Figure 7. Development of a mathematical... | Rockefeller University Press

Figure 7.

$Figure 7. Development of a mathematical model of primary ciliogenesis. (A) Plot of the single-cell measures of cell area for peripheral, central, and ciliary profiles. Three independent experiments were performed (n = 406 cells; two to five fields per experiment were examined). (B) Plot of the total number of cells (black dots) over time. Fitting of “fast” and “slow” dynamics (gray dashed lines) intersects at the transition point (2.68 d). Prediction of the total number of cells by a Hill function of the cell cycle using a Hill coefficient of 100 (solid black line). (C) Plot of the number of cells with midbody remnant or PC versus the total number of cells. Two dynamic regimens that intersect at a total number of ∼73 cells are distinguished. Slope values less than 1 mean that a fraction of the new cells in the system does not conserve the remnant. Three independent experiments were performed (n = 207 to 847 cells per time point; two to five fields per time point and per experiment) in B and C. (D) Rationale of the probabilistic population-based mathematical model. (i and ii) An initial set of cells is allowed to proliferate and develop up to a given time t. (iii) Each individual cell in the population is defined as a numerical entity with four variables: its area, age, type, and cell cycle length (T). (iv) Cells can be in one of four distinct configurations depending on whether they lack or have a midbody remnant (MB) in a peripheral or central position or a ciliary structure. These configurations were named as no MB, peripheral, central, and ciliary, respectively. (v) The cell area for each individual cell in the population was obtained from a gamma distribution with standard deviation equal to 30% of the mean. (vi) When the age of a cell reaches the duration of its cell cycle, a division event occurs and a new cell with a peripheral remnant is generated. (vii) Based on the experimental data, we set the probability of conserving the remnant as a Hill function of the cell area, with a transition point at 200 µm2. In the same way, the probability of transition from peripheral to central remnant (viii) and from central remnant to ciliary (ix) configurations were also set as Hill functions of the cell area at transition points of 400 and 200 µm2, respectively. (x) The cell cycle length of each individual cell was obtained from a Hill function of the cell area with transition at 200 µm2.$

Development of a mathematical model of primary ciliogenesis. (A) Plot of the single-cell measures of cell area for peripheral, central, and ciliary profiles. Three independent experiments were performed (n = 406 cells; two to five fields per experiment were examined). (B) Plot of the total number of cells (black dots) over time. Fitting of “fast” and “slow” dynamics (gray dashed lines) intersects at the transition point (2.68 d). Prediction of the total number of cells by a Hill function of the cell cycle using a Hill coefficient of 100 (solid black line). (C) Plot of the number of cells with midbody remnant or PC versus the total number of cells. Two dynamic regimens that intersect at a total number of ∼73 cells are distinguished. Slope values less than 1 mean that a fraction of the new cells in the system does not conserve the remnant. Three independent experiments were performed (n = 207 to 847 cells per time point; two to five fields per time point and per experiment) in B and C. (D) Rationale of the probabilistic population-based mathematical model. (i and ii) An initial set of cells is allowed to proliferate and develop up to a given time t. (iii) Each individual cell in the population is defined as a numerical entity with four variables: its area, age, type, and cell cycle length (T). (iv) Cells can be in one of four distinct configurations depending on whether they lack or have a midbody remnant (MB) in a peripheral or central position or a ciliary structure. These configurations were named as no MB, peripheral, central, and ciliary, respectively. (v) The cell area for each individual cell in the population was obtained from a gamma distribution with standard deviation equal to 30% of the mean. (vi) When the age of a cell reaches the duration of its cell cycle, a division event occurs and a new cell with a peripheral remnant is generated. (vii) Based on the experimental data, we set the probability of conserving the remnant as a Hill function of the cell area, with a transition point at 200 µm². In the same way, the probability of transition from peripheral to central remnant (viii) and from central remnant to ciliary (ix) configurations were also set as Hill functions of the cell area at transition points of 400 and 200 µm², respectively. (x) The cell cycle length of each individual cell was obtained from a Hill function of the cell area with transition at 200 µm².