A total quasi-steady-state formulation of substrate uptake kinetics in complex networks and an example application to microbial litter decomposition

We demonstrate that substrate uptake kinetics in any consumer-substrate network subject to the total quasi-steady-state assumption can be formulated as an equilibrium chemistry (EC) problem. If the consumer-substrate complexes equilibrate much faster than other metabolic processes, then the relationships between consumers, substrates, and consumer-substrate complexes are in quasi-equilibrium and the change of a given total substrate (free plus consumer-bounded) is determined by the degradation of all its consumer-substrate complexes. In this EC formulation, the corresponding equilibrium reaction constants are the conventional Michaelis-Menten (MM) substrate affinity constants. When all of the elements in a given network are either consumer or substrate (but not both), we derived a first-order accurate EC approximation (ECA). The ECA kinetics is compatible with almost every existing extension of MM kinetics. In particular, for microbial organic matter decomposition modeling, ECA kinetics explicitly predicts a specific microbe's uptake for a specific substrate as a function of the microbe's affinity for the substrate, other microbes' affinity for the substrate, and the shielding effect on substrate uptake by environmental factors, such as mineral surface adsorption. By taking the EC solution as a reference, we evaluated MM and ECA kinetics for their abilities to represent several differently configured enzyme-substrate reaction networks. In applying the ECA and MM kinetics to microbial models of different complexities, we found (i) both the ECA and MM kinetics accurately reproduced the EC solution when multiple microbes are competing for a single substrate; (ii) ECA outperformed MM kinetics in reproducing the EC solution when a single microbe is feeding on multiple substrates; (iii) the MM kinetics failed, while the ECA kinetics succeeded, in reproducing the EC solution when multiple consumers (i.e., microbes and mineral surfaces) were competing for multiple substrates. We then applied the EC and ECA kinetics to a guild based C-only microbial litter decomposition model and found that both approaches successfully simulated the commonly observed (i) two-phase temporal evolution of the decomposition dynamics; (ii) final asymptotic convergence of the lignocellulose index to a constant that depends on initial litter chemistry and microbial community structure; and (iii) microbial biomass proportion of total organic biomass (litter plus microbes). In contrast, the MM kinetics failed to realistically predict these metrics. We therefore conclude that the ECA kinetics are more robust than the MM kinetics in representing complex microbial, C substrate, and mineral surface interactions. Finally, we discuss how these concepts can be applied to other consumer-substrate networks.