Fig 1.
Model of an OPC and illustration of the proliferation/migration rules.
(a) Schematic drawing of an OPC where the cell center and the filipodia are visible. The cell is modeled by a 100 μm diameter sphere, represented by a dashed line drawn around the cell extensions. (b) A cell without overlap with other cells keeps moving with a constant velocity in the same direction. The direction of the motion changes only when the cell has overlaps with other cells. (c) The cell undergoes mitosis: a new cell is created and its center is placed at the distance R from the center of the first cell. (d) The two cells move in opposite direction in order to reduce the overlapping. After separation, they keep moving in the same direction, at a constant velocity.
Fig 2.
Evolution of the cell density versus time for cells with a fixed lifetime clock threshold.
The proliferation parameter is λ = 0.05 per iteration and the lifetime threshold is D = 400 iterations. (a) The cells are represented by spheres whose color is correlated to the value of their lifetime clock: blue cells have been created recently and have a low lifetime clock, whereas red cells are close to the lifetime threshold. (b) Cell number versus time (average over 10 simulations, the error bars are smaller than the thickness of the line).
Fig 3.
Evolution of the cell density, with and without a lesion.
The graphs in (a) display the temporal evolution of the cell density (up) and the density per day of proliferating (bottom, blue curve) and differentiating (bottom, red curve) cells, when starting the simulation with one cell. In (b), a lesion is made at time t = 125 days: all the cells inside a sphere of 250 μm radius centered at the center of space, are killed (see (c)). The graphs in (b) display the temporal evolution of the cell number (up) and the numbers of proliferating (bottom, blue plain curve) and disappearing (bottom, blue dashed curve) cells per day inside the sphere corresponding to the initial lesion, see (c) (average over 20 simulations, the error bars are not represented to avoid overloading the figure but they can be estimated from the amplitude of the fluctuations). In (c) and (d), the color of the cells is correlated with the value of their lifetime clock (with a maximum lifetime threshold of 1000 h). In (c) and (d), in order to be able to see the lesion, only a 200 μm thick slice centered at the origin is represented. In (c), the system is represented just after the 250 μm radius lesion. (d) The lesion is filled up after 33 days of evolution by the migration and the proliferation of the cells at the border of the lesion. The newly formed cells or migrating cells that have reset their clock by loosing their contact with the neighboring cells inside the perimeter of the lesion appear in blue.
Fig 4.
Total and proliferating cell densities in real gliomas.
The graphs in (a) compare the mean total cell density (left) and the mean MIB-1 positive cell density (the MIB-1 positive cells are the cells that have entered the cell cycle, i.e. the proliferating cells) (right), inside (red bars) and outside (blue) real gliomas. The data come from 9 different patients, 22 samples inside the tumor (i.e. inside the signal abnormality on T2 MRI scans) and 16 samples ouside. In (b) left, a histological sample of a low-grade glioma, with a hematoxylin-eosin staining, displays a quasi-normal cell density. In (b), right, the same sample stained with the proliferation staining MIB-1, reveals a limited increase in the proliferating cell density compared to normal tissue. The detailed data have been published in [11].
Fig 5.
Comparison of the different scenarios of glioma appearance.
(a) and (b), an immortal cell appears at time t = 0, (c) and (d), a cell without contact inhibition appears at time t = 0. (a) and (c) Temporal evolution of the total cell density. (b) and (d) Normal (blue lines) and tumoral (red lines) proliferating (plain curve) and disappearing (dashed curve) cell densities, in a 1 mm3 cube.
Fig 6.
Formation of a glioma by the appearance of an over proliferating cell.
(a) Normal OPCs (blue) at equilibrium proliferate (ρ = 0.05/h) and differentiate, as described in the text. In (b), a newly created cell is characterized by an over-proliferating (ρ = 0.25/h) phenotype, in red (t = 0). The daughters of this abnormal cell keep the over-proliferating character. In (c) the system is represented at t = 1500 h = 62.5 days, the developing glioma appears in dark red; in (d) the system is represented at t = 3000 h = 125 days.
Fig 7.
Properties of a glioma formed by the appearance of an over proliferating cell.
(a) Normal (blue circles) and glioma (red circles) cell densities versus the distance to the center of space, for the glioma of Fig 6. Eight graphs corresponding to eight time points are represented from t = 0 (appearance of the first glioma cell, dark red and blue graphs), to t = 336 days (very light red and blue graphs), with a time interval of 42 days. (b) Temporal evolution of the mean radius of the glioma of Fig 6. (c) Temporal evolution of the total cell density, when an over proliferating cell appears at time t = 0. (d) Normal (blue lines) and tumoral (red lines) proliferating (plain curve) and disappearing (dashed curve) cell densities, in a 1 mm3 cube, where an over proliferating cell appears at time t = 0.