Fig. 4: Decomposition of the dissipative cost α.

a The dissipative cost, \(\alpha=-{\bar{\sigma }}_{{{\rm{sb}}}}/\bar{y}+{\bar{\sigma }}_{{{\rm{pd}}}}/\bar{y}-\bar{g}/{\bar{\rho }}_{{{\rm{C}}}}\), is decomposed into the free energy lost due to substrate consumption, \(-{\bar{\sigma }}_{{{\rm{sb}}}}/\bar{y}\), the free energy created due to product formation, \(-{\bar{\sigma }}_{{{\rm{pd}}}}/\bar{y}\), and the free energy stored into biomass, \(\bar{g}/{\bar{\rho }}_{{{\rm{C}}}}\), all per unit biomass synthesized (see Box 2 for the definitions, overbars denote means within types, Supplementary Information D). Notice that the free energies of formation of biomass, \(\bar{g}\), and of most chemical species are negative, making \({\bar{\sigma }}_{{{\rm{sb,pd}}}} > 0\). The contribution from free energy storage in biomass is small and its variability is not visible (Supplementary Information I2). Substrate and product free energy fluxes are large and variable, yet compensate each other to result in a comparatively small and conserved cost of biomass. The box plots are defined as in Fig. 2a. Each box describes n = 102 data points. Inset. Histograms of α, \({\bar{\sigma }}_{{{\rm{sb}}}}/\bar{y}\), and \({\bar{\sigma }}_{{{\rm{pd}}}}/\bar{y}\), showing skewness and small variability of α. The cost as a function of the influx of free energy of substrates (b), and of the outflux of free energy of products (c). Compared to the large variability in the free energy influx and outflux, the cost is largely conserved. The red dashed line corresponds to α = 500 kJCmol⁻¹. d Free energy outflux of metabolic products vs free energy influx of substrates. The data covers only a small linear space within the physically realizable region (unshaded area), indicating that the cost of growth is much smaller than influx/outflux of free energy. The shaded area corresponds to violation of the second law, which requires α > 0 (a small offset due to biomass free energy is not visible).