Extended Data Figure 5. The total-flux feedback model.

Several key observations can be explained by a highly simplified regulatory scheme in which glycerol uptake is inhibited by a signal that reflects the total carbon-uptake flux—a total-flux sensor. In this scheme (Panel a), glycerol and lactose uptake j_G and j_L both contribute to the total carbon-uptake flux j_tot. This total flux is sensed by a total-flux sensor, which represses glycerol uptake, but only if j_tot exceeds a threshold that is set to coincide with the carbon flux obtained on glycerol alone. Thus, glycerol uptake is suppressed by any substrate that supplies a larger carbon-uptake flux than glycerol can provide, but not by substrates that produce a smaller flux.

Panel b demonstrates graphically how total-flux feedback determines the uptake of glycerol. Because j_G = j_tot − j_L, the steady-state value of j_G obtained for a given j_L can be found by plotting both j_G(j_tot) (red solid curve) and j_tot − j_L (green dashed lines, for various values of j_L ) as a function of j_tot and determining their intersection (blue triangles). We assume that j_G responds sensitively to j_tot, with a threshold j_th (red arrow) set slightly above the flux on glycerol alone, j_G,0. Thus, it is seen that glycerol uptake is inhibited if j_L > j_th (the hierarchical utilization regime, intersection c). Yet, if j_L < j_th, glycerol uptake is adjusted such that j_tot ≈ j_th ≈ j_G,0 (the supplementation regime; intersection a and b).

cAMP–Crp signaling can function as a total-flux sensor because transcriptional activation by cAMP–Crp is a decreasing function of j_tot (Fig. 4c)⁵. It transmits information on j_tot to the glycerol uptake through differential regulation of glpK and glpD expression (Fig. 3b,c).