Modeling cell populations metabolism and competition under maximum power constraints
Fig 8
Stable stationary states and dynamics of the self-limiting autocatalytic cycle.
Panel (A) shows the model state space defined by the curves for the power (bold black), P(Q) = r·Q·(1−Q/K), the heat flow (black), Jh(Q) = P(Q)/η and the stability potential (dot dashed), V(Q) = a·Q3+b·Q2 (coefficients in Eq 8). The colored dots on the curves represent the steady-states for P, Jh and V as a function of Q (0<Q<K) for the three possible different growth regimes, respectively, defined by the product r·τ: sub-optimal, r·τ = 1.5 (azure), optimal or maximum power state (Pmax), r·τ = 2 (blue), and super-optimal, r·τ = 10 (dark-blue). This is associated with the stock N = K-Q (dashed lines) that decreases for increasing Q to fulfill the mass balance constraint. Panels (B) and (C) show the time evolution associated with the configurations defined by the three different growth regimes (azure, blue, dark blue), respectively, for the stocks Q and N (dashed), and for the flows P and Jh. Panel (D) shows the application of the formulation to estimate the stationary states of normal and neoplastic plasma cells.