Mitosis

The inhibition of mitosis and the induction of apoptosis in KG1a and MV4–11 cells were induced respectively by exposure to camptothecin (Sigma-Aldrich, Saint-Quentin Fallavier, France), a cytotoxic quinoline alkaloid which inhibits the DNA enzyme topoisomerase I [10] (link), [11] (link) and by AZD8055 (AstraZeneca Cancer & Infection Research Area, Alderley Park, UK) [12] (link), a selective inhibitor of mTOR kinase, respectively. Cells were seeded at 2×10⁵ cells/mL (5% CO₂ incubator at 37°C). KG1a cells were cultured for 6h with camptothecin at a final concentration of 1 µM and MV4–11 cells were cultured for 24 h with AZD8055 at a final concentration of 10 nM and 100 nM. The stock solutions were diluted to ensure a final concentration of <0.03% for DMSO (Sigma-Aldrich). Control cultures were treated with an equivalent volume of DMSO in MEM alpha medium which did not induce apoptosis.
Quiescence was induced in KG1a cells by contact with BM MSCs [13] (link). Adherent culture-amplified MSCs were used at passage 2 (P2). KG1a cells were co-cultured on P2-MSCs for 72 h (37°C in 95% humidified air and 5% CO₂) at a starting concentration of 1.5×10⁴/cm².
The accumulation of KG1a cells in the M phase was induced by exposure to colcemid (KaryoMax Colcemid, Life Technologies), used for arresting the dividing cell at metaphase of mitosis. Cells were cultured 30 min and 1 h with colcemid at a final concentration of 0.1 µg/mL.
Lymphocytes stimulation was induced by exposure to phytohemagglutinin (PHA) (Remel™, Oxoid™, Haarlem, The Netherlands), which is used to stimulate mitotic division of lymphocytes. Whole blood cells were cultured 72 h with PHA at a final concentration of 170 µg/mL according to the manufacturer’s recommandations.
All experiments were performed in triplicate.

The mathematical model continues to be based purely on the classical definition of cancer as uncontrolled proliferation of cells with the potential for invasion and metastasis, simplified for gliomas, which practically do not metastasise. Thus, the model defines the behaviour of gliomas in words and mathematics as follows:
This is a classical conservation–diffusion equation (Murray, 2003 ), in which c(x, t) defines the concentration of malignant cells at location x and time t, D (mm² day⁻¹) is the random motility (dispersal) coefficient defining the net rate of migration of the tumour cells, ρ (per day) represents the net proliferation rate of the tumour cells (including mitosis and cell loss), K is the limiting concentration of cells that a volume of tissue can hold (i.e., the carrying capacity of the tissue) and ∇² represents the dispersal operator, the Laplacian, expressed mathematically as the sum of three second derivatives in space (Strang, 1991 ). The model has been adapted to use the BrainWeb Atlas (Collins et al, 1998 (link)) to accommodate an irregularly shaped tumour located anywhere within 3-dimensionally continuous heterogeneous tissue with differences in grey and white matter, anatomically accurate to 1 mm³ (Swanson, 1999 ; Swanson et al, 2003a ). The model can accommodate different velocities of glioma cell motility in grey and white matter (Swanson, 1999 ) but, since the original MRIs were not available, this feature was not used in the present analysis.
Equation (1) implies mathematically that the ‘edge’ of the visible tumour advances asymptotically as a ‘traveling wave,’ (Swanson, 1999 ) which expands radially and linearly, according to Fisher's approximation or Skellam's model (Shigesada and Kawasaki, 1997 ): . Although there is no true edge to an infiltrating tumour, such as a glioma, any point on the ‘gradient’ between the T1-Gd and T2 circumferences (Figure 3) moves as part of the ‘traveling wave.’ In general, as shown schematically in Figure 3, proliferation (ρ) tends to drive the wave up (but not above the carrying capacity K) and dispersal (D) tends to drive the gradient centrifugally.
The ‘gradient’ between the T1-Gd and T2 images can be expressed in a different way, involving the ratio D/ρ. This ‘gradient’ has not been quantitatively defined but can be approximated from the observations of Kelly et al (1987) (link), Kelly (1993) (link) and Dalrymple et al (1994) (link), who reported that the T1-Gd circumference approximates the edge of the ‘solid tumour’ and that the T2 circumference represents not only the extent of oedema but also a zone of a low concentration of ‘isolated tumour cells.’ We hypothesised that these circumferences might represent concentrations of tumour cells equal to 80 and 16%, respectively, of the maximum concentration (Figure 3). That tumour cells extend much farther then even the imageable abnormality is evidenced by malignant cells being cultured by Silbergeld and Chicoine (1997) (link) from as far away as 4 cm. A close study of other solutions of the model Eq. (1) finds a highly non-linear relationship between the ratio D/ρ and the average radii of spheres equivalent to the volumes defined by T1-Gd and T2, r_T1 and r_T2, respectively (Harpold et al, 2007 (link)). The equation by no means is a simple ratio of any part(s) of the MR images, but includes fractional exponents of ratios of differences that make it highly non-linear.
Our model consists of the following two parts: (1) Eq. 1, the spatio-temporal bio-mathematical formulation of the proliferation and dispersal of the tumour cells, both visible (detectable by scans) and invisible (diffusing into the surrounding normal-appearing tissue), and (2) the use of Fisher's approximation ( ) to estimate the time required for the tumour to expand from its detectable actual size at diagnosis to its size at death (Woodward et al, 1996 (link)).

