei move after exiting S-phase. We ran the program using the cell-cycle length parameters of E11.5 and E14.5 cells that were measured in a previous study (Takahashi et al, 1995). The positions of nuclei that were modelled as having exited S-phase 3–6 h earlier before the end of the simulation were plotted (Figure 7Cb). The average position of such nuclei was more distant from the apical surface when the cell-cycle length was shorter (E11.5). This result can be explained as occurring because a shorter cell cycle increases the frequency of basal-to-apical nuclear migration that occurs once in a cell cycle, resulting in more frequent displacements by G2 nuclei in the apical VZ. For in vivo experiments, we injected two thymidine analogues (CldU and IdU) into pregnant mice at different times (6 and 3 h, respectively) before ﬁxation of the embryos. With this procedure, CldU single-labelled cells can be identiﬁed as having been in S-phase 3–6 h before ﬁxation. As we did in the in silico experiments, we measured and plotted the distance of the CldU single-labelled nuclei from the apical surface at each stage (Figure 7Da and b). Histograms showing the distribution of nuclear positions indicate that the peak of the distribution was in the middle of the VZ at E11.5 but that it shifted signiﬁcantly closer to the apical surface and showed a narrower distribution by E14.5 in both the model (Figure 7Ea) and in the developing brain (Figure 7Eb) (for the statistical test, see the Supplementary data). This qualitative correlation supports a model in which apical-to-basal nuclear Mechanisms of interkinetic nuclear migration Y Kosodo et al migration is mainly driven by the displacement of nuclear migration in the basal-to-apical direction during G2-phase. Discussion In this study, we focused on how the timing and direction of INM are determined with respect to the cell cycle in neural progenitor cells. Our results indicate that there are different modes of nuclear migration depending on the phase of the cell cycle; active migration occurs during G2-phase, and passive migration during G1-phase. Several lines of evidence have suggested that the dynein motor system drives nuclei from the basal region toward the centrosome on the apical surface of the VZ (Tsai et al, 2005; Tamai et al, 2007; Xie et al, 2007; Del Bene et al, 2008), and that the connection between dynein and the nuclear envelope is maintained by SUN-domain proteins and KASH-domain proteins (Del Bene et al, 2008; Zhang et al, 2009). As their loss-of-function results in defects in INM and post-mitotic neuronal migration (Tsai et al, 2005; Zhang et al, 2009), these molecules appear to be part of ubiquitous machi- neries for microtubule-based nucleokinesis. Therefore, no spe- ciﬁc molecular mechanism has so far been shown to link nuclear migration to cell-cycle progression. Here, we have demonstrated that cell-cycle progression from G1- to S-phase is a prerequisite for basal-to-apical nuclear migration, and that Tpx2 regulates this migration. Tpx2 begins to be expressed in S-phase and accumulates in the nucleus. Upon entry into G2- phase, Tpx2 redistributes into the apical process and promotes nuclear migration. In Arabidopsis, a similar translocation of Tpx2 from the nucleus to the prospindle prior to nuclear envelope breakdown has been identiﬁed (Vos et al, 2008). Our results thus suggest that translocation of nuclear Tpx2 to the apical process upon entry into G2-phase is critical for the microtubule-dynein-driven nuclear migration that occurs dur- ing G2-phase, while other molecules discussed above might be needed for Tpx2 to function in nuclear migration to the apical surface. We propose that the regulation of Tpx2 distribution is part of the mechanism that determines the timing of basal-to- apical nuclear migration. How does Tpx2 function in nuclear migration in the apical process during G2-phase? Tpx2 is known to act in mitotic spindle organization at M-phase by controlling aurora A kinase (Barr and Gergely, 2007). Aurora A, in turn, activates transforming acid coiled-coil protein (TACC), which promotes microtubule extension from centrosomes (Kinoshita et al, Figure 7 Computational modelling of INM combined with in vivo experiments. (A) (a) Scheme of nuclear movement posited in the model. The nucleus goes to the centre of gravity of an area that is unoccupied by neighbouring nuclei within the SR. r, radius of nucleus; SR, searching radius. (b) One of the frames from the sequential movie of modelling analyses visualized for interpretations (see Supplementary Movie S11). Some nuclei are highlighted by colour codes according to their phase in the cell cycle: blue, G1/S; green, G2; orange, M. Nuclei can cross the border of the lateral and basal sides but not that of the apical side. See details in Supplementary data. (B) Movement of 12 individual nuclei acquired from the computational model without (a) or with (b) basal-to-apical nuclear movement during G2-phase. x-coordinate: time, y- coordinate: distance from the apical surface. Note that the patterns of apical-to-basal movement and the points reached before entering G2- phase differ signiﬁcantly among nuclei (b). (C) (a) Effect of changing parameters in the computational model. Average distances from the apical surface of 200 nuclei and their phase in the cell cycle in the simulation were plotted. Length of G1-phase in E11.5 (3.2 h) and E14.5 (9.3 h) and whether cell division at M-phase is occurring ( þ or ) are indicated. (b) Relative positions of nuclei that exited S-phase between 3–6 h before the end of the simulation using the cell-cycle parameters for E11.5 (grey) or E14.5 (green). (D) (a) Incorporation of CldU (magenta) and IdU (green) into the nuclei of neural progenitor cells of mouse brains 6 and 3 h before ﬁxation, respectively. Blue arrow: the presence of a CldU single-labelled nucleus implies that it exited S-phase between 6 and 3 h before ﬁxation. Distance from the apical surface (yellow dashed line) was measured (d). Bar ¼ 50 mm. (b) Positions of nuclei that exited S-phase between 6 and 3 h before ﬁxation in E11.5 (grey) and E14.5 (green) embryonic mouse brains. (E) Histogram view of the results of the double-labelling experiment acquired from the computational model (a, see (C)) or in vivo mouse brains (b, see (D)). Proportions of nuclei (x-coordinate) at speciﬁc distances from the apical surface (y-coordinate, rounded off to a two-digit number). & 2011 European Molecular Biology Organization The EMBO Journal VOL 30 | NO 9 | 2011 1701