An entropy-like index of bifurcational robustness for metabolic systems

Metabolic kinetic modeling provides insight into complex biological questions, but hurdles remain

Metabolic models containing kinetic information can answer unique questions about cellular metabolism that are useful to metabolic engineering. Several kinetic modeling frameworks have recently been developed or improved. In addition, techniques for systematic identification of model structure, including regulatory interactions, have been reported. Each framework has advantages and limitations, which can make it difficult to choose the most appropriate framework. Common limitations are data availability and computational time, especially in large-scale modeling efforts. However, recently developed experimental techniques, parameter identification algorithms, as well as model reduction techniques help alleviate these computational bottlenecks. Opportunities for additional improvements may come from the rich literature in catalysis and chemical networks. In all, kinetic models are positioned to make significant impact in cellular engineering.

Acceleration Strategies to Enhance Metabolic Ensemble Modeling Performance

Developing reliable, predictive kinetic models of metabolism is a difficult, yet necessary, priority toward understanding and deliberately altering cellular behavior. Constraint-based modeling has enabled the fields of metabolic engineering and systems biology to make great strides in interrogating cellular metabolism but does not provide sufficient insight into regulation or kinetic limitations of metabolic pathways. Moreover, the growth-optimized assumptions that constraint-based models often rely on do not hold when studying stationary or persistor cell populations. However, developing kinetic models provides many unique challenges, as many of the kinetic parameters and rate laws governing individual enzymes are unknown. Ensemble modeling (EM) was developed to circumnavigate this challenge and effectively sample the large kinetic parameter solution space using consistent experimental datasets. Unfortunately, EM, in its base form, requires long solve times to complete and often leads to unstable kinetic model predictions. Furthermore, these limitations scale prohibitively with increasing model size. As larger metabolic models are developed with increasing genetic information and experimental validation, the demand to incorporate kinetic information increases. Therefore, in this work, we have begun to tackle the challenges of EM by introducing additional steps to the existing method framework specifically through reducing computation time and optimizing parameter sampling. We first reduce the structural complexity of the network by removing dependent species, and second, we sample locally stable parameter sets to reflect realistic biological states of cells. Lastly, we presort the screening data to eliminate the most incorrect predictions in the earliest screening stages, saving further calculations in later stages. Our complementary improvements to this EM framework are easily incorporated into concurrent EM efforts and broaden the application opportunities and accessibility of kinetic modeling across the field.

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.

Metabolic systems modeling for cell factories improvement

Techniques for modeling microbial bioproduction systems have evolved over many decades. Here, we survey recent literature and focus on modeling approaches for improving bioproduction. These techniques from systems biology are based on different methodologies, starting from stoichiometry only to various stoichiometry with kinetics approaches that address different issues in metabolic systems. Techniques to overcome unknown kinetic parameters using random sampling have emerged to address meaningful questions. Among those questions, pathway robustness seems to be an important issue for metabolic engineering. We also discuss the increasing significance of databases in biology and their potential impact for biotechnology.

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.