Fig. S1 shows further evidence that StableMARK labels the subset of stable MTs. Related to Figs. 1 and 2. Fig. S2 demonstrates that StableMARK prefers binding to expanded lattices in vitro. Related to Fig. 2. Fig. S3 data depicts live-cell imaging of the behavior of individual stable MTs. Related to Fig. 3. Fig. S4 shows further evidence that StableMARK at low levels has minimal effects on MTs and organelle transport. Related to Figs. 4 and 5. Fig. S5 gives further data on the dynamics of StableMARK-decorated MTs. Related to Fig. 6. Fig. S6 provides more data on stable MTs during cell division. Related to Fig. 8. Fig. S7 shows data that demonstrate the localization of StableMARK to stable MTs in different cell lines. Video 1 (related to Fig. 3) shows StableMARK and mCherry-tubulin in a U2OS cell. Video 2 (related to Fig. 3 A) shows StableMARK and mCherry-tubulin in a U2OS cell. Video 3 (related to Fig. 3 B) shows StableMARK and mCherry-tubulin in a U2OS cell. Video 4 (related to Fig. 3 C) shows StableMARK in U2OS cell. Video 5 (related to Fig. 3 E) shows StableMARK in U2OS cell. Video 6 (related to Fig. 5 C) shows cesicles labeled with mCherry-Rab6a moving over StableMARK-positive MT in a U2OS cell. Video 7 (related to Fig. 6 B) shows laser-induced severing of MTs in U2OS cell expressing StableMARK and mCherry-tubulin. Video 8 (related to Fig. 6 D) shows EB3-tdTomato comet growing from StableMARK-labeled MT in U2OS cell. Video 9 (related to Fig. 7 B) shows transient binding of StableMARK to MTs labeled with mCherry-tubulin in U2OS cell. Video 10 (related to Fig. 8 C) shows mitosis in stable U2OS Flp-In cell(s) expressing StableMARK.

MEFs were maintained as previously published (Hall et al., 2013 (link)). SNAP labeling was performed as previously described (Quidwai et al., 2021 (link)). Ependymal cells were isolated and cultured as published in Delgehyr et al., 2015 (link). mTECs were isolated and cultured as described in Eenjes et al., 2018 (link); You et al., 2002 (link). RPE1-hTERT (female, human epithelial cells immortalized with hTERT, Cat. No. CRL-4000) from ATCC were grown in Dulbecco's Modified Eagle Medium (DMEM, Life Technologies) or DMEM/F12 (Thermo Fisher Scientific, 10565042) supplemented with 10% fetal bovine serum at 37°C with 5% CO₂. For live imaging, the membrane was cut out and placed cilia down on a glass dish (Nest, 801002) in a drop of media. PCM1^−/− RPE1 cells were generated as described previously (Kumar et al., 2021 (link)) (all figures except for Figure 8—figure supplement 1, in which case they were generated as in Gheiratmand et al., 2019 (link)). hTERT-RPE1: Source ATCC, confirmed mycoplasma negative and verified by STR profiling. Two PCM1^−/− RPE1 cell lines were generated using single guide RNAs (Supplementary file 1). Loss of PCM1 was confirmed by genotyping, immunoblotting, and immunofluorescence. Monoclonal PCM1^−/− RPE1 cell lines stably expressing eGFP or eYFP-PCM1 (plasmid a gift from Bryan Dynlacht; Wang et al., 2016 (link)) were generated using lentiviruses and manually selected based on fluorescence. To synchronize cells in G1/S aphidicolin (Sigma) was added to the culture medium at 2 μg/ml for 16 hr. To arrest cells in mitosis, taxol (paclitaxel; Millipore-Sigma) was added to the culture medium at 5 μM for 16 hr prior to rounded up cells being collected by mitotic shake-off. For arrest in G0, cells were washed 2× with phosphate-buffered saline (PBS; Gibco) and 1× with DMEM (without serum) before being cultured in serum-free DMEM for 16 hr. To disrupt cytoplasmic microtubules, cells were treated with 20 μM nocodozole (Sigma, SML1665) for 1–2 hr prior to fixation.

To assess the distribution of proliferating cells in the VZ, lizards injected with [³H]-thymidine with a survival time of 1.5 h were used (n = 5). The VZ was divided in six different regions, including three sulcal zones (sulcus medalis, sulcus lateralis and sulcus ventralis/terminalis) and three intersulcal zones (intersulcus corticalis, intersulcus lateralis, and intersulcus septalis) (Figure 1B). The number of [³H]-thymidine labeled cells was counted in all these regions relative to the total number of cells. This quantification was performed in two telencephalic levels: one pre-commissural (anterior) and one post-commissural (posterior), analyzing for each level a total of 7 semithin sections which were 9 μm apart to avoid counting the same cell twice. Different types of counts were performed by quantifying the total number of labeled cells/1000 cells considering sulci vs. intersulcal regions, comparing between the different sulci and intersulcal regions and differentiating between the pre- and post-commissural levels for each animal.
To characterize the ultrastructure of VZ proliferative cells and their derivatives, the brains of specimens with 1.5, 6, 12, 24, and 72 h survival times were examined. Between 50 and 150 [³H]-thymidine-positive ([³H]-thy⁺) cells were analyzed for each survival time, including at least two different antero-posterior levels per lizard. These cells were studied by transmission electron microscopy (TEM) to determine their ultrastructural characteristics. Counts were also made of the number of cells in mitosis (M phase) labeled relative to the total number of [³H]-thy⁺ cells.
The analysis of specimens with long survival times (1, 3, 6, and 12 months) focused mainly on the cell layer of the MC, although we also investigated whether there were labeled cells in the walls of the LVs. Within the MC we analyzed the ultrastructure of 25–50 [³H]-thy⁺ cells from each survival time to see to which neuronal type they corresponded.