Prediction of metabolic function from limited data: Lumped hybrid cybernetic modeling (L-HCM).

Motivated by the need for a quick quantitative assessment of metabolic function without extensive data, we present an adaptation of the cybernetic framework, denoted as the lumped hybrid cybernetic model (L-HCM), which combines the attributes of the classical lumped cybernetic model (LCM) and the recently developed HCM. The basic tenet of L-HCM and HCM is the same, that is, they both view the uptake flux as being split among diverse pathways in an optimal way as a result of cellular regulation such that some chosen metabolic objective is realized. The L-HCM, however, portrays this flux distribution to occur in a hierarchical way, that is, first among lumped pathways, and next among individual elementary modes (EM) in each lumped pathway. Both splits are described by the cybernetic control laws using operational and structural return-on-investments, respectively. That is, the distribution of uptake flux at the first split is dynamically regulated according to environmental conditions, while the subsequent split is based purely on the stoichiometry of EMs. The resulting model is conveniently represented in terms of lumped pathways which are fully identified with respect to yield coefficients of all products unlike classical LCMs based on instinctive lumping. These characteristics enable the model to account for the complete set of EMs for arbitrarily large metabolic networks despite containing only a small number of parameters which can be identified using minimal data. However, the inherent conflict of questing for quantification of larger networks with smaller number of parameters cannot be resolved without a mechanism for parameter tuning of an empirical nature. In this work, this is accomplished by manipulating the relative importance of EMs by tuning the cybernetic control of mode-averaged enzyme activity with an empirical parameter. In a case study involving aerobic batch growth of Saccharomyces cerevisiae, L-HCM is compared with LCM. The former provides a much more satisfactory prediction than the latter when parameters are identified from a few primary metabolites. On the other hand, the classical model is more accurate than L-HCM when sufficient datasets are involved in parameter identification. In applying the two models to a chemostat scenario, L-HCM shows a reasonable prediction on metabolic shift from respiration to fermentation due to the Crabtree effect, which LCM predicts unsatisfactorily. While L-HCM appears amenable to expeditious estimates of metabolic function with minimal data, the more detailed dynamic models [such as HCM or those of Young et al. (Young et al., Biotechnol Bioeng, 2008; 100: 542-559)] are best suited for accurate treatment of metabolism when the potential of modern omic technology is fully realized. However, in view of the monumental effort surrounding the development of detailed models from extensive omic measurements, the preliminary insight into the behavior of a genotype and metabolic engineering directives that can come from L-HCM is indeed valuable.