Fig. 1: Chemical reaction network (CRN) gears unveil the optimal transduction efficiency for any given network and under any external condition.
From: Gears in chemical reaction networks for optimizing energy transduction efficiency
a Free energy transduction in a generic CRN between input process a and output process b. The chemostatted species are colored, and the spontaneous direction of the processes is from + → − , corresponding to negative Gibbs free energy changes ΔaG, ΔbG < 0. Process a flows in its spontaneous direction, \({{\mathcal{I}}}_{a} > 0\), enabling process b to flow against its spontaneous direction, \({{\mathcal{I}}}_{b} < 0\). The efficiency of this transduction is the ratio between the output and the input flux of free energy. b Example of a nonlinear multi-gear CRN. In the bottom right, a schematic representation of the CRN that highlights its structure. c The three gears ψα, ψβ, and ψγ of the CRN (external elementary flux modes, EFMs). They correspond to the three possible closed paths of reactions and are provided explicitly in Supplementary Information Eq. (S4). Some reactions must occur twice due to the dimerizations C ↔ C2 and D ↔ D2. Below, the corresponding gear’s efficiencies are defined as the ratio between the # of times they produce the output b and the # of times they consume the input a, multiplied by ΔbG/ΔaG. ψγ is a futile gear as it only consumes the input. d, e Upper bounds on the transduction efficiency as a function of the load (quantified by the ratio ΔbG/ΔaG), imagining that the concentration of [B+] is increased. The second law for the full CRN only implies a transduction efficiency η < 1, whereas the second law refined at the gear level provides additional information: the maximum value for η is set by the gear with the highest efficiency \({\eta }_{{\mathfrak{g}}}\) that is thermodynamically feasible, i.e., \({\eta }_{{\mathfrak{g}}} < 1\), Eq (4). At low [B+], the best gear is ψα, but switches to the lighter ψβ as [B+] increases.
