A model for an early stage of tomato fruit development: cell multiplication and cessation of the cell proliferative activity

Abstract

Changes in cell number during the early period of tomato fruit development were analysed by means of a deterministic model of cell multiplication. The period commenced at the seed stage with one theoretical cell undergoing intensive cell division, and ended when the cell number became nearly constant. The model takes into consideration the proliferative activity of the fruit cell population which, a few days before flower anthesis, begins to decrease progressively after each mitotic cycle. Model parameters, namely the time at which proliferative activity diminishes, its rate of decrease and the length of the cell cycle, were estimated by fitting the model to observed cell population dynamics in tomato fruits growing in three different positions on the truss. It is hypothesized that the molecular mechanism responsible for the cessation of mitosis in growing fruits is associated with shortening of telomeric ends of nuclear DNA, as suggested previously for other growing cell populations.

Fig. 1. Schematic representation of the algorithm of the model after time B when the proliferative activity decreases after each cell cycle. Circles symbolize the mitotic cycles. Arrows pointing downwards show the proportion of non‐proliferating cells that appears after each cycle. θ₁ = 1 and θ_i = θ₁δ^{i – 1} where i – 1 is the number of cell cycles performed after time B.

Fig. 2. Comparison between the observed dynamics of cell number in tomato fruits at positions 1 (A), 3 (B) and 5 (C) in the truss (symbols) and the curves calculated by the model, considering either τ (bold line), δ (thin line) or B (broken line) to be dependent on fruit position.

Fig. 3. Sensitivity analysis of the model to a ± 1 % variation of parameter B (A), τ (B) and δ (C). Broken lines represent the number of cells calculated by the model adjusted on experimental data obtained for fruit 1. Bold and thin lines are the number of cells calculated by the model after a respective 1 % increase or 1 % decrease of the parameter value.

Fig. 4. Sensitivity analysis of the model to the simultaneous variation of two parameters by ± 1 %: B and τ (A); B and δ (B); and τ and δ (C). Broken lines represent the number of cells calculated by the model adjusted on experimental data obtained for fruit 1. + and – indicate, respectively, 1 % increase or 1 % decrease of the parameter value.