Kinetically accessible yield (KAY) for redirection of metabolism to produce exo-metabolites.

The product formation yield (product formed per unit substrate consumed) is often the most important performance indicator in metabolic engineering. Until now, the actual yield cannot be predicted, but it can be bounded by its maximum theoretical value. The maximum theoretical yield is calculated by considering the stoichiometry of the pathways and cofactor regeneration involved. Here we found that in many cases, dynamic stability becomes an issue when excessive pathway flux is drawn to a product. This constraint reduces the yield and renders the maximal theoretical yield too loose to be predictive. We propose a more realistic quantity, defined as the kinetically accessible yield (KAY) to predict the maximum accessible yield for a given flux alteration. KAY is either determined by the point of instability, beyond which steady states become unstable and disappear, or a local maximum before becoming unstable. Thus, KAY is the maximum flux that can be redirected for a given metabolic engineering strategy without losing stability. Strictly speaking, calculation of KAY requires complete kinetic information. With limited or no kinetic information, an Ensemble Modeling strategy can be used to determine a range of likely values for KAY, including an average prediction. We first apply the KAY concept with a toy model to demonstrate the principle of kinetic limitations on yield. We then used a full-scale E. coli model (193 reactions, 153 metabolites) and this approach was successful in E. coli for predicting production of isobutanol: the calculated KAY values are consistent with experimental data for three genotypes previously published.

Stability of Ensemble Models Predicts Productivity of Enzymatic Systems.

Stability in a metabolic system may not be obtained if incorrect amounts of enzymes are used. Without stability, some metabolites may accumulate or deplete leading to the irreversible loss of the desired operating point. Even if initial enzyme amounts achieve a stable steady state, changes in enzyme amount due to stochastic variations or environmental changes may move the system to the unstable region and lose the steady-state or quasi-steady-state flux. This situation is distinct from the phenomenon characterized by typical sensitivity analysis, which focuses on the smooth change before loss of stability. Here we show that metabolic networks differ significantly in their intrinsic ability to attain stability due to the network structure and kinetic forms, and that after achieving stability, some enzymes are prone to cause instability upon changes in enzyme amounts. We use Ensemble Modelling for Robustness Analysis (EMRA) to analyze stability in four cell-free enzymatic systems when enzyme amounts are changed. Loss of stability in continuous systems can lead to lower production even when the system is tested experimentally in batch experiments. The predictions of instability by EMRA are supported by the lower productivity in batch experimental tests. The EMRA method incorporates properties of network structure, including stoichiometry and kinetic form, but does not require specific parameter values of the enzymes.

An entropy-like index of bifurcational robustness for metabolic systems.

Natural and synthetic metabolic pathways need to retain stability when faced against random changes in gene expression levels and kinetic parameters. In the presence of large parameter changes, a robust system should specifically avoid moving to an unstable region, an event that would dramatically change system behavior. Here we present an entropy-like index, denoted as S, for quantifying the bifurcational robustness of metabolic systems against loss of stability. We show that S enables the optimization of a metabolic model with respect to both bifurcational robustness and experimental data. We then demonstrate how the coupling of ensemble modeling and S enables us to discriminate alternative designs of a synthetic pathway according to bifurcational robustness. Finally, we show that S enables the identification of a key enzyme contributing to the bifurcational robustness of yeast glycolysis. The different applications of S demonstrated illustrate the versatile role it can play in constructing better metabolic models and designing functional non-native pathways.

Ensemble Modeling for Robustness Analysis in engineering non-native metabolic pathways.

Metabolic pathways in cells must be sufficiently robust to tolerate fluctuations in expression levels and changes in environmental conditions. Perturbations in expression levels may lead to system failure due to the disappearance of a stable steady state. Increasing evidence has suggested that biological networks have evolved such that they are intrinsically robust in their network structure. In this article, we presented Ensemble Modeling for Robustness Analysis (EMRA), which combines a continuation method with the Ensemble Modeling approach, for investigating the robustness issue of non-native pathways. EMRA investigates a large ensemble of reference models with different parameters, and determines the effects of parameter drifting until a bifurcation point, beyond which a stable steady state disappears and system failure occurs. A pathway is considered to have high bifurcational robustness if the probability of system failure is low in the ensemble. To demonstrate the utility of EMRA, we investigate the bifurcational robustness of two synthetic central metabolic pathways that achieve carbon conservation: non-oxidative glycolysis and reverse glyoxylate cycle. With EMRA, we determined the probability of system failure of each design and demonstrated that alternative designs of these pathways indeed display varying degrees of bifurcational robustness. Furthermore, we demonstrated that target selection for flux improvement should consider the trade-offs between robustness and performance.

Genome Sequence of the Extreme Obligate Alkaliphile Bacillus marmarensis Strain DSM 21297.

Bacillus marmarensis strain DSM 21297 is an extreme obligate alkaliphile able to grow in medium up to pH 12.5. A whole-shotgun strategy and de novo assembly led to the generation of a 4-Mbp genome of this strain. The genome features alkaliphilic adaptations and pathways for n-butanol and poly(3-hydroxybutyrate) synthesis.

Optimization-driven identification of genetic perturbations accelerates the convergence of model parameters in ensemble modeling of metabolic networks.

The ensemble modeling (EM) approach has shown promise in capturing kinetic and regulatory effects in the modeling of metabolic networks. Efficacy of the EM procedure relies on the identification of model parameterizations that adequately describe all observed metabolic phenotypes upon perturbation. In this study, we propose an optimization-based algorithm for the systematic identification of genetic/enzyme perturbations to maximally reduce the number of models retained in the ensemble after each round of model screening. The key premise here is to design perturbations that will maximally scatter the predicted steady-state fluxes over the ensemble parameterizations. We demonstrate the applicability of this procedure for an Escherichia coli metabolic model of central metabolism by successively identifying single, double, and triple enzyme perturbations that cause the maximum degree of flux separation between models in the ensemble. Results revealed that optimal perturbations are not always located close to reaction(s) whose fluxes are measured, especially when multiple perturbations are considered. In addition, there appears to be a maximum number of simultaneous perturbations beyond which no appreciable increase in the divergence of flux predictions is achieved. Overall, this study provides a systematic way of optimally designing genetic perturbations for populating the ensemble of models with relevant model parameterizations.