Modeling cell populations metabolism and competition under maximum power constraints
Fig 9
Competition dynamics and energetic constraints.
This figure shows how to constrain and balance the stock-flow model used to describe the growth of interacting cell populations. Both (A) and (B) represent a system of stocks competing for space. In diagram (A), the upper right shows the mass balance constraint on N, with power inflows proportional to ENQ1 or Q2 and respectively with outflows proportional to Q1 or Q2. The interaction term is a Lotka-Volterra-like proportional to Q1·Q2. The primary energy inflow, Jin = k0,1ENQ1+k0,2ENQ2 is transformed into useful power flows P1 = k1ENQ1 = η1Jin,1 and P2 = k2ENQ2 = η2Jin,2 for the two stocks with efficiencies, η1 and η2; The efficiencies ξ1 and ξ2 control the partitioning energy outflows R1 = k3Q1 = Q1/τ1; and R2 = k4Q2 = Q2/τ2 between recycling feedback flows and the heat flows. The total heat flow Jh = Jin = P1/η1+P2/η2 sinks out of the boundary at the bottom of the diagram, with 0<δ<1 being the phenomenological efficiency for the direct interaction term.