Figure 2

Figure 2 Mathematical model.

(A) Sketch of five processes and two subpopulations of beta cells considered in the mathematical model. N_p(t) is the time-dependent number of proliferative beta cells and N_q(t) of quiescent beta cells. Proliferative cells from N_p(t) may reversibly switch to the quiescent state N_q(t) with a rate k_i and back to proliferation with a rate k_a. Cell cycle duration is T_c, neogenesis rate is v, and death rate is δ. The latter two processes affect both subpopulations. Cell death is initially absent and starts at an estimated onset time of 16.3 dpf. (A’) Results of the fitted model for WT (black) and p35 (red) conditions, respectively. Experimental data at the time points 5, 15, 20, 23, 27, and 30 dpf (from Fig. 1E; Appendix Fig. S1B) is shown as the mean (circle) and 2 SD (risers). Color code as shown on the top of panel A’: blue and red circles represent experimental data of beta-cell numbers in WT and p35, respectively; black solid line and red dashed line depict the model simulation of WT and p35. n = at least 5 independent samples per group at each developmental time point. (B-B’) Results for the model variant with 1-day short burst of cell death around 20 dpf. This variant is not able to represent the shallower slope for WT cell count data after 20 dpf. (C-C’) Results for model variant without cell death for both experimental conditions. All other model parameters were estimated; however, the best-fitting curves show large discrepancies for both conditions at 30 dpf, thereby falsifying the assumption of absent cell death. Error bars in A’-C’ are SEM. (D) Snapshots from simulation movie (Movie EV1) of a stochastic, cell-based model with the same mechanisms and parameter values as in (A) confirms the results from (A). Source data are available online for this figure.