Description of the mathematical model for ploidy profile dynamics.

(A) Kinetic scheme describing the sequential reaction of endoreduplication. k₂ⁱ and γ₂ⁱ denote the rate constant of endoreduplication from 2ⁱC to 2ⁱ⁺¹C cells and the removal constant of cells from the 2ⁱC population, respectively (1 ≤ i ≤ 5). b indicates the rate constant of mitotic cell division of 2C cells. This scheme could be simplified in this case as given by a single constant rate of endoreduplication k in time. (B) Time evolution of the probability of each ploidy obtained by the analytical solution with k = 0.5. (C) Parameter dependency for optimizing a ploidy profile with the mathematical model. Color-coded RSS values with various parameter combinations are shown. The white dotted line indicates a minimum RSS in a combination of the parameters k and t. The color bar is scaled from minimum to maximum in this diagram. (D) Valley-like dynamics of the relationship between t and RSS with k = 0.5. The RSS reached the minimum when t = 2.27. (E) Based on the relationship between t and RSS with k = 0.5, an optimized ploidy profile was obtained using t = 2.27. The probability distribution of each ploidy level from the experimentally measured data (Exp.), the mathematically modeled data at t = 2.27 (mod.), and the Poisson distribution (Poi.) are indicated. The probabilities of 2C (green), 4C (blue), 8C (orange), 16C (red), and 32C (black) are shown.