Modeling cell populations metabolism and competition under maximum power constraints
Fig 7
Self-limiting autocatalytic cycle model.
The figure shows how to constrain and balance the stock-flow model used to describe the growth of a single cell population. Diagram (A) represents a self-limiting autocatalytic cycle with the relevant flows interacting through the production process and proportional to E·N·Q and the outflow proportional to Q. Upper right a summary of the system dynamics for the stock N and Q with the first law constraining the kinetic coefficients. Panel (B) shows the non-equilibrium thermodynamics representation for the self-limiting cycle in diagram (A). We define: the primary energy inflow, Jin = k0ENQ; the stock of limiting factors, N, with its inflow and outflow from the external environment JN,in = JN,out; the production and consumption processes efficiencies, η and ξ; the cells stock, Q, with its net power inflow, P = k1ENQ = ηJin, and energy outflow, R = k2Q = Q/τ; the recycling and control feedback flows, ξ·R and P–(1–ξ)·R; the total heat flow, Jh = P/η = Jin, which is the sum of the heat flows associated to the production, P/η–(1–ξ)·R, and consumption process, (1–ξ)·R. Jh is a measure of the irreversibility of the modeled growth process.