Figure 2
From: Cell lineage branching as a strategy for proliferative control
Effects of disturbances on the performance of renewal control. In all panels, time is given in units of cell cycles (normalized by v) and the system is at steady state at time t = 0. \( {\overline{x}}_2^{*} \) is the desired (unperturbed) terminal cell population. For parameter values used see Additional file 1: Table S1. (A) Cartoon representation of renewal-controlled two-stage cell lineage. Red line represents negative feedback regulation of p r . (B) Shown is terminal cells (solid line) and stem cells (dashed line) response to stochastic fluctuations on d (n = 2). (C-D) Shown is stem cell population over time in response to periodic oscillations of d with frequency 0.01 (panel C) and 0.04 (panel D). Feedback suppresses the oscillations at low frequency (C) but amplifies them at higher frequency (D) (E) Plotted is the terminal cell population response to stem cell loss at a constant. Stronger feedback reduces steady state error but also introduces stronger oscillations. (F) Shown is the terminal cell population after abrupt removal of half the terminal cell population x 2 at t = 0. Aggressive feedback has faster rise time but causes oscillations in terminal cell population. (G) Main plot shows terminal cell response to stochastic disturbances directly affecting the stem cell population. The inset shows the standard deviation (std) of responses for each feedback level. Moderate feedback can reduce the variance, but more aggressive levels increase variance. (H) Shown is the distribution of stem and terminal cell populations for the response shown in (G) with n = 2. (I) Shown is the plot of the sensitivity function S for renewal control as a function of disturbance frequency (normalized by v). Aggressive feedback improves performance at low frequency (smaller |S|) but by necessity this results in poorer performance at a higher frequency range (larger |S|). For additional disturbances see Additional file 1: Figure S2.