Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

BACKGROUND: Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. RESULTS: We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. CONCLUSION: Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases

Exploring the gap between dynamic and constraint-based models of metabolism

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of E. coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identied by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.This research was supported by PhD Grants SFRH/BD/35215/2007 and SFRH/BD/25506/2005 from the Fundacao para a Ciencia e a Tecnologia (FCT) and the MIT-Portugal Program through the project "Bridging Systems and Synthetic Biology for the Development of Improved Microbial Cell Factories" (MIT-Pt/BS-BB/0082/2008)

A critical review on modelling formalisms and simulation tools in computational biosystems

Integration of different kinds of biological processes is an ultimate goal for whole-cell modelling. We briefly review modelling formalisms that have been used in Systems Biology and identify the criteria that must be addressed by an integrating framework capable of modelling, analysing and simulating different biological networks. Aware that no formalism can fit all purposes we realize Petri nets as a suitable model for Metabolic Engineering and take a deeper perspective on the role of this formalism as an integrating framework for regulatory and metabolic networks.Research supported by PhD grant SFRH/BD/35215/2007 from the Fundacao para a Ciencia e a Tecnologia (FCT) and the MIT-Portugal program

The Carbon Assimilation Network in Escherichia coli Is Densely Connected and Largely Sign-Determined by Directions of Metabolic Fluxes

Gene regulatory networks consist of direct interactions but also include indirect interactions mediated by metabolites and signaling molecules. We describe how these indirect interactions can be derived from a model of the underlying biochemical reaction network, using weak time-scale assumptions in combination with sensitivity criteria from metabolic control analysis. We apply this approach to a model of the carbon assimilation network in Escherichia coli. Our results show that the derived gene regulatory network is densely connected, contrary to what is usually assumed. Moreover, the network is largely sign-determined, meaning that the signs of the indirect interactions are fixed by the flux directions of biochemical reactions, independently of specific parameter values and rate laws. An inversion of the fluxes following a change in growth conditions may affect the signs of the indirect interactions though. This leads to a feedback structure that is at the same time robust to changes in the kinetic properties of enzymes and that has the flexibility to accommodate radical changes in the environment

Impact of kinetic isotope effects in isotopic studies of metabolic systems

Background: Isotope labeling experiments (ILEs) are increasingly used to investigate the functioning of metabolic systems. Some enzymes are subject to kinetic isotope effects (KIEs) which modulate reaction rates depending on the isotopic composition of their substrate(s). KIEs may therefore affect both the propagation of isotopes through metabolic networks and their operation, and ultimately jeopardize the biological value of ILEs. However, the actual impact of KIEs on metabolism has never been investigated at the system level. Results: First, we developed a framework which integrates KIEs into kinetic and isotopic models of metabolism, thereby accounting for their system-wide effects on metabolite concentrations, metabolic fluxes, and isotopic patterns. Then, we applied this framework to assess the impact of KIEs on the central carbon metabolism of Escherichia coli in the context of C-13-ILEs, under different situations commonly encountered in laboratories. Results showed that the impact of KIEs strongly depends on the label input and on the variable considered but is significantly lower than expected intuitively from measurements on isolated enzymes. The global robustness of both the metabolic operation and isotopic patterns largely emerge from intrinsic properties of metabolic networks, such as the distribution of control across the network and bidirectional isotope exchange. Conclusions: These results demonstrate the necessity of investigating the impact of KIEs at the level of the entire system, contradict previous hypotheses that KIEs would have a strong effect on isotopic distributions and on flux determination, and strengthen the biological value of C-13-ILEs. The proposed modeling framework is generic and can be used to investigate the impact of all the isotopic tracers (H-2, C-13, N-15, O-18, etc.) on different isotopic datasets and metabolic systems. By allowing the integration of isotopic and metabolomics data collected under stationary and/or non-stationary conditions, it may also assist interpretations of ILEs and facilitate the development of more accurate kinetic models with improved explicative and predictive capabilities

Dynamic metabolic control: towards precision engineering of metabolism

Advances in metabolic engineering have led to the synthesis of a wide variety of valuable chemicals in microorganisms. The key to commercializing these processes is the improvement of titer, productivity, yield, and robustness. Traditional approaches to enhancing production use the “push–pull-block” strategy that modulates enzyme expression under static control. However, strains are often optimized for specific laboratory set-up and are sensitive to environmental fluctuations. Exposure to sub-optimal growth conditions during large-scale fermentation often reduces their production capacity. Moreover, static control of engineered pathways may imbalance cofactors or cause the accumulation of toxic intermediates, which imposes burden on the host and results in decreased production. To overcome these problems, the last decade has witnessed the emergence of a new technology that uses synthetic regulation to control heterologous pathways dynamically, in ways akin to regulatory networks found in nature. Here, we review natural metabolic control strategies and recent developments in how they inspire the engineering of dynamically regulated pathways. We further discuss the challenges of designing and engineering dynamic control and highlight how model-based design can provide a powerful formalism to engineer dynamic control circuits, which together with the tools of synthetic biology, can work to enhance microbial